Apr 3, 2000 - If f defines the ratio of mass of fuel and oxidizer in the unburned gas/ ..... upstream heat transfer to the burner, suggested first by Botha and Spalding [22] ...... measurements with a Burleigh Model WA-4500 pulsed wavemeter.
EFFECTS OF BURNER STABILIZATION ON NITRIC OXIDE FORMATION AND DESTRUCTION IN ATMOSPHERICPRESSURE FLAT PREMIXED FLAMES
ALEXEI SEPMAN
RIJKSUNIVERSITEIT GRONINGEN
Effects of burner stabilization on nitric oxide formation and destruction in atmospheric-pressure flat premixed flames
Proefschrift
ter verkrijging van het doctoraat in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr. F. Zwarts, in het openbaar te verdedigen op vrijdag 22 september 2006 om 14.45 uur
door Alexei Vladimirovich Sepman geboren op 4 augustus 1972 te St.Petersburg, Russia
Promotor: Copromotor:
Prof. Dr. H.B. Levinsky Dr. A.V. Mokhov
Beoordelingscommissie: Prof.dr. J.J. ter Meulen Prof.dr. L.P.H. de Goey Prof.dr.Ir.H.J. Heeres
ISBN 90-367-2702-2 ISBN 90-367-2701-4 (electronic version)
TABLE OF CONTENTS
Introduction Scope of this thesis
Chapter 1: Background Information on Laminar Premixed One-Dimensional Flames 1.1 A Few Aspects of Physics and Chemistry of Flames 1.1.1 The laminar premixed flame 1.1.2 The governing equations 1.1.3 Chemical kinetics 1.1.4 Chemical mechanisms 1.1.5 Boundary conditions for burner stabilized and free flames 1.1.6 Burner-flame heat transfer 1.2 Mechanisms of NO formation 1.2.1 The thermal mechanism 1.2.2 The Fenimore mechanism 1.2.3 Other mechanisms
Chapter 2: Burners and gas handling system 2.1 Transport and analyzing of the cold gas mixture 2.2 Burners Appendix 2A: Estimations of uncertainties in equivalence ratio determination
Chapter 3: Chapter 3: LIF and CARS methods 3.1 Introduction 3.2 CARS technique 3.2.1 Introduction 3.2.2 Background 3.2.3 Experimental 3.2.4 Experimental set-up 3.2.5 Temperature dependence of N2 CARS spectrum 3.3 Laser-Induced Fluorescence 3.3.1 Introduction 3.3.2 General theory 3.3.3 Experimental 3.3.4 Experimental set-up 3.3.5 Timing of signals 3.3.6 Calibration procedure 3.3.7 Linearity of the detection system
1 2
4 6 7 8 9 12 12 15 18
20 22 24
30 31 32 35 35 37 40 40 47 47 49 51 55
Chapter 4: Temperature measurements on burner-stabilized flames Abstract 4.1 Introduction 4.2 Hydrogen-air flames 4.2.1 Temperature measurements in hydrogen- air flames 4.2.2 The sensitivity of the heat transfer method 4.3 Methane-air flames 4.3.1 Temperature measurements in methane-air flames 4.3.2 Effects of preheating on flame temperature
57 58 60 65 70 73
Chapter 5: The Calibration of LIF signal by CRDS and reburning of NO in H2/Air and CH4/Air flames Abstract 78 5.1 Introduction 79 5.2 CRDS technique 5.2.1 Background 80 5.2.2 Principles of the method 80 5.2.3 Experimental setup 85 5.2.4 Evaluation of the exponential decay time from the measured signal 85 5.3 NO measurements in methane and hydrogen flames 5.3.1 CRD background in methane and hydrogen flames 86 5.3.2 NO absorption spectra 88 5.3.3 Effective absorption length 93 5.3.4 NO mole fraction in stoichiometric and lean H2/N2/Air flames 97 Chapter 6: A study of NO formation in preheated fuel-rich CH4/Air flames Abstract 6.1 Introduction 6.2 The NO and temperature measurements at φ = 1.0, 1.3, 1.5 and 1.6 6.3 NO concentration as a function of the flame temperature
101 102 103 118
Chapter 7: Experimental Study of NO Reburning in Atmospheric- Pressure Laminar Rich-Premixed CH4/Air/N2/NO Flames Abstract 7.1 Introduction 7.2 Experimental Approach 7.3 Data Reduction and Analysis 7.4 Results and discussion
127 128 128 128 132
Summary Samenvatting References Acknowledgement
141 143 146 157
Introduction Combustion is the oldest technological process known to mankind. It is applied in industrial processes, power generation, transportation systems, heating of houses, waste disposal, and many other facets of everyday life. However, there are also harmful effects associated with combustion, such as the formation of pollutants like nitrogen oxides, unburned hydrocarbons, carbon monoxide, and soot. Worldwide emissions of nitrogen oxides (NO and NO2, collectively known as NOx) have been increasing for decades [1] and remain a major environmental challenge. Emissions of the nitrogen oxides contribute [2] to formation of photochemical smog and ozone in urban air, and to acid rain. Interest in NOx emissions arose in the early 1950s; when the role of the nitrogen oxides in the formation of photochemical smog was established [3]. From the late 1950s to the mid 1960s in the USA, tests were performed by manufactures of combustion equipment to evaluate methods for reducing these emissions. However, motivation to pursue this line of research was limited by the lack of regulations concerning NOx emissions. Enactment of such regulations in many industrial countries over the last three decades has intensified efforts towards developing NOx control technologies [4]. It soon became clear that the development of more effective NOx control technologies, made necessary by increasingly stringent regulations, could only be realized by a better understanding of NOx formation mechanisms. For this reason, fundamental research on NOx emissions, including the development of new diagnostic techniques for measurement in harsh combustion conditions and modeling of combustion processes, has being sponsored in those countries facing pollutant regulations. However, despite great advances made in identifying and testing the chemical mechanisms of NOx formation and consumption [5], the accuracy with which NOx formation can be predicted is still not sufficient for practical requirements. Although modern combustion models can usually predict the NO concentration in laboratory flames to within a factor of 2 [6,7], this accuracy is insufficient for making specific recommendations for altering the combustion in practical devices. European environmental regulations, for example, demand that the emissions regulations be met with an accuracy of 20% [8], and thus much empirical work is still necessary to adapt practical systems to satisfy the regulations. Therefore, providing accurate experimental data obtained in readily modeled flames is of great importance for assessing the adequacy of model predictions, and in particular for assessing the chemical mechanisms. Obviously, experimental variation of well-defined flame conditions such as temperature, pressure and equivalence ratio is crucial for determining the range of validity of a model. The objective of this thesis is twofold: first, to provide accurate measurements of flame properties relevant for NOx formation, particularly local NO mole fraction and gas temperature, for use in the description and discussion of NO formation and consumption, and second, to compare and analyze the agreement between experimental and simulated data. The experiments are performed in atmospheric-pressure, one-dimensional, laminar premixed flames. Laser-induced fluorescence (LIF) and cavity ring-down spectroscopy (CRDS) were employed to determine the absolute NO concentration, and coherent antiStokes’ Raman scattering (CARS) was used to measure the flame temperature. Flames are examined at different equivalence ratios, whereby the range of flame temperatures studied was extended by varying heat transfer to the burner, and by preheating the initial
1
mixture. The experimental observations are compared with the predictions of onedimensional flame calculations. Scope of this thesis In this thesis, a laser-based diagnostic study of NO formation and consumption in premixed flames burning with different degrees of stabilization on flat-flame burners is presented. Chapter 1 gives some important definitions, provides basic information on physics and chemistry of premixed laminar one-dimensional flames, burner-flame heat transfer, and includes a short discussion on the current insights into the chemical processes leading to NO formation. In Chapter 2, details of the gas-handling system and the burners used in experiments are given. Chapter 3 presents the theoretical and experimental description of coherent anti-Stokes’ Raman scattering (CARS) and laserinduced fluorescence (LIF). In Chapter 4, a method for extending the range of conditions for testing the performance of chemical mechanisms with respect to burning velocity is described. The sensitivity of the method to variation in the individual rates of the important reactions is demonstrated using hydrogen-air flames as an example. In Chapter 5, quantitative aspects of using cavity-ring down absorption spectroscopy for measurements of NO mole fractions in premixed atmospheric-pressure flames are discussed. Chapter 6 concerns a LIF and CARS study of NO formation in preheated, fuelrich, methane-air flames. Chapter 7 presents measurements of the temperature dependence of NO consumption for atmospheric-pressure, flat, fuel-rich and stoichometric CH4/N2/Air flames seeded with low concentrations of NO.
2
CHAPTER 1 Background Information on Laminar Premixed One- Dimensional Flames
3
Since this thesis discuses flame properties such as burning velocity, temperature, and NO formation, this chapter will provide the background of these subjects. 1.1 A Few Aspects of Physics and Chemistry of Flames 1.1.1 The laminar premixed flame Flat premixed laminar flames have long been a standard object for the investigation of combustion processes. The one-dimensional character of these flames presents a great advantage for numerical modeling and generally allows an unambiguous modelexperiment comparison. It is convenient to divide the premixed laminar flame into three regions, see figure 1.1: the preheating zone, the reaction zone, and the burned gas zone. In the first zone, a cold mixture is preheated due to transport of species and heat from the reaction zone but no reaction occurs. The reaction zone, commonly known as a flame front, is a thin layer, of the order of a millimeter at atmospheric pressure, where the fuel is rapidly oxidized. The flame front is characterized by steep temperature and species gradients. The thickness of flame front is a function of flame conditions [9], such as pressure and ratio of fuel and oxidizer; for burner-stabilized flames it depends also on the exit velocity of the gases. The flame front is rich with radicals; some of them, such as CH, C, C2, and CHO, can significantly radiate in the visible and UV regions. Because of this radiation, most of the flame reaction zones are coloured; for example, the CH4/Air flame zone is of blue colour. For a more detailed description of flame emission, the reader is referred to [10]. In the burned gas zone, radical recombination takes place, and in hydrocarbons flames also CO molecules are converted to CO2. In this zone, the temperature and concentrations of the major species are close to their equilibrium values. In contrast, the concentrations of the minor species can deviate significantly from their equilibrium values in the same region. Throughout this thesis, the term “adiabatic flame temperature” will be frequently met. The temperature that a closed system achieves in the thermodynamic state is called the adiabatic temperature. An important characteristic of a premixed flame is the equivalence ratio, a non-dimensional variable that serves to express the ratio of fuel to oxidizer in the cold mixture. If f defines the ratio of mass of fuel and oxidizer in the unburned gas/air mixture, the equivalence ratio φ is given by φ= f f , (1.1) st where fst expresses the ratio in the mixture at the stoichiometric condition (the amount of oxidizer is just enough for complete oxidation). Flames at φ > 1, φ = 1 and φ < 1 are termed fuel-rich, stoichiometric, and fuel-lean, respectively. Another important parameter, often used to characterize the flame system, is the burning velocity. The burning velocity is defined as the velocity with which a flat 1-D flame front propagates with respect to the unburned fuel-air mixture. The burning velocity primarily depends on the initial parameters of the unburned mixture, such as temperature, equivalence ratio, and pressure [9]. Figure 1.2 illustrates the modeled flame velocity as a function of the equivalence ratio for CH4/Air flames; calculations were made using the GRI-Mech 3.0
4
Preheating zone
Reaction zone
Burned gas zone
Temperature
Oxidizer
Products
Temperature
Concentration
Fuel
Intermediates
Distance
Figure 1.1. Schematic representation of the combustion zones. 45 40
Flame velocity, cm/s
35 30 25 20 15 10 5 0 0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Equivalence ratio
Figure 1.2. The calculated flame velocity as a function of equivalence ratio in the methane-air flames.
5
chemical mechanism [11] in the PREMIX code in the CHEMKIN II package [12]. Figure 1.2 shows that the burning velocity is maximal at equivalence ratio ~ 1.05 and decreases in richer and leaner flames. If the interests of combustion science were limited to the final chemical changes in a flame system, without going into the details of the combustion process, comprehensive information on the equilibrium state of the system could be relatively simply deduced from thermodynamics, see for example [13]. The approach to the combustion system from the thermodynamical point of view could actually be justified in the case when the rates of transport processes like convection, heat transfer, and diffusion would be slow in comparison with those of the chemical reactions. However, in most combustion situations, the characteristic times of the chemical reactions and transport processes are on the same scale. Therefore to gain information on kinetically controlled processes like pollutant formation or ignition, the detailed picture of the combustion process is required. To obtain this it is necessary to solve the governing equations with detailed chemical mechanism of the system. The solution of these equations requires knowledge of the transport properties and the reaction rates of the system. 1.1.2 The governing equations In the beginning, it seems appropriate to note that the governing equations for conservation of the mass, species, and energy are derived from the Boltzmann kinetic equation, see [14,15], which describes the evolution of the molecular distribution function. This function gives the probability finding the number of particles per unit volume of the six-dimensional coordinate-momentum space at given time. The internal structure of the particles will not be considered here. All macroscopic parameters of a system are completely determined if the distribution function is known. In the case of equilibrium, this function is independent of position and time and reduces to the Maxwell distribution function. In a flame front, which is in principle a nonequilibrium system, the distribution function is generally unknown. However, since a flame distribution function does not deviate significantly from the Maxwell distribution function, the governing equations can be derived from the Boltzmann kinetic equation without actually specifying the form of the distribution function [14,15]. The governing equations in a flame system take the most simple form for steady state laboratory-scale one- dimensional flames. Neglecting the effects due to pressure deviation, viscosity, radiation and external forces, the governing equations are as follows [13]: 1) The equation of overall conservation of mass d l ∑ N i miυ = 0 , dx i
(1.2)
where υ is the mass average velocity and commonly known as flow velocity, Ni and mi are the molar number density and the mass for the chemical species i , respectively, l is the total number of chemical species, and x is the distance normal to the flame front. 2) The equation of conservation of a particular species
6
d N i (υ + Vi D ) = K i , dx
(
)
i = 1,.., l
(1.3)
where Ki is the net molar rate of change of species i per unit volume and per unit time due to chemical reaction (which is discussed in the next paragraph and here is supposed to be known ), and Vi D is the diffusion velocity, representing the macroscopic flow of species i relative to the mass average velocity. The diffusion velocity, according to Fick’s law, is proportional to the concentration gradient [9]. The conservation equation of a particular species has (l - 1) independent equations. Since chemical reactions do not create or destroy matter as a whole
∑m K i
i
=0,
i
if eq. (1.3) is multiplied by mi and summed over all species i, one gets the equation of overall conservation of mass. 3) The equation of energy conservation
d dT ∑ N i (υ + Vi D ) ⋅ I i − λ = 0, dx i dx
(1.4)
where Ii is the specific enthalpy of species i, λ is the thermal conductivity coefficient, and T is the temperature. When the equation of state
P = ∑ N i RT ,
(1.5)
i
where P is the pressure and R is the universal gas constant, is added to the system of conservation equations, the total system consists of (l + 2) linearly independent equations. Assuming that the diffusion velocity is a known function of flame temperature and species concentrations [13], the system contains (l + 2) unknown parameters: velocity υ, temperature T, and species molar concentrations Ni. Thus, provided that the boundary conditions for differential equations (1.2-1.4) are specified, see below, solution of this system of equations is possible. 1.1.3 Chemical kinetics The equation of conservation of species (1.3) includes the net rate of change of species due to chemical reactions. The quantity Ki expresses the time derivatives of the concentration of some species i involved in the reaction. Consider the chemical reaction of the general type kf
aA + bB + cC + ... ⇔ dD + eE + fF + ... , kr
(1.6)
7
where A, B, C, … represent the different species involved in the reaction, a, b, c, … denote the numbers of moles of species A, B, C,…, kf and kr are rates constant of forward and reverse reactions. Then, the rate law of change of species A is written as follows, KA =
dA = − k f N Aa N Bb N Cc ... + k r N Dd N Ee N Ff ... . dt
(1.7)
In equilibrium, the net rate of change of species A should be zero, therefore
N Dd N Ee N Ff ... k f = = K eq , N Aa N Bb N Cc ... k r
(1.8)
where Keq is the equilibrium constant, which can be found from thermodynamics [13]. Thus the rate of change of A species is expressed through the following equation N d N e N f ... K A = k f N Aa N Bb N Cc ... − D E F . K eq
(1.9)
The rate constant is often a strong nonlinear function of temperature and usually presented in a simple standard form E k f = AT b exp(− A ) (1.10) RT where A, b, and EA are three empirical parameters. 1.1.4 Chemical mechanisms Chemical mechanisms governing combustion systems present a detailed description of the transformation of reactants into products. The design of a satisfactory mechanism, the mechanism which will describe the essential details of chemical transformation for a certain range of combustion conditions, requires generally a large number, in some cases thousands, of elementary reactions. Testing a chemical mechanism using flame measurements is complicated by uncertainties in transport properties and boundary conditions [16]. It is clear that in order to improve the performance of the constructed mechanism, the mechanism should be tested over a broad range of flame parameters. There are several analysis methods frequently employed for the design procedure. Among them are sensitivity and reaction flow rate analyses, serving to identify ratelimiting steps and the characteristic reaction paths, respectively. For a detail description of the analysis methods, see [9]. The flames studied in this thesis have been modeled using the GRI-Mech 3.0 mechanism [11], which is often employed for flame simulations in the literature. GRIMech 3.0 describes natural gas combustion, including NO formation and reburn chemistry. The mechanism contains 325 elementary chemical reactions and 53 species.
8
1.1.5 Boundary conditions for burner stabilized and free flames The integration of the overall mass conservation equation (1.2) yields
ρυ = M ,
(1.11)
where M is a constant of integration, expressing the mass rate of flow (g/cm2s), and ρ is the overall mass density given by
ρ = ∑ ni mi ,
(1.12)
i
where ni is the number density for the chemical species i. For a burner stabilized flame, M is a known constant, while for freely propagating flames M is an unknown parameter, which must be determined. Therefore, an additional condition is required in the case of a free flame. The location of the flame front can provide this condition. The location can be fixed, for example, by specifying the flame temperature at one point. Let us consider now the boundary conditions for the equations of conservation of a particular species (1.3) and energy (1.4), see also figure 1.3. The equations (1.3) and (1.4) are the second-order differential equations (the diffusion velocity is proportional to the concentration gradient) and have the general form [9]
F ( f ( x)) ≡ A
∂2 f ∂f + B +C = 0, 2 ∂x ∂x
(1.13)
where f is T or Ni. The solution of this equation requires two boundary conditions (“cold” and “hot”), which will satisfy these conditions only for one value of M. The general form of the boundary conditions for eq. (1.13) is given by [17,18]
α1 f ( x) + α 2
df ( x) = C1 , x= l1 dx
(1.14)
β1 f ( x) + β 2
df ( x) = C 2 , x= l2 dx
(1.15)
where α1, α2, β1, β2, C1, C2 are constants that are chosen on the basis of the particular physical conditions, and l1 and l2 are the distances at which the cold and hot boundary conditions are specified. From the above equations it follows that in order to impose the boundary condition at some position for eq. (1.13), the value of the function f or its gradient must be known at this position or gradient of the function should be linearly dependent on the function. For both the free and burner stabilized flames, the hot boundary conditions for Ni and T (at position denoted by subscript “f”) are often imposed as vanishing gradients [19,20]
9
dN i = 0, dx f
dT =0, dx f
(1.16)
i.e β1 and C2 in eq. (1.14) are equal zero. For numerical calculations the usual practice is to transport the cold boundary from − ∞ (denoted by subscript “u”) to the position of the burner surface (denoted by subscript “c”) [20]. For the free flames, gradients of the species concentration and temperature at the burner surface are zero (to insure the adiabatic condition), i.e. α2 = 0 in equation (1.14). That leads to following cold boundary conditions [21] Tc = Tu , N c = N u .
(1.17)
In a burner stabilized flame, the burner surface acts as a heat sink. Therefore, if sufficient cooling of the burner surface is assumed, the cold boundary condition for temperature is given by [20] Tc = Tu ,
(1.18)
In general the concentrations of all species at the cold boundary are not known. To solve this problem, the integration of eq. (1.3) is carried out between the unburned mixture and the new cold boundary, assuming that no chemical reactions occur between integration limits (u and c) and the diffusion velocity at x = u is zero. This integration gives the following cold boundary conditions for the species concentrations [20] N i ,c +
N i ,cVi ,Dc
υc
= N i ,u
υu . υc
(1.19)
It is useful for the further discussion of the experiments conducted with preheating of the cold methane/air mixtures (Chapters 4, 6), to compare the solutions of equation eq. (1.13) for different temperatures imposed at the cold boundary. Let us suppose that for given initial conditions (mass flux, equivalence ratio), f(x) (Ni and T) is the solution of these equations in the case of the burner stabilized flame. Since the system F(f(x))=0, see eq. (1.13) is invariant to a shift in coordinate, all functions of type f(x+ δx) will satisfy this system. Therefore a function f(x+ δx) will be the solution of the conservation equations with different cold boundary conditions. If the new cold boundary temperature is not high enough to allow significant reactions, the cold boundary conditions for species, eq. (1.18), is not changed. Numerical simulations show that at Tc below 800 K chemical reactions are still not significant. From the above discussion it follows that the increase in the initial mixture temperature to Tpr (preheating) and the
10
T, Xi
T, Xi
Xu Xc
Xu
T(x)
T(x)
Xi(x)
Xi(x)
Tu
Tu u
c
x
f
u
f
c
(a)
x
(b)
Figure 1.3. Typical concentration (expressed as mole fraction Xi= Ni/N, where N is the total molar number density) and temperature (T) profiles in a burner-stabilized (a) and free (b) flames. of cold boundary temperature of the non-preheated mixture to Tc=Tpr as far as Tpr
NCO − −− > NH − −− > N − −− > NO. O
H
H
(R1.6)
O2, OH
16
At higher equivalence ratio, the NO formed reacts back to HCN [5] and fixed-nitrogen species become important. Summarizing the discussion above, the Fenimore prompt NO mechanism (for the rest of this thesis referred to as the Fenimore mechanism) is initiated by reactions of hydrocarbon radicals, primarily CH radicals, which exist only in the flame front at the level of a few ppm, with molecular nitrogen. Products of this reaction form NO through a number of oxidation steps. Being the rate-controlling step of the Fenimore mechanism, reaction (R1.4) has relatively low activation energy in comparison with the reaction (R1.1). That makes the “prompt” chain the major source of NO formation at low temperatures; the formation is still significant at 1000 K (see [5]). The Fenimore mechanism is the dominant source of the NO formation in fuel-rich hydrocarbon flames, due to the increase in CH concentration and negligible Zeldovich NO formation (extremely low oxygen concentration) [5,33-35]. The formation of Fenimore NO has three important aspects: the peak CH concentration and the relative position of the temperature and CH profiles, the rate of the reaction (R1.4), and the rates of interconversion among the fixed-nitrogen species. Despite great advances made in the understanding the Fenimore NO formation, there are still a lot of uncertainties regarding this mechanism. For example, to date, precise data on the rate constant of the reaction (R1.4) are rare in the literature (see [25,36] and references therein) and the known determinations have relatively large uncertainties. The value of the rate coefficient for the reaction CH+N2 in GRI-Mech 3.0, see above, was primarily derived from relatively low flame temperature measurements, below 1930 K at the position of the peak CH concentration [33], and extrapolated to high temperature shock tube measurements, above 2340 K, [25,36]. Considering relatively big combined scatter in the high temperature determination of the rate constant in shock tube studies, the temperature dependence of this reaction requires validation in a large range of temperatures. Furthermore, recent theoretical [37] and experimental [38] studies suggest that the reaction CH+N2 produces primarily H+ NCN instead of HCN + N. Experiments performed in flames where the Fenimore mechanism is expected to be a dominant source of NO formation show deviations, sometimes considerable, between the measured and predicted NO concentrations, see for example [6,7,39-42]. Apart from that there are substantial uncertainties with respect to reactions important for CH formation from C2H2 and for CH consumption (see [43] for details). Thus NO formation via the Fenimore prompt mechanism is still not clear and needs further investigation. The current uncertainties in the mechanism suggest that the experimental study of the NO formation should be accompanied by extensive variation of flame parameters like mass flux and equivalence ratio. The measured NO concentration then might contribute to better understanding of the underlying chemical model.
17
1.2.3 Other mechanisms N2O mechanism
The mechanism of NO formation via N2O molecules is considerably more simple than the Fenimore prompt route N2 +O+M N2O + M N2O + O NO + NO.
(R1.7) (R1.8)
The mechanism involves formation of N2O and its subsequent conversion to NO [44]. The contribution of this mechanism to NO formation, usually negligible in comparison with those from the Zeldovich and Fenimore routes gains in importance in lean flames [45] and at low temperatures [44].
NO formation via N2H route.
In 1995, Bozelli and Dean [46] proposed a new route for NO formation via the oxidation of NNH radicals N2 + H NNH NNH +O NH+NO
(R1.9) (R1.10)
In a stoichiometric CH4/Air flame at 1800 K, the NO formation via the new mechanism is estimated to be one order magnitude higher [46] than that predicted by the frequently used scheme of Miller and Bowman [5].
18
CHAPTER 2 Burners and gas handling system
19
In this chapter, the experimental set up used for transporting, mixing, and analyzing the cold gases, and the description of burners used in the measurements are presented. Uncertainties in the initial mixture parameters are estimated in Appendix 2A. 2.1 Transport and analysis of the cold gas mixture
Figure 2.1 shows the experimental set-up used for transporting, mixing, and analyzing the “cold” gases. Pure methane or hydrogen supplied in the cylinders under initial pressure of ~ 200 bar was used as a fuel. The purity of the fuel, better than 99.99 %, was guaranteed by manufacturer. Pressurized dry filtered air (6 bar) was used as an oxidizer. Homogenous mixing of the fuel and air was performed in the mixing tube at pressure ~ 2.5-3 bars. The mixture homogeneity was verified by measuring the distribution of fuel concentration above the burner. In calibration (see next chapter, LIF experimental procedure) and reburning (see Chapters 5 and 7) experiments, this mixture was seeded with N2, either pure, or containing ~ 5000 ppm of NO (relative uncertainty in NO mole fraction ~ 1 %). A small part of the cold mixture, typically a few tens of milliliters per minute, was pumped to the analyzing system, see figure 2.1, while the rest continued to the burner system. To simplify the control over flow rate of the mixed gases through the burner, a by-pass burner was included into the burner system. That made it possible to vary the flow rate without adjusting flows of individual gases. Flow rates of all cold gases and the gas mixture proceeding to the burner were measured by calibrated Brooks mass flow meters. The analyzing system included a Maihak Unior 610 infrared analyzer for the methane concentration, oxygen meter PMA 25, M&C, and UV absorption analyzer (Limas 11 UV, Advanced Optima) for the NO mole fraction measurements. The UV analyzer was also employed for NO mole fraction measurements reported in Chapter 7. The composition of the gas-air mixture with equivalence ratio φ can be formally written
φ gas + Zair + βΝ 2 ,
(2.1)
where Z is the stoichiometric factor for air, giving number of moles of air required for stoichiometric combustion of 1 mole of gas, β is number of moles of added N2. For simplicity, it is assumed throughout this thesis that air is composed of 20.95% O2 and 79.05% N2, thus the parameter Z is 9.547 and 2.387 for methane-air and hydrogen-air mixtures, respectively. In the experiments reported in this thesis the equivalence ratio for H2/Air flames ranged from 0.6 to 1.2 and for CH4/Air flames from 1.0 to 1.9. For the flames with added N2, the parameter β was ~0.5 so if N2 was seeded with NO, the NO mole fraction in the unburned mixture was approximately 200 ppm.
20
CH4 cal
NO cal
Exaust Analyzing system
R
R CH4 meter Pomp
O2 meter NO meter
5 way valve Pressure meter P
Mixing tube Air
R
CH4
R
H2
R
N2
R
N2 with NO
R
Burner
By pass burner Burner system Mass flow meter Valve
R
System consisting of pressure reducer and pressure meter
Figure 2.1. The experimental set-up used for transporting, mixing, and analyzing the “cold” gases. Since the accurate knowledge of the equivalence ratio and flowrate of the gas-air mixture is essential for the reproducibility and interpretation of the experimental results, special attention was paid to determine these parameters carefully. For this purpose, a set of the calibrated Brooks mass flow meters, having accuracy better than 3 % full scale, was always used, at at least 50% of full scale. From eq. (2.1) where for simplicity β is taken to be zero, it follows that the unburned mixture composition and, consequently, the equivalence ratio is fully determined when the concentration of one of the mixture components (fuel, oxygen or nitrogen) or flow rates of fuel and air are measured. Therefore, this experimental set up can provide three independent methods for the determination of the equivalence ratio in CH4/Air flames and two for H2/Air flames. In CH4/Air flames, φ can be calculated through measured concentration of methane or oxygen in the mixture, or by measured flow rates of methane and air (for details see Appendix 2A). In H2/Air flames, φ can be calculated through measured concentration of oxygen in the mixture, or by measured flow rates of hydrogen and air (see Appendix 2A). To choose one of these methods, the relative uncertainty of the methods was estimated as functions of equivalence ratio and fuel (Appendix 2A). On the basis of these estimates, the equivalence ratio in the methane-air mixtures was determined from measurements of the CH4 concentration, providing better accuracy and reproducibility than that obtained
21
from the measured oxygen concentration and gas and air flows. As a result in this thesis all equivalence ratio measurements made in methane/air flames had an accuracy better than 2 %. In the experiments on hydrogen-air mixtures, the equivalence ratio was calculated from the measured oxygen concentration using paramagnetic detection, this method proved to have better accuracy than through measurements of gas and air flows. The accuracy of the measured φ was better than 5 % (Appendix 2A). In the LIF calibration experiments, the NO mole fraction in the unburned mixture was determined through flow rates of the gases with the accuracy better than 3 %. In the reburning experiments (Chapter 7), the NO mole fraction in the unburned mixture was directly measured by the UV absorption with the accuracy better than 2 %. The infrared and oxygen analyzers, as well as UV nitric oxides meter were calibrated for the zero point and full scale before the daily measurements to ensure the stated accuracy and reproducibility in the equivalence ratio determination. Analog signals from the mass flow meters and analyzers were digitized by a Data Acquisition/ Switch Unit (Agilent 34970A); the digital signals were written to a PC. In all experimental results presented in this thesis, the gas exit velocity is given in terms of the mass flux, ρυ (g/cm2s), where ρ is the overall mass density, υ is the average gas velocity. The convenience of such presentation follows from eq. (1.11). According to this equation, the mass flux remains unchanged for one-dimensional flames with constant flame cross-section. The mass flow meters used in the experiments provided information on the volumetric flow rates, liters per minute at normal conditions (temperature 0 C and pressure 1 atm). 2.2 Burners
The experiments presented in this thesis have been performed on premixed atmospheric-pressure one-dimensional laminar flames, burning with different degrees of stabilization on the flat-flame burners. Flame stabilization is based on the technique of the upstream heat transfer to the burner (see Chapter 1). Two types of burners were used in measurements. First, the McKenna Products water-cooled porous plug sinter was used for gas-air mixtures at room temperature. Second, a perforated ceramic tile (Stettner) was built into a housing made of high-temperature-resistant stainless steel, used for preheated methane-air mixtures. The perforations in the ceramic tile were 1.1 mm in diameter on 1.3 mm centers. Both burners had 6 cm diameters. Over the last decades, the McKenna Products burner has become a standard tool for researchers working with flat flames, because it provides very stable flames, whose structure may be considered as one-dimensional. The sinter plug of this burner is manufactured either of bronze or of stainless steel and is surrounded by a sintered section for a shielding gas, usually nitrogen or argon. In the experiments performed in methaneair flames, the McKenna Products burner with the stainless steel disk was used. Hydrogen-air flames were stabilized on the McKenna burner with the bronze sinter because of the superior heat-transfer through the sinter to the cooling water. The flow rate of the cooling water was approximately 0.8 l/m for all flames. In the preheating experiments, the home-built burner was used, see figure 2.2. In these experiments, the combustion air was heated electrically, and the methane was injected downstream of the heater (Leister le 5000, Electro-Lufterhitzer). The distance
22
CH4
To the analysing system
AIR
N2 HEATER BURNER Figure 2.2. The home-built burner system used in the preheating experiments. between the point of injection and the burner was chosen to ensure mixture homogeneity; this was verified by probe measurement of the equivalence ratio above the burner surface under non-combusting conditions. To compensate for heat losses on the way to the burner, the stainless housing was also heated electrically by a hot plate. The temperature of the preheated methane-air mixture was continuously monitored by a calibrated thermocouple inserted through the housing just upstream of the burner surface. The housing itself was built in two versions, both with and without a 1 cm annulus for a nitrogen shroud. Since the heater used in the preheating experiments was not hermetically sealed, part of the air entering it leaked out. Because of that, in the preheating experiments the flow rates of gases directed to the burner were determined by measured flow rate of methane, Q methane, and methane concentration in the fuel-air mixture, [methane]% through the following expression Qtot =
Qmethane 100% . [methane]%
(2.2)
To allow the measurements of the vertical and horizontal temperature and NO concentration profiles, the burner was placed on a 3-D precision positioner (FINN Corporation) with precision 0.1 mm. The lowest vertical position above the ceramic burner where reliable measurements were possible was 1-2 mm above the surface.
23
Appendix 2A: Estimations of uncertainties in equivalence ratio determination
Using notation of eq. (2.1) where for simplicity we only consider the mixture of fuel and air, e.g. β is zero, the equivalence ratio can be expressed through 1) fuel volume concentration [F]
φ=
[F ] ⋅ Z ; (1 − [ F ])
(2A.1)
2) oxygen volume concentration [Ο 2 ]
φ=
Z ⋅ (0.2095 − [Ο 2 ]) ; [Ο 2 ]
(2A.2)
3) flow rates Qi of fuel and air
φ=
Q fuel ⋅ Z Qair
;
(2A.3)
One of the most important questions to be considered when choosing one method or another is the relative uncertainty in equivalence ratio determination for each method. If y is a function of n measured parameters:
y = f ( xi ) ,
i = 1,...n
(2A.4)
then its propagation error is given by following expression [47] : 2
∂f ∆y = ∑ ∆xi , i ∂xi
(2A.5)
where ∆xi is uncertainty in the ith measured parameter. On the basis of eq. (2A.5), the relative uncertainty calculated for 1) fuel volume concentration is φ + Z = φ Z
∆φ
2
[∆F ] ; [F ]
(2A.6)
24
2
where
[∆F ] is relative uncertainty in fuel concentration measurements, [F ] 2) oxygen volume concentration is 2
[∆Ο 2 ] ; [Ο 2 ]
φ + Z = φ φ
∆φ
where
[∆Ο 2 ] [Ο 2 ]
(2A.7)
2
is relative uncertainty in oxygen concentration measurements,
3) through measured flow rates of fuel and air is 2
[∆Q fuel ] and [∆Qair ] are relative uncertainties in fuel and air flow rate where [Q ] [Q ] fuel air measurements, respectively. Calculation of the uncertainty associated with flow rate measurements is quite straightforward, since the typical accuracy of Brooks flow meters, better than 3 % from the maximum flowrate Qimax , already includes the uncertainty of the factory-performed calibration procedure and of long term use (on monthly basis). Assuming that max max Qair ≈ Q max fuel ⋅ Z ⋅ φ and Q fuel ≈ Q fuel ⋅ 0.75 , ∆φ φ is approximately 0.06. Although the operational principles of the methane and oxygen analyzers are different, the former uses an absorption based technique and the latter being paramagnetic detection, the analysis of the uncertainties in the methane and oxygen concentration measurements can be conducted in the same manner. Both devices produce an output current I, which changes linearly with the concentration of measuring component, F, F = aI + b ,
(2A.9)
where a and b are determined by the calibration constants and factory settings, see figure 2A.1, a=
Fc − F0 , Ic − I0
(2A.10)
25
b = F0 −
Fc − F0 I0 , Ic − I0
(2A.11)
where Fc and F0 are the calibration parameters representing the percentage concentration of the studied component in the test gases used for the full scale and the zero points calibration, respectively, and Ic and I0 are the corresponding currents.
F Full scale point
Fc +b I a F=
Zero point
F0
Ic
I0
I
Output current Figure 2A.1. The simplified operational principle of the measuring device Since the test gas for the zero point calibration normally does not contain the measuring component, F0 is zero. Substitution of eqs. (2A.10) and (2A.11) to eq. (2A.9) results in F=
Fc (I − I 0 ) . Ic − I0
(2A.12)
Calculation of the relative uncertainty in a component concentration measurement yields the following expression 2
2
2
2
2
2
∆Fc ∆I c ∆I 0 Fc ∆F ∆I Fc I 0 F = F + I F I − I + 1 + I − I + I − I 1 − F . (2A.13) c 0 0 0 c c c
Figure 2A.2 illustrates the relative uncertainty in methane and oxygen concentration measurements calculated using eq. (2A.13) as a function of their percent concentration in studied mixture. The figure shows that methane and oxygen meters have similar accuracy for the given values of the factory settings and the calibration constants.
26
When a component concentration is above 2 %, its relative uncertainty is better than 2%. Calculations demonstrate that the main contributor to the relative uncertainty at these concentrations is the second term under square root on the right side of eq. (2A.13). When the component concentration decreases from 2 % towards 0 %, its relative uncertainty increases rapidly due to increasing uncertainty in current measurements, the forth term under square root on the right side of eq. (2A.13). 0.1 0.09 0.08
CH4 meter
0.07
O2 meter
[∆ F/F]
0.06 0.05 0.04 0.03 0.02 0.01 0 0
2
4
6
8
10
12
14
16
18
20
[F] , %
Figure 2A.2. The calculated accuracy in methane and oxygen concentration measurements using the Maihak Unior 610 infrared analyzer and PMA 25 oxygen analyzer. Figure 2A.3 shows the relative uncertainties in equivalence ratio calculated using the measured percentage of the methane concentration in the CH4/Air mixture, the oxygen concentration in the CH4/Air and H2/Air mixtures, and using the measured flow rates of fuel and air as a function of equivalence ratio. From fig. 2A.3 it is obvious that the measurements of the CH4 concentration by the Maihak Unior 610 infrared analyzer provides better accuracy (< 2 % in the range of equivalence ratios of interest) than that obtained by the calculation from the measured oxygen concentration and gas and air flows. Since the accuracy of the methane and oxygen measurements are practically the same (fig. 2A.3), the major difference between the relative uncertainties in the equivalence ratio calculated through the measured O2 and CH4 concentrations results from the difference in the pre-square root factors in eqs. (2A.6) and (2A.7). Indeed in eq. (2A.6), the pre-square root factor for CH4, (φ+Z)/Z, is close to unity unless φ is very big, while in eq. (2A.7), the pre-square root factor for O2, (φ+Z)/φ, is largely determined by the value of the stoichiometric factor for air (~ 10 for methane-air mixture).
27
0.2 0.18 methane, Phi[O2]
0.16
methane, Phi[CH4]
0.14
hydrogen, Phi[O2]
∆φ/φ
0.12
Phi[Flows]
0.1 0.08 0.06 0.04 0.02 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
φ
Figure 2A.3. The relative uncertainties in equivalence ratio determination based upon measurements of methane concentration in CH4/Air mixture, flow rates of fuel and air, and oxygen concentrations in H2/Air and CH4/Air mixtures.
Figure 2A.3 demonstrates that for the experiments concerned with the hydrogen-air mixtures, the measurements of the oxygen concentration provide better accuracy (< 5% in the range of the equivalence ratios of interest) than from the measured gas and air flows. The figure also shows that the accuracy of the equivalence ratio determined from the measured oxygen concentration is considerably better for the hydrogen-air mixture in comparison with that for the methane-air mixture. As can be seen from eq. (2A.7) the relative uncertainty calculated through the oxygen concentration is proportional to (φ+Z)/φ. Since stoichiometric air factor for methane-air mixture is ~ 4 times that for the hydrogen-air mixture, the accuracy of the equivalence ratio determination for the CH4/Air mixture is considerably worse than that for H2/Air.
28
CHAPTER 3 LIF and CARS methods
29
In this chapter the theoretical and experimental aspects of coherent anti-Stokes Raman scattering (CARS) and laser-induced fluorescence (LIF) techniques are discussed. 3.1 Introduction
One of main objectives of this thesis is to provide accurate and detailed measurements of NO and temperature in one-dimensional flames over the vast set of flame parameters. Apart from accuracy, sensitivity, spatial and temporal resolution of the experimental data are absolutely essential for testing of chemical mechanisms [48]. In principle there are a big number methods for measuring NO concentration and temperature, such as probe, optical and laser-based diagnostic techniques. However, not all of them can provide the needed quality of the experimental data. Thus, the principal disadvantages of the probe methods are their poor temporal resolution and the fact that in the presence of the physical probe the flame behavior can be altered [49,50]. Also, the application of the physical probe has high-temperature limit due to material considerations. Furthermore, measurement of species concentrations by probe techniques combines the sampling procedure with the following analysis of the stored mixture. The sample analysis can be performed with a high degree of accuracy by such techniques as electron spin resonance, mass spectrometry and gas chromatography, see [51] for references. However, the constitution of the gas under analysis may significantly differ from that in the flame prior to the introduction of the probe, see [52]. When probe thermometry is concerned, it should be taken into account that probes do not measure the flame temperature, and the received temperature has to be corrected for such effects as radiation heat losses, conduction, and catalytic processes on the probe surface [48]. The optical techniques include a wide variety of methods based on the interpretation of the emission and absorption radiation. The main advantages of the optical methods are that they are non-invasive, i.e. permit the study of the system without disturbing it, and have no high-temperature limit. The principal disadvantages are their poor spatial resolution and the fact that they average signal over the path length used [53]. For the last decades, progress in the combustion science has been largely associated with the intense development of laser-based spectroscopic diagnostic techniques. These techniques have proven to be capable of providing more precise and detailed information as to chemical and physical processes occurring in combustion than conventional spectroscopic and probe methods. Because of that, in this thesis, we decided to employ the laser-based diagnostic techniques for measurements of NO and temperature. In particular, for NO measurements we use Laser-Induced Fluorescence (LIF), which has thus far proved to be the best method for quantitative NO determination. For flame temperature determination we employ Coherent Anti-Stokes Raman Scattering (CARS) for N2 thermometry, which has been demonstrated to be capable of providing the accuracy of a few tens of degrees with high spatial and temporal resolution, see for example [6,54], and is so far perhaps the best method for flame thermometry [48].
30
3.2 CARS technique 3.2.1 Introduction.
Apart from being non-invasive, having high-spatial and temporal resolution, coherent anti-Stokes Raman scattering (CARS) possesses a number of valuable features making it attractive for flame diagnostics. While presenting the same spectroscopic information as spontaneous Raman scattering, the CARS technique results in much better signal to noise ratio due to its coherent nature and the high conversion efficiency of the signal. Laserlike behavior of the CARS radiation permits the capture of the entire signal within a very small solid angle, which greatly minimizes the collection of incoherent interferences such as natural flame emission. The main drawbacks of CARS are the presence of a nonresonant background, which limits the CARS detectivity at a value of approximately 0.1% at atmospheric pressure [55], and the sensitivity to laser instabilities. For a detailed discussion of the theoretical aspects of the CARS method the reader is referred to the following books/reviews: [48,55,56]. Application of CARS to various combustion environments is reported in many reviews and articles, and references can be found in above-mentioned publications. 3.2.2 Background
CARS is observed in a medium with Raman active vibrational transitional frequency ωv when two laser beams at frequencies ω1 and ω2, usually called “pump” and “Stokes” beams, respectively, such that ωv = ω1 - ω2 are directed to the medium. As a result of the laser interaction with the medium, the molecular transition at ωv is excited. Inelastic scattering of the wave at ω1 by molecular vibrations leads then to an appearance of a new wave at the frequency ω3 = 2ω1 - ω2 (CARS signal), as illustrated in figure 3.1. Providing the phase matching condition is fulfilled, namely, k3 - 2k1 + k2 = 0, where ki is the wave vector of beam i, the CARS signal at a location z will be in phase with that generated at z + ∆z . In such a case the resulting amplitude of the signal is maximal. The absolute magnitude of the wave
ω1
ω2
ω1
ω3
ωv Figure 3.1. Schematic illustration of a CARS process. Solid lines – real states, dashed lines – virtual states.
31
vector ki at frequency ωi is ωi ni / c, where ni is the refractive index at frequency ωi, and c , the speed of light. Since gases are essentially dispersionless, i.e. the refraction index is practically independent of frequency, phase matching occurs when the incident beams are aligned collinear to each other. Although most easily implemented, collinear phase matching leads to poor spatial resolution, mainly due to fact that the CARS signal is generated along the whole path length [56]. To overcome this difficulty, cross-beam phase matching is often employed, such as planar BOXCARS [57], termed that on the basis of the shape of the phase matching scheme, see figure 3.2. In this approach, the pump beam at ω1 is split in two parallel beams. These beams together with ω2 beam then are transported to a common focus, where the CARS signal is generated. The intersection of the beams defines the measuring volume. Resolution of a millimeter or better is effortlessly reached [55]. The recording of the entire CARS spectrum follows by successive or instantaneous exiting of the Raman resonances of interest. The former is performed by scanning ω2, and by keeping ω1 constant. The single pulse detection of the anti-Stokes Raman spectrum, first demonstrated by Roh et al. (1976) [58], is achieved by using a broadband dye laser for ω2 together with a spectrograph and multichannel optical detector such as a CCD camera.
k2
k1
k3
k1
ω1 ω1 ω2
ω3
Figure 3.2. Planer BOXCARS phase matching scheme. With the assumption of phase matching and ignoring dispersion in the susceptibility, one can write the intensity of the CARS signal in the following way [59]
32
2
2 4πω I CARS = 2 3 I 12 (ω 1 ) I 2 (ω 2 ) χ CARS l 2 , (3.1) c where I1 and I2 are the intensities of the pump and Stokes beams at ω1 and ω2, XCARS is the third order nonlinear CARS susceptibility, and l is the phased matched interaction distance. Since the intensity of the CARS signal is proportional to I12I2, eq. (3.1), it is advantageous to focus the pump and Stokes beams in the studied volume. It is interesting to notice that the value of focal length has a little effect on the intensity of the CARS signal. When the Gaussian laser beams are considered, their interaction might be assumed to generate the CARS signal from a small cylindrical volume about the focus with diameter δ and length 6l [60] given by
δ =
4 fλ dπ
(3.2)
l=
πδ 2 , 2λ
(3.3)
and
where f is the focal length of the lens, d is the beam diameter in the plane of the lens, λ is the laser wavelength. The total CARS beam power PCARS some distance beyond the focal volume then is independent of the focal length PCARS = I CARS
where P1 and P2 are the powers at ω1 and ω2, respectively. More accurate calculation, see [56] for references, shows that there is a modest increase in the CARS signal in going from long to short focal length. The CARS susceptibility depends on both temperature and density and can be written as a sum of a resonant and nonresonant terms [55] XCARS = ∑ ( X ‘ + iX ‘‘ ) j + Xnr.
(3.4)
j
The resonant susceptibility is described by real part X ′, which exhibits “dispersive” behavior, and imaginary part X ′′ , which shows “lineshape” behavior, and is given as [55,61] ( χ ' + iχ " ) j = K j
Γj , 2∆ω j − iΓ j
(3.5)
where Γj is the linewidth for transition frequency ωj, ∆ωj ≡ ωj-(ω1-ω2) is the detuning, and Kj is given as
33
Kj =
4πc 4 δσ 1 N∆ j g j , 4 hω 2 δΩ j Γ j
(3.6)
where N is the total species number density, ∆j is the fractional population difference between the states involved in the transition, gj is the linestrength factor, h is the Planck’s constant and (δσ/δΩ)j is the Raman crossection for transition j. The nonresonant susceptibility Xnr results from distant off-resonant electronic transitions. It provides a weak frequency spectrum that interferes with the resonant spectrum. As can be seen from the above equations, the CARS signal gets contributions from the variety of vibrational-rotational Raman lines (accessible by the frequency difference ω1 - ω2) of varying amplitude and width. The temperature dependence of the CARS spectrum results from the fact that the CARS susceptibility depends on the fractional population difference between the higher and lower levels. The fraction of molecules in a vibrational rotational level is given in thermal equilibrium by a Boltzmann distribution. Providing that the resonant and nonresonant susceptibilities are known, calculated CARS spectra can be generated. The temperature might be extracted then from the spectral shape of the measured CARS signals by fitting them to the calculated spectra. It should be noted that eq.(3.1) gives the CARS signal as it enters the detection system. Thus, the CARS spectrum should be convoluted with a slit function of the detector system [55].
34
3.2.3 Experimental
In all experimental data presented in this thesis, the flame temperature was measured with broadband planar BOXCARS for nitrogen thermometry. Nitrogen was chosen as a temperature indicator because this molecule is a dominant component in fuel/air combustion processes, and has relatively well-known molecular parameters [62-64]. 3.3.4 Experimental set-up
Figure 5.3 shows the experimental configuration used for broadband CARS measurements in our laboratory. A Nd:YAG laser (Quanta-Ray Pro-Series, SpectraPhysics) at a repetition rate of 10 Hz and with pulse duration of ~ 10 ns generated ~ 500mJ pulse energy at the wavelength 532 nm. The linewidth of the laser line was approximately 1 cm-1, according to the laser specification and verified by our own
L
FIBER
w3 F
w1
DM
BD
w1 w2
w3
M
L Wheel of filters L
SPECTROGRAPH PC
BURNER
CCDC
L M
DELAY LINE
SH
ATTENUATOR
M
D
w1
M
w1 M
M
w2 SH
Nd:YAG laser
BS
M M
D
Dye laser M
M
Figure 3.3. CARS experimental set up. Code: SH, beam shutter; D, diaphragm; BS, beam splitter; M, mirror; L, lens; BD, beam dumper; DM, dichroic mirror; F, coloured glass filter; PC, personal computer. measurements with a Burleigh Model WA-4500 pulsed wavemeter. 40 % of this radiation was split off and used to pump a dye laser (Quanta-Ray PDL 2, Spectra-Physics). The
35
dye laser produced up to 70 mJ at ω2 using 1:1 dye mixture of Rhodamine 610 and Rhodamine 640. In the oscillator of the dye laser, a grating was replaced by a highly reflecting mirror, producing a broadband output of width of the order of 100 cm-1. The laser beam at ω1 was directed by a number of mirrors, passed through a continuously variable attenuator, Newport Corp. model 935-10, and then was split in two beams by a 50 % splitter, with approximately 40 mJ in each. The laser beams at ω1 and ω2 were arranged in the BOXCARS configuration (the distance between beams ~ 2 cm, and all beam diameters are ~ 1 cm) and were focused with f = 50 cm lens, yielding the coherent anti-Stokes signal at ω3. To ensure that the laser beams at ω1 and ω2 were temporally recombined in flame, a delay line was introduced in the optical path of the pump beam, see figure 3.3. The spatial resolution of the CARS experiment was determined by the focal volume of diameter ~ 100 µm and length ~ 2 mm. To position the pump beam waist at the crossing point, the adjustable telescope built into the dye laser was used. After spectral separation from the laser beam at ω1 by a dichroic mirror and coloured glass filter, the CARS beam was focused by a lens to a fiber (inner diameter ~ 100 µm). At the fiber output, the CARS signal was focused onto the entrance slit of a 0.85 m double spectrometer, (SPEX 1403, reciprocal linear dispersion 0.4 nm/mm) through a wheel of neutral density filters. The detection of the broadband CARS signal was performed by a gated (100 ns) CCD (Princeton Instruments) camera with array consisting of 1340×100 pixels, 20µm×20µm each. The stepping motor (SMD38/IEEE, Bentham) for the filter wheel was connected to a computer via the IEEE/488 interface. That arrangement let us automatically adjust the intensity of the CARS signal coming to the CCD camera to avoid CCD camera saturation and ensure sufficient signal-to-noise ratio. Every measured spectrum was averaged over 100 laser pulses. The output signal with adjustable delay ± 500ns to the laser pulse was used to ensure timing between the data collection and the laser output signal. This signal was sent to the camera controller (ST-133, Princeton Instruments), which started the data acquisition if the start command from computer had been received, ~ 450 ns prior to the laser pulse. The overall experimental performance was controlled by computer providing the start command for the experiment, storing the measured data, determining various process characteristics such as the CCD exposure time, typically 0.01s, the number of pulses to be averaged, 100, binning in Y direction, 100 pixels, and so on. (The CCD allows to unite the multiple pixel charges in both horizontal and vertical direction into a single “super” pixel; this procedure is referred to as binning.) Binning in vertical direction was made to enhance the CARS signal. The background signal was measured by blocking the Stokes beam by an electro-mechanical shutter (see figure 3.3), and subtracted from the measured signal. In all reported temperature measurements CARS spectra were normalized with dye spectra obtained by measuring nonresonant CARS spectra in methane. The normalization procedure was necessary to compensate for the spectral non-uniformity of the broadband laser output. The measurements of the CARS and dye spectra were conducted within a few minutes from each other to minimize the possible fluctuation of the dye spectra. It was observed that the maximum position of the dye spectra, especially when the dye was in circulation for several weeks, could be shifted during 20 minutes operation in such a way to lead to a difference in the determined temperature of ~ 70 K .
36
3.2.5 Temperature dependence of N2 CARS spectrum
To illustrate the temperature dependence of the N2 CARS spectrally resolved signal, figure 3.4 shows four spectra measured at different temperatures in CH4/Air flames. As can be seen from the figure, the spectra display strong temperature sensitivity. The first band, with the peak intensity at approximately 473.6 nm, corresponds to the υ = 0 → υ = 1 vibrational transition, where υ is the vibrational quantum number. The fundamental band becomes broader and acquires clearly visible rotational structure with increasing temperature. The second band results from overlap of the υ =1 → υ =2 “hot” band with rotational transitions with high J numbers from the fundamental band. The second band becomes observable only at temperatures higher than 1000 K; the reason for that is the high-energy spacing between the ground and first vibrational levels of N2 ~2330 cm-1. 6
Iintensity, a.u
5
4
T=2227 K T=1400 K
3
T=1087 K T=300 K
2
1
0 473
473.2
473.4
473.6
473.8
474
474.2
474.4
474.6
474.8
Wavelength, nm
Figure 3.4. The measured temperature variation of the CARS spectrum of N2 (methane/air flames). Temperatures were extracted from the measured spectra by fitting them to the spectra calculated using the CARP-PC [65] program. As an example, figure 3.5 shows the measured spectrum of N2 with a computer fit to 1900 K; measurement was made in an atmospheric-pressure methane-air flame. At this relatively high temperature, the calculated and measured spectra display two vibrational bands with rotational structure.
37
4 3.5
Intensity, a.u.
3 2.5
Calc Exp
2 1.5 1 0.5 0 473
473.2
473.4
473.6
473.8
474
474.2
474.4
474.6
Wavelength, nm
Figure 3.5. Experimental (dots) CARS spectra of N2 and computer fit (line) to a temperature 1900 K.
The accuracy of the temperature measurements was evaluated by comparing the temperatures measured in near-adiabatic flames with calculated adiabatic values. By near-adiabatic flames, we mean flames with the negligible heat transfer to the burner. The measurements were performed in methane and hydrogen flames at different equivalence ratios. As an example of typical experimental data, figure 3.6 shows the measured temperature as a function of the equivalence ratio for near adiabatic methane-air flames. The experimental data are contrasted with the calculated results. The comparison of the measured and calculated temperatures reveals that the accuracy of the CARS temperature measurements for lean and slightly rich methane-air flames, equivalence ratios from 0.6 to 1.3, and lean hydrogen-air flames, φ from 0.4 to 0.6, is better than 30K (near-adiabatic hydrogen flames at higher equivalence ratios were inaccessible due to flow limitations). The accuracy of the observed temperatures for the rich methane-air flames (equivalence ratio higher than 1.3) appears to be better than 50 K. The measured temperatures are systematically higher than the calculated adiabatic values for fuel-rich methane-air flames.
38
2350
Temperature, K
2250 2150 2050 1950
Experiment Calculation
1850 1750 0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Equivalence ratio
Figure 3.6. Experimental temperature as a function of the equivalence ratio for near adiabatic methane-air flames. The data are contrasted with calculated adiabatic values.
39
3.3 Laser-Induced Fluorescence 3.3.1 Introduction
Laser-induced fluorescence (LIF) is the fluorescent emission of light from atoms or molecules following their excitation to an upper state by laser radiation. LIF is one of the most frequently applied diagnostic techniques for detection of minor species in combustion. The success of the LIF method is predominately based on its high spatial resolution and sensitivity, usually at the ppm level, selectivity, very low background, as well as relatively simple experimental implementation. LIF has been applied to detect various combustion intermediates consisting of combinations of O, N, H, C, and S, including the atoms themselves, see [48,66]. The electronic transitions for these intermediates are generally situated in the visible and UV regions, which are readily accessible by means of tunable lasers. LIF is also used to measure other flame parameters such as temperature. Although the fluorescence signal is relatively easy to measure, conversion of this signal to concentration is a considerably more difficult problem. Apart from the information on the flame temperature, a quantitative interpretation of the LIF signal requires the detailed knowledge of the rates of various collisional processes and a calibration procedure [48]. A theoretical description of the LIF physics, experimental details, as well as measurement strategies can be found in the following books/reviews [48,51,53,66,67] and references therein. 3.3.2 General theory
The quantitative aspects of the LIF method will be discussed here with the NO molecule as an example. It is assumed that in the absence of laser radiation only ground vibrational level of the X2Π electronic state is populated. It is also assumed that laser radiation excites a single rotational level of the A2Σ+ (υ = 0) state. The other rotational levels of this electronic-vibrational state can be populated through rotational relaxation, see figure 3.7. The populations of the upper and lower rotational levels coupled with the laser radiation are Nu and Nd. The fluorescence signal (photons), F, collected by an optical system during time τL from the A2Σ+ state is determined by the following expression: Ω F= Vτ L ∑ N ( j )∑ A0 k ( j , i ) , (3.7) 4π j k ,i where Ω /4π is the solid angle detected, V = S·l (cm3) the detected volume, expressed by the laser beam cross-section S and the path length l determined by the collection optics, N(j) is the population of the jth rotational level of the A2Σ+(υ=0) exited state (cm-3), A0k(j,i), the spontaneous emission rate from the jth level to the ith rotational level of X2Π (υ=k) state (s-1); the laser pulse is assumed to be rectangular with pulse length τL equal to the full width at half maximum (FWHM). From eq. (3.7) it follows that for narrowband detection, detection is performed from a single quantum state, the fluorescence intensity is proportional to the population of the exited level. While in the case of broadband 40
detection it is proportional to the sum of the excited state rotational population weighted by the spontaneous emission rate sum. For NO the rate of spontaneous emission A depends only slightly on rotational level [68], so it can be assumed that for all j
∑A
ok
( j , i ) = const = A .
(3.8)
k ,i
Therefore A can be removed from the summation over i, and the fluorescence signal will be proportional to the total population in the upper electronic state, NA , : F = NAA
Ω Vτ L . 4π
(3.7a)
To couple the signal with the species total population or the temperature it is necessary to consider the dynamics of the excitation process. Rate equations for the temporal derivatives of the excited rotational levels j ≠ u and u are given, respectively, by dN ( j ) = ∑ N ( j ' )Θ( j ' , j ) − N ( j ) ∑ Θ( j , j ' ) + Q( j ) + A + Wion dt j '≠ j j '≠ j
(3.9)
and
dN u = N d bdu + ∑ N ( j )Θ( j, u ) − N u bud + ∑ Θ(u, j ) + Q(u ) + A + Wion , dt j ≠u j ≠u
(3.10)
where Θ(j,j') is the rotational relaxation rate from rotational level j to j', Q(j) is the total quenching rate from level j, Q( j ) = ∑ Qok ( j , i ) , i ,k
bdu and bud are rates of absorption and stimulated emission, respectively, for the lasercoupled rotational levels, and Wion is the photoionization rate. It should be noted that the rate equations can be accurately applied when characteristic laser pulse times are considerably longer then the elastic collision times (dephasing times). For atmosphericpressures flames the dephasing times are ~ 0.1 ns [48], therefore eqs. (3.9) and (3.10) are valid for laser pulse lengths above 1 ns. At laser pulse lengths smaller than 1 ns, the description of the dynamics of the excitation process requires the quantum-mechanical treatment [69]. The case of very short laser pulse will not be considered here any further. Since the NO concentration at flame conditions is relatively low, and rotational energy transfer in the excited state is rapid, narrowband detection might not provide sufficient signal-to-noise ratio, see [39] , therefore this case will not explored here further. Rates of absorption and stimulated emission are connected to the Einstein coefficient for stimulated emission, Bij (cm3J-1s-2), through the relation [66]
41
Wion
A State Θ
u
Q, A
bdu
bud
X State V
V’=0
V’’=N V’’=3 V’’=2 V’’=1
d
Θ
V’’=0 Figure 3.7. Excitation scheme used for LIF modeling. Laser radiation excites a single rotational level u of the A2Σ+ (υ = 0) state from a rotational level d of X2Π (υ = 0) ground electronic state. Excitation is followed by electronic quenching, Q, vibrational, V, and rotational, Θ , relaxation. Also included are rates of absorption and stimulated emission, bdu and bud, respectively, spontaneous emission, A, and photoionization, Wion.
42
bij =
Bij ⋅ I ⋅ G L c2
,
(3.11)
where I is the irradiance, given in W/cm2, c the speed of light, and GL (cm) a convolution integral reflecting the overlap between laser and absorption linewidth ∞
G L (v) = ∫ g A (v − v0 ) g L (v − v L )dv ,
(3.12)
−∞
where v0 is the wavenumber of the absorption line center (cm-1), vL the wavenumber of the laser line center (cm-1), gA and gL the absorption and laser line profiles, respectively. They are normalized as ∞
∞
−∞
−∞
∫ g A (v − v0 )dv = ∫ g L (v − v L )dv = 1 .
(3.13)
The total population in the upper electronic state NA can be expressed by following equation, received by summation of eq. (3.9) over all rotational levels j ≠ u and adding result to eq. (3.10), dN A = N d bdu − N u bud − N A (Q + A + Wion ) , dt
(3.14)
assuming that Q(j) is constant for all rotational levels in the exited state, Q=Q(j). The solution of eq. (3.14), apart from rates of photoionization, quenching, and stimulated emission (spontaneous emission rate can be neglected since for NO at atmospheric pressure Q >> A, see [66]) requires the knowledge of the populations of the two laser-coupled levels. The population of these levels is connected through the collisions to all other rotational levels, so it is necessary to solve the rate equations for all rotational levels. The limited information about the rates of collisional relaxation, for temperatures higher than room temperature [70,71], makes the exact solution of eq. (3.14) difficult. Furthermore, at present, the state-to-state collisional quenching rates are unknown, and the known rate is the sum of quenching rates to all vibrational and rotational levels of the ground electronic state. Therefore in the general case it is not possible to couple the population of the excited electronic state with the total population. However, in a few limiting cases, this all-inclusive collisional information is unnecessary, and the fluorescence signal can be related to the total population using simple equations. To evaluate the validity of the steady state approach one must compare the laser pulse duration with the effective lifetime, τeff=1/(Wion+Q+A). For typical combustion conditions τeff is ~ 2 ns nanosecond, see [39]; this time is sufficiently small to treat the excitation dynamics in quasi-steady state even for excitation with nanosecond pulsed lasers, see [39,67].
43
1
Low laser Energy
In the case of low laser energy, eq. (3.14) becomes (neglecting the photoionization and stimulated emission, and assuming the steady state condition dNA/dt=0) NA =
N d0 bdu , Q
(3.15)
where N d0 is the equilibrium population of the lower laser-coupled rotational level. The fluorescence signal for this case is F=
A Bdu P Ω EG (v) f d X NO l , 2 Q c kT 4π
(3.16)
where fd is the fractional population in level d, XNO is the NO mole fraction, P is the pressure, T is the temperature, E is the pulse energy. In this approach, the fluorescence signal depends linearly on the laser energy. The first term in equation (3.16), A/Q, called the fluorescent quantum yield, represents the number of photons emitted per molecule excited. For a methane-air flame at ~ 2000 K, the NO fluorescent quantum yield is approximately 10-2 [66]. At present, the majority of NO measurements have been conducted by linear fluorescence, see [72-75]. Linear fluorescence is complicated by the dependence of the fluorescence signal upon the laser energy and the quenching. While the influence of the former can be dealt with by normalizing the signal by the measured laser power, the latter presents a considerably bigger challenge since it is a function of the temperature and the flame composition. Since the equation for total population is linearly proportional to the quenching, any ambiguity in the magnitude Q strongly affects the measured concentration. Several strategies have been proposed for establishing a value of the fluorescence quantum yield, such as calculation through known mixture composition [76] and direct measurements of the fluorescence decay, generally applicable in low-pressure flames [33]. Another point to be considered while operating at low laser power is the signal-to-noise-to ratio. For example, let us estimate the number of signal photons registered by the detector for a single laser pulse in the case of broadband detection for a typical methane-air flame condition (T = 2000 K), Fr, Fr = F ⋅ ε ⋅ ϑ ,
(3.17)
where ε is the efficiency of collection optics (~ 20 %), ϑ is the quantum efficiency of the detector (~10 %). Let us assume that the laser line with a FWHM of 1 cm-1 is centered on the molecular transition Q11(14.5), v0=vL, (G(v0) then can be approximately taken as 1cm) and the laser energy is 2 µJ per 10 ns pulse. The stimulated absorption Einstein coefficient for this transition is 2.25×1023 cm3J-1s-2 [77]. For A2Σ+(υ=0) state, the rates of spontaneous emission and quenching (hydrocarbon flame at 2000 K) are ~ 4.6×106 s-1 [78] and 5×108 s-1 [79], respectively. At T =2000 K, the fractional population in the rotational level J=14.5 of the X2Π (υ=0) state fJ is ~ 0.0054. Assuming 1 mm spatial 44
resolution, and solid angel ~ 0.0028 str, the number of signal photons per pulse per one ppm of NO is approximately 0.03. Thus if it was desired to measure 10 ppm of NO with a signal-to-noise ratio 20 (± 5 % error), S/N=(0.03×10×Naver)0.5, where Naver is the number of pulses averaged, more than 1000 laser pulses would have to be averaged. Taking into account that a typical laser repetition rate is 10 Hz, a measurement would require about 2 minutes. 2
Two-level model
Hear we assume the steady state condition dNA/dt=0 and that the rotational relaxation and photoionization are negligibly small. In this case, Nu = NA, then N d0 = N d + N A ,
(3.18)
In the case of low laser energy, the equation for the fluorescence signal is exactly the same as eq. (3.16). In the so-called saturation regime, bdu and bud >> Q, and the fluorescence signal is given by F=A
gu P Ω f d X NO Vτ l , gu + gd kT 4π
(3.19)
where gu and gd are the degeneracies of the laser-coupled rotational levels. In this regime, the fluorescence intensity does not depend on the laser intensity or quenching. Physically it means that the laser absorption and stimulated emission become so large that they dominate the state-to-state energy transfer in two-level system. In the beginning of above paragraph, the photoionization rate was assumed to be negligible. Let us now consider this assumption in regard to laser energy; the photoionization rate is given by the following expression [66] Wion =
σ ion I hvo c
(3.20)
where σi is the photoionization cross section (cm2), h is the Plank’s constant (J·s). As in the previous exercise we assume a laser beam with a duration of 10 ns has uniform energy distribution in a cylinder with a diameter of ~ 0.5 mm. Then for a laser energy of 1 mJ and σi = 7×10-19 cm2 [80], the photoionization rate is approximately 4 ×107 s-1. Therefore the rate of photoionization at a laser energy of a few milijoules is comparable with that of quenching ( ~ 5×108 s-1). In the case of a real molecule, the saturation condition is given by bdu and bud >> Q/(Nu/NA), or in terms of the laser energy Q ⋅τ L ⋅ S 2 1 . E >> c ⋅ (3.21) Bdu G (v0 ) N u NA
45
At the low limit of NA/Nu (unity), the rotational relaxation is negligibly small (two level model), and E >> 0.04 (mJ). The upper limit of NA/Nu (1/fu), the rotational relaxation is much faster than quenching, and E >> 6 (mJ). The rates of rotational relaxation of NO, based on room-temperature cross sections from [70,71], are of the same magnitude as the quenching rate. Therefore, a laser pulse energy on the order of several millijoules should be sufficient to reach the saturation regime. It should be noted that, practically, complete saturation is unachievable at the outer edges of the focused laser beam, and it is also not possible to saturate during the entire duration of the laser pulse. Quantitative measurements of NO at atmospheric-pressure hydrocarbon flames while operating at high laser power have been reported in the literature, see for example [39,81]. In these works it was demonstrated that NO is easily saturated (when millijoule pulse energies were used) and the NO detection limit on the order of 1 ppm is reachable. It should be noted that results presented in these works do not give an answer as to whether fluorescence is inhibited by photoionization or stimulated emission or both. Having appreciated the shortcomings of linear fluorescence (mainly the dependence of the LIF signal on the quenching and the possibly low signal-to-noise ratio) and considered fruitful applications of the saturated LIF for NO measurements in atmospheric-pressure flames [39,81] we decided to measure the NO concentration employing high laser powers in this thesis.
46
3.3.3 Experimental
The absolute NO concentration was derived from measurements of broadband laserinduced fluorescence following the excitation of the A2Σ+-X2Π (0-0) rotational lines near 44241 cm-1 (226 nm). The spectral feature consists of the overlapping rotational lines P11(23.5) + Q11(14.5)+QP21(4.5)+ Q22(20.5) + QR12(20.5)+ SR21(8.5) + RQ21(8.5) and has a comparatively high intensity and relatively modest temperature dependence [81]. The feature is well separated from adjacent NO lines, see figure 3.8, and from O2 lines of the Schumann-Runge system [75,82]. Conversion of the fluorescence signal to absolute NO concentration was conducted using the method reported by Mokhov et al. [81]. In that work, the temperature dependence of laser-induced A2Σ+-X2Π fluorescence in the burned gases of natural gasair flames, seeded with known amount of NO, was studied. It appeared that the measured dependence, when millijoule pulse energies were used, was best described by the temperature dependence obtained from a model in which quenching corrections are neglected, as in the case of the saturated two-level model. The absolute NO concentration was determined using the measured intensities of the seeded flame as a calibration factor, see below for more details. The accuracy of the LIF measurements described here was better than 5 %, see [81]. 5
Intensity, a.u.
4
3
2
1
0 44220
44225
44230
44235
44240
44245
44250
Wavenumber, cm
44255
44260
44265
44270
-1
Figure 3.8. Calculated excitation spectrum of NO using the LIFBASE program [77]. The vertical lines mark the spectral region chosen for diagnostic. 3.3.4 Experimental set-up
Figure 3.9 shows a schematic of the LIF experimental setup. As a source of ultraviolet radiation, a Nd:YAG pumped tuneable dye laser with a wavelength extender was used (Continuum Powerlite 8010/ND6000/UVX). The dye mixture of Rhodamine 590, ~72 %, and Rhodamine 610, ~28 %, was used. The dye laser output beam was doubled, and then mixed with the residual infrared beam to generate UV radiation at
47
wavelengths near 226 nm, with bandwidth of approximately 1 cm-1. The energy of the laser beam at 226 nm, measured by a pyroelectric joulemeter (Molectron Model J3–05), was typically 2.0-3.5 mJ per 10 ns pulse. The laser beam was focused by a quartz lens (f = 850 mm) through the diaphragm into the flame, giving a beam waist of ≤ 0.5 mm. Fluorescence was collected at right angles by a quartz camera lens (Nikon f/4.5). An interference filter centered at 250 nm with a FWHM of approximately 45 nm, was placed in front of the camera to reduce the Rayleigh-scattered signal and to transmit much of fluorescence from the A2Σ+(υ = 0) state, see figure 3.10. The detection of fluorescence was performed by a gated (200 ns) ICCD camera (Princeton Instruments) with an array consisting of 1024×256 pixels, 26µm ×26µm each. Every measured signal was averaged over 100 laser pulses.
LASER SYSTEM M Nd:YAG
Dye laser
WE
EXT Q Sw
POSITIONER
CC BD
CC
L1
BS
D
B
M L2 POWER METER
RECORDER
Intensifier DELAY LINE D1 D2
CCD HV cable
JM
CC
CC
25-pin cable
PG-200
CC CC
CONTROLLER PC
Data Acquisition Box
CC
RECORDER
RS 232 OSCILLOSCOPE
HB-IB
CC
CC - coaxial cable HV - high voltage
Figure 3.9. LIF electronic block diagram. Code : M, mirror; SH, shutter; B, burner; BD, beam dumper; JM, joulemeter; PC, personal computer. For detailed description see text.
48
120
100 (0,1)
80 (0,0)
(0,2)
60 (0,3)
40 (0,4)
20 (0,5) (0,6)
0 215
225
235
245
255
265
275
285
295
305
Wavelength, nm
Figure 3.10. Calculated emission spectrum of the A 2 Σ + (ν = 0) − X 2Π (ν = k ) transitions at T = 1900 K (calculation made using the LIFBASE program [77]). The vertical lines mark the spectral region corresponding to the FWHM region of the interference filter used in the experiments. 3.3.5 Timing of signals
Since the Nd:YAG laser used in the LIF experiments had no sync output providing an adjustable signal prior to the laser pulse, the synchronization of the ICCD intensifier gating with the laser output signal was performed by running the Nd-YAG laser in the External Q-Switch mode. In this mode, the external signal arriving on the input connection of the laser microprocessor system leads to the simultaneous generation of the high-voltage pulse opening Q–switch, e.g. initiating generation of a short laser pulse with high peak power. When operating in the external Q-switch mode, it is of a great importance to provide right timing between the external signal and the signal discharging the flash lamps of the laser. To build up a maximal population inversion in the laser active medium, the signal firing the flash lamps (supplied by laser system) must precede the Q-Switch signal by approximately 200 µs (according to the laser manual). Since the laser system provided the output for a signal synchronized with the pulse firing the flash lamps, this synchronized signal was chosen as the time origin for further synchronization. The signal, “FIRE COMMAND” (see Figure 3.11 for graphical representation), was sent to the adjustable delay line containing two outputs, see figure 3.9. One of the output signals, “EXTERNAL Q SWITCH”, was delayed by ~200 µs relative to “FIRE COMMAND” signal, needed for the population inversion to build up, and then proceeded to the External Q-Switch input. The second output signal, “TRIGGER IN”, preceded the first one by 0.5 µs and was used as an external trigger to the programmable pulse generator (PG-200, Princeton Instruments) providing high-voltage gating of the ICCD intensifier. The gating signal, “TO ICCD”, was delayed relative to the triggering pulse by
49
600 ns, and had a width of 200 ns; these time characteristics were chosen experimentally base (by detecting the laser beam image on ICCD camera) in such a way to ensure that the laser output, “LASER OUTPUT”, was approximately in the middle of the pulse gate. Prior to the gate signal, the generator triggered the camera controller (ST-138, Princeton Instruments) starting the data acquisition, “CCD COMMANDS”.
Figure 3.11. Timing and voltage of the most important signals of the synchronization process in LIF experiments.
50
Figure 3.11 shows the timing relationship and voltage of the most important signals of the synchronization process. The overall experimental performance was controlled by computer providing the start command for the experiment, storing the measured data, determining process parameters such as the exposure time (typically 0.01s), the number of pulses to be averaged (100), binning (40 pixels in Y direction) and so on. Binning in the vertical direction was made to gain in speed and noise performance of ICCD; the number of pixels grouped, 40, was chosen experimentally (by detecting the laser beam image on ICCD camera) in such a way to ensure that the entire spatial (vertical) distribution is detected. Before every fluorescence measurement, a small offset, mainly from dark current, was measured. This offset was subtracted from the fluorescence signal to prevent it from having any influence on the data. The offset measurements were performed with the laser beam blocked by a shutter, see figure 3.9. During the LIF measurements, the energy of the laser radiation was constantly measured and recorded by the detection system consisting of the Molectron pyroelectric Jolemeter probe (Model J3–05), Powermeter (EPM 1000, Molectron), and flatbed recorder (BD 112, Kipp&Zonen). The analog output of the EPM 1000 was also digitized by a Data Acquisition/Switch Unit (Agilent 34970A), and the digital signals were written to the PC. 3.3.6 Calibration procedure
The detected signal I can be formally presented as a sum of the fluorescence signal from NO and background signal, Ibg, see figure 3.12, I (v) = CP(T , v)[ NO ] fl + I bg (T ) ,
(3.22)
where v is the laser wavenumber, C is a constant representing such parameters as measured volume, the collection solid angle, and etc., P is the fluorescence temperature dependence due to the total density, the Boltzmann population of the initial state of the excitation line, the rates of quenching processes and the spectral overlap between the laser and absorption lines (see above), T is the flame temperature, and [NO]fl is the NO mole fraction in the flame. Therefore to calculate the NO concentration from eq. (3.22) one must know the values of C and Ibg. The fluorescence temperature dependence P was determined in abovementioned work [81]. In this work it was shown that for the LIF setup used, which was also used for LIF measurements in this thesis, the coefficient P(T) is independent of quenching in a stoichiometric natural gas-air flame, when millijoule pulse energies were used as mentioned above. The independence of the NO LIF signal upon the quenching means that in the present LIF setup other deexcitation processes such as the stimulated emission or photoionization dominate over the quenching in the stoichiometric flames. The only reason for possible deviation from this behavior in flames with different equivalence ratios could be extremely high quenching rates in comparison with that in the stoichiometric flame. But the calculations based on the quenching data from [83] showed that at fixed temperature the quenching rates in the rich flames with φ ≤ 1.6 differ less than 50% from that in stoichiometric flames. Therefore it is reasonable to suppose that the NO LIF signal is independent upon the quenching not only in the stoichiometric but in the rich flames with φ ≤ 1.6 as well.
51
To establish the magnitude of the background signal, the fluorescence measurements were made with the laser tuned to the peak of the chosen spectral feature near 44241 cm-1 and off-resonance at 44246 cm-1 in every flame measured, see figure 3.12. Since the NO fluorescence signal is linearly proportional to the NO concentration, the ratio of I1-Ibg to I2-Ibg is independent of the NO concentration in flame I 1 − I bg I 2 − I bg
= L(T , ϕ , v1 , v 2 ) ,
(3.23)
where L is a function of temperature, equivalence ratio, and two wavenumbers v1 and v2. Thus the background in a flame can be determined if L(T,φ) is known for a given pair of wavenumbers.
Figure 3.12. Method for subtracting off non-NO background signal by tuning off the NO peak to wavenumber 44246 cm-1.
Figure 3.13 shows two excitation spectra measured in near adiabatic stoichiometric CH4/Air/N2 flames; one is seeded with NO and one is unseeded, and otherwise identical. The figure also includes the calculated LIFBASE spectrum for linear fluorescence. Comparison of the two experimental spectra reveals that the unseeded spectrum is located slightly above the seeded one at the spectral minima. Such behavior is indicative of the presence of the non-NO background in the unseeded flame. The magnitude of this background is found from
52
I 1S − I bg I 2 S − I bg
=
I 1NS − I bg I 2 NS − I bg
(3.24)
,
where subscripts S and NS denote the seeded and the unseeded flames, respectively, and is ~ 5 % of the intensity of the NO fluorescence signal at 44241 cm-1. The procedure described above should in principle be applied to every flame measured. However, calculations show that L(v1,v2) is a weak function of temperature and equivalence ratio due to the broad laser bandwidth (~ 1 cm-1) and the choice of v1 and v2. For example, in the temperature range from 1500 K to 2300 K, L(v1,v2) changes by less than 10 %. Considering that and taking into account the fact that the magnitude of the background for the vast majority of the flames reported in this thesis did not exceed 10 % of the intensity of fluorescence signal, we use the value of L which was measured in near adiabatic stoichiometric CH4/Air/N2 flames to establish the background for all flames studied. To evaluate the constant C, the calibration procedure discussed below for methane-air flames was applied. Two vertical fluorescence profiles at v1 = 44241 cm-1 were measured in near adiabatic stoichiometric flames doped with the same amount of N2. The first profile was measured when the added N2 contained NO at a maximum fraction of ~ 5000 ppm (~ 200 ppm in the unburned fuel/air mixture) and the second when the added N2 was “neat”. Since the flame temperature was unaffected by such a small composition change, which was verified by measurements (CARS) and equilibrium calculation, the temperature profile (CARS) was only measured in the unseeded flame. The difference in the measured fluorescence signals for seeded and unseeded calibration flames, taken at a distance of ~ 1.5 cm above the burner surface to minimize the temperature and NO concentration gradients, then is cal cal cal cal I cal = CP(Tcal )([ NO]cal s + [ NO ] fl ) + I bg − CP (Tcal )[ NO ] fl − I bg =
(3.25) = CP (Tcal )[ NO]
cal s
where Tcal is the flame temperature in the calibration flame, [ NO]cal and [ NO]cal s fl are the NO mole fraction in the seeded and unseeded calibration flames, respectively. It follows from eqs. (3.22) and (3.25) that [ NO] fl =
( I (v1 ) − I bg ) ⋅ P(Tcal ) I cal (v1 ) ⋅ P (T )
[ NO]cal s
(3.26)
This calibration procedure relies on two assumptions. First, that the seeded NO mole fraction is preserved in flame front and, second, that the seeding does not have an effect on the flame NO concentration; see Chapter 7 for more detailed discussion. Whereas these assumptions appear justified in near-adiabatic fuel-lean and stoichiometric methane-air flames [81], the fate of seeded NO in hydrogen-air flames seems to be
53
5 without seeded NO
4
Intensity, a.u.
seeded with NO
3
2
1
0 44230
44232
44234
44236
44238
44240
44242
44244
44246
44248
44250
Wavenumber, cm-1
(a) 5
Intensity, a.u.
4
3
2
1
0 44230
44232
44234
44236
44238
44240
44242
44244
44246
44248
44250
Wavenumber, cm-1
(b)
Figure 3.13. Excitation spectra in the CH4/Air/N2 flames : (a) bold line - N2 with NO (~ 200 ppm in the unburned gas/air/nitrogen mixture), line with dots – N2 without NO; (b) calculated using the LIFBASE program [77].
54
uncertain (see Chapter 5 for references). To follow the fate of seeded NO in these flames and to find conditions suitable for application of the calibration procedure, CRDS measurements were performed in hydrogen flames seeded with NO, as discussed in Chapter 5. Unfortunately, strong broadband absorption by hot CO2 near 226 nm [84] precludes using absorption methods for measuring low (less than a few hundreds ppm) NO concentrations in atmospheric-pressure hydrocarbon flames. 3.3.7 Linearity of the detection system
Before performing quantitative measurements, the linearity of the detection system was verified. For this purpose, the fluorescence measurements were made at room temperature. A mixture of air and seeded N2 was used. To maintain the composition of the mixture, only the NO concentration in N2 was varied, keeping flow rates of air and N2 constant. Measurements were performed at a distance of 1cm above the McKenna burner through which the gas mixtures were directed. Figure 3.14 shows the NO fluorescence intensity as a function of seeded NO concentration. The vertical axis represents the difference between fluorescence intensities measured at seeded and unseeded conditions. The results presented in figure 3.14 show excellent linear dependence between the measured fluorescence and the seeded NO concentration. 6
Intensity, a.u.
5
4
3
2
1
0 0
50
100
150
200
250
300
350
400
450
[NO]added, ppm
Figure 3.14. NO fluorescence intensity measured in a cold mixture as a function of the seeded NO concentration. See text for details.
55
CHAPTER 4 Temperature measurements on burner-stabilized flames
56
Abstract
In this Chapter, we investigate the effects of varying the degree of burner stabilization on the flame temperatures of H2/Air and CH4/Air flames. We also report the measurements of flame temperatures in stoichiometric and fuel-rich CH4/Air flames subjected to varying degrees of preheating, up to 400 K. The temperature was measured by coherent anti-Stokes Raman scattering (CARS). Excellent agreement between the experimental results with one-dimensional model predictions over a wide range of conditions indicates that the burners used in the experiments produce well-defined flat flames. The agreement illustrates the predictive power of GRI-Mech in flame calculations to determine burning velocity. It increases our confidence that possible disagreements between measured and calculated NO concentrations (in later Chapters) are only due to uncertainties in NO formation chemistry. We also show that the variation in flame temperature with mass flux and preheating in burner-stabilized flames can be used to extend the range of reliability for predictions of phenomena related to burning velocity, by testing chemical mechanisms with a wider combination of equivalence ratio and temperature (over 700 K) than possible by using the free-flame burning velocity solely as a function of equivalence ratio. Sensitivity analysis for flame temperature, conducted for H2/Air flames, shows that the impact of the various reactions changes with mass flux, and thus with flame temperature; reactions that are of modest importance in free flames can become dominant at low temperature. In addition, because of the high accuracy of the temperature measurements, the data are capable of discerning differences in rate coefficients substantially smaller than their current uncertainty. Thus, these data can be useful as an experimental benchmark for mechanism optimization. Based on the experimental results of this chapter, the reproducibility of the temperature measurements for methane/air flames is estimated to be better than 40 K, and for hydrogen/air flames better than 30 K.
57
4.1 Introduction
Flat burner-stabilized flames are important for both industrial and combustion research applications. Radiant surface-combustion burners, the operational principle of which is essentially identical to that of water-cooled flat-flame burners [6], are effectively employed in industry to reduce NOx emissions [85]. The well-defined flow field in flat burner-stabilized flames presents also a great advantage for studying chemical pathways and testing the predictive power of chemical mechanisms by comparison of the experimental and modeled data. Accurate and detailed information on temperature in these flames is absolutely essential for these aims. One of the methods for testing the predictive power of a mechanism (as well as for optimizing them [86,87]) has been to compare the numerical and experimental determinations of the free-flame burning velocity of one-dimensional flames. A wellknown limitation to this use of burning velocity data is that this parameter is sensitive to only a limited number of reactions [87]. When considering a mechanism for a specific fuel, another limitation is that, in general, the only parameter varied for mechanistic purposes is the equivalence ratio. The variation in flame temperature achieved is inextricably tied to changes in equivalence ratio; this results in a relatively limited sampling of parameters. Thus, the contributions of the important reactions at stoichiometric conditions are only tested along the temperature profile ending at the (high) adiabatic stoichiometric temperature. A widened range of conditions with which the modeled predictions could be compared would clearly enhance the reliability of the simulations. In this chapter, we propose a method for extending the range of parameter variation for testing the performance of chemical mechanisms with the respect to burning velocity. Specifically, we use the modified version of the heat transfer method used by Kaskan [23] to derive the overall activation energies. Rather than deriving an “overall” flame parameter, we compare the variation in temperature with mass flux with that obtained from detailed flame calculations. Using CARS to measure temperature, as discussed in Chapter 3, an accuracy of better than 40 K can be achieved [41], offering the potential of highly reliable data. It is interesting to discuss briefly the methodology described above in the context of various methods for measuring burning velocity. We first point out that the “heat-transfer method” for determining the free-flame burning velocity [22,88] relies upon finding the exit velocity at which the flame becomes adiabatic. With an eye towards detailed modeling, it will be clear that the predicting the changes in burning velocity with varying heat transport, from near extinction to adiabatic, is preferable to predicting only the extrapolated free-flame value. Two other important methods for deriving onedimensional free-burning velocities, using twin counterfow flames [89] and expanding spherical flames [90], also rely upon accounting for complicating multidimensional factors intrinsic to the methods: in the former method, the measured burning velocities are extrapolated to zero stretch, while in the latter method flame curvature must be minimized. Detailed modeling of the variation in burning velocity as a function of stretch or curvature [91] would extend the range of validity of the models used, and significantly enhance our insight into these phenomena. In a sense, the method we describe above is the simplest, since heat transfer in flat flames is still sufficiently one-dimensional. Also, inasmuch as the flame temperature is varied in the heat-transfer method, it is perhaps the
58
best methods for exploring sensitivities in chemical mechanisms, as will be shown below. The counterflow and spherical flame methods, on the other hand, are most likely to be more suitable for exploring the sensitivity of transport models to stretch and curvature. One hurdle for doing so, however, is that such simulations are by definition multidimensional, and thus significantly more complex to perform accurately. In the first part of this chapter, we report the measurements of the flame temperature as a function of mass flux in hydrogen-air flames at lean, stoichiometric, and rich conditions. Further on, using these flames we demonstrate the sensitivity of the modified version of the heat transfer method to variation in the individual rate coefficients of important reactions. By important reactions we mean here reactions that are significant for the response of flame temperature to varying mass flux. In the second part, we report the measurements of flame temperature as a function of mass flux in methane-air flames and compare them with the modeled data. In addition, we consider the effects of preheating of the rich methane-air mixtures on the variation in temperature with mass flux (see also Chapter 1). Flames were stabilized either on McKenna burners for measurements using fuel-air mixtures at room temperature, or on a perforated ceramic tile for experiments on preheated methane/air mixtures (Chapter 2).
59
4.2 Hydrogen-air flames 4.2.1 Temperature measurements in hydrogen- air flames
Figures 4.1, 4.2, 4.3 and 4.4 show typical vertical temperature profiles measured in hydrogen-air flames at equivalence ratios 0.6, 0.8, 1.0 and 1.2, respectively. At every equivalence ratio, the experimental results are presented for various mass fluxes, ρυ, at heights from 0.1 to 2.1 cm above the burner surface. At high mass fluxes (temperatures above ~ 2000 K), the profiles continue to rise in the post-flame region, φ = 1.0, ρυ = 0.056 g/cm2s (figure 4.3), due to slow radical recombination, while at lower mass fluxes, temperatures below ~ 2000 K, the profiles are flat over much of the measured domain. The rapid decrease in temperature above ~ 1.6 cm for φ = 0.6, ρυ =0.0057 g/cm2s (figure 4.1), φ = 0.8, ρυ = 0.0056 g/cm2s (figure 4.2), φ = 1.0, ρυ = 0.0039 g/cm2s (figure 4.3) is due to mixing with the nitrogen shroud at these low mass fluxes, see discussion below. The uncertainty in the temperature measurements (usually better than 30 K) is shown in the figures. In figure 4.5, typical experimental profiles for various equivalence ratio and mass fluxes are compared with modeled data (GRI-Mech 3.0). The figure shows that there is an excellent agreement between them; the predictions, with few exceptions, being within the experimental error. 1900 1800 1700 Temperature, K
Both mixing with the nitrogen shroud and radiative losses can cause the decrease in the temperature in the post-flame gases. Supposing that the flame is optically thin, the flame radiation spatial temperature decay rate, dT/dx, can be calculated using the energy balance equation in the following way dT dT dt Q 1 = ⋅ = ⋅ dx dt dx ρ ⋅ C p υ
(4.1)
where ρ is the overall mass density (kg/m3), Cp is the heat capacity at constant pressure for the burnt gases (J/kgK), υ is the mass average velocity (m/s), and Q is the heat loss per unit volume due to radiation (W/m3). The latter can be calculated using the StefanBoltzmann law for a gray body 4 Q = 4 K pσ (T flame − Tair4 ),
(4.2)
where Kp is the Planck absorption coefficient (1/m) (for hydrogen-air flames Kp ≅ Kp,H2O), σ - Stefan-Boltzmann constant (W/m2K4), Tflame and Tair are the flame and ambient air temperatures (K), respectively. Calculation of the spatial temperature decay rate using the GRI-Mech 3.0 calculations and the water vapor infrared mean absorption coefficient, Kp,H2O , from [92] gives the value of ~ 11 K/cm for hydrogen-air flame at φ = 1.0 and T = 2000 K. Calculations show that the temperature decay rate enhances with the decrease in the flame temperature, reaching ~ 85 K/cm at T = 1500 K, by and large because of the increase in the residence time and the reduction of the flame temperature. The rapid temperature decreases for low temperature flames, see the figures above, have considerably higher rates (~ 1500 K/cm) than calculated using eq. (4.1), therefore we can only conclude that the mixing with the nitrogen shroud at these low mass fluxes is the reason for these decreases. It should be noted that the estimations presented above provide the extreme case; more detailed calculations [93] reveal that temperature gradient in the burnt gases are smaller than that for the optically thin limit. Since most of the measured temperature profiles are flat, and the form of the calculated profiles at the higher temperatures mirror the experimental profiles very well, even though they are not flat, for the rest of the discussion we will consider the variation of temperature with conditions at a fixed height above the burner surface. For comparison, it is preferable to chose the point as high above the burner surface as possible; however, radiative heat transfer and/or mixing limit the maximum height. Therefore, for all profiles at mass flux greater than 0.006 g/cm2s, we use a point at 1.5 cm, while for fluxes less than 0.006 g/cm2s, temperatures are taken at a point in the flat region. The calculated temperatures are taken at the same point as in the experiments. In figures 4.6, 4.13, 4.7 and 4.8, we show the variation of flame temperature at fixed height with mass flux for φ = 0.6, 0.8, 1.0 and 1.2, respectively. Here we note that the data reflect the functional behavior of burning velocity with flame temperature observed by Kaskan [23] (Kaskan’s data are generally within 30 K of our data). We also note that GRI-Mech 3.0 predicts the results within the accuracy of the measurements. While still within the uncertainty of the measurements, the data at φ = 0.6 suggest a slight
63
1900 1800
Temperature, K
1700 1600 1500 1400 1300 1200 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
2
Mass flux, g/cm s
Figure 4.6. Flame temperature vs. mass flux at φ = 0.6. Points: measurements, ● – this work; - Kaskan (1956); lines: calculations using GRI-Mech 3.0 (solid line) or GRIMech 2.11 (dashed line).
2100 2000
Temperature, K
1900 1800 1700 1600 1500 1400 1300 1200 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
2
Mass flux, g/cm s
Figure 4.7. Flame temperature vs. mass flux at φ = 1.0. Points: measurements, ● – this work; - Kaskan (1956); lines: calculations using GRI-Mech 3.0 (solid line) or GRIMech 2.11 (dashed line).
64
1900 1800
Temperature, K
1700 1600 1500 1400 1300 1200 1100 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
2
Mass flux, g/cm s
Figure 4.8. Flame temperature vs. mass flux at φ = 1.2. Points: measurements, ● – this work; - Kaskan (1956); lines: calculations using GRI-Mech 3.0 (solid line) or GRIMech 2.11 (dashed line). divergence from the calculation above ρυ = 0.05 g/cm2s. At φ = 1.0, the calculation appears to overestimate slightly the results below ~ 1900 K. Also shown are calculated results using GRI-Mech 2.11 [94]. For most of the curve, the predictions of GRI-Mech 2.11 lie just outside the limits of error. We also report here that calculations using the Warnatz mechanism [95] yield results nearly indistinguishable from those of GRI-Mech 3.0. Whereas the GRI-Mech exercise only compares one point at each of these equivalence ratios (the free flame burning velocity), figure 4.6 tests the agreement of the mechanism over a span of 500 K, figure 4.7 over a range of more than 700 K, and fig 4.8 over a span of 600 K. The data at φ = 0.8 yield similar results. We point out here that varying heat flux to vary flame temperature is substantially easier to implement experimentally than the alternative method, i.e., replacing N2 in air by Ar and CO2 [96]. 4.2.2 The sensitivity of the heat transfer method to individual rate constants
Using GRI-Mech 3.0, we calculated coefficients of the flame temperature sensitivity for the rates of different chemical reactions, (Ai/Ti)·(∂T/∂Ai), where Ai is the temperature independent pre-exponential factor for ith reaction, and T is the flame temperature. After multiplying by the relevant flame temperatures, the temperature normalized sensitivity coefficients Ai⋅(∂T/∂Ai) have a simple physical meaning, namely, they reflect the change in the flame temperature when the variation in the rate of ith chemical reaction is of the same order of magnitude as the rate itself. To illustrate the dependence of flame temperature on the rate constants of the various elementary reactions, the normalized coefficients are plotted versus the one-dimensional mass flux for the stoichiometric flame, figure 4.9.
65
80 60
Sensitivity, K
40 20
O+H2H+OH H+O2+H2OHO2+H2O
0 -20
0
0.05
0.1
0.15
H+O2O+OH OH+H2H+H2O H+HO2OH+OH
-40
H+HO2O2+H2
-60 -80 -100 Mass flux, g/cm2s
Figure 4.9. Sensitivity of flame temperature to variation in rate constant as a function of mass flux for a stoichiometric hydrogen/air flames. We restrict the data to the mass fluxes below 0.14 g/cm2s, because the precision of the sensitivity coefficient calculations is worsened when the free-flame mass burning rate (~ 0.18 g/cm2s) is approached (the adiabatic temperature is not dependent on the reaction rates). The sign of the sensitivity coefficient is chosen to reflect the flame temperature change upon an increase in rate constant. Thus, the negative sign for the sensitivity of the reaction OH+H2 H+H2O means that an increase in the rate of this reaction will lead to a decrease in the flame temperature at a given mass flux. For the majority of the reactions, the sensitivity changes by less than uncertainty of the temperature measurements over the whole range of the exit velocity. Because of that, these reactions are not included into the figure. We also want to note that the sensitivity of any given reaction does not change sign upon variation of mass flux. Actually, it means that the flame temperature at any given flow rate and equivalence ratio is decreased by chainbranching and increased by chain-terminating processes. Or analogous to the free flame [95], burner-stabilized flame propagation is accelerated by chain-branching and inhibited by chain-terminating processes independent of the variations in the mass flux and equivalence ratio. Over most of the range shown in the figure, OH+H2 H+H2O, which shows the largest sensitivity in the free-flame burning velocity [95], also has the greatest effect on the flame temperature in our case. However, below ~ 0.04 g/cm2s the importance of this reaction begins to wane, while that of other reactions increases significantly. Interesting is that the major chain-termination reaction, H+O2+H2O HO2+H2O, which has only moderate influence under adiabatic conditions [95], gains steadily in importance with decreasing mass flux. Similarly, the major chain-branching reaction, H+O2 OH+O, which is subordinate to OH+H2 in the free flame, becomes the most important reaction below ~ 0.03 g/cm2s. We note here that the slope of the curves of flame temperature versus mass flux becomes large as the mass flux becomes very small. Thus, a small 66
fluctuation in ρυ can result in large fluctuations in temperature, causing extinction. Interesting is that at low ρυ the major chain-branching and chain-terminating reactions strongly dominate the sensitivity. This fact suggests that an analysis of the major chainbranching and chain-terminating reactions in this region may permit prediction of extinction due to flame-burner transfer as performed for flammability limits in [97]. To illustrate the dependence of the sensitivity coefficients on equivalent ratio, we show the results at φ = 0.6, 0.8, 1.0 and 1.2 for the reactions OH+H2 H+H2O, H+O2 OH+O, and H+O2+H2O HO2+H2O, in figures 4.10, 4.11 and 4.12, respectively. Mass flux, g/cm2s
0
Sensitivity, K
-10
0
0.05
0.1
-20
Phi=1.2
-30
Phi=1.0
-40
0.15
Phi=0.8 Phi=0.6
-50 -60 -70 -80 -90
Figure 4.10. Sensitivity coefficient for OH+H2 H+H2O as a function of mass flux for different equivalence ratios. Considering the sensitivity curves corresponding to the reaction H2+OH H+H2O (figure 4.10), we see that the curves at φ = 0.6, 0.8 and 1.0 converge to similar values at low mass flux. While the sensitivity at φ = 1.2 decreases to substantially lower values at the same mass flux.
67
Sensitivity, K
80 70
P hi=1.2
60
P hi=1.0 P hi=0.8
50
P hi=0.6
40 30 20 10 0 0
0 .05
0 .1
0 .1 5
2
M a s s flux , g /c m s
Figure 4.11. Sensitivity coefficient for H+O2+H2O HO2+H2O as a function of mass flux for different equivalence ratios. Mass flux, g/cm2s 0
0.05
0.1
0.15
-10
Sensitivity, K
-30 -50 -70 -90
-110 -130
Phi=1.2 Phi=1.0 Phi=0.8 Phi=0.6
-150
Figure 4.12. Sensitivity coefficient for H+O2 OH+O as a function of mass flux for different equivalence ratios.
68
When comparing figures 4.11 and 4.12, it is interesting to observe the convergence of the sensitivities for the chain-terminating reaction (fig. 4.11), while the chainbranching reaction (fig. 4.12), gains strongly in significance with increasing equivalence ratio. It appears that the decreasing availability of oxygen renders the contribution of this chain-branching reaction essential for propagation. Having determined the reactions that are significant for the response of the flame temperature to varying mass flux, we now illustrate the utility of the experimental method for assessing (or “adjusting ”) individual rate coefficients. As an example, we consider the effects of increasing or decreasing the pre-exponential factor in GRI-Mech 3.0 for OH+H2 H+H2O by 50% (the uncertainty given for this rate constant in [98]) on the calculated temperatures. In figure 4.13, we plot the calculated results together with the measured temperatures for φ = 0.8. Two points are worth noticing in fig. 4.13. First, the changes in the predicted temperatures when varying the rate coefficient are not symmetrical: increasing the rate has much less effect than decreasing the rate. Second, the variation in the predicted temperature caused by an uncertainty of 50 % in the rate constants is significantly larger than the experimental uncertainty. Thus, because of CARS measurements of flame temperature yield high accuracy, the comparison of calculations with the experimental data has the potential for testing even fine changes in elementary rate constants. It is apparent that this type of measurement could be used beneficially in multiparameter optimization schemes such as GRI-Mech.
2100 2000
Temperature, K
1900 1800 1700 1600 GRI 3.0
1500
H2+OH --> H+H2O +50%
1400 H2+OH --> H+H2O -50%
1300 1200 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
2
Mass flux, g/cm s
Figure 4.13. Flame temperature vs. mass flux at φ = 0.8. Points: measurements; lines: calculations using GRI-Mech 3.0, for different values of the pre-exponential factor for OH+H2 OH+O.
69
4.3 Methane-air flames 4.3.1 Temperature measurements in methane-air flames
Figures 4.14 and 4.15 show typical experimental vertical temperature profiles in the region from 1 to 21 mm above the McKenna Products burner (Chapter 2) for equivalence ratios 1.0 and 1.3, respectively. At high mass fluxes (post-flame temperatures above ~2000 K), the experimental temperatures for φ = 1.0 reach their maximum near 5 mm and remain flat thereafter. At lower mass fluxes, the profiles are flat over much of the measured domain. The figure 4.14 shows a modest decrease in temperature above 1 cm for ρυ = 0.0106 g/cm2s reflecting the effect of radiative loses, see below. The experimental profiles for φ = 1.3 are generally flat at temperatures above ~ 1950 K. At lower temperatures, the figure shows the slow decrease in temperature above 1.6 cm for ρυ = 0.017 g/cm2s and above 1 cm for ρυ = 0.0096 g/cm2s. The estimations of the radiative spatial temperature decay rate using eq. (4.1) and assuming that for methane-air flames Kp ≅ KH2O+KCO2, the mean absorption coefficients are taken from [92], give the values of ~ 40 K/cm and ~ 115 K/cm for φ = 1.3 flames at T = 2000 K and T = 1850 K, respectively. Taking into account that the above estimations represent the extreme case [93], we conclude that the calculated values account for the measured post-flame temperature decreases. The uncertainties in the temperature measurements (usually better than 40 K) are shown in the figures. For the purpose of comparison with the numerical data, the figures include the profiles calculated using GRI-Mech 3.0 [11]. The comparison of the measured and modeled results for φ = 1.0 shows that they agree very well, and with exception of the post-flame region (above 1cm) for ρυ = 0.0106 g/cm2s, are within the experimental error. The figures also reveal that while the experimental profiles reach their maximum temperatures near 5 mm, the calculations reach these levels only above 10 mm. This observation is consistent with results in near-adiabatic flames [41]. The maximum calculated temperature rise in the domain of the figure (> 5 mm) is less than 60 K, while the rise between 20 mm and 10 cm is less than 20 K. Apart from the post-flame regions, where the radiative heat loses affect the measured temperatures, the experimental and modeled results agree very well for φ = 1.3. Unlike to the stoichiometric case, the calculated temperature profiles are practically flat above 5 mm, the maximum temperature rise between 5 mm and 10 cm is less than 20 K, i.e. is well within the accuracy of the measurements, 40 K. To facilitate the further discussion, we plot the measured temperature as a function of the mass flux. To minimize variation in temperatures caused by the initial temperature rise, noticeable at temperatures in excess of ~ 2000 K (see figure 4.14), by radiative heat loses and by mixing with the nitrogen shroud, we use the temperature at 5 mm above the burner surface. These plots are shown in figs. 4.16 and 4.17 for φ = 1.0 and 1.3, respectively. In figure 4.16, flame temperature varies from the adiabatic stoichiometric value (~2220 K), when ρυ is higher than the free-flame burning velocity (flame is no longer one-dimensional but still adiabatic), to nearly 1600 K at ρυ = 0.0034 g/cm2s. For φ = 1.3, the temperature varies between approximately 2075 K and 1700 K, figure 4.17. Decreasing the mass flow rate further to achieve lower temperatures than 1600 and
70
2300 2200
Temperature, K
2100 2000 1900 1800 1700 1600 1500 1400 1300 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Distance, cm
Figure 4.14. Vertical profiles of temperature in methane/air flames at φ = 1.0. Points: measurements; lines: calculations using GRI-Mech 3.0. ◊ - ρυ = 0.044 g/cm2s; Χ ρυ = 0.038 g/cm2s; ● - ρυ = 0.024 g/cm2s; - ρυ = 0.0106 g/cm2s. 2100
Temperature, K
2000 1900 1800 1700 1600 1500 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Distance, cm
Figure 4.15. Vertical profiles of temperature in methane/air flames at φ = 1.3. Points: measurements; lines: calculations using GRI-Mech 3.0. □ - ρυ = 0.0236 g/cm2s; ρυ = 0.017 g/cm2s; Χ - ρυ = 0.0096 g/cm2s.
71
2300
Temperature, K
2200 2100 Exp
2000
GRI 3.0, 5mm
1900
GRI 3.0, 10cm
1800 1700 1600 0
0.01
0.02
0.03
0.04
0.05
0.06
Mass flux, g/cm2s
Figure 4.16. Temperature of CH4/Air flame as a function of mass flux at φ = 1.0. Points: measurements; lines calculation using GRI-Mech 3.0. Experimental points are taken at 5 mm above the McKenna burner surface, calculations at 5 mm and 10 cm.
2150
Temperature, K
2050
1950
1850 Exp GRI 3.0, 5mm
1750
GRI 3.0, 10cm
1650 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
2
Mass flux, g/cm s
Figure 4.17. Temperature of CH4/Air flame as a function of mass flux at φ = 1.3. Points: measurements; lines calculation using GRI-Mech 3.0. Experimental points are taken at 5 mm above the McKenna burner surface, calculations at 5 mm and 10 cm.
72
1700 K for φ = 1.0 and 1.3, respectively, results in the flame being extinguished for both equivalence ratios. The analysis of the experimental data in these figures allows to determine the free burning velocity for each φ by estimating the mass flux at a cusp (discontinuity of the first derivative), see Table 1. It should be noticed that the accuracy of this method is rather low (~ 10 %) due to a relatively modest temperature variation with mass flux at high ρυ.
Table 4.1. Free burning velocities determined from the plots of the flame temperature versus the mass flux with accuracy ~ ±10 % and calculated using GRI-Mech 3.0 chemical mechanism for different degrees of preheating, burners and equivalence ratios (see text for more details). Figures 4.16 and 4.17 also include the calculated results for temperatures at 5 mm above the burner and at the maximal temperature (at the end of computational interval). The agreement between the predictions at their maximal value and measured results is excellent for both equivalence ratios. At high temperatures for φ = 1.0, the data calculated at 5 mm are just outside the limits of error. That reflects the fact that the experimental temperature profiles reach their maximum earlier than the calculated ones. In spite of these small differences, figure 4.16 tests the agreement of the chemical mechanism over a span of more than 600 K, and figure 4.17 over a span of 350 K. 4.3.2 Effects of preheating on flame temperature
The effect of preheating on the variation in measured flame temperature with mass flux is illustrated in figure 4.18, which shows the variation as a function of preheating for φ = 1.3. Experiments were performed on the home-built burner (Chapter 2). Following the method of presentation for methane-air mixtures at room temperature, we use the temperature at 5 mm above the burner surface. It should be noted that all measured
73
temperature profiles for different degrees of preheating are flat at least for the first 10 mm, see Chapter 6 for examples. The figure shows that all experimental points and calculated data coincide to within of the experimental error (± 40 K), with the exception of the experimental points taken above the free-flame burning velocity for a given preheating temperature. In this case the flame temperature remains constant at higher mass flux, for the same reason as given before. The estimated free burning velocities, see above, for different initial temperatures of the air-methane mixture are presented in Table 1.
2400 2300
Temperature, K
2200 2100
no preheat, calc. 100 K preheat, calc. 200 K preheat, calc. 300 K preheat, calc. 400 K preheat, calc. no preheat, exp. 100 K preheat, exp. 200 K preheat, exp. 300 K preheat, exp. 400 K preheat, exp.
2000 1900 1800 1700 1600 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
2
Mass flux, g/cm s
Figure 4.18. Temperature of CH4/Air flame as functions of mass flux and preheating at φ = 1.3. Measurements performed above the home-built burner. Points: calculations using GRI-Mech 3.0, lines: measurements. We note that figure 4.18 tests the agreement of the chemical mechanism over a span of 600 K, much wider than that ( ~ 350 K) for air-methane mixture at room temperature, figure 4.17. These figures also reveal the well-known fact [41] that the temperature measurements obtained with the McKenna (figure 4.17) and perforated ceramic tile (fig.4.18) burners are identical for the same ρυ. The experimental data presented in figs. 4.18 and 4.21 show also that at constant mass flow rate the flame temperature is independent of the degree of preheating: when the exit velocity is lower than the free-flame burning velocity, any additional enthalpy from preheating is transferred to the burner, see also the discussion in Chapter 1. This is further illustrated for the flames using the calculated (GRI-Mech 3.0) temperature profile for φ = 1.3 and ρυ = 0.01 g/cm2s, shown in figures 4.19 and 4.20. Figure 4.19 shows the
74
1900 1700
Temperature, K
1500 1300 1100
GRI 3.0, no preheat GRI 3.0, 100 K preheat
900
GRI 3.0, 200 K preheat GRI 3.0, 300 K preheat
700
GRI 3.0, 400 K preheat
500
GRI 3.0, 500 K preheat
300 0.00
0.05
0.10
0.15
0.20
0.25
Distance, cm
Figure 4.19. Calculated temperature profiles in methane/air flame with φ = 1.3 and ρυ = 0.01 g/cm2s.
2000 1800
Temperature, K
1600 1400 1200
no preheat
1000
100 K preheat 200 K preheat
800
300 K preheat
600
400 K preheat
400
500 K preheat
200 0 -0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Distance, cm
Figure 4.20. Calculated temperature profiles shifted to 798 K at X = 0; φ = 1.3 and ρυ = 0.01 g/cm2s. For further details see text.
75
profiles as obtained from the calculations, while in figure 4.20 the profiles are shifted in accordance with the discussion in Chapter 1 (increasing the temperature of the mixture only shifts T(x) towards the origin, yielding profile T(x+dx)). Thus, although somewhat counter-intuitive (or even fortuitous) when thinking in terms of the details of flameburner interaction, the constancy of the flame temperature at constant φ and ρυ is “simply” a necessary consequence of the governing equations. 2200 2150
Temperature, K
2100 2050 2000 1950
no preheat
1900
100 K preheat 200 K preheat
1850
300 K preheat
1800
GRI 3.0
1750 1700 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
2
Mass flux, g(/cm s)
Figure 4.21. Temperature of CH4/Air flame as functions of mass flux and preheating at φ = 1.5. Measurements performed above the home-built burner. Points: measurements, lines: calculations using GRI-Mech 3.0. The variation in measured flame temperature with mass flux as a function of preheating is also shown in figure 4.21 for φ = 1.5. Ηere too, we see that within the experimental error all curves are identical. Comparison of the experimental data with predictions reveals an excellent agreement between them. This Chapter reported the database of the temperature measurements performed in H2/Air and CH4/Air flat laminar atmospheric pressure premixed flames. Special attention was paid to investigate the effects of varying the degrees of the burner stabilization and preheating on flame temperature. The experimental data were compared with the model predictions.
76
CHAPTER 5 The Calibration of LIF signal by CRDS and reburning of NO in H2/Air and CH4/Air flames
77
Abstract
A combination of pulsed CRDS, CARS and LIF was used to determine absolute concentrations of NO in atmospheric-pressure flames. The NO A2 Σ (v = 0) - X2 Π(v = 0) absorption band has been measured in the 44210 – 44260 cm-1 spectral region by measuring the cavity ring-down times. This spectral region offers isolated spectral features useful for NO detection. Measurements in atmospheric-pressure methane-air flames were frustrated by strong broadband absorption at 226 nm by hot CO2 molecules, which increased the NO detectability limit to several thousand ppm. This absorption renders the cavity ring-down method for measuring the native concentrations of NO in atmospheric-pressure hydrocarbon flames problematic. In hydrogen-air flames, this broadband absorption was substantially lower, yielding an NO detectability limit of the order of 10 ppm. Comparison of absorption cross-sections derived from the cavity ringdown spectra with literature data suggests that absorption by water molecules is the main contribution to the additional cavity losses in these flames. Special attention has been paid to account for effects of the cold boundary layers on the NO mole fractions measured by the CRDS method. For this purpose, the radial profiles of temperature and NO mole fraction were measured along the absorption path by CARS and LIF, respectively. The measurements show that temperature and concentration nonuniformities cannot be neglected as a source of significant errors in flames burning in the open atmosphere. Even in the McKenna Products burner, which was specially designed for laser-diagnostic purposes, the effective absorption length was ten percent larger the burner diameter. At φ = 0.8 and 1.0, the LIF data are in perfect agreement with the results of CRDS measurements, at φ = 0.6, there is a deviation between the CRDS and LIF results, of at most ~20 %. The measured NO mole fractions in atmospheric-pressure hydrogen-air flames with φ = 0.6, 0.8 and 1.0 at temperatures above ~ 1750 K are in good agreement with those calculated using GRI-Mech 3.0. Since no loss of seeded NO is observed at these temperatures, the measurements verify that these conditions are suitable for the calibration of LIF signals. However, at lower temperatures a considerable discrepancy between measurements and detailed calculations was observed.
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5.1 Introduction
Laser-induced fluorescence (LIF) has thus far proved to be the best method for insitu measurement of NO [99]. Despite its numerous advantages, LIF suffers from a number of intrinsic drawbacks. One of the most problematic is the dependence of the LIF signal upon collisional processes, which are generally difficult to account for, and necessitates calibration (Chapter 3). Usually, this is performed by seeding the unburned gas-air mixture with a known amount of NO [42,81]. This calibration procedure is based on the assumption that there is no net reduction of the seeded NO in the flame front. Whereas this assumption appears justified [34,81] in (near) freely propagating fuel-lean and stoichiometric flames, experiments and detailed calculations [34,81] indicate that a significant part of seeded NO is removed in rich-premixed methane-air flames. Unfortunately, the mechanism of NO formation and consumption in hydrocarbon flames is too uncertain to assess the fate of seeded NO quantitatively. Even in hydrogen flames, some uncertainty remains over the consumption of seeded NO in the flame front. In experiments using LIF [73] in low-pressure flames, no significant removal of the seeded NO was observed. In contrast, a study using molecular beam mass spectrometry in lowpressure hydrogen flames [100] and chemiluminescence measurements [101] in atmospheric-pressure fuel-rich hydrogen flames demonstrated significant NO removal. A reliable independent verification of the concentration of seeded NO in the hot gases of all these flames would help remove much of the uncertainty surrounding NO calibration measurements. Cavity ring-down absorption spectroscopy (CRDS) is an excellent candidate for the calibration of NO LIF, due to its potentially high sensitivity. Moreover, integrating the absorption coefficient over the absorption line eliminates the dependence of the signal upon collisional processes. The application of CRDS to measuring NO in the infrared region at atmospheric pressure is frustrated by strong background absorption of H2O molecules, which are present both in flames and in the surrounding air. Until recently, use of the ultraviolet bands of the nitric oxide for CRDS measurements was hampered by the lack of highly reflecting mirrors in this spectral region. The NO concentration in seeded low-pressure methane-air flames [102,103] and in the exhaust of a diesel engine [104] has been measured by CRDS. To our knowledge, there have been no reports of the application of CRDS to the measurement of NO in atmospheric pressure flames, to date. In this Chapter, the quantitative aspects of using CRDS at 226 nm for measurements of the NO mole fractions in the burned gases of premixed atmospheric-pressure flames are investigated. Further, the NO concentrations in seeded hydrogen-air flames at different equivalence ratios are reported.
79
5.2 CRDS technique 5.2.1 Background
Cavity ring-down spectroscopy (CRDS) is a relatively new absorption technique, which was originally developed for measurement of the reflectivity of HR mirrors [105]. However, it was soon realized that the technique is capable of quantitative detection of trace species in flames with potentially high sensitivity [106]. To date, CRDS technique has been applied for quantitative measurements of minor species, see for example [48]. Being a successor to the conventional absorption method, CRDS offers the advantage of a relatively simple quantification of number density; by integrating the absorption coefficient over the absorption line, the dependence on the signal upon collisional processes is eliminated. Moreover, due to its enhanced sensitivity in comparison to conventional absorption, CRDS possesses the ability to detect extremely low number density. However, the application of the CRDS method to flame diagnostics is hampered by its poor spatial resolution and sensitivity to inhomogeneities in the distribution of absorbing species in the optical path. Also, as with all absorption methods, the presence of interfering species seriously affects the selectivity of the method. Because of these limitations, the CRDS is generally the second choice when it is possible to apply traditional LIF, which is potentially background free and possesses high spatial resolution. However, in situations where the application of LIF is impossible or complicated, for example for molecules that do not fluoresce, CRDS might be very valuable. CRDS is also an excellent candidate for the calibration of the LIF signal, see for example [102,107]. Discussion of the theoretical and experimental aspects of the CRDS technique can be found in reviews [108-110]. 5.2.2 Principles of the method
The basic CRDS experiment includes the source of laser radiation, the optical cavity usually formed by two identical highly reflective mirrors, and a fast photo detector placed behind the exit mirror, see figure 5.1. The laser pulse is injected into the cavity along the cavity axis through the entrance mirror and then travels back and forth between the mirrors. The intensity of the laser beam in the cavity will gradually decrease in time due to the cavity losses. The temporal decrease in the pulse intensity transmitted through the exit mirror is recorded by the detector. When the total cavity losses are only determined by the reflectivity of the mirrors, the intensity of the transmitted signal after n round trips starting from some time t0, P(t0+ntr), is given by [108] P(t 0 + nt r ) = P0 R 2 n ,
(5.1)
where P0 is the initial intensity of the transmitted signal at t0, R is the mirror’s reflectivity, and tr is the round-trip cavity time, tr = 2L/c, L is the cavity length and c is the speed of light. Assuming that R is close to unity, equation (5.1) can be approximated by P(t 0 + nt r ) = P0 exp(− 2n(1 − R) ) .
(5.2)
80
We can rewrite the expression for the intensity of the transmitted signal (5.2) in terms of the observation time, t-t0,: t − t0 , P(t ) = P0 exp − τ0
(5.3)
where τ0, the exponential decay time of the empty cavity, is determined by the reflectivity of the cavity mirrors: tr . (5.4) τ0 = 2(1 − R) When an absorbing medium is introduced into the cavity, its presence will increase the round-trip losses in the cavity. If the behavior of the medium obeys Beer’s law, the exponential decay time of the cavity in the presence of the intracavity medium can be written as [108] : tr τ (v l ) = . (5.5) L 2(1 − R + ∫ α (vl , l )dl ) 0
where α(vl,l) is the medium’s absorption coefficient at frequency vl at the point located at distance l from the entrance mirror. The absorption coefficient α(vl,l) can be presented as a sum of the absorption coefficient αM(vl,l) of the component being detected and a background from all other absorbers αbg(vl,l). If equations (5.4) and (5.5) are combined, the medium absorbance at a frequency v, assuming, for a moment, that there is no background absorption, is given as the difference of the reciprocal exponential decay times for the filled and empty cavities multiplied by the round-trip cavity time: L
11
1
∫ a (v)dl = 2 τ − τ t r , 0 0
(5.6)
or L
∫ a(v)dl = (1 − R) 0
∆τ
τ
,
(5.6a)
where ∆τ is the difference of the cavity-down times, ∆τ = τ – τ0. The minimum absorbance measured with the CRDS technique, as follows from eq. (5.6a), is limited by the mirror reflectivity and the accuracy of determining the time decay, ∆τ/τ. For the reported accuracy of (∆τ/τ)min on the order of a few tenths of a percent [111,112] and R = 0.999, the minimum measured absorbance is about a few ppm. However, when CRDS is used to measure species concentration in flames, the method sensitivity might be considerably worse than this due to the additional absorption losses from the flame.
81
M Nd:YAG
Dye laser
F
WE
RING DOWN CAVITY
P
PMT B
M
PC
OSCILLOSCOPE
Figure 5.1. Schematic of typical CRDS experimental set up. Code: WE, wavelength extender; M, mirror; P, pinhole; B, burner; F, filter; PMT, photomultiplier; PC, personal computer.
Despite its apparent simplicity, the theory of the CRDS technique is a more complicated subject than appreciated from the first casual look. Thus, for example, the validity of Beer’s law for the absorbing medium, used when deriving the expression for the time dependence of the intensity transmitted by the cavity mirror, eq. (5.3), is not always correct. Further, two reflective mirrors of the cavity form a finesse Fabry-Perot resonator supporting a vast number of discrete modes. It means that if a laser pulse with much larger spatial extend than the cavity length is introduced into the cavity, laser beam will experience the constructive and destructive interferences. Under these conditions, the laser radiation is only present at the cavity mode frequencies. Therefore to avoid missing the spectral feature of absorption line it is necessary that the width of laser, ∆vl, and absorption, ∆vs, lines must be much larger than the mode spacing, ∆vm. In addition, when the line width of the laser is greater than the line width of the absorbing species, the signal transmitted through the exit mirror will exhibit nonexponential behavior, since the attenuation of laser radiation will occur by both the absorber and the mirrors, while offresonance frequencies will be attenuated only by the mirrors. Thus, the following condition, common to all absorption spectroscopy, should be fulfilled ∆vs >> ∆vl. To describe the time dependence of the intensity of the transmitted signal by a single exponent the following conditions must be satisfied [108,110]:
82
∆vs >> ∆vl >>∆vm.
(5.7)
Deriving species concentration directly from the fit of the cavity ring-down time τ(vl) is complicated by the dependence of the spectral line profile on local collisional processes. Using the integral absorption coefficient, however, affords the possibility of eliminating this collisional dependency. Integrating the local absorption coefficient of the species under investigation over the path length and frequency (expressed in cm-1), and using well-known quantum-mechanical relations [113] we obtain: L +∞
πe 2
0 −∞
mc 2
∫ ∫ α M (v, l ) ⋅ dv ⋅ dl =
L
⋅ ∑ f ik ⋅ ∫ N i (l ) ⋅ dl , i ,k
(5.8)
0
where Ni is a population of the species in quantum state i, fik is the oscillator strength for the transition between quantum states i and k, and e, m and c represent the standard fundamental constants. However, it is often possible to find a spectral region in which only a few transitions have substantial strength. If this region is sufficiently large, the infinite integration limits can be replaced by the region’s lower and upper boundaries. The summation in eq. (5.8) is then only performed over the transitions lying in this region. The contribution of the transitions lying outside the bounds can be regarded as (part of) the background. In the case of a Boltzmann distribution over the internal degrees of freedom, Ni is related to the species mole fraction XM through: −
Ni = X M ⋅
Ei kT
P gi ⋅ e ⋅ , kT Z (T )
(5.9)
where P is the pressure, T is the temperature, gi and Ei are the degeneracy and energy of the quantum state i, respectively, Z(T) is the internal partition function and k is the Boltzmann constant. Combining equations 5.5, 5.8 and 5.9, we receive the following expression for the species mole fraction at some distance lo between the detectors: 1 1 tr ∫ − ⋅ dv τ ( v ) τ (v ) bg v1 v2
X M (l 0 ) =
πe 2 mc
2
−
⋅
Ei kT ( l0 )
,
(5.10)
g ⋅e P ⋅ l eff ∑ f ik ⋅ i kT (l 0 ) Z (T (l 0 )) i ,k
where
τ bg (v) =
tr 21 − R + ∫ α bg (v, l ) ⋅ dl 0 L
(5.11)
83
and leff is an effective absorption path length determined by: L
l eff = ∫ G (l ) ⋅ dl = 0
X M (l ) ⋅ T (l 0 ) ∫ X (l ) ⋅ T (l ) ⋅ 0 M 0 L
∑ f ik ⋅ g i ⋅ e
−
Ei kT ( l )
i ,k
∑ f ik ⋅ g i ⋅ e
Ei − kT ( l0 )
⋅
Z (T (l 0 )) ⋅ dl . Z (T (l ))
(5.12)
i ,k
The spectral region v1, v2 is usually selected such that the background ring-down time, τbg(v), has only a slight frequency dependence. In this case, it is sufficient to approximate the background by a linear dependence 1 1 1 1 v − v1 , = + − ⋅ τ bg (v) τ bg (v1 ) τ bg (v 2 ) τ bg (v1 ) v 2 − v1
(5.13)
which renders additional measurements of the background unnecessary. As can be seen from equation (5.10), the local temperature T(l0) should be known to derive the species mole fraction from the measured absorption coefficient. Moreover, as is well known for all line-of-sight measurement, the effective absorption length is dependent upon both the temperature and concentration distributions along the absorption path; and only in the case of a spatially uniform distribution does leff coincide with absorbing layer length. If this is not the case, leff should be determined by measuring the temperature and concentration distributions, or otherwise properly estimated, as done in [102] for measurements of NO in a low-pressure chamber. For flames burning in the open air, such as those discussed here, mixing with the surrounding air will alter the distributions of both NO and temperature in the hot gases, introducing uncertainty into leff.
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5.2.3 Experimental setup
The measurements were performed in premixed atmospheric-pressure stoichiometric and lean H2/N2/Air flames, and in a limited number of CH4/N2/Air flames. The ratio of N2 to fuel in the mixtures did not exceed 0.2; this reduced the adiabatic temperatures by at most 100 K compared to the undiluted flames. The added N2 was either “neat”, or contained NO at a maximum fraction of 4950 ppm, see Chapter 2. The flow rates of gases were measured by calibrated mass flow meters, while the equivalence ratio was determined by measuring the oxygen concentration in the unburned mixture using paramagnetic detection. The total flow rates for every equivalence ratio were 0.01, 0.02 and 0.04 g/cm2s. The flames were stabilized on a McKenna Products water-cooled sinter burner, with a bronze disk of 6 cm diameter (Chapter 2). Additionally, for control purposes, measurements were also performed at room temperature. In this case, the absorption layer was created by flowing seeded nitrogen in a horizontal tube with open ends. The basic CRDS setup is similar to that illustrated in figure 5.1. A Sirah PrecisionScan tunable dye laser pumped by second harmonic of a Spectra-Physics Quantra Ray Pro 250-10 Nd:YAG laser was used to generate wavelengths near 226 nm, with bandwidth .∆vl ~ 0.05 cm-1 and pulse duration τl ~ 10 ns, by mixing the dye output with the third harmonic of the same YAG laser. The laser beam was shaped by a pinhole and introduced into a CRD cavity formed by two spherical mirrors with reflectivity better than 98.6 % and a 6 m radius of curvature, separated by distance L = 62.5 cm. At this distance between the mirrors, the longitudinal mode spacing, . ∆vm = 1/2L ~ 0.008 cm-1, is less than the laser line width ∆vl and the cavity round-trip time, tr=2L/c ~ 4.2 ns, is less than the duration of the laser pulse, τl. The light transmitted by the cavity was measured by an Electron Tubes 9659QB3 photomultiplier. The signal was digitized and averaged over 64 laser pulses by a 500 MHz Hewlett Packard 54615B oscilloscope with 8-bit analog-digital converter. Absorption measurements were conducted at a height of 0.5 cm above the burner surface, at low laser pulse energy (~ 0.05 mJ) to ensure linear behavior of the photomultiplier. At the same height, the radial distributions of flame temperature and NO concentrations were measured, by coherent anti-Stokes’ Raman scattering and LIF (Chapter 3), respectively, by moving the burner with a precision positioner in steps of either 2 or 3 mm. The general reproducibility of the temperature measurements was better then 40 K (95% confidence limit), and mainly resulted from the uncertainty in flow measurements. The temperature accuracy, estimated by comparison of the measured temperature in a near-adiabatic flame with that calculated at adiabatic equilibrium, was better than 30K (Chapter 3). 5.2.4 Evaluation of the exponential decay time from the measured signal
The collisional width of the NO absorption line, ∆vc , in flames is of order of ~ 0.5 cm-1 [114,115]. Comparing ∆vc with the laser line width ∆vl and the longitudinal mode spacing ∆vm we can conclude that the inequality (5.7) is satisfied. That means that P(t) can be described by single exponential decay, eq. (5.3), see above. In general, the measured signal is a convolution of the light intensity P(t) and the instrument function f(t) of the detection system
85
+∞
PM (t ) =
∫ P(t ' ) ⋅ f (t − t ' ) ⋅ dt .
(5.14)
−∞
At high background and/or high concentrations of the species to be detected, the cavity ring-down time becomes comparable to the time resolution of the detection system, which is determined by the photomultiplier rise time and the oscilloscope bandwidth. The function f(t-t´) can then no longer be regarded as a delta function. In the present work, f(tt´) is approximated by a Gaussian function exp(-(t-t´)2/ τd2). The integration of the equation (5.14) then yields
−
PM (t ) = Ce
t −t0
τ ( vl )
t − t0 τd , ⋅ erfc − − 2τ (vl ) τd
(5.15)
where erfc(x) is a complimentary error function and C a numerical coefficient. The parameters τ(vl) and τd were determined from the experimentally measured signals by using the Levenberg-Marquardt method to solve the nonlinear least squares problem [116]. For this purpose, the subroutine LMDIF from the MINPACK library [91] was incorporated in the control and data acquisition program. Because τd is a property of the experimental setup, to minimize the computational time it was determined only once at high concentrations of seeded NO; for the remainder of the experiments only the cavity ring-down time τ(vl) was fit. For the experiments described below, τd was roughly 15 ns. 5.3 NO measurements in methane and hydrogen flames 5.3.1 CRD background in methane and hydrogen flames
Our initial attempts at recording the NO spectra in atmospheric methane-air flames at 226 nm were frustrated by strong background absorption, which wholly masked the NO absorption even when several hundred ppm were seeded in the unburned air-gas mixture. The most plausible explanation for this high-level background is absorption by CO2 molecules. According to [84,117], the broadband CO2 absorption cross-sections at 226 nm and 2000 K is ~ 4·10-20 cm2/molecule. In this case, a mole fraction of CO2 of 10% in a stoichiometric methane-air flame corresponds to an absorption coefficient of ~ 1.5·10-2 cm-1. For an absorption length of 6 cm, eq. (5.5) gives a ring-down time of ~ 20 ns, corresponding well with our observations, and being close to the response time of the detection system. These results show that measurement of NO, even at high concentrations (hundreds of ppm), in atmospheric-pressure hydrocarbon flames is futile; as such, we abandoned hydrocarbon flames and shifted our attention to hydrogen flames. Experiments conducted on various hydrogen flames without NO addition, at temperatures for which the mole fraction of native flame NO is expected to be negligibly small, showed indeed a substantially lower background in comparison with methane-air
86
0.025
0.020
Exp Calculated
0.015
0.010
0.005
0.000 1400
1500
1600
1700
1800
1900
2000
Temperature, K
Figure 5.2 Absorption cross-section for H2O at 226 nm as a function of temperature. Squares : experiments, solid line: calculated by using extrapolation formulae from [84]. flames. Moreover, it was observed that the ring-down times decreased with increasing flame temperature and increasing equivalence ratio (from lean towards stoichiometric), and did not depend on the wavelength in the spectral region considered (225.9–226.1nm). As a result, it seems reasonable to suggest that absorption by water molecules is the main contribution to the additional losses in these flames. Although the quantitative measurements of the background signal, and identification of its main contributors, are not the objectives of the present work, it is of interest to examine the absolute values of the additional absorption losses. Towards this end, the room temperature CRD spectrum in air was subtracted from the flame spectra. Assuming all additional losses arise from water in the flame, the absorption cross-sections of the H2O molecule at different temperatures and equivalence ratios were calculated from the measured cavity ring-down spectra, using equilibrium values of the water concentration. The cross-sections thus derived are presented in figure 5.2, together with the results from recent shock-tube measurements of water absorption [84,117]. The maximum difference between the two methods is less than a factor of three. We regard this agreement as good, considering that in the present work no special attention was paid to assess and minimize the additional losses in the flame, and that the results from the shock tube [84,117] are extrapolated to the spectral region used here. We further remark that our data show the same trend as older measurements of the water absorption coefficient [118], which lie systematically lower than the data in [84,117].
87
5.3.2 NO absorption spectra
Survey CRD spectra were measured in the spectral region 44210 – 44260 cm-1, in steps of 0.075 cm-1. The spectral feature used in LIF measurements of absolute NO mole fraction is also in this region. This feature is composed of overlapping rotational lines P11(23.5) + Q11(14.5) + QP21(4.5) + Q22(20.5) + QR12(20.5) + SR21(8.5) + RQ21(8.5) in the NO A2 Σ(v=0)-X2 Π(v=0) band. This feature is expected to be useful for cavity ring-down measurements as well, because its lines are positioned sufficiently far away from the rest of the NO spectral lines, and the spectral region around this feature is free from absorption bands of molecular oxygen [82]. Moreover, numerical simulations using the LIFBASE program [77] show that the total integrated absorption coefficients of all NO lines in this feature have only a slight temperature dependence. The experimental absorption spectrum (plotting reciprocal ring-down time vs. frequency) of nitrogen containing 5 ppm NO flowing in a tube with length of 23.4 cm is presented in figure 5.3. Absorption spectra were also measured in a hydrogen-air flame with equivalence ratio φ = 0.8, and mass flow of 0.02 g/cm2s, resulting in a flame temperature of 1670 K. To achieve a signal-to-noise ratio in the flame similar to that obtained at room temperature, significantly more NO should be seeded in the unburned gas mixture. The measured flame absorption spectrum produced by ~ 200 ppm NO in the unburned air-gas mixture is presented in figure 5.4. Figures 5.3 and 5.4 also show the NO spectra from LIFBASE, which are in agreement with the measurements; this further illustrates that the spectral region chosen is free from interferences from other flame species. The spectral feature proposed for cavity ring-down measurements is easily distinguishable at both room and flame temperatures and is the region marked by vertical lines in the fig.5.3 and 5.4. This region, between 44238.8 cm-1 and 44246.2 cm-1, was chosen as the integration interval for deriving absolute values of the nitric oxide mole fraction. Numerical calculations with the broadening parameters taken from [114,115] were performed to estimate the error introduced by approximating the integral absorption coefficient for the spectral lines by the summation over this limited spectral interval, with steps 0.075 cm-1. The spectral line parameters needed for calculations of the NO mole fractions were taken from [77,119], and are given in Table 5.1. Line R12(20.5) Q22(20.5) Q11(14.5) P21(14.5) P11(23.5) R11(8.5) Q21(8.5) R21(4.5)
Ei, cm-1 874.745 874.754 374.572 374.572 960.864 133.709 133.709 40.162
fik 3.88E-05 2.67E-04 2.48E-04 5.06E-05 1.37E-04 1.15E-04 1.36E-04 8.67E-05
Table 5.1. The rotational lines with corresponding wavenumbers, energy of low levels and oscillator strength for a (0-0) (A-X) system of NO. The wavenumbers and oscillator strengths are from the LIFBASE database [77] and energies of lower levels are from [119].
88
The NO internal partition function Z(T) was calculated using tabulated thermodynamic data [120]. The calculations show that this approximation of the integrated absorption underestimates the value of the total integrated absorption by 6% at 300 K and by less then 2.5% for temperatures above 1000 K. For all measurements performed at room temperature, the mole fractions derived were thus increased by 6%. No corrections were applied to the flame measurements, where noise levels and uncertainties in broadening parameters are substantially larger than this relatively small systematic error. The measured cavity ring-down spectrum also allows estimation of the detectability limit for NO in the present setup. As can be determined from fig. 5.4, the r.m.s. noise δ(1/τ) in the measured reciprocal cavity ring-down time is roughly 0.5 µs-1. Equation (5.10) can be rewritten as N +1 1 1 X M = CM ⋅ ∑ − τ ibg i =0 τ i
⋅∆v ,
(5.14)
where CM is a coefficient containing, among other quantities, the dependence upon the distribution of temperature and NO concentration, N is number of steps when scanning the spectral region between ν1 and ν2, ∆ ν = ( ν2- ν1)/N is the frequency step, and τi and τibg are the reciprocal cavity ring-down time and reciprocal background time in the i-th step, respectively. Defining the detectable limit XLM as the mole fraction giving a ringdown signal of the same magnitude as the noise, eq. (5.14) yields X LM = C ⋅ (v 2 − v1 )
2 1 ⋅δ N τ
(5.15)
The numerical value of coefficient C, estimated from the fig. 5.4, is ~15 ppm/(µs-1cm-1). After substitution of this value in (5.15) together with ν2-ν1 = 7.4 cm-1 and ∆ ν = 0.075 cm-1, we obtain XLM ~ 8 ppm for δ(1/τ) = 0.5 µs-1. It should be pointed out that further improvement in the detectability limit would be rather difficult, since this can only be achieved through a substantial increase in the data acquisition time, which was already sizeable in the present experiments (~ 20 minutes).
89
Reciprocal cavity ring-down time , µs-1.
14 13 12 11 10 9 8 7 6 44215
44220
44225
44230
44235
44240
Wavenumber, cm
44245
44250
44255
44260
-1
Absorption coefficient, a.u.
120
100
80
60
40
20
0 44215
44220
44225
44230
44235
44240
44245
44250
44255
44260
-1
Wavenumber, cm
Figure 5.3. Measured (upper) and calculated (lower) spectra of 5 ppm NO in N2 at 300 K with absorption path length of 23.4 cm. The vertical lines mark the spectral region chosen for the quantitative diagnostics.
90
Reciprocal cavity ring-down time, µ s-1
24 22 20 18 16 14 12 10 8 44215
44220
44225
44230
44235
44240
Wavenumber, cm
44245
44250
44255
44260
-1
Absorption coefficient, a.u.
120
100
80
60
40
20
0 44215
44220
44225
44230
44235
44240
44245
44250
44255
44260
-1
Wavenumber, cm
Figure 5.4. The same as in figure 5.3 in flame with φ = 0.8 and T = 1674 K and 200 ppm NO in unburned mixture.
91
Before performing quantitative measurements, the linearity of the detection system was verified. For this purpose, only the NO concentration in N2 was varied, keeping the flow rates of all gases constant. Because of its small concentration in the unburned gas mixture, nitric oxide has only marginal influence on flame chemistry; this assures the constancy of all flame parameters when varying the NO seeding. The flame at φ = 0.8 and total mass flux of 0.02 g/(cm2s) was used. The temperature of this flame (~ 1670 K) is sufficiently low to guarantee negligible natural flame NO mole fractions (estimated using flame calculations at 1-2 ppm). The results, presented in figure 5.5, show excellent linear dependence between reciprocal cavity ring-down time at the maximum of the spectral feature and the seeded NO concentration. Finally, the NO concentrations in N2 at room temperature were extracted from the cavity ring-down measurements following the procedure described above. The difference between the measured NO concentrations and the known seeded value did not exceed 3%, validating the experimental procedure and NO spectroscopic data used. 7
(1/τ-1τ0), µ s-1
6 5 4 3 2 1 0 0
20
40
60
80
100
120
140
160
180
200
[NO]added, ppm
Figure 5.5. Reciprocal cavity ring-down time as a function of seeded NO concentration. τ0 is the cavity ring-down time without seeded NO.
5.3.3 Effective absorption length
The value of the effective absorption length, leff , in eq. (5.12) was derived from the measured radial profiles of temperature and NO mole fraction. The temperature profiles were measured using CARS. The NO profiles were determined in two ways: directly, measured using LIF and indirectly, calculated from the measured temperature profiles.
92
Unfortunately, both procedures are not free from limitations. The former relies on the calibration procedure assuming no removal of the seeded NO in the flame front [81], while the latter is based on assumption that NO concentration in boundary layer changes only due to mixing with surrounding air [121]. The excellent agreement between these two independent methods, described below, gives us confidence in the accuracy of the results. The measured radial profiles of temperature and NO concentration are presented in figure 5.6. The LIF measurements were analyzed in accordance with Chapter3.
1.2 2000
0.8
1500
0.6 1000
0.4
T, K
XM (l)/XM(0)
Temperature, K
1
NO calculated 0.2 NO measured (LIF)
500
0
0 -4
-3
-2
-1
0
1
2
3
-0.2 4
Distance, cm
Figure 5.6. Temperature and relative NO concentration radial profiles at a height of 5 mm above the burner surface for the flame with equivalence ratio φ = 0.8, mass flux ρυ = 0.02 g/cm2s and 229 ppm seeded NO.
The profiles of NO mole fraction were derived from the temperature profiles using the same method described for Bunsen flames [121], with small modifications. To do so, we make three assumptions. Firstly, that the post-flame gases mix with ambient air homogeneously, i.e. the diffusion coefficients of all species involved are the same. Secondly, we assume that no appreciable chemical reactions occur during and after mixing. Thirdly, the change in the temperature after the flame front is determined only by mixing of the burned gases with cold air. When all three conditions are met, the species concentrations and temperature are only functions of the local equivalence ratio φ. Whereas all three conditions will be inappropriate for fuel-rich hydrogen-air flames (the significantly different transport properties violate the first assumption, and the tendency
93
of excess hydrogen in the hot, post-flame gases to burn in the mixing layer with surrounding air will violate the second and third assumption), fuel-lean and stoichiometric flames will meet all of these requirements. Recalling that the equivalence ratio is determined through the overall one-step combustion reaction, and supposing that air is composed of 20.95% O2 and 70.95% N2, we can define the composition of the lean and stoichiometric H2/N2/Air flames at low (< 2000 K) temperatures by
where β is nitrogen/hydrogen ratio in unburned gas mixture. At high temperatures (> 2000 K) the right side of eq. (5.16) should be modified by adding the moles of minor species such as H, O, OH etc. It is worth noting here that eq. (5.16) shows that the number of moles decreases upon going from reactants to products. Making use of conservation of enthalpy at constant pressure, from equation (5.16) it follows that:
φ ⋅ I H (T0 ) + 0.5I O (T0 ) + (1.887 + φ ⋅ β ) ⋅ I N (T0 ) + φ ⋅ ∆I = 2
2
2
φ ⋅ I H O (TF ) + (1.887 + φ ⋅ β ⋅ I N (TF ) + 0.5(1 − φ ) ⋅ I O (TF ) 2
2
,
(5.17)
2
where T0 and TF are the temperatures of the unburned reactants and combustion products, respectively, and IM denotes the enthalpy of substance M. Heat transfer upstream to the burner surface for the flames at low mass flux has been included by adding an additional term φ∆I to the left side of (5.17). If the unburned gas/air mixture were to be preheated, ∆I would be positive and when the heat transfer to the burner deck are dominant, ∆I is negative. If the temperature TF is known (in our case from the CARS measurements), then eq. (5.17) can be solved numerically to obtain the equivalence ratio φ. Mixing of the combustion products with surrounding air can thus be regarded as gradually changing the local equivalence ratio φ from φ0 in the unburned gas/air mixture to zero. In this case, it follows from eq. (5.16) that the NO mole fraction (or that of some other minor component), XM, varies according to X M (φ ) φ 4.773 + φ 0 + 2φ 0 ⋅ β = ⋅ . X M (φ 0 ) φ 0 4.773 + φ + 2φ ⋅ β
(5.18)
The radial profiles obtained by direct measurement using LIF and derived from the temperature are shown in figure 5.6. Here, the normalized radial profiles of NO mole fraction, i.e., the local mole fraction at position l, XM(l), divided by the mole fraction at the center of the burner, XM(0),are presented at a height of 5 mm above the burner, for φ = 0.8, mass flux ρv = 0.02 g/(cm2s) and 200 ppm NO in the unburned air-gas mixture. (When corrected for the change in the number of moles, this results in a mole fraction of 229 ppm in the hot gases.) The temperature profile consists of a core region at constant flame temperature bounded by a mixing layer close to the edges of the burner where the temperature decreases to that of the surrounding air. The temperature in the hot core is determined by
94
the heat transfer to the burner [6,41] and is governed by the mass flux, ρυ. As can be seen from the figure, both methods yield the same normalized NO profiles. Since the same temperature profile was used to derive the NO mole fraction from both the measured LIF signal and the mixing approximation, the profiles from both methods show the same fluctuations. Only marginal differences were observed at other equivalence ratios and mass fluxes, lending credence to the validity of both methods. The impact of the nonuniformity in the profiles of temperature and NO mole fraction along the absorption path on the determination of leff is illustrated in figure 5.7, for flames with ρυ = 0.01, 0.02 and 0.04 g/cm2s at φ = 0.8. Decreasing the mass flux increases the time needed for the combustion products to reach the observation point, while the characteristic diffusion time remains essentially constant. This relative diffusion enhancement results in reducing the diameter of the hot core, as seen in figure 5.7a. It is also interesting to note that the temperature gradients at the burner edges are practically equal for the flows shown. For the reasons mentioned above, the fluctuations in the NO profiles in figure 5.7b follow those in the temperature profiles. The rapid decrease in the temperature in the edges of the burner causes the maxima of the frequency-integrated absorption, G(l) in eq. (5.12), to appear, as shown in figure 5.7c. Fortunately, in the present situation this increase in G(l) at the edges is only moderate (~ 20%). Integration of G(l) yielded values of the effective absorption lengths of 6.14, 6.62 and 6.61 cm for ρυ =0.01, 0.02 and 0.04 g/cm2s, respectively. Similar results were obtained for other flames, where, as a rule, the effective absorption length was 10% larger than the burner diameter (6 cm). The absolute NO mole fractions presented below were derived from the measured cavity ring-down times using the experimentally determined leff.
95
2000
Temperature, K
1800 1600 1400 1200 1000
0.01 g/cm2-s
800
0.02 g/cm2-s
600
0.04 g/cm2-s
(a)
400 200 -4
-3
-2
-1
0
1
2
3
4
Distance, cm 1.2
X M (l)/XM (0)
1 0.8 0.6
(b)
0.4 0.2 0 -4
-3
-2
-1
0
1
2
3
4
Distance, cm 1.2 1
G(l)
0.8 0.6
(c) 0.4 0.2 0 -4
-3
-2
-1
0
1
2
3
4
Distance, cm
Figure 5.7. Temperature (a), relative NO concentration (b) and profiles function G(l) (c) from the equation (5.12) at flame with φ = 0.8 at mass flux rates of 0.01 (triangles), 0.02 (diamonds), 0.04 g/cm2s (squares).
96
5.3.4 NO mole fraction in stoichiometric and lean H2/N2/Air flames
The experimental procedure described above has been used to measure the NO mole fractions in seeded H2/N2/Air flames at equivalence ratios φ = 0.6, 08 and 1.0. The NO mole fraction added to the unburned mixtures was nominally 200 ppm. The flame temperature was varied at fixed equivalence ratio by changing the flow rates of the unburned fuel-air mixture. As discussed above, the cavity ring-down measurements were supplemented by CARS and LIF measurements to provide the temperature and effective absorption length necessary for the quantitative analysis. To assess the overall reproducibility, the measurements for the same experimental conditions were performed repeatedly with a few days between the experiments. For comparison, the structure of the burner-stabilized flames was calculated using the GRI-Mech 3.0 chemical kinetics mechanism and transport data. Figure 5.8 presents the ratio of the NO mole fraction measured by the cavity ring-down technique at 5 mm above the burner to the seeded NO mole fractions (corrected for the change in the number of moles, as described above), as a function of flame temperature at different equivalence ratios. As can be seen from this figure, the scatter in the experimental data is not higher than ± 5%. 1.1
XNOmeas/XNOadd
1 0.9 0.8 0.7
φ
CRDS 0.6 CRDS 0.8 CRDS 1
0.6 0.5 1400
1500
1600
1700
1800
1900
2000
Temperature, K
Figure 5.8. Ratio of measured and calculated NO mole fraction at 5 mm above the burner as a function of flame temperature at different equivalence ratios of 0.6 (squares), 0.8 (circles) and 1.0 (triangles).
97
1.5
2000
1.4
1800
1.3
1600
1.2
1400
1.1
1200
1
1000
0.9
800
0.8
600
0.7
400
0.6
200
0.5
0 0
2
4
6
8
10
12
14
16
18
20
Temperature, K
X
NO NO meas/X add
At flame temperatures above ~ 1750 K, there is good agreement (± 5%) between the measured and seeded NO mole fractions. At lower temperatures, the measured NO mole fractions are systematically lower than the seeded values, for the equivalence ratios measured. The difference between the measured and seeded NO mole fraction reaches 30% at ~ 1450 K, which is substantially higher than the estimated experimental uncertainty. We point out here that the results obtained with GRI-Mech 3.0 show no loss of NO under these conditions. To trace the axial behavior of the NO concentration, we measured the vertical profiles of NO and temperature (Chapter 3) in the H2/Air flames seeded with NO (~ 200 ppm) at equivalence ratio ranging from 0.6 to 1.0. Calibration of the LIF signal was performed in lean flames at temperatures in excess of 1750 K, the conditions verified to be suitable for calibration by CRDS measurements, as discussed above. NO profiles measured in these flames are flat (see figure 5.9 as an example) suggesting that any possible NO removal occurs in a very thin zone close to the burner surface.
22
Distance, mm
Figure 5.9. Axial profiles of the temperature and ratio of measured and calculated NO mole fraction at φ =0.8. (◊ and ) – (T and NO) at ρυ = 0.038 g/cm2s; ( and ) – (T and NO) at ρυ = 0.022 g/cm2s; (○and ●)– (T and NO) at ρυ = 0.0098 g/cm2s;
98
Figure 5.10 shows the ratio of the CRDS NO mole fraction to the LIF NO mole fraction measured at 5 mm above the burner as a function of flame temperature at different equivalence ratios. The results show that at φ = 0.8 and 1.0, the LIF data are in perfect agreement with the results of CRDS measurements, while at φ = 0.6, the observed deviation between the CRDS and LIF results was ~ 15%. 1.2 1.1
XNOCRDS/XNOLIF
1 0.9 0.8
φ 0.6 0.8 1
0.7 0.6 0.5 1400
1500
1600
1700
1800
1900
2000
Temperature, K
Figure 5.10. The ratio of the CRDS NO mole fraction to the LIF NO mole fraction measured at 5 mm above the burner as a function of flame temperature at different equivalence ratios (squares), 0.8 (circles) and 1.0 (triangles). The analysis of the chemical mechanism shows that there is no simple way to bring the experimental and simulated results into considerably better agreement for all equivalence ratios merely by changing the rate constants of the reactions important for NO formation and consumption in these flames. Since the LIF measurements indicate that the NO removal occurs only at the distances close to the burner surface for all equivalence ratios studied, it seems to be of interest to consider the role of the burner surface in the combustion process, besides revaluating key NO formation/destruction reactions. This Chapter discussed quantitative aspects of using cavity-ring down absorption spectroscopy for measurements of NO mole fractions in premixed atmospheric-pressure flames. To account for effects of the cold boundary layers on the NO mole fractions a combination of pulsed CRDS, CARS and LIF techniques was employed.
99
CHAPTER 6 A study of NO formation in preheated fuel-rich CH4/Air flames
100
Abstract
Measurements of temperature and NO mole fraction are reported in flat, laminar, stoichiometric and fuel-rich premixed methane-air flames subjected to varying degrees of preheating, up to 400 K. Varying the initial mixture temperature in the range 300-700 K, we observe differing degrees of growth in the NO mole fraction with increasing temperature for the different equivalence ratios studied. The temperature and NO mole fraction were measured by coherent anti-Stokes Raman scattering (CARS) and laserinduced fluorescence (LIF), respectively. At φ = 1, plotting the measured NO mole fraction as a function of flame temperature shows the exponential growth characteristic for the Zeldovich mechanism. At φ = 1.3, the plot of NO versus flame temperature shows a region of more than 400 K in which the NO mole fraction grows only by a factor of 2, reflecting the behavior of the Fenimore mechanism. At temperatures above ~ 2250 K, the NO formation initiated by O + N2 becomes important, and the mole fraction begins to rise more steeply. At φ = 1.5, the NO mole fraction is less than 10 ppm between 1750 and 1950 K, but increases by a factor of 9 within the next 200 K. At φ = 1.6, the NO mole fraction is less than 5 ppm between 1900 and 2000 K, but increases by a factor of 10 within the next 150 K. Calculations using GRI-Mech 3.0 capture the essence of this behavior well, but show quantitative shortcomings for the fuel-rich flames. Comparison with the calculated equilibrium mole fractions as a function of temperature shows the observed NO mole fractions under fuel-rich conditions to be generally in excess of their equilibrium values. The experimental profiles and the GRI-Mech calculations indicate that relaxation to equilibrium is very slow, even at high temperatures. With an eye towards low-NOx combustion equipment, the results at φ ≥ 1.5 are encouraging for further investigation of rich-premixed flames.
101
6.1 Introduction
Lean-premixed combustion has proven to be an effective NOx control strategy, particularly for natural-gasfired systems; this method is used to obtain low emissions in combustion equipment ranging from large-scale stationary gas turbines to condensing boilers for household use. In industrial combustion systems, however, the necessity of preheating the combustion air using “waste” heat to improve process efficiency tends to negate lean-premixing for NOx control in natural-gas flames; the substantial increase in flame temperature upon preheating and dominance of the Zeldovich mechanism result in copious quantities of NO being formed. In this regard, it would be interesting to consider the effects of preheating on NO formation in fuel-rich premixed methane flames, where, at least naively, the much lower activation energy of the reactions involved in the primary steps in the Fenimore mechanism, see Chapter 1, leads one to expect a less drastic increase in NO with increasing flame temperature. In addition, the equilibrium mole fraction of NO decreases to single-digit ppm levels in the fuel-rich regime, suggesting the possibility for low- NOx operation. To date, only a limited number of measurements probing NO formation in richpremixed methane flames using quantitative, noninvasive techniques has been reported. For example, measurements using laser-induced fluorescence (LIF) of NO and CH at low pressure have been performed at equivalence ratios of 1.13 [74] ,1.2 [40] and 1.27 [34] with varying N2/O2 ratios, to provide mechanistic insight into the Fenimore mechanism, and to assist in the construction of quantitatively correct chemical mechanisms. Also with an eye towards comparison with model predictions, LIF measurements of the pressure dependence of NO formation at atmospheric pressure and higher [42] have been performed at a fixed degree of burner-stabilization for a number of fuel-rich CH4/N2/O2 flames up to φ = 1.6. LIF measurements of NO concentration were obtained in laminar, premixed counterflow CH4/N2/O2 flames at atmospheric pressure with equivalence ratio up to 1.5 [122]. Atmospheric pressure measurements using LIF of NO [123] were also performed along the centerline of the methane-air Bunsen flame for equivalence ratios 1.38, 1.52 and 1.70 and in steady laminar opposed-flow partially premixed methane-air flames having fuel-side equivalence ratios 3.17, 2.17 and 1.8 [124]. Picosecond laserinduced fluorescence was applied in methane/air counterflow diffusion flames at atmospheric pressure to obtain spatial profiles of NO concentration [125]. Substantial reduction in the NO mole fraction (LIF) under fuel-rich conditions was observed by applying upstream heat transfer and flue-gas recirculation to flat, atmospheric-pressure, methane-air flames (upstream heat transfer at φ = 1.15, 1.3, 1.4 [6]; and flue-gas recirculation at φ = 1.3 [41]). In most of the abovementioned studies it was demonstrated that the various versions of the GRI – Mech inadequately predict NO formation under fuel-rich conditions. The studies cited have been restricted to reactants at room temperature; to our knowledge, no investigations of the dependence of NO formation on the temperature of the fuel-air mixture in rich-premixed flames have been reported. This chapter reports measurements of the NO (LIF) and temperature (CARS) profiles (Chapter 3) in the burned gases of flat, rich-premixed flames with up to 400 K preheating, made in the burner specially designed for this purpose (Chapter 2). The experimental results are contrasted with those obtained from preheated stoichiometric flames. The experimental
102
observations are compared with the predictions of one-dimensional flame calculation obtained with GRI-Mech 3.0 (Chapter1). 6.2 The NO and temperature measurements at φ = 1.0, 1.3, 1.5, and 1.6
Typical experimental NO mole fraction and temperature profiles for various equivalence ratios, mass fluxes, and degrees of preheating are illustrated in figures 6.16.4; the Table1 provides overview of the measurement scheme. The vertical profiles of NO mole fraction
φ
Figure
1.0 1.3 1.5 1.6
6.1. 6.2. 6.3. 6.4.
dT = 0 K NO T 1a 1b 1a 1b 1a 1b
dT = 100 K NO T 2a 2b 2a 2b 1a 1b
dT = 200 K NO T 3a 3b 3a 3b 2a 2b a b
dT = 300 K NO T 4a 4b 4a 4b 2a 2b a b
dT = 400 K NO T 4a
4b
a
b
Table 6.1. The measurement scheme. and temperature at φ = 1.0, 1.3 and 1.5 were obtained by moving the burner with a precision positioner, see Chapter 2, up to a distance of 22 mm above the burner surface). For φ = 1.6, the measurement domain was increased up to 30 mm. Postponing the detailed discussion of the data at different equivalence ratios and degrees of preheating, we note differences between the NO profiles at the stoichiometric and fuel-rich flames. Independently of the initial mixture temperature, the NO profiles for φ = 1.0 are flat after the initial rise at temperatures below ~ 2000 K, while at higher temperatures, they experience a post-flame increase whose slope increases with increasing flame temperature. For fuel-rich flames, φ = 1.3 and 1.5, nearly all NO profiles are essentially flat even at temperatures in excess of 2300 K, see figs. 6.2 and 6.3. At φ = 1.6, at temperatures higher than ~ 2050 K, the NO concentration profiles show growth, noticeable even at 10 mm above the burner surfaces, see figs. 6.4 and 6.14. At lower temperatures, all NO profiles are essentially flat. For all equivalence ratios, the temperature profiles are flat, at least for several measurement points above the burner. The decrease in the temperature profiles at downstream distances is caused by radiative losses, and by mixing with air/nitrogen at very low exit velocities (Chapter 4). The uncertainties in the NO and temperature measurements are shown in the figures.
103
90 80 70
NO, ppm
60 50 40 30 20 10 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
1.8
2
2.2
Distance, cm
( 6.1.1a) 2300 2200
Temperature, K
2100 2000 1900 1800 1700 1600 1500 1400 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Distance, cm
( 6.1.1b) Figure 6.1.1. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.0 for 0 K preheating. - ρυ = 0.035 g/cm2s; □ ρυ = 0.024 g/cm2s; - ρυ = 0.018 g/cm2s; Χ - ρυ = 0.012 g/cm2s; ● ρυ = 0.0087 g/cm2s.
104
140 120
NO, ppm
100 80 60 40 20 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Distance, cm
(6.1.2a) 2400 2300
Temperature, K
2200 2100 2000 1900 1800 1700 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Distance, cm
(6.1.2b) Figure 6.1.2. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.0 for 100 K preheating. - ρυ = 0.047 g/cm2s; □ ρυ = 0.031 g/cm2s; - ρυ = 0.021 g/cm2s; Χ - ρυ = 0.016 g/cm2s; ● ρυ = 0.0112 g/cm2s.
105
140 120
NO, ppm
100 80 60 40 20 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
1.4
1.6
1.8
2
2.2
Distance, cm
(6.1.3a) 2400 2300
Temperature, K
2200 2100 2000 1900 1800 1700 1600 1500 0
0.2
0.4
0.6
0.8
1
1.2
Distance, cm
(6.1.3b) Figure 6.1.3. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.0 for 200 K preheating. - ρυ = 0.033 g/cm2s; □ ρυ = 0.026 g/cm2s; - ρυ = 0.021 g/cm2s; Χ - ρυ = 0.015 g/cm2s; ● ρυ = 0.0092 g/cm2s.
106
250
NO,ppm
200
150
100
50
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
1.4
1.6
1.8
2
2.2
Distance, cm
(6.1.4a) 2400
Temperature, K
2300 2200 2100 2000 1900 1800 0
0.2
0.4
0.6
0.8
1
1.2
Distance, cm
(6.1.4b) Figure 6.1.4. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.0 for 300 K preheating. - ρυ = 0.053 g/cm2s; □ ρυ = 0.037 g/cm2s; - ρυ = 0.027 g/cm2s; Χ - ρυ = 0.022 g/cm2s; ● ρυ = 0.018 g/cm2s.
107
70 60
NO, ppm
50 40 30 20 10 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
1.4
1.6
1.8
2
2.2
Distance, mm
(6.2.1a) 2200
Temperature, K
2100 2000 1900 1800 1700 1600 0
0.2
0.4
0.6
0.8
1
1.2
Distance, cm
(6.2.1b) Figure 6.2.1. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.3 for 0 K preheating. - ρυ = 0.0252 g/cm2s; -
ρυ = 0.022 g/cm2s; ρυ = 0.008 g/cm2s.
Χ
-
ρυ = 0.016 g/cm2s;
□ - ρυ = 0.01 g/cm2s; ○
-
108
70 60
NO, ppm
50 40 30 20 10 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Distance, cm
(6.2.2a) 2200
Temperature, K
2100 2000 1900 1800 1700 1600 1500 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Distance, cm
(6.2.2b) Figure 6.2.2. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.3 for 100 K preheating. - ρυ = 0.036 g/cm2s; -
ρυ = 0.0234 g/cm2s; ρυ = 0.01 g/cm2s.
Χ
-
ρυ = 0.017 g/cm2s;
□ - ρυ = 0.0136 g/cm2s; ○ -
109
80 70
NO, ppm
60 50 40 30 20 10 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2
2.2
Distance, cm
(6.2.3a) 2300 2200
Temperature, K
2100 2000 1900 1800 1700 1600 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Distance, cm
(6.2.3b)
Figure 6.2.3. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.3 for 200 K preheating. - ρυ = 0.042 g/cm2s; ρυ = 0.033 g/cm2s; Χ - ρυ = 0.0256 g/cm2s; □ - ρυ = 0.0176 g/cm2s; ○ ρυ = 0.013 g/cm2s.
110
120 100
NO, ppm
80 60 40 20 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
1.4
1.6
1.8
2
2.2
Distance, cm
(6.2.4a) 2500 2400
Temperature, K
2300 2200 2100 2000 1900 1800 1700 0
0.2
0.4
0.6
0.8
1
1.2
Distance, cm
(6.2.4b) Figure 6.2.4. Vertical profiles of NO mole fraction (a) and temperature methane/air flames at φ = 1.3 for 300 K and 400 K preheating. □ - ρυ 400 K preheating; ○ - ρυ = 0.0535 g/cm2s, 400 K preheating; - ρυ 300 K preheating; - ρυ = 0.045 g/cm2s, 300 K preheating; Χ - ρυ 300 K preheating; ● - ρυ = 0.021 g/cm2s, 300 K preheating.
(6.3.1b) Figure 6.3.1. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.5 for 0 K and 100 K preheating. - ρυ = 0.0174 g/cm2s, 100 K preheating; - ρυ = 0.0146 g/cm2s, 100 K preheating; Χ - ρυ = 0.012 g/cm2s, 100 K preheating; □ - ρυ = 0.01 g/cm2s, 0 K preheating; ○ - ρυ = 0.0056 g/cm2s, 0 K preheating.
112
90 80 70
NO, ppm
60 50 40 30 20 10 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2
2.2
Distance, cm
(6.3.2a) 2300 2200
Temperature, K
2100 2000 1900 1800 1700 1600 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Distance, cm
(6.3.2b) Figure 6.3.2. Vertical profiles of NO mole fraction (a) and temperature (b) measured in methane/air flames at φ = 1.5 for 200 K and 300 K preheating. ■ - ρυ = 0.028 g/cm2s, 300 K preheating; Χ - ρυ = 0.0257 g/cm2s, 300 K preheating; ● - ρυ = 0.021 g/cm2s, 300 K preheating; ◊ - ρυ = 0.021 g/cm2s, 200 K preheating; □ - ρυ = 0.016 g/cm2s, 200 K preheating; - ρυ = 0.0086 g/cm2s, 200 K preheating.
113
90 80 70
NO, ppm
60 50 40 30 20 10 0 0
5
10
15
20
25
30
Distance, cm
(6.4a) 2200 2100
Temperature, K
2000 1900 1800 1700 1600 1500 0
5
10
15
20
25
30
Distance, cm
(6.4b) Figures 6.4 (a) and (b). Vertical profiles of NO mole fraction (fig. 6.4a) and temperature (fig. 6.4b) measured in methane/air flames at φ = 1.6 for 200 K, 300 K and 400 K preheating . - ρυ = 0.028 g/cm2s, 400 K preheating; - ρυ = 0.024 g/cm2s, 400 K preheating; Χ - ρυ = 0.019 g/cm2s, 300 K preheating; □ - ρυ = 0.016 g/cm2s, 200 K preheating.
114
Considering the large variation of initial mixture temperature and mass flux at a given equivalence ratio, see figs. 6.1-6.4, the choice of optimal comparison procedure is not obvious. In an attempt to systematize the effect of preheating on the experimental results, figure 6.5 summarizes the NO mole fraction and temperature profiles in near adiabatic flames at φ = 1.0, 1.3 and 1.5, for 300 K preheating (initial temperature, T0 = 600 K); for these measurements, the exit velocity was increased to the point at which the maximum temperature no longer varied with velocity [6]. The rapid rise to nearly 225 ppm for φ = 1.0, reflects the vigorous Zeldovich formation in the hot (~ 2350 K) postflame gases and is the obvious reason one wishes to avoid oxygen-rich regions in preheated combustion. This is in marked contrast to the two fuel-rich flames, whose profiles rise rapidly to roughly 80 ppm and remain constant thereafter, characteristic for the Fenimore mechanism, in spite of temperatures in excess of 2100 K. We note that slightly more NO is produced at φ = 1.5 than at φ = 1.3. Comparison of the results is complicated by the fact that the same degree of preheating results in large differences in post-flame temperature at the different equivalence ratios. Furthermore, practical systems using air preheating aim at constant oven temperature, and thus at constant flame temperature. In figure 6.6, we therefore present the measured and calculated NO profiles at these three equivalence ratios, at a constant flame temperature of 2150 K. The conditions were obtained by varying the preheating and mass flux (ρυ0) through the burner (Chapter 4). Also shown are the NO profiles calculated using GRI-Mech 3.0 chemical mechanism [11] The input mass flux in the calculations was adjusted, using the experimental conditions of preheating and equivalence ratio, to yield the same maximum temperature observed in the experiments. The differences between experimental and calculated mass flux were always less than 10%, and usually better than 5%. The conditions used presented in fig. 6.6 are: φ = 1.0, T0 = 300 K, ρυ = 0.032 g/cm2s; φ = 1.3, T0 = 700 K, ρυ = 0.038 g/cm2s; and φ = 1.5, T0 = 600 K, ρυ = 0.033 g/cm2s. At a given equivalence ratio and flame temperature, the NO mole fraction obtained was independent of the method for achieving the final temperature. Even at 2150 K, the NO profiles for the fuel-rich flames are flat after the first few millimeters, indicative of the low concentration of oxygen atoms necessary for the Zeldovich mechanism. In contrast, the stoichiometric profile still grows, albeit more slowly than in fig. 6.5. At this flame temperature, the stoichiometric flame generates the lowest NO mole fraction, at least for the first 2 cm, and the richest flame the highest (at 2150 K, the maximal NO mole fraction for φ = 1.6 is close to that for φ = 1.5). The calculated profiles using GRI-Mech 3.0 qualitatively predict the trends described above well, although the absolute NO mole fraction is overpredicted for the rich flames [41,42]. The experimental profile for the stoichiometric flame rises more quickly than the computations, and is consistent with the differences in the temperature profiles shown in fig. 6.7, as seen in near-adiabatic flames [41].
115
2400
350
2200
300 Τ, φ=1.0
250
Τ, φ=1.3
1800
Τ, φ=1.5
200
ΝΟ, φ=1.0
1600
ΝΟ, φ=1.3
1400
150
NO, ppm
Temperature, K
2000
ΝΟ, φ=1.5
100
1200 1000
50
800
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Distance, cm
Figure 6.5. Vertical profiles of NO mole fraction and temperature measured in methane/air flames at 300 K preheating, φ = 1.0, 1.3 and 1.5. 160
NO, ppm
140 120
φ=1.0
100
φ=1.3 φ=1.5
80
3.0, φ=1.0
60
3.0, φ=1.3 3.0, φ=1.5
40 20 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Distance, cm
Figure 6.6. Vertical profiles of NO mole fraction for fixed maximum temperature, 2150 K; φ = 1.0, 1.3 and 1.5. Points: measurements; lines: calculations using GRI-Mech 3.0. For other conditions, see text.
116
2300
Temperature, K
2100
1900
φ=1.0 φ=1.3
1700
φ=1.5 3.0, φ=1.0
1500
3.0, φ=1.3 3.0, φ=1.5
1300 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Distance, cm
Figure 6.7. Vertical profiles of temperature for same conditions as in figure 6.6.Points: measurements; lines: calculations using GRI-Mech 3.0.
Increasing the flame temperature to 2300 K illustrates the differences between the NO formation mechanisms under rich and stoichiometric conditions, as shown in figure 6.8 for φ = 1.0 (T0 = 500 K, ρυ = 0.057 g/cm2s) and 1.3 (T0 = 700 K, ρυ = 0.062 g/cm2s). Increasing the flame temperature by 150 K doubles the NO mole fraction in the stoichiometric flame, while the NO in the fuel-rich flame increases by only 20 %. (The volumetric flow rates for φ = 1.5 and 1.6 were too low to reach a flame temperature of 2300 K). Whereas at 2150 K (fig. 6.6) stoichiometric conditions gave the least NO in the measurement domain, the NO mole fraction from the stoichiometric flame at 2300 K rises to twice that of the fuel-rich flame in the same distance. Also noteworthy is the better agreement in the first 7 mm of the calculated NO profile for φ = 1.0, in spite of a similar discrepancy in the temperature profile observed in fig. 6.7. The calculations indicate enhanced Fenimore activity in the stoichiometric flame front with preheating, yielding an increase of 5-10 ppm NO in the flame front per hundred degrees increase in flame temperature. The progressively decreasing slope of the experimental NO profile (also present, although less pronounced, in fig. 6.5) is most likely caused by a modest decline in temperature arising from radiative losses in the hot gases.
117
2400
240 220
2200
200 180 160
1800
140
1600
120 100
1400
NO, ppm
Temperature, K
2000
80
1200
Τ, φ=1.0 Τ, 3.0, φ=1.0 ΝΟ, φ=1.0 ΝΟ, 3.0, φ=1.0
1000
60
Τ, φ=1.3 Τ, 3.0, φ=1.3 ΝΟ, φ=1.3 ΝΟ, 3.0, φ=1.3
40 20
800
0 0
0.2
0.4
0.6
0.8
1 1.2 1.4 Distance, cm
1.6
1.8
2
2.2
2.4
Figure 6.8. Vertical profiles of NO mole fraction and temperature for fixed maximum temperature, 2300 K; φ = 1.0 and 1.3. Points: measurements; lines: calculations using GRI-Mech 3.0. For other conditions, see text.
6.3 NO concentration as a function of the flame temperature
To facilitate further discussion on the variation in NO mole fraction with preheating, we plot the measured NO mole fraction as a function of the measured temperature, as done in [6]. To reflect the amount of NO formed in the flame front, and to minimize variations in the data caused by processes beyond experimental control (such as radiative losses and downstream mixing with air/nitrogen at very low exit velocities), we use the mole fractions and temperatures at 5 mm above the burner surface for φ = 1.0, 1.3 and 1.5. At φ = 1.6, since the NO profiles still grow at 5 mm distance, we use the mole fractions and temperatures at 10 mm, where the profiles are essentially flat. These plots are shown in figures 6.9, 6.10, 6.11 and 6.12 for φ = 1.0, 1.3, 1.5 and 1.6, respectively. Since nearly all of the NO profiles for the fuel-rich flames were flat at the corresponding distances, this choice of position has no further consequences for the discussion. Although obvious given the range of temperatures under consideration, it is worth remembering that above ~ 2000 K the NO mole fractions in the stoichiometric flames continue to grow substantially. To avoid ambiguity in the choice of the origin in freely propagating flames, we restrict the data to those taken in flames with significant heat transfer to the burner, where the origin coincides with the burner surface. Included in the figures are the calculated data (GRI-Mech 3.0) near 5 mm for φ = 1.0, 1.3, 1.5 and 10 mm φ = 1.6, as well as the equilibrium NO mole fractions as a function of temperature. The exponential rise expected for the Zeldovich mechanism is apparent in the stoichiometric data in figure 6.9. These measurements extend those reported in ref. [41]
118
by nearly 150 K; for all data points taken under the same conditions, the differences with ref. [41] were less than the 5 ppm stated above. The calculated data are given for two distances above the burner, 4.7 and 5.4 mm, to show that the difference with measurements is nearly insensitive to the choice of origin. The divergence between the calculations and measurements with increasing temperature reflects the fact that the experimental temperatures reach their maximum value more rapidly than the calculations. As to be expected for the temperatures reported here, the NO mole fractions at 5 mm are significantly below their equilibrium values. However, the approach to equilibrium is substantially accelerated with increasing flame temperature [5], as illustrated here by comparing the stoichiometric profiles in figs. 6.1, 6.5, 6.6 and 6.8. That the data for different exit velocities and preheating lie within a very narrow band shows that the NO mole fraction at a given temperature is independent of how the final temperature is obtained, see Chapter 1; note that this phenomena is observed in the fuel-rich flames as well (see figures 6.10- 6.12). The results for φ = 1.3, shown in figure 6.10, extend the range of measurements reported in ref. [6] by nearly 300 K, and form a vivid contrast with the stoichiometric results. Between roughly 1850 and 2250 K, the NO mole fraction grows slowly (by less than a factor of 2), and essentially linearly. When taken over this large range of temperature, the qualitative agreement between calculations and measurements appears significantly better than that reported earlier [41]. The calculations show this linear region to be the result of increasing Fenimore production, with increasing CH mole fraction and concomitant increased nitrogen fixation. One feature that is well captured is the upturn in the NO mole fraction above ~ 2250 K. At these high temperatures the calculations show that the increase in oxygen atom concentrations in the flame front leads to substantial Zeldovich formation. This is illustrated in fig. 6.10 by the calculated results obtained by excluding the O + N2 reaction from the mechanism, showing the entire upturn to be Zeldovich in origin. We remark here that this behavior as a function of flame temperature is similar to that observed for φ = 1.15 described in ref. [6], where varying the heat transfer to the burner using room-temperature reactants also showed a slowly increasing NO mole fraction with temperature, over a region spanning 300 K. Under those conditions, however, presumably because the equivalence ratio was closer to stoichiometric, Zeldovich formation became important at a substantially lower temperature (~ 2050 K) than at φ = 1.3.
119
160 140
NO, ppm
120 100
no preheat 100K preheat 200K preheat 300K preheat GRI 3.0, at 4.7 mm
80 60
GRI 3.0, at 5.4 mm Equil. NO/15
40 20 0 1700
1800
1900
2000
2100
2200
2300
2400
Temperature, K
Figure 6.9. NO mole fraction measured at 5 mm above burner surface plotted against flame temperature at the same position, φ =1.0. Points: measurements; lines: calculations using GRI-Mech 3.0 at 5 mm above burner surface, with and without O+N2 reaction, and equilibrium mole fraction NO. 160 140
no preheat 100K preheat 200K preheat
NO, ppm
120 100
300K preheat 400K preheat GRI 3.0, with N2+O
80 GRI 3.0, without N2+O
60
Equil., NO/3
40 20 0 1700
1800
1900
2000
2100
2200
2300
2400
Temperature, K
Figure 6.10. NO mole fraction measured at 5 mm above burner surface plotted against flame temperature at the same position, φ =1.3. Points: measurements; lines: calculations using GRI-Mech 3.0 at 5 mm above burner surface, with and without O+N2 reaction, and equilibrium mole fraction NO.
120
180 160
no preheat 100K preheat
140
NO, ppm
200K preheat
120
300K preheat
100
400K preheat GRI 3.0, with N2+O
80
GRI 3.0, without N2+O
60
Equil., NO
40 20 0 1650
1750
1850
1950
2050
2150
2250
Temperature, K
Figure 6.11. NO mole fraction measured at 5 mm above burner surface plotted against flame temperature at the same position, φ =1.5. Points: measurements; lines: calculations using GRI-Mech 3.0 at 5 mm above burner surface, with and without O+N2 reaction, and equilibrium mole fraction NO.
140 120 100
200 K preheat
NO, ppm
300 K preheat
80
400 K preheat GRI 3.0 1cm
60
Equil., NO
40 20 0 1700
1800
1900
2000
2100
2200
2300
Temperature, K
Figure 6.12. NO mole fraction measured at 1 cm above burner surface plotted against flame temperature at the same position, φ =1.6. Points: measurements; lines: calculations using GRI-Mech 3.0 at 10 mm above burner surface and equilibrium mole fraction NO.
121
Consideration of the equilibrium NO as a function of temperature in fig. 6.10 shows that up to ~ 2125 K, the NO mole fraction is above its equilibrium value, in stark contrast with the stoichiometric flames in fig. 6.9. Since the NO profiles are flat, at least over the 2 cm range of the measurements, relaxation to equilibrium is very slow. At flame temperatures between 1900 K and 2100 K, the CHEMKIN calculations show a modest, slow decrease in mole fraction at several centimeters above the origin, but at 8 cm this decrease is still less than 10%. Above ~ 2125 K, the NO mole fraction is again subequilibrium, and the system must apparently rely on the reaction O + N2 to approach equilibrium, as in oxygen-rich combustion. However, given the exceptionally low concentrations of oxygen and nitrogen atoms far downstream of the flame front at this equivalence ratio (recall that the experimental NO profiles even at 2300 K are essentially flat), the Zeldovich mechanism will be too slow at all but exceptionally high temperatures to significantly drive the system to equilibrium. At the timescales characteristic for practical devices, the NO mole fraction is frozen at its sub-equilibrium value, just as it appears to be frozen at its super-equilibrium value below 2125 K. At temperatures below ~ 1900 K, the calculated mole fraction begins to drop sharply. Thus, the approach to equilibrium is accelerated with increasing flame temperature in stoichiometric flames, but appears to be only slightly affected at φ = 1.3 below ~ 2250 K. Of course, the differences in behavior with respect to the approach to equilibrium follow from the differences in how the operative mechanisms are coupled to premixed flame structure. In contrast to the Zeldovich mechanism at φ = 1.0, which is active throughout the entire high temperature domain, the Fenimore mechanism (including reburning reactions) is intimately coupled to the consumption of the fuel. In premixed flames at φ = 1.3, it is thus restricted to a very small spatial region, at temperatures significantly lower than the post-flame temperature. Hence, unlike Zeldovich kinetics, the Fenimore kinetics at this equivalence ratio are not directly coupled to the post-flame temperature, and once the fuel has been consumed NO formation and consumption via the Fenimore mechanism are effectively exhausted, leaving the system with no fast route to equilibrium. Turning to the results for φ = 1.5, shown in figure 6.11, we see that the NO mole fraction at temperatures below 1950 K is consistently lower than ~ 10 ppm. The NO then increases 9-fold as the temperature rises to more than 2100 K. The calculated dependence captures the features of the experiments well; when allowing for the experimental uncertainty, even the quantitative agreement seems reasonable. Examination of the calculations at temperatures above 1950 K shows a strong increase in nitrogen fixation via the Fenimore mechanism (witness the marginal difference when excluding O + N2 in the figure). The analysis of the calculations indicates that as the temperature increases there are two contributions to the increasing NO mole fraction: more nitrogen is fixed (higher CH concentrations), and the conversion of HCN to NO, predicted to be slow at lower temperatures, is accelerated (see figure 6.13). Interesting is that in this region the kinetics of NO produced in the flame front appear to outrun the growth in the equilibrium curve; here too, relaxation to equilibrium appears to be very slow.
122
90 80
T=1910K
70
T=1970K
HCN, ppm
60
T=2040K
50
T=2110K
40
T=2190K
30 20 10 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Distance, cm
Figure 6.13. Vertical profiles of HCN mole fraction calculated in methane/air flames using GRI-Mech 3.0 at different temperatures, φ = 1.5. Figure 6.12 shows the measured NO mole fraction as a function of flame temperature for φ = 1.6. The qualitative behavior of the measured dependence is similar to that for φ = 1.5. At temperatures below ~ 2000 K, the NO mole fraction is lower than 10 ppm. While at higher temperatures the NO mole fraction increases rapidly, approximately by a factor of 10 between 2000 and 2150 K; it is interesting to note that the similar rise at φ = 1.5 starts at ~ 1950 K. The calculated dependence matches the experiments reasonably well. Similarly to φ = 1.5, the calculation indicates that the rapid increase in the NO mole fraction with temperature is the result of increasing CH concentration together with conversion of HCN to NO. Also, we note that above ~ 2050 K the measured NO mole fraction is above its equilibrium values. We also carried out the experiments with preheating for equivalence ratios 1.7 and 1.9. However, the volumetric flow rates for these equivalence ratios were too low to reach the temperatures in excess of 1965 K. At temperatures below ~ 1965 K, the measured NO mole fractions were on the level of few ppm over the whole measurement domain. The modeled and equilibrium NO mole fractions are below 10 ppm for these conditions. Although the agreement between measurements and calculations engenders confidence in the mechanism, we remark that comparisons of the NO profiles at temperatures below 2000 K point to significant qualitative discrepancies. Whereas all of the measured NO profiles are flat between 5 and 20 mm, the calculated profiles show growth in the NO mole fraction well outside the limits of experimental error (increases of up to 35 ppm in the same distance), arising from the slow HCN → NO conversion, see figure 6.13. Furthermore, although, the high-temperature NO profiles at φ = 1.6 continue to increase above 5 mm distance from the burner, see fig. 6.4a, the calculated profiles show considerably steeper rise at the same distance and continue to increase at distances where the experimental profiles already flat. Figure 6.14 illustrates the measured and 123
calculated NO profiles at φ = 1.6 (flame temperature ~ 2115 K). The experimental NO profile shows an increase of ~ 20 ppm in the NO mole fraction in the distance between 5 and 12 mm (the biggest measured increase), and is flat thereafter. The calculated profile shows growth of more than 35 ppm in the same distance and still increases at downstream distances (up to ~ 25 mm). The calculation indicates that a rapid rise in the NO mole fraction (until ~ 2 mm above the burner surface) coincides with the location of the CH profile. At downstream distances, the NO growth results from the HCN → NO conversion. Figure 6.14 also includes the NO+HCN+NH3 profile (the NH3 concentration has the small but not negligible value of ~10 ppm in the flame front). After the initial rise coinciding with the location of the CH profile, the NO+HCN+NH3 profile is practically flat over the distance of 10 mm, and then shows the small decrease at downstream distances. The rate production analysis of nitrogen bound species reveals that the modest decrease in the NO+HCN+NH3 mole fraction from 10 to 40 mm (~ 13 ppm) is mainly caused by the reaction NO+N O+N2. In other words, the Zeldovich mechanism works in the reverse direction converting the NO and N pools to molecular nitrogen. Comparison of the measured NO growth with the calculated one implies that the predicted conversion of the nitrogen fixed molecule(s) to NO is too slow. With an eye towards the quantitative disagreement between the measured and calculated NO profiles, it is useful to estimate the Fenimore NO concentration. It can be calculated by integrating the CH+N2 reaction rate, using the calculated CH and T profiles, assuming that all HCN and N produced by this reaction is converted to NO and neglecting the reverse reaction. We determine the Fenimore contribution, (NO)Fenimore, using [126] (NO)Fenimore = 2 ⋅ ∫ k (Τ( x)) ⋅ CH ( x) ⋅[ Ν 2 ]( x) ⋅
dx , υ ( x)
(6.1)
where k(T(x)) is the rate constant of the reaction CH+N2, CH(x) and T(x) are the CH concentration and temperature profiles, [N2] (x) and υ(x) are absolute nitrogen number density and flow velocity. The integration up to 3 mm of the calculated profiles for the above discussed flame provides the Fenimore contribution of ~ 125 ppm. The contribution is accounted for by the summation of the NO, HCN and HCN concentrations, see figure 6.14. As can be seen from eq. (6.1), the NO mole fraction formed via the Fenimore mechanism depends on a number of parameters, such as a area of the CH profile, the relative position of the CH distribution relative to the temperature, the rate constant of the reaction CH+N2. Since the behavior of the nitrogen fixed molecules and CH radicals are an important feature of NO formation in this region of equivalence ratio and temperature, more detailed experimental information on the HCN and CH concentrations in these flames is desirable before drawing mechanistic conclusions. At any rate, even allowing for the possibility of residual HCN, there is a potential for low NOx emissions using richpremixed conditions in combination with preheating.
124
160
NO, ppm
120
2000
100
1800
80
1600
60
NO, EXP
1400
NO, GRI 3.0
40
Temperature, K
2200
140
NO, GRI 3.0 with Exp T
1200
NO+HCN+NH3, GRI 3.0
20
T, EXP
0
1000
T, GRI 3.0
0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3
3.3
3.6
3.9
4.2
Distance, cm
Figure 6.14. Vertical profiles of NO mole fraction and temperature measured in methane/air flames at φ = 1.6 for flame temperature of 2115 K. Points: measurements; lines: calculations using GRI-Mech 3.0 with calculated and measured temperature profiles.
Chapter 6 reported effects of varying the degree of the burner stabilization and preheating (up to 400 K) on NO concentration and temperature in laminar premixed methane-air flames at equivalence ratios 1.0, 1.3, 1.5 and 1.6. The experimental data on NO concentration were contrasted with the model predictions and the results calculated for thermodynamic equilibrium.
125
CHAPTER 7 Experimental Study of NO Reburning in Atmospheric- Pressure Laminar RichPremixed CH4/Air/N2/NO Flames
126
Abstract
Concentrations of nitric oxide in atmospheric-pressure laminar rich-premixed CH4/Air/N2 flames were measured by using a combination of LIF and CARS methods. The nitrogen in the unburned gas mixture was either neat or doped with NO. The flame temperature was varied over 400 K by changing the total gas flow. The absolute calibration of the LIF measurements was performed at the stoichiometric equivalence ratio where the added nitric oxide is expected not to be removed in the flame front. For the analysis of the experimental data the normalized difference between the NO concentrations in seeded and non-seeded flames was introduced. The advantage of using this normalized difference is its independence upon the distance after the flame front in high temperature flames and canceling a background signal when it is calculated from measured LIF signals. The measured flame temperatures show good agreement with the temperatures calculated by using the GRI-Mech 3.0 chemical mechanism at all total gas flows and equivalence ratios employed in this work. The calculations predict qualitatively the measured NO profiles well. The same non-monotonic behavior of the measured and calculated NO profiles at points close to the flame front is observed in the seeded free flames. Quantitatively, the normalized difference of the NO concentrations is underestimated at φ = 1.3 and 1.4 while at φ = 1.5 excellent agreement between the calculations and measurements is observed. This underestimation tends to lessen with decreasing flame temperatures. The efforts to improve the agreement between calculations and measurements by varying the pre-exponential factor of the rate constants failed, implying that the key channels for the formation and destruction of the nitric oxide be reconsidered. In this regard quantitative HCN detection and additional NO measurements at different levels of doping the unburned gas-air mixture with the nitric oxide can be very useful.
127
7.1 Introduction
In this Chapter we examine the temperature dependence of the fate of added NO in atmospheric-pressure flat fuel-rich and stoichometric CH4/N2/Air flames seeded with low concentrations of nitric oxide. This is extension of our previous work reported in Chapter 6, where we studied NO formation in methane-air flames by applying upstream heat transfer to vary flame temperature. Seeding the flame with known amount of NO can substantially change the relations between different paths in NO formation/destruction that will expand the testing domain of the mechanism. Moreover, this type of flame can be used to model NO reburning in staged combustion, which has proven to be an effective NOx reduction technique (see [127] and references therein). From the experimental point of view seeding provides an additional benefit because the corresponding high levels of NO concentration can be easily detected. Further, studies of flames doped with nitric oxide are also of special interest for laser induced fluorescence (LIF) NO detection, relying on the calibration procedure described earlier [81,83,128130]. To date, the experimental studies of hydrocarbon flames doped with NO were restricted to low pressure [34,102,131-135]. Besides, these experiments were carried using the unburned air-gas mixture at room temperature; we are not aware of any investigations of NO formation and destruction in NO-seeded flames where the temperature of reactants was varied. In the present work, we employ LIF and coherent anti-Stokes Raman scattering (CARS) to measure the nitric oxide concentration and temperature, respectively, while the flame temperature variations cover a 400 K span. The measured results are compared to predictions of one-dimensional flame calculations. 7.2 Experimental Approach
The measurements were performed in fuel-rich and stoichometric premixed CH4/Air/N2 flames, where the added N2 was either ‘neat’ or contained 4950 ppm of NO, giving approximately 200 ppm NO in the unburned gas (Chapter 2). The flames were stabilized above a 6-cm diameter water-cooled bronze burner (McKenna products, Chapter 2) and surrounded by a coflow of nitrogen to prevent mixing with ambient air. The experiments were carried out in flames at φ = 1.0, 1.3, 1.4 and 1.5. For every equivalence ratio the experiments were started at low exit velocities, in flames close to extinction. Then the total mass flow was gradually increased up to the point at which the flame temperature no longer varied with exit velocity, and its one-dimensional structure was not yet visibly disturbed. At this point, heat losses to the burner deck are negligibly small and the flame can be regarded as an adiabatic free flame. The optical setup used for the CARS and LIF measurements was described in detail in Chapter 3. The onedimensional flame calculations are obtained with GRI-Mech 3.0 (Chapter1). 7.3 Data Reduction and Analysis
The experimental results in flames seeded with the nitric oxide have been presented in [34] as a reburn coefficient, which is, when corrected for dilution, the difference between the NO concentrations in the unburned gas-air mixture and flame. Since the concentration of the native NO in the flames studied in this work (Chapter 6) is not
128
negligible in comparison with the seeded NO level (~200 ppm), the presentation of experimental data in such a manner is not illustrative. In this chapter we present our experimental results as the difference between the NO concentrations in the seeded and unseeded flames. For this purpose we introduce a coefficient α that is determined in the following way: ″ X (x ) − X NO ′ (x ) W ( xu ) α = NO ⋅ , (7.1) ″ W ( x ) X NO ( xu ) where the W (x) is the mean molecular weight at axial distance x, single and double accents denote variables in the non-seeded and seeded flames, respectively, and xu refers to a point in the cold gas-air mixture. The main advantage of this representation, besides removing the dependency upon dilution (see below), is that the coefficient α is independent of the distance x after the flame front at higher temperatures, when a significant amount of the nitric oxide is produced by the Zeldovich mechanism. It removes the ambiguity related to the distance and gives the possibility to compare flames with different equivalence ratios and temperatures without referencing to the measured profiles. The proximity of the coefficient α to 1 in the post-flame gases in the stoichiometric flames forms the basis for deriving the absolute NO concentrations from the measured LIF profiles (Chapter 3). The measured LIF signal can be presented as I LIF = C ⋅ P(T ) ⋅ X NO + I BG
(7.2)
where C is a proportionality coefficient, IBG is a background signal, XNO is the NO mole fraction, and P(T) is a temperature dependent factor. Taking into account that the background signals are the same in the seeded and non-seeded flames we receive an expression for deriving the NO concentration from the measured LIF signal: X NO ( x) =
I LIF ( x) − I BG W cal ( x) P(Tcal ) ″ ⋅ ⋅ ⋅ X NOcal ( xu ) , ″ ′ W cal ( x ) P(T ) I LIFcal − I LIFcal u
(7.3)
where the subscript cal refers to the measurements in the calibration flame (Chapter 3). Combining the formulas (7.1) and (7.3), the coefficient α is given by ″ ′ I LIF − I LIF W cal ( x) W ( xu ) P(Tcal ) α ( x) = ⋅ ⋅ ⋅ . ″ ′ W cal ( x ) W ( x) P(T ) I LIFcal − I LIFcal u
(7.4)
This formula shows an additional benefit of using the coefficient α: backgrounds in the LIF signals in the seeded and non-seeded flames have been canceled. Due to the large concentration of inert N2 in the air/gas mixture, and because the number of moles does not change in the overall reaction of methane oxidation, W (x) changes slightly in the flame front and then remains practically constant. This results in the dilution factor 129
W ( x) W ( xu ) being close to 1. For flames investigated in the present work, maximal dilution occurs at φ = 1.5, where W ( x) W ( xu ) ≅ 0.9. Although the introduction of the dilution factor W ( x) W ( xu ) in equation (7.3) seems to be a reasonable way to account for change in the number of moles, we think it is of interest to provide the strict mathematical argument for its appearance in the equation. The evolution of nitric oxide concentration in a one-dimensional flame while proceeding from the point xu in the unburned air/gas mixture to some point x in the flame is described by species continuity equation (1.3). This equation can be rewritten as
ρ ⋅υ ⋅
d ( X NO / W ) d D + ρ ⋅ X NO ⋅ VNO / W − K NO = 0 , dx dx
(
)
(7.5)
D where ρ is the mass density, υ is the velocity, VNO is the NO diffusion velocity, KΝΟ is the net chemical NO production rate. Integrating this equation from xu up to x, neglecting the diffusion fluxes at the boundaries one receives
X NO ( x) = X NO ( xu ) ⋅
W ( x) W ( x) x + ∫ K NO ( x) ⋅ dx . ρ υ xu W ( xu )
(7.6)
As can be seen from this equation, the change in the seeded NO mole fraction through the flame is result of two processes: dilution and chemical production/destruction. Combining the equations (7.1) and (7.6) we receive the following expression for the coefficient α
α = 1+
x W ( xu ) (K NO " ( x) − K NO ' ( x)) ⋅ dx . ∫ ρυ ⋅ X NO ″ ( xu ) xu
(7.7)
It should be pointed out that the coefficient α is independent of x only in the hightemperature flames, where the chemical NO production rates are the same in both seeded and non-seeded flames. It is certainly incorrect in rich flames where ΚΝΟ′(x) and KNO″(x) are not the same. This restriction is not of importance, because all experiments performed in this work in rich flames revealed flat NO profiles, showing that the net chemical formation rates of nitric oxide are small in the post-flame front zone (slow relaxation of NO concentrations to equilibrium) and thus α is independent of distance x. To illustrate this procedure for treating the data, figure 7.1 shows the dependence of the computed coefficient α and the NO mole fractions, with and without 200 ppm NO seeded in the unburned mixture with composition determined by the formula (2.1) (Chapter2), upon the distance x for a free flame at φ = 1.0. The significant rise in the post-flame front zone of the unseeded flame of the native NO mole fraction (up to ~ 65 ppm at a height of 1.0 cm) reflects the Zeldovich formation. The same NO growth is observed in the seeded flame. Prior to this rise, on a spatial scale that cannot be resolved experimentally in atmospheric-pressure flames, the seeded NO concentration in the flame
130
α
NO, ppm
1.2
250
α
1.1
200
ΝΟ (200) 1
ΝΟ (0) 150
0.9 100 0.8 50
0.7 0.6
0 0
0.1
0.2
0.3
0.4 0.5 0.6 Distance, cm
0.7
0.8
0.9
1
Figure 7.1. Calculated profiles of coefficient α (solid line) and NO mole fractions in seeded (dashed line) and non-seeded (dotted line) free stoichiometric CH4/N2/Air flames. front quickly decreases to about ~ 70 % of its initial level, partially restores, and then experiences a small depletion before recovering. According the GRI-Mech mechanism, the first depletion occurs due to fast conversion of NO to NO2, the calculations show that at the same distance there is a sharp peak (~ 60 ppm at maximum) in the NO2 concentration. Further downstream, the increasing hydrogen atom concentration leads to conversion of NO2 back to NO through the reaction NO2 + H NO + OH. Because the chemical mechanism requires nitric oxide as the product of all reactions of NO2 with flame components, NO2 formation and destruction only redistribute NO and NO2 concentrations while keeping the total concentration constant. The NO2 conversion back to NO is not completed when the removal of the nitric oxide starts through its reactions with hydrocarbon radicals forming approximately 10 ppm HCN. Further downstream, O atoms initiate HCN conversion back to NO through a route HCN + O → NCO → NH → N, HNO → NO,
(7.8)
which will decrease the HCN concentration to the sub-ppm level at the height of 2 mm. This conversion is accompanied by the launching of NO formation through the Zeldovich mechanism, resulting in the very steep increase in the NO mole fraction, more prominent than the analogous rise in the non-seeded flame. Because of the monotonic character of the NO profile in the non-seeded flame the calculated α profile shows the same depletions in the flame front. Further downstream the coefficient α remains constant at a 131
level of ~ 0.96, demonstrating the assumption about independence of the net NO chemical formation rate upon the NO concentration in the post-flame front zone is valid in this flame. 7.4 Results and discussion
The measured and modeled vertical temperature profiles in the free flames at φ = 1.3, 1.4 and 1.5 are presented in figure 7.2 and show good agreement, except for first two points in the flame at φ = 1.5. This small disagreement can be easily corrected by shifting the measured profile 0.5 mm further downstream, which is opportune because of the spatial similarity of the free flames [136]. The calculated temperatures display the slight post-flame front temperature rise due to the recombination of flame radicals, while the experimental data there are practically constant. However, this modest rise (≤ 20 K on the computational interval from 5 to 100 mm) is well within the accuracy (±40 K) of our measurements. The same excellent agreement between the calculated and measured temperatures was observed in the burner-stabilized flames, see also Chapter 4. Whereas the agreement in the free flames is solely of thermodynamic origin, the agreement in the burner-stabilized flames illustrates the predictive power of the GRI-Mech in the flame structure calculations, as discussed earlier. It increases our confidence that the possible disagreement between the measured and calculated NO concentrations is only due to uncertainties in the NO formation and consumption chemistry. (At the same time it cannot be excluded that the chemical mechanism incorrectly predicts a component having marginal influence on the temperature but being crucial for NO formation.) The nitric oxide concentration profiles derived from the LIF signals in the seeded and non-seeded with NO free flames at φ = 1.3, 1.4 and 1.5 are shown in figure 7.3 (upper chart). As can be seen, changing the equivalence ratio brings significant consequences for the NO reburn process: whereas at φ = 1.3 the NO concentrations increases from the 200 ppm in the unburned mixture to the ~ 250 ppm in the post-flame gases, substantial reduction (up to ~ 70 ppm) of the seeded NO is observed at φ = 1.5. According to GRIMech 3.0, this behavior is due to the slowing of the HCN conversion with increasing φ. Whereas HCN formation through reactions of the CH radical with NO and N2 remains significant with increasing φ, the increasing shortage of the oxygen atoms retards the HCN conversion to NO through route (7.8). In the non-seeded flames, the measured NO concentration downstream of the flame front is around 55 ppm at φ = 1.3 and 1.4 but substantially decreases to below 10 ppm at φ = 1.5. It should be pointed out that this observed decrease of the NO concentration should be treated very carefully as a basis for creating low-NOx devices, because of the possible formation of significant amounts of HCN, which can be converted back to NO in the next combustion stage when the remaining fuel is burned out. Comparison of the experimental NO profiles with the calculated ones (presented in the lower chart) shows good qualitative agreement. Even at the limited spatial resolution of the measurements, we are able to catch in the seeded flames the numerically predicted peculiarities such as an initial growth of the NO concentrations at φ = 1.3, a local minimum at φ = 1.4 and a local maximum at φ = 1.5. Quantitatively, the agreement
132
2100 1900
T, K
1700
1.3 1.4
1500
1.5 1.3
1300
1.4 1.5
1100 900 0
0.1
0.2
0.3
0.4 0.5 0.6 Distance, cm
0.7
0.8
0.9
1
Figure 7.2. Temperature profiles at φ = 1.3 (squares, solid line), 1.4 (diamonds, dashed line) and 1.5 (triangles, dotted line). Markers and lines denote measurements and calculations using GRI-Mech 3.0, respectively. between the experimental and calculated NO profiles is moderately good at φ = 1.3, gets worse at φ = 1.4 and becomes surprisingly very good at φ = 1.5. The same degree of disagreement between the experiment and calculations is observed in the non-seeded flames. The quantitative differences between the experiment and calculations at φ = 1.3 and 1.4 become even more pronounced when the results are presented as the coefficient α (see figure 7.4). While the measured α at φ = 1.3 is close to 1, similar to the stoichiometric flame, the calculated α ~ 0.8. The same numerical undeprediction (~ 20%) is observed at φ = 1.4 as well. The closeness of α to 1 at φ = 1.3 is quite remarkable because the equilibrium NO concentration in the free flame at this equivalence ratio is ~ 20 ppm, which is much lower than the NO concentration in the unburned air-gas mixture, and one could not expect that the NO formation rates are the same in the seeded and non-seeded flames. To illustrate the dependence of the formation and destruction of nitric oxide on the heat transfer to the burner surface, in figure 7.5 we plot α, measured at 5 mm above the burner surface, as a function of the measured temperature at the same position for the flames at equivalence ratios φ = 1.0, 1.3, 1.4 and 1.5. For clarity, the experimental data at temperatures above 2070 K are not shown in figure 7.5; at these temperatures, which can be only reached in the stochiometric flame, α ~ 1. Since all measured profiles of temperature and NO LIF are flat at distances above 3 mm from the burner surface, the choice of position has no further consequence for the discussion. Figure 7.5 also includes the modeled temperature dependence of α for the given equivalence ratios.
133
250
200 [NO], ppm
1.3 seeded 1.3 non-seeded
150
1.4 seeded 1.4 non-seeded 1.5 seeded
100
1.5 non-seeded
50
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.7
0.8
0.9
1
Distance, cm 250
[NO], ppm
200
150
100
50
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Distance, cm
Figure 7.3. Experimental (upper) and calculated (lower) NO profiles, φ = 1.3 (squares, solid lines), 1.4 (diamonds, dashed lines) and 1.5 (triangles, dotted lines). Markers and lines denote experimental and calculated NO concentrations, respectively. The filled markers and thick lines correspond to flames seeded with NO while non filled markers and thin lines correspond to non-seeded flames. Vertical line in the lower figure shows the position of the first measurement point.
134
1.1 1 0.9 0.8 α
0.7 0.6
1.3
0.5
1.4 1.5
0.4
1.3
0.3
1.4 1.5
0.2 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance, cm
Figure 7.4. Profiles of the coefficient α at φ = 1.3, 1.4 and 1.5. Same use of symbols as in figure 7.3. The experimental data show that the coefficient α > 0.9 at φ = 1.0 and temperatures above 1780 K. The measured α at φ = 1.3 grows rapidly (by a factor of ~ 1.7), and essentially linearly, when the flame temperature increases from 1800 K to 1950 K, and then remains constant close to 1. An even more rapid growth of α is observed at φ = 1.4, where α increases from 0.35 to 0.7 when the temperature increases from 1800 K to 1930 K. The growth shrinks at φ = 1.5, where α increases by less than 20% in the temperature interval between 1780 and 1890 K. The common tendency in increasing α with increasing the flame temperature and decreasing the equivalence ratio can be explained by the following simple considerations. The coefficient α grows when the products of the initial NO consumption, such as HCN and NH3, are converted back to NO. This conversion takes place through the reactions of the intermediates with oxygen atoms. Increasing the flame temperature and decreasing the equivalence ratio increases the O atom concentrations, and thus α. Comparison of the measured and modeled (thick lines) results shows quite good qualitative agreement at all equivalence ratios. The difference between the experiment and calculations is maximal for free and weakly stabilized flames at φ = 1.3 and 1.4, and improves at lower temperatures. At φ = 1.5, there is no actual difference. The reason for this disagreement can probably be the underestimation in the calculations of the conversion of HCN and NH3 back to NO. At φ = 1.5, and in highly stabilized (low temperature) flames at other equivalence ratios, this conversion is practically frozen and therefore has marginal influence on the numerical results.
135
1 0.9 0.8
α
0.7 1 1.3 1.4 1.5 1 1.3 1.4 1.5
0.6 0.5 0.4 0.3 0.2 1750
1800
1850 1900 1950 Temperature, K
2000
2050
Figure 7.5. Coefficient α as a function of temperature. Points denote experimental α. Thick lines correspond to calculations with using unchanged reaction rates in GRI-Mech 3.0. Thin lines correspond to calculations where rate constant of the reaction H + CH3 + (M) CH4 + (M) is decreased by 30%.
136
Whereas optimizing the chemical mechanism is far beyond the scope of the present work, it is of interest to analyze how the agreement with the mechanism can be improved by changing the rates of the chemical reactions. Toward this end, we calculate the sensitivity coefficients of the NO concentration for the rates of the different reactions, Ai⋅∂XNO/∂Ai, where Ai is the pre-exponential factor for the i - th reaction. In this definition, the sensitivity coefficients indicate the change in the NO concentration when the variation in the rate of the i - th reaction is the same order of magnitude as the rate itself. As a starting point, the flame at φ = 1.4 was chosen for the sensitivity calculations, where both agreement and disagreement between the experimental and numerically simulated α was observed (figure 7.5). The calculated sensitivity coefficients are presented in figure 7.6. For clarity, the reactions having the sensitivity coefficients with absolute values below 5 and 10 ppm in seeded and non-seeded flames, respectively, are omitted. As can be seen from figure 7.6, in the non-seeded flame the NO concentration is sensitive to the rates of the reactions H +O2 O + OH
(R7.1)
H + CH3 + (M) CH4 + (M)
(R7.2)
and
which are key combustion reactions [11,87]. The effect of these reactions on NO formation is indirect: the variation of their rate constants disturbs the flame temperature and radical distributions that leads to changing the NO concentrations. The reaction (R7.1) can be excluded from our optimization process because its non-monotonic temperature dependence and very low sensitivity coefficient for the free flame. On the other hand, reaction (R7.2) seems to be suitable for optimizing: according figure 7.6 decreasing its rate constant has marginal influence on the NO formation at low temperatures but results in increasing the calculated NO concentration at high temperatures in the non-seeded flame at φ = 1.4. It should be pointed out that because of the large impact of the reactions (R7.1) and (R7.2) on all combustion properties, changing their rates for optimizing the NO formation should be always performed very carefully or be avoided altogether. The reaction CH + N2 HCN +N
(R7.3)
is the rate-limiting step in the Fenimore mechanism of the NO formation (Chapter 1). The rate of this reaction has been changed during the optimization of the GRI-Mech 3.0 [11]. Because the sensitivity coefficient of the reaction (R7.3) is positive, the rate constant of this reaction should be increased to match the measured NO concentrations in the free flame at φ = 1.4 presented in figure 7.3. Unfortunately, this increase will result in increasing the calculated NO concentrations at φ = 1.3, where substantial NO overprediction is observed both in the present work (see figure 7.3 and Chapter 6) and in
137
30.00 H+O2O+OH
Sensitivity, ppm
20.00
H+CH3(+M)CH4(+M) CH+N2HCN+N CH+H2H+CH2
10.00
H+CH4CH3+H2
0.00 -10.00 -20.00 -30.00 1750
1775
1800
1825
1850
1875
1900
1925
1875
1900
1925
Temperature, K 0
Sensitivity, ppm
-10 -20 -30 -40
H+O2O+OH H+CH3(+M)CH4(+M)
-50
CH3+NOHCN+H2O HCCO+NOHCNO+CO
-60 1750
1775
1800
1825
1850
Temperature, K
Figure 7.6. Sensitivity coefficients in non-seeded (upper) and seeded with 200 ppm NO (lower) CH4/Air/N2 flames at φ = 1.4 as a function of temperature.
138
[41] when using the unchanged rate constant for this reaction. The last two reactions for the non-seeded flame mentioned in figure 7.6, namely CH + H2 H + CH2
(R7.4)
H + CH4 CH3 + H2,
(R7.5)
and
affect the CH concentration and have moderate (at maximum ~ 5 ppm) sensitivity coefficients. When the unburned air-gas mixture is seeded with nitric oxide, the sensitivity coefficients for the reactions (R7.1) and (R7.2) are increasing in comparison with those in the unseeded flames, while the variation of the rates of the reactions (R7.3), (R7.4) and (R7.5) has a marginal influence on the NO concentrations. Instead, reactions which remove the nitrogen oxide CH3 + NO HCN +H2O
(R7.6)
HCCO + NO HCNO + CO
(R7.7)
and
appear in the sensitivity plot for the seeded flame in figure 7.6. Because of the weak temperature dependence of the sensitivity coefficients of the reactions (R7.6) and (R7.7) the variation of their rate constants will not improve agreement between the experiment and calculations. The temperature dependence of the rate constant of reaction (R7.1) has the same non-monotonic character as in the non-seeded flame and again should be not considered for optimization. Varying the rate constant of reaction (R7.2) seems to be useful in the seeded flame. The sensitivity coefficient of this reaction has a large negative magnitude at high temperatures and becomes relatively small at low temperatures. As can be seen from figure 7.3 the calculated NO concentration in the seeded flame is much lower than the measured one. Therefore decreasing the rate constant of the reaction (R7.2) is expected to result in increasing the calculated NO concentrations and thus improving the agreement between experiment and calculations in the free, seeded flames. Furthermore, we can hope that at low temperatures the sensitivity coefficient is sufficiently small to avoid worsening the good agreement between the experiment and calculations in the highly stabilized flames. To test this hypothesis we performed the calculations with the rate constant of reaction (R7.2) decreased by 30%. The thin lines in figure 7.5 represent the results of these calculations. As can be seen, decreasing the rate constant of reaction (R7.2) does not improve the agreement between experiment and calculations for the flames at φ = 1.4: at low temperatures the calculated coefficients α are higher than those measured, and at high temperatures the increase in the calculated α is not sufficient to match the measured values. Decreasing the rate constant results in good agreement at φ = 1.3 for temperatures below 1900 K while above 1900 K the calculated α are still lower than measured, and at φ = 1.5 all calculated coefficients α lie above those measured. Moreover, even this relatively modest (30%) variation of the reaction (R7.2) rate constant significantly changes other flame parameters. For example, the calculated free burning velocity for the methane-air flame at φ = 1.43 in this case is 15.0 cm/s, which is 20% higher than measured in [137].
139
Based on the NO sensitivity analyses we can conclude that varying the rate constants in the GRI-Mech 3.0 is not capable of improving the quantitative agreement between experiment and calculations. The improvement can be reached only by reconsidering the key channels for the formation and destruction of the nitric oxide. It should be pointed out that after releasing GRI-Mech 3.0 a significant amount of new information about the chemical reactions in the C/H/N/O system became available. For example, at the present time there is both theoretical and experimental evidence that the reaction CH+N2 has alternative products, namely H and NCN (Chapter 1). Further, the fate of HCNO which is the product of the reaction (R7.7) needs to be clarified [138]. This new kinetic information should be incorporated in the comprehensive mechanism of the NO formation and destruction in hydrocarbons flames and we hope that the experimental data presented here will be useful in performing this task. This Chapter presented the extension of the work reported in the previous Chapter. Here we examined the temperature dependence of the reburning of the nitric oxide in atmospheric-pressure flat CH4/N2/Air flames (φ = 1,0 1.3, 1.4 and 1.5) seeded with low concentrations of NO. The experimental data were compared with the model predictions.
140
Summary
In recent years, increasingly stringent regulations for NOx emissions have been a driving force behind the development of new sophisticated combustion technologies. A better understanding of pollutant formation mechanisms is essential for developing of control strategies yielding the lowest emissions. By comparing measured NO concentration with the results of numerical models, this thesis provides new insight into NO formation and consumption in flat, burner-stabilized methane/air and hydrogen/air flames at atmospheric pressure. Special attention is paid to the fuel-rich methane-air flames occurring in a wide variety of practical systems. In these flames, NO formation is dominated by the Fenimore mechanism, which is the most complex and least well understood of the known NO formation routes. The experimental results are compared with the predictions of one-dimensional flame calculations, using the GRI-Mech 3.0 chemical mechanism, in which the energy equation is solved. In addition, the experimental data with quantified uncertainty presented in this thesis can serve as targets for developing and optimizing chemical mechanisms and for testing the predictive power of flame models. Accurate local temperature measurements are necessary to derive NO concentrations, and are also essential for obtaining meaningful comparison with the model calculations. In the experiments described in this thesis, coherent anti-Stokes’ Raman scattering is used to measure the flame temperature; the accuracy of the CARS temperature measurements is better than 50 K for all flames studied, as shown in Chapter 3. The main body of the temperature database is summarized in Chapters 4 and 6. Chapter 4 reports the effects of varying the degree of burner stabilization and preheating on flame temperatures. Excellent agreement between the experimental results and one-dimensional model predictions over a wide range of conditions illustrates the predictive power of GRI-Mech in burning velocity calculations. The faithful reproduction of the temperature profiles is necessary for the comparison between the measured and calculated NO concentrations, and increases our confidence that the possible disagreement between them is only due to uncertainties in the NO formation chemistry. Chapter 4 also shows that the variation in flame temperature (over 700 K) with mass flux and preheating in burner-stabilized flames can be useful for mechanism optimization with respect to burning velocity. Due to the high accuracy of the temperature measurements, the data are also capable of discerning differences in reaction rate coefficients substantially smaller than their current uncertainty. It is further shown that at constant mass flux and equivalence ratio the flame temperature is independent of the degree of preheating. To provide the both accuracy and highest spatial resolution in the experimental results, laser-induced fluorescence, which has proved to be the best method for quantitative measurement of NO, is used for the determination of the nitric oxide concentration. The calibration procedure required for quantification of the experimental data was supported by a combination of pulsed CRDS, CARS and LIF, discussed in Chapter 5. Measurements of NO by CRDS in atmospheric-pressure methane-air flames are frustrated by strong broadband absorption by hot CO2 molecules, which increases the NO detectability limit to several thousand ppm. In hydrogen-air flames, this broadband absorption is substantially lower, yielding an NO detectability limit of the order of 10
141
ppm. The absolute NO concentration in methane/air flames is calibrated using the measured intensities of seeded and non-seeded, near-adiabatic, stoichiometric flames. In Chapter 6, the effects of preheating on NO formation in laminar, rich-premixed, methane-air flames (φ = 1.3, 1.5 and 1.6) are examined, and contrasted with the results obtained on preheated stoichiometric flames. Varying the initial mixture temperature in the range 300-700 K, we observe differing degrees of growth in the NO mole fraction with increasing temperature for the different equivalence ratios studied. When plotted as a function of flame temperature, the stoichiometric flames show the exponential growth expected from the Zeldovich mechanism. At φ = 1.5 and 1.6, the NO is entirely produced via the Fenimore mechanism, and is seen to increase by a factor of 9- 10 within 200 K or less, much more steeply than for the stoichiometric conditions. At φ = 1.3, the NO mole fraction, formed through the Fenimore mechanism, grows by less than a factor of 2 over a region of more than 400 K. At flame temperatures above ~ 2250 K, the O + N2 reaction initiates significant NO production at this equivalence ratio. Comparison with the results calculated for thermodynamic equilibrium shows that over a wide range of conditions the NO mole fraction in the hot gases of rich-premixed flames is “superequilibrium”, in stark contrast with stoichiometric flames, and that relaxation processes for achieving equilibrium are very slow, even at temperatures as high as 2200 K. Calculations using GRI-Mech 3.0 predict the effects of preheating in the stoichiometric flames well, both qualitatively and quantitatively. The predictions at φ = 1.3 are in good qualitative agreement with the measurements, but are ~ 60% too high for most of the flames examined. At φ = 1.5 and 1.6, the variation of the NO mole fraction at 5 and 10 mm, respectively, plotted as a function of flame temperature is well predicted. However, comparisons of the NO profiles point to significant discrepancies. Whereas all of the measured NO profiles are flat (temperatures < 2000K) or experience modest increase (temperatures > 2000K), the calculated profiles show considerably steeper rise in the NO mole fraction. This is most likely due to inadequacies in the predicted conversion of HCN→ NO. With an eye towards low-NOx combustion equipment, the results at φ ≥ 1.5 are encouraging for further investigation. The data obtained at a given equivalence ratio and at different degrees of preheating and stabilization show that the NO mole fraction at a given flame temperature is independent of how the final temperature is obtained. Chapter 7 provides an extension of the measurements reported in Chapter 6, and discussed the fate of NO seeded in the unburned gas-air mixture in atmospheric-pressure flat CH4/N2/Air flames (φ = 1,0 1.3, 1.4 and 1.5). For the analysis of the experimental data the normalized difference between the NO concentrations in seeded and non-seeded flames is introduced, rather than a traditionally employed reburn coefficient. The advantage of using this normalized difference is its independence from the axial position in high-temperature flames, and the cancellation of the background signal when it is calculated from the measured LIF signals. The calculations qualitatively predict the measured NO profiles well. Non-monotonic behavior of the measured and calculated NO profiles close to the flame front is observed in the seeded free flames. When plotted as a function of flame temperature, the “normalized difference” is underestimated at φ = 1.3 and 1.4 while at φ = 1.5 excellent agreement between the calculations and measurements is observed. This underestimation improves with decreasing flame temperatures. The reason for this disagreement is probably due to the underestimation of the conversion of HCN and NH3 back to NO in the calculations. 142
Samenvatting
De laatste jaren zijn de steeds stringenter wordende eisen ten aanzien van de NOxemissie de drijvende kracht achter de ontwikkeling van nieuwe generaties verbrandingstechnologie. Verbeterd inzicht in de vormingsmechanismen van milieuschadelijke stoffen is essentieel voor het ontwikkelen van strategieën om de laagste emissies van deze stoffen te verwezenlijken. Door het vergelijken van gemeten concentraties van stikstofoxide met de resultaten van numerieke modellen levert dit proefschrift nieuwe inzichten in NO-vorming en –consumptie in vlakke brandergestabilieseerde methaan/lucht en waterstof/lucht vlammen bij atmosferische druk. Speciale aandacht wordt besteed aan brandstofrijke methaan-lucht vlammen, welke in een groot scala van praktische systemen voorkomen. In deze vlammen wordt NOvorming gedomineerd door het Fenimore mechanisme, dat de meest complexe en minst begrepen van de NO-vorming routes is. De experimentele resultaten worden vergeleken met voorspellingen van eendimensionale vlam berekeningen op basis van het GRI-Mech 3.0 chemisch mechanisme. Daarnaast kunnen de experimentele data in dit proefschrift, waarbij de data voorzien zijn van bekende onzekerheidsgrenzen, worden als “targets” gebruikt voor het ontwikkelen en optimaliseren van chemische mechanismen alsmede voor het testen van het voorspellende vermogen van vlammodellen. Nauwkeurige locale temperatuursmetingen zijn noodzakelijk voor het verkrijgen van NO-concentraties en zijn essentieel voor betekenisvolle vergelijkingen met model berekeningen. In het onderzoek dat in dit proefschrift wordt beschreven wordt coherent anti-Stokes’ Raman scattering (CARS) gebruikt voor het meten van de vlamtemperatuur; de nauwkeurigheid van de met CARS bepaalde temperatuur was beter dan 50 K voor alle bestudeerde vlammen, zoals in Hoofdstuk 3 wordt besproken. In Hoofdstuk 4 worden de effecten van het variëren van de mate van branderstabilisatie en voorverwarming op de vlamtemperatuur vermeld. De uitstekende overeenkomst tussen de experimenteel verkregen resultaten en eendimensionale modelberekeningen voor een grote verscheidenheid aan condities, illustreert het voorspellende vermogen van GRI Mech in het berekenen van verschijnselen die aan de verbrandingssnelheid zijn gelieerd. De zeer goede overeenkomst tussen de berekende en voorspelde temperatuursprofielen is een voorwaarde voor de vergelijking tussen gemeten en berekende NO concentraties, en geeft vertrouwen dat waargenomen verschillen voornamelijk toe te wijzen zijn aan onnauwkeurigheden in de chemie van NO-vorming zelf. Hoofdstuk 4 toont ook dat de variatie in vlamtemperatuur (meer dan 700 K) verkregen door het variëren van de massaflux en de voorverwarming in brandergestabiliseerde vlammen bruikbaar kan zijn voor het optimaliseren van chemische mechanismen in relatie tot de verbrandingssnelheid. Dankzij de hoge nauwkeurigheid van de temperatuursmetingen is het mogelijk de gevolgen van veranderingen in de grootte van reactie snelheidsconstanten waar te nemen die substantieel kleiner zijn dan hun huidige onzekerheid. Verder wordt aangetoond dat bij constante massaflux en equivalentieverhouding, de vlamtemperatuur onafhankelijk is van de mate van voorverwarming (zie tevens Hoofdstuk 1) Voor de hoogste nauwkeurigheid en ruimtelijke resolutie van de experimentele resultaten wordt laser-geïnduceerde fluorescentie (LIF), die zich bewezen heeft als beste methode voor kwantitatieve metingen van NO, gebruikt voor het meten van de NOconcentratie. De calibratiemethode, die voor het verkrijgen van absolute concentraties uit
143
de LIF-data toegepast wordt, is onderbouwd door CRDS-, CARS- en LIF-metingen, die in Hoofdstuk 5 zijn besproken. NO-metingen met behulp van CRDS in methaan/lucht vlammen bij atmosferische druk worden gefrustreerd door sterke breedband absorptie van hete CO2-molekulen, die de NO-detectielimiet verhoogt tot enkele duizenden ppms. In waterstof/lucht vlammen is deze breedband absorptie substantieel minder en wordt een NO-detectielimiet in de order van 10 ppm verkregen. De absolute NO-concentratie in methaan-lucht vlammen worden gecalibreerd door gebruik te maken van gemeten LIFintensiteiten in stoichiometrische bijna-adiabatische vlammen, met en zonder toegevoegd NO. In Hoofdstuk 6 zijn de effecten bestudeerd van voorverwarming van het brandstof/lucht mengsel op NO-vorming in laminaire, brandstofrijke voorgemengde methaan-lucht vlammen (φ =1.3, 1.5 en 1.6). De resultaten tonen andere tendensen in vergelijking met de resultaten verkregen in voorverwarmde stoichiometrische vlammen. Door de mengseltemperatuur te variëren van 300 tot 700 K worden verschillen in de groei in de NO molfracties bij toenemende temperatuur voor verschillende equivalentie verhoudingen gezien. Wanneer de resultaten als functie van de vlamtemperatuur worden uitgezet, tonen de stoichiometrische vlammen een op basis van het Zeldovich mechanisme verwachte exponentiele groei. Voor φ =1.5 en 1.6, wordt de NO volledig gevormd volgens het Fenimore mechanisme en is een toename in NO-molfractie met een factor 9-10 waargenomen bij een toename in temperatuur van minder dan 200 K; dit is veel steiler gezien bij φ = 1. Bij φ = 1.3, groeit de NO-molfractie, gevormd via het Fenimore mechanisme, minder dan een factor 2 over een gebied van meer dan 400 K. Bij vlamtemperaturen boven de ~2250 K initieert de reactie O+N2 een significante NOproductie. Een vergelijking met de resultaten berekend op basis van thermodynamisch evenwicht laat over een grote verscheidenheid aan condities zien dat de NO-molfractie in de hete gassen van de brandstofrijke voorgemengde vlammen in “superevenwicht” is, dit in sterk contrast met stoichiometrische vlammen, en dat relaxatie processen naar evenwicht erg langzaam zijn, zelfs bij temperaturen van 2200 K. De berekeningen met behulp van GRI Mech 3.0 voorspellen de effecten van voorverwarming in stoichiometrische vlammen goed, zowel kwantitatief als kwalitatief. De voorspellingen voor φ=1.3 tonen een goede kwalitatieve overeenkomst, maar zijn ~ 60% te hoog voor het merendeel van de bestudeerde vlammen. Bij φ = 1.5 en 1.6, worden de NO molfracties op respectievelijk 5 en 10 mm als functie van de vlamtemperatuur goed voorspeld. Desalniettemin, laten vergelijkingen van de NO-profielen significante verschillen zien. Terwijl alle gemeten NO-profielen vlak zijn (bij temperaturen 2000 K), tonen de berekende profielen een aanzienlijke stijging in de NO-molfractie. Dit wordt waarschijnlijk veroorzaakt door tekortkomingen in de voorspelde conversie van HCN→NO. Met het oog op lage NOx verbrandingssystemen, zijn de resultaten bij φ ≥ 1.5 bemoedigend voor praktische toepassingen. De data verkregen bij een gegeven equivalentieverhouding en bij variërende voorverwarming en branderstabilisatie tonen aan dat de NO-molfractie alleen afhankelijk is van de eindtemperatuur. Hoofdstuk 7 vult de metingen vermeld in Hoofdstuk 6 aan, en bespreekt het lot van NO dat aan het brandstof-luchtmengsel is toegevoegd in vlakke CH4/N2/lucht vlammen (φ=1.0, 1.3, 1.4 en 1.5) bij atmosferische druk. Om de experimentele data te analyseren is het genormaliseerde verschil tussen de NO-concentraties in de vlammen met en zonder
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toegevoegde NO geïntroduceerd, in plaats van het in de literatuur toegepaste ‘reburn’ coëfficiënt. Het voordeel van het genormaliseerde verschil zijn onafhankelijkheid van de axiale positie in de vlammen met hoge temperatuur, en het wegvallen van de noodzaak om het achtergrondsignaal te meten wanneer het genormaliseerde verschil berekend wordt op basis van de gemeten LIF signalen. De berekeningen voorspellen de gemeten NO profielen kwalitatief goed. Een niet-monotoon gedrag van de gemeten en berekende NO-profielen dichtbij het vlamfront wordt geobserveerd in vrije vlammen met NOtoevoeging. Wanneer het genormaliseerde verschil wordt uitgezet tegen de vlamtemperatuur, onderschatten de berekeningen de resultaten voor φ =1.3 en 1.4, terwijl voor φ = 1.5 een uitstekende overeenkomst tussen berekeningen en metingen is te zien. Deze onderschatting verbetert met afnemende temperatuur. De reden voor de te lage voorspellingen kan waarschijnlijk worden toegeschreven aan het onderschatten van de conversie van HCN en NH3 terug naar NO.
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