Numerical Investigation of the different Spray combustion Models

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 18 (2016) pp 9393-9399 © Research India Publications. http://www.ripublication.com

Numerical Investigation of the Different Spray Combustion Models under Diesel Condition F. Lakhfif1*,1, Z. Nemouchi2, F. Mebarek-Oudina1 1

*Department of Physics, Faculty of Science, University 20 Aout1955- Skikda, B.P 26 Skikda 21000, Algeria. 2 Department of Mechanical Engineering, University of Constantine 1 Algeria.

off length, are compared with the experimental spray data from the literature engine combustion network (ECN). Results show the ability of this reaction mechanism with two components and this model, to predict the main characteristics of Diesel flame, even to make changes of secondary break-up models, with some limit, and show the agreement with experimental data. The results show so the effects of various break-up models on combustion spray characteristics.

Abstract In this paper, a CFD open-source platform has been developed to evaluate the potential of integrating detailed chemistry of two components into different spray models under Diesel engine conditions. In this simulation, Diesel fuels have been represented by two components (n-heptane and toluene), with a skeletal mechanism which involves 68 species and 280 reactions. There are three spray models implemented: the ETAB (Enhanced TAB), the Cascade Atomization and Drop Break-up (CAB) and the Kelvin-Helmholtz and RayleighTaylor (KH-RT) break-up models. Then, the results obtained of the main characteristics of Diesel flame such as liquid length, vapour penetration, ignition delay time, and flame lift-

Keywords: Break-up models; tip penetration; Diesel fuel; spray combustion; reaction mechanism.

NOMENCLATURE. Symbols : We

Greek symbols

Subscript

Weber number, m²

ρ

density, (kg/m )

g

CD

drag coefficient

τ

characteristic time (s)

l

liquid

R

radius (m) mixture concentration:

reaction rate surface tension (N/m)

chemical

C

 

ch mix

mixing

µ

dynamic viscosity (kg/ms)

y

deformation velocity deformation paramter

ω

droplet oscillation frequency

Ω

wavelength rate

Λ

perturbation growth rate

x

3

ABBREVIATIONS ETAB

Enhanced TAB

CAB

Cascade Atomization and Drop Break-up

KH-RT

Kelvin-Helmholtz and Rayleigh-Taylor

ECN

Engine Combustion Network

LTC

Low Temperature Combustion

LOL

Lift Of Flame lenght

SMD

Sauter Mean Diameter

PaSR

Partially Stirred Reactor

Ta

Taylor number

Oh

Ohnesorge number

gaz

1. INTRODUCTION The fuel spray process is important for the combustion and emission formation in direct injection Diesel engines. In particular, the droplet size and heating are considered to be one of the major factors in determining combustion performance. The description of the break up mechanisms is a challenging problem. It requires complex mathematical formulations of the instabilities that occur in an interface between phases in a flow. These are usually the result of the instabilities of Rayleigh-Taylor (RT), or of Kelvin-Helmholtz (KH) type. in secondary atomization, five distinct modes of droplet breakup were proposed by (Pilch et al , 1987).And Many numerical models have been proposed, where the classic break-up models TAB (Taylor Analogy Break-up), RD (Reitz and Diwakar) and WAVE do not incorporate the break-up modes ( Reitz , 1996). A different approach to the modeling of the primary break-up is incorporated in the Enhanced Taylor

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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 18 (2016) pp 9393-9399 © Research India Publications. http://www.ripublication.com Analogy Break-up (ETAB) model introduced for nonevaporating sprays by Tanner (Tanner, 1997). and later, the CAB model is an extention of the ETAB model, to model secondary break-up in the Stripping and in the Catastrophic regimes (Tanner, 2003). Recently, A complete analysis of the RD (Reitz and Diwakar), wave and KH-RT atomization and drop break-up models and compare the predictive capabilities of these models with respect to the experimental fuel spray of a heavy-duty diesel engine (Hossainpour et al, 2009). and the Infinite Thermal Conductivity (ITC) and Effective Thermal Conductivity (ETC) liquid phase models of heating and evaporating droplet, were explored using three droplet breakup models - the model Reitz and Diwakar (RD) , the WAVE model, and the TAB model, (Abdelghaffar et al, 2011).

MODELS Primary break-up: The aim of the primary break-up model is to provide all starting conditions for the calculation of secondary break-up, and to determine the distributions of size and velocity of droplets formed at the end of primary break-up These conditions are mainly affected by turbulence and cavitation

u0  C

2P

l

d   D0 Where D0 is orifice diameter and α represent cavitation parameter equal 0.44 in this study.

In order to provide accurate engine simulations, it’s necessary to use the detailed kinetics. Practical diesel fuels consist of a great number of aliphatic and aromatic compounds (Farrell et al, 2007), and their combustion is too complex to be modeled. Diesel fuels have been represented by n-heptane as a surrogate (Kong, 2007; Som et al, 2010). The chemical mechanism were used the reduced n-heptane oxidation chemistry, with the detailed kinetics of aromatics up to four aromatic rings, (Golovitchev et al, 1999; Sing, 2006) and to predict the details of the flame structure and emissions for the (low temperature combustion) LTC conditions. Further, n-dodecane is more suitable than n-heptane as a surrogate component for diesel, and their skeletal mechanism are developed (Westbrook, 2009; Zhaoyu, 2014), the interaction turbulence combustion was modelled by the Partially Stirred Reactor (PaSR) concept (Karlsson et al, 1995). And this model was further developed (Nordin, 2001).

Secondary break-up The Enhanced TAB Model The enhanced TAB (ETAB) model (Tanner, 1997), uses the droplet deformation dynamics of the standard TAB model, but the droplet disintegration is modeled by an exponential law which relates the mean product droplet size to the break-up time of the parent drop. This assumption leads to: dm  3K br m dt The break-up constant Kbr depends on the break-up regime and is given by parent drop properties only. Bag break-up occurs if We Wet, with Wet is the regime-dividing Weber number. In fact,

 k1 K br    k2 We

Engine combustion network (ECN) provides an experimental database for diesel spray at various conditions in the constant volume vessel (Pickett et al, 2012; Meijer et al, 2012; Kastengren et al, 2013). Whose aim is to enhance the knowledge of the physics of spray as well as validation of numerical models (Bogin et al, 2009). The ECN has identified the so-called spray-A condition a priority for performing numerical simulations. Modeling spray-A is important because n-Dodecane, which is a reasonable surrogate for diesel fuel, is used in this spray (Jangi et al, 2015), recentely, Wang, H et al are developed heptane and toluene mechanism to prediction combustion and soot, The final mechanism consists of 71 species and 360 reactions (Wang et al, 2013), Malaguti, S et al. simulate diesel fuel with the five compononts of reacting Diesel sprays (Malaguti et al, 2014).

if We  Wet (bag breakup) if We  Wet (stripping breakup)

The values for k1 and k2 have been determined to match the drop sizes and velocities from the experimental results. In the present computations break-up regimeWet is set to default value at 81. The uniform distribution becomes r  exp(  K br t ) a Where a and r are the radii of the parent and product drops, respectively. Also, the product droplets are initially supplied with a velocity component perpendicular to the path of the

 where A is a parent drop with a value v  A.x constant determined from an energy balance consideration. Where the value of A gives A = 0.69. This indicates that only 70% of the parent drop deformation velocity goes into the normal velocity component of the product droplets. The break-up length, L, of a high velocity liquid jet injected into a gas  g  l is given by the correlation

In the present work, the CFD code has been used the detailed chemical kinetics of n-heptane and toluene and applied to predict the effects of several break-up models on the main characteristics of a diesel spray.especially, the ETAB (Enhanced TAB), the CAB and the KH-RT break-up models. And the mechanism consists of 68 species and 280 reactions. In order to verify the accuracy of the results, the obtained numerical results are compared with the experimental results performed at ECN.

L  u 0 t bu  C

l d0 g

Where do is the nozzle diameter and uo the jet exit velocity.

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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 18 (2016) pp 9393-9399 © Research India Publications. http://www.ripublication.com The constant C is nozzle dependent and is usually determined from experiments. In this study, we set c=10.0, Bag Break-up Factor k1=0.2222 and Stripping Break-up Factor k2=0.2222

 RT  2C RT

Which gt and CRT are the acceleration in the direction of travel, and the constant of RT model.

The Cascade Atomization and Drop Break-up (CAB) model The Cascade Atomization and Drop Break-up Model CAB, is extension and development of the ETAB model (Tanner, 2003), The main difference being the definition of the breakup constant, these break-up regimes are classified with respect to increasing gas Weber number into the bag break-up regime (Wecrit< We < Webs), into the stripping break-up regime (Webs< We Wesc), where the regime-dividing Weber numbers are taken to be Webs = 80 and Wesc = 350. K br

k  1    k2 We  3 4  k3We

3 gt (l   g )

Combustion model Combustion model In this study, Diesel fuels have been represented by n-heptane and toluene, the chalmers mechanisme of reaction of nheptane and toluene (Golovitchev, 2008), was modified and we change their coefficient, finally the skeletal mechanism which involves 68 species and 280 reactions. The Partially Stirred Reactor (PaSR) combustion model developed by Golovitchev (Golovitchev et al, 2003), was used to model the combustion process. In the PaSR approach, a computational cell is split into two different zones, reaction zone and no reaction zone. The reaction zone is treated as a perfectly stirred reactor (PSR), in which all compositions are assumed to be perfectly mixed with each other. Three average concentrations, was the mean mixture concentration in the feed, reaction zone and at the exit of the reactor

if Wecri  We  Webs if Webs  We  Wesc if Wesc  We

In addition to the TAB model constants, the following user accessible model constants are available for the CAB breakup model. In this study, we set Bag Break-up Factor k1=0.05 and Stripping Break-up Factor k2=0.2222 and catastrophic Break-up Factor k3 =0.22222.

respectively c , c and c . The reaction rate of this computational cell is determined by the fraction of the reactor in this cell. It’s assumed to be proportional to the ratio of the chemical reaction time  ch to the total conversion time in the 0

The Kelvin-Helmholtz and Rayleigh-Taylor (KH-RT) model The KH-RT model (Patterson and Reitz, 1999;Beale and Reitz ,1998) was a combination of two instability analysis for liquid jets , KH and RT instabilities, where the KH instability was used for the primary break-up simulation and the RT instability were used for the secondary break-up simulation. This model was widely used for Diesel sprays. The perturbation growth rate  KH and wavelength  KH a break-up time and droplet diameter can be determined

 KH  9.02

3

 KH

rc  B0  KH

 KH 

reactor, the sum of the micro-mixing time time

Where

The model constant

 d r 3

 mix and

reaction

 ch  ch   mix

 mix  cmix k /  cmix was set to 0.03 , This constant can,

however, vary between 0.001-0.3, depending on the flow condition. The reaction time was derived from the laminar reaction rate. Thus, the overall reaction rate  and the homogeneous reaction rate  of this computational cell have the relationship.

The break-up time is than given by

3.726 B1r  KH  KH

The rate of change of the radius of the calculated using

 ch ,

k* 

r (1  0.45oh 0.5 )(1  0.4Ta 0.7 ) (1  0.865We1.67 ) 0.6

(0.34  0.38We 2 )  (1  Oh)(1  1.4Ta 0.6 )

1

c1  c 0    k * dt

parent parcel is

SOOT The soot formation mechanism (Golovitchev et al, 1999), consists of a series of elementary reaction steps leading from acetylene and hydrogen to the formation of first aromatic ring A1. Reaction leading to the formation of phenyl A1 radical and the first aromatic ring is followed by successive stages of H abstraction C2H2 addition (HACA mechanism), thus, yielding, a chain of aromatic rings. Toluene can form A1 without the presence of acetylene. The incipient soot was formed from

dr r  rc  dt  KH In the RT model, the frequency of the fastest growing wave is given by

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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 18 (2016) pp 9393-9399 © Research India Publications. http://www.ripublication.com long chain acetylene C6H2 “graphitization” process. C6 H 2   H 2  6C ( s)

and

acenaphthylene

via

A2 R5   4 H 2  12C( s ) Heat transfert: The corrélation of Ranz and Marshall has been corrected to include the effect of distortion of droplet (Arcoumanis et al, 1997)

Figure 1: Penetration lengths of the liquid with various breakup models and experimental data 3. RESULTS AND DISCUSSION The simulations were performed using the KIVAII CFD which is modified to use CHEMKIN as the chemistry solver. The RNG–k–ε turbulence model was used for modeling turbulent mixing (Han and Reitz 1995). Chemical reactions were modeled using detailed chemistry coupled with CFD model (KIVA–CHEMKIN) proposed (Kong and Reitz, 2007). The chemistry was modeled using a skeletal reaction mechanism for n_heptane and toluene with 68 species and 280 reactions. In the KIVA–CHEMKIN model, NOx emissions are modeled using a reduced NOx chemistry that was derived from the GRI NOx mechanism. Finally, the computational model has been applied to simulate the overall combustion processes of at the ECN spray A. Details of operating conditions in the constant volume combustion chamber at Sandia National Laboratories are given in Tab. 1. The simulation carried out with a 2D structured axisymmetric mesh in order to reduce the computational time, which, furthermore, allowed a greater chemical reaction mechanism size. a mesh grid size 0.5×1 mm, and fixed time step 5.0E- 7 s.

Figure 2: Comparaison vapor fuel penetration with various break-up models and experimental data

Table 1: Details of operating conditions in the constant volume combustion chamber at ECN

Figure 3: Predicted Sauter Mean Diameter for different break-up models

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Figure 4: Comparaison of calculeted ignitiion delay time with various break-up models vs. experimental data for variation ambient temperature

Figure 7: the axisymmetric SOOT distributions at 1 ms, based on: a) KHRT,b) CAB and c) ETAB break-up models

Figure 5: Comparaison of predicted flame lift-off length with various break-up models vs. experimental data for variation ambient temperature

Figure 8: Effects of break-up models on soot formation

Figure 1 compares the tip penetration of liquid fuel using the different break up models and experimental data. As can be seen, the tip penetration of liquid increase with the time and tends to stabilize in value 10 mm, the ETAB, CAB and KHRT models can predicted the tip penetration of liquid, and their value tends to fluctuate around experiment data value. The results obtained are in agreement with experimental data reported by ECN. Figure 2 compares the tip penetration of vapor with the different break up models against experimental data of spray A. As can be seen, the tip penetration of vapor increase with the time, in the first part, the CAB and the ETAB models are better predicted the tip penetration of vapor than KH-RT model, the rate of fuel vaporization is higher in KH-RT model. And in the second part, after the intersection with curve of experimental data, the value of KH-RT model leds above experiment data than other models.

Figure 6: The axisymmetric simulated temperature contour plot at 1 ms, based on the a) KHRT,b) CAB and c) ETAB break-up models.

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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 18 (2016) pp 9393-9399 © Research India Publications. http://www.ripublication.com Figure 3 illustrates the SMD (Sauter mean diameter) in the different break up models, it can also be noted that the SMD tends to stabilize above values in the different break up models. The value of SMD is almost identical in the CAB and ETAB models and near value of the KH-RT model. In three models, the Particle frequency (SMD) is underestimated the nearly 13 μm.

CONCLUSION In This paper, the spray combustion has been simulated by a model based on reaction mechanism with two components, nheptane and toluene, with a skeletal mechanism which involves 68 species and 280 reactions and Re-Normalization Group (RNG) k-ε for turbulence model, the correction of Arcoumanis to include the effect of distortion of droplet for the heat transfer model. And the combustion process is described using the Partially Stirred Reactor (PaSR) model. This model applies to different break-up models (the ETAB (Enhanced TAB), the CAB and the KH-RT break-up models) under Diesel engine condition, and the effect of these models on spray characteristics was investigated. The results were validated and compared against the experiments ECN data for liquid length, vapor fuel penetration, ignition delay time, and flame lift-off length for variations in ambient temperature. The following conclusions are obtained: 1. The three fuel spray break-up models predict the penetration lengths of the liquid, and the results obtained are in agreement with experimental data. 2. The CAB and the ETAB models better predicted the tip penetration of vapor than KH-RT model against experimental data. 3. In three models, the particle frequency (SMD) is underestimated the nearly 15 μm 4. The reaction mechanisms give well predictions for ignition delay, even to make changes of the secondray break-up model. 5. The reaction mechanisms give well predictions for lift of flame length. 6. The initial ambient temperature has the greatest effect on the ignition delay and lift of flame length. 7. The effects of different models are sensed on combustion spray characteristics and the three fuel spray break-up models predicting different shape and spacial distribution of temperature and soot formation.

Figure 4 compares the Ignition delay plotted with the different break up models against experimental data of spray A. In this study the Ignition delay, has been defined as the time from start of injection to the time where the maximum temperature of the domain is when T ≥ 1900 K in a particular cell. Usually, coincides with appearance of OH. The initial ambient temperature has the greatest effect on the ignition delay process by increasing all of the reaction rates involved in ignition and the Ignition delay décrease with high temperature, the three break-up models shows a good agreement against expiremental data for 900 and 1100 k the initial ambienttemperature, and the for 800 k has sensor difference with ignition delay calculeted with various models against expiremental data. . Figure 5 compares the Lift-of flame length plotted with various break up models against experimental data. The Liftof flame length has been defined as the length from the injector to the closest layer where OH mass fraction reaches 0.03%. The high initial ambient temperature, décrease the Lift-of flame length (LOL). The resultats shows various break-up models in a good agreement against expiremental data. Figure 6 shows the predicted of SOOT versus time based on the ETAB, CAB and KH-RT break-up models. The predicted of SOOT, using the ETAB appear higher than the values obtained with the CAB or TAB models. The observed SOOT profiles reflect the effects of heat release, heat transfer Figure 7 shows the axisymmetric temperature distributions based on the ETAB, CAB and KH-RT break-up models. The left t parts plots the ETAB model and the CAB model in middle, the parts righ displays KH-RT model .The results are presented as iso-contours of temperature for different moments after injection. The different shapes are presented, where the CAB model show champignon shape, and different than the ETAB or KH-RT models.The KH-RT model is associated with longer shape distribution than other break up models, This can be attributed to the fact of the penetration lengths of the vapor fuel and droplet heating.

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