Accepted Manuscript Computational Fluid Dynamics Modeling and Experimental Validation of Heat Transfer and Fluid Flow in the Recovery Boiler Superheater Region Viljami Maakala, Mika Järvinen, Ville Vuorinen PII: DOI: Reference:
S1359-4311(18)30358-2 https://doi.org/10.1016/j.applthermaleng.2018.04.084 ATE 12081
To appear in:
Applied Thermal Engineering
Received Date: Accepted Date:
16 January 2018 16 April 2018
Please cite this article as: V. Maakala, M. Järvinen, V. Vuorinen, Computational Fluid Dynamics Modeling and Experimental Validation of Heat Transfer and Fluid Flow in the Recovery Boiler Superheater Region, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.04.084
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Computational Fluid Dynamics Modeling and Experimental Validation of Heat Transfer and Fluid Flow in the Recovery Boiler Superheater Region Viljami Maakalaa,∗, Mika J¨arvinenb , Ville Vuorinenb b Aalto
a Andritz, Helsinki, Finland University, Department of Mechanical Engineering, Espoo, Finland
Abstract Development of predictive computational fluid dynamics (CFD) methods for recovery boilers would be highly beneficial for the development of such very large-scale energy production applications. Herein, unique experimental data is compared with a developed CFD framework demonstrating the predictive character of the present simulations. The novelty of the work consists of the following: 1) We report two sets of previously unpublished full-scale temperature and flow field measurements from the recovery boiler superheater region. The data from these challenging measurements is very valuable, since reported experimental data on recovery boilers is scarce in literature. 2) We introduce a detailed, three-dimensional CFD model for the recovery boiler superheater region. The results of the model are verified computationally and validated with the experimental data. 3) We demonstrate the added-value of the developed CFD model with a detailed analysis of the three-dimensional flow field and heat transfer results. In addition, we consider the implications of the three-dimensional solution for the estimation of fouling. Keywords: heat transfer, efficiency, measurements, computational fluid dynamics, recovery boiler
1. Introduction Recovery boilers are an integral part of the chemical recovery cycle of pulp mills. Such boilers are utilized to combust black liquor, which contains the cooking chemicals along with lignin and other organic compounds separated from the wood during the pulping process. The two main functions of recovery boilers are to regenerate the chemicals, such that they can be re-used in the pulping process, and to generate high-pressure steam for heat and power generation. Black liquor is considered a renewable fuel, since its combustible part originates from wood, and thus recovery boilers are an important source of renewable energy. Figure 1 shows a modern, high-capacity recovery boiler. The global production of chemical kraft pulp is approximately 130 million air dry tonnes per year and it is expected to grow by approximately 1% per year (P¨oyry, 2015). The production of one tonne of air dry pulp produces one and a half tonnes of dry black liquor solids. This means that 195 million tonnes of dry black liquor solids are combusted in recovery boilers every year. In terms of energy, this is 731 TWh per year, assuming a typical higher heating value of 13.5 MJ/kg for the dry black liquor solids. Most of the energy generated in the recovery boilers is utilized for the process purposes of the pulp mills, but especially modern units generate substantial amounts of additional energy, which can be utilized for supplying renewable electricity to the power grid. As an example, in Finland in 2016, 8% of total electricity and 18% of renewable electricity
Figure 1: A modern, high-capacity recovery boiler. The boiler consists of two main sections: a furnace section and a heat transfer section, which are separated by the nose. The superheater region, which is the focus of this work, is highlighted. High-capacity recovery boilers are physically large, even 20 m wide, 20 m deep, and 80 m high.
author. Email: [email protected]
Preprint submitted to Applied Thermal Engineering
April 13, 2018
Nomenclature f~ ~g ~u Dn, eff eavg h h hn Jn k kfluid kgas kint l Nu p p q qconv qrad r r Rn Re sdeposit S rad stube
body force [N] gravitational acceleration [m/s2 ] velocity [m/s] effective diffusivity of the species n [m2 /s] average relative error [%] representative cell size [mm] sensible enthalpy [J/kg] sensible enthalpy of the species n [J/kg] diffusion flux of the species n [kg/(m2 s)] turbulent kinetic energy [m2 /s2 ] inner tube surface to water/steam heat transfer coefficient [W/(m2 K)] flue gas side convective heat transfer coefficient [W/(m2 K)] water/steam side (internal) heat transfer coefficient [W/(m2 K)] characteristic length [m] Nusselt number [-] apparent order of the discretization method [-] pressure [Pa] surface heat flux [W/m2 ] convection heat flux [W/m2 ] radiation heat flux [W/m2 ] refinement ratio [-] tube radius [m] source of the species n from chemical reactions [kg/(m3 s)] Reynolds number [-] deposit thickness [m] radiation source term [W/m3 ] tube thickness [m]
T T gas T int T surface T 15 T 70 y+ Yn GCIavg
temperature [K] flue gas temperature [K] water/steam side (internal) temperature [K] surface temperature [K] sticky temperature [K] flow temperature [K] dimensionless wall distance [-] mass fraction of the species n [-] average grid convergence index [%]
Greek Symbols λ thermal conductivity [W/(mK)] λdeposit deposit thermal conductivity [W/(mK)] λeff effective thermal conductivity [W/(mK)] λtube tube thermal conductivity [W/(mK)] µeff effective viscosity [kg/(ms)] ρ density [kg/m3 ] Abbreviations CFD computational fluid dynamics ES equiangle skewness FSR full superheater region GCI grid convergence index HHV higher heating value NHV net heating value OQ orthogonal quality RANS Reynolds-averaged Navier-Stokes SH superheater SSR slice superheater region
was produced by black liquor combustion in recovery boilers (Statistics Finland, 2017).
(2012) studied the causes for asymmetric furnace temperatures using CFD modeling and compared the results against validation measurements. Bergroth et al. (2010) and Engblom et al. (2010a) focused on understanding the physical and chemical phenomena occuring in combustion on the char bed, which is located at the bottom of the furnace, and developed a CFDbased model for the dynamic evolution of the char bed. Ferreira et al. (2010) utilized CFD modeling to study the effects of various combustion air injection schemes. Li et al. (2012) developed thermal boundary conditions for the furnace walls and compared CFD results against measurements. Multiple researchers have also focused on black liquor combustion. Walsh and Grace (1988), Frederick (1990), Saastamoinen (1996), and Verrill and Wessel (1998) have studied droplet combustion and published increasingly detailed CFD-applicable models. The most detailed CFD-applicable droplet combustion model upto-date has been developed by J¨arvinen et al. (2002, 2011). Our earlier work was also connected to combustion in the recovery boiler furnace (Maakala and Miikkulainen, 2015; Maakala et al., 2017).
In recent years, the global goals regarding the climate change mitigation have focused considerable attention on energy generation from renewable sources. Accordingly, the traditional role of the recovery boilers as chemical recovery units is changing, and focus is shifting toward simultaneously maximizing the generation of renewable energy. To achieve these goals, it is important to understand the combustion and heat transfer processes of such boilers and to develop modeling methods for optimizing their efficiency. Computational fluid dynamics (CFD) modeling can be considered to be an established research tool for ensuring and optimizing the performance of recovery boilers, in both research organizations and industry. CFD modeling of recovery boilers was pioneered approximately 30 years ago when several research groups independently developed the first comprehensive CFD models for recovery boilers (Grace et al., 1989; Jones, 1989; Walsh, 1989; Sumnicht, 1989; Karvinen et al., 1991; Salcudean et al., 1993; Abdullah et al., 1994). Since then, the work has been continued and increasingly detailed recovery boiler CFD models have been developed (Blasiak et al., 1997; Wessel et al., 1997; Vakkilainen et al., 1998; Mueller et al., 2004; Jukola et al., 2014).
Several researchers have published data measured from recovery boilers and performed important validation work of CFD models. In addition to the previously mentioned, Grace et al. (1998), Saviharju et al. (2004, 2007), Brink et al. (2010), Miikkulainen et al. (2010), Vainio et al. (2010), and Engblom et al. (2010b) have contributed to model validation. However,
The main focus of the recent research has been the modeling of the furnace processes and combustion. Engblom et al. 2
the amount of published measurement data and validation work of recovery boiler CFD models is limited, since full-scale measurements on a recovery boiler are extremely challenging and time consuming. In addition, physical scale modeling of recovery boilers is impractical or even impossible. A considerable amount of CFD research has also been done in connection to coal-fired utility boilers. Yin et al. (2002, 2003) and He et al. (2007) simulated coal-fired boilers with a particular focus on the gas flow deviations and uneven wall temperatures in the upper furnace and crossover pass regions. Le Bris et al. (2007), D´ıez et al. (2008), and Choi and Kim (2009) simulated the combustion processes with a focus on the modeling of NOx emissions. Park et al. (2010), Edge et al. (2011), and Schuhbauer et al. (2014) studied the combustion processes and the steam cycle via coupled CFD-process simulations. Nikolopoulos et al. (2011) and Al-Abbas et al. (2012) simulated lignite-fired boilers under air-fired and oxy-fuel conditions. Drosatos et al. (2016) modeled a lignite-fired boiler under full load and various partial load conditions. Drosatos et al. (2014, 2017) presented decoupled simulations of the furnace and convective section in two lignite-fired boilers. In the present work, we mainly focus on the superheater region of the recovery boiler (see Figure 1). After combustion in the furnace, the hot flue gas flows to the superheater region. The purpose of the superheater region is to heat the high-pressure steam flowing inside the superheaters to a high temperature via heat transfer from the hot flue gas. Since approximately 30% of the recovered energy is captured through heat transfer to the superheaters, they are one of the largest and most important heat transfer surfaces in the recovery boiler. In addition, the performance of the superheaters is critical for the efficiency and availability of the whole recovery boiler power plant. Hence, it can be understood that the superheater region has been one of the focal research topics in the past. Vakkilainen et al. (1991, 1992) studied the optimal shape of the boiler nose using both physical and CFD modeling. Kawaji et al. (1995) developed a model for predicting heat transfer in the superheater region. Saviharju et al. (2004) modeled the superheater region in two recovery boilers and reported full-scale measurements for model validation. Lepp¨anen et al. (2014a) modeled the flow field in the superheater region and developed new deposition models. P´erez et al. (2016) developed a detailed CFD model for predicting deposition rates and shapes. Deposition has been the focus of other researchers as well, for example, Jokiniemi et al. (1996), Pyyk¨onen and Jokiniemi (2003), Wessel and Baxter (2003), and Weber et al. (2013). Our recent, ongoing work has also focused on better understanding of the superheater region. In Maakala et al. (2015), we utilized CFD modeling, optimization, and surrogate modeling to optimize heat transfer to the superheaters. Modeling of the heat transfer sections of boilers is challenging due to the very large dimensions and complex geometries. One of the standard modeling approaches is the distributed resistance method, also known as the porous media method, which was originally developed for the modeling of heat exchangers (Patankar and Spalding, 1974). In fact, this approach has been widely utilized for simulating various types of heat ex-
changers (Prithiviraj and Andrews, 1998a,b; Hayes et al., 2008; Shi et al., 2010; Kritikos et al., 2010; Yang et al., 2014). The distributed resistance method has often been utilized in boiler simulations in a simple manner with approximated pressure loss coefficients and predetermined volumetric heat sink values (Le Bris et al., 2007; D´ıez et al., 2008; Choi and Kim, 2009; Miikkulainen et al., 2010; Al-Abbas et al., 2012; Maakala and Miikkulainen, 2015). Yin et al. (2002, 2003) and He et al. (2007) modeled the first two superheaters as thin, constanttemperature platens and the rest of the superheaters and reheaters as porous media with predetermined pressure loss coefficients. Park et al. (2010) applied the distributed resistance method in a more sophisticated manner, such that the heat sink values were connected to a process simulation model. Drosatos et al. (2014, 2017) calculated the pressure loss coefficients from empirical correlations and solved the heat transfer using the macro heat exchanger model. Schuhbauer et al. (2014) utilized pressure loss coefficients based on design data and modeled heat transfer by considering convection and radiation separately. The convective coefficients were calculated from empirical Nusselt number correlations. The radiative coefficients were calculated based on the flue gas properties and particle load. In addition, the heat sink values were coupled with a process simulation model. The review by D´ıez et al. (2005) presents several heat transfer models for coal-fired boilers, many of which are applicable in the context of the distributed resistance method. The computational cost of the distributed resistance method is small and it is a reasonable simplification especially when the focus of the research is not a detailed solution in the heat transfer section. However, the distributed resistance method has several disadvantages. Paraphrasing Zhang et al. (2009), the three main drawbacks are: 1) many additional geometrical parameters, such as volumetric porosities and surface permeabilities, must be known, 2) distributed resistances and heat transfer coefficients must be provided from existing experimental correlations, and 3) detailed characteristics of flow and heat transfer on the flue gas side are not obtained as a part of the solution. In addition, as has been highlighted by Schuhbauer et al. (2014), the model does not correctly take into account the thermal radiation interaction between the flue gas and the porous media, since the tube surfaces are not physically present in the model. The three-dimensional slice model, also known as the slice superheater region (SSR) model, is another method which has been used, in particular, in recovery boiler simulations (Saviharju et al., 2004; Lepp¨anen et al., 2013, 2014a,b; Lepp¨anen and V¨alim¨aki, 2016; Maakala et al., 2015, 2016). This approach takes advantage of the repeating pattern of the superheater platens and considers only a thin slice of the full threedimensional geometry. This simplification can be considered valid for the central region of the heat transfer section when: 1) the effect of the side walls to the flow field can be considered minor, and 2) the flow field is even and not swirling at the furnace outlet. These conditions typically hold reasonably well in high-capacity recovery boilers, since they are physically wide and the combustion air is injected in a symmetric fashion from the front and rear walls, and a significant distance before 3
the furnace outlet. The three-dimensional slice model is adequate for a multitude of purposes but it does not fully resolve the complex three-dimensional flow structures, which are also connected to other processes, such as heat transfer, deposition, and fouling. Based on the presented literature review, we identify the following research gaps: 1) To the best of our knowledge, all of the previously published recovery boiler superheater region CFD models have considered only a thin slice of the full geometry or utilized the distributed resistance approach. A full three-dimensional model has not been developed and full threedimensional results have not been published. 2) The amount of experimental data, especially from full-scale measurements, available for recovery boiler model validation is small. Consequently, the amount of published validation studies is also small. 3) Understanding of the three-dimensional physical phenomena in the superheater region is limited. Because a full three-dimensional model has not been available, the complex three-dimensional character of the flow field is not known. In addition, it is not well-understood how the three-dimensional flow field phenomena affect processes such as heat transfer, deposition, and fouling. The purpose of this work is to improve the understanding of the complex three-dimensional physical phenomena in the recovery boiler superheater region. We present and validate a new CFD model which includes the full superheater region geometry and many state-of-the-art sub-models for describing the flow field, heat transfer, and special characteristics related to the recovery boiler process. Specifically, the main objectives of this work are:
values for the flow field at the nose level, when the flue gas enters the superheater region. The domain outlet is located well after the boiler bank region to ensure that the outlet boundary condition will not affect the solution in the superheater region. The boiler walls, rear wall screen, and boiler bank are so called boiling surfaces, which are used for boiling water into steam. Because of the phase change of water, temperature inside these surfaces is assumed to be constant. The superheaters 1A, 1B, 2, 3, and 4 are used for heating high-pressure steam to a high temperature. Thus, temperature of the steam flowing inside the superheaters depends on the heat transfer rate from the flue gas. The boundary conditions are described in more detail in the Subsection 2.3. Figure 2b shows an isometric view of the FSR model. Each heat transfer surface consists of a row of platens (in the zdirection). In reality, each platen consists of a number of tightly spaced tubes but in this work the geometry is simplified such that the individual tubes are not considered. Because the geometry is fully symmetric in the z-direction a symmetry boundary condition is used in the middle of the boiler. Figure 2c shows the slice superheater region (SSR) model which has been used in previous research (Saviharju et al., 2004; Lepp¨anen et al., 2013, 2014a,b; Lepp¨anen and V¨alim¨aki, 2016; Maakala et al., 2015, 2016). In the SSR model, only a single gap between two superheater platens is modeled in the z-direction by utilizing symmetry boundary conditions on both sides. This is a reasonable approach for obtaining the solution in the central part of the boiler but no information is obtained about three-dimensional flow phenomena or variation of the fields in the z-direction. The present FSR model is thus a significant improvement compared to the SSR model. In addition to the extended domain, the FSR model includes many state-of-the-art sub-models for describing the flow field, heat transfer, and special characteristics related to the recovery boiler process, which have not been utilized in the previous superheater region models. These sub-models are described in the following subsections.
1. Presenting a detailed, three-dimensional CFD model for the recovery boiler superheater region, called the full superheater region (FSR) model. 2. Reporting two sets of previously unpublished full-scale temperature and flow field measurements from the recovery boiler superheater region. The data from these challenging measurements is very valuable, since the amount of reported experimental data from recovery boilers is small. 3. Verifying the results of the FSR model computationally and validating them with the experimental data. 4. Showing the added-value of the FSR model by a detailed analysis of the three-dimensional flow field and heat transfer results and by discussing the implications of the threedimensional solution for the estimation of fouling.
2.2. Governing Equations and Modeling The full superheater region (FSR) model solves the governing equations for mass continuity, momentum, turbulence, species, energy, and radiation. The equations are solved in the steady-state, Reynolds-averaged form and incompressible flow is assumed. The mass continuity equation is ∂ρu j =0 ∂x j
2. Full Superheater Region CFD Model 2.1. General Description of the Model
where ρ is the density and u j are the components of velocity (tensor notation). The steady-state Navier-Stokes momentum equations are
Figure 2a shows the domain of the full superheater region (FSR) model. The part of the domain which is marked as the superheater region is the target of the accurate solution. It extends from the nose level to the beginning of the boiler bank area. The domain inlet is located well below the nose level for computational reasons, that is, for obtaining realistic, developed
∂ρu j ui ∂ ∂ui ∂u j ∂p 2 ∂ρk = (µeff ( + )) − − ∂x j ∂x j ∂x j ∂xi ∂xi 3 ∂xi + ρgi + fi 4
for i = 1, 2, 3
Figure 2: a) A side view of the domain of the full superheater region (FSR) model. Superheater is abbreviated as SH. b) An isometric view of the domain of the FSR model. The boiler walls are transparent to show the construction of the heat transfer surfaces (superheaters, rear wall screen, and boiler bank). c) The domain of the slice superheater region (SSR) model that has been used in previous research. A single gap between two superheater platens is modeled.
where µeff is the effective viscosity, p is the pressure, k is the turbulent kinetic energy, gi is the gravitational acceleration in the xi -direction, and fi are the other body forces in the xi -direction. The momentum equations are closed using the k-ω SST turbulence model (Menter, 1994). A pressure-based solver is used and the pressure-velocity coupling is implemented with the segregated SIMPLE scheme (Patankar and Spalding, 1972). The transport equations for the N species are
Even though species sources from chemical reactions are not included in this work, the species transport equations are included herein since they are considered to be a feature of the model. Therefore, additional species and chemical reactions can be readily included in future work. The additional computational cost associated with solving the scalar species transport equations is considered minor.
∂ρu j Yn ∂ ∂Yn = (ρDn,eff )+Rn for n = 1, 2, ..., N species (3) ∂x j ∂x j ∂x j
Table 1: The heat capacity functions used for the species. The functions are piecewise-polynomial with the form c p (T ) = α0 + α1 T + α2 T 2 + α3 T 3 + α4 T 4 . Species
where Yn is the mass fraction of the species n. Dn,eff is the effective species diffusivity and Rn is the species source from chemical reactions. The transport equations are solved for the gaseous water (H2 O), oxygen (O2 ), and carbon dioxide (CO2 ). The mass fraction of nitrogen (N2 ) is found by subtracting the mass fractions of the other species from one. The heat capacity, thermal conductivity, and viscosity of the individual species are functions of temperature (see Table 1). Mass-weighted species mixing laws are used for obtaining the local flue gas properties. The density of the flue gas is assumed to be a function of temperature by the ideal gas law. In the present work, combustion processes are assumed to be completed when the gas enters the superheater region, thus species sources from chemical reactions are not included. This assumption has been confirmed in multiple measurement campaigns (see, e.g., Saviharju et al. (2004) for experimental data from four recovery boilers).
Range: 300 ≤ T < 1000 [K] H2 O 1.563e+3 1.604e+0 O2 8.348e+2 2.930e−1 CO2 4.299e+2 1.874e+0 N2 9.790e+2 4.180e−1 Range: 1000 ≤ T < 5000 [K] H2 O 1.233e+3 1.411e+0 O2 9.608e+2 1.594e−1 CO2 8.414e+2 5.932e−1 N2 8.686e+2 4.416e−1
−2.933e−3 −1.496e−4 −1.966e−3 −1.176e−3
3.216e−6 3.414e−7 1.297e−6 1.674e−6
−1.157e−9 −2.278e−10 −4.000e−10 −7.256e−10
−4.029e−4 −3.271e−5 −2.415e−4 −1.687e−4
5.543e−8 4.613e−9 4.523e−8 2.997e−8
−2.950e−12 −2.953e−13 −3.153e−12 −2.004e−12
The particle phase in the recovery boiler superheater region can be considered to consist of carryover (combusted black liquor droplets) and of fume (condensed sodium and potassium 5
salts). In this work, the average carryover concentration was measured to be 1.1 g/Nm3 , which is in line with values reported in Vakkilainen (2005). The fume concentration is approximated to be 15.6 g/Nm3 , according to the work of Mikkanen et al. (1999). Based on these values, the total volume fraction of the particles is approximately 1.4 × 10−6 and the particle loading ratio is approximately 1.3 × 10−2 (see Elghobashi (1994) and Di Giacinto et al. (1982) for details). Therefore, the effect of the particles on the flow field is considered minor and it is not included in the model. Since particle-based erosion is typically minor in recovery boilers (Vakkilainen, 2005), a one-way coupled solution of the particle tracks is not included in this work. The energy equation is N ∂ρu j h ∂ ∂T X = (λeff − hn Jn, j ) + S rad ∂x j ∂x j ∂x j n=1
where h is the sensible enthalpy, λeff is the effective thermal conductivity, T is the temperature, hn is the sensible enthalpy of the species n, Jn, j is the diffusion flux of the species n in the x j -direction, and S rad is the radiation source term. The term S rad is solved from the radiative transfer equation using the discrete ordinates method (Raithby and Chui, 1990). The non-gray weighted sum of gray gases method with five wavelength bands is used for the local flue gas radiation properties (Dorigon et al., 2013). The effect of the recovery boiler fume on radiation is taken into account by assuming that in the superheater region the fume consists mainly of sodium sulfate (Na2 SO4 ) particles with a diameter of 1 µm (McKeough and Janka, 2001). As was mentioned before, the fume particle concentration is approximated to be 15.6 g/Nm3 in the flue gas (Mikkanen et al., 1999). The contribution of the fume on the scattering coefficient is calculated with a model based on the work by Wessel et al. (2000). The effect of the fume on the absorption coefficient is neglected because it is considered to be minor compared to the effect of the flue gas itself (Wessel et al., 2000). The equations are solved using a commercial CFD solver and the sub-models are programmed as user-defined functions. The computational grids used are block-structured and comprised entirely of hexahedral cells (Figure 3). Local mesh refinements are handled via the standard 2:1 cell splitting approach. The ICEM CFD program is used for grid generation. Details of the numerical grids are reported in Subsection 4.1 together with the results of the model verification.
Figure 3: The final computational grid from the side. The cell sizes are shown in the coordinate directions. The detailed view shows the mesh between the superheater platens. For visualization purposes, the resolution shown between the platens (z-direction) is only one-fourth (25 mm) of the final grid resolution (6.25 mm). The refinement region covers the superheater region (see Figure 2a), which is the area of interest in this work.
and because no detailed information about the inlet profiles is available, the inlet boundary conditions are set using constant profiles. In accordance with this approach, the inlet of the computational domain is located well below the nose level, for two reasons: 1) for obtaining a realistic, developed flow field for the flue gas at the nose level and 2) for reducing the sensitivity of the solution to the uncertainties in the selection of the inlet profiles. We consider the present approach acceptable for the purposes of this work but acknowledge that more detailed information regarding the inlet profiles could have increased the accuracy of the solution. The values of the boundary conditions are mainly based on the experimental data obtained from the measurement campaign, which include the boiler operating parameters (e.g., fuel flow and combustion air flow) and the measured values (e.g., fuel composition, flue gas composition, and steam flow and temperature before and after each superheater). Two sets of measurements, A and B, were taken on the boiler on different days. Accordingly, the boundary conditions corresponding to each set are somewhat different. Table 2 summarizes the values of the boundary conditions at the model inlet. The mass flow boundary condition is utilized for the momentum equations. The mass flow rate at the inlet was obtained from a balance calculation using the mea-
2.3. Boundary Conditions As was mentioned previously, the goal of the present work is an accurate solution in the superheater region (see Figure 2a). It is assumed that the profiles at the nose level, when the flue gas enters the superheater region, are mainly defined by the geometry and are not any more significantly affected by the combustion processes and air injection schemes in the furnace. This typically holds reasonably well in modern recovery boilers, since the combustion air is injected in a symmetric, nonswirling fashion from the front and rear walls, and a significant distance before the furnace outlet. According to these reasons, 6
sured fuel and air mass flows. The calculated value was confirmed with a measured value collected from the boiler control system. The inlet velocity given in the table was calculated from the mass flow rate. The inlet temperature was calculated using CFD such that the measured temperature was approximately obtained at the measurement location closest to the inlet (point 5 in Figure 5). The turbulence intensity at the inlet was estimated to be 15%, which corresponds to a relatively high turbulence level, as indicated by previous simulations (Maakala and Miikkulainen, 2015). In addition, preliminary CFD simulations indicated that the value of the turbulence intensity at the nose level is not very sensitive to the precise value of the turbulence intensity at the domain inlet. The flue gas composition was obtained in a similar fashion as the mass flow rate, that is, calculated from a balance and confirmed with the measured values. Table 2: The values of the boundary conditions at the model inlet in the measurement sets A and B. The length scale of the Reynolds number (Re) at the inlet is the hydraulic diameter of the furnace cross section. The Reynolds number in the superheater region is given for reference, where the length scale is the spacing between the superheater platens.
Velocity Temperature Turbulence intensity Re, inlet Re, superheater region Flue gas composition Carbon dioxide (CO2 ) Gaseous water (H2 O) Oxygen (O2 ) Nitrogen (N2 )
4.6 m/s 1 340 K 15% 284 000 15 000
4.7 m/s 1 410 K 15% 266 000 14 000
Balance, measurements Measurements Estimation, previous work -
19 wt% 15 wt% 3 wt% 63 wt%
19 wt% 14 wt% 4 wt% 64 wt%
Balance, measurements Balance, measurements Balance, measurements Balance, measurements
Figure 4: a) A schematic of the boundary between the flue gas side and the water/steam side. The T int and kint , which are given as boundary conditions, are circled. The red line shows the temperature profile and the dashed green line indicates the average deposit thickness. b) The water/steam side temperature T int on the heat transfer surfaces. On the boiling surfaces, the T int is constant. On the superheater surfaces, the T int is interpolated in the x-direction using their steam inlet and outlet temperatures, and is constant in the y- and z-directions.
is the tube thermal conductivity, sdeposit is the deposit thickness, and λdeposit is the deposit thermal conductivity. The boundary conditions on the heat transfer surfaces are summarized in Table 3 and visualized in Figure 4b. The temperatures, pressures, and steam flow rates before and after each superheater were collected from the boiler control system during the measurement campaign. Therefore, the average heat transfer rates to the superheaters could be calculated. The measured temperature values were directly utilized to set the T int boundary conditions. The average heat transfer rates were used for setting the kint boundary conditions, such that the kint values were adjusted during the CFD simulations until the calculated average heat transfer rates were obtained. Similar approaches have been utilized in previous research (Saviharju et al., 2004; Lepp¨anen et al., 2014a; Schuhbauer et al., 2014). Table 3 also shows the estimated sdeposit values, which have been calculated from the kint values using the Equation (6). The value of λdeposit = 1.5 W/(mK) has been used in the estimations, following Schuhbauer et al. (2014) and Lepp¨anen et al. (2014a). The sdeposit values were not directly used in the simulations. The present approach can be understood by considering the challenges associated with direct, a priori estimation of the kint from the Equation (6). In the present work, the kfluid , stube , and λtube are well known or can be readily estimated. However, the sdeposit and λdeposit are very hard to estimate and, based on the measured values, they constitute over 95% of the total thermal resistance. In the literature, typical reported values for the sdeposit are between 5–60 mm (Adams, 1997; Li et al., 2013; Lepp¨anen et al., 2014a) and for the λdeposit between 0.1– 2.5 W/(mK) (Rezaei et al., 2000; Baxter et al., 2001; Zbogar
The thermal boundary conditions are set using the standard convective boundary condition, where the water/steam side temperature T int (internal temperature) and the water/steam side heat transfer coefficient kint (internal heat transfer coefficient) are given as boundary conditions. The surface heat flux q and the surface temperature T surface are calculated as a part of the CFD solution from the following system of equations q
= kgas (T surface − T gas ) + qrad = kint (T int − T surface )
where kgas is the convective heat transfer coefficient on the flue gas side, T gas is the flue gas temperature, and qrad is the radiation heat flux. The schematic of the boundary in Figure 4a clarifies how the variables are defined. The significance of the water/steam side heat transfer coefficient kint is seen from the equation (see also Figure 4a) ! sdeposit 1 stube kint = 1/ + + (6) kfluid λtube λdeposit where kfluid is the heat transfer coefficient from the inner surface of the tube to the water/steam, stube is the tube thickness, λtube 7
Table 3: The boundary conditions on the heat transfer surfaces in the measurement sets A and B. The T int values were measured and the kint values were calculated from the measured values such that the average heat transfer rates observed during the measurement campaign were satisfied. The simulations converged well to the tabulated kint values. The sdeposit values (not directly used in the simulations) were estimated from the kint values using the Equation (6).
Walls and roof Rear wall screen Boiler bank Superheater 1A Superheater 1B Superheater 2 Superheater 3 Superheater 4
Set A T int [K]
Set A k h int i
Set A sdeposit [mm]
Set B T int [K]
Set B k h int i
Set B sdeposit [mm]
598 598 598 598–616 616–644 638–690 682–753 736–788
58 140 183 111 52 43 53 48
25 10 8 13 28 34 27 30
597 597 597 598–615 615–642 639–689 686–751 741–788
58 83 170 58 35 30 33 28
25 17 8 25 42 48 45 53
W m2 K
et al., 2005). Depending on the time after the boiler startup, ash composition, sootblowing, and the location of the particular heat transfer surface, the sdeposit can vary from values close to zero (clean tubes) to values that completely plug the flue gas passages. On the other hand, the λdeposit is affected by the particle size distribution, porosity, and sintering degree of the deposit. Therefore, it is evident that: 1) the heat transfer coefficient kint is highly sensitive, in particular, to the sdeposit and λdeposit and 2) the a priori estimation of the sdeposit and λdeposit is very challenging due to the complex nature of the recovery boiler process. The approach of calculating the kint through the measured average heat transfer rates is further justified in the present work, since the goal is the validation of the CFD model, submodels, and the flow and temperature field solutions in typical operating conditions of the recovery boiler. The essential feature, and an advantage, of this method is that the measured values (temperatures and heat transfer rates) from the water/steam side can be utilized as boundary conditions. Therefore, the surface temperature and heat flux profiles are calculated as a part of the CFD simulation together with the three-dimensional flow and temperature field solutions.
W m2 K
Table 4: The main operating parameters of the boiler. The values are reported according to the conventions given in Vakkilainen (2005), where additional details can be found. The following abbreviations are used: ds (dry solids), tds/d (tonnes of dry solids per day), HHV (higher heating value), and NHV (net heating value). Parameter Boiler type Fuel type Black liquor capacity, tds/d Black liquor HHV, MJ/(kgds) Black liquor dry solids content, wt% Thermal capacity, MW Air ratio (λ) Main steam flow, kg/s Main steam temperature, K Main steam pressure, bar Boiler efficiency (NHV), % Reduction efficiency, %
Value Kraft recovery boiler (subcritical) Softwood black liquor 2 400 13.0 72 360 1.13 92 788 110 87 96
pulp mill. Hence, the number of measurement locations and repeated measurements normally have to be limited in full-scale measurement campaigns. Furthermore, the locations available for measurements are limited by the number of openings existing in the boiler walls. On the other hand, the flow and temperature fields are always time-dependent even in steady boiler operation, and thus each pointwise recording should be measured multiple times to obtain a reliable time-averaged value. In the measurement campaign, the flow and temperature fields were measured from the openings in the boiler side walls (Figure 5). In the x- and y-directions, the number of measurement locations was limited by the number of openings available. In the z-direction, all of the measurements were carried out at the same depth of approximately 1.7 m. This was mainly because of the limited physical dimensions of the probes, but also because of the previously mentioned time constraints. Due to the challenging conditions and limited time available for the measurements, it was possible to repeat each measurement only
3. Measurements The measurement campaign was conducted on a modern, medium-capacity recovery boiler. The main operating parameters of the boiler are shown in Table 4. In this work, we report two sets of measurements, called sets A and B, which were taken at the boiler on different days. Full-scale measurements on a recovery boiler are time consuming and expensive because of the large number of personnel required for the measurements, sample taking, and operating the boiler in a steady fashion. The high-temperature and dusty conditions inside the boiler are especially challenging. Additional time is required every time the boiler operation mode or load is changed because it takes several hours for the recovery boiler operation to reach a steady state after every change. The total time available for measurements is often limited by the 8
from one to three times at each measurement location. The photos taken during the measurement campaign illustrate the challenging conditions in the recovery boiler superheater region (Figure 5). The flue gas temperatures were measured using a suction pyrometer (Figure 6a). The suction pyrometer draws the flue gas inside the ceramic sleeve, where a thermocouple for measuring the temperature is located. The purpose of the ceramic sleeve is to shield the thermocouple from direct thermal radiation heat transfer, which would introduce bias to the measurements. The velocity measurements were done using a special twochamber Pitot probe (Figure 6b). The Pitot probe is air cooled and designed for high-dust conditions. The probe is rotated manually around its axis in the measurement location to find the orientation which shows the largest pressure difference between the two chambers. The flow direction is obtained from the orientation and the velocity magnitude can be calculated from the pressure difference. Because of the nonstandard shape of the two-chamber Pitot probe, the velocity calculation formulas have been calibrated with measurements done using a standard Pitot probe. The construction of the Pitot probe (Figure 6b) effectively filters out the velocity vector component parallel to the shaft of the probe, i.e., z-direction. Because of this, we are assuming that the probe measures the xy-velocity direction and xy-velocity magnitude. The effect of this assumption was later confirmed by the modeled results to be minor because the z-component of the velocity was relatively small in the measurement locations. In addition to the temperature and flow field measurements, samples of black liquor, auxiliary fuel, ash, carryover, smelt, and circulation water were collected during the measurement campaign. The flue gas composition was measured and the boiler operation data was collected from the control system.
the convergence criteria for reaching a steady state had to be somewhat relaxed around the corner vortex region. The results indicated that grid convergence was achieved in the x- and ydirections with a resolution of 100 mm. The GCI error estimates were 1.9% in temperature, 8.9% in velocity magnitude, and 3◦ in velocity direction. Next, grid convergence is assessed by further grid refinement in the z-direction. This is important because a fine grid resolution in the z-direction is essential for accurately capturing the flow structures inside the relatively small gaps between the superheater platens. Table 5 summarizes the computational grids that are used in the verification. Table 5: The computational grids used in the verification. The cell sizes are given in the refinement region (see Figure 3). The representative cell sizes and refinement ratios were calculated according to Celik et al. (2008). The first cell y+ values and the errors in platen heat transfer were obtained by twodimensional simulations of flow between two superheater platens. The errors in platen heat transfer are relative to a dense grid solution (64 cells between platens). The values of equiangle skewness and orthogonal quality range from 0 (degenerate) to 1 (excellent).
Total cells Cell x-size Cell y-size Cell z-size Representative cell size, h Refinement ratio, r Cells between superheater platens First cell y+ between platens Error in platen heat transfer Equiangle skewness, mean / min Orthogonal quality, mean / min
4.8 M 100.00 mm 100.00 mm 25.00 mm 60.09 mm 8 118.8 1.7% 0.85 / 0.32 0.93 / 0.49
9.0 M 100.00 mm 100.00 mm 12.50 mm 47.70 mm 1.26 16 65.9 1.5% 0.84 / 0.31 0.92 / 0.48
17.4 M 100.00 mm 100.00 mm 6.25 mm 37.86 mm 1.26 32 44.5 0.5% 0.84 / 0.31 0.92 / 0.48
4. Results The grid resolution in the z-direction was further verified by two-dimensional simulations of flow between two superheater platens (see Table 5). The first cell y+ value is in the appropriate range of 30 < y+ < 200 with all of the grids. The error in platen heat transfer is also reasonably low with all of the grids, between 1.7%–0.5%, with the resolution of 32 cells providing the lowest error value of 0.5%. The velocity and temperature profiles between the platens are adequately captured when the resolution is between 16–32 cells. Thus, based on the twodimensional simulations, we consider that the flow field and heat transfer between the superheater platens can be accurately described with the resolutions of the grids 2 and 3. Next, the grid convergence is studied using the full threedimensional model. Table 5 shows the equiangle skewness (ES) and orthogonal quality (OQ) values for the three-dimensional grids. The mean values of both ES and OQ are high and their minimum values are well above the typically accepted minimum values of 0.05 (ES) and 0.01 (OQ). Therefore, according to these measures, the numerical grids are of high quality, especially considering the present relatively complex geometry. Figure 7 shows the solved temperature profiles along the
4.1. Model Verification The accuracy of the computational solution is assessed with a grid convergence study. The uncertainty due to discretization is reported using the standard grid convergence index (GCI) method (Celik et al., 2008). Because of the large size of the modeled domain it was not possible to study grid convergence with the available computers by refining the grid simultaneously in all three coordinate directions. Thus, grid convergence was studied by first refining the grid in the x- and y-directions and then in the z-direction. The results concerning the grid refinement in the x- and ydirections were reported in our previous work (Maakala et al., 2016). The most significant observation was that the steadystate RANS solution does not achieve perfect iterative convergence, which is typical in such high Reynolds number flows in complex geometries (see Grace (1995) for details). Iterative convergence was satisfactory in the majority of the superheater region, except in the vortex region in the corner of the front wall and the roof (near the points 1, 2, and 3, see Figure 5), where minor transient behavior remained in the solution. Thus, 9
Figure 5: The measurement points and lines which are used for profiles when comparing modeled results to the measurements. The line 1 is drawn from between the points 1 and 2 because they are not exactly aligned in x-direction. I) View from the opening in point 1. Lightly fouled platens of the superheater 2 can be seen. II) A cooled carryover probe that has been held inside the boiler for approximately five minutes. White fume deposition can be seen on the surface. III) View from the opening in point 7. Localized deposition can be seen in the central region of the superheater 4. IV) View from the opening in point 11. Deposition can be seen on the platens of the superheater 4.
the grid 3 are 0.6% in temperature, 3.8% in velocity magnitude, and 2◦ in velocity direction. We consider the error estimates reasonably low and the computational solution reliable. The results in the rest of this study are reported using the finest grid 3 offering the lowest GCI error level. Table 6: The values calculated for the discretization error on the grid 3 using the GCI method. The values are shown for temperature (T ), velocity magnitude (~u mag), and velocity direction (~u dir). The GCIavg is the estimate for the average discretization error.
Apparent order of the method, p Average relative error, eavg Average grid convergence index, GCIavg
Figure 6: a) The suction pyrometer used for the temperature measurements. b) The two-chamber Pitot probe used for the velocity measurements.
5.03 1.1% 0.6%
5.29 7.2% 3.8%
4.84 3◦ 2◦
4.2. Model Validation The accuracy of the model is next validated with the experimental data. During the measurement set A, the boiler was operating at 87% heat load of the full capacity. The velocity measurements were repeated from one to three times at each measurement location while the temperatures were measured only once. During the measurement set B, the boiler was operating at 84% heat load of the full capacity. Only temperature was measured at each location but the measurements were repeated twice. The confidence intervals for the measured values were calculated using the t-distribution with a 95% confidence level.
lines 1–6, which cover the whole superheater region and the majority of the measurement locations. As can be seen from Figure 7, effect of the grid refinement is minor in the solved profiles. Apparent differences can be seen only along the lines 1 and 2, which are close to the corner vortex region. The error bounds calculated for the dense grid solution using the GCI method are small in the majority of the superheater region. Table 6 summarizes the values calculated for the discretization error using the GCI method. The GCI error estimates on 10
measure and to model. The difference at the point 19 could also be explained by a corner vortex, which might exists in reality but is not captured by the model. Another possible explanation is localized fouling, which is not included in the model but is quite common in practice in the boiler bank region. At most of the measurement locations, the relative difference is clearly below 15% (colored green). Thus, we consider the overall match between the modeled results and the measurements to be relatively good. In velocity direction (Figure 8), the average absolute difference between the modeled and measured values is 15◦ . The largest differences (above 30◦ , colored red) are observed at the points 4 (51◦ ) and 1 (37◦ ). However, the modeled values are clearly inside the confidence intervals of the measurements at both locations. The point 1 is also in the challenging corner vortex region. We consider that the solved velocity direction values correspond well to the measurements. Figure 9 shows the solved temperature field. The solved and measured values of temperature are shown at each measurement location. The average absolute difference between the modeled and measured values is 30 K or 3%. The largest differences (above 5%, colored red) are seen at the points 20 (8%), 2 (7%), and 6 (5%). The difference at the point 20 can be possibly explained by localized fouling in the boiler bank region. The difference at the point 2 can be explained by the corner vortex region. Some of the differences can also result from uncertainties in the measurements. Since the temperatures were measured only once at each location, it is possible that all of the measured values are not representative of time-averaged boiler operation. Despite the various uncertainties, we consider that the measured and modeled values of temperature correspond well to each other. Figure 10 shows the solved and measured values of velocity magnitude (a), velocity direction (b), and temperature (c) along the lines 1–6. The velocity magnitude profiles correspond very well to the measurements on the lines 2, 4, 5, and 6. There are only relatively small differences on the lines 1 and 3. The velocity direction profiles are inside the confidence intervals of the measurements at each of the points. The solved values are also close to the measured mean values. The confidence intervals are wide since the direction measurements were challenging due to the fluctuating flow field in the recovery boiler. In the temperature results, there are apparent differences between the modeled and measured values only at some individual points, most notably, on the lines 1 and 3. On average, the solved profiles of velocity magnitude, direction, and temperature correspond well to the measured values. It is significant that the solved profiles clearly follow the measured profiles.
Figure 7: The temperature profiles along the lines 1–6 (see Figure 5) solved using the grids 1–3. The GCI error bounds are shown in gray. The profiles of velocity magnitude and velocity direction show similar results and are thus omitted for brevity.
Even though the measured mean values are considered representative, the large confidence intervals calculated with the rather strict 95% confidence level demonstrate the experimental uncertainty associated with these challenging measurements. Therefore, a perfect correspondence between the measured and modeled values cannot be expected. 4.2.1. Validation Against the Measurement Set A Figure 8 presents the solved velocity field by streamlines. The solved and measured values of velocity magnitude and direction are shown at each measurement location. The average absolute difference between the modeled and measured velocity magnitudes is 0.9 m/s or 20%. The largest differences (above 30%, colored red) are observed at the points 11 (61%), 12 (58%), 1 (43%), 19 (39%), and 7 (34%). We do not consider the differences at the points 7, 11, and 12 to be very significant because of the wide confidence intervals of the measurements at these locations. In addition, at these locations the modeled values are inside, or close to, the confidence intervals of the measurements. The difference at the point 1 can be explained by the corner vortex region, which is very challenging both to
4.2.2. Validation Against the Measurement Set B Figure 11 shows the simulated temperature field while Figure 12 shows the solved profiles along the lines 1–6. The simulated and measured values are shown at each measurement location. In this set, the measured mean values calculated with two measurements are more reliable than the values from single measurements in the set A. However, the confidence intervals, calculated with the 95% confidence level, are very large 11
Figure 8: The solved velocity field shown by streamlines on the xy-surface corresponding to the measurement locations. The solved (not in parentheses) and measured (in parentheses) velocity magnitude and velocity direction values are shown at each measurement location. The measurement locations have been colored by the relative difference of the modeled and measured values. At each location, the upper color corresponds to velocity magnitude and the lower color to velocity direction. The measured values are from the set A.
because of only two repeated measurements. The average confidence interval is ±311 K and the average absolute difference between the repeated measurements is 49 K.
ure 13, which shows the modeled values in comparison to the measured values in both sets, A and B. The overall match between the modeled and measured values is considered good.
The average absolute difference between the modeled and measured temperature values is 35 K or 4% (see Figure 11). The largest differences (above 5%, colored red) are at the points 3 (12%), 18 (10%), 14 (7%), and 12 (6%). Again, the difference at the point 3 can be explained by the corner vortex region, where both the numerical solution and measurements are challenging. It is unclear whether the other differences result from experimental or modeling error since the measurement uncertainties are still reasonably large. Regardless, the differences are small (below 3%, colored green) in most of the measurement locations.
4.3. Analysis of the Three-dimensional Simulation Results The added-value of the present CFD model is next illustrated with a detailed analysis of the three-dimensional simulation results. The focus is on new results which have not been reported in previous modeling or experimental studies along with findings that the simplified models, which were discussed in the literature review, cannot adequately capture. The results in this section correspond to the CFD simulation of the measurement set A.
The solved temperature profiles correspond very well to the measurements on the lines 1, 3, and 4 (Figure 12). On the other lines, there are apparent differences only at individual points. The profiles are also inside the confidence intervals of the measurements and they follow the shapes outlined by the measured mean values. We consider that the measured and modeled values correspond well to one another also in this measurement set.
4.3.1. Vortex Structures and Overall Character of Heat Transfer The three-dimensional character of the flow field is demonstrated in Figure 14a, which shows the vortex structures identified via the standard Q-criterion method. The vortex in the corner of the front wall and the roof is clearly visible (I). In addition, there is a symmetric vortex pair in the front cavity region (II) and complex vortex structures below the boiler nose (III). When the flow enters between the superheater platens, the
The results of the model validation are summarized in Fig12
Figure 9: The solved temperature field shown by contours on the xy-surface corresponding to the measurement locations. The solved (not in parentheses) and measured (in parentheses) values are shown at each measurement location. The measurement locations have been colored by the relative difference of the modeled and measured values. The point 5 is the inlet temperature reference location. The measured values are from the set A.
large-scale vortex structures are effectively filtered out and thus small-scale vortices are seen throughout this region. Figures 14b and 14c show the simulated heat flux solution on the walls, boiling surfaces, and superheaters. The vortex structures shown in Figure 14a affect the heat flux solution, particularly on the boiler walls. This indicates that the threedimensional flow is closely connected to the heat transfer. The heat flux to the furnace walls is clearly greater in the central region of the walls than close to the corners (IV). In the superheater region, the heat flux to the furnace walls reduces sharply when the flow enters between the superheater platens (V). The heat flux is highest to the superheaters which are directly exposed to thermal radiation heat transfer from the furnace, that is, from below the nose (VI). However, there is substantial local variation in the heat flux to the superheaters and the boiling surfaces because of the effect of the flow field (VII). These results indicate that the heat transfer solution is strongly affected by the geometry, flow field, and radiation heat transfer effects.
most likely a major portion of the radiation heat flux is due to close range radiation from the flue gas flowing through the superheaters. This consideration is also supported by the two-dimensional simulations of flow between two superheater platens (see Subsection 4.1), where the contribution of the radiation heat transfer was significant. The ratio of the radiation heat flux to the total heat flux is highest for the superheater 2 (0.70) and superheater 3 (0.66), which are directly exposed to thermal radiation from regions below the nose. Figure 16 shows the ratio of the radiation heat flux to the total heat flux in detail on the boiler walls (a) and on the superheaters and boiling surfaces (b). The ratio varies locally from the values on the boiler walls which are close to 1.0 (I) to the values on the superheater 4 which are close to 0.0 (II). The local variations in the gas and surface temperatures and the shadowing effects of the geometry affect these values significantly. Since the share of the radiation heat transfer is large in the whole superheater region, its accurate modeling is considered highly important for the overall accuracy of the heat transfer solution. For an accurate solution of the radiation heat transfer, the full three-dimensional representation of the superheaters is considered important. This is due to the global character of the radiation heat transfer process and the shadowing effects of the geometry.
4.3.2. Radiation and Convection Heat Transfer The average ratios of the radiation heat flux to the total heat flux on the superheater surfaces are shown in Figure 15a. The ratio is substantial for all of the superheaters, between 0.45–0.70. Considering the layout of the superheater region, 13
Figure 10: The solved profiles on the lines 1–6 (see Figure 5) compared to the measured values. The error bounds are estimated for the solved profiles using the GCI method. The horizontal lines show the 95% confidence intervals. The inlet temperature reference location (point 5) is indicated with a blue square. The measured values are from the set A.
The convection heat transfer is studied by calculating the average Nusselt numbers on the superheater surfaces. The Nusselt number is defined as kgas l Nu = (7) λ where kgas is the convective heat transfer coefficient of the flue gas, l is the characteristic length, and λ is the thermal conductivity of the flue gas. The characteristic length is defined as the streamed length of a single tube, l = πr, where r is the tube radius, since this is the typical convention used in experimental
correlations. The Nusselt numbers are calculated from the Equation (7) by using the simulated kgas values, following a similar approach as in Jang and Yang (1998). The values are compared to a wellestablished experimental correlation for tube bundles in cross flow (Gnielinski, 1975), which was recently utilized for the superheaters and reheaters of a coal-fired boiler by Schuhbauer et al. (2014). The experimental correlation is considered for two conditions: 1) cross flow perpendicular to the tubes and 2) 14
Figure 11: The solved temperature field shown by contours on the xy-surface corresponding to the measurement locations. The solved (not in parentheses) and measured (in parentheses) temperature values are shown at each measurement location. The measurement locations have been colored by the relative difference of the modeled and measured values. The point 5 is the inlet temperature reference location. The measured values are from the set B.
cross flow 35◦ oblique to the tubes. Additional details can be found in the mentioned publications and in VDI-Gesellschaft (1993). Figure 15b shows the average Nusselt numbers on the superheater surfaces. The profiles from the CFD simulation and the experimental correlations show a similar trend. Compared to the Nusselt numbers from the CFD solution, the values from the experimental correlation for perpendicular flow (Exp 1) are on average 18.4% higher and the values from the experimental correlation for oblique flow (Exp 2) are on average 13.9% lower. It is considered that the match between the experimental correlations and the CFD solution is acceptable, since neither of the assumptions for the flow direction holds exactly in the present geometry. The local variation in the flow direction over the superheater tubes can be significant (see Figure 8). The results indicate that with the experimental correlations an average accuracy of roughly 10–20% can be achieved. However, applying the correlations in the present geometry is challenging, since it is difficult to estimate the direction of the flow field a priori or to simulate it accurately without including the geometry of the superheaters in the model. Therefore, the full three-dimensional representation of the superheaters is considered important also for an accurate solution of the convective heat transfer.
4.3.3. Heat Flux Profiles in the Width Direction The total heat flux and thermal radiation heat flux profiles of each superheater are shown in the width direction of the boiler (z-direction) in Figure 17. The simulated average heat flux values match the corresponding values observed during the measurement campaign, since the average heat transfer rates were used for defining the boundary conditions (see Subsection 2.3). However, the results show that the heat flux profiles differ significantly from the average values. The heat flux is substantially higher to the platens in the central region than to the platens close to the side walls (I). The largest differences are noted at the superheater 4, where the heat flux toward the platens in the central region is over 90% higher compared to the platens near the side walls. In Figure 17, there is a clear depression in the heat flux profiles in the central region of the superheaters 3, 4, 1B, and 1A (II). The CFD solution indicates that this phenomenon could result from a small, lower temperature vortex region which occurs in the central part of the boiler when the flow entering the superheater region separates from the boiler nose. The vortex region is not visible in Figure 14a since the view is obstructed by the superheater platens and the large number of small-scale vortex structures. 15
Figure 13: The modeled values in comparison to the measured values. Inside the dashed error bounds, the match between the modeled and measured values is considered to be good (colored green in Figures 8, 9, and 11). The values from the set A are indicated with blue circles and the values from the set B are indicated with red squares. Confidence intervals are not shown.
range is utilized to illustrate the implications of the threedimensional CFD solution for the estimation of fouling. The potential deposits are assumed to consist of 50 wt% carryover particles (combusted black liquor droplets) and 50 wt% fume particles (condensed sodium and potassium salts). The chemical compositions of the carryover and fume were obtained from the samples taken during the measurement campaign. Furthermore, it is assumed that the potential deposits are carried with the flue gas flow and that they are at the same temperature as the flue gas. The locations where the fouling potential of the ash is highest are then identified as the regions where the flue gas temperature is in the sticky temperature range. The transport of the ash particles to the heat transfer surfaces is not modeled. This simple approach is considered only as an indicative worst-case estimate for the purposes of the present discussion, and it is not intended to be a detailed model for fouling (for detailed models, see Weber et al. (2013)). Figure 18 shows the potential regions of fouling on the furnace walls, superheater 2, and superheater 4. The identified regions are clearly connected to the three-dimensional vortex structures of the flow field (compare Figures 14a and 18a). On the furnace walls, the largest regions are in the central part of the front wall (I) and the corners of the rear wall (II). Significant sticky areas are also in the corner region of the front wall and the roof (III). These numerical observations can be linked to practical observations, which typically indicate deposition in these regions. On the superheater 2, the regions containing sticky ash are mainly in the top part, top corners, and near the
Figure 12: The solved profiles of temperature along the lines 1–6 compared to the measured values. The average GCI error estimate (Table 6) is used for the error bounds of the solved profiles since only the dense grid solution is available for this measurement set. The estimated error bounds are so small that they are barely visible. The horizontal lines show the 95% confidence intervals. The inlet temperature reference location (point 5) is indicated with a blue square. The measured values are from the set B.
4.3.4. Implications for the Estimation of Fouling Recovery boiler ash is considered sticky (i.e., fouling) if it is between 15% and 70% in the liquid phase (Isaak et al., 1986; Tran et al., 2002). Below 15% liquid content, the particles are too dry and therefore not sticky. Above 70% liquid content, the particles can be sticky, but the deposits stop growing since additional material transported to the surfaces becomes molten and flows off. The sticky temperature T 15 (15% liquid content) and flow temperature T 70 (70% liquid content) are typically used to characterize the sticky temperature range of the ash, T 15 –T 70 . This range can be obtained via thermodynamic calculations if the chemical composition of the ash is known (Backman et al., 1987). In general, the melting behavior of the ash can vary significantly depending of the pulp mill and process conditions. It is especially sensitive to the chloride and potassium content of the ash. The sticky temperature range is an established concept and it has been utilized in a number of previous studies, such as, Mueller et al. (2003, 2005). Next, a simple approach based on the sticky temperature 16
Figure 14: a) Three-dimensional vortex structures identified via the standard Q-criterion method with Q = 0.01 and colored by the magnitude of vorticity. b) Heat flux toward the boiler walls. c) Heat flux toward the superheaters and boiling surfaces.
Figure 15: a) The ratio of the radiation heat flux to the total heat flux on the superheater surfaces. The average values (Mean) and standard deviations (Stdev) are shown. b) The average Nusselt numbers on the superheater surfaces. The values are shown from the present simulation (CFD) and from an experimental correlation (Gnielinski, 1975), with cross flow conditions perpendicular to the tubes (Exp 1) and 35◦ oblique to the tubes (Exp 2).
side walls. On the superheater 4, the regions of sticky ash are almost in the opposite locations, that is, mainly in the central part. This numerical result is also supported by practical observations. Deposition was observed visually during the measurement campaign in the central part of the superheater 4 (see Figure 5). The results indicate that the fouling behavior of the ash can be considerably non-intuitive, since it is closely connected to the three-dimensional flow and temperature field solutions. The potential locations of fouling can also vary notably between different superheaters. The results indicate that for an accurate solution of fouling in the superheater region, a detailed fouling model should be coupled with a three-dimensional CFD model.
Figure 16: The ratio of the radiation heat flux to the total heat flux on the a) boiler walls and b) superheaters and boiling surfaces.
5. Conclusions We presented a new model for the recovery boiler superheater region, called the full superheater region (FSR) model, and reported two sets, A and B, of previously unpublished fullscale temperature and flow field measurements from the superheater region. The accuracy of the computational solution was 17
structures and their consequent impact on the heat transfer, b) the detailed heat flux solutions toward the furnace walls, boiling surfaces, and superheaters, c) the detailed analysis of the radiation and convection heat transfer, and d) the quantitative variation of the heat flux profiles of the superheaters in the width direction. 5. The results indicated that the fouling behavior of the ash is closely connected to the three-dimensional flow and temperature field solutions. It was considered that for an accurate solution of fouling a detailed fouling model should be coupled with a three-dimensional CFD model. The results of this work and the developed CFD model are valuable for optimizing the efficiency of recovery boilers. Due to the large size of the global pulp industry, the amount of black liquor combusted in recovery boilers every year is very large. Therefore, the potential in optimizing the recovery boilers for the generation of renewable energy is tremendous. In the present work, the developed CFD framework was utilized in connection to recovery boilers but it could also be applicable to other types of large-scale energy production applications, such as biomass-fired industrial boilers or utility boilers. Acknowledgments The authors wish to thank Ilkka V¨alipakka, Lars-Gunnar Magnusson, Niko Mets¨amuuronen, and Arto Paunonen who were responsible for the measurement campaign. The support obtained from the mill personnel during the campaign is also acknowledged. In addition, we gratefully acknowledge Mohammad Hadi Bordbar for implementing and providing the code for the non-gray weighted sum of gray gases method and for his valuable advice with radiation modeling.
Figure 17: The total heat flux and radiation heat flux profiles of each superheater in the width direction of the boiler (z-direction, see Figure 5 for the locations of the superheaters). The heat fluxes have been calculated for each platen as area-weighted averages. The positive platen numbers correspond to the right side of the boiler and the negative platen numbers to the left side of the boiler. The average total heat flux is also shown.
verified with a grid convergence study by utilizing the standard grid convergence index (GCI) method. The modeled results were validated against the measurement sets A and B. The added-value of the CFD model was illustrated with a detailed analysis of the three-dimensional simulation results. Based on the results, we make the following conclusions: 1. The error estimates calculated with the GCI method were considered low and the computational solution reliable. 2. The overall match between the modeled and measured values was considered good and the model validation successful. Due to the experimental uncertainty associated with these challenging measurements, a perfect correspondence could not be expected. 3. The present measurement data is considered extremely valuable, since reported experimental data on recovery boilers is scarce in literature. Further comprehensive measurement campaigns are necessary for the development and validation of the recovery boiler CFD models. 4. To the best of our knowledge, the following results were reported for the first time: a) the three-dimensional vortex 18
Figure 18: The identified regions of potential fouling on the a) furnace walls, b) superheater 2 (SH 2), and c) superheater 4 (SH 4). The regions where the temperature of the ash is in the sticky range are shown in yellow (T 15 –T 70 ). The regions where the temperature of the ash is outside the sticky range are shown in blue (below T 15 or above T 70 ). The figures b and c show the yz-surfaces in the middle of the superheaters in the x-direction (the surfaces are also marked in the figure a). In the figures b and c, the superheater platens are visible as vertical black lines.
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