A Premixed FlameletâPDF Model for Biomass Combustion in a Grate

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Energy & Fuels 2008, 22, 1570–1580

A Premixed Flamelet-PDF Model for Biomass Combustion in a Grate Furnace B. A. Albrecht†,§, S. Zahirovic‡, R. J. M. Bastiaans*,†, J. A. van Oijen†, and L. P. H. de Goey† Combustion Technology, Department of Mechanical Engineering, Technische UniVersiteit EindhoVen, Den Dolech 2, 5600 MB EindhoVen, The Netherlands, and Institute for Resource Efficient and Sustainable Systems, Graz UniVersity of Technology, Infeldgasse 21B, 8010 Graz, Austria. ReceiVed December 13, 2007. ReVised Manuscript ReceiVed March 10, 2008

In this paper, a new modeling approach for biomass furnaces is presented. A flamelet model is applied for the prediction of combustion and NOx emissions in a pilot-scale low-NOx biomass grate furnace. The model describes the combustion chemistry using premixed flamelets. The chemical system is mapped on three control variablessthe mixture fraction, enthalpy, and a reaction progress variablesby means of the flamelet-generated manifold chemical reduction technique (FGM). The density and source terms are tabulated as functions of the control variables in a preprocessing step to speed up the numerical calculations. The turbulence-chemistry interaction is described by an assumed shape probability density function (PDF) approach. Generally, transport equations are solved for mean and variance of mixture fraction, mean progress variable, and the mean enthalpy. The FGM-PDF model is first validated for a diffusion flame: Sandia Flame D. Good agreement of predictions with measurements is found. The model is then applied to a 2D cross section of a biomass combustion grate furnace. FGM-PDF is compared with the standard eddy dissipation concept model (EDC). The predictions of the two models are similar. The FGM-PDF model reduces the calculation time with GRI-Mech2.11 reaction mechanism from weeks to hours, when compared to EDC. Furthermore, in FGM-PDF more physics can be taken into account thanks to the integration of flamelets in the turbulence-chemistry interaction.

1. Introduction

being determined by the turbulent mixing rate. Therefore, accurate predictions of intermediates and pollutants cannot be achieved. An improved version of EDM is the eddy dissipation concept (EDC).3,4 This model can handle complex reaction mechanisms but uses an implementation of turbulence-chemistry interaction based on homogeneous reaction. Furthermore, it requires a very high computational time. The model proposed here for the modeling of biomass grace furnaces is based on a (premixed) flamelet-PDF (probability density function) approach implemented in RANS. The combustion system is described with detailed chemistry by premixed flamelets, the advance of chemical reaction being monitored by a reaction progress variable. The turbulence-chemistry interaction is accounted for with an assumed shape PDF approach. Therefore, this combustion model has a low calculation time (comparable to EDM) and is thought to improve the accuracy of gas-phase species and temperature predictions due to the more physical turbulence-chemistry interaction compared to EDC.

The use of grate furnaces is regarded as a popular combustion technology used for thermal conversion of solid biomass fuels. The combustion of solid biomass in these furnaces can lead to a considerable exhaust of NOx, originating from the nitrogen present in biomass fuels. The levels of NOx emitted depend on the amount of the nitrogen in the fuel as well as on the design and operation parameters of the furnace. As NOx compounds are harmful to the environment, governments continue to lower their emission limits. Therefore, research is done into the reduction of NOx emissions. To optimize the design of biomass combustion furnaces in general and for NOx emission reduction by primary measures in particular, numerical models can be used. The requirements for these models are twofold: the model has to be sufficiently detailed to predict the NOx production accurately, and the calculation time of the model must be within reasonable limits to be able to calculate the emission levels for different design parameters and operating conditions. Combustion modeling for industrial applications like biomass furnaces relies usually on the Reynolds averaged Navier-Stokes (RANS) simulation approach. Within RANS, the most commonly used combustion model is the computationally inexpensive eddy dissipation model (EDM) coupled with a global reaction scheme.1,2 The problem with EDM is that it does not take into account detailed chemical kinetics, the reaction rates

In this paper, a flamelet model is used for the modeling of combustion and NOx emissions in biomass grate furnaces. The model was reported in detail elsewhere;5,6 here only a brief description of the model is given. The model contains the

* To whom correspondence should be addressed. E-mail: r.j.m.bastiaans@ tue.nl. † Technische Universiteit Eindhoven. ‡ Graz University of Technology. § Present address: Advanced Engineering Engines, DAF Trucks N.V., Hugo van der Goeslaan 1, P.O. Box 90065, 5600 PT Eindhoven, The Netherlands.

(1) Scharler, R.; Fleckl, T.; Obernberger, I. Prog. Comput. Fluid Dyn. 2003, 3, 102–111. (2) Scharler, R. Ph.D. Thesis, Graz University of Technology, Austria, 2001. (3) Fluent 6.1 User’s Guide; Fluent Inc.: Lebanon, NH, 2003. (4) Gran, I.; Magnussen, B. Combust. Sci. Technol. 1996, 119, 191– 217.

2. The FGM-PDF Combustion Model

10.1021/ef7007562 CCC: $40.75  2008 American Chemical Society Published on Web 05/03/2008

Flamelet-PDF Model for Biomass Combustion

Energy & Fuels, Vol. 22, No. 3, 2008 1571

following elements. A laminar database is constructed using the flamelet generated manifold (FGM) chemical reduction method.7 This method tabulates all the thermochemical variables (species mass fractions, temperature, density, etc.) made available as solutions of freely propagating, premixed flame simulations. This is tabulated as a function of the mixture fraction, enthalpy, and a progress variable, referred to as control variables. A turbulent database is consequently calculated by using an assumed shape PDF-averaging approach for the control variables. This results in an extension of the control variables with the variances of the original (laminar) control variables. In this paper, the enthalpy is considered as distributed according to a delta function and thus the variance of enthalpy is not taken into account. The obtained database serves as a look-up table and is calculated in a preprocessing step to speed up the turbulent flame simulations. During a simulation, turbulent transport equations for the control variables are solved. The simulation makes use of the density and progress variable source term given by the table look-up. At the end of the simulation, the species mass fractions and the temperature corresponding to the values of the control variables in every point of the computational domain are retrieved from the tables and thus the complete structure of the combustion system is made available. Due to the fact that the model uses the FGM technique to reduce the chemical kinetics and a PDF approach for the turbulence-chemistry interaction, the model will be referred to as the FGM-PDF model. 3. Turbulent Transport Equations for Control Variables 3.1. Laminar Control Variables. In the FGM-PDF model, transport equations for control variables are solved together with the averaged equations of continuity and momentum. In this section we will present the equations for the control variables. Therefore, we first have to mention the definition of the control variables that we apply. For the mixture fraction, the Bilger formulation8 modified to exclude the oxygen terms was employed. This is similar to that used in the experimental work on Sandia Flame D, which is the flame chosen for the validation of the FGM-PDF model9,10

( (

)( ) (

ZC 1 ZH +2 2 MH MC Z) ZC 1 ZH +2 2 MH MC fu

) )

ZC 1 ZH +2 2 MH MC ox Z ZC 1 H +2 2 MH MC ox

(1)

In eq 1, ZH and ZC are the element mass fractions for hydrogen (H) and carbon (C), respectively, and MH, MC are their molar masses. Following eq 1, Z varies between 0 in the oxidizer stream (denoted with “ox”) and 1 in the fuel stream (denoted with “fu”). For the progress variable, it is natural to take a combination of reaction products, but even intermediates and reactants can be taken into account. The choice of the combination of species (5) Ramaekers, W. J. S. M.Sc. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2005. (6) Albrecht, B. A.; Bastiaans, R. J. M.; van Oijen, J. A.; de Goey, L. P. H. Submitted for publication in Flow, Turbulence Combust., 2008. (7) van Oijen, J. “Flamelet-Generated Manifolds: development and application to premixed laminar flames”; Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2002. (8) Bilger, R. W.; Starner, S. H.; Kee, R. J. Combust. Flame 1990, 80, 135–149. (9) Barlow, R. S.; Frank, J. H. Piloted CH4/air flames C, D, E and F release 2.0, Sandia National Laboratories, Livermore, 2003; http://www.ca.sandia.gov/TNF. (10) Barlow, R. S.; Frank, J. H. Proc. Combust. Inst. 1998, 27, 1087.

used as a progress variable is not unique. The requirement imposed on such a combination is the monotonical variation of its mass fraction between reactants and products with a reasonable resolution for the entire range. Therefore, the mass fraction of CO2 was chosen as the progress variable Y ) YCO2

(2)

In our FGM-PDF combustion model, we will use the scaled form of the progress variable, denoted by c (between 0 and 1, like the mixture fraction), for the PDF closure and the unscaled form Y in the transport equations. The motivation of this approach is given in the following. In the present model, all the thermochemical variables (species mass fractions, density, temperature, etc.) are functions of the mixture fraction and the progress variable. It follows that the turbulence-chemistry interaction is described by the joint PDF of these two control variables. In the presumed shape PDF approach used here, the shape of the single-variable PDF is assumed. The joint PDF can be constructed from the single-variable PDF if the variables are statistically independent. Because the fluctuations of an unscaled progress variable Y are strongly related to the fluctuations of the mixture fraction Z, the joint PDF of Z and Y cannot be decomposed in independent factors. To remove the correlation (or at least to reduce it significantly), a scaled progress variable c is used instead of Y.11,12 The scaled progress variable c is defined as Y - Yu (3) Yb - Yu In eq 3, Yu is the unscaled progress variable in the reactants (unburnt mixture) and Yb in burnt products at equilibrium. Thus, upon entering the turbulent lookup table the progress variable is first scaled to retrieve data. This way of modeling is preferred above the use of c directly in the transport equations because that would introduce additional terms in these equations. These additional terms are related to the dependency of c on Z in the denominator in eq 3.12 The modeling of these terms is complex and approximations have to be used to close them.11 In principle, the combination of a mixture fraction and a progress variable determines the chemical state of the system if it were adiabatic. In the application of a biomass grate furnace, however, use is made of recirculation of flue gases and also secondary air is introduced in the furnace. Therefore, the scaled enthalpy, h, is needed to include these effects c)

h)

H - Hmin Hmax - Hmin

(4)

where H is the actual (total) enthalpy, Hmax is the adiabatic enthalpy for a specific Z, and Hmin is the enthalpy of the burnt products corresponding to Z, when brought to the ambient temperature Tmin ) 298 K. The scaled enthalpy, h, was used as control variable in the turbulent database while in the transport equations solved by the FGM-PDF model the unscaled enthalpy H was involved. This approach is similar to that used for the progress variable and is motivated by the fact that solving a transport equation for a scaled variable (like h and c) leads to extra source terms. These are caused by the dependence of the denominator of eq 4 on Z. 3.2. Turbulent Control Variables: PDF Averaging. In the present study, the averaging procedure for any turbulent (11) Louis J. J. J. “On Turbulent Combustion of Coal Gas”; Ph.D. Thesis, University of Twente, 1997. (12) Bray, K.; Domingo, P.; Vervisch, L. Combust. Flame 2005, 141, 431–437.

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fluctuating quantity φ, which, in terms of the control variables is defined as φ(Z,c,h), is based on Favre averaging, given by ˜(Z,c,h) φ˜ ) ∫10∫10∫10φ(Z,c,h)P

dZ dc dh

(5)

with P˜(Z,c,h) ) FP(Z,c,h)/Fj. Because of the introduction of the scaled progress variable, we removed correlation with the mixture fraction. This allows us to compute the joint PDF as a product of marginal PDF’s of Z, c, and h P(Z,c,h) ) P(Z) P(c)P( h)

(6)

for the enthalpy this is trivial because it is taken as a delta function distribution. For the marginal PDF’s of Z and c, we follow many other investigators, e.g.,refs 13, 14, by assuming a β-function shape PDF. These PDF’s depend on the mean and variance of the control variables ˜,Z ˜ ′′2) P(Z) ) P(Z,Z

(7)

˜

P(c) ) P(c,c˜,c′′2)

(8)

resulting in ˜) φ

∫∫ 1

0

1

0

˜(Z,Z ˜,Z′′ ˜2)P ˜(c,c˜,c′′ ˜2) dZ dc φ(Z,c,h)P

(9)

This introduces another complication because we need an averaged scaled mean and variance of the progress variable. In other words, we need expressions for c˜ and in terms of Y˜ and. The complete derivation of these explicit relations is given in ref 6 and the result is ˜c )

˜-Y ˜u Y ˜b - Y ˜u Y

(10)

and u2 u b b ˜2 + Y ˜2 - Y ˜ ˜ ˜ - 2Y (Y - Yu)c˜ - (Y - Yu)2˜c2 Y′′ ˜ (11) c′′ 2 ) b u ˜ (Y - Y )

To close the system, we only have to additionally tabulate the terms consisting of Yu and Yb as functions of Z˜ and in the database. 3.3. Transport Equations. The laminar transport of Z, Y, and H is given by standard convection-diffusion transport equations, which differ from each other only through the presence of a source term in case of Y (the mixture fraction and the enthalpy have no source terms, they are conserved scalars). The turbulent transport equations for the mean of Z, Y, and H are derived by Favre averaging their laminar counterparts. The variance equations can be derived from the scalar laminar transport equations by multiplying both sides with the fluctuation of the scalar followed by Favre averaging (for derivation, see, for example, ref 15). The steady-state transport equations for the control variables read

((

) ) (( ) ) (( ) )

˜ ˜ µt ∂Z ˜˜ u jZ ∂F ∂ ) F ˜D + ∂xj ∂xj Sct ∂xj

(12)

˜ ˜ µt ∂Y ˜jY ∂Fu ∂ ) FD + + ωY ∂xj ∂xj Sct ∂xj

(13)

˜ ˜ µt ∂H ˜jH ∂Fu ∂ FD + ) ∂xj ∂xj Sct ∂xj

(14)

(13) Correa, S. M.; Shyy, W. Prog. Energy Combust. Sci. 1987, 13, 249–292. (14) Jones, W. P.; Whitelaw, J. H. Combust. Flame 1982, 48, 1–26.

((

) )

((

) )

˜′′2 ˜′′2 ˜ ∂Z ˜ ∂Fu µt ∂Z ˜jZ µt ∂Z ˜ε ˜ 2 ∂ ) FD + + C1 - C2F Z ′′ ∂xj ∂xj Sct ∂xj Sct ∂xi ∂xi ˜k (15) ˜′′2 ˜′′2 ˜ ∂Y ˜ ∂Fu µt ∂Y µt ∂Y ˜jY ˜ε ˜ 2 ∂ ) FD + +2 - C2F Y ′′ + ˜k ∂xj ∂xj Sct ∂xj Sct ∂xi ∂xi 2Y ′′ ωY (16) In the equations, Fj is the mean density, u˜j is the mean velocity vector, D is the molecular diffusion coefficient, µt is the turbulent viscosity, Sct is the turbulent Schmidt number, ω j Y is the mean chemical source term of the progress variable, C1 and C2 are modeling constants, k˜ is the mean turbulent kinetic energy, and ε˜ is the mean dissipation rate. In the equations given above, the gradient transport assumption15 coupled with unity Lewis numbers for all variables have been used to model the turbulent diffusion terms. Besides these equations, the Favre-averaged Navier-Stokes equations and equations for k˜ and ε˜ , given by the turbulence model, are solved during a simulation. Furthermore, the values of constants Sct, C1, and C2 are 0.85, 2.43, and 2.0, respectively. These values are recommended in ref 3 for the mixture fraction. In this work, they have been also adopted for the mean and variance of the progress variable. To conclude, the turbulent database is constructed a priori to speed up the numerical simulations. This is basically a fivedimensional look-up table where the density, source term of progress variable, temperature, and species mass fractions are ˜2 , c˜, ˜ given as functions of Z˜, Z′′ c′′2 , and h˜. Transport ˜ . Then c˜, c˜′′2 are equations are solved for Z˜, Z˜′′2, Y˜, Y˜′′2, and H calculated with eqs 10 and 11 from Y˜ and Y˜′′2. The scaled ˜ . Then, Z˜, Z˜′′2, c˜, enthalpy, h˜, is determined with eq 4 from H 2 ˜ c˜′′ , and h are used to retrieve the density and the chemical source terms of Y˜ and Y˜′′2 from the turbulent database. The density and the source terms are then used back in the transport equations. The other variables from the database (temperature and species mass fractions) are retrieved at the end of the simulation for post-processing. 4. Validation of the FGM-PDF Combustion Model The FGM-PDF model was validated for a diffusion turbulent flame, the Sandia Flame D. This flame was selected for model validation because it is very well documented9,10,16 and it received considerable attention from different investigators.17–22 In this paper, only a selection of the results obtained with the (15) Peters, N. Turbulent combustion; Cambridge University Press: London, 2000. (16) Schneider, Ch.; Dreizler, A.; Janicka, J.; Hassel, E. P. Combust. Flame 2003, 135, 185–190. (17) Ihme, M.; Pitsch, H. LES of a non-premixed flame using an extended flamelet/progress variable model, 43rd AIAA Aerospace Sciences Meeting and Exhibit, 10-13 Jan 2005, Reno, NV; Paper 2005-0558. (18) van Kuijk, H A.J.A.; Bastiaans, R. J. M.; van Oijen, J. A.; de Goey, L. P. H. Modelling NOx-formation for application in a biomass combustion furnace. In Proceedings of the European Combustion Meeting 2005; Vandooren, J., Ed.; Combustion Institute: Louvain-la-Neuve, Belgium, 2005; Paper 160. (19) Zahirovic, S.; Scharler, R.; Obernberger, I. Advanced gas phase combustion models: valiadation for biogases by means of LES and experiments as well as application to biomass furnaces. In Proceedings of The 7th European Conference on Industrial Furnaces and Boilers; Porto, 18-21 April 2006. (20) Pitsch, H.; Steiner, H. Phys. Fluids 2000, 12:10, 2541–2554. (21) Xu, J.; Pope, S. B. Combust. Flame 2000, 123, 281–307. (22) Roomina, M. R.; Bilger, R. W. Combust. Flame 2001, 125, 1176– 1195.


FGM-PDF model for Sandia Flame D is presented. For more results and a comprehensive analysis of the simulations, the reader is referred to ref 6. 4.1. Computational Mesh, Boundary Conditions, and Flamelet Generation. Sandia Flame D is a piloted jet flame, the fuel consisting of a mixture of CH4 (25 vol % ) and air (75 vol % ). The fuel nozzle has a diameter of D ) 7.2 mm and it is surrounded by a pilot nozzle with a diameter of Dp ) 2.53D and an air coflow. The pilot produces the same equilibrium composition as a mixture of the main fuel and oxidizer with a mixture fraction of Z ) 0.27, which is slightly lean compared with the stoichiometric mixture fraction of Z ) 0.35. The bulk velocities of the fuel jet, pilot and air coflow are 49.6, 11.4, and 0.9 m/s, respectively. The corresponding fuel stream based Reynolds number is Re ) 22 400. Due to the symmetry of the flame, a 2D axisymmetric modeling domain was employed. The structured numerical grid (125D × 42D) consists of 359 × 113 nodes. The central fuel jet (half of it) contains 5 cells on the radius with a minimum cell size of 0.7 mm. Stretching is applied toward the outer lateral boundary. The minimum axial cell size is 1.2 mm and stretching is applied toward the outlet. At the inlet boundary all required quantities are specified according to the experimental data given in ref 16 for the fuel jet, pilot and coflowing air stream. The flamelets used for the creation of the database have been computed with the laminar flame code CHEM1D.23 The chemistry was described with the GRI-Mech3.0 reaction mechanism.24 The turbulence model was the realizable k-ε model.3,25 The laminar database was constructed from 100 premixed flamelets with mixture fractions covering the flammability range from Z ) 0.18 to Z ) 0.56. These flammability limits correspond to the values reported in ref 26. Outside this range, all the variables have been interpolated between the values at the flammability limits and at the inlets (Z ) 0 and Z ) 1). The reason for taking premixed flames, even in this nonpremixed test case, is in the generality of the method. Parametrization on the basis of mixture fraction and a progress variable was already introduced by, e.g., ref 27, but they used nonpremixed flamelets as a basis. Here we will use premixed flamelets because then the progress is well-defined. In this way, the use of a scalardissipation rate is circumvented which is associated with additional assumptions. If the chemistry is close to equilibrium, it does not matter what flamelets are used. Moreover, in the grate furnace, gradients of progress variable are assumed to be larger than the gradients of mixture fraction, the latter being associated with the size of the grate. As in most investigations, in this test case heat loss is not taken into account, so the equation for enthalpy was not used. The turbulent database contains 51 points for mean mixture fraction, 40 for the mean progress variable, and 10 for each variance. The points for the mean mixture fraction and progress variable are equidistant while those for their variances are clustered in the region of small values. 4.2. Simulation Results for Sandia Flame D. In Figure 1, the predictions given by the FGM-PDF model along the (23) CHEM1D, A one-dimensional laminar flame code, Eindhoven University of Technology; http://www.combustion.tue.nl/chem1d. (24) Bowman, G.; Frenklach, M.; Gardiner, B.; Smith, G.; Serauskas, B. GRI-Mech, Gas Research Institute, Chicago, IL; http://www.me.berkeley.edu/gri-mech/index.html. (25) Jones, W. P.; Launder, B. E. Int. J. Heat Mass Transfer 1972, 15, 301–314. (26) Cashdollar, K. L.; Zlochower, I. A.; Green, G. M.; Thomas, R. A.; Hertzberg, M. J. J. Loss PreVention Process Ind. 2000, 13, 327–340. (27) Pierce, C. D.; Moin, P. J. J. Fluid Mech. 2004, 504, 73–97. (28) van Kuijk, H. A. J. A.; van Oijen, J. A.; Bastiaans, R. J. M.; de Goey, L. P. H. Combust. Flame, in press.


centerline are compared with measurements. The prediction of the flow field (Figure 1a) shows that the axial velocity is well predicted in the first and last part of the domain, but it is overpredicted around x/D ) 25. On the other hand, the turbulent kinetic energy is underpredicted in the interval x/D ) 10-30. In Figure 1b, the mean and variance of the mixture fraction are presented. Both quantities are in reasonable agreement with the measurements in spite of the deviations in the flow field. It can be noticed that the shape and the magnitude of the variance of the mixture fraction are well predicted, but the maximum value is slightly shifted to the left. Panels c-f of Figure 1 present predictions of species and temperature, given by the combustion model. In general, all main species (CH4, O2, CO2, and H2O) and the temperature show good agreement between simulations and experimental data. As for the intermediates (CO and H2), it can be seen that these are overpredicted for x/D < 40. The difference in the accuracy of the predictions for CO2 and CO (see Figure 1d) could be explained by the fact that probably the formation of CO does not follow closely the progress of CO2 (which is the progress variable). It follows that, to improve the prediction of CO, an extra transport equation for the CO mass fraction might be needed. Nevertheless, this step was not taken in the present investigation. It is also worth mentioning that modest predictions of CO and H2 were also reported by other investigators (see for example ref 20), in spite of the fact that in ref 20 a much more elaborate model was used which combines the Lagrangian flamelet model and unsteady flamelets with LES. In Figure 1f, besides the temperature, the mass fraction of NO is also plotted. It can be observed that the predicted profile of NO is close to the measurements only in the central part of the domain. Thus, the magnitude of the maximum value of NO is well predicted though its position is shifted to the left. In the rest of the domain, however, the predicted NO is practically zero, while the experimental data show that NO is present. This shows that the transport of NO is not well represented in the model and it can be improved by solving an extra transport equation for the NO mass fraction. In conclusion, the FGM-PDF model gives a reasonable agreement for predictions of the experimental data for Sandia Flame D. The overprediction of CO and H2 in the rich domain indicates that these intermediates are in reality determined by the turbulent transport (diffusion) rather than by the chemical composition corresponding to the local combination of mixture fraction and progress variable. A similar finding was also reported in ref 20. This can be resolved by solving extra transport equations for these species. In the next section, the FGM-PDF model is used for the simulation of a biomass grate furnace. Because of the fact that CO and H2 are not intermediates but main species in this case (they are components of the fuel), it is expected that the prediction of CO and H2 will be improved with respect to the Sandia Flame D. This will be confirmed by the results presented in the following section. 5. Application of FGM-PDF to a Biomass Grate Furnace In cooperation with Graz University of Technology (TUGraz), the FGM-PDF model was applied to a pilot-scale lowNOx biomass grate furnace for the prediction of combustion and NOx emissions. In Figure 2 the general layout of such a furnace is shown. Low-NOx grate furnaces are divided into a primary and a secondary combustion zone by staged supply of the combustion air. The design of the primary combustion zone ensures sufficient residence time in an oxygen-lean atmosphere


Albrecht et al.

Figure 1. Axial profiles of (a) mean axial velocity and turbulent kinetic energy, (b) mean mixture fraction and mixture fraction variance, (c) mean mass fractions of CH4 and O2, (d) mean mass fractions of CO2 and CO, (e) mean mass fractions of H2O and H2 and (f) mean temperature and mean mass fraction of NO (lines, predictions; symbols, measurements).

Figure 2. Schematic of a biomass grate furnace. Courtesy of TU-Graz.

in order to reduce nitrogen oxides formed during the conversion of the solid biomass fuel on the grate. The secondary combustion

zone is designed as an oxygen-rich zone to provide for flue gas burnout. The staged flue gas recirculation is introduced for temperature control in the furnace in order to prevent ash slagging or sintering as well as for enhancement of turbulent mixing, resulting in a faster CO burnout and more efficient NOx reduction. The biomass fed into the furnace is transported by the grate from left to right. The primary air as well as a part of the total amount of the recirculated flue gas is blown from below. The fuel dries and undergoes gasification/combustion reactions on the grate. As a result, a gaseous mixture of gasification/combustion products and air is formed just above the grate. This mixture starts to burn in the primary combustion zone and is then mixed with the rest of the recirculated flue gas and secondary air (see Figure 2) injected through the nozzles. After leaving the secondary combustion zone, the combustion products exit the furnace and than pass through the boiler. In contrast to the simulation of Sandia Flame D, here the enthalpy is required. The combustion inside the furnace is considered adiabatic (no heat loss to the walls), and therefore the transport equation of the enthalpy has no source term.



Table 1. Fuel Composition and Operating Parameters for the Furnace quantity

value

operating parameter

value

thermal load (kWth) water content (wt % db) C content (wt % db) H content (wt % db) O content (wt % db) N content (wt % db) ash content (wt % db) LHV (MJ/kg wb)

500 8 49.5 5.6 40.1 0.27 4.53 16.73

recirculation ratioa primary air ratiob grate effective air ratioc effective air ratiod total air ratioe

0.37 0.60 0.78 0.95 1.60

a Mass of flue gas recirculated/mass of total flue gas in the furnace. Based on the total amount of primary air. c Based on the total amount of primary air and recirculated flue gas supplied below the grate. d Based on the total amount of primary air and total amount of recirculated flue gas. e Based on the total amount of combustion air injected. b

Table 2. Composition of Fuel and Oxidizer Streams species (mass fractions)

fuel

oxidizer

CO H2 CH4 CO2 H2O NO NH3 N2 O2 temperature (K) stoichiometric mixture fraction

0.100 0.005 0.010 0.200 0.095 5 × 10-5 3 × 10-4 0.590 1386 0.63

0.767 0.233 361

However, the recirculation and addition of secondary air results in changing enthalpy boundary conditions at the inflows. Thus, the transport equation of H resembles the mixture fraction, but it has different boundary conditions. It should be noted that the combustion inside the furnace is in fact not adiabatic, heat being lost through radiation. Here radiation was not considered because the aim of the investigation was to compare the FGM-PDF flamelet model with the EDC model rather than to reproduce the exact conditions in the furnace. To keep the number of control variables to a minimum, the variance of the progress variable was removed. This is justified by the expected modest influence of the variance of the progress variable, as observed in case of Sandia Flame D (as shown in ref 6). 5.1. Mixture Fraction Based Grate Profiles. Grate profiles of species, temperature, and velocity at the top of the biomass layer are used as boundary conditions of the gas phase turbulent combustion problem. The measurements are founded on realistic solid biomass fuel composition and operation parameters (see Table 1) and have been measured by TU-Graz. An empirical model for fixed bed combustion of solid biomass fuels developed in ref 2 and extended in order to allow for release of the NOx precursors (NO and NH3 as well as HCN in small amounts1) was applied for the calculation of the composition, temperature, and velocity of the flue gas released as a function of the position on the surface of the fuel bed. Based on the species mass fractions along the grate, provided by TU-Graz, the element mass fractions Zj are calculated. From that the mixture fraction Z is calculated with eq 1. Z ) 1 (fuel) is defined at the position on the grate where the combined element mass fraction (first term in the numerator of eq 1) is maximum. The oxidizer is defined as air (Z ) 0). The composition and temperature of the fuel (Z ) 1) and oxidizer (Z ) 0) as well as the stoichiometric mixture fraction are shown in Table 2. From a fundamental point of view in combustion of hydrocarbon with air there are four elements present, C, H, O, and

Figure 3. Comparison of new (solid line) and original (dashed line) CO mass fraction profiles on the grate: x is the distance along the grate and L is the total length of the grate (L ) 2.84 m). Table 3. Boundary Conditions for Gas Recirculation and Secondary Air Inlets recirculation gases YO2 YCO2 YH 2 O YN2 temperature (K) velocity (m/s) mixture fraction enthalpy (kJ/kg) turbulence intensity (%) hydraulic diameter (m) secondary air YO2 YCO2 YH 2 O YN 2 temperature (K) velocity (m/s) mixture fraction enthalpy (kJ/kg) turbulence intensity (%) hydraulic diameter (m)

EDC

FGM-PDF

0.079 0.174 0.057 0.690 473 18.814 10 0.034

0.174 18.814 0.456 -2131a 10 0.034

0.233 0 0 0.767 298 18.783 10 0.034

0 0 18.783 0 0 10 0.034

a The negative value of the total enthalpy is caused by the negative value of the enthalpy of formation of products.

N. Therefore, in principle, only four transport equations are needed to describe the mixing process. Additionally, since the element mass fractions sum up to unity, three equations are required. In the present method, in fact we assume that there is correlation in the fuel and in the oxidizer; i.e., ZH is coupled to ZC, and ZO is coupled with ZN. This removes two equations, so that only a single mixture fraction would be sufficient. Now, new approximated grate profiles of the species can be generated, assuming that the species Yi present on the grate result from the mixing of the new defined fuel and oxidizer, in terms of Z. fu ox ) Yox Ynew i i + Z(Yi - Yi )

(17)

where Yi stands for CO, H2, CH4, CO2, H2 O, NO, and NH3. As an example, the comparison of the original and new profile of CO mass fraction is given in Figure 3. It can be noticed that the new profile does not match always with the original one. This is caused by the fact that the Zj present on the fuel bed have slightly different profiles from each other and as a result they cannot exactly be described by a single mixture fraction, but the correspondence is good enough. It should be noted that it is not the scope of the present investigation to achieve a very accurate description of the species released from the biomass


Albrecht et al.

Figure 4. Comparison of 2D biomass grate furnace profiles predictions with FGM-PDF model (left) and EDC model (right).

bed, but rather to compare the FGM-PDF model with the EDC model, for a specific choice of boundary conditions. The new profiles based on the single mixture fraction approach are considered a good choice, since Yi ≈ Ynew i . A comparison of the results achieved with the EDC model for the original and new profiles is presented at the end of section 5.4. The choice of the EDC as reference for comparison with FGM-PDF is justified by the fact that EDC is the only turbulent combustion model standard available which can handle variable fuel inlet composition profiles together with detailed reaction mechanisms. 5.2. Boundary Conditions. Based on the geometry of the low-NOx pilot-scale furnace depicted in Figure 2, a 2D computational domain was constructed. The unstructured mesh has 120 000 cells with a minimum edge size of 1 mm around the inlets and a maximum edge size of 20 mm. At the grate, the boundary conditions for the EDC simulations consisted of profiles for species mass fractions, temperature, and velocity. The species and temperature have been calculated by using eq 17, while the velocity has been taken directly from the data provided by TU-Graz. As for FGM-PDF simulations, the profiles needed are the mixture fraction, progress variable, enthalpy variable, and velocity. The Z profile is calculated with eq 1, while the profiles of Y and H are calculated with eq 17. Furthermore, for both EDC and FGM-PDF simulations, the

boundary conditions for the turbulence quantities were 30% for the turbulence intensity and 1.5 m for the hydraulic diameter. The boundary conditions used in EDC and FGM-PDF simulations for the gas recirculation and secondary air inlets are given in Table 3. In case of the FGM-PDF calculations, boundary conditions for the variance of the mixture fraction have also been set. Thus, at the grate, a profile was specified for the variance of the mixture fraction. This profile has the shape of the maximum possible value of the variance of the mixture fraction ˜2 ) Z ˜(1 - Z ˜) Z′′ max

(18)

Due to the fact that the values given by eq 18 are unrealistically large, the magnitude of the variance of Z was taken equal to 2 ˜ 20% of Z′′ max . This magnitude ensures that at the grate the creation and destruction of source terms in the transport equation of the variance of mixture fraction (see eq 15) are balancing each other. As for the other two inlets (gas recirculation and secondary air), the variance of the mixture fraction was set to zero. 5.3. Manifold Construction. As in the case of Sandia Flame D, a flow solver with the realizable k-ε turbulence model was employed for a biomass grate furnace simulations. The chemistry was described by the GRI-Mech2.11 detailed mechanism.24



Figure 5. Comparison of 2D biomass grate furnace profiles predictions with FGM-PDF model (left) and EDC model (right).

This mechanism was selected because it is the most detailed reaction mechanism for hydrocarbon combustion with less than 50 species (the maximum number of species that can be used by the EDC model in the flow solver). The laminar database was constructed from 41 × 41 (41 Z values for each of the 41 h levels) premixed flamelets with mixture fractions covering the flammability range from Z ) 0.4 to Z ) 0.8 and scaled enthalpy variable from 0 (products at ambient temperature) to 1 (adiabatic). The flamelets and their flammability limits were calculated with the laminar flame code CHEM1D.23 Outside the flammability range, all variables have been interpolated between the values at the flammability limits and at the inlets (Z ) 0 and Z ) 1). The turbulent database contains 41 × 41 × 21 × 11 points corresponding to the mean mixture fraction, mean enthalpy, mean progress variable, and mixture fraction variance, respectively. The points for the mean mixture fraction, enthalpy, and progress variable are equidistant while those for the mixture fraction variance are clustered in the region of small values. 5.4. Results and Discussion. In Figures 4 and 5, a comparison of the results obtained with the FGM-PDF model and the EDC model is given. It can be noticed that the simulation does not reproduce exactly the position of the flows entering the furnace from figure 2. Thus, the recirculated gases are introduced through a small orifice placed in the vertical left wall

and the secondary air enters the furnace through 4 tiny holes in a single row, after the first turn of the gases in the furnace. In Figure 4a, at the bottom of the furnace, the distribution of the mixture fraction on the grate can be seen. The mixture fraction is 1 somewhere in the middle of the grate, where only gaseous fuel is present, and 0 at the sides of the grate, where only air is present. In between, there are mixtures of fuel and air with mixture fractions between 0 and 1. This distribution of the mixture fraction on the grate corresponds to the different degrees of biomass conversion to gasification/combustion products along the grate when blowing air from below. Later on, the streams with different mixture fractions coming from the grate mix with each other and start to burn, leading to a more homogeneous mixture with rising temperature (see also Figure 4b). The recirculated gases are than mixed with the main flow. As a result, the temperature decreases (locally) and the mixture is diluted. After the first turn in the furnace, the main flow meets the secondary air flows. Thus, the rest of the fuel present in the mixture is combusted and the mixture fraction decreases, the mixture changing from slightly rich to lean (Zst ) 0.63). In Figures 4c and 5a, the mass fractions of CO2 and CO are shown. They represent the main product and fuel, respectively. The predictions given by FGM-PDF and EDC are generally in good agreement, but the flame predicted by the FGM-PDF model seems to start sooner (see Figure 4, b and c).


Albrecht et al.

Figure 6. Comparison of 2D biomass grate furnace predictions with EDC model for the new (left) and original (right) fuel-bed profiles.

The higher concentration of CO2 in the flame formed around the main fuel stream indicates that the FGM-PDF model predicts conditions closer to equilibrium in that region. Compared to EDC, conversion is faster in FGM because source terms are overpredicted due to the low variance of mixture fraction. It appears that the production of the variance of mixture fraction at the inflow boundary is relative small, due to mixture fraction gradients that are small and given by the size of the grate. Furthermore, the composition is already close to equilibrium at the grate. In FGM the small variances are directly taken into account whereas in EDC it takes a little longer due to the integration of the large consumption rate. Also the turbulence model is not ideal. As for CO, the very good agreement between the two models proves that CO is indeed much better predicted by FGM-PDF in the case of the biomass grate furnace than for Sandia Flame D, as argued before. In Figure 5, b and c, NO and NH3 mass fraction are presented, respectively. In the conditions present in the furnace, it can be assumed that two mechanisms of NO formation are active: thermal (T > 1800 K) and fuel NO (from NH3). Thus, Figure 5, b and c, shows a correlation between the consumption of NH3 and the production of NO, while Figures 5b and 4b indicate that the peak value of NO correspond to the top temperature locations.

It should be mentioned that in Figures 4 and 5 the same color scale was used for EDC and FGM-PDF results corresponding to a certain quantity. The only noticeable differences between the maximum values predicted by the two models have been observed for temperature and NO mass fraction. Hence, the maximum value of temperature was 1910 K for FGM-PDF as compared to 1870 K for EDC (see Figure 4b) while the maximum value of NO mass fraction was 3.63 × 10 -4 for FGM-PDF as compared to 2.22 × 10 -4 for EDC (see Figure 5b). In conclusion, the predictions given by FGM-PDF model agree generally well with the predictions of EDC model, while the computational time is decreased from weeks (EDC) to hours (FGM-PDF). The only important difference between the models is noticed for NO (63%), which is very sensitive to temperature differences. This is caused by the fact that NO is a slow species and therefore it cannot be well predicted by databases based on steady-state flamelets. To improve the prediction of NO, an extra transport equation should be solved. However, in this investigation this step was not taken. In order to evaluate the influence of the approximation made when constructing the new profiles (based on the mixture fraction) on the predictions, a comparison with the original profiles is given in Figures 6 and 7. The same EDC model with



Figure 7. Comparison of 2D biomass grate furnace predictions with EDC model for the new (left) and original (right) fuel-bed profiles.

GRI-Mech2.11 mechanism was used in this comparison. All the quantities are plotted using the same scale for the new and original profiles. The results presented in Figures 6 and 7 show a reasonable agreement between the two simulations. Quantitatively, however, significant differences are calculated for temperature and CO 2. Thus, the top temperature is 1870 K for the new profiles as compared with 1770 K for the original ones and the maximum mass fraction of CO2 is 0.237 for the new profiles and 0.260 for the original profiles. These differences are caused by the fact that, when constructing the new profiles, element and enthalpy conservation was not enforced separately on each of them but rather globally through the mixture fraction. A better approximation of the profiles could be achieved by introducing an additional degree of freedom. This can be realized by adding a second mixture fraction. In this investigation, however, we did not aim to a very accurate description of the species released from the biomass bed, but rather to compare the FGM-PDF model with the EDC model, for a specific choice of boundary conditions. In reality the “fuel” leaving the grate is not of constant composition and will contain higher hydrocarbons and HCN. It is shown that the calculation results are sensitive to the fuel composition profile at the grate so one may expect the effect of reducing the equation set to only one mixture fraction to be significant. In order to handle nonconstant fuel composition,

only one mixture fraction will not suffice anymore and more have to be added. For more complex fuels, a more extended kinetic scheme has to be employed to generate the manifold. Besides this, attention should be given to the physical validation with measurements. Moreover, the correctness of the predictions associated with turbulence modeling is an important item for future research. Another important aspect is the conversion in the fuel bed and the coupling with the present gas phase combustion model. At the moment our efforts are dedicated to the last issue (e.g., ref 28), although the other issues need attention in the future as well. In the present study, radiation was not taken into account, although it is important for the coupling of the gas-phase turbulent combustion with the grate. For this, the prediction of radiant species is important. These include water and carbon dioxide, which are easily predicted by both methods, and soot. The application of FGM enables us to include soot quite easily as well. In this case, the manifold should be created with a detailed scheme including higher hydrocarbons. This is possible with marginal additional computational costs, which have to be invested in the creation of the manifold. However, the present EDC calculations in a 2D domain were already very expensive. To take a large chemical mechanism into account with EDC is almost impossible. The coupling of the grate with the gas phase


turbulent combustion for the radiant energy fluxes will be implemented in new projects. 6. Conclusions A new FGM-PDF procedure was applied to model combustion in a grate furnace. This FGM-PDF combustion model was validated for a piloted diffusion turbulent flame, the Sandia Flame D. The comparison of the predictions for the validation case leads to the following conclusions. The FGM-PDF model gives generally good agreement of predictions with measurements. The overprediction of CO and H2 in the rich domain indicates that these intermediates are in reality determined by the transport (diffusion) rather than by the chemical composition corresponding to the local combination of mixture fraction and progress variable. A similar finding was also reported in ref 20. Therefore, the predictions of CO and H2 can be improved by solving extra transport equations for these species. The FGM-PDF model was successfully applied to a biomass combustion grate furnace. Realistic species profiles on the grate were assumed. An enthalpy variable had to be added to take into account the influence of the recirculation gases and secondary air on the combustion. The results of FGM-PDF have been compared with the EDC model. Overall good agreement was found between the two models. The main difference is that FGM-PDF predicts a faster conversion of the fuel bed species into products. Furthermore, slightly higher temperatures accompanied by higher NO levels are predicted by FGM-PDF. From the paper, it is clear that the usability of the method is very high due to high accuracy and small computational times. This is true if the fuel has a constant composition. When the fuel has local changes in composition then more (element fractions) conservation equations have to be applied. It is shown that deviations of constant composition change the result. However, the largest absolute differences appear in the tem-

Albrecht et al.

perature and CO2 predictions in which the spatial structure remains the same. Furthermore, there is a relative large influence of the amount of primary air, recirculation, and secondary air in the results. On top of this, the applied turbulence model will not be able to provide perfect quantitative results. Thus, the present approach is a good approach to guide the design, recirculation, and staging strategy with respect to emissions. In conclusion, this paper presents the use of a flamelet model (FGM-PDF) for a very complex industrial application: a biomass grate furnace. The FGM-PDF model produces comparable results with EDC, using a detailed chemical description of the combustion system (as in the EDC) but at much lower calculation time and memory usage. Thus, the calculation time with GRI-Mech2.11 was reduced from weeks (EDC) to hours (FGM-PDF). Furthermore, FGM-PDF is based on more physical grounds than EDC with respect to the modeling of turbulentchemistry interaction thanks to the flamelet structure integrated in its PDF approach. For more quantitative predictions, reproducible measurements must be used to validate the method. For the simulation of fuels with changing composition, more mixture fractions should be taken into account. Turbulence modeling can be improved by switching to Reynolds stress models in ensemble averaging or by introducing large eddy simulations. It is questionable whether these improvements pay off in the design process. At the moment, research is conducted in the description of conversion in the fuel bed (e.g., ref 28) and coupling of the bed with the present gas phase combustion model. Acknowledgment. The present research was funded by EU within the European project OPTICOMB, NNE5-2001-000639. The authors thank Robert Scharler and Ingwald Obernberger from Graz University of Technology for their valuable contribution to this work. EF7007562

A Premixed FlameletâPDF Model for Biomass Combustion in a Grate

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