A second application is the comprehensive modeling of turbulent combustion and heat transfer in a float glass melting furnace, shown schematically in Fig. 8.. Preheated air is forced through one of several (six shown) portnecks with natural gas burners positioned at the outlet. The flame jet spreads over the glass melt, and exhausts through portnecks on the opposite side of the furnace through regenerators designed to recoup the energy in the combustion gas. Some time later in a repeating cycle, the flow reverses and the now-hot exhaust regenerator is used to preheat the inlet combustion air. The high air
Influence
Base Case 1.2 (b)
0.8
X,m q", qM'
0.6 ' [ _ 1 Gray Gas 438.9 243.5
/I EAJ=O.8 _ • Convolution 381.6 214.3 - - - - -Superposition 403.4 229.0 0.4 .~ ",,=C.2[ - - -Superposition 422.6 60.8
"'-'..: (kW/m')
0.2 ~_....
~~403.4 229.0 398.0 224.6 389.6 217.9 388.0 216.6 (kW/m')
;;/
{?,j'-Base Case
( :.;, - ã[COJ=O ',. ---[COJ=[CO,J=O
, '~-.. ["(J/2
-':::-.. '
--
---:.::::..:.:::..:----
Oc...~--'-'-~...-L...~...~...~_'_='~...J
-400 -200 0 200 400 600 -500 -250 0 250 500 750 1000
-dqldx, kW/m' -dq/dx, kW/m'
Predictions of radiative flux divergence, and incident and net flux on the melt surface:
of a) of species concentrations, and b) modeling approach.
1.2 (a)
x,m0.8 0.6 0.4 02
0-600
Figure 7.
Figure8. Schematic iUustration of float glass furnace.
preheat (typically 1400 K) and combustion temperatures make thermal NO. a major environmental issue. While regenerative preheating of the combustion air increases the energy efficiency, it results in dramatic increases in the exhaust pollutant emissions.
The turbulent mixing, reaction, and heat transfer have been modeled comprehen- sively for one port module of the float glass furnace illustrated in Fig. 8. Exploiting the symmetry, the model extends geometrically from the centerplane of a port to a verti- cal plane halfway between adjacent ports. Furnace dimensions and boundary conditions may be found elsewhere [20]. PCGC-3, a generalized, comprehensive, three- dimensional combustion code developed at Brigham Young University for modeling turbulent combustion in practical systems was used. Thek-e model was employed for turbulence closure, and the mixture fraction-PDF approach was used to describe chemical reaction. The discrete ordinates model was used to solve the Radiative Transfer Equa- tion. ¥ore details of the code may be found elsewhere [21]. The local gas enthalpy is coupled to the radiative transfer via the radiative source term. In tum, the radiative trans- fer is coupled to the local enthalpy and species conservation via dependence of the radia- tive properties on local thermodynamic state. Simulations were perfonned with 96,228 (108 x 27 x 33) cells, which was a compromise between computation time and accu- racy. The radiative properties were modeled in two ways: 1) The local absorption coef- ficient was calculated from a local emissivity by a gray model approach using the rela- tion 7(=-In(l -e)/L,whereL is the geometric mean beam length for the furnace. The local emissivity was determined from curve-fits of the Hottel charts as a function of local gas composition and temperature. 2) The SLW model was used for a CO/HP mixture of varying concentration and temperature using the convolution approach with three optimized gray gases, as summarized previously. Inputs and modeling approach for the two different simulations were, in all other aspects, identical.
Figure 9 shows predictions of gas temperature averaged over cross-section at each position along the axis of the flame jet between inlet and exhaust ports for the two ra- diative property models. While this average temperature may not be the most appropri- ate figure of merit for comparing the simulations, it nevertheless illustrates differences in predicted temperature for the two modeling methodologies. The rapid initial rise due to ignition is seen in the figure, after which the SLW model prediction is observed to rise more quickly than the gray model approach. The difference in exhaust gas tempera-
2200
lo: 2100
:>~
eIII 2000
a. 1900 {!!.E
III 1800
'"
e 1700
~0; 1600
- Gray Model, "=-In(l -r)/L
~ 1500 - - - SLW Model
14000 2 4 6 8 10
DistanceAlong Flame Jet Axis, m
Figure9. Profiles of predicted cross-section averaged temperature as a function of distance along the flame jet axis for both conventional and SLW radiative property models.
ture between the two models is greater than 100 deg K. While this may not seem sig- nificant, it should be emphasized that 100 deg K at these high temperatures has a dra- matic impact on the NOxproduction rate, which doubles for every 90 deg K rise in tem- perature in this range [22]. Indeed, the SLW model simulations performed here predicted NOxlevels at the furnace exit nearly three times higher than the gray model prediction.
Using the gray model approach yields erroneously low temperatures, with the perception of lower exhaust emissions. Further, the heat transfer efficiency is lower as predicted by the more accurate SLW model, evidenced by the higher furnace exhaust temperatures.
Parametric simulations revealed that the direct integration approach and an increase in the number of gray gases from three to five yielded SLW predictions virtually identical to the superposition approach data presented here.
5. Summary
This paper has summarized the SLW model for predicting radiative transfer in high tem- perature gases. The model yields nearly the accuracy of costly line-by-line predictions at significant computational savings. Its use in industrial applications has shown the im- portance of accurate radiative transfer modeling both from the standpoint of energy effi- ciency and environmental pollution.
Acknowledgments. Much of this work was supported by the U.S. National Science Foundation through the Advanced Combustion Engineering Research Center.
6. References
1. Goody, R.M. and Yung, Y. L.: Atmospheric Radiation,Clarendon Press, Oxford, 1989.
2. Arking, A. and Grossman, K.: The influence of line shape and band structure on temperatures in planetary atmospheres,J. Atmosph. Sci., 29 (1972),937-952.
3. Domoto, G.A.: Frequency integration for radiative transfer problems involving homogeneous non-gray gases: The inverse transmission function,J.Quant. Spectr. Rad. Transfer,14 (1974), 935-952.
4. Hottel, H.C. and Sarofim, A.F.: Radiative Transfer,McGraw-Hili, New York, 1967.
5. Modest, M.F.: The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative trans- fer,ASMEJ.Heat Transfer,113 (1991), 650-656.
6. Denison, M.K. and Webb, B.W.: A spectral line-based weighted-sum-of-gray-gases model for arbi- trary RTE solvers,ASMEJ.Heat Transfer,115(1993), 1004-1012
7. Denison, M.K. and Webb, B.W.: An absorption-line blackbody distribution function for efficient cal- culation of gas radiative transfer,J.Quant. Spectr. Rad. Transfer,50 (1993), 499-510.
8. Denison, M.K. and Webb, B.W.: k-distributions and weighted-sum-of-gray-gases--a hybrid model, Heat Transfer -1994,2(1994),19-24.
9. Denison, M.K. and Webb, B.W.: Development and application of an absorption-line blackbody distri- bution function for CO2,Int.J.Heat Mass Transfer,38 (1995),1813-1821.
10. Denison, M.K. and Webb, B.W.: The spectral line-based weighted-sum-of-gray-gases model in non- isothermal non-homogeneous media,ASMEJ.Heat Transfer,117 (1995), 359-365.
II. Denison, M.K. and Webb, B.W.: The spectral-line weighted-sum-of-gray-gases model forHplC02
mixtures,ASMEJ.Heat Transfer,117 (1995), 788-798.
12. Denison, M.K. and Webb, B.W.: The absorption-line blackbody distribution function at elevated pres- sure,Radiative Transfer-1, Proceedings of the First International Symposium on Radiation Transfer,Ed.
M.P.Mengti~,Begell House, New York, pp. 228 - 238, 1996.
13. Denison, M.K.: A Spectral Line-Based Weighted-Sum-of-Gray-Gases Modelfor Arbitrary RTE Solvers, Ph.D. Dissertation, Department of Mechanical Engineering, Brigham Young University, Provo, Utah, 1994.
14. Rothman, L.S., Gamache, R R., Tipping, R.H., Rinsland, C.P., Smith, M.A.H., Chris Benner, D., Malathy Devi, V., Flaud, J.M., Camy-Peyret, C., Perrin, A., Goldman, A., Massie, S.T., Brown, L.R.: The HI- TRAN molecular database: Editions of 1991 and 1992,J.Quant. Spectr. Rad. Transfer,48 (1992), 469- 507.
IS. Goody, R.M., West, R., Chen, L., and Chrisp, D.: The correlated-k method for radiation calculations in nonhomogeneous atmospheres,J. Quant. Speetr. Rad. Transfer,42 (1989), 539-550.
16. Lacis, A.A., and Oinas, V.: A description of the correlated k-distribution method for modeling nongray gaseous absorption, thermal emission, and multiple scattering in vertically inhomogeneous atmospheres, J.Geophys. Res.. 96 (1991), 9027-9063.
17. Solovjov, V.P.: Spectral line Weighted-Sum-of-Gray-Gases Modeling of Radiative TransferinMulti- component Gas Mixtures,Ph.D. Dissertation, Department of Mechanical Engineering, Brigham Young University, 1998 (in preparation).
18. Edwards, D.K.: "Molecular Gas Band Radiation," inAdvancesinHeat Transfer, Vol. 12, pp. 115-193, Academic Press, New York, 1976.
19. Walters, D.V. and Buckius, R.O.: Mean emission length approach to multidimensional radiative trans- fer including scattering and real gas absorption,Int.J.Heat Mass Transfer,35 (1992),131-140.
20. Newbold, J.: Combustion Measurements and Modeling ofan Industrial, Gas-Fired, Flat-Glass Furnace, M.S. Thesis, Department of Mechanical Engineering, Brigham Young University, Provo, Utah, 1997.
21. Hill, S.c. and Smoot, L.D.: A comprehensive three-dimensional model for simulation of combustion systems: PCGC-3,Energy Fuels,7 (1993),874-883.
22. Baulch, D.L., Drysdall, D.D., Home, D.G., and Lloyd, A.C.: Evaluated Kinetic Data for High Tem- perature Reactions,Butterworth, New York, 1973.
T.W. TONG and A. TARAFDAR Department ofMechanical Engineering Colorado State University
Fort Collins, CO80523-1374, USA
1. Introduction
In the past decade, considerable effort has been devoted to establishing a body of knowledge concerning heat transfer and combustion in porous radiant burners (PRBs).
The operation of PRBs typically involves feeding premixed gaseous fuel and air into a porous medium. By adjusting the fuel-air flow rate properly, combustion can be stabilized either inside the porous medium or in a region downstream from but very close to the porous exit plane. The heat of combustion released in the combustible mixture heats up the solid matrix, which emits radiant energy to a heat load. Due to enhanced rates of heat removal from the combusted gas, the flame temperature in a PRB is a few hundreds of °C lower than that in a conventional open-flame burner. As a result, PRBs generate lower emissions of NOx. Suitable applications for PRBs include situations where radiant heating is required and/or low NOx emission is desired. The objective of this chapter is to present an overview of the research aimed at gaining an understanding of the thermal behavior of PRBs. The presentation will draw upon the research conducted by the first author and his former colleagues at Arizona State University. For a more comprehensive review of this subject and access to an extensive list of the relevant references, the reader is referred to a recent review article published by Howell et al. [I].
2. Mathematical Modeling
One approach to gain an understanding of the thermal behavior of PRBs is to develop mathematical models that describe the relevant transport processes taking place. By modeling PRBs as an inert porous region in an adiabatic duct into which a fuel-air mixture is fed (Fig. I), one can develop a model that reveals important trends of the thermal characteristics of PRBs (Sathe et al. [2]; Sathe et al. [3]; Tonget al. [4]). The length of the porous medium is considered to be L. The flame may be located either inside or outside of the porous medium. The flow and heat transfer are considered to be one-dimensional and steady. Viscous effects are neglected. The solid matrix is assumed to be gray and emitting, absorbing, and scattering radiant energy. Scattering of radiant energy is treated as isotropic. Gaseous radiation is neglected compared to solid radiation.
The solid properties are assumed to be homogeneous and constant. To consider non-local thermal equilibrium between the gas and the solid phases, separate energy equations are used. With these assumptions and the configuration of the duct configuration shown in Fig. I, one can develop the following governing equations for multi-mode heat transfer and combustion in the porous medium (Satheet al. [2]).
89
A. Bejan et al. (eds.), Energy and the Environment, 89-100.
©1999Kluwer Academic Publishers.
Duct
Continuity Equation
Figure I. Schematic diagram of a porous radiant burner.
-(pu¢)=od
dx (1)
where ¢ is the porosity so that ¢<1for 0<x<Land ¢=1 elsewhere., The symbols are defmedinthe Nomenclature.
Species Conservation Equation
(k =I,K) (2)
where Vk is the diffusion velocity that is given by the sum of the diffusion velocities due to mole fraction gradients and thermal gradients (Keeet al. [5]).
Gas Energy Equation
(3)
Solid Energy Equation
Radiative Transfer Equation (RTE)
ai(x,,u) ( " ( ) .(T) 1 'fã( '\""
,u---+ aa +asJ' x,,u =aa1b s +-as Ix,,u)U,u
ax 2 -I
where ,u' is a dummy variable of integration.
Coupling between Eqs. (4)and (5)
1
qr =21l fi(x,,u'),u'd,u'
-I
Equation ofState
Boundary Conditions
(4)
(5)
(6)
(7)
The gas temperature and the species concentration is specified at the inlet section (x=-Xi)'while vanishing gradients are imposed at the exhaust section (x=xe).
(8) At X=Xe, dYk =dTg =0
dx dx
The boundary conditions for solid temperature are given assuming that the solid loses heat convectively to the gas so that
Atx=O, -k dTs =h(T -T)
s dx g s
(9) At x=L, k dT,. =h(T -T )
S dx g s
The upstream boundary condition for the radiant intensity is given assuming that the upstream environment can be characterized by a gray diffusely emitting and reflecting surface. On the downstream side, the burner is assumed to be seeing a black environment at Tb =298 K. Thus, we have
I
At x=O, j+(O)=&iJr;)+rd fr(o,-,u').u'd,u'
-I (10)
The foIlowing non-dimensional parameters result when Eqs. (1) through (10) are written in non-dimensional form (Satheet al. [2]),
where ae=ao+as'