NUMERICAL SIMULATION OF COMBUSTION IN INERT POROUS MEDIA

Transcription

1 Proceedngs of COBEM 2007 Copyrght 2007 by ABCM 19th Internatonal Congress of Mechancal Engneerng November 5-9, 2007, Brasíla, F NUMERICAL SIMULATION OF COMBUSTION IN INERT POROUS MEIA Roberto Carlos Moro Flho Marcelo J S de Lemos epartamento de Energa - IEME Insttuto Tecnológco de Aeronáutca ITA São José dos Campos SP - Brasl rmoro@.ta.br delemos@mec.ta.br Abstract. Ths paper presents numercal methods for the smulaton of combuston processes n porous meda usng a 1-step global mechansm. The model s based on a macroscopc formulaton of the heat and mass transport equatons for lamnar and turbulent flow. The concept of the double-decomposton, whch consders both tme fluctuatons and spatal devatons about mean values s used. The effects of the model on temperature, and speces are examned. Keywords: porous meda burner, premxed flame, numercal smulaton. 1. INTROUCTION Accordng to Pantang et al. (2006), porous meda combuston devces can be classfed nto two categores, one n whch the combuston s lly confned wthn the pores of the porous structure and the other one n whch the combuston takes place over the surface of the porous matrx. The frst one s recevng more attenton of researchers due to the numerous advantages, burnng of lean combustble mxtures, hgher ranges of flame stablty, lower pollutant formaton, etc. (Howell et al. (1996)). Systems based on fludzed bed combuston, n-stu combuston for ol recovery, household heatng combuston, are just a few examples of such applcatons (Trms and urst (1996)). In most of the studes of premxed combuston wthn nert porous meda the flow s assumed to be lamnar and one-dmensonal, the change n the pressure across the flame s generally neglgble compared to the absolute pressure, and the pressure s assumed constant (Baek (1989),Yoshzawa et al. (1988),Hsu et al. (1993),Neef et al. (1999)). The use of sngle-step global chemstry (Mohamad et al. (1994)) s common. The nadequaces of global knetcs are well recognzed, Hsu et al. (1993) presents a comparson between one-step and mult-step chemstry. Turbulence modelng of combuston wthn nert porous meda has been conducted by Lm and Matthews (1993)on the bass of an extenson of the standard k - ε model of Jones and Launder (1972). Work on drect smulaton of turbulence n premxed flames, for the case when the porous dmenson s of the order of the flame thckness, has also been reported n Sahraou and Kavany (1995). Studes on macroscopc transport modelng of ncompressble flows n porous meda have been based on the volume-average methodology for ether heat or mass transfer. In turbulent flows, when tme fluctuatons of the flow propertes are also consdered n addton to spatal devatons, there are two possble methodologes to follow n order to obtan macroscopc equatons, one, can be the applcaton of tme-average operator followed by volume-averagng, and, the other, the applcaton of volume-averagng before tme-averagng s appled. However, both sets of macroscopc transport equatons are equvalent when examned under the recently establshed double decomposton concept (Pedras and de Lemos (2000),Pedras and de Lemos (2001a),Pedras and de Lemos (2001b),Pedras and de Lemos (2001c)). The works of Pedras and de Lemos have been extended to heat and mass transfer n porous meda where both tme fluctuatons and spatal devatons were consdered for temperature(pedras et al. (2003)) and mass fracton(e-lemos e Mesquta (2003)). Because of mportant nfluence of lateral heat loss n porous medum burners, a two dmensonal model s necessary. The present paper follows the foregong works and presents a two dmensonal mathematcal model for lamnar and turbulent pre-mxed flame combuston n porous meda although n ths frst work only computatons of a one-dmensonal lamnar pre-mxed flame of methane/ar s presented. The numercal methodology employed s based on the control-volume approach wth a boundary-ftted non-orthogonal coordnate system. The reactor conssts of a two-regon burner wth a small pore sze upstream and a large pore sze downstream n order to acheve steady combuston n the porous meda, the flame can be stablzed at the nterface between the two dfferent porosty blocks. The effects of thermal power and excess ar rato are dscussed. Radaton, dsperson, thermal nonequlbrum, and turbulence, are subjects of ongong nvestgatons and wll be addressed n subsequent papers. 2. MACROSCOPIC TRANSPORT EQUATIONS

2 Macroscopc transport equatons for turbulent flow n a porous medum are obtaned through the smultaneous applcaton of tme and volume average operators over a generc flud property ϕ (see Pedras and de Lemos (2000),Pedras and de Lemos (2001a),Pedras and de Lemos (2001b),Pedras and de Lemos (2001c),Pedras and de Lemos (2003)). 2.1 Macroscopc contnuty equaton. u = 0 (1) where, u s the average surface velocty (also known as seepage, superfcal, flter or arcy velocty). Equaton (1) represents the macroscopc contnuty equaton for an ncompressble flud. 2.2 Macroscopc momentum equaton u u 2 µφ c Fφρ u u ρ = ( φ p ) + µ u ( ρφ u u ) u + (2) φ K K where the last two terms n equaton (2), represent the arcy-forchhemer contrbuton. The symbol K s the porous medum permeablty, c F = s the form drag coeffcent (Forchhemer coeffcent), p s the ntrnsc (volumeaveraged on flud phase) pressure of the flud, ρ s the flud densty and s a ncton of temperature, µ represents the flud dynamc vscosty and φ s the porosty of the porous medum. The turbulence s modeled usng a macroscopc k ε model gven by, ρ ρ where, µ t φ k [ ( k )] φ u = µ + ( φ k ) ρ u u : u + c ρ ρφ ε u k (3) σ k K µ t φ [ ( )] ε φ ε u ε ε = µ + ( φ ε ) + c1 ( ρ u u : u ) + c c 2 k ρ c2 ρφ u (4) σ ε k K k 2 µ t = ρc φ µ k ε 2 (5) and, v 2 ρφ u u = µ t 2 φρ k I (6) φ 3 s the macroscopc Reynolds tensor whch s modeled n analogy wth Boussnesq hypothess and ts generalzed form proposed by Kolmogorov (1942). 2.3 Macroscopc Energy Equaton ( ρ c p ) ( T ) = { K eff, f T } + φ HS f u (7) where, T s the averaged temperature for both the sold and the lqud accordng to the concept of local thermal H equlbrum Kavany (1995), s the heat of combuston, S s the rate of el consumpton determned by a one-step Arrehnous rate equaton, to be shown below, K s the effectve conductvty tensor gven by, eff

3 Proceedngs of COBEM 2007 Copyrght 2007 by ABCM 19th Internatonal Congress of Mechancal Engneerng November 5-9, 2007, Brasíla, F 3 K eff = φ k f + 1 s I + K { tor + K dsp + Kdsp,t + K t (8) 3β tortuosty dsperson turbulence 16σ ( ) ( T ) φ k + where, k f and k s are the thermal conductvtes for the flud and for the sold, β s the extncton coeffcent, σ s the Stefan-Boltzmann constant. 2.4 Macroscopc Mass Transport Equaton eff ( u m ) = ( φ m ) + φ S (9) where m s the local mass fracton for the el. The effectve dsperson tensor, eff, s defned as: eff = dsp + dff + t + dsp, t = dsp 1 µ µ φ t 1 µ φ + + I = + φ, dsp ρ Sc l Scl, t ρ Scl, ef ef I (10) where dsp s the dsperson tensor and, t + dsp, t µ t φ 1 = ρ Sc, l t I (11) dff = µ φ 1 I = I ρ Sc (12) 2.5 Combuston model Premxed el and ar enter the system whch s characterzed by two regons havng dfferent porostes. The regon at the upstream end has a lower porosty than the one at the downstream end whch works as a combuston chamber. The combuston reacton s assumed to occur n a sngle step accordng to the chemcal equaton CH 4 + 2(1 + Ψ)( O N 2 ) CO2 + 2H 2O + 2ΨO (1 + Ψ) N 2 (13) by, where, ψ s the excess ar n the reactant stream at the nlet of porous foam and s related to the equvalent rato Ф 1 Ψ = 1 (14) Φ where, ( m / m ox ) Φ = (15) ( m / m ) ox st The rato of el consumpton s gven by, 2 Ox a S = ρ A m m exp[ E / R T ] (16) where, A s the pre-exponental factor, E a s the actvaton energy and R s the unversal gas constant. The gas densty s updated usng the deal gas equaton n the form, * ρ = P R T (17) 0 / where, P 0 s a reference pressure, whch s kept constant durng the relaxaton process, and gas molecular mass. R * = R / M and M s the

4 3. NUMERICAL MOEL The governng equatons were dscretzed usng the fnte volume procedure Patankar (1980) wth a boundary-ftted non-orthogonal coordnate system. The SIMPLE algorthm for the pressure-velocty couplng was adopted to correct both the pressure and the velocty felds. The process starts wth the soluton of the two momentum equatons. Then the velocty feld s adjusted n order to satsfy the contnuty prncple. Ths adjustment s obtaned by solvng the pressure correcton equaton. After that, the turbulence model equatons and the energy equaton are relaxed to update the k, ε and mass fracton felds. etals on the numercal dscretzaton can be found n de Lemos and Pedras (2001). A computatonal grd of 266x30 nodes are used n x- and y-drecton. 4. RESULTS AN ISCUSION 4.1 Geometry and coordnate system Fgure 1 presents the geometry of the porous meda burner consstng of two dstnct regons wth dfferent porostes and permeablty. The gas mxture enters at the nflow boundary at the left, and the combuston products leave the burner at the outflow boundary at the rght. The walls are mpermeable and solated. The porosty φ 1 s smaller than φ 2. All numercal parameters are found n Table 1, the actvaton energy and the pre-exponental factor were obtaned from Mohamad et al. (1994). q w =0 u n T n H y x φ 1 2 x 1 =0.5L q w =0 φ L 4.2 Boundary condtons Fgure 1. Geometry of a porous nert meda burner and coordnate system. The followng boundary condtons are mposed on the soluton: at x=0, u= u n, v=0, T = T n, m = m,n, (18) at x=l, T x = m x u = x v = x = 0 (19) where, u and v are the components of arcy velocty vector n x and y. The non-slp condton for velocty s appled on both walls. 4.3 Temperature, concentraton, and volumetrc rate of el consumpton profles

5 Proceedngs of COBEM 2007 Copyrght 2007 by ABCM 19th Internatonal Congress of Mechancal Engneerng November 5-9, 2007, Brasíla, F Fgure 2 presents the temperature, mass fracton of el, and volumetrc rate of el consumpton profles for a rectangular adabatc burner wth an nlet velocty of 0.40 m/s, an excess ar rato of 0.67, and an nlet temperature of 335 K. The values for the one dmensonal plots were taken at the center lne of the combustor. The profles ndcate that the effect of the porous matrx on the flame structure s the ncrease of the flame thckness due to the hgh conductblty of the sold phase. Table 1. Operatng Condtons Quantty Value Actvaton energy (J/mol) - E a 130x10 3 K 1 (m 2 ) 3.827x10-10 K 2 (m 2 ) 9.375x10-9 φ φ Pre-exponental factor n reacton rate A (m 3 /kg.s) 3.0x10 8 Length of the combustor L (cm) 8 H (cm) 4 R (kj/kmol.k) R * (kj/kgk) P 0 (kn/m 2 ) m el,n T n (K) 335 Fgure 3 presents the pressure drop at the center lne of the combustor where, PN P P P P MIN = (20) MAX MIN The nflexon pont at the abscssa x/l=0,5 represents the nterface between the two porous materals. It was observed wth addtonal smulatons that the combuston affect the pressure drop slghtly when compared wth the flow wthout combuston.

6 1800 4, , , ,5 T (K) ,0 m x 100, S kg/m³s 1, T S m 1,0 0, ,2 0,4 0,6 0,8 1 x/l Fgure 2.Axal temperature, mass fracton of el, and volumetrc rate of el consumpton profles, y/h=0.5, Ψ= ,0 PN 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0,00 0,20 0,40 0,60 0,80 1,00 x/l Fgure 3. Pressure drop at the center lne of the combustor, u n =0.4 m/s. 4.4 Effect of nlet velocty on Temperature Profle Fgure 4 presents the effect of ncrease of nlet velocty on temperature profle for a rectangular adabatc burner wth an excess ar rato of 1.0. The fgure ndcates that, for lamnar flows, the flame moves downstream, and stablzes n an adabatc temperature hgher.

7 Proceedngs of COBEM 2007 Copyrght 2007 by ABCM 19th Internatonal Congress of Mechancal Engneerng November 5-9, 2007, Brasíla, F T (K) u n = 0,15 m/s u n = 0,21 m/s ,2 0,4 0,6 0,8 1 x/l Fgure 4. Temperature profles for dfferent nlet veloctes, Ψ=1.0. Note that decreasng the nlet velocty decreases the temperature, ncreasng the excess ar rato decreases the temperature also. 5. CONCLUSION The model can be used to predct the felds of temperature, mass fracton of the el, pressure drop, velocty and the effect of the ncrease of the power n a two dmensonal steady-state combuston problem wthn porous nert meda. Further work wll be carred out n order to smulate turbulent combuston n a porous medum wth the macroscopc two-energy equaton model. 6. ACKNOWLEGEMENTS The authors are thankl to CNPQ and FAPESP, Brazl, for ther fnancal support durng the preparaton of ths work. 7. REFERENCES

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