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Show A solution for equation 1 has been discussed by Gosman, et ale (1969), based on a macrocontrol volume formulation. The geometry is subdivided into control volumes as shown in Figure 1. A flow solution is found based on the equations for mass, momentum, and turbulence using the fine grid . In the combustion model, other equations are solved using a slightly coarser grid to increase computational efficiency without loss of accuracy (Fiveland and Wessel, 1988). Integration of equation lover a typical control volume results in an equation of the form: ap +p - L ai +i + S. Vp N,S,E W,F,B (2 ) The summation in equation 2 extends over all neighbor computational cells and the value S. defines the source of + in the volume (Patankar, 1980). The coefficients (ap ' aE' aw, etc.) depend on flow rates across the volume faces <peueAe , PwuwAw' etc.) and on diffusion conductances <reAe/Ax, rnAn/AY, etc.) All control volumes in the enclosures are described by equation 2, resulting in a system of N-algebraic equations with N unknowns which can be solved for the transported quantity, +, throughout the computational domain. I I I I i , i --!- ~ ; -Y- -----------.--_ ..... ! I , !_-, , I~l 1\ I! j II' : . , L ! ~ 1- i,- I I ,-:- ~ II II: / I I I ~ t111 FLOW MODEL P BN R P BN R AP = AIR PORT BNR = BURNER I- , I j-- I ~ I - - '~ \ - - V !1.1 :. - ; I I : I I f-~ , i I I I I - - - --- ! / I II I,: , , II :: I I , ' , , - ----- I ; ! I I I V --~ /1 I I L -- I I I ! i /' LV I I I II, ' , , , COMBUSTION MODEL Figure 1. Finite-difference control volumes for the flow and combustion models. Averaging Procedure for Turbulent Quantities Turbulent fluctuations in the mixing of the reactants and products affect the mean chemical rates which have reaction time scales comparable with the 7 |