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Show and the production term becomes : P = «)(£)4+4tt)(£ (8) The flame surface destruction term is represented by the mutual annihilation or chemical shortening term. The rate of mutual annihilation of flame surface ( i dt ) is proportional to the mass of fuel burnt per second (we consider a small volume): (P2ULSJV), and inversely proportional to the mass of fuel to bum : (pYjuV). Hence : d{pSf) 2 UL S2 dt P YJu f In the present study, the destruction term in Eq. (3) is modelled as D = p2y^Sj ; this term will destroy the surface where fuel is not present. Note that, in all the flamelet models (Duclos et al. [8]), the consumption term is proportional to the square of the flame surface. Finally, the balance equation for flame surface per unit mass becomes : d(pu,S}) d ( LL, dS,\ (UL e\(VL\ 2UL 2 + P -T + °T \TT- \S,-?***} (9) More research effort is needed in order to include propagation and curvature effects on flame production/destruction mechanisms and also to determine how these efects act as source or consumption in the F S D balance equation. In the present study, the fuel consumption rate term is formulated as : w/« = -p2ULSf (10) Concerning the determination of UL and /;, one of the several possibilities consists in a local study of laminar suained flamelet with detailed chemistry and uansport coefficients (Sennoun [20]) for a large range of strain rates, equivalence ratios, fresh gases temperatures, and pressures. In the present study, the flame thickness values are obtained from the reference paper of Blint [2] and the laminar flame speed values are obtained from correlations of Metghalchi and Keck [14] which take into account the fresh gas temperature To, pressure and equivalence ratio tp: *-*•©)"(£)' a = 2.18 - 0.18(y> - 1) and b = -0.16 + 0.22(^> - 1) ULo = Bm + B2{<p - ipmf Tr and pr are reference temperature (300 K) and pressure (1 atm), respectively, and the constants are : Bm = 0.39m/s, B2 = -1.39m/s, and <pm = 1.08. The chemical kinetic mechanism used in this study is the one-step overall scheme which considers oxidation process to occur directly to CO2 and H20 : CnH2n+2 + -(3n + 1)02- > nC02 + (n + \)H20 The advantages are immediately obvious in that only 4 chemical species are involved in the formulation. Since a linear function of the amount of fuel (propane, n=3) reacted, the heat release rate calculation is also quite simple. The energy equation is solved in terms of the fluid stagnation enthalpy. The fluid temperature is then computed from the enthalpy. The equation for temperature is written as : T = T0 + ±(f^Yk{hk-hl)\ (12) 5 |