OCR Text |
Show The equation set simulates a two-dimensional turbulent reactive flow. Equations are solved for <f) equal to time-mean axial and tangential velocities u and v, stagnation enthalpy h, fuel mass fraction Yfu, turbulent kinetic energy k, dissipation rate e, and flame surface density Sf. This last quantity was given a special attention in our previous work (Ref [19]), because it represents the key of the success of turbulent combustion description based on flame surface density concept. The exchange coefficient Tf and source term S^ for turbulent reactive flow are compiled in Table 1. The values of the constants of the k-e model are also given in the table. The mean density is obtained from the equation of state for a perfect gas : K p = PRT^2(Yk/Mk) (3) t=i where p is the pressure, R the universal gas constant, p the density, T the temperature, Y k the mass fraction of species k, M k the molecular weight of chemical species k. The combustion model used in this study is well detailed in our previous work ( Ref [19]). The fuel consumption rate term is formulated as : w/u = ~P2ULSj (4) and the balance equation for flame surface per unit mass is written as : aS?»-Kte&M*«i)(fe)*-'fc« where UL is the laminar flame speed, UL0 the same quantity for stoichiometric flame and // the flame thickness. Concerning the determination of U L and //, one of the several possibilities consists in a local study of laminar strained flamelet with detailed chemistry and transport 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 [1] and the laminar flame speed values are obtained from correlations of Metghalchi and Keck [13] The chemical kinetic mechanism used is the one-step overall scheme which considers oxidation process to occur directly to C02 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. 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 : r=r°+^fey*(**-**)) (7) where hk is the enthalpy of the chemical species k : hk = h°k + J h°k being the heat of formation of chemical species k, and Cp the mean specific heat obtained by a linear combination of the components specific heats, CPk, as follows : A' C„ = £Y*CPfc (9) jfc=i For each chemical species, k, Gordon and M c Bride [7] propose : CPk = aQk + alkT + a2kT2 + a3fcr3 + a^T4 (10) 3 |