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Show where hk is the enthalpy of the chemical species k : T hk = h°k + f CPkdT (13) To 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 : K Cp = T,YkCp> <14) jt=i For each chemical species k, Gordon and Mc Bride [9] propose : CPk = a0k + alkT + a2kT2 + a3kT3 + a4kT4 (15) NUMERICAL SOLUTION The combusting flow investigated numerically and experimentally by Montazel is re-evaluated in the present paper. The experimental combustion chamber used by Montazel [15] is shown in Figure 1. It is a rectangular parallelepiped. The height and length of the combustion chamber are respectively 50 and 345 m m . Two premixed propane-air flows are injected through two narrow slots ( 5 m m width) in the upper and lower sides of the burner. Use has been made of the axial symmetry condition, so that only half of the physical domain is solved. The computational domain corresponds to the internal dimensions of the experimental combustion chamber : 35 m m high and 295 m m long. The computational grid used in the present calculations has 80 x 25 nodes in the longitudinal and transversal directions, respectively. The reason for this is to allow comparison with the previous numerical predictions of Montazel who used a quite similar grid. The same grid is used for all the cases solved. Initial conditions are defined by a zero mean velocity field. The domain is filled with a propane-air mixture with an equivalence ratio of 0.7. The inlet velocity V 0 is equal to 24 m/s and the fresh gas temperature T 0 is 300 K. Near all solid surfaces, the velocity component parallel to the given wall, the turbulent kinetic energy and the turbulent dissipation rate are treated through a local wall log-law described by Launder [11]. The axisymmetric condition assumes that fluxes at the plane of symmetry are zero. The ignition of the flame is done by imposing a non-zero value for the flame surface density Sf. Note that several numerical tests have been made on the initial value of Sf and they have confirmed the independence of the converged solution from the initial value of Sf. Combustion is supposed adiabatic, i.e. the heat losses due to radiation and heat transfer to the walls are neglected. Following Montazel [15], this assumption is reasonable, because the combustion chamber walls remain so hot after flame extinction that fresh premixed gas ignits spontaneously without need of spark ignition. Numerical simulations are carried out by solving the basic set of governing equations for two-dimensional steady turbulent premixed propane-air reactive flow : continuity, momentum, enthalpy, fuel mass fraction, turbulent kinetic energy, turbulent energy dissipation and flame surface density (Table 1). The equations are discretized on a staggered, nonuniform cartesian grid using a finite-volume procedure (Patankar [16]) with a hybrid differencing scheme for the convective terms. The mean flow equations are solved by using the S I M P L E C procedure (Van Doormaal and Raithby [22]) for handling the pressure-velocity coupling. The set of algebraic equations which gives rise to a tri-diagonal system of equations are solved by the line-by-line TriDiagonal Matrix Algorithm ( T D M A ). RESULTS AND DISCUSSION In this section, we discuss the results of the numerical calculations obtained with the new turbulent premixed combustion model described above, and compare those to numerical calculations and exprimental measurements available in the literature. 6 |