2D-DNS and 2D-RANS Simulations of Supersonic QUASI-2D Turbulent Reacting Shear Flow

Abstract

Numerical studies of quasi-2D supersonic turbulent hydrogen-air mixing and combustion in free shear layer configuration are performed using 2D-DNS [1] and RANS equations. In order to produce the roll-up and pairing of vortex rings, an unsteady boundary condition is applied at the inlet plane. Frequencies of initial velocity perturbations have been taken in accordance with linear stability theory. The influences of different inflow perturbations on mixing layer structure are presented. At the outflow, the non-reflecting boundary condition is adopted. In the case of RANS simulation two-parameter k-e turbulence model is used. Thermal conduction is described by Fourier’s law, while diffusion of species by Fick’s law. Equation of state for thermally perfect multispecies gas is used. Thermodynamic parameters, such as specific heat, enthalpy, entropy and internal energy are determined by fourth order degree polynomial formula, which has dependence on temperature. Temperature is determined using Newton-Raphson iteration procedure. The Wilke’s formula is used to determine the mixture viscosity coefficient. Approximation of convection terms are performed by the ENO-scheme of third-order accuracy and approximation of diffusion terms – by second-order central-difference operators. For the description of reaction pathways of hydrogen, a seven species chemical reaction model by Jachimowski is adopted. Chemical reaction source term implicitly includes in mass fraction transport equations, where linearization is applied using Taylor decomposition. The hydrogen flow parameters are M₀ = 2.0, T₀ = 2000 K, P₀ = 101325 Pa, and air flow parameters are M_∞ = 2.1, T_∞ = 2000 K, p_∞ = 101325 Pa. Convective Mach number is M_c = 0.38, where effect of compressibility is significant.