GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES

Based on the gas-kinetic unified algorithm (GKUA) for flows from rarefied transition to continuum, the effect of rotational non-equilibrium is investigated involving the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant, then the unified Boltzmann model equation involving rotational non-equilibrium effect is presented for various flow regimes. The molecular velocity distribution function is integrated by the weight factor on the energy of rotational motion, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The discrete velocity ordinate technique and numerical quadrature methods are applied to discretize the velocity space, and the gas-kinetic finite-difference numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in rotational non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of the Boltzmann kinetic model equation involving rotational non-equilibrium effect is presented for the whole range of flow regimes. As the applications of the GKUA, the hypersonic flows of diatomic gas involving rotational non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-25, the two-dimensional planar Ramp flow with the whole range of Knudsen numbers of 9×10^-4-10 and the three-dimensional re-entering hypersonic flows around sphere, tine double-cone and spacecraft body. The computed results match the relevant experimental data, DSMC results, and the solutions of the generalized Boltzmann equation (GBE) and ellipsoidal statistical (ES) model equation well. It is tested and validated from this study that the GKUA solving the Boltzmann model equation in rotational nonequilibrium can simulate the complex hypersonic flow problems and flow mechanisms from high rarefied free-molecule flow to continuum flow regimes with good reliability and precision.