A hybrid Navier-Stokes/Boltzmann method for computation of non-equilibrium hypersonic flows.

摘要

A unified computational methodology and a code for computing hypersonic flows at all Knudsen numbers encompassing all the flow regimes from continuum, transition to rarefied is developed. In the developed hybrid Navier-Stokes (NS)/Boltzmann approach, the Knudsen layers and the flowfield in transition and rarefied regimes are computed by solving the Boltzmann equation while the flow computations in continuum regime (majority of the flowfield for a space vehicle in low earth orbit) are performed by the Navier-Stokes solver. The Classical Boltzmann Solver (CBS) for monoatomic gases is tested by simulating the flow fields of hypersonic flow past 2-D blunt bodies in the continuum-transition regime. The effect of Knudsen number Kn varying from 0.01 to 10 is investigated for Mach 3 flow past a blunt body. The solver is also applied to a Mach 10 hypersonic flow past a cylindrical leading edge at Kn = 0.01 and 0.1. The CBS solutions are compared with the Navier-Stokes, augmented Burnett, and Direct Simulation Monte Carlo (DSMC) solutions. The approach for developing the hybrid NS/Boltzmann method is described. The hybrid Navier-Stokes/Boltzmann approach is found to be significantly more efficient than the Classical Boltzmann Solver.; The hypersonic flow fields for a diatomic gas such as nitrogen are also computed by solving the Generalized Boltzmann Equation (GBE or the Wang-Chang Uhlenbeck equation) by accounting for both the translational and rotational degrees of freedom. Computations are performed for 1-D shock structure in nitrogen and are compared with the experimental data. Computations are also performed for flow past a 2-D blunt body bathed in nitrogen at high Mach numbers. It is shown that the numbers of the energy levels as well as the size of the velocity space need to be chosen carefully to maintain accuracy and efficiency of the numerical solutions.