Computation of Hypersonic Flows over Flying Configurations Using a Nonlinear Constitutive Model

Abstract

The linear Navier–Stokes–Fourier (NSF) constitutive relations are derived on the assumption of the small deviation from local thermodynamic equilibrium, and consequently they may fail in describing flows removed far from local equilibrium, like rarefied hypersonic flows. In this paper, a nonlinear constitutive model of diatomic gases named as “nonlinear coupled constitutive relations” (NCCR) is presented. The model conceptually starts from Eu’s generalized hydrodynamics and is developed for simulating rarefied hypersonic gas flows with a goal of recovering NSF’s solutions in near-continuum regime and more accurate in transition regime. To enhance stable computation, an undecomposed algorithm is further developed for the nonlinear constitutive model within finite volume framework. An analysis is carried out to compare the algorithm with Myong’s original decomposed algorithm. Local nonequilibrium flow regions are also investigated for rarefied hypersonic flows over a cone tip, a hollow cylinder-flare, and a hypersonic technology vehicle–type flying vehicle. The convergent solutions of NCCR model are compared with NSF, direct simulation Monte Carlo (DSMC) calculations, and experimental data. It is demonstrated from results of general flow-field and surface properties that the NCCR model is as computationally efficient as the NSF model in continuum regime, and, at the same time, more accurate in comparison with DSMC and experimental data than NSF in nonequilibrium flows.