A Unified Framework for Modeling Continuum and Rarefied Gas Flows

Abstract

The momentum and heat transport in rarefied gas flows is known to deviate from the classical laws of Navier and Fourier in Navier-Stokes-Fourier (NSF) equations. A more sophisticated Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe gaseous and thermal transport both in continuum and rarefied gas flows. We first develop a unified numerical framework for modeling continuum and rarefied flows based on the NCCM model both in two and three dimensions. Special treatment is given to the complex highly nonlinear transport equations for non-conserved variables that arise from the high degree of thermal nonequilibrium. For verification and validation, we apply the present scheme to a stiff problem of hypersonic gas flows around a 2D cylinder, a 3D sphere, and the Apollo configuration both in continuum and rarefied situations. The results show that the present unified framework yields solutions that are in better agreement with the benchmark and experimental data than are the NSF results in all studied cases of rarefied problems. Good agreement is observed between the present study and the NSF results for continuum cases. The results show that this study provides a unified framework for modeling continuum and rarefied gas flows.

Entropy Conditions Involved in the Nonlinear Coupled Constitutive Method for Solving Continuum and Rarefied Gas Flows

“…This case is of a high Kn number and in the region of far-equilibrium states. The present authors also validated hypersonic gas flows around a 3D Apollo 6 command module with Ma = 5.0, Kn = 0.5 in the earlier study [4], and good agreement between the results of the NCCM and the DSMC method was observed in this case. Here, we just give the results as can be seen in Figure 9 to prove that the NCCM can solve the problems of far equilibrium.…”

“…Here, we just give the results as can be seen in Figure 9 to prove that the NCCM can solve the problems of far equilibrium. More details can be seen in reference [4]. The present authors also validated hypersonic gas flows around a 3D Apollo 6 command module with Ma = 5.0, Kn = 0.5 in the earlier study [4], and good agreement between the results of the NCCM and the DSMC method was observed in this case.…”

“…In other words, the NSF equation can be regarded as the low-order approximation of NCCM, Burnett, and Grad. Further discussion can be found in [4,22]. (2) All three of these nonlinear relationships are consistent in the near-equilibrium region.…”

“…Because the time is reversed, the positions of the post-collision and pre-collision terms are exchanged in Equation (4). This reversion transforms the Boltzmann collision integral into the negative of the original one before the time reversal.…”

“…The numerical study of continuum-rarefied gas flows is of great interest because it can provide fundamental knowledge regarding flow physics and provide a theoretical tool to precisely predict the aerodynamic or aerothermodynamic performance of hypersonic vehicles and/or Micro-Electro-Mechanical Systems [1][2][3][4]. For more than 150 years, the Navier-Stokes-Fourier (NSF) equations have been accepted as the model that describes flow dynamics.…”