Nonlinear coupled constitutive relation model for monatomic gas in the OpenFOAM framework

Abstract

In high-speed rarefied gas flow simulations, the linear constitutive relations of the classical Navier-Stokes-Fourier (NSF) equations are no longer successfully applied. In the present work, the two-dimensional nonlinear coupled constitutive relations (NCCR) model of the monatomic gas in an algebraic-type form is successfully implemented in the rhoCentralFoam in OpenFOAM to simulate the high-speed rarefied gas flows. Methods: This solver initially resolves the NSF equations using high-resolution central schemes in the finite volume method. The implicit NCCR model is solved by the iterative process with the initial values from the linear constitutive relations of the NSF model. After the convergence, these nonlinear constitutive relations are embedded in the NSF equations to continue the solution. Results: This new modified solver would be validated for the argon gas flows past a circular cylinder in cross-flow at Mach of 5 and Kn = 0.05 and the sharp leading edge flat plate at Mach of 4 and Kn = 0.0042. Conclusion: The simulation results show that the NCCR model agrees well with the DSMC data for the temperature contours for both cases and the temperature and velocity along the shock stand-off distance and is better than the NSF model in the high-speed rarefied gas simulations for the circular cylinder case.