Modified Nonlinear Coupled Constitutive Relations Model for Hypersonic Nonequilibrium Flows

To obtain accurate physical description of nonequilibrium flows, Eu proposed a set of generalized hydrodynamic equations (GHEs) using a nonequilibrium ensemble method. However, Eu's equations are very difficult to solve by employing the well-established numerical schemes for hyperbolic partial differential equations. Recently, a simplified nonlinear model based on Eu's equations has been proposed by Myong for GHEs in conjunction with hyperbolic conservation laws, which is called the nonlinear coupled constitutive relations (NCCR) model. However, in the NCCR model, two specific terms in the evolution equation of heat flux are omitted for providing simplification, which reduces the accuracy of GHEs to some degree especially for hypersonic flows. To address this deficiency in NCCR, a modified NCCR+ model is proposed in this paper, which includes the two omitted terms in the NCCR model. NCCR+ model is applied to compute the hypersonic flow past an Apollo capsule at different altitudes and in expansion corners in a tube with various expansion angles. It is found that the computed NCCR+ solutions are almost identical to the Navier-Stokes (NS) solutions at low Knudsen numbers, but as the Knudsen number increases, the difference between the NCCR+ model solutions and the NS results increases rapidly and the NCCR+ solutions become closer in agreement with the direct simulation Monte Carlo data. By adding the two omitted terms in the NCCR model, the NCCR+ model also improves the overall accuracy of the original NCCR model. The results presented in this paper demonstrate the potential of the NCCR+ model in simulation of nonequilibrium hypersonic flows in both compression and expansion regions at moderate Knudsen numbers.