Numerical simulation of hypersonic thermochemical nonequilibrium flows using nonlinear coupled constitutive relations

To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect,a Nonlinear Coupled Constitutive Relations(NCCR)model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper.Three typical cases are intensively investigated for further validation,including hypersonic flows over a two-dimensional cylinder,a RAM-C II flight vehicle and a type HTV-2 flight vehicle.The results predicted by NCCR solution,such as heat flux coefficient and electron number densities,are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations,especially in the extremely nonequilibrium regions,which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects.The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.

A review of the mathematical modeling of equilibrium and nonequilibrium hypersonic flows

This paper systematically reviews the mathematical modeling based on the computational fluid dynamics(CFD)method of equilibrium and nonequilibrium hypersonic flows.First,some physicochemical phenomena in hypersonic flows(e.g.,vibrational energy excitation and chemical reactions)and the flow characteristics at various altitudes(e.g.,thermochemical equilibrium,chemical nonequilibrium,and thermochemical nonequilibrium)are reviewed.Second,the judgment rules of whether the CFD method can be applied to hypersonic flows are summarized for accurate numerical calculations.This study focuses on the related numerical models and calculation processes of the CFD method in a thermochemical equilibrium flow and two nonequilibrium flows.For the thermochemical equilibrium flow,the governing equations,chemical composition calculation methods,and related research on the thermodynamic and transport properties of air are reviewed.For the nonequilibrium flows,the governing equations that include one-,two-,and three-temperature models are reviewed.The one-temperature model is applied to a chemical nonequilibrium flow,whereas the two-and three-temperature models are applied to a thermochemical nonequilibrium flow.The associated calculations and numerical models of the thermodynamic and transport properties,chemical reaction sources,and energy transfers between different energy modes of the three models are presented in detail.Finally,the corresponding numerical models of two special wall boundary conditions commonly used in hypersonic flows(i.e.,slip boundary conditions and catalytic walls)and related research,are reviewed.

The thermochemical non-equilibrium scale effects of the high enthalpy nozzle

The high enthalpy nozzle converts the high enthalpy stagnation gas into the hypervelocity free flow.The flow region of the high enthalpy nozzle consists of three parts:an equilibrium region upstream of the throat,a non-equilibrium region near the throat,and a frozen region downstream of the throat.Here we propose to consider the thermochemical non-equilibrium scale effects in the high enthalpy nozzle.By numerically solving axisymmetric compressible Navier-Stokes equations coupling with Park’s two-temperature model,the fully non-equilibrium solution is employed throughout the entire nozzle.Calculations are performed at different stagnation conditions with the different absolute scales and expansion ratio.The results of this study are twofold.Firstly,as the absolute scale and expansion ratio increase,the freezing position is delayed,and the flow approaches equilibrium.Secondly,the vibrational temperature and Mach number decrease with the increase in the nozzle scale and expansion ratio,while the speed of sound,static pressure,and translational temperature increase as the nozzle scale and expansion ratio increase.