ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Nonlinear coupled constitutive relations and its validation for rarefied gas flows
Received date: 2014-08-14
Revised date: 2014-10-29
Online published: 2014-11-02
Supported by
National Research Foundation of Korea (2012-R1A2A2A02-046270)
Being the new constitutive equations for gas flow, the innovation of nonlinear coupled constitutive relations (NCCR)lies in the transport equations of viscous stress and thermal conduction, which are derived from Boltzmann equations by consideration of the entropy and expressed in terms of nonlinear coupled functions. In the continuum state, the NCCR shows linear relations in viscous stress and thermal conduction which is the same as the classical Navier-Stokes equations using Newtonian law of viscosity and the Fourier law of heat conduction. And, in the rarefied state, the relations of viscous stress and thermal conduction become more nonlinear. So, the constitutive relations are extended greatly by NCCR. To solve the high nonlinear of NCCR equations, mixed modal discontinues Galerkin method is proposed in solving the conservation laws with NCCR in which the setting of viscous stress and heat flux on the solid wall are avoided. Numerical study and validations are conducted in subsonic, supersonic and hypersonic gas flows around a cylinder, NACA0012 airfoil and cavity flow. Investigations show that NCCR can capture detailed flow properties which include pressure distribution, contour of velocity, density and temperature, as well as heat flux in solid wall and the NCCR data are closed to those of direct simulation of Monto Carlo (DSMC) or experiment while Navier-Stokes fails. Furthermore, numerical studies on gas flow around a cylinder also show that NCCR results are the same as that of Navier-Stokes in continuum state and the difference becomes to be distinguished with Knudsen number increasing. It can be concluded that NCCR provides a new method to solve continuum-rarefied gas flows.
XIAO Hong , SHANG Yuhe , WU Di , SHI Yangyang . Nonlinear coupled constitutive relations and its validation for rarefied gas flows[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015 , 36(7) : 2091 -2104 . DOI: 10.7527/S1000-6893.2014.0300
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