Novel Method to Calculate Vibrational Thermal Conduction in Hypersonic Nonequilibrium Flow

Abstract

A new method is proposed to express the vibrational thermal conduction in the computation of hypersonic thermochemical nonequilibrium flows with the two-temperature model. To overcome numerical difficulties such as the nonphysical oscillation of the vibrational temperature near the cold wall, the vibrational thermal conduction is modeled directly with the gradient of nonequilibrium vibrational energy and coupled to the diffusive flux of vibrational energy. In such a way, the proposed method needs neither the vibrational temperature nor the vibrational thermal conductivity, which are prerequisites in the conventional method to calculate vibrational thermal conduction. The effectiveness of the new method is demonstrated in the numerical simulation of the thermochemical nonequilibrium flow over a sphere-cylinder geometry. The results show that the sizes of the first grids away from the wall can be much larger than those with the conventional method, improving significantly the efficiency of the computation. Using the more primitive variable (nonequilibrium vibrational energy) rather than the representative variable (vibrational temperature), the new method has some theoretical advantages, especially under the extreme circumstances, where it is required to describe the microscopic processes directly and the meaning of vibrational temperature may have some ambiguity.