Theoretical modeling of heat transfer to flat plate under vibrational excitation freestream conditions. (April 2020) - Yu, Yong-Liang; Li, Xian-Dong; Wang, Zhi-Hui; Bao, Lin
Highlights: The theoretical modeling method is employed to study the effects of vibrational accommodation incompleteness on heat transfer to a flat plate under vibrational excitation freestream conditions. For the vibrationally frozen boundary layer flow model, the boundary condition for the conservation equation of the vibrational energy is introduced based on analysis of the microscopic accommodation process. A criterion is introduced to characterize the nonequilibrium degree of vibrational accommodation effects, and a formula based on the criterion is derived to predict the flat plate's aero-heating performance in the vibrationally excited flows. The significance of the nonequilibrium vibrational accommodation effects in ground-to-flight extrapolation is emphasized by discussing a virtual heat flux measurement experiment. Abstract: In the hypersonic shock tunnel experiment, the high temperature reservoir gas expands so drastically that the vibrational energy of the gas is frozen at a high level in the test section, which could significantly affect the aero-heating measurement and ground-to-flight extrapolation. In this paper, theoretical modeling and direct simulation Monte Carlo methods are employed to study the effects of vibrational accommodation incompleteness on heat transfer to a flat plate under vibrational excitation freestream conditions. The microscopic process of the energy transfer by the gas molecule-surface collision is analyzed, and a criterion is introduced to characterize the nonequilibrium degree of the vibrational energy accommodation. Based on this criterion, an analytical formula is derived for prediction of the heat transfer performance, and its reasonability and effectiveness are also shown by the numerical results. It is found that the heat flux reduction could be as high as 18% compared to the vibrational equilibrium or complete accommodation cases. A further discussion of the heat flux measurement by coaxial thermocouple shows that a measurement deviation up to 62% could be induced by the difference between the sensor and test model's material properties.