Effects of Vibrational Thermal Accommodation in Hypersonic Flows over Spheres

Hypersonic flows are characterized by strong non-equilibrium of translational, rotational, and vibrational energy modes, each of which contributes to surface heating. Prediction of surface heat flux in hypersonic flow is dependent upon accurate modeling of energy accommodation of the gas molecules to the surface. The ability to understand and predict overall heating, especially near the stagnation point, is critical for design of thermal protection systems. Under continuum assumptions, the surface is usually modeled as fully accommodating, where the energy distributions of molecules reflected from the surface correspond to the surface temperature. However, in certain high-speed or rarefied conditions, this approximation can break down significantly. This study uses the direct simulation Monte Carlo method to investigate the importance of vibrational thermal accommodation to heat flux prediction on spheres over a range of freestream Knudsen numbers. Each case is simulated with the compression side of the sphere placed downstream of the hypersonic freestream flow. All cases are simulated both with full accommodation of all energy modes (translational, rotational, and vibrational) and with full accommodation of all energy modes except vibrational, which does not accommodate at all, and thereby does not contribute to surface heat flux. In the less rarefied cases where vibrational accommodation is allowed, vibrational heat flux makes up a substantial portion of the overall heating, and there is a visible reduction in overall stagnation heating when this accommodation is prohibited. In the least rarefied case, the reduction is partially offset by an increase in the heat fluxes of the other modes. The more rarefied cases show little vibrational heating at the stagnation point, even when vibrational energy accommodates, so there is little change in the heating profiles, both overall and per energy mode, when vibrational accommodation is prohibited. This behavior can be attributed to low vibrational excitation along the stagnation line for the more rarefied cases. Stagnation and local heating results are compared against existing correlations. It is found that vibrational accommodation only substantially affects stagnation point heating in less rarefied flows. Heat fluxes across the surface of the sphere with and without vibrational accommodation are compared in each case. When these local heat fluxes are expressed as a fraction of the corresponding stagnation point heat flux, minimal change is observed between accommodation conditions in all cases.