Comparative study of equilibrium and non-equilibrium predictions by different models for a hypersonic cone at high-altitude

TL;DR

This study compares equilibrium and non-equilibrium gas models in simulating hypersonic flow over a cone at high altitude, highlighting differences in flow features, temperature distributions, and aerodynamic predictions.

Contribution

It provides a systematic comparison of various gas models, revealing their differences in predicting flow structures, temperatures, and aerodynamic forces in hypersonic conditions.

Findings

Equilibrium models predict higher drag and heat flux than non-equilibrium models.

Discrepancies are prominent in shock layer and wake regions, especially in temperature distributions.

Three-temperature models with and without slip conditions yield largely consistent results.

Abstract

Targeting a cone with the half-angle as 10-deg at M = 27 and H = 72 km, simulations were conducted comparatively to analyze the predictions by different equilibrium and non-equilibrium gas models. Following validation and grid studies, systematic comparisons on aerodynamic performance, flow structures, and characteristic distributions were performed. The key findings are: (1) While the overall flow structures are broadly similar, discrepancies exist in the features at the base locations, e.g., the diverse high-temperature distributions. Notably, the vibrational temperatures distribute differently under slip and non-slip boundary conditions near the wall; (2) The equilibrium gas model predicts higher drag coefficient, wall heat flux, and skin friction than those of non-equilibrium models. Predictions also vary among the non-equilibrium models themselves. Specifically, compared to the three-temperature model, the one- and two-temperature models predict larger drag coefficients with the relative difference exceeding 5%. Nevertheless, the results from the three-temperature model with and without slip conditions are largely consistent; (3) The disparities between equilibrium and non-equilibrium characteristics are primarily manifested in the shock layer and wake regions. Within these regions, the overall temperature for the equilibrium gas is lower than that for the non-equilibrium cases, while in the latter specific non-equilibrium features are distinctly exhibited, e.g., the translational-rotational temperature is generally higher than that from the one-temperature model, and the vibrational-electronic temperature shows the opposite trend. Notably, in the slip flow within the three-temperature model, the translational-rotational temperature is higher and, particularly, the vibrational temperature is even larger than counterparts of the non-slip flows near the wall and base center line.