Numerical studies on steady interaction of low enthalpy hypersonic double wedge flows using different gas models

Abstract

Numerical investigations and analyses are carried out on the interactions of low enthalpy hypersonic 30–55° double wedge configuration, particularly focusing on steady cases at conditions similar to the experimental setup by Swantek & Austin [AIAA 2012–284], with $Ma=7$ and $h_0=2.1MJ/kg$. To achieve a steady solution, Reynolds numbers ($Re$) lower than those in the experiment are used. For increased accuracy, a third-order scheme ${\text{WENO}3-\text{PRM}}_{1,1}^2$ [Li et al., J. Sci. Comput., 88(3) (2021) 75–130] with improved resolution is employed. Meanwhile, three gas models, i.e., the perfect, equilibrium, and non-equilibrium gas models, are used to analyze the difference potentials that arise from the physical model. After validating the methods, grid convergence studies are first conducted at $Ma=7$ and $Re=2.5\times {10}^5/m$, to determine the appropriate grid resolution for the main computations. Subsequently, comprehensive numerical studies are carried out on the steady interactions and their evolution at $Ma=7$ and $h_0=2.1MJ/kg$. Specifically: (a) The upper limits of $Re$ are identified where the flows remain steady with the transmitted shock impinging on the aft wedge, and the corresponding interaction characteristics as well as differences in the three gas models are investigated qualitatively and quantitatively, e.g., the shock system, vortex structures, distributions such as pressure, Mach number, and specific heat ratio. Notably, a quasi-normal shock wave is observed within the slip line passage in the case of the perfect gas model. (b) The flow characteristics of the three models, including the interaction pattern, geometric features of triple points, impingements, and separation zone, are studied and compared for $Re=4,3,\text{and}2\times {10}^4/m$. Differences primarily emerge between the results of the perfect gas model and the real gas models. Specifically, a transmitted shock reflecting above the separation zone is observed in the case of the perfect gas model. The effect of the gas model on temperature and specific heat ratio distributions, as well as the heat transfer and pressure coefficients over the wedge surface are investigated. For an in-depth understanding, the shock polar method is applied for comparison with computational results, while a 1D flow model is proposed to explain the occurrence of the quasi-normal shock wave. Consequently, overall reasonable agreements are achieved. Finally, the effects of variations in Mach number and enthalpy are determined, by alternatively varying the two parameters around $Ma=7$ and $h_0=2.1MJ/kg$ at $Re=4\times {10}^4/m$, focusing on alterations in interaction characteristics, thermodynamic properties, and aerodynamic performance.