A Three-Dimensional Two-Temperature Gas-Kinetic Scheme with Generalized Kinetic Boundary Condition for Hypersonic SBLI

TL;DR

The paper tackles hypersonic SBLI under thermal non-equilibrium by developing a 3D two-temperature Gas-Kinetic Scheme on unstructured meshes. It introduces a Generalized Kinetic Boundary Condition that decouples vibrational energy accommodation from translational-rotational relaxation, and employs a Discontinuity Feedback Factor to preserve accuracy near shocks. Validation against sharp double cone and hollow cylinder-flare experiments shows accurate prediction of flow structures and surface loads, with vibrational accommodation ($ ext{α}_v$) identified as the dominant factor in peak heat flux. Parametric density studies and a 2° angle-of-attack case demonstrate robustness across topologies and three-dimensional effects, highlighting the method’s potential for reliable, physics-based hypersonic aerothermodynamics in non-equilibrium regimes.

Abstract

Accurate prediction of aerothermal loads in hypersonic flows is critical yet challenging due to the coupling of Shock-Wave/Boundary-Layer Interactions (SBLI) and thermal non-equilibrium. This work presents the development of a three-dimensional two-temperature Gas-Kinetic Scheme (3D 2T-GKS) on unstructured meshes. The scheme resolves translational-rotational and vibrational energy modes within a unified kinetic framework. A key innovation is the integration of a Generalized Kinetic Boundary Condition (GKBC), which physically decouples the thermal accommodation of vibrational energy from the translational-rotational mode, thereby offering a more accurate model for gas-surface interactions. Additionally, a Discontinuity Feedback Factor (DFF) is employed to capture strong shock waves with reduced numerical dissipation compared to classical limiters. The method is rigorously validated against standard experimental benchmarks, including the sharp double-cone and hollow cylinder-flare configurations. Numerical results demonstrate that the proposed solver, augmented by the GKBC, accurately captures complex wave structures, separation topologies, and surface heat flux distributions. These findings confirm the robustness and fidelity of the 3D 2T-GKS for simulating complex hypersonic non-equilibrium flows.

Figures (20)

• Figure 1: Schematic of the double cone geometry.
• Figure 2: Close-up views of the medium grid ($500 \times 250$) distribution: (a) near the cone-cone junction and (b) near the flow reattachment region.
• Figure 3: Grid convergence results on three resolution levels: (a) surface pressure, (b) wall shear stress, and (c) surface heat flux distributions.
• Figure 4: Flow structure over the sharp double-cone configuration computed using the fine grid. The cyan region indicates the separation vortex, and the red solid line in the zoomed-in view marks the sonic line.
• Figure 5: Contours of the Discontinuity Feedback Factor (DFF) for Run35.

Theorems & Definitions (1)

• Remark 3.1