Numerical Investigation of Supersonic and Hypersonic Flows over a Flat Plate using a Thermally Perfect Gas Model

Abstract

High-speed external flows with free-stream Mach numbers exceeding 4-5 (M∞ > 4-5) exhibit strong shock waves, steep temperature gradients, and molecular vibrational effects, leading to the breakdown of the calorically perfect gas assumption. This work investigates supersonic and hypersonic flow over a flat plate geometry to isolate and understand the physics under such conditions. An in-house Computational Fluid Dynamics (CFD) solver, implemented in Python and based on the MacCormack explicit finite-difference scheme, was developed for this purpose. The solver models a thermally perfect gas, incorporating temperature-dependent specific heats using two widely referenced formulations from the literature, namely, a polynomial functional form and an exponential functional form that is based on quantum theory. Comparative simulations using a calorically perfect gas model are performed to quantify the effect of incorporating a thermally perfect gas model. Viscosity is evaluated using Sutherland’s law, while thermal conductivity is obtained from a constant molecular Prandtl number assumption. Near-wall resolution is achieved through y+ based meshing strategies, ensuring accurate boundary-layer characterization, and a mesh sensitivity study was performed to confirm grid independence of the results.

Analysis of predicted pressure, temperature, density, and Mach number distribution is done across both the calorically perfect gas and thermally perfect gas models. The influence of specific heat formulations on boundary-layer development and thermal gradients is systematically evaluated. The results demonstrate the necessity of temperature-dependent thermodynamic modelling to accurately predict the thermal and aerodynamic characteristics of high-speed flows. The insights obtained are directly applicable to the preliminary design of hypersonic vehicles, including missiles and high-speed aircraft. Possible extensions to this work can include the incorporation of automated mesh generation and the adaptation of the solver to handle blunt bodies, wedges, and lifting surfaces under high-speed flow conditions.