Work

Temperature–velocity relation for laminar adiabatic and diabatic hypersonic boundary layers

Year: 2025

Type: article

Abstract: We study the temperature–velocity (TV) relation for laminar adiabatic and diabatic hypersonic boundary layers. By applying an asymptotic expansion to the compressible boundary-layer temperature equation, we derive a first-order equation for the TV relation, where the zeroth-order solution is found to be the classical Crocco–Busemann quadratic relation. The ensuing relation predicts accurately the temperature profile by using the velocity for hypersonic boundary layers with Chapman, power and Sutherland viscosity laws, arbitrary heat capacity ratios, variable Prandtl numbers close to unity and Mach number of up to 10. The Mach-number- and wall-temperature-independent quantities in our relation are also investigated. The present relation has the potential to function as a temperature wall model for laminar hypersonic boundary layers, especially for cold-wall cases.

Source: Journal of Fluid Mechanics

DOI: 10.1017/jfm.2025.10843

Authors: Dongdong Xu, Xianliang Chen, Lin Fu

Institution: Hong Kong University of Science and Technology

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Natural Science Foundation of China, Hong Kong Government, Basic and Applied Basic Research Foundation of Guangdong Province