Evaluation of Fay and Riddell formula under hypersonic flight conditions

Abstract

Purpose

The Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.

Design/methodology/approach

The stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.

Findings

The comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.

Originality/value

The results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

Citation

Lee, S., Yang, Y. and Kim, J.G. (2023), "Evaluation of Fay and Riddell formula under hypersonic flight conditions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 1, pp. 14-41. https://doi.org/10.1108/HFF-01-2022-0051