Prediction of strong shock structure using the bimodal distribution function

TL;DR

This paper develops a modified Mott-Smith method to accurately predict high Mach number shock structures, showing good agreement with experimental and DSMC data across various gases and Mach numbers.

Contribution

It introduces a new formalism for shock prediction at very high Mach numbers, improving upon existing theories with better accuracy.

Findings

Predicted shock profiles match experimental data well.

The method accurately models shock structures for Mach numbers up to 50.

Good agreement with DSMC solutions at very high Mach numbers.

Abstract

A modified Mott-Smith method for predicting the one-dimensional shock wave solution at very high Mach numbers is constructed by developing a system of fluid dynamic equations. The predicted shock solutions in a gas of Maxwell molecules, a hard sphere gas and in argon using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution and other solutions computed from some existing theories for Mach numbers M<50. In the limit of an infinitely large Mach number, the predicted shock profiles are also compared with the DSMC solution. The density, temperature and heat flux profiles calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions