Prediction of shock structure using the bimodal distribution function

TL;DR

This paper improves the prediction of shock wave structures by modifying the Mott-Smith method, achieving better agreement with experimental and simulation data for various Mach numbers.

Contribution

A modified Mott-Smith approach using distribution functions to accurately predict shock structures in gases, validated against experiments and DSMC simulations.

Findings

Good agreement with experimental data for density and temperature profiles.

Accurate prediction of shock thickness at low Mach numbers.

Enhanced modeling of shock wave structure in gases.

Abstract

A modification of Mott-Smith method for predicting the one-dimensional shock wave solution is presented. Mott-Smith distribution function is used to construct the system of moment equations to study the steady-state structure of shock wave in a gas of Maxwell molecules and in argon. The predicted shock solutions using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution and the solutions predicted by other existing theories for Mach numbers M<11. The density, temperature, heat flux profiles and shock thickness calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions. In addition, the predicted shock thickness is in good agreement with the DSMC simulation result at low Mach numbers.