Reinterpreting Shock Wave Structure Predictions using the Navier-Stokes Equations

TL;DR

This paper introduces a transformed version of the Navier-Stokes equations to improve shock wave profile predictions, demonstrating better agreement with experimental data across various Mach numbers.

Contribution

The paper presents a novel velocity variable transformation of the Navier-Stokes equations, enhancing their ability to predict shock wave structures.

Findings

Re-casted Navier-Stokes equations align better with experimental shock profiles.

Improved predictions across a range of Mach numbers.

Numerical solutions show enhanced accuracy over classical equations.

Abstract

Classical Navier-Stokes equations fail to predict shock wave profiles accurately. In this paper, the Navier-Stokes system is fully transformed using a velocity variable transformation. The transformed equations termed the re-casted Navier-Stokes equations display physics not initially included. We then analyse the stationary shock structure problem in a monatomic gas by solving both the classical and the re-casted Navier-Stokes equations numerically using a finite difference global solution (FDGS) scheme. The numerical results are presented for different upstream Mach numbers ranging from supersonic to hypersonic flows. We found that the re-casted Navier-Stokes equations show better agreements with the experimentally measured density and reciprocal shock thickness profiles.