Mach Wave and Acoustical Wave Structure in Nonequilibrium Gas-Particle Flows

The fundamentals of linear and nonlinear waves in gas-particle flows are studied, emphasizing the relaxation processes in such a mixture.

Joseph T. C. Liu (Author)

9781108964883, Cambridge University Press

Paperback / softback, published 7 October 2021

75 pages
22.8 x 15.2 x 0.5 cm, 0.127 kg

In this Element, the gas-particle flow problem is formulated with momentum and thermal slip that introduces two relaxation times. Starting from acoustical propagation in a medium in equilibrium, the relaxation-wave equation in airfoil coordinates is derived though a Galilean transformation for uniform flow. Steady planar small perturbation supersonic flow is studied in detail according to Whitham's higher-order waves. The signals owing to wall boundary conditions are damped along the frozen-Mach wave, and are both damped and diffusive along an effective-intermediate Mach wave and diffusive along the equilibrium Mach wave where the bulk of the disturbance propagates. The surface pressure coefficient is obtained exactly for small-disturbance theory, but it is considerably simplified for the small particle-to-gas mass loading approximation, equivalent to a simple-wave approximation. Other relaxation-wave problems are discussed. Martian dust-storm properties in terms of gas-particle flow parameters are estimated.

1. Introduction
2. Conservation equations of gas-particle flows
3. Small perturbation equations in a stationary frame
4. Aerodynamic interpretation of acoustics in gas-particle flows
5. Steady small-perturbation theory
6. Some limiting cases
7. Two-dimensional steady supersonic flow
8. Approximate consideration based on a 'rarefied' particle cloud
9. Particle collision with the wall and the normal force
10. The wall-pressure coefficient
11. Numerical examples
12. Relation to other relaxation wave problems
13. Concluding remarks. Appendix A. Appendix B. References.

Subject Areas: Aerospace & aviation technology [TRP], Transport technology & trades [TR], Technology, engineering, agriculture [T]