Analytical Solution for Isothermal Flow in a Shock Tube Containing Rigid Granular Material |
| |
Authors: | Ali Nemati Hayati Mohammad Mehdi Ahmadi Soheil Mohammadi |
| |
Institution: | 1.Department of Civil Engineering,Sharif University of Technology,Tehran,Iran;2.School of Civil Engineering,University of Tehran,Tehran,Iran |
| |
Abstract: | Analytical solution of shock wave propagation in pure gas in a shock tube is usually addressed in gas dynamics. However, such
a solution for granular media is complex due to the inclusion of parameters relating to particles configuration within the
medium, which affect the balance equations. In this article, an analytical solution for isothermal shock wave propagation
in an isotropic homogenous rigid granular material is presented, and a closed-form solution is obtained for the case of weak
shock waves. Fluid mass and momentum equations are first written in wave and (mathematical) non-conservation forms. Afterwards
by redefining the sound speed of the gas flowing inside the pores, an analytical solution is obtained using the classical
method of characteristics, followed by Taylor’s series expansion based on the assumption of weak flow which finally led to
explicit functions for velocity, density and pressure. The solution enables plotting gas velocity, density and pressure variations
in the porous medium, which is of high interest in the design of granular shock isolators. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|