Linear Waves and Shock Waves in Flexible and Rigid Porous Media.pdf

9Linear Waves and Shock Waves in Flexible and Rigid Porous Media David Smeulders and Marinus van Dongen 9.1 Introduction Wave phenomena in permeable media are quite interesting from the point of view of gas dynamics. Such waves are strongly dispersive: a weak shock wave incident on a rigid gas-filled porous sample, for example, generates a compres- sive reflection wave with increasing pressure jump as it propagates backward. The incident shock that transmits into the pores has a sharp pressure jump that resembles a typical pressure jump across a shock wave, followed by a more gradual pressure increase which finally reaches asymptotic values. As the pres- sure wave propagates, the pressure jump decreases, but the final asymptotic value remains almost unchanged [1]. Because of the large compressibility con- trast between the gas and the solid matrix, there is effectively no pressure transmission into the solid matrix. For flexible media, such as foams, addi- tional phenomena become important. The deformations of the foam can be large, and when a shock wave reflects from a slab of foam adjacent to a solid wall, the end wall pressures observed are much higher than expected. A survey on experimental and theoretical investigations of wave propagation in foams is given by Skews [2]. Initially, the modeling of these wave phenomena was based on the assumption that the foam and the gas could effectively be considered as one phase. An example is the pseudogas model of Gel’fand et al. [3], that was later modified by Bazhenova and Gvozdeva [4]. Such models are rather successful, although not all phenomena observed can be explained. The differ- ences between observation and theory are often attributed to the two-phase character of the wave phenomena. Baer [5] studied wave phenomena in a foam by applying a nonlinear two phase model, with viscous and viscoelastic inter- action terms. By varying the parameters he was able to obtain a satisfactory numerical simulation of the experime