A simple constitutive model for predicting the pressure histories developed behind rigid porous media impinged by shock waves

Abstract

Shock wave attenuation by means of rigid porous media is often applied when protective structures are dealt with. The passage of a shock wave through a layer of porous medium is accompanied by diffractions and viscous effects that attenuate and weaken the transmitted shock, thus reducing the load that develops on the target wall that is placed behind the protective layer. In the present study, the parameters governing the pressure build-up on the target wall are experimentally investigated using a shock tube facility. Different porous samples are impinged by normal shock waves of various strengths and the subsequent pressure histories that are developed on the target wall are recorded. In addition, different standoff distances from the target wall are investigated. Assuming that the flow through the porous medium is close to being isentropic enabled us to develop a general constitutive model for predicting the pressure history developed on the target wall. This model can be applied to predict the pressure build-up on the target wall for any pressure history that is imposed on the front face of the porous sample without the need to conduct numerous experiments. Results obtained by other investigators are found to be in very good agreement with the predictions of the presently developed constitutive model.

Analysis of the pressure buildup behind rigid porous media impinged by shock waves in time and frequency domains

“…In the past, the same shock tube facility was fitted with a long driver in order to generate a step function loading, which is more typical for conventional shock tubes. The results from this earlier study were used to formulate the RS model (Ram & Sadot 2013). Some of these results are also used in the present study to demonstrate some of the new points that are raised in the discussion section.…”

“…As a result, the pressure buildup profile could be predicted for a given incident shock wave and standoff distance. Ram & Sadot (2013) also showed that this model could be used to predict the pressure buildup using a variety of porous-like barriers such as a series of grids or perforated plates. While the RS model predicts very well the pressure buildup as a result of the impingement of constant-velocity shock waves (step jump) on the front face of porous samples, its validity is yet to be checked against other imposed pressure profiles such as the one that results from the impingement of blast waves (close to exponentially decaying).…”

“…Figure 2(b) shows a replot of the results shown in 2(a) in scaled time and normalized pressure according to the following definitions (Ram & Sadot 2013):…”

“…As shown, the experimental result from a single shock tube experiment should be replotted in a scaled form accounting for the influence of the standoff distance, sample length and the incident shock wave Mach number (Ram & Sadot 2013). An exponential function, which is a function of α, should be fitted to the experimental results.…”

“…It was not until Li, Levy & Ben-Dor (1995), Levy et al (1996Levy et al ( , 1998Levy et al ( , 1999 and Levi-Hevroni et al (2002 incorporated a more accurate presentation of the energy and the momentum transfer inside the porous medium that the model was capable of properly predicting the shock wave propagation inside a rigid porous sample. The aforementioned studies showed that in order to actually solve the system of governing equations, one has to determine the values of the parameters, namely the tortuosity, T * , and the Forchheimer coefficient, F. Ram & Sadot (2013) developed an empirical model (referred to as the RS model) which accounts for the physical parameters affecting the pressure buildup profile at the shock tube end wall. The model was described as a solution to the following firstorder differential equation:…”