The contribution of shock tubes to simplified analysis of gas filtration through granular media

Abstract

A hybrid method for the problem of transient shock-induced filtration of the gas flow through granular media is developed. The hybrid method combines a controlled shock-tube test and Morrison's simplified approach to the problem of gas filtration. It is demonstrated that most pressure traces that have been recorded in various laboratories with a large variety of granular material samples and under different conditions are limited to situations in which the pressure losses in the flow are dominated by the Forchheimer mechanism. The hybrid method enables these results to be described by a single, universal pressure curve, and specification of the Forchheimer coefficient which is one of the two key parameters responsible for the correct simulation of the filtration-flow behaviour. The second key parameter, the Darcy coefficient, cannot be evaluated by the available experimental results. To overcome this shortcoming, a new controlled laboratory test that provides a wider range of the flow conditions, from the Forchheimer to the developed mixed flow, was conducted. In turn, a comprehensive gas dynamic analysis of the transient flow inside the shock tube enables us to define, from the single controlled laboratory test, the two coefficients of the Forchheimer resistance law, a and b.