On the Propagation of the Pressure Pulse Due to an Unconfined Gas Cloud Explosion. A Theoretical Analysis

Summary

A critical analysis of flow models used in computer codes for the simulation of the propagation in air of a pressure pulse due to a gas cloud explosion is presented. In particular, weaknesses of simple linear acoustic model are pointed out, and a more reliable non-linear isentropic model is proposed. A simple one-dimensional theory is used to evaluate as a function of the relative overpressure the speed of an incident normal shock-wave, as well as the strength and speed of the wave after reflection on a simplified rigid obstacle. Results obtained with the different models are compared to those obtained from the full Euler equations. A theoretical analysis of pulse de-formation during its propagation is presented, and the ability of each model to correctly simulate that purely non-linear phenomenon is discussed. In particular, the formation of a sharp pressure pulse (shock-up phenomenon) is analyzed in detail.

From our analysis, the accuracy of the linear acoustic model for the evaluation of strength and speed of incident and reflected waves is found to be quite poor except for very weak overpressures. Additionally, such a model is completely unable to simulate pulse deformations. As a result, it should be expected to lead to important errors in the simulation of pulse interaction with non-rigid obstacles, even at very weak overpressures. As opposed to that very simple model, the proposed non-linear isentropic model is found to lead to an excellent accuracy in the prediction of all wave characteristics mentioned above and in the simulation of pulse deformation if overpressure is not too large.