Violent flows in aqueous foams I: Physical and numerical models

Abstract

Mitigation of blast waves by aqueous foams is an important technological issue. Despite many theoretical and experimental works on the subject, it has not been possible until now to have simple analytical expressions or abaci giving the pressure as a function of the distance to the charge, of its strength and of the characteristics of the foam. This naturally leads to attempts at using numerical simulations to obtain the desired results. The flow in an aqueous foam is complex as three fluids (air, steam and water) and phase transitions are involved, and moreover, the geometry of the free surfaces between these fluids is quite complicated. In this work, our aim is to build a code to handle this question. We rely on the classical averaged model for multifluid flow, which allows bypassing the local geometrical complexity of the flow at the cost of new variables, the volumetric rate of presence of each fluid. Since our goal is to simulate blast waves from a point, we shall safely assume that the flow has spherical symmetry. Hence, the models derived will be one dimensional. In this paper, we shall introduce closed systems of equations and describe their discretization via a finite volume method, the efficiency of which has already been demonstrated in the context of thermohydraulics. We restrict ourselves to the one-dimensional Cartesian case. Numerical benchmarks are provided in order to check the correct behavior of the code in terms of numerics and physics ( e.g. phase transition). In the companion paper, D’Alesio et al. [29], we extend the code to the spherical case and give simulation results in the case of strong shock waves propagating in foams.