Over the last decades, numerous studies have dealt with the propagation of shock or blast waves in aqueous foam, highlighting the outstanding mitigation properties of this medium. Most experimental works (Hartman et al., 2006 ; Britan et al., 2013) have considered the phenomenon from a macroscopical point of view, relying on pressure recordings to evidence the changes the wave undergoes when it propagates in the foam and yielding overpressure and impulse attenuation factors as a function of the foam properties (essentially bubble size and liquid fraction). Yet, although several potential attenuation mechanisms have been identified, their respective part on mitigation depending on the pressure wave and foam properties largely remain to be determined.

In this work, we perform a parametric experimental study of a pressure wave propagating in a volume of wet aqueous foam. We use a square cross-section (8cm x 8cm) shocktube to produce the shock waves. The test section is equiped with up to 8 pressure transducers and partially filled with aqueous foam so that gauges are located upstream, inside and downstream the foam. Windows allow the visualization of the waves using a standard shadowgraphy set-up. We focus on a tight control of the foam parameters (mean bubble diameter, liquid fraction and rheological properties of the foaming liquid), ensuring we vary each of them independently from the others. By adjusting both the length and the initial pressure of the high-pressure section of the shocktube, we can control the shape and maximum overpressure of the wave at the time it enters the foam. We study both sustained shock waves and impulsive pressure waves (similar to blast waves).

Experiments consider several aspects of the studied phenomenon : air-to-foam transmission, propagation in the foam and foam-to-air transmission of the shock wave are studied. We analyse the evolution of the wave velocity, maximum overpressure, average pressure gradient and precursor overpressure as the wave propagates in the foam. Attention is also paid to the structure of the wave when it exits the foam, which can be complex, notably because of the precursor wave in the foam. Depending on the length of the foam volume and the overpressure and shape of the incident wave, a compression wave or a shock wave is observed at this stage.

Experimental results are compared to CFD simulations assuming the foam behaves as an effective medium at a macroscopical scale. Liquid foams are known to behave as shear-thinning fluids, with rheological properties highly dependent on the foam parameters. In our simulations, a Herschel – Bulkley law is chosen to account for this behaviour. The quantitative values of the model parameters (yield stress threshold and yielding viscosity) are determined experimentally.

References: 
W. Hartman, B. Boughton, and M. Larsen. Blast mitigation capabilities of aqueous foam, Technical Report SAND2006-0533, Sandia National Laboratories, 2006.
Britan A., et al., "Macromechanical modeling of blast-wave mitigation in foams. Part I: review of available experiments and models", Shock Waves, vol. 23, p. 5-23, 2013