Passage of waves in fluids through damping interlayers and their interaction with barrier

Interaction of a wave in a liquid-gas mixture with a barrier after passage through a porous solid medium is analyzed, taking into account the relaxation mechanism. A momentary compression of the liquid is assumed to occur under load, while the pressure in air bubbles is assumed to change adiabatically and deformation of air bubbles can be described by the viscous term in the Rayleigh-Lamb equation alone. The corresponding two equations of change of state, through deformation and relaxation respectively, together with the Euler equation and the equation of continuity in Lagrange variables constitute a closed system of equations which is solvable by the method of characteristics. Pressure transients have been calculated by this method for three forms of pressure wave (step of finite duration, step of finite duration, descending ramp of finite duration) in glycerin with air bubbles passing through a 3 mm thick porous damper before reaching an immovable solid barrier to which the damper adheres. The damper effectiveness, characterized by amper action time which shortens the wave barrier interaction time, is found to be approximately proportional to the volume fraction of air in the liquid within the 0.02-0.4 range and also approximately proportional to the thickness of the damping layer.