The presence of entrained gas bubbles in a bubbly media leads to both dispersive and dissipative effects on a pressure wave traveling through the system. The complete set of equations used to model this process involves the combination of macroscopic pressure propagation and Rayleigh-Plesset oscillations of individual gas bubbles. This results in disparate temporal and spatial scales that are difficult to solve numerically inside of a CFD framework.
This paper presents a simplification to the set of governing equations that specifically eliminates the need to model individual bubble oscillations by using a cycle-averaged approximation. Results generated with the simplified model are verified against equivalent results considering the full set of governing equations. The approximation is shown to capture the behavior of interest — e.g., the variation in gas phase volume that alters the bulk modulus of the bubbly media or the net transfer of mechanical energy to heat — without the additional effort required to model rapid dynamics that do not contribute substantially to the pressure wave decay.
