Paper presented at the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, 19-21 July, 2010.
Air release in hydraulic systems and components leads to a bubbly two-phase mixture with properties that are different from those of monophase liquids; e.g. altered in viscosity and speed of sound. As a result, the system eigenfrequencies change and noise may be generated. In most cases, the driving force of air release is a pressure drop induced shift in the solubility equilibrium. Different air release models are derived by means of conservation laws of mass, momentum and energy. The considerations are carried out for non-interacting bubbles in finite and infinite domains, where a spherical nucleus is the starting point of the analysis. In particular, the mass
transfer of dissolved air is described by an advection-diffusion equation formulated in terms of Lagrangian coordinates. These are initialised on the phase boundary of spherical air bubbles. The solubility equilibrium is modelled in terms of Henry's law and the conservation of momentum leads to an extended Rayleigh-Plesset equation representing the bubble dynamics. In order to study and compare the properties of the models, the resulting differential equations are solved numerically. Thereby, the time-dependent diffusion boundary layer on the bubble surface is resolved by adapted grids. The simulations reveal that advection has to be considered for strong pressure gradients, which induce a velocity field around the air bubble. In contrast, slow bubble growth can be
sufficiently described by the diffusion equation in the case of small bubbles. Thermal effects play a minor role for pressure oscillations outside the eigenfrequency of the air bubble and common liquids such as water or oils.