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Simulations of gas-liquid compressible-incompressible systems using SPH. (English) Zbl 1411.76140
Summary: Gas bubbles immersed in a liquid and flowing through a large pressure gradient undergo volumetric deformation in addition to possible deviatoric deformation. While the high density liquid phase can be assumed to be an incompressible fluid, the gas phase needs to be modeled as a compressible fluid for such bubble flow problems. The Rayleigh-Plesset (RP) equation describes such a bubble undergoing volumetric deformation due to changes in pressure in the ambient incompressible fluid in the presence of capillary force at its boundary, assuming axisymmetric dynamics. We propose a compressible-incompressible coupling of smoothed particle hydrodynamics (SPH) and validate this coupling against the RP model in two dimensions. This study complements the SPH simulations of a different class of compressible-incompressible systems where an outer compressible phase affects the dynamics of an inner incompressible phase. For different density ratios, a sinusoidal pressure variation is applied to the ambient incompressible liquid and the response of the bubble in terms of volumetric deformation is observed and compared with the solutions of the axisymmetric RP equation.
76M28 Particle methods and lattice-gas methods
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
76T10 Liquid-gas two-phase flows, bubbly flows
Full Text: DOI
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