Analysis of multi-phase incompressible fluid flow in a rectangular geometry using level set method with and without surface tension

Abstract

Multi-phase fluid flows can be observed almost everywhere in nature and have a wide of range applications in engineering and natural processes such as atomization of jets and sprays, breaking waves, emulsions, boiling phenomenon, ship hydrodynamics, waterfalls and bubbly motion in cooling towers of nuclear power plants etc. In this paper, a physically possible mass conservative level set method of COMSOL multi-physics software has been illustrated to numerically investigate multi-phase fluid flow problem with and without considering surface tension concentrated on the interface. Here, the interface is represented by 0.5 iso-contour of the level set function 𝜙 where the value of 𝜙 is zero for the fluid inside the interface and 1 for the fluid outside the interface. In order to preserve the mass of the individual fluid phase present in actual physical problem, reinitialization procedure is made integral to the level set advection equation which is also known as governing equation of the dynamically evolving moving interface to keep the thickness (i.e. 𝜖) of the interface constant across which the level set function 𝜙 varies smoothly from 0 to 1.The re-initialization process which is also called intermediate step consists of an artificial compressive flux try to compress the interface when its width is enhanced by the diffusion term, thus they are acting in opposite sense. When these two terms are in equilibrium then only finite thickness of the moving interface (i.e. 𝜖) will be obtained. “P1+P1” discretization scheme is employed to discretize the incompressible Navier stokes equation whereas “linear” discretization technique is implemented to discretize the governing equation for the dynamically evolving interface. Single bubble rising problem in a matrix involving large density ratio (i.e. 1000) with and without considering surface tension have been numerically investigated using the proposed physically possible mass conservative level set method. However, transient evolution of a single bubble in a horizontal developing flow field without considering surface tension has also been numerically simulated to illustrate the robustness of this proposed numerical method. In all these case studies excellent mass conservation of the secondary fluid i.e. the bubble has been reported by using the proposed mass conservative level set method. Few benchmark incompressible two-phase flow problems in a rectangular geometry which includes merging of two-bubble having same density in a matrix with and without considering surface tension and rising of a single bubble involving different density ratios, viscosity ratios and also different magnitude of surface tension have been numerically computed for the purpose of proposed model validation.