Finite Element Modeling of Multiphase Flows using Arbitrary Lagrangian Eulerian Approach

Vemula, N V Prasanth and Dixit, Harish Nagaraj (2019) Finite Element Modeling of Multiphase Flows using Arbitrary Lagrangian Eulerian Approach. Masters thesis, Indian institute of technology Hyderabad.

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Abstract

Fluid flow solvers generally deal with Eulerian approach linked with Volume of Fluid(V.O.F.) or Level set(L.S.) methods for multiphase flows. But If the primary objective is to track the interface along with solving Navier Stokes in multiphase, then these may not offer appreciable results without heavy computational effort. Also for flows, where length scales are in the order of characteristic length, which are regarded as Micro fluidics where surface tension plays a dominant role, Finite volume methods are not suggested. As surface tension only acts at the interface, According to F.V.M. interface is a diffuse region rather a discrete boundary. Imposing surface tension computationally, creates a spurious numerical currents, which is not advisable. This project aims at analyzing the fluid flows using Galerkin Finite Element approach and discrete interface model for simulating the multiphase flows. Arbitrary Lagrangian Eulerian approach is incorporated for moving mesh, where interface is treated as pure Lagrangian and the interior mesh is amended accordingly in weighted sense. For multiphase flows, the mesh near the boundary has large distortions creating computational constraint; So, Mesh Smoothing is also incorporated. Finite Element method on the other hand considers relatively very few elements compared to other Eulerian methods like Finite Volume for interface tracking, Also can incorporate Discrete interface model, where the interface is just a membrane unlike a defined region. The properties are a smooth variation across the interface in Volume of Fluid, where in A.L.E. the properties vary like a Heaviside variation the interface. Being discrete Interface model, there is freedom of defining the interface as accurate as necessary demanded by the problem. So, being a sharp interface, there are no spurious currents at the interface. Hence Finite Element modeling is highly suggestible for fluid flows involving interface tracking or multiphase flows where surface tension plays a major role. For the problems dealing with high Reynolds number flows i.e., flows with inertia forces dominant make Galerkin formulation inaccurate. The advection term is odd order making system of equation non-symmetric which led the emergence of new methods like Petrov-Galerkin, which is similar to upwind scheme in general computational methods. Since here we deal with low Reynolds number problems, Galerkin approach gives good results.

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