The aim of the paper is to simulate numerically the Fluid-Structure Interaction for flow through valves of a hermetic compressor using immersed boundary method. The paper is primarily concerned with the mathematical structure and implementation of the Immersed Boundary Method which includes both the Immersed Boundary form of the equations of motion and also the Immersed Boundary numerical Scheme. The flow pattern of the fluid in the compressor is intimately connected with the performance of the valves, and this paper presents a solution of the Navier-Stokes equations in 2D of a Newtonian fluid under laminar regime, in the presence of moving immersed boundaries, being the fluid treated as isothermal. The immersed boundary method has evolved into a generally useful method for problems of Fluid-structure interaction. In this approach, the mathematical formulation employs a mixture of Eulerian and Lagrangian variables, the fluid is represented in a Eulerian co-ordinate frame and the structures or the interacting surfaces are considered in a Lagrangian co-ordinate frame. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function, constructed according to the principles established in [1], which plays a prominent role. In the numerical scheme motivated by the Immersed Boundary formulation, the Eulerian variables are defined on a fixed Cartesian frame, and the Lagrangian variables are defined on a curvilinear mesh that moves freely through the fixed Cartesian mesh without being constrained to adapt to it in any way at all. Eulerian/Lagrangian identities govern the transfer of data from one mesh to another. A structured non-uniform staggered grid based two dimensional finite volume model is used to solve the equations of the fluid flow in laminar regime and a second-order Adams Bashforth-Crank Nicholson scheme is used for temporal discretization and pre-conditioned Bi-conjugate gradient stabilized method is used to solve the derived system of equations. The numerical results presented show the average volumetric flow and the respective temporal valve displacements for different Laminar Reynolds numbers.
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