An Analytical Approach for Modeling Fluid-structure Interaction Problems in Axisymmetric Domains

Few analytical approaches have been proposed so far for solving Fluid- Structure Interaction (FSI) problems in the literature. In fact, FSI is generally so complicated that its analytical solution remains almost unavailable. Inspired by this fact, here an analytical methodology is presented for modeling steady-state fluid-structure interaction problems in axisymmetric domains. For this purpose, the Navier-Stokes equations for the flow of the incompressible viscous fluid, and the linear elasticity equations for the deformation of the solid structure are expressed in axisymmetric coordinates. Appropriate boundary conditions are also employed that are capable of coupling the fluid and solid domains by imposing kinematic and dynamic constraints on the fluid-structure interaction interface. The set of fluid and structure equations are solved by MATLAB symbolic toolbox. The accuracy of the presented analytical approach is verified in two different ways. First, by specializing the results for the simple case of a thick cylindrical pressure vessel, second, by comparing the analytical results for flow through a nozzle with numerical results obtained by ANSYS/CFX simulation. Variation of the stress components is obtained in the nozzle wall. The results of the analytical approach are in good agreement with those of the numerical modeling. The proposed methodology can be used for fast yet efficient solution of fluid-structure interaction problems in axisymmetric configuration.