A Numerical Algorithm for High Reynolds Number Fluid-structure Interaction Simulations

Open Access
Author:
Lieberknecht, Erika Nikole
Graduate Program:
Aerospace Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
None
Committee Members:
  • Robert Francis Kunz, Thesis Advisor
  • Jonathan S Pitt, Thesis Advisor
  • Scott Miller, Thesis Advisor
  • George A Lesieutre, Thesis Advisor
Keywords:
  • high Reynolds numbers
  • fluid-structure interaction
  • Streamline Upwind Petrov-Galerkin
  • turbulence
  • finite element method
Abstract:
A finite element based algorithm for high Reynolds number (10^6 − 10^8 ) flow is implemented to simulate fluid-structure interaction (FSI). Applicable to several engineering disciplines, FSI is the interaction between a deformable solid body and fluid flow, with particular interest in large deformations and fully coupled interactions. Numerical modeling of high Reynolds number flow requires care to preserve the FSI interface and fluid boundary layer. High Reynolds number flows are naturally turbulent, so the governing equations for the fluid are time averaged, resulting in the Reynolds Averaged Navier-Stokes (RANS) equations. A turbulence model is added to the fluid formulation to close the system of equations. The resulting fluid equations are cast in an Arbitrary Lagrangian-Eulerian (ALE) frame of reference, and the solid and mesh governing equations remain in the Lagrangian frame of reference. The solid and mesh formualtions are discretized using the classical Galerkin FEM, while the fluid formulation is discretized using the Streamline Upwind Petrov-Galerkin (SUPG) method for stabilization of FEM based instabilites. A partioned approach is presented for the mesh and fluid implementations followed by discussion for a monolithic approach. The method of manufactured solutions (MMS) is used to verify the mathematical accuracy of the implemented algorithm. To show the effectiveness of the mesh formulation, a mixing problem is presented with appropriate results. To validate the fluid formulation, the fixed NACA0012 test case, from NASA, is simulated and compared to experimental results.