Title: First Stages Of A Viscous Finite Element Solver For
Non-Inertial And Aeroelastic Problems
Author(s): N. J. Moffitt
Date: December 2004
Pages: 232
Formats: pdf (9 MB)
Abstract:
Scope and Method of Study: In 2003, Tim Cowan generated a finite element Euler solver for aeroelastic and
non-inertial problems. This thesis concentrates on the expansion of the Euler
equations to the full Navier-Stokes equations for laminar cases. The study
develops the needed terms to adapt the equations, implements the equations in a
Fortran program, and then finishes by verifying and validating the code.
Findings and Conclusions: Suggestions are given for the appropriate mesh to calculate the proper flow
attributes and local shear stress distribution of a laminar boundary layer. Flow
attributes are important if an understanding of the complexities of the flow are to
be investigated, but the local shear stress and overall drag on the surface are used
to calculate the forcing functions for the structural and dynamics solver contained
in the package. Suggestions were also made for stable CFL values used to
evaluate steady solutions and stable time steps to generate unsteady solutions.
Several viscous test cases were used varying across the subsonic, transonic, and
supersonic regimes. Test cases include the Blasius solution, circular cylinder, and
several airfoil solutions. Also several solutions were found to match pictures of
very slow flow and viscous flows with Reynolds numbers up to the onset of
turbulence. Several investigations were made past the onset of transition and
turbulence to investigate the ability of the solver in these areas.
After verification and validation of the viscous solver, the solver was found to
work well for the cases test in the subsonic, transonic, and supersonic laminar
solutions. But the solver does not possess a turbulence model, and therefore
cannot properly predict separation or properties in a transitional or turbulent
boundary layer. The inclusion of as many test cases in all areas of subsonic,
transonic, and supersonic flow was sought; but, caution is given for solutions
investigated that do not resemble the verification or validation test cases in any
way.
Revised: 19 Jan 2005 [CRO]