Details

Autor(en) / Beteiligte

• Rajasekharan, Ajaykumar

Titel

Variationally consistent multiscale formulations and ALE time integrators for large eddy simulation of turbulent flows on dynamic grids

Ort / Verlag

ProQuest Dissertations Publishing

Erscheinungsjahr

2008

Link zum Volltext

• ProQuest

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• Simulation of turbulent flows on dynamic grids is important for many low speed turbulent flow applications. Some examples include the use of moving mesh to simulate the flow structure inside the cylinder of a reciprocating combustion engine, separated flow over pitching and heaving airfoils, study of aerodynamic mechanisms of insect flight, etc. Accurate and efficient large eddy simulation (LES) computations of such flows present a formidable research challenge. Capturing the unsteady aerodynamic flow characteristics of such flow configurations warrants the development of new robust mathematical formulations, closure models and numerical procedures to describe the flow physics accurately in a moving computational domain. The requirement of new robust mathematical formulations is addressed in this dissertation by devising a three-field formulation of the variational multiscale (VMS) method for LES of compressible turbulent flows on unstructured grids. The deficiencies of the static VMS-LES formulation are then addressed by developing a variationally consistent dynamic VMS-LES extension. The key features of this dynamic model include two variational analogues of Germano's algebraic identity, and a computationally efficient, agglomeration-based numerical procedure. Agglomeration is used both for separating a priori the scales and computing dynamically a Smagorinsky parameter and the turbulent Prandtl number on unstructured finite volume or finite element meshes. Numerical predictions of low-speed, 20 degrees angle of attack, turbulent flows past a 6:1 prolate spheroid and a forward swept scaled wing are presented. The flow computations on moving grids also require the development of accurate and stable moving grid extensions of standard time-integration schemes on fixed grids. This issue is addressed in this dissertation by exploring the efficacy of previous frameworks for accuracy and stability devised for multistep implicit time integration schemes. In particular, a general framework for devising arbitrary Lagrangian-Eulerian (ALE) extensions of explicit Runge-Kutta (ERK) schemes is presented. This includes the derivation of a genuine discrete geometric conservation law (DGCL) for the ALE extension of second order explicit Runge-Kutta (ERK-2) scheme. It is then shown that satisfying this DGCL is a necessary and sufficient condition for preserving nonlinear stability for computations on moving grids. A flow computation of dynamic-stall over a pitching NACA-0012 wing is then presented.