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Renjitham Sankaran, Simtha

Mechanical Engineering

2012

PhD

Accurate solution of detached vortices is critical for many aerodynamic problems involving vortex structures, such as in vortex-body interaction during store separation, interaction of wake turbulence from heavier aircraft with lighter aircraft; and blade-vortex interaction noise and vibrational problems for helicopters during descend flight and maneuvers. In these types of flows, vortices must be numerically simulated without loss of circulation due to numerical dissipation. Several computational methods are known that discretely conserve vorticity field, but in most cases. these methods have been developed for Cartesian grids. The overall objective of the current research is to develop an overset grid method for solution of the integral vorticity-velocity formulation of the Navier-Stokes equations for flow past fixed and moving bodies. This method is developed in a progressive manner in the current dissertation. We first consider solution of the heat equation for an unsteady thermal conduction problem on a overset grid consisting of an inner body-fitted grid and an outer Cartesian grid.
Next, we examine accuracy of different advection schemes on a Cartesian grid, with the objective of identifying a conservative scheme with low dissipation and no spurious oscillations that performed well for abruptly-varying fields typical ofthose observed in vorticity transport problems. These different capabilities are next combined with a velocity solution method for the Biot-Savart integral using an adaptive, optimized multipole acceleration method. The integration is performed over all inner grid cells, over all "active cells" of the outer grid that lie entirely outside of the inner grid, and over sub-elements of a set of overhanging cells of the outer grid that overlap part of the inner grid. A level-set function is introduced in which the zero level-set surfaces coincides with the outer surface of the inner grid. This level-set function is used to rapidly subdivide the overhanging grid cells into triangular sub-cells in 2D (or tetrahedral sub-cells in 3D) which lie entirely outside .ofthe inner grid, while omitting the parts ofthese cells that lie inside the inner grid, so as to avoid double-counting the vorticity in these regions during computation of the BiotSavart integral.
The pressure is solved as a post-processing variable using a boundaryelement formation that requires evaluation of an integral using a parallel method to that used for velocity calculation. The overset grid method is applied to simulation of vorticity transport in two-dimensional flow past stationary and moving bodies. A wide range of test cases are examined and used to validate the method. A three-dimensional form ofthe method has been developed and tested for different types of vortex flow problems.