Validation of an Unstructured Flow Solver for Oblique Shocks and Expansion Fans

A Thesis Presented for the Master of Science in Computational Engineering Degree, The University of Tennessee at Chattanooga

James Beasley, December 2004

Many important Computational Fluid Dynamics (CFD) problems require the use of a flow solver that utilizes unstructured grids (a.k.a. “unstructured flow solver”). The present study focuses on the validation of the UT SimCenter at Chattanooga’s unstructured compressible flow solver for supersonic inviscid flow by comparing computed and analytical pressure distributions for a variety of ramp and expansion geometries. This is a first step in the process of validating the unstructured grid solution algorithm for general flow fields. During the course of this work, an automated unstructured grid generation package with solution adaptive grid capability was developed in the UT SimCenter. Another aspect of this study is the evaluation of this newly developed capability. Grids have been constructed using two different grid generators. The one developed in the UT SimCenter has the capability to automatically generate a grid and concentrate grid nodes in regions of large solution gradients, while the other requires that the grid be generated manually. The only way to refine the resulting manually generated grid is to construct an entirely new grid with more nodes. Simulations have been performed utilizing both of these approaches for identical geometries and flow conditions in order to compare solution accuracy. From the results of this study, computed pressure distributions for both oblique shocks and expansion fans have been shown to be in excellent agreement with those derived analytically for a wide variety of flow angles and Mach numbers. In addition, results indicate that, for the cases studied, grid adaptation results in more accurate solutions using fewer nodes than those not using adaptive grids.

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