Document Type

Honors Capstone Project

Date of Submission

Spring 5-1-2008

Capstone Advisor

John F. Dannenhoffer III

Honors Reader

Mark N. Glauser

Capstone Major

Mechanical and Aerospace Engineering

Capstone College

Engineering and Computer Science

Audio/Visual Component

no

Capstone Prize Winner

no

Won Capstone Funding

no

Honors Categories

Sciences and Engineering

Abstract

Forces acting on an airfoil are often found using computational fluid dynamics, and the accuracy of the solution is highly dependent on the type and resolution of the grid used to capture the flow. The simplest way to increase the resolution of a grid is to globally increase the number of grid points. This method results in significantly higher accuracy at the expense of computing time, and therefore is not generally the best solution. Alternatively, the error can be reduced without significantly increasing the computation time if the grid points are moved such that the points cluster around areas of high errors. Previous efforts have used gradients of properties such as pressure or density as a surrogate for error. These techniques have limited success since the errors in the force calculation are not always linked to high solution gradients; the grid points that are closest to the airfoil have the largest impact on the accuracy of the force calculations, while the flow behind an airfoil does not affect the lift and drag on the airfoil. A previously proposed solution to this problem came in the form of using adjoint flow equations, which provide a direct link between the computed force coefficients and truncation errors in the flow field. This method has been developed theoretically, but has only been verified computationally using an unstructured grid. The focus of this paper is to implement the adjoint adaptation for structured grids and to examine the error in force calculations for several different types of grids. A newly-written program which applies an elliptic grid smoother to an algebraic grid was used to generate the grids. Once this elliptic grid was created, it was read into a separate flow solver to find the coefficients of lift and drag of the airfoil. A double wedge airfoil in a supersonic stream was selected to test the program because an analytical solution for lift and drag could be used for comparison.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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