An Analytical Asymptotic Solution Method of the Euler Equations for Efficient Flow Analysis and Aerodynamic Design
Shim, Jeonghwan
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/85074
Description
Title
An Analytical Asymptotic Solution Method of the Euler Equations for Efficient Flow Analysis and Aerodynamic Design
Author(s)
Shim, Jeonghwan
Issue Date
2002
Doctoral Committee Chair(s)
Lee, Ki D.
Department of Study
Aerospace Engineering
Discipline
Aerospace Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Language
eng
Abstract
An efficient flow analysis and aerodynamic design tool was developed based on analytical asymptotic solutions of the Euler equations. The solution algorithm uses an analytical asymptotic formulation in the streamline coordinate system, wherein the governing equations are transformed into a non-homogeneous Cauchy-Riemann system. A sequence of coordinate transformations, mappings, and asymptotic expansions places the governing equations in a form suitable for classical mathematical techniques. The homogeneous solution to the governing system is obtained by the conformal mapping and Fourier analysis, and provides an exact solution for incompressible flows and an accurate approximate solution for compressible flows. The non-homogeneous solution is obtained by Green's function formulation and accounts for higher order compressibility effects. The focus of efforts has been on the evaluation of components of the analytical solution algorithm in terms of solution quality and computational efficiency, as compared to the conventional CFD method. The formulation was extended to cascade flow problems by a new mapping procedure, which preserves the Cauchy-Riemann form of the governing equations and therefore enables us to use the same analytical solution procedure. For transonic flow problems, the mass flux formulation has been derived and used with the Rankine-Hugoniot equations for locating shock waves and corresponding entropy jumps. Transonic flow solutions around 2D airfoils were obtained by an analytical shock modeling from the homogeneous solution, as a first-order approximation. Finally, in order to demonstrate the computational efficiency of the method, an analytic-based aerodynamic design tool was developed by combining the analytical flow solution with numerical optimization methods which include a genetic algorithm. Results from the current study show that the computational cost for flow analysis and aerodynamic design can be reduced significantly by using the analytical asymptotic solution method.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
