Loading...
Computation of plane potential flow in multiple connected domains using series methods and conformal mapping
Mears, Justin Laurence
Mears, Justin Laurence
Files
Loading...
dissertation
Adobe PDF, 3.49 MB
Authors
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2023-12
Type
Dissertation
Genre
Keywords
Subjects (LCSH)
Electronic dissertations
Citation
Abstract
This paper presents a method for calculating potential flow in the exterior of multiplyconnected circle domains in the complex plane. The method employs a Laurent series expansion of the potential function on the circular boundaries, which can be easily written into a linear system for finding the Laurent coefficients. This system exhibits the form of “identity plus a low-rank matrix”, enabling efficient utilization of conjugate-gradient-like methods.
Through the use of conformal mapping, the method is extended to calculate the potential flow in multiply-connected domains exterior to any closed curves. This is achieved by computing the potential flow over an appropriate circle domain and mapping this result to the desired physical domain using an approximation of the Laurent series for the conformal map. Circulations around each boundary can be specified or calculated, with a specific focus on multi-element airfoils where the circulations are determined to satisfy the Kutta condition at trailing edges.
Comparisons with alternatives methods for computing flow in circle domains, namely reflection and least-squares methods, are included to demonstrate the accuracy and efficiency of the new method. Finally, there are many examples of flow calculations over multiplyconnected regions with smooth boundaries and multi-element airfoils.
Table of Contents
Description
Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
Publisher
Wichita State University
Journal
Book Title
Series
Digital Collection
Finding Aid URL
Use and Reproduction
© Copyright 2023 by Justin L. Mears
All Rights Reserved