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Computing potential flows around Joukowski airfoils using FFTs

Brontsema, F. (2007) Computing potential flows around Joukowski airfoils using FFTs. Bachelor's Thesis, Mathematics.

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Abstract

In this bachelor thesis we are going to discuss 2-dimentional potential airflows around so called Joukowski airfoils. The reason for doing this is an assignment for the course Computational methods of science, also see [1]. In this assignment (discussed in section 3.1.1) we determine the speed and pressure around a cylinder using FFT’s. When we know the pressure we can say something about the net (lift) force acting on the body. As you can image, a cylinder is not a very interesting model. So the goal of this thesis is to find a way to transform this flow around the cylinder onto a profile that is more interesting. We do this by using the Joukowski transformation which maps a cylinder on an airfoil shaped body, the so called Joukowski airfoil. Before we can transform the speed around the cylinder we must first determine the speed around a cylinder with circulation. We have to do this in order to satisfy the so called Kutta-Joukowski condition. This condition states that the flow should leave the body smoothly. We determine the speed around a cylinder with circulation with the help of the Hess and Smith method combined with FFT’s. The Hess and Smith method is a boundary integral method for flows around arbitrary shapes, that uses sources and circulations to create a flow. As a check we also solve the problem using super positioning of singularities. After this we transform the flow to a flow around the Joukowski airfoil in such a way that it is physically realistic. In the last section we will discuss the most interesting results obtained. 3

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:28
Last Modified: 15 Feb 2018 07:28
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/8397

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