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 2dimentional 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 KuttaJoukowski 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:  https://fse.studenttheses.ub.rug.nl/id/eprint/8397 
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