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# hw8 - number of panels eg 10 20 40 80 and so on A...

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AAE333 Fall 2009 Problem Set #8 Due: Monday 11/02/9 10% bonus if turned in on Friday 10/30/9 (I intend to add another part to this problem before 4PM on Monday Oct 26) 1.) You are going to find the incompressible potential flow over an ellipse at zero angle of attack using the source panel method described in Sec 3.17. There are two matlab files you will need, both in the HW8 folder of the class webpage: function [U,V]=velfrompanel(x1,y1,x2,y2,xc,yc) calculates the x & y velocity components (U,V) at a specified point (xc,yc) induced by a unit strength source sheet connecting specified points (x1,y1) and (x2,y2) ellipse_examp.m A script the sets up the flow over a 10% ellipse and solves for the source strengths, the surface flow speed and the pressure coefficient. You may use these files to do the first part of this assignment: a) Consider an ellipse with 0.15 thickness to chord ratio. Determine how the solution from the panel method depends on the

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Unformatted text preview: number of panels: eg 10, 20, 40, 80 and so on. A reasonable single measure of the solution accuracy might be the value of the flow speed at the point of max thickness (x=0). Discuss this… how many significant figures do you have in the solution, and how does it depend on the number of panels b) The exact solution for this ellipse is known: If the ellipse is represented by x=(1+b)cos (th); y = (1-b) sin(th) where th ranges from 0 to 2pi (and b determines the thickness to chord ratio) Then the flow speed on the surface is 2*Uinf/[ (1+b)*sqrt(1+ e^4 x^2/y^2) ] Where e is short for (1-b)/(1+b) Show that the maximum speed in the analytical solution is exactly greater than the free stream speed by a factor of (1+ thickness/chord) c) Compare the numerical solutions from part a) to the analytical solution. How does the maximum speed match up, in particular? AAE333 Fall 2009...
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hw8 - number of panels eg 10 20 40 80 and so on A...

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