HW32solution

HW32solution - 1 1 1 2 2 1 2 1 2 1 1 2 1 2 2 1 2 2 cr cr cr...

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AAE 334, Fall 2011 SOLUTION Homework 32. Due Friday, December 9 at the beginning of class. Solve for critical Mach number as an angle of attack for the following low-speed airfoil pressure data. Use the Prandtl-Glauert rule. List for each case the spanwise position, , where the flow is sonic . The minimum pressure point on the wing at each angle of attack is the point with the most negative pressure coefficient. For the wing below at these three angle of attack, it appears that the minimum pressure is found at the leading edge, where the flow accelerates around the upper surface of the nose at AOA>0. Given Results min , po c c x / cr p c , cr M 8.1 o -2.738 0 0.67 -3.04 0.43 12.1 o -3.691 0 0.50 -4.00 0.39 15.1 o -2.037 0 0.33 -2.33 0.48 To solve for critical Mach number, find the intersection of the Prandtl-Glauert scaling of the min , po c values and Equation 11.60,  
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Unformatted text preview: 1 1 1 2 2 1 2 1 2 1 1 2 1 / 2 2 1 / 2 2 , cr cr cr cr cr p M M M M c In Matlab, I just used a few lines: % hw32.m % gam = 1.4; % ratio of specific heats cpo = [-2.738 -3.691 -2.037]; % Cpo values Mcr = [NaN NaN NaN]; % for i = 1:3 Mcr(i) = fzero(@(x) (cpo(i)/sqrt(1-x^2))-((2/(gam*x^2))* ... (((2+(gam-1)*x^2)/(gam+1))^(gam/(gam-1))-1)), 0.2 ); end Critical pressure coefficient values are not asked for but are found this way: cpcr = cpo ./ sqrt(1-Mcr.^2) (data and figure below from “Airfoil modification effects on subsonic and transonic pressure distributions and performance for the EA-6B airplane,” Allison, Dennis O. and Sewall, William G., NASA Langley Research Center, NASA-TP-3516, 1995.)...
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This note was uploaded on 02/21/2012 for the course AAE 334 taught by Professor Collicott during the Fall '09 term at Purdue.

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HW32solution - 1 1 1 2 2 1 2 1 2 1 1 2 1 2 2 1 2 2 cr cr cr...

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