PS7_solution

1 to e32 and solve for mcr this value turns out to be

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Unformatted text preview: o be ( ) This value is reasonably close to the experimental critical Mach number of 0.725 with a percentage deviation of 2.43%. Karman-Tsien √ 0 1 √ To find Mcr from the Karman-Tsien rule, we equate, E3.1 to E3.3 and solve for Mcr. This value turns out to be ( ) This value compares very well with that of the experimental critical Mach number of 0.725 with a percentage deviation of 0.51%. Laitone √ * , * √ + + To find Mcr from the Laitone rule, we equate, E3.1 to E3.4 and solve for Mcr. This value turns out to be ( ) This value is reasonably close to the experimental critical Mach number of 0.725 with a percentage deviation of 2.61%. Thus, the Karman Tsien rule worked the best in predicting an accurate value for the critical Mach number. The Laitone rule gave the least value for the critical Mach number as it is the most sensitive to non-linear effects. The Prandtl-Glauert rule gave the largest value for the critical Mach number as it does not account for non-linear effects. MATLAB CODE %%HA 7 - P3 clc clear close all load('naca0012_x.dat'); %%Load airfoil x co-ordinates load('naca0012_y.dat'); %%Load airfoil y co-ordinates %Plot airfoil geometry figure(1) plot(naca0012_x,naca0012_y) axis('equal') xlabel('x') ylabel('y') title('NACA 0012') load('naca0012_0_cp.dat') Cp_0=naca0012_0_cp; %%Define incompressible pressure coefficient array M_array=[0.4,0.6,0.7,0.75]; %Store the required Mach numberss in M_array for i=1:4 %Case index M=M_array(i); ...Compute the compressible Cp values along the airfoil topsurface %Pradtl Glauert Cp_M_PG=Cp_0/sqrt(1-M^2); %Karman Tsien Cp_M_KT=Cp_0./(sqrt(1-M^2)+M^2/(1+sqrt(1-M^2))*Cp_0/2); %Laitone's rule gamma=1.4; Cp_M_L=Cp_0./(sqrt(1-M^2)+M^2*(1+(gamma-1)/2*M^2)... /(2*...
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