PS7_solution

The moment coefficients for the two airfoils are the

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Unformatted text preview: profile of an airfoil. The moment coefficients for the two airfoils are the same -they have the same angle of attack and the same camber. PROBLEM 3a NACA 0012 0.3 0.2 0.1 y 0 -0.1 -0.2 -0.3 0.2 0.4 0.6 0.8 1 x Fig.1. Airfoil Geometry. PROBLEM 3b The pressure coefficient plots based on different compressibility rules are shown in figures 2-5. M=0.4 -1 Cp__PG Cp__KT Cp__L -0.8 -0.6 -0.4 Cp -0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x Fig.2. Pressure coefficient variation along the length of the airfoil at M=0.4. M=0.6 -1 Cp__PG Cp__KT Cp__L -0.8 -0.6 -0.4 Cp -0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x Fig.3. Pressure coefficient variation along the length of the airfoil at M=0.6. M=0.7 -1 Cp__PG Cp__KT Cp__L -0.8 -0.6 -0.4 Cp -0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x Fig.4. Pressure coefficient variation along the length of the airfoil at M=0.7. M=0.75 -1 Cp__PG Cp__KT Cp__L -0.8 -0.6 -0.4 Cp -0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x Fig.5. Pressure coefficient variation along the length of the airfoil at M=0.75. PROBLEM 3c From figures 2-5 we see that at a low subsonic Mach number of 0.4, all three methods do a good job in predicting the compressible pressure coefficient and the plots match well with the experimental data given in the lecture notes. As the Mach number is increased, the Laitone method gives the highest peak value for the pressure coefficient. The Prandtl-Glauert rule is the least sensitive to Mach number variation compared to the other two methods which account for non-linear effects in the compressible potential equation. Overall, the Karman-Tsien rule gave the best representation of the compressible coefficient values. It must be pointed out that all three rules give the same vale for Cp over the airfoil surface where local Mach numbers are well below sonic conditions. PROBLEM 3d The expression for...
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