Aerodynamics

The tasks for this problem are as follows:

(a) Download the data files. Plot the geometry of the airfoil using the x/c and y/c data given in the files. (Make the scaling of the x and y axes the same so that the airfoil has its true shape. This can be done within Matlab by using the axis(’equal’) command.)

(b) For the data at an angle of attack α = 0◦, plot the incompressible pressure dis- tribution, Cp0(x) (use the x/c data in the Cp file, not the geometry file). In aero- dynamics we plot Cp for airfoils with the negative axis upward, so that (usually) the curve for the upper surface will be on top (lower pressure) and the curve for the lower surface will be on the bottom. You can do this within Matlab by using the following command after the plot command: set(gca,’ydir’,’reverse’). If you do not want to do this, another method of accomplishing the same effect is to plot −Cp instead of Cp. (Note that you do not need to separate the data into Cp on the lower and upper surfaces. We just want to plot the data as it is given in the file.)

(c) Using the data at an angle of attack α = 0◦, compute Cp(x) for M∞ = 0.50, 0.65 and 0.70. using three methods, (i) the Prandtl-Glauert rule, (ii) the Karman- Tsien rule, and (iii) the Laitone rule. Plot the results with curves for the three methods together on the same plot, one plot for each Mach number. For each of the Mach numbers compute the critical value of the pressure coefficient, Cpcr.

Also compute the minimum values of the pressure coefficient, Cminp , for each of

the three scaling methods. Is Cminp lower than Cpcr for any of the cases (i.e. do any of the methods predict supercritical flow)?

(d) For the data at an angle of attack α = 8◦, plot the incompressible pressure distribution, Cp0(x) (use the x data in the Cp file, not the geometry file).

(e) Using the data at an angle of attack α = 8◦, compute Cp(x) for M∞ = 0.25, 0.30 and 0.35. using three methods, (i) the Prandtl-Glauert rule, (ii) the Karman- Tsien rule, and (iii) the Laitone rule. Plot the results with curves for the three methods together on the same plot, one plot for each Mach number. For each of the Mach numbers compute the critical value of the pressure coefficient, Cpcr.

Also compute the minimum values of the pressure coefficient, Cminp , for each of

the three scaling methods. Is Cminp lower than Cpcr for any of the cases (i.e. do any of the methods predict supercritical flow)?

3. For each of the angles of attack in problem 2, determine the critical Mach number, Mcr, predicted using the three different compressibility rules. To do this you will need to solve a nonlinear equation. Write a Matlab program to do this using the fsolve command and turn in a listing of your program along with the results. (If you want help using fsolve see the sample program in the files ps7 3sample.m and ps7 3samplefun.m.)