Python Code to Calculate The Flow Over This Airfoil - Computer Science Assignment Help

Assignment Task 

1. Consider the asymmetric cambered double-wedge airfoil shown below. It has chord length of c, fractional maximum thickness t, and fractional maximum camber m. The maximum thickness and camber (if any both occur at p times the chord from the leading edge. It faces a supersonic freestream of Mach number Moo at an angle of attack a. For reference, see Example Problem 7.5 of Houghton et al. textbook (2013 edition).

Note that in the textbook problem, p is restricted to be 0.5; we allow it to be a variable. 

(a) Write a Python code to calculate the flow over this airfoil, using shock-expansion theory. The inputs to the code should be (a) t, (b) m, (c) p, (d) a, and (e) Moo. The outputs from the code should be (i) sectional lift coefficient, and (ii) sectional wave drag coefficient. If you want, you can also calculate and return the sectional pitching moment (for no extra credit!).

(b) Ackeret theory predicts that lift is independent of camber, and wave drag increases with camber, so that (wave) drag-to-lift ratio increases with camber. See if shock-expansion theory leads to the same conclusions by systematically exercising your code for various choices of the five input parameters. Ideally, you should create several plots of ci/cd vs. m for various choices of the other parameters, viz. a, Moo, t and p. Note that m can also be negative. If you find any differences in your outcome compared to linear theory, try to explain them. If you are NOT finding any differences, then you are not exercising hard enough! 
 

(c) Ackeret theory predicts (prove this in the next question) that drag is minimized if the airfoil is symmetric (i.e., if p = 0.5). See what shock-expansion theory has to say about this by systematically exercising your code again. Ideally, you should create several plots of cd vs. p for various choices of the other parameters, viz. a, Moo, t and m.

(d) Using the theory of Ackeret (i.e., linearized supersonic aerodynamics theory), show that the minimum drag is attained by such a double-wedge airfoil if p = 0.5 (for arbitrary t, m, a, and Mo„ > 1). For this, you should derive all steps in detail. Start from the following basic expression for pressure coefficient (do not derive it!)  264  cm VM2 —1 . = - 1  on the upper surface, on the lower surface. 

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