/n Assignment 4: Supersonic Flow over a Cone ASEN 5151 Spring 2024 For this assignment you should upload your submission in two parts: • Any written work for each part, along with any code outputs (tables or graphs - includ- ing any requested numerical outputs) compiled into a single PDF document should be uploaded to the "Assignment 4" assignment on Gradescope. • All code used to generate your results should be uploaded to the "Assignment 4 - Code" assignment on Gradescope. If either part is missing, you will receive a zero for the entire assignment. Write a code to solve the conical shock wave problem in which you specify the cone angle Sc and freestream Mach number M₁ and calculate the shock wave angle, 0. The inputs to your program should be the specific heat ratio y, the freestream Mach number M₁, the cone angle dc, the convergence tolerance for the cone angle ɛ, and the number of integration points N to be used. The outputs to your code should consist of the shock wave angle 0s, the stagnation pressure ratio across the shock p02/P01, the cone surface Mach number Mc, the cone surface pressure coefficient (Cp)c, and at each angular location, the non-dimensionalized velocity components V, and V2, the Mach number M, and the local-to-freestream ratios of static pressure, static temperatures, and static density, p/p₁, T/T₁, and p/p₁. To check for convergence of the cone angle, compute the relative error and compare with the convergence tolerance ε: r و - relative error || Sc — § (²) | |8c| To demonstrate your program, run it for a freestream Mach number of M₁ = = 2.4, a cone - (8, 16, 32) for air (y = 1.405) semi-angle of c = 16°, using three different grid spacings: N with a cone angle convergence criteria of € = 10-6. For each grid spacing, please output the following to at least 5 significant figures: (a) The shock wave angle; (b) The cone surface pressure coefficient; (c) The cone surface Mach number. Compare to the NACA 1135 charts. In addition, include plots of the Mach number and pressure distribution (P/P₁) between the shock and cone surface. For your x-axis, plot the coordinate as descending (such that from left-to-right you march from the shock to the cone surface). For both plots, include all three grid solutions on one plot to verify grid convergence. Finally, export a .dat file with the angular distribution of , Vr, V₁, M, P/P₁, and T/T₁ for the N - 16 grid reported to 5 significant figures. Include this table in your PDF write-up. = 1