EAE 126 - Theoretical and Computational Aerodynamics Spring 2024
Project 5: Steady, Inviscid, Adiabatic, Linear Subsonic, and Irrotational flows
over Airfoils โ Numerical Solutions
Problem 1: [๐๐๐กโ๐๐ 30 ๐๐ก๐ ; ๐
๐๐ ๐ข๐๐ก๐ 25 ๐๐ก๐ ; ๐๐๐๐๐๐๐๐๐๐๐ 25๐๐ก๐ ; ๐ท๐๐ ๐๐ข๐ ๐ ๐๐๐ 10 ๐๐ก๐ ]
[๐๐๐กโ๐๐ 30 ๐๐ก๐ ]
Solve two dimensional airfoils at angle of attack using finite differences on Cartesian grids and
linearized boundary conditions using relaxation procedure.
โข [๐
๐๐ ๐ข๐๐ก๐ 15 ๐๐ก๐ ] For each of the four cases:
(๐ผ,๐โ)=(0ยฐ,0),(0ยฐ,0.3),(5ยฐ,0),(5ยฐ,0.3); Plot
o Airfoil Geometry
o ๐ข-velocity contour
o Residuals (convergence study)
o Surface pressure distribution for both upper and lower surface
โข [๐
๐๐ ๐ข๐๐ก๐ 10 ๐๐ก๐ ] Calculate ๐ถ๐ฟ, ๐ถ๐ท, and ๐ฅ๐๐, tabulate data and plot
o versus angle of attack (๐ผ = 0ยฐ,2ยฐ,4ยฐ,5ยฐ) at ๐โ=0.3
o versus Mach number ๐โ=(0,0.1,0.2,0.3) at ๐ผ = 5ยฐ
Repeat the above steps for the following five airfoils
a. Flat plate
b. Cambered plate
c. Biconvex Airfoil
d. NACA 0012
๐ฆ(๐ฅ)=10๐๐[0.2969โ๐ฅ
๐โ0.126(๐ฅ
๐)โ0.3537(๐ฅ
๐)2+0.2843(๐ฅ
๐)3โ0.1015(๐ฅ
๐)4]
e. Ellipse (thickness problem only, no need to compute and update ฮ)
4 ๐บ๐๐๐๐๐ก๐๐ฆ ร (4 ๐ผ๐๐๐๐ฃ๐๐๐ข๐๐ ๐๐๐ ๐๐ + 1 ๐๐ข๐๐๐๐๐ฆ)+ 1 ๐ธ๐๐๐๐๐ ๐ = 21 ๐๐๐ก๐๐ ๐น๐๐๐ข๐๐๐
[๐ท๐๐ ๐๐ข๐ ๐ ๐๐๐ 10 ๐๐ก๐ ] Technical discussion on method, results (or expected results), correctness,
source of error, potential improvements, etc.
Problem 2: (Extra Credit 20 pts)
(1) Axis-symmetric flows over a body of revolution/ellipsoid of ๐
(๐ฅ) is a circular arc. Find the
pressure distribution. Then calculate the flow over a body of revolution at small angle of attack.
Compute and plot ๐ถ๐ฟ, ๐ถ๐ท, ๐ถ๐, and ๐ฅ๐๐ versus angle of attack (๐ผ= 0ยฐ,2ยฐ,4ยฐ,5ยฐ) at ๐โ=0.3,
and versus Mach number ๐โ=(0,0.1,0.2,0.3) at ๐ผ = 5ยฐ.
(2) Repeat Problem 1 with Joukowsky airfoil.
