* The compressibilty correction rule for thin wing The effect of compressibility in 3-D flows is somewhat less dramatic than with 2-D flows, but many of the same effects become important. Many of the same techniques for predicting linear compressibility effects work in 3-D too. For example we can transform the 3-D Prandtl-Glauert equation into the 3-D Laplace equation for incompressible flow by changing variables Just as in 2-D
*The compressibilty correction rule for thin wing The effect of compressibility in 3-D flows is somewhat less dramatic than with 2-D flows, but many of the same effects become important.Many of the same techniques for predicting linear compressibility effects work in 3-D too. For example, we can transform the 3-D Prandtl-Glauert equation into the 3-D Laplace equation for incompressible flow by changing variables just as in 2-D
a9 a. ao +~,2 0 2 Defining the geometry of a finite wing: y=f(x, z) So the boundary condition is: dB
0 ˆ ˆ ˆ 2 2 2 2 2 2 2 = + + x y z Defining the geometry of a finite wing: y=f(x,z) So the boundary condition is: x y V y = ˆ
Transform the(x,y,z)and 9 in the following way 人.x 1 =1 B203b,203b,0203b 0 2 O22A7 2元:a42
0 2 2 ˆ 2 2 2 ˆ 2 2 2 ˆ 2 2 = + + x y z Transform the (x,y,z) and in the following way: ˆ ˆ = ˆ = = = z y x z y x
Bn 2 If +0+00=0 Derive the boundary ao a, ao condition on 012,05 ox Ox n ,as If O an 2 Then 05
If ˆ 2 ˆ 2 ˆ 2 2 x y z = = 0 2 2 2 2 2 2 = + + = = y x y x y V y ˆ Derive the boundary ˆ condition: x y V y = ˆ = V y x 2 ˆ 1 2 ˆ = y x If Then = V
B222 57 77 βyz 0=B2 0=B
ˆ 2 ˆ 2 ˆ 2 2 x y z = = 1 2 ˆ = y x 2 ˆ = = = = z y x ˆ 1 = = = = z y x