2 Aerodynamics
101
Fig. 2.32 Pressure coefficient and aerodynamic force along a chord line
airfoil is
C L =
1
0
(C pd − C pu )dξ =
1
0
C pd dx +
1
0
(−C pu )dξ
L = ρV ∞ u + ρV ∞ d =
1
2
ρV
2
∞ bC L
d =
1
2
V ∞ b
1
0
C pd dξ, , u =
1
2
V ∞ b
1
0
(−C pu )dξ ,
where C pu and C pd are the pressure coefficients acting on the airfoil
surface, respectively. ξ is x /b.
Obviously, at any position away from the leading edge, the value of γ
(x) depends on the difference of vorticity integral value in the local upper
and lower wing boundary layer. According to the velocity distribution
characteristics in the upper and lower wing boundary layer, the distribution of γ (x) along the chord line should be the change curve that gradually
reduces from the leading edge to the rear edge, as shown in Fig. 2.33.
It can be seen that the attached vorticity based on the concept of ideal
fluid flow actually refers to the difference of vorticity integral value in the
viscous boundary layer near the wall of the upper and lower wing surfaces
in the steady flow around the airfoil. If the ideal fluid flow model is used
instead of the boundary layer flow, it should be considered as the shape
of the ideal fluid flow around the boundary curve of the airfoil surface