Unseparated Flow Near a Trailing Edge with a Flap
We start by considering a flow of finite width past a trailing edge with a flap. This scheme corresponds to the second poweraugmented flow model, discussed at the beginning of this section. The flow picture and the auxiliary plane C are shown in Fig. 8.10, where X = —x/h, Y = y/h — 1, bf = bf/h, bf sin Of < 1. In the latter relationship the equality sign corresponds to the case, when the flap touches the ground.
Application of the method of singular points gives the results, presented below. The complex conjugate velocity in the ( plane can be derived in the form
d w /( — 1 £ + св*/п
d2 = VC+T
The derivative of the complex velocity potential with respect to the auxiliary variable ( is obtained as
d w (2 — a2
dc= ac2b2y
0 c a 1 b £ b. Fig. 8.10. The flow region past a flap of the wing in the extreme ground effect: physical and auxiliary planes. The resulting mapping function is /£fl £ — ce*/* £2 — a2 
t t + c) In addition, for £ = 6, v** = dw/dZ, or 6—1 b + cef/n 










Note that in this problem the channel flow velocity near the flap is calculated as one of the results of the solution. In a twodimensional problem the magnitude of <5) is assumed to be known because the flow rate and the velocity on the jet boundary are the same as those in front of the wing. Then from conditions (8.101)(8.104), we can obtain the following system of three equations for the determination of constants a, 6, and c:
(8.106a)
(8.1066)
(8.106c)
/1 +t t — cefl* V1 — t t + c) 
where
Knowing a, 6, and c, we can determine the remaining unknowns using the formulas
+ Ь2^’ 
(8.108) 
2 

7Г 
(8.109) 
. 2 v 

(‘fK 
(8.110) 
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