# 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 power-augmented 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= ac2-b2y 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

 D Oj А О В C (8.99) /0—1 b + c°t/n v° = (&+Ї Г^с) ‘

 (8.105)  Note that in this problem the channel flow velocity near the flap is cal­culated as one of the results of the solution. In a two-dimensional 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)