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

Подпись: (8.97)d w /( — 1 £ + св*/п

d2 = VC+T

The derivative of the complex velocity potential with respect to the aux­iliary variable ( is obtained as

Подпись: (8.98)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:

Подпись:(8.106a)

(8.1066)

(8.106c)

/1 +t t — cefl* V1 — t t + c)

Подпись: t2 — a2 t(b2 - t2)
Подпись: (8.107)

where

Knowing a, 6, and c, we can determine the remaining unknowns using the formulas

+-

Ь2^’

(8.108)

2-

(8.109)

. 2 v

(‘-fK

(8.110)

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