The Model of Flow Past a Leading Edge with a Winglet

Following we consider a separate small wing (winglet) in front of the leading edge. This winglet may be used to control the efficiency of power-augmented mode. In a corresponding local flow, this device is approximately represented by a point vortex of a given circulation Г. The flow pattern and auxiliary plane C are presented in Fig. 8.9.

The images of the vortex and the stagnation point, appearing in the flow domain due to it, have (in the auxiliary plane) coordinates Co = 9 +1/ and Ci = d + ic. In the physical plane z, the vortex of circulation (—Г) is located at a point Zg = Xq + iYg – The method of singular points gives the following results. The complex conjugate velocity in physical plane can be obtained in the form

du; _ c-i C + a (C — Co)(C — Co) (C + CiXC + Ci) d z C + lC-a (C + Co)(C + Co) (C-CiKC-Ci)’

where C designates the conjugate complex coordinates. The complex potential and its derivatives in the C plane are represented by the following expressions:

Fig. 8.9. The flow region past a leading edge with a forward winglet: physical and auxiliary planes.


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