By R. A. Wallis
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Additional resources for Axial Flow Fans. Design and Practice
50) ; when substitution is made in eq. 55) 2ik, Substituting in eq. 53), the relation between roughness height and the Reynolds number above which the surface is fully rough is given by \ ~ 8 5 ( ^ - 1 ( 3 . 56) 50 BOUNDARY LAYER A N D SKIN FRICTION RELATIONS Eqs. 56) are graphically presented in Fig. 7 ; the various régimes are indicated. Using the foregoing data, the skin friction coefficient, γ, has been presented as a function of Reynolds number and equivalent roughness height in Fig. 8. The transitional curves are completely arbitrary, especially at the lower Reynolds numbers where they may join either the laminar or turbulent skin friction curves for smooth surfaces.
Owing to the presence of adverse pressure gradients and other variables the effect of roughness on drag can best be determined by experiment on the actual aerofoil or a model of it. By combining eqs. 60) u as the roughness limit for aerodynamic smoothness. On fan blades, an increase in drag causes a decrease in efficiency and a possible early onset of the stall; the latter restricts the maximum lift which the blade can supply. If the blades were very rough, as the result of rough casting or the presence of mud, the fan characteristic might be affected owing to a reduced deflection of the stream.
This subject is a very complex one and hence only the salient features will be outlined here. Large disturbances in the flow constitute one of the main causes of transition. I t is believed that the instantaneous velocity at a point near the surface approaches zero when the component due to the disturbance has a large enough negative value. In other words transition is believed to be related to intermittent separation. Industrial installations contain many disturbance sources and hence information on this aspect is very appropriate.