By Antony Kay
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Additional resources for German Jet Engine and Gas Turbine Development, 1930-45
Stability calculations show that on a flat plate this occurs at Re ~ lOll. The complicated series of events between the point where instability first sets in until transition occurs has only recently been clarified (see Klebanoff, Tidstrom, and Sargent, 1962). Transition is strongly influenced by the pressure gradient in the flow; a negative ("favorable") pressure gradient tends to delay it and a positive ("adverse") one tends to make it occur sooner. As a practical rule of thumb one can state that the laminar boundary layer can only be maintained up to the point of minimum pressure on the airfoil.
The practical significance of the mapping theorem is that it can be used to transform one irrotational, constant-density flow 'W 1 (r) with elementary + 1. The Joukowsky-Kutta Transformation Z = l2 r+I' (2-131) Here I is a positive real constant, and the so-called singular points of the transformation where the dZ/dr = 0 are located at r = ±l, corresponding to Z = ±2l. When applied to suitably located circles in the t-plane, (2-131) is well known to produce ellipses, flat plates, circular arc profiles of zero thickness, symmetrical and cambered profiles with their maximum thickness far forward and with approximately circular-arc camber lines.
Both laminar and turbulent boundary layers will separate if they have to go through extensive regions of adverse pressure gradients. Separation will always occur for a subsonic flow at sharp corners, because there the pressure gradient would become infinite in the absence of, a boundary layer. Typical"examples of unseparated and separated flows are shown in Fig. 4-1. In th& separated flow there will always be a turbulent wake . Unseparated Row Separated Row (a) (b) FIG. 4-1. Examples of high Reynolds number flows.
German Jet Engine and Gas Turbine Development, 1930-45 by Antony Kay