EXISTING METHODS FOR CALCULATING TURBULENT BOUNDARY LAYERS 

 IN A PRESSURE GRADIENT 



Interest in effects of pressure gradient on turbulent boundary lay- 

 ers has centered largely on adverse (positive) pressure gradients causing sep- 

 aration of flow such as occur in diverging conduits and on the suction side 

 of airfoils at large angles of attack. (A review of the literature on this 

 subject appears in Reference 4.) Since separation of flow is characterized 

 by a reversal in the direction of flow at the surface, the velocity profile 

 of the boundary layer suffers marked changes in shape as the flow approaches 

 the point of separation, as seen in Figure 3- Hence the study of flow lead- 

 ing to separation must be directed towards the determination of the manner in 

 which the shape of the velocity profile is affected by pressure gradients, as 

 well as by other factors, such as Reynolds number. 



Since a single parameter for the shape of the velocity profile 

 greatly simplifies the mathematical analysis, considerable effort towards this 

 goal has been expended by various investigators. Gruschwitz 5 plotted u/U 

 against y/o in his experimental study of velocity profiles and, as shown in 

 Figure 3, obtained a family of velocity profiles in various pressure gradients. 

 He concluded that the value of u/U at some standard value of y/$ could be used 

 to characterize the shape of the velocity profile for any pressure gradient. 

 Following this concept Gruschwitz defined a form parameter 77 such that 



v = 1 -(-§-)' = 1 -y z [9] 



V U ly =e 



where y ={rr) ■ Since the shape parameter H, which can be written 



\U ly = 9 



"-J>-*Mf) [101 



is also a function of the shape of the velocity profile, it cannot be inde- 

 pendent of 77 if the single-parameter relationship holds. 



This is confirmed by Gruschwitz who plotted H against 77 for a series 

 of test data. As seen in Figure 4, a fairly smooth variation between 77 and H 

 results. It is to be noted that Kehl, 6 from tests covering a wider range of 

 Reynolds numbers than Gruschwitz, found that 77 is not a unique function of H 

 but that it varies slightly with Reynolds number. 



