A,25 • EFFECT OF MACH NUMBER ON TRANSITION 



value of Ret of 5 million at ilf = 1.5, Re^, falls to 2 million at Af = 3.7 

 and rises to about 3 million at ilf = 5. 



Only a few scattered measurements have been made on fiat plates at 

 supersonic speeds. An incidental measurement [102] in the NACA Ames 

 6-inch heat transfer wind tunnel at a Mach number of 2.4 gave an Re^, of 

 1.4 million. The authors interpret the data as showing values as low as 

 560,000 at the lowest tunnel pressure. In another study [103] a crude 

 analysis of skin friction data gave extrapolated values from 2.6 to 4.4 

 million. Measurements in the JPL 20-inch supersonic wind tunnel by 

 Coles [104] gave values decreasing from about 2.25 million at a Mach 

 number of 2 to about 1.1 million at M = 3.6, increasing to about 1.2 

 million at ilf = 4.5, the position of minimum shear being taken as the 

 beginning of transition. Other measurements in the same wind tunnel by 

 Laufer and Marte [92] give somewhat higher values, but the damping 

 screen configuration may have been different and the surface temperature 

 method was used. A single measurement [105] in the GALCIT 5-inch 

 hypersonic wind tunnel gave a value of at least 5 million at ilf = 5.8. 



In addition to cones and flat plates, a hollow cylinder with sharp lead- 

 ing edge gives a boundary layer with zero pressure gradient. Brinich [106] 

 made measurements on a hollow cylinder 5.31 inches outside diameter, 

 4.75 inches inside diameter, 33 inches long, with 5° beveled leading edge 

 and 0.003-inch leading edge radius in the NACA Lewis 1 X 1-foot varia- 

 ble pressure wind tunnel at a fixed Mach number of 3.12. The transition 

 Reynolds number varied with the pressure, increasing from 1.5 to 4 million 

 as the pressure increased. Brinich attributes this to the variation of the 

 Taylor turbulence parameter (Art. 11) with pressure at a constant turbu- 

 lence level. As the pressure increases, the boundary layer thickness de- 

 creases. Thus the ratio of the scale of the turbulence to the boundary 

 layer thickness increases and the turbulence has less effect in reducing 

 the transition Reynolds number. On this view there would be both a 

 Mach number and a density effect, since the thickness increases with in- 

 creasing Mach number. In a wind tunnel of constant stagnation pressure 

 increasing Mach numbers are accompanied by reduced density so that 

 both effects would combine to reduce transition Reynolds number with 

 increasing Mach number for a fixed turbulence level when turbulence 

 effects on transition predominate in determining the location of transition. 



Brinich discovered [107] a large downstream displacement of the tran- 

 sition point when the sharp leading edge was very slightly blunted. 

 Moeckel [108] gave a theory of this effect, attributing it to the formation 

 of an inviscid shear layer by the curved leading edge shock wave which 

 reduces the local Reynolds number at the outer edge of the boundary 

 layer. Bertram [109] made an analysis of the available data and sug- 

 gested that the most suitable nondimensional parameter is a Reynolds 

 number based on leading edge thickness. The transition Reynolds num- 



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