A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



Laufer and Marte [92] made measurements on a 5° included angle 

 cone in the JPL 20-inch wind tunnel, first with damping screens in the 

 settling chamber of the tunnel, and then with a turbulence grid. The 

 turbulence levels u' /U in the settling chamber were 0.6 per cent and 

 6 per cent, respectively, with little change with Mach number and tunnel 

 pressure. Unfortunately techniques for turbulence measurements in the 

 test section at supersonic speeds are not well developed. Tests were run 

 at Mach numbers of 1.79, 2.55, and 4.50. At ilf = 1.79, increasing the 

 turbulence tenfold reduced the transition Reynolds number from 4.3 

 million to 3.3 million; at 2.55 there was no effect of turbulence, the 

 transition Reynolds number being about 3.0 million. Similarly there was 

 no effect at 4.50, the transition Reynolds number being about 2.7 million. 

 Other measurements were made in the JPL 12-inch wind tunnel at 

 M = 2.6 with similar results. 



Measurements of transition on a 10° included angle cone have been 

 made in numerous NACA wind tunnels [95,96,97]. The values vary from 

 400,000 to 8 million with no clear pattern of variation with Mach number 

 or Reynolds number per foot. Turbulence measurements were not avail- 

 able. The design of the 1 X 1-foot variable Reynolds number wind tunnel 

 at the NACA Lewis Laboratory has been twice modified to reduce its 

 turbulence level, raising the maximum value of Re^, for the 10° cone from 

 700,000 to 1.3 million and then to about 4 million. Apparently the lowest 

 turbulence wind tunnel in which tests have been made on cones is the 

 NACA 4-foot supersonic pressure tunnel [97]. Measurements on a 10° 

 cone at Mach numbers of 1.41, 1.61, and 2.01 and over a Reynolds num- 

 ber range from 0.8 to 9.5 million per foot give values of Re^ increasing 

 from 7 to 8 million as the Reynolds number per foot increases from 4 to 9 

 million with no effect of Mach number. The schlieren technique was used. 



Lange, Gieseler, and Lee [98] report values of Re^ for a 5° cone in the 

 NOL aeroballistics wind tunnel No. 2 decreasing from 3.4 million at a 

 Mach number of 1.9 to one million at ilf = 4.2. 



The effect of Mach number variation alone is indeterminate from the 

 data available. According to stability theory [IV, F] as developed by Lees 

 and Lin [99,100] the critical Reynolds number for instability of the lami- 

 nar layer decreases slowly with increasing Mach number for a body with- 

 out heat transfer. The experimental picture is complicated by possible 

 variation of the turbulence level with Mach number, tunnel pressure, 

 compressor staging, etc. The measurements giving the highest values of 

 Re^, show no appreciable effect for Mach numbers from 1.4 to 2.0, but 

 this is a relatively small range of Mach number and the scatter of the 

 measurements is large. The general trend over a wider range of Mach 

 number [92,101] in wind tunnels for which the observed values are some- 

 what lower is a decrease with Mach number to a minimum value near 

 M = 3.7, followed by an increase with Mach number. Typically from a 



< 56) 



