439 



The amplification factor, o_, is defined as 



0,2 04 06 08 1 2 3 4 



Reynolds Nuniber xlO" 



FIGURE 12. Length to height ratio of separation bubble, 

 L/H, as a function of Reynolds number for hemispherical 

 nose. 



appearances of the separation bubbles near transition, 

 as illustrated in Figure 8. The length to height 

 ratio of the separation bubbles (Figure 12) is not 

 very dependent on the Reynolds number. For the SST 

 hemispherical nose an average value of 10.8 is found. 

 To compare experimental values of L with theoret- 

 ical ones, it is necessary to calculate the location 

 of transition on the separated shear layer. Recently, 

 Van Ingen (1975) presented a calculation method for 

 the laminar part of separation bubbles in which 

 also the location of transition is predicted. The 

 method is based on a solution of the Navier-Stokes 

 equations, valid near the separation point. A 

 relation is found for the separation streamline 

 leaving the wall at an angle, 6. By using constant 

 values of B, a^, and m^gp, to be obtained experi- 

 mentally, a formula is derived to calculate the 

 length of the separation bubble. It is assumed 

 that the separation streamline is straight and 

 that the angle 5 is given by 



tan 6 



B 



Re, 



(3) 



Sep 



where Reg^gp is the Reynolds number based on the 

 momentum thickness at separation, given by 



Re„ 



Sep 



= c 



(4) 



sep 



TABLE 1. Separation Streamline Angle 6 For SST 

 Hemispherical Nose, Derived from Holograms. 



Re 



10 



-5 



Rer 



sep 



Jn 



neutral 



(5) 



where a/^neutral ■'■^ ^^^ ratio of the amplitude of 

 a disturbance to its amplitude at neutral stability, 

 m^g is the value of m at separation (m^gp = 0.09). 

 According to Dobbinga et al. (1972) , b is usually 

 between 15 and 20, but lower values are also found. 

 To obtain B for the present case, the separation 

 streamline angle, 6, was derived from a series of 

 holograms. The results are presented in Table 1. 

 The average value of B is 12.0. 



With Van Ingen ' s method, the location of transi- 

 tion has been calculated for Og = 7 and a^ = 8, 

 using m^gp = 0.09 and B = 12. The results are 

 plotted in Figure 10. It is found that most experi- 

 mental data points lie between the two theoretical 

 curves. The best fit would be obtained for a^ = 7.5. 

 It should be noted that the present experimental 

 data refer to the beginning of transition. In a 

 recent paper. Van Ingen (1976) attempted to corre- 

 late the amplification factor with the turbulence 

 level, Tu. For a^ = 7.5, predicting the beginning 

 of transition, we find Tu = 0.15^. Although the 

 turbulence level in the high speed tunnel has not 

 been measured, it is possible to obtain an approx- 

 imate value (without considering noise aspects). 

 Arakeri (1975a) measured the location of transition 

 on a 1.5 caliber ogive in the axisymmetric test 

 section of the CIT high speed water tunnel. The 

 turbulence level in this tunnel was 0.2^. Recently, 

 Arakeri (1977) performed similar measurements in 

 the NSMB high speed water tunnel. The agreement 

 between the transition data indicates that the 

 turbulence level in both tunnels was approximately 

 the same. Hence, the turbulence level in the NSMB 

 tunnel may have been close to 0.2%, which is con- 

 sistent with the value derived earlier. The above 

 considerations on the turbulence level are, however, 

 not confirTned by the measurements of Gates (1977) , 

 who found that the turbulence level had no effect 

 whatsoever on the location of transition on a 

 hemispherical nose . 



As shown in Figures 9 through 12, the appearance 

 of the laminar separation biibble on the Teflon 

 hemispherical nose is the same as for the SST 

 hemispherical nose. From Figure 10 it is found 

 that the higher surface roughness of the Teflon 

 body has no effect on transition. Apparently, the 

 amplification of disturbances mainly occurs down- 

 stream of separation. 



The blunt nose exhibited a laminar boundary layer 

 with normal transition to turbulence. Laminar flow 

 separation did not occur. A photograph showing 

 transition is presented in Figure 13. A plot of 

 the transition data is given in Figure 14. Since 

 the outflow of the sodiirai chloride solution from 

 the nose of the model was in some cases quite 

 unstable, the determination of the precise location 

 of transition provided some difficulties, but an 

 upper or lower bound could still be indicated. In 

 Figure 14 these data points are marked with an 

 arrow. When the arrow is pointing upward the data 

 point is considered to be the lower bound; when the 

 arrow is pointing downward the data point is con- 

 sidered to be the upper bound. Silberman et al. 

 (1973) made laminar boundary layer calculations for 

 a series of blunt noses having Cpj^^j^^^ values ranging 



