95 



2,5x10^ 3.5x10^ 



BODY REYNOLDS NUMBER- UD/i/ 



45x10^ 



FIGURE 20. The length of the separated region as a 

 function of freestream turbulence level for the 

 hemisphere body. 



IxlO* 2x10* 3x10* 



BODY REYNOLDS NUMBER-UD/i/ 



4x10^ 



FIGURE 21. The location of transition on the Schiebe 

 body as a function of turbulence level. 



(1972) have summarized the available experimental 

 data and semi-empirical correlations at that time 

 for the combined effects of pressure gradient and 

 freestream turbulence level upon transition. How- 

 ever, this correlation does not predict an insensi- 

 tivity to increasing turbulence levels . No doubt 

 this discrepancy is related to the question of how 

 the freestream disturbances are assumed to inter- 

 act with the boundary layer. For example, van 

 Driest and Blumer (1963) accounted for the effect 

 of freestream turbulence by using Taylor's assump- 

 tion that the unsteady perturbation induced in- 

 stantaneous variations in the velocity gradient. 

 But, as just noted, this type of correlation did 

 not work. Later, Spangler and Wells (1968) demon- 

 strated that not only the intensity, but also the 

 energy spectrum and the nature of the disturbance 

 must be taken into consideration. Reshotko (1976) 

 and Mack (1977) have re-emphasized Spangler and 

 Wells' conclusions and pointed out the lack of un- 

 derstanding of the interaction mechanism between the 

 freestream disturbance and the boundary layer* is 

 one of the major obstacles in the consistent predic- 

 tion of transition. Thus, although the effect of 

 freestream turbulence on these bodies cannot be pre- 

 dicted with confidence, we at least may offer some 

 speculation based on these ideas to explain the be- 

 havior on the hemisphere nose body. 



It is readily possible using the approximate 

 method of transition prediction suggested by Jaffe 

 et al. (1970) in conjunction with the stability 

 charts for the Falkner-Skan profiles computed by 

 Wazzan et al. (1968b) to determine the critical 

 frequency, or most unstable frequency for growth, 

 for each body at a number of velocities. These 

 estimates are presented in Table 2. We then esti- 

 mate with the aid of measured energy spectra of 

 grid generated turbulence, Tsuji (1956) that there 

 is approximately sixty times as much energy avail- 

 able in the freestream at the critical frequency of 

 the NSRDC body than there is at the critical fre- 

 quency of the hemisphere nose body. Furthermore, 

 the distance from the position of neutral stability 

 to the position of separation is only 0.07 diameters 

 on the hemisphere nose model whereas on the NSRDC 



body it is 0.40 diameters. Thus on the NSRDC body 

 not only is there considerable more energy available 

 at the critical frequency, but there is also more 

 opportunity for disturbances to grow than for the 

 hemisphere nose body. This same trend is also found 

 for the Schiebe body at the low turbulence levels. 

 The critical frequencies are even less than those 

 of the NSRDC model (Table 2). There is, therefore, 

 more energy available at those frequencies than even 

 on the NSRDC model. Finally, the distance from the 

 position of neutral stability to transition is be- 

 tween 0.40 to 0.60 diameters — much the same as for 

 the NSRDC model. 



We find it somewhat reasonable then, in retro- 

 spect, for the hemisphere body to be found insensi- 

 tive, in the present experiments, to the freestream 

 disturbances. Regrettably, the present visual 

 observations are not sufficiently quantitative to 

 shed light on this basic problem of boundary layer 

 receptivity to external disturbances and their sub- 

 sequent growth into turbulence. 



By using an oil film technique, Brockett (1972) 

 found the NSRDC model to have a critical velocity 

 of 2.8 meters per second at 20°C and Peterson (1972) 

 reports 4.2 meters per second at 10 °C in the NSRDC 

 12-inch water tunnel. The seime body in the HSWT 

 was found to have a critical velocity of about 9.2 

 meters per second and it was observed to be above 

 7.6 meters per second in the LTWT at 0.05 percent 

 turbulence level. To reduce the value of the criti- 

 cal velocity to 4 meters per second in the LTWT re- 

 quired a 316 percent turbulence level, which is as 

 can be seen from Table 1 a very high value for a 

 water tunnel test section. (Initially it was thought 

 unlikely that the disturbance level in the NSRDC 

 facility is this high. However, after inspecting a 

 drawing of the facility [Figure 2.3 pg. 26, Knapp 

 et al. (1970)] such a high level does not seem so 

 unlikely.) However, in this as well as in most 

 water tunnel facilities the energy spectrum is not 

 known, forestalling therefore a direct comparison 

 of transition phenomena. 



The present observations of transition on the 

 Schiebe body at the lowest turbulence level are 

 compared with calculations of Wazzan* and experi- 



-*This is the concept of boundary layer receptivity devel- 

 oped by M. V. Morkovin [see the review of Reshotko (1976) \ 



*Private conmiunication. 



