48 



Discussion 



CARL GAZLEY, Jr. 



Several of us* at Rand and UCLA have made a 

 series of computations which serve to illuminate 

 some of the experiments described by Professor 

 Reshotko. His experiments with non-uniform wall 

 temperature distribution indicate the sensitivity 

 of the boundary-layer stability to the way the 

 surface temperature changes with distance along the 

 plate. For the power-law variation, AT = Ax , 

 Reshotko 's experiments for AT < 8°F appear to 

 indicate decreased stability and increased ampli- 

 fication rates as the experiment n decreases toward 

 zero. Our computations indicate the same trend at 

 low temperature differences, but also show a 

 reversal at a temperature difference of about 20°F 

 with an increasing stability with increasing n 

 above this AT. In fact, very large increases occur 

 for a AT above 30°. 



Our results were obtained both by exact numer- 

 ical techniques based on the Orr-Sommerfeld equa- 

 tion [Wazzan and Gazley (1978)] and by a modifiac- 

 tion of the Dunn-Lin approximation [Aroesty et al. 

 (1978)]. The results for flat-plate flow in terms 

 of the minimum critical Reynolds number based on 

 displacement thickness are shown in Figures 1 and 

 2 for values of n = 1 and 2 as a function of the 

 local temperature difference. The modified Dunn- 

 Lin approximation is seen to agree remarkably well 

 with the exact computations. More extensive 

 results of that approximation are shown in Figure 3 

 for values of n ranging from zero to 2 . For temp- 

 erature differences above about 30°F, the advanta- 

 geous effects of am increasing temperature differ- 

 ence are seen to be very large. 



LOCAL iT ■ T • T . F 

 w e 



FIGURE 1. Variation of critical Reynolds Number with 

 local temperature difference. Flat plate with linear 

 increase of temperature difference. 



— MODIFIED DUNN-LIN 

 APPROXIMATION 



D EXACT COMPUTATIONS 



20 30 



LOCAL JT ■ T 



T , F 



FIGURE 2. Variation of critical Reynolds Number with 

 local temperature difference. Flat plate with tempera- 

 ture difference increasing with the square of distance. 



10 20 30 40 5(1 



LOCAL dT ■ T - T . °F 

 w e 



FIGURE 3. Variation of Critical Reynolds Number with 

 local temperature difference for several surface- 

 temperature distributions. 



REFERENCES 



Wazzan, A. R. , and C. Gazley, Jr. (1978). The Com- 

 bined Effects of Pressure Gradient and Heating on 

 the Stability and Transition of Water Boundary 

 Layers. The Rand Corporation, R-217S-ARPA. 

 Aroesty, J., et al . (1978). Simple Relations for 

 the Stability of Heated Laminar Boundary Layers in 

 Water: Modified Dunn-Lin Method. 



*J. Aroesty, C. Gazley, Jr., G. M. Harpole , 

 W. S. King, and A, R. Wazzan 



