41 



420i 



60 





 0*400 600 800 1000 1200 



DISTANCE DOWN THE PLATE, Rj.=s/X 

 a) Theory 



lA- 



0' 400 600 800 1000 1200 



DISTANCE DOWN THE PLATE. Rj . = \/ X 



b) Experiment 



FIGURE 10. Neutral stability characteristics 

 for uniform wall temperature. T„ = 75°F. 



Skramstad (1948) , and Wortmann (1955) . and provide 

 further verification of the departure from parallel- 

 flow solutions in the region Rfj^* 500. The agree- 

 ment obtained allows one to proceed to the case of 

 the heated plate with some credibility. 



Experimentally determined neutral curves in the 

 (Uj-, Rg*) plane for nominal uniform wall tempera- 

 ture differences of T^^-T(„ = 0,5,8°F are compared 

 to the parallel flow results of Lowell (1974) in 

 Figure 10. The experimental results are curves 

 faired through the measured neutral points, which 

 have not been shown for the sake of clarity. Com- 

 parison between the calculated parallel-flow re- 

 sults and experiment indicates that the departures 

 between the two found near (Rg*) n^i^ crit ^°^ ^^^ 

 unheated case persist in the heated cases. It is 

 readily seen that with increases in T^-T„, 



(Rj;*) . „ .. increases and also the range of 



' 'mm.crit . . ,.^. ^. 



frequencies receiving amplification decreases. 



Note that while the theoretical neutral curves 

 according to Lowell's parallel flow calculation 

 nest within each other, this does not happen ex- 

 perimentally until Rg* exceeds 860. 



Predicted and measured values of (R(5*)min crit 

 are compared in Figure 11. The measured rate of 

 increase in (R6*)min crit compares favorably with 

 that predicted by Lowell (1974) and by Wazzan et al. 

 (1970) . Over the range of values of T^,-T„, covered 

 by the present work it is conjectured that the 



uj 1000-- 



CO 



o 



O 



z 



< 



U I 



800- 



600 



400 



ii 



1 ~^ 2 4 6 



I i' WALL TEMPERATURE DIFFERENCE, T^-T„ (°F) 



non-parallel flow nature of the boundary layer 

 serves to reduce the value of (R5*)min.crit t>y 

 cibout 120 units from that predicted for parallel 

 flow. This reduction seems independent of the 

 level of wall heating. A more complete description 

 of these results ig given in Strazisar, Reshotko, 

 and Prahl (1977) . 



Non-Uniform Wall Temperature Distributions 



As indicated earlier, the two types of non-uniform 

 wall temperature distributions studied are a) the 

 power-law type in which (T„-T„) = Ax" and b) step 

 changes in wall temperature of magnitude AT = T^- 

 T„ occuring at location Xg . In the discussions 

 that follow, n is the exponent of the power-law 

 wall temperature distribution and s = Xg/Xj-^f is 

 the fraction of the distance to the measuring 

 station (x^gf = 5.5 inches) at which the step 

 change in wall temperature is located. 



The Mean Flow - Mean velocity profiles for 

 varying values of n, s and T„(Xref)-Tco are compared 

 to the Blasius profile in Figure 12. The discrep- 



X - 5.5 inches 

 Ug = 4.65 ft/sec 

 T„ = 75 ° F 



FIGURE 11. Effect of heating on minimum critical 

 Reynolds number. 



FIGURE 12. Mean velocity profiles for varying wall 

 temperature distributions . 



