39 



which is the measured 6 for the case shown. For 

 n > 6 the measured velocity is uniform to within 1%. 

 The unheated boundary layer thickness for this case 

 is 6 = 0.066 inches (n=6.3). Note that velocities 

 measured in the region n ^ 0.75 are consistently 

 higher than would be expected from the straight-line 

 nature of the velocity profile in this region. 

 These velocities may be subject to wall interference 

 effects due to the size of the hot-film probe rel- 

 ative to the boundary layer. At the last measured 

 point, ri=0.5, the prongs of the hot-film probe 

 touch the wall. The probe prong diameter is 0.010 

 inches (ri=0.95 in the present case), while the 

 sensing element diameter is 0.003 inches (ti=0.29). 

 The discrepancy shown in Figure 6 between measured 

 and calculated profiles for T^,-Tco = may be due to 

 the integrated effect of the upstream pressure 

 distribution on the measured profile. Note that 

 the difference between the heated and unheated 

 velocity profiles is within experimental error. 

 The heated profile is slightly fuller than the 

 unheated profile in agreement with Lowell's numer- 

 ical solutions of the variable fluid property 

 boundary layer equations . The calculated ratio of 



6* 



heated' "unheated 



for this case is 0.968 while 



the measured ratio is 0.967. 



Mean temperature profiles measured at varying 

 values of T -T_^ and R are compared to Lowell's 

 (1974) solution of the boundary layer energy equa- 

 tion in Figure 6 . Note that the thermal boundary 

 layer thickness is smaller than the velocity bound- 

 ary layer thickness by approximately the ratio 



SW& 



Pr-V3 = 0.54, where the Prandtl number of 



water is taken as 6.3 at T„ = 75°F. Further de- 

 tails concerning the mean flow field may be found 

 in Strazisar (1975) . 



The Disturbance Flow Field - While the CWRU 

 Water Tunnel has a relatively low turbulence level 

 of 0.1% to 0.2%, this is still much higher than 

 Ross et al. (1970) in air. It has nevertheless 

 been ascertained by Strazisar (1975) that the pres- 

 ent ribbon-generated disturbances do not interact 

 with disturbances of other frequencies present in 

 the tunnel turbulence and furthermore display the 

 linearity required in order that the disturbances 

 be considered "infinitesimal". 



The development of ribbon-generated disturbances 

 just downstream of the ribbon is investigated to 

 insure that the disturbances develop fully before 



reaching the station where growth rates are first 

 measured, namely x = 5 inches. Figure 7 shows 

 the results foi' a decaying disturbance with 

 "r = 138 X 10"^, R6* = 601 at x - 5.5 inches. The 

 dimensionless frequency oij- is defined uij. = (2-nf) 

 v/Ug where f is the ribbon frequency. (The exper- 

 imental lower branch neutral point at Rg* = 601 is 

 at (Dj, = 150 X 10"^.) Points in the region n < 0.75 

 are shown as broken symbols due to possible inter- 

 ference effects because of probe proximity to the 

 wall. The disturbance amplitude distribution 

 through the boundary layer attains its final shape 

 at x = 4.5 inches but the peak amplitude rises be- 

 tween X = 4.0 and x = 4.5 inches. Downstream of 

 X = 4.5 inches both the shape and peak amplitude 

 of the disturbance display expected behavior as 

 seen by comparison with the calculated eigenfunction 

 for this frequency and Reynolds number obtained 

 using Lowell's (1974) program. Since the measured 

 wavelength of this disturbance is 0.66 inches the 

 appropriate disturbance eigenfunction is seemingly 

 established in less than 1-1/2 wave lengths. 



A measured disturbance temperature amplitude 

 distribution is compared with the corresponding 

 numerical solution in Figure 7. The calculated 

 distribution is scaled by equalizing the area 

 under the measured and calculated distributions 

 in the region 0.75 < n < 3. The shape of the 

 disturbance temperature amplitude distribution is 

 also found to be virtually independent of the 

 disturbance frequency at a fixed Rg*. 



Disturbance Growth Rates - Measured disturbance 

 growth rates as a function of frequency for uni- 

 form wall temperature are shown in Figure 8 for 

 R^* = 800. The dimensionless spatial growth rate 



= 1 ^ ^* 

 i A dx R6* 



where A is the amplitude of the disturbance at the 

 particular frequency under consideration. The 

 solid lines in Figure 8 are curves faired through 

 the measured points. The curve through the cir- 

 cular symbols is for the unheated plate. It is 

 evident that with increased heating of the plate, 

 the growth rates progressively decrease and the 

 range of disturbance frequencies receiving ampli- 

 fication is diminished. Similar behavior is in- 

 dicated at other Reynolds numbers as well. 



— Lowell's solution 



T„-T„ = 0°F /J =-.0036 

 O T^-T„ = 0°F R5. = 940 

 A T,„-T_=7.8°F R,- = 909 



FIGURE 6. Mean velocity and temperature pro- 

 files for uniform wall heating. 



