37 



l.Or 



m/sec (ft/sec) « (ft) 



15.2 (50) 15.2 (50) 

 15.2 (50) 3.05 (10) 



21.1 (SO) 15.2 (50) 

 2^.^ (80) 3.05 (10) 



.1 .2 .3 A 



Power Punt Thermal Efficiency, n^^^ 



FIGURE 4. Effect of thermal efficiency of propulsive 

 power plant on drag reduction. 



of surface roughness on transition are possibly 

 more pronounced for heated surfaces than for un- 

 heated. These factors are presently being studied 

 both experimentally and analytically by a number 

 of investigators for the purpose of obtaining an 

 objective evaluation of the practical capabilities 

 of this relatively simple and readily available 

 means of drag reduction. The related experimental 

 investigations done at CWRU will be described in 

 the next two sections . 



4. STABILITY EXPERIMENTS IN WATER 



The first experimental study of flat plate boundary- 

 layer stability in air was by Schubauer and Skram- 

 stad (1948) who used hot wire anemometry to measure 

 the growth characteristics of sinusoidal velocity 

 disturbances introduced into the boundary layer by 

 a vibrating ribbon. Ross et al.(1970) repeated the 

 Schubauer and Skramstad experiment to obtain data 

 for comparison with improved numerical solutions 

 of the Orr-Sommerfeld equation. Similar stability 

 experiments have been performed in water by Wortmann 

 (1955) and Nice (1973) . The results of these ex- 

 periments are in agreement with the numerical solu- 

 tions of the Orr-Sommerfeld equation except near 

 the minimum critical Reynolds number, where the de- 

 parture from parallel-flow theory seemingly results 

 from the breakdown of the parallel flow assumption. 

 Among the attempts to correct the parallel-flow 

 formulation, those of Bouthier (1972, 1973) and 

 Saric and Nayfeh (1975, 1977) using the method of 

 multiple scales yield numerical results which dis- 

 play the best agreement with experimental results . 

 A natural extension of the above work is in the 

 investigation of factors which can increase bound- 

 ary layer stability. As indicated earlier, one of 

 these factors is wall heating in water. The ob- 

 jective of the experimental work done at CWRU was 

 to see if the predicted increase in stability due 

 to heating is in fact realized. To this end the 

 stability of flat plate boundary layer was investi- 

 gated on both a heated and unheated plate. For 

 the heated plate, the case of uniform wall temper- 



ature may be more interesting from an engineering 

 viewpoint. For example, since the portion of the 

 plate upstream of the minimum critical point of 

 the unheated plate is stable without heating, why 

 not begin heating at the minimum critical point 

 and use more advantageously, the power that would 

 have gone to heating the leading edge region? 



To systematize the approach to the problem, two 

 types of nonuniform wall temperature distributions 

 were studied: step changes in wall temperature 

 of magnitude AT occuring at a location Xg,- and 

 power law wall temperature distributions of the 

 form T^{x)-T„ = Ax^ for n both positive and nega- 

 tive . The temperature Tco is that of the external 

 stream. In order to isolate the effect of the 

 parameters, n and X3, on the boundary layer sta- 

 bility, one of two quantities must be held fixed - 

 either the total heating power put into the plate, 

 '^total ' °^ ^^^ local wall temperature difference 

 at some reference location T^{:x.^^f) -T^. Since 

 heat losses from the test plate used in this ex- 

 periment could not be accurately measured, the 

 total heating power put into the plate could not 

 be related to the total convective heat transfer 

 to the boundary layer. Therefore the wall tem- 

 perature difference at Xj-gf, T^^{Xj-gf ) -Too, was held 



constant as n and x were varied, with x 



ref 



chosen 



in the region in which stability measurements were 

 performed. 



Experiment 



The experiment was performed in a low turbulence 

 water tunnel which has a test section 15.5 in. long, 

 9 in. wide, and 6 in. high. The free stream tur- 

 bulence intensity in the test section is 0.1 - 0.2% 

 for free stream velocities Ug _< 11 ft/sec. 



The flat aluminum test plate, which is 13.6 in. 

 long, 9 in. wide, and 0.625 in. thick is suspended 

 from a frame which fits the top of the test section 

 as shown in Figure 5 . The origin of the coordinate 

 system is located at the leading edge. The x- 

 coordinate is the running length measured in the 

 streamwise direction, y is measured normal to the 

 surface, and z is the spanwise coordinate measured 

 from the plate centerline. The rounded leading edge 

 (1/32 inch radius) is located 0.425 in. below the 

 top of the test section, thus forming a slot which 

 spans the top of the test section. The turbulent 

 wall boundary layer of the water tunnel is removed 

 by suction through this slot. Suction is adjusted 

 so as to locate the flow stagnation point at a 

 stable position just downstream of the leading edge 

 on the test side of the plate. A laminar boundary 

 layer then develops along the plate starting from 

 the stagnation point location. 



Plate heating is provided by eleven electric 

 heating elements positioned as shown in Figure 5. 

 Plate surface temperature is monitored by eleven 

 thermistors imbedded in the surface of the plate 

 along the centerline. However, because of the 

 large temperature gradients which occur in the 

 plate, the thermistors do not yield an accurate 

 indication of the plate surface temperature. The 

 surface temperature is determined from boundary 

 layer temperature profiles measured with a hot- 

 film anemometer operating as a resistance thermom- 

 eter. 



The pressure distribution on the plate surface 

 in both the spanwise and streamwise direction is 



