78 



In this equation, U (x) is the external flow velocity 

 and Re is the Reynolds niomber based upon free stream 

 velocity U^ and boundary layer thickness 5 . This 

 is known as the "modified Orr-Sommerfeld equation," 

 the variable viscosity terms. 



Wazzan et al. have solved Eq. (2) numerically 

 for the boundary layer over a heated flat plate, 

 using velocity profiles generated by the method of 

 Kaups and Smith (1967). The solutions determine 

 the critical Reynolds number, which is the lowest 

 Reynolds number at which any disturbance has a 

 positive amplification rate. The last step of the 

 calculation is to relate the critical Reynolds 

 number to the transition Reynolds number, using the 

 "e to the ninth" criterion of A. M. O. Smith (1957). 

 According to this empirical criterion, transition 

 occurs when the most unstable disturbance has grown 

 to e^ (which is 8,103) times its original amplitude. 

 The linear theory is used in calculating the growth 

 of the disturbance to this amplitude. 



Strasizar, Prahl, and Reshotko (1975) have 

 measured growth rates of disturbances generated by 

 a vibrating ribbon in a heated boundary layer. They 

 found neutral stability curves and were able to 

 determine critical Reynolds numbers for wall over- 

 heats of up to 5°F (2.8°C). They found that in this 

 range of overheats the critical Reynolds numbers 

 are in reasonable agreement with the theoretical 

 predictions. These experiments were performed at 

 moderate Reynolds numbers and did not yield data on 

 transition or on stability at higher overheats. 



The results of the Wazzan et al. calculations 

 predict that the transition Reynolds number of a 

 zero pressure gradient boundary layer should increase 

 with wall temperature up to about 70°F (39°C) of 

 overheat if the free stream temperature is 60 °F 

 {16°C) . At that overheat, the transition Reynolds 

 number should be in excess of 2 x 10 (based upon 

 distance from the leading edge) . Thus the experi- 

 ment designed to investigate these predictions must 

 be able to generate a very high Reynolds number 

 boundary layer while maintaining low free stream 

 disturbance levels. The wall should be very smooth 

 and its temperature must be precisely controlled. 

 These are the chief considerations that led to the 

 experimental geometry described below. 



2. EXPERIMENTAL APPARATUS 

 Configuration 



A facility in which water is recirculated through 

 the test section was not used for two reasons. (1) 

 Heat is continuously added to the test section so 

 that a recirculating experiment would require some 

 sort of heat exchanger. (2) The free stream tur- 

 bulence level in the test section must be less than 

 0.05 percent, which has previously been difficult 

 to achieve in a recirculating water facility. The 

 experiment must then be of the "blow-down" type, 

 in which water is removed from one reservoir and 

 discharged into another. Run times of more than 

 twenty minutes are desired, which requires large 

 reservoirs. This led to the selection of the Colo- 

 rado State University Engineering Research Center 

 as the site of the experiment. Here the water 

 supply is Horsetooth Reservoir, which provides 

 water to the laboratory through a 0.6 m diameter 

 pipe at a total pressure of 6.8 x 10^ N/m^ (100 lb/ 

 in.^). The discharge runs into a smaller lake be- 



FLOW TUBE 



24 IN. DIA 



DISCHARGE 



LINE 



BALL VALVE 



VIBRATION 

 ISOLATION 

 SECTION 



FIGURE 1. Experimental geometry. 



low the laboratory. At the maximum flow rate of 

 this experiment (200 liters/sec) , the run time is 

 effectively unlimited. 



The flow tube apparatus consits of a settling 

 chamber for turbulence management, a contraction 

 section, a test section and various types of instru- 

 mentation described below. A diagram of the experi- 

 mental geometry is shown in Figure 1. 



Settling Chamber 



The inside diameter of the settling chamber is 0.6 

 m, the same as that of the supply line from the 

 reservoir. The test section is 0.102 m in diameter, 

 so that the contraction ratio is 35:1. The settling 

 chamber is made up of four separable sections, as 

 shown in Figure 2. The sections are made of fiber- 

 glass to avoid heat transfer through the walls, and 

 their total length is 3.35 m. Each end of each 

 section is counter-bored to hold a . 15 m long 

 aluminum cylinder with a 1.3 cm wall thickness. 

 Each cylinder will hold one or more turbulence 

 manipulators, including screens, porous foam, or 

 honeycomb material. This design allows the settling 

 chamber to be assembled in different configurations, 

 so that it can be optimized experimentally. 



The details of the design and optimization of 

 the turbulence management system have been reported 

 separately [Barker (1978) ] . The configuration 

 shown in Fibure 2 was arrived at after a great 

 deal of testing. There is a considerable body 

 of literature on the subject of turbulence 

 management, and this provided some guidelines 

 for the optimization of the present system. 

 The most detailed recent study is that of Loehrke 

 and Nagib (1972) , who measured mean velocity and 

 turbulence level downstream of various turbulence 

 manipulators . Further recommendations for the 

 construction of a turbulence management system 

 have been given by Corrsin (1963) , Bradshaw (1965) , 

 and Lumley and McMahon (1967) . 



At the downstream end of the settling chamber is 

 an additional 0.30 m long section containing porous 

 wall boundary layer suction. Hot film anemometer 

 surveys in the settling chamber have shown that 

 at test section velocities above 9 m/sec (0.26 m/sec 

 in the settling chamber) the boundary layer becomes 

 turbulent before the flow enters the contraction. 

 A thin turbulent boundary layer entering the strong 

 favorable pressure gradient of the contraction 



