38 



cesL seciLon 

 upscream Flange 



aluminum suction 

 cransitijn piece 



plexlglas place 

 BOun-ciog frame 



\ ribbon ' 



thermistors 



X (inches) 



FIGURE 5. Test plate installation. 



monitored using static pressure taps in conjunction 

 with a manometer board. Artificial velocity dis- 

 turbances are introduced into the boundary layer 

 with a phosphorbronze ribbon 0.001 in. thick and 

 0.125 in. wide which is stretched across the plate 

 surface 3.75 inches behind the leading edge. Ribbon 

 vibration is achieved by passing a sinusoidal cur- 

 rent through the ribbon in the z-direction in the 

 presence of a magnetic field maintained by horseshoe 

 magnets located on top of the plate. 



A traversing mechanism located in the water 

 tunnel dif fuser downstream of the test section is 

 used to position hot-film anemometer probes in the 

 X and y direction for boundary layer profile 

 measurements. The z-position of the probes is 

 fixed at the plate centerline. 



Temperature measurements in the thermal boundary 

 layer are made with a DISA 55D01 anemometer and a 

 55F19 hot-film boundary layer probe operated in the 

 constant current mode as a resistance thermometer. 

 This unit is calibrated against the free stream 

 temperature measured by the3rmistors extending in- 

 to the free stream through the side walls of the 

 test section. Boundary layer velocity measurements 

 are made with a DISA hot-film system consisting of 

 two 55F19 probes , a llMOl constant temperature 

 anemometer equipped with a 55M14 temperature com- 

 pensated bridge, a linearizer, r.m.s. voltmeter, 

 and d.c. voltmeter. The system is calibrated 

 against the velocity measured by a pitot-static 

 tube located in the center of the test section. A 

 General Radio 1900-A wave analyzer is used to 

 measure the r.m.s. amplitude of the anemometer 

 signal resulting from ribbon-generated disturbances 

 in the boundary layer. 



The mean velocity profile is measured at x = 5.5 

 inches, which is the center of the region in which 

 disturbance growth rates are measured. This posi- 

 tion is also the value of Xj-gf , the point at which 

 the local wall temperature is held constant as the 

 temperature distribution parameters n and Xg are 

 varied. The displacement thickness, 6*, is deter- 

 mined by plotting the mean profile and using a polar 

 planimeter to graphically perform the integration 



6* 



/vXq/ (1 

 u„ 



-) dn , where n 



f/u7\ 



'x=5.5" 



Since the maximum wall temperature difference used 

 in the present work, is T„-T„ = 8°F, the error in- 



curred by using the incompressible formulas given 



here to calculate 6* and n is only about 0.1%. All 



experimental results reported below are therefore 



based on the incompressible forms of 6* and r\. The 



Reynolds number, R.. = u S*/v, is formed using the 



6* e 

 kinematic viscosity evaluated at the free stream 



temperature . 



For a fixed Reynolds number and ribbon frequency, 

 the ribbon-generated disturbance amplitude is 

 measured at five stations spaced 0.25 in. apart 

 between x = 5 inches and x = 6 inches. In this 

 region the pressure gradient is small (Falkner-Skan 

 g < 0.02) and there is no interaction between the 

 ribbon-generated disturbance and the natural dis- 

 turbances present in the boundary layer. The dis- 

 turbance amplitude recorded at each station is the 

 peak amplitude, defined as A(x) = [u' (ri,x) /uelmax' 

 found by searching through the boundary layer in 

 the y-direction. The spatial disturbance growth 

 rate is then calculated from the slope (dA/dx) 

 of a polynomial-curve fit of the A(x) data. By 

 repeating the above process for several different 

 frequencies the growth rate vs. frequency charac- 

 teristics of the boundary layer are determined for 

 a fixed Reynolds number and temperature distribution. 



All stability measurements reported here for 

 non-uniform wall temperature distributions were 

 performed near R.^ = 800. At Reynolds numbers 

 higher than 800 the ribbon-generated disturbances 

 become more difficult to follow since background 

 noise levels in the boundary layer increase with 

 Reynolds number. At Reynolds numbers lower than 

 800 the disturbance growth rates are already small 

 for uniform wall temperature in the range 3°F - T^, 

 (x)-Tco ^ 8°F, and measurement of the decreased 

 growth rates resulting from non-uniform wall tem- 

 perature distribution is subject to large relative 

 errors. 



Results and Discussion 



Uniform Wall Temperature Distributions 



The Mean Flow - A comparison between heated and 

 unheated mean velocity profiles measured under 

 identical flow conditions is shown in Figure 6 

 together with the calculated unheated profile ob- 

 tained using Lowell's (1974) program for 6 = -0.0036, 



