Experiments on Heat-Stabilized Laminar 

 Boundary Layers in a Tube 



Steven J. Barker 



Poseidon Research* and University 



of California at Los Angeles 



ABSTRACT 



There has been considerable recent interest in the 

 stabilization of water boundary layers by wall 

 heating. Calculations based upon linear stability 

 theory have predicted transition Reynolds numbers 

 as high as 2 x 10° for a zero pressure gradient 

 boundary layer over a heated wall. The flow tube 

 experiment described in this paper was intended to 

 investigate these predictions. The test boundary 

 layer develops on the inside of a cylindrical tube, 

 0.1 ra in diameter and 6.1 m in length. The dis- 

 placement thickness is small relative to the tiibe 

 radius imder nearly all operating conditions . The 

 tube is heated by electrical heaters on the outside 

 wall . The location of transition can be determined 

 by a heat flux measurement, by flush-mounted hot 

 film probes , or by flow visualization at the tube 

 exit. 



A transition Reynolds number of 10 can be ob- 

 tained without heat, which shows that free stream 

 turbulence and other perturbations are well con- 

 trolled. At 7°C wall overheat, a transition 

 Reynolds number of 42 x 10° has been obtained, 

 which is at least as high as the prediction for 

 that overheat. However, as temperature is further 

 increased there have been no additional increases 

 in transition Reynolds number, which is in contra- 

 diction to the theory . 



Possible reasons for the differences between 

 theory and experiment have also been investigated. 

 New test section exits have been developed to 

 determine the effects of downstream boundary con- 

 ditions upon the flow. An instriimented section 

 has been used to measure detailed velocity profiles 

 in the boundary layer, and determine intermittency 

 as a function of azimuthal angle. From these 

 measurements we can evaluate the possibility of 



* ■ • . ^ 



This work was performed by the Marine Systems Division o£ 



Rockwell International, and Poseidon Research. It was 



sponsored by the Defense Advanced Research Projects Agency. 



buoyancy-generated instabilities in the tube. 

 Future tests will also investigate the influence 

 of free stream turbulence, streamwise vorticity 

 in the boundary layer, and wall temperature vari- 

 ations . 



1 . INTRODUCTION 



Numerical calculations such as those of Wazzan, 

 Okamura, and Smith (1968, 1970) have predicted large 

 increases in the transition Reynolds numbers of 

 water boundary layers with the addition of wall 

 heating. The stabilizing mechanism is the decrease 

 in fluid viscosity near the wall resulting from the 

 heating. This increases the negative curvature 

 of the velocity profile, making the flow more stable 

 to small disturbances. The present study is an 

 experimental investigation of these predictions, 

 using the boundary layer developing on the inside 

 wall of a cylindrical ttibe. This boundary layer is 

 thin relative to the tube diameter, so that it 

 approximates a boundary layer over a flat plate. 



The numerical predictions of Wazzan et al. are 

 based on two-dimensional, linear stability theory. 

 The mean flow is assumed plane and parallel, and 

 the superimposed small disturbance is described by 

 a stream function. 



ii (x,Y,t) = <ti(y) exp ia{x-ct) 



(1) 



Here (j) (y) is the disturbance amplitude, a is the 

 wavenumber and is assumed real, and c is the wave 

 velocity which may be complex. The imaginary part 

 of c determines whether the disturbance is tempo- 

 rally amplified or damped. If we siibstitute this 

 stream function into the Navier-Stokes equations 

 and linearize, taking account of the variation of 



viscosity ]i 



(U - c) {(()' 



k 

 a <t>) 



with distance from the wall 

 2 



we find 



[)) - U" 



-[p(<i>"" 



+ 2p' ((| 



a Re 

 ') + y"(q 



2a 



2 , 



(2) 



77 



