A,23 • SUBSONIC TRANSITION. HEAT TRANSFER EFFECTS 



oscillograms show the typical transition behavior. Nevertheless there is 

 some question as to whether the phenomenon is analogous to other cases 

 of transition described. It seems more likely that the outer boundary of a 

 turbulent jet is very ragged and constantly changing with time as readily 

 observed in the smoke stream from a factory chimney. The apparent 

 transition is then to be interpreted as the intermittent striking of the 

 hot wire by the turbulent jet. 



A, 23. Transition at Subsonic Speed as AiFected by Heat Transfer. 



When a heated plate is placed vertically in still air, convection currents 

 are set up. If the temperature difference between the plate and air is not 

 too large, or more accurately if the Grashoff number gh^{T^ — T^)/v'^T^ 

 is not too large, the motion will be laminar in character. Here g is the 

 acceleration of gravity, h is the vertical height of the plate, T^, is the 

 plate temperature, T^ the free air temperature, and v the kinematic vis- 

 cosity. According to Hermann [88], transition to turbulence occurs at a 

 Grashoff number of about 10^ for which Re^* is about 300. 



The stabilizing and destabilizing effects of gravitational forces pro- 

 duced by density differences arising from heating and cooUng in forced 

 air flow are analogous to those of centrifugal forces in curved flow dis- 

 cussed in Art. 20. According to Prandtl [77] the controlling parameter is 

 the ratio of —gdp/dy to 2p{du/dyy. When this parameter is greater than 

 1, the flow is very stable and the critical Reynolds number is infinite. 

 Schlichting [89] found that the effect of gravity made all oscillations in a 

 laminar boundary layer stable, provided —gdp/dy exceeded -^p{du/dy)l 

 where {du/dy)^ is the value of du/dy at the wall. Reichardt's measure- 

 ments [90] are in fair agreement with Schlichting's result. 



Liepmann and Fila [12] investigated the effect of surface temperature 

 on transition in incompressible flow, for heating only, and under con- 

 ditions where the effects of gravitational forces were negligible. For the 

 unheated plate the transition Reynolds number was only about 500,000, 

 although the free stream turbulence was in one series 0.17 per cent and 

 in another 0.05 per cent. The low value is attributed by the authors to 

 lateral spreading of turbulence from the wind tunnel walls. The transition 

 Reynolds number decreases as the surface temperature is increased, fall- 

 ing to about 400,000 at 100°C at a turbulence level of 0.05 and to about 

 250,000 at 100°C at a turbulence level of 0.17. The Reynolds numbers 

 are based on the free stream value of the viscosity. If the viscosity at the 

 wall is used, the transition Reynolds numbers at 100°C are 260,000 and 

 185,000, respectively. The observed effects are believed to be due to the 

 effect of the variation of viscosity with temperature in producing inflec- 

 tion points in the velocity distribution curve; not to the influence of 

 gravitational forces. Velocity profiles with inflection points are much 

 more unstable than those without inflection points. 



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