A • TRANSITION FROM LAMINAR TO TURBULENT FLOW 



A,24. General Remarks on Transition at Supersonic Speed. 



When a body travels at supersonic speed through the air, its surface be- 

 comes heated above the temperature of the surrounding undisturbed air. 

 If the body is insulated and there is no transfer of heat by radiation to or 

 from it, the surface reaches a constant temperature T^ equal to the tem- 

 perature of the air adjacent to the surface. This temperature is somewhat 

 less than the local adiabatic stagnation temperature Tl and is known as 

 the recovery temperature. If the local air temperature just outside the 

 boundary layer is T^, the ratio (7", — T^)/{Tl — T^) is called the recovery 

 factor r. For laminar flow the recovery factor is approximately equal to 

 the square root of the Prandtl number Pr, the name given to the non- 

 dimensional parameter tiCp/k formed from the viscosity ju, specific heat at 

 constant pressure Cp, and thermal conductivity A; of the air. For turbulent 

 flow r = \/Pr approximately. 



For the circumstances described there is no heat lost from the body 

 by convection. Art. 25 discusses the data on transition under these con- 

 ditions. The indirect effect of aerodynamic heating appears as an effect 

 of Mach number, since the changes in the density and velocity distribu- 

 tion accompanying the temperature rise in the boundary layer modify 

 the stabihty of the layer. 



Heat transfer to or from the body exerts a marked influence on tran- 

 sition as discussed later in Art. 26. Heat flow from the air to the body 

 (cooling the body) increases the transition Reynolds number, whereas 

 heat flow from the body to the air (heating the body) decreases it. These 

 effects are quite substantial and sometimes overlooked. It is very difficult 

 to reahze experimentally the condition of complete absence of heat flow 

 to or from the body, especially for experiments in which the relative speed 

 cannot be maintained for long periods, as in firing ranges and blowdown 

 wind tunnels. In a firing range, the body is usually initially at free air 

 temperature. The recovery temperature is much higher and the experi- 

 mental conditions are those of a cooled body. In a blowdown wind tunnel, 

 the body is usually initially at or near the stagnation temperature which 

 is only a little above the recovery temperature. The free stream temper- 

 ature is very much lower and the experimental conditions are those of a 

 heated body. These differences account for the commonly observed rise 

 of transition Reynolds numbers with Mach number in firing range data 

 (the effective cooling increasing with Mach number because of the rising 

 stagnation temperature) and the fall with Mach number in blowdown 

 wind tunnels (the effective heating increasing with Mach number because 

 of the falling free stream temperature). 



Effects of free stream turbulence, pressure gradient, nose shape, and 

 roughness are found at supersonic as well as at subsonic speed. The effect 

 of nose shape differs in that a bow shock wave is present at supersonic 

 speed which modifies the viscosity, density, and speed of the flow near 



< 54) 



