G,4 • TRANSPIRATION-COOLED BOUNDARY LAYER 



The cooling fluid continuously absorbs heat from the hot gas and in this 

 process the over-all heat transfer from hot gas to the wall is diminished. 

 In the foregoing discussion the cooling medium is assumed to be a gas. 

 If a liquid coolant is used and the mass flow of the coolant is great enough, 

 then the liquid evaporates from the upper surface of the wall. The heat 

 transfer from the hot gas to the wall is essentially the same as in the case 

 when a gas coolant is used. It is evident that cooling with a liquid is more 

 effective than cooling with a gas since considerable heat is absorbed by the 

 vaporization process. There is a boundary layer on the coolant entrance 

 side of the wall within which the coolant temperature increases from the 

 initial value Tq to the temperature with which the coolant enters the 

 pores. The thickness of this boundary layer and the temperature increase 

 within it, however, are much smaller than on the hot side of the wall. 



G,4. Heat Transfer in Transpiration-Cooled Boundary Layer. 



General Problems. It is well known that fluid flowing along a solid 

 wall builds up a boundary layer along the surface of the wall. When a 

 temperature difference exists between the fluid and the wall, a thermal 

 boundary layer is built up along the wall, which, for gases, has a thick- 

 ness of the same order of magnitude as a hydrodynamic boundary layer. 

 The transfer of heat between a fluid stream and wall mainly takes place 

 within this boundary layer. The boundary layers may be laminar or 

 turbulent. Since the amount of coolant injection necessary to keep the 

 same wall temperature is, for the turbulent boundary layer, about twice 

 that for the laminar one, it is important to study the conditions of flow 

 for each particular case. 



In the combustion chamber of jet motors, due to the rough combustion 

 process, the flow is certainly of the turbulent type. Considering the high 

 negative pressure gradient in the flow through the nozzle, the flat plate 

 solution is assumed to yield some indication of heat transfer in transpi- 

 ration-cooled turbulent boundary layer in combustion chambers and 

 nozzles. Furthermore, due to the extremely high accelerations at the 

 throat of the nozzle, the flow in the nozzle might be laminar in some cases. 

 In addition to reducing turbulence, a negative pressure gradient tends to 

 increase the stability of the laminar boundary layer in the nozzle. 



On the other hand, the flow along a gas turbine blade is expected to 

 be laminar in the region around the nose of the blade. Due to the exist- 

 ence of pressure gradient along the blade surface, the boundary layer 

 solution for the flat plate can no longer be applied here. Although a 

 positive pressure gradient in the flow direction would decrease the heat 

 transfer from the hot fluid to wall, the stability of the laminar layer is 

 decreased. The exact location of the transition to turbulent flow cannot 

 be exactly predicted yet by calculation, although a reasonable indication 

 can be expected from the stability analysis which is discussed later. The 



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