G,6 • COMPARISON WITH EXPERIMENTAL RESULTS 



and the experimental data show close agreement for small coolant injec- 

 tion. Since the variation of the fluid properties was not taken into con- 

 sideration in the theory it might be the main reason for the discrepancy 

 between the theory and experiment, especially in the case of large coolant 

 injection. 



The rate of heat transfer per unit area radially outwards at the wall 

 can be calculated by integrating the energy equation (Eq. 5-49) across 

 the radius of the circular pipe. 



1 d 



i: 



gw = p ^ / pCpTur dr— p^CpjOy,Tyr (5-65) 



From the condition of heat balance at the wall (the heat transfer by the 

 hot gas to the wall is absorbed by the coolant) one obtains 



q^ = p^v^p^{T^ - To) (5-66) 



Combining Eq. 5-65 and 5-66, after integrating between two cross sec- 

 tions, Zi and U, one obtains the temperature difference ratio as follows: 



T — T 

 T, - To 



y Tjl' 2 1 C,^ Q \W,\uj2 \UJ, 



(5-67) 



where W = PcU^, Q = pjJx, and the quantities ( )i and ( )% represent 

 the values at stations, U and U, respectively. 



G,6. Comparison with Experimental Results on Transpiration 

 Cooling. 



Experimental Results vs. Theory. The systematic experimental 

 study of transpiration cooling was initiated at the Jet Propulsion Labo- 

 ratory by Duwez and Wheeler in 1946 [37,38,39,4.0,41,42]. The experi- 

 mental investigation was limited to the case of a cylindrical duct made 

 of porous material through the walls of which the coolant was injected. 

 The test section containing the porous-wall duct was one inch in diameter 

 and eight inches long and a gasoline-air flame served as the source of 

 hot gas. The gas temperature ranged from 1100 to 1900°F with Mach 

 numbers approaching 1.0 and Reynolds numbers up to 140,000. For the 

 detailed description of experimental equipment, [38] should be consulted. 



The main object of the experiments is to establish a relation between 

 the surface temperature of the porous material and the weight rate of 

 coolant flow for different conditions of temperature and velocity in the 

 main stream of hot gas. Four significant variables were measured in the 

 experiments, namely the temperature Tg of the main stream of gas, the 

 weight rate of flow of the hot gas W, the weight rate of flow of coolant Q, 

 and the surface temperature T^ of the porous wall at several points along 



(475 ) 



