G,6 • COMPARISON WITH EXPERIMENTAL RESULTS 



and the wall temperature decreases with the increase of coolant injection, 

 it can be seen that the film heat transfer coefficient h^ decreases as the 

 coolant injection increases. This is shown in Fig. G,4c. 



The above phenomena were also observed in the case of heat transfer 

 in the turbulent boundary layer on a flat plate with coolant injection at 

 the wall. This can be seen in Fig. G,4g and G,4h. 



The result obtained from the study of laminar pipe flow with fluid 

 injection at the wall has shown that the effect of fluid injection at the 

 wall is to accelerate the main stream velocity. Hence the velocity gradient 

 at the wall, which determines the wall friction, increases. On the other 

 hand, the result of the study of heat transfer of a laminar pipe flow with 

 coolant injection shows that the heat transfer coefficient at the wall de- 

 creases with an increase in the rate of coolant injection. This phenomenon 

 thus indicates that the analogy between the heat transfer and momentum 

 transfer does not exist in transpiration-cooled pipe flow. 



For turbulent pipe flow the connection between the pressure drop and 

 the flow volume which, in turn, determines the wall shearing stress must 

 be obtained from tests. Wheeler [^^] has made some preliminary pressure- 

 drop studies in a transpiration-cooled pipe. From the test data an empiri- 

 cal expression is formulated 



where W is the weight rate of flow in the main stream, R is the gas con- 

 stant, Tg is the main stream temperature, g is the acceleration of gravity, 

 and D is the diameter of the pipe. The first term on the right-hand side 

 of Eq. 6-2 represents the head loss, which was observed with no coolant 

 flow where / is the friction factor corresponding to Blasius formula for a 

 smooth pipe. The second term expresses the additional loss which occurred 

 when coolant was added. For isothermal flow the exponent n becomes 

 unity. The parameter B seems to depend somewhat on the initial value 

 of / and on the nature of the cooling gas, being greater for the less dense 

 gas. The exact factors which control the parameter B and n cannot be 

 determined from the present preliminary data. 



The importance of Eq. 6-2 is realized when one considers that the 

 shearing stress at the wall Tw may be determined experimentally by the 

 measurement of the pressure drop. Once Eq. 6-2 is exactly established 

 the shearing stress at the wall Tw and the heat flow to the wall from the 

 hot gas gw can be determined in the transpiration-cooled turbulent bound- 

 ary layer. 



General Discussion on Transpiration Cooling. On comparing 

 the theoretical curves computed from [27] with the experimental results, 

 it is seen that the shape of the curves is correct but that the theoretical 

 wall temperature for a given coolant flow is lower than the measured 



(479 > 



