G • COOLING BY PROTECTIVE FLUID FILMS 



The results of the experiments showed that the critical velocity of 

 injection is increased when (1) the main stream air velocity is increased, 

 (2) the coolant viscosity is increased, (3) the slot width is decreased, and 

 (4) the density of the coolant is decreased. It further indicates that in- 

 clined injection of the coolant increases the critical velocity of injection 

 considerably more than the case of injection perpendicular to the main 

 stream flow. 



Comparison of the effectiveness of film and transpiration cooling. Eckert 

 [50] has made a comparison of the relative effectiveness of film and tran- 

 spiration cooling which is based on a turbulent flow along a flat plate 

 with constant gas velocity and temperature. The Reynolds number for 

 the turbulent gas flow is assumed equal to 10^ and the Prandtl number is 

 equal to 0.7. Air is considered as the coolant, as well as the outside flow 

 gas. The parameters used in the comparison are the ratio of the temper- 

 ature difference, the difference of wall temperature and coolant temper- 

 ature to the difference of hot gas temperature and coolant temperature; 

 and the ratio of coolant mass flow to the gas mass flow. 



In the transpiration-cooling calculation the relation between the ratio 

 of the temperature difference and the ratio of the mass flow is derived 

 from the heat balance equation at the wall. The heat transfer coefficient 

 used herein is obtained from sublayer theory in the turbulent flow [51]. 

 In the film-cooling calculation the Wieghardt method [5S] is used to deter- 

 mine the temperature difference ratio in relation to the mass flow ratio 

 for a single slot. Although the temperature conditions within the bound- 

 ary layer in [52] are opposite to the conditions found in film cooling, the 

 results obtained in [52] can be used for the film-cooling process as long as 

 the temperature differences are small enough to permit the gas property 

 to be considered constant. 



A comparison of the relative effectiveness of the two cooling methods 

 considered is shown in Fig. G,7b. Transpiration cooling is much more 

 effective than film cooling with a single slot and gives much lower wall 

 temperature for a specified coolant flow. In other words, transpiration 

 cooling requires a much smaller amount of coolant to cool the wall to a 

 predesignated temperature. It must be borne in mind that in the film- 

 cooling calculation the wall temperature cannot be made constant as in 

 the case of transpiration cooling, and it represents the highest temper- 

 ature occurring within the wall. At smaller downstream distances, the 

 temperature decreases toward the value To obtained immediately behind 

 the slot. The effectiveness of the film cooling therefore is increased by 

 increasing the number of slots along the plate, and it is expected that 

 the film cooling eventually transforms into transpiration when the num- 

 ber of slots becomes very large. 



There are, of course, other considerations, aside from that of a minimum 

 of coolant, which influence the choice of the cooling method for a particu- 



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