F,ll • HEAT TRANSFER 



In order to show that Eq. 11-17 gives recovery factors which are also 

 independent of Mach number, at least in the first approximation, it is 

 necessary to introduce the Mach number into the friction coefficient. 

 Thus, assuming that Eq. 11-17 can be used to represent compressible flow 

 if wall conditions are substituted into the equation, the factor 



1 + r 



Ml 



should be multiplied into c//2 wherever c//2 appears. It must then be 

 remembered that the friction coefficient becomes the compressible flow 

 coefficient. 



0.92 

 0.90 

 0.88 

 0.86 

 0.84 

 0.82 



i^cAHt^f^t^^ 



(0.7 1)^ 



Eq. 11-17, Prt = 0.86 



Priam = 0.71 



o BRL Me = 2.2 10° cone 



+ MIT Me = 3.0 Plate 



A NACA Me = 3.8 10° cone 



I JO = 100°F 



105 



10* 



107 



II 



Ree 



Fig. F,llb. Recovery factor for a turbulent boundary layer on a flat 

 plate as a function of Reynolds number for air. Mg = 0. 



That the turbulent recovery factor given by Eq. 11-17 is essentially 

 independent of Mach number for a flat plate (or a cone) in a wind tunnel 

 with Re = 10^ is seen in Fig. F,llc, in which some data of MIT and 

 NACA (1 by 3-ft No. 1 tunnel) are also plotted. The values of c//2 used for 

 the calculation were obtained from the data of Coles [31]. This apparent 

 independence further justifies the analysis leading to Eq. 11-17. Fig. 

 F,lld indicates the turbulent recovery factor variation during free flight. 

 The difference between Fig. F,llc and F,lld is due to the difference be- 

 tween the molecular Prandtl number variation in wind tunnel and free 

 flight. The NBS-NACA molecular Prandtl number variation was assumed 

 [5]. The laminar flow recovery factors are shown in Fig. F,llc and F,lld 

 for the purpose of comparison. 



Owing to the method of calculation, it is hardly expected that the 

 curves of Fig. F,llc and F,lld are meaningful at the higher Mach num- 



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