A, 20 • FLOW BETWEEN ROTATING CYLINDERS 



Kenyon, and Allen [76] in a wind tunnel of low turbulence (u' = 0.02 

 per cent). The observed values of Ret ranged from 3.2 to 3.8 million for 

 the body of fineness ratio 9 and from 3.6 to 4.3 million for the body of 

 fineness ratio 7.5, the exact value being dependent on the axial location 

 of transition. 



The effect of local surface roughness in the form of a wire ring on the 

 surface in a plane normal to the body axis was studied by Fage and 

 Preston [74]- The results were similar to those already described for wires 

 on a flat plate. As the speed was increased, transition moved forward 

 from its original position in the absence of the wire until at some speed 

 it reached the position of the wire where it remained at higher speeds. 

 The Reynolds number formed from the wire diameter and the velocity in 



0.6 



b 0.4 



X 



6-0.2 



0.4 0.8 1.2 1.6 2.0 2.4 2.8 



Fig. A, 19. Effect of roughness on transition Reynolds number of bodies of revolution. 



the boundary layer at a distance from the surface equal to the wire di- 

 ameter varied from 205 to 450 with an average value of 390 for tran- 

 sition to just reach the wire. Values of ii^xjv are plotted against rf/5* in 

 Fig. A, 19. 



To summarize, the available data on transition on bodies of revolution 

 confirm the importance of pressure gradient, air stream turbulence, and 

 surface roughness and waviness as important controlling variables in addi- 

 tion to Reynolds number, but do not permit a clear separation of the 

 separate effects. Neither do the data give a conclusive demonstration that 

 bodies of revolution give the same values of Re^, as two-dimensional bodies 

 with the same pressure distribution, air stream turbulence, and surface 

 roughness. In the limited data available, the maximum value of Re^ ob- 

 served on bodies of revolution was about 4 million as compared with 14 

 million for airfoils. 



A,20. Transition in Flow between Rotating Cylinders. Transi- 

 tion in the flow between rotating cylinders is a complex phenomenon but, 

 as in the case of boundary layer flow, follows an instability of the laminar 

 flow. Prandtl \77\ discussed the stability of two-dimensional flows in which 



<49 ) 



