411 



0.9 - 

 0.8- 

 0.7 - 

 0.6- 

 0.5- 

 0-4- 



osj— - 



• PROPELLER A SLIP = 3 TUNNEL 

 o „ TANK 



X „ „ „ = 0.6 



□ „ B „ = 0.3 



■O SASAJIMA (1975) TANK " 



♦ ., ., TUNNEL 



10 



2,0 



RBm X 10 



FIGURE 15. Effect of Reynolds number on the 

 critical radius. 



It is important to note that in Figure 12 at 50% 

 slip the radius where laminar separation occurs 

 near midchord is not the critical radius , although 

 in this case the difference between both is small. 

 With increasing Reynolds number, however, the region 

 of laminar separation near midchord will decrease, 

 while the critical radius will remain unchanged. 

 The distance between the sharp corner in the paint 

 streaks of Figure 12b and the critical radius will 

 therefore increase with increasing Reynolds number. 



An increase of Reynolds number causes a shift 

 in the chordwise position of the transition region 

 at radii inside the critical radius, as is illus- 

 trated in Figure 16. This was also observed on 

 the pressure side. In Figure 17 the chordwise 

 position of the transition region is given at 

 r/R=0.7 as a function of the sectional Reynolds 

 number, which is related to the entrance velocity 

 and the chordlength of the propeller section at 

 that radius. The transition region is averaged in 

 Figure 17. This makes clear that a complete turbu- 

 lent boundary layer at a radius of 0.7R requires 

 sectional Reynolds numbers of about 5xl06. At the 

 suction side , turbulent flow at this radius also 

 occurs when the loading is increased, i.e. the 

 critical radius is smaller than 0.7. 



Empirical criteria for transition of the boundary 

 layer to turbulence have been given as a relation 

 between the Reynolds numbers based on the length 

 from the stagnation point, Rej., and based on the 

 momentum thickness , Reg. [Michel (1951), Smith 

 (1956) ]. Van Oossanen used the Smith line 



Re 



Strans 



1.174 Re, 



0.46 



(10) 



as a criterion. When the relation between Reg and 

 Rejj over the chord was calculated, both on the 

 suction side and on the pressure side, this relation 

 was so closely parallel to the criterion of Eq. 10 

 that no reliable intersection was possible. When 

 there is a strong negative pressure peak at the 

 leading edge the relation between Reg and Re^^ is 

 such that Eq. 10 always predicts transition very 

 close to the leading edge. When the pressure 

 distribution was nearly shockfree, the prediction 

 was erroneous. 



To calculate the transition region, calculation 



: 0.73x10 



CRITICAL RADIUS 

 TRANSITION 



FIGURE 16. Effect of Reynolds number on the transi- 

 tion region. Propeller A at 30% slip. 



