404 



-fr 



ELECTROLYSIS GRID 



be derived with suitable accuracy. Since the 

 propeller thrust is least sensitive to viscous 

 effects this quantity gives the most reliable 

 verification of calculations. When the propeller 

 geometry and the nominal inflow are known two 

 approaches are available to obtain the distribution 

 of propeller loading, viz. the lifting line theory 

 and the lifting surface theory. Hereafter, both 

 approaches will be considered with models going 

 back to the work of Lerbs (1952) for the former 

 and Sparenberg (1960) for the latter theory. 



DETAIL ELECTROLYSIS GRID 



FIGURE 5. Test equipment for open-water tests. 



a few minutes the viscosity of the lead-oxide is 

 too low and the blades are cleaned by the flow. 



The paint is put on the propeller blades at the 

 leading edge to about 10/? of the chord. The layer 

 must be rather thick to provide enough paint to 

 cover the whole blade. Some pictures were taken 

 with UV light using the fluoriscent properties of 

 the pigment. The bulk of the pictures of the paint 

 tests was taken in colour photography with natural 

 light. This gave good colour prints, but unfortu- 

 nately the contrast in monochrome paper turned out 

 to be rather poor. 



Roughness at the Leading Edge 



To trip the boundary layer to turbulence the leading 

 edge of the propeller blades was covered with 

 carborundum. The leading edge of the propeller 

 blade is wetted with watery thin varnish to about 

 0.5 mm from the leading edge. This is done by 

 touching the leading edge with a pad wetted with 

 varnish. The softness of the pad determines the 

 length of the wetted area from the leading edge . 

 Then carborundum is put on the wetted area by 

 spreading the grains on a felt cloth and by wiping 

 the wetted leading edge with that cloth. Two grains 

 sizes were used: 30 ym (31-37) and 60 um (53-62). 

 Microscopic inspection afterwards is necessary. An 

 example is given in Figure 6. 



Lifting Line Calculations 



The lifting line theory concentrates the loading of 

 a propeller section at one point. Using the induc- 

 tion factor method [Wrench (1957)], a relation 

 between the hydrodynamic pitch angle, Q^, and the 

 circulation, r, at each section is found. 



B. (i) = F[r(r)] 



(5) 



When a given propeller is analysed B^ and V are 

 unknown. To find them a second relation is necessary, 

 which is derived from two-dimensional profile 

 characteristics. The lift coefficient 



=L = 



da 



(a+Up) 



(6) 



where a^ is the zero lift angle of the propeller 

 section. Since the angle of attack a is taken from 



a = (B - B.). (7) 



P 1 



where Bn i^ the known geometrical pitch angle, a 

 second relation is formulated between Cl (or r) 

 and Bi, in which dC^/da, is assumed to be known. 



When the two-dimensional value for dC-j^/da , based 

 on the geometry of the propeller section, is used 

 the results are rather drastically wrong. This is 

 caused mainly by the finite length of the propeller 

 section, which creates a distribution of induced 

 velocities affecting camber and angle of attack. 





CALCULATION OF PRESSURE DISTRIBUTION 



The analysis of boundary layer phenomena and of 

 cavitation on propeller blades becomes very specu- 

 lative when the pressure distribution is not known. 

 No firm experimental verification of calculations 

 of the pressure distribution is available yet, only 

 the total thrust and torque give some evidence of 

 the value of calculations. The calculations are 

 always potential flow calculations and the effect 

 of viscosity on the propeller sections cannot yet 



K- 



H 



eOfim 

 CARBORUNDUM 



h- 



SOM-m 



CARBORUNDUM 



FIGURE 6. Microscopic picture of leading edge 

 roughness . 



