Propeller Pressure Field in a Nonuniform Flow 



f B„(r')(9;_^^/2)(^) 



KB = r 



mn I 



dr' ,- 



and /v^^ and K^^ are defined by analogous expressions. In the above formulas n 

 and m have to satisfy the relations 



m + n I 



^± I z 



where ? = l, 2, 3, ... is the harmonic number. 



Although Eq. (4) is derived on the basis of lifting line theory, it can be eas- 

 ily extended for the case of a lifting surface propeller representation. However, 

 in this case, to calculate the vibratory pressure one should know the chordwise 

 distribution of the bound vorticity on the blade of a propeller operating in a 

 wake. 



NUMERICAL RESULTS AND COMPARISON WITH 

 EXPERIMENTAL DATA 



Calculations of the loading- induced pressure have been made by means of 

 Eq. (4) to evaluate quantitatively the effect of inflow nonuniformity on the vibra- 

 tory pressure generated by a propeller under different inflow conditions. Nu- 

 merical computations have been performed with a digital computer. Nonstation- 

 ary circulation around the blade section has been determined by the (3/4) -line 

 method. 



The calculations have shown that the most pronounced effect of the flow 

 nonuniformity on the pressure amplitude is felt in the points of the hull with an- 

 gular coordinates corresponding to the position of the blade under maximum 

 loading conditions. Furthermore, the calculations confirmed the conclusion 

 drawn in Ref. 6 that the influence of nonuniform inflow conditions on the pres- 

 sure amplitude increases with distance from the propeller plane. This is ex- 

 plained by the fact that in nonuniform flow a propeller-induced pressure decays 

 with distance from the propeller much more slowly than in the uniform flow. 



The results of calculations of the pressure amplitudes generated by a five- 

 bladed propeller on the hull of a single -screw ship are shown in Fig. 3. The 

 amplitudes of the first and second harmonics of the blade -frequency pressure 

 were calculated at the points immediately above the propeller, i.e., at the region 

 of maximum blade loading. The calculated pressures were doubled to account 

 for the hull surface effect. The amplitudes of the first harmonic were also 

 computed assuming the propeller to operate in a circumferentially uniform flow 

 with the radial distribution of velocities corresponding to that of a real wake 

 (line 3 in Fig. 3). It is evident from Fig. 3 that in this particular case the effect 

 of nonuniformity causes an increase of 40 to 60 percent over the pressures cor- 

 responding to the propeller operating in a circumferentially uniform flow. 



