Propeller Excitation and Response of 230000 TDW Tankers 



Applying symmetrical hysteresis effect, (although non- symmetrical in 

 the tip region) and assuming that time dependent factors, such as 

 inertia and duration of transient pressure, do not influence the onset 

 of cavitation, a simple "maximum bubble radius" concept has been 

 used to establish the extent of cavitation. Further, it has been assum- 

 ed that the degree of turbulence of the inlet flow is so large that no 

 laminar separation occurs. Also when ignoring effects of sudden 

 charges of angle of incidence and several other effects, we find that, 

 for several cases considered, the quality of the results obtained, 

 when operating in behind condition, is satisfactory for engineering 

 purposes [l9j . 



The thickness of the sheet of cavities at 0. 95 r/R is found 

 by estimating the height of the tip vortex, as described in [_18J . The 

 radial thickness distribution is then found by linear interpolation, as 

 the radial inception point is already determined. The method is briefly 

 outlined in Appendix B. 



VI. 4. Calculation of Pressure Fluctuations on the Hull 



Finally, in this section we will illustrate how simple mathe- 

 matical models may be used in this case to approximate the compli- 

 cated transfer function, giving rise to a fluctuating hull pressure 

 field, during the formation of unstable cavities. 



The acceleration potential caused by the cavity formation may 

 be found by solution of the Volterra integral equation, if the forma- 

 tion be accurately represented at any time during growth and collapse. 

 The vapour/liquid mixture representing a pulsating volume cannot be 

 said to constitute a surface of known shape. Consequently, an ideal 

 mathematical model of moderate complexity should be employed, 

 together with empirical corrections found by experiments. 



The mathematical model now in use at DnV Q20J is described 

 in some detail in Appendix C. The cavitation patterns observed on- 

 board T/T 'Norse King", simulated as shown in Figures 37 and 38, 

 have been used to obtain the results, presented in Figure 39. Clearly, 

 the calculated values for blade frequency pressures on the hull clo- 

 sely resemble full scale values recorded. Also twice blade frequency 

 components, as calculated, correspond approximately with values 

 recorded, see Figure 40. 



VII. SUMMARY AND CONCLUSIONS 



The most important conclusions to be drawn from the results 

 of the present investigation can be summarised as follows : 



601 



