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frequency KP are all larger than the measured values, and this is because the calculated cavitation extensions are larger than those of model tests.

Table 2: Comparison of measured and computational 2KP for the blade frequency and twice blade frequency under two water surface conditions.

G

Meas.

Calculated

Amplitudes

Ratio

Meas'd/Calc'd

Ratio

Free

Rigid

Free

Rigid

Blade Frequency

3

0.165

0.254

0.282

0.650

0.585

0.901

4

0.105

0.082

0.117

1.280

0.897

0.701

5

0.069

0.054

0.090

1.278

0.767

0.600

Twice Blade Frequency

3

0.065

0.128

0.146

0.508

0.445

0.877

4

0.024

0.040

0.054

0.600

0.445

0.741

5

0.016

0.020

0.038

0.800

0.421

0.526

(“G” is the gage number)

6
Conclusions

In this paper, the flow field around a ship hull and its propeller is solved by coupling a higher order potential based panel method and a lifting surface vortex lattice method. The advantages of this method are: First, potentials on the ship hull surface can be directly calculated, and the computational time is less than a velocity based panel method since only one scalar term (potential) rather than three components of velocities needed to be computed. Secondly, the propeller induced potentials can be directly added to potentials on the ship hull surface. Thirdly, the term in the Bernoulli's equation can be easily calculated by differentiating the solved potentials in time. Finally, this higher order panel method has been proved to be more accurate than a low order panel method at the same given computational time.

The unsteady flow around a propeller is analyzed by MIT-PUF-3A. By investigating the computational results, it is found that the cavitation extensions calculated by PUF-3A are overestimated for conventional model propeller geometries when comparing to the model test results. This may be due to the cavity model in PUF-3A is corresponding to the full-scale.

The computational results have been compared with the experimental data. For pressure fluctuations on a flat plate generated by propellers in a nonuniform inflow, the computational results agree well with the experimental data for cavitation numbers higher than 1.5. For cavitation numbers lower than 1.5, the pressure fluctuations have been overestimated. For pressure fluctuations on a ship hull, the differences between the computed and measured values are relatively large at the point above the propeller. However, the differences can be explained, and the reasons are described in the paper. The comparisons between computed and measured values at other points are good.

For future works, the pressure fluctuations at the actual measured point of Gage 3 (outside the shil hull) should be calculated to confirm our inferences. The effective wake should be calculated by a more accurate method such as solving the Navier-Stokes equations. Finally, the computed hydrodynamic results should be incorporated with structure and vibration calculations.

Acknowledgment

This work was supported by the National Science Council, Taipei, and the project number is NSC-85– 2611-E-019–018. Additional support was provided by China Ship Building Corporation, Keelung, under project CSBC-RD-0372. The authors would like to thank Mr. Y.-H Lee at NTOU, Mr. J.-T.Chen and Mr.S.-K.Chou at USDDC for their assistances in generating hull panels.

References

[1] William K.Blake, Justin E.Kerwin, K. Meyne, E.Weiendorf, and J.Frisch. Design of apl c-10 propeller with full-scale measurements and observations under service conditions. In Transactions, SNAME, 1990.

[2] J.P.Breslin, R.J.Van Houten, J.E.Kerwin, and C-A Johnsson. Theoretical and experimental propeller-induced hull pressures arising from intermittent blade cavitation, loading, and thickness. Trans. SNAME, 90, 1982.

[3] H.-F.Chen. The application of higher order doublet panel method on computation of ship potential flow field (in Chinese). Master's thesis, Department of Mechanical and Marine Engineering, National Taiwan Ocean University, June 1995.



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