臺灣博碩士論文加值系統

摘要

本論文最主要目的為依據線性聲學理論建立一套新且有效可計算船用螺槳於遠、近場所造成之葉頻噪音之數值方法。其中，船殼所引發之散射及自由液面引發之反射效應都將被考慮。
本方法中，首先於時域中推導出螺槳非定常片狀空泡及非定常力於遠場與近場引發噪音滿足線性聲波方程式之解，而自由液面效應則以映射法模擬之。本文將於時域中進行推導，且對旋轉聲源與場點間之距離無須作任何假設，因此本方法適用於遠、近場之計算。且能清楚計算於近場中，旋轉聲源與場點間距離隨時間變化引起之都普勒效應。求解螺槳非定常片狀空泡及非定常推力於遠場所引發之噪音時，可將佈滿整個葉片之音源以一等強度點音源代替之。但對非定常扭矩力於遠場所引發之噪音而言，則不可以一有效點音源替代之，否則將會有明顯之誤差存在。於近場計算時，不管何種音源皆須佈滿整個葉片始不致造成計算誤差。
至於船體散射問題之求解，本文發展一新的時域疊代方法。此時域疊代方法可同時解多頻散射之問題。疊代過程中，時間內插以傅利葉級數替換之，可有效的降低時間內插所造成之誤差。此方法可以有效替代傳統頻率域邊界元素法。計算過程中，此方法之收斂非常穩定，且高、低頻之計算例結果都和頻率域邊界元素法所得之結果吻合，然計算時間明顯縮短。
為探討於考慮自由液面效應情況下，螺槳直接葉頻輻射音與船殼散射音互相干擾之聲場，本文以一貨櫃船為計算實例。於此例中，本文方法計算之螺槳對船殼所誘導之激振力和滿足拉普拉斯(Laplace)方程式之高階小板法所計算之結果相似。

Abstract

The main objective of this thesis is to develop a new and efficient numerical method for predicting the far-field and near-field blade-rate noises of marine propellers operating in a non-uniform ship wake by linear acoustic theory. In addition, both the scattering effect from the ship hull and the reflecting effect from the free surface are included.
In the present method, an exact analytic solution satisfying the linear wave equation for predicting acoustic pressure caused by unsteady sheet cavitations, unsteady thrusts and torques can be derived directly in time domain. The free surface effect is simulated by imaged method. The deriving process has no approximation about the distance between the noise source and field points. Thus, this method can be used to predict the acoustic pressure at both far and near fields, and the Doppler effect can be demonstrate in the near field evidently. The variation of the distance between the noise source and the field points will cause obvious in the near field. It is found that for computing far-field acoustic pressure induced by the unsteady sheet cavitation and thrust, noise sources on a blade can be replaced by an effective point noise source. However, in doing so, errors appear on the computation of the acoustic pressure induced by the unsteady torque force. In the near field, any kind of noise sources should be distributed on the entire propeller blades in order to avoid the errors, especially for unsteady thrust and torque.
An iterative method in time domain for computing multi-frequency waves scattered from underwater obstacles is also developed. These equations derived in the present method are expressed in some forms relative to the retarded time, and the Fourier series is used to minimize the numerical error due to time interpolations. This iterative method is an alternative to the frequency-domain boundary element method (BEM); however, this method is more efficient than the BEM, and is found very robust. Computational results of the present method and BEM show good agreements for both low frequency and high frequency cases.
To investigate the acoustic fields radiated by the propeller and scattered from the ship hull with free surface effect, a case of container ship is calculated in this thesis. Meanwhile, the pressure fluctuations induced by the propeller on the ship hull predicted by the present method is similar to the results by a higher-order panel method satisfying the Laplace equation in this case.

Contents ............................................. V

List of Figures ......................................VIII

List of Tables.........................................XII

Nomenclature..........................................XIII

1 Introduction....................................1
1.1 The Noise Types Generated by Operating
Marine Propellers..........................1
1.2 The Discrete Blade-Rate Noise due to Marine
Propellers.................................2
1.3 Scattering Problems........................4
1.4 Objectives of This Distribution ...........6

2 The Blade-Rate Noise Radiated From Operating
Marine Propellers...............................8
2.1 Linear Acoustic Theory ....................8
2.2 Noise Source..............................10
2.2.1 Unsteady Source Strength of
Propeller Sheet Cavity Volume...11
2.2.2 Unsteady Force of a Propeller...12
2.3 Derivation of the Acoustic Pressure in Free
Field in Time Domain.......................13
2.3.1 The Acoustic Pressure due to a
Unsteady Propeller Sheet Cavitation ................................13
2.3.2 The Acoustic Pressure due to
Unsteady Propeller Force........17
2.4 Investigation of the Frequency Shift.......22
2.4.1 Frequency Shift for the Noise due
to Unsteady Propeller Sheet
Cavitation.......................23
2.4.2 Frequency Shift for the Noise due
to Unsteady Propeller Thrust.....24
2.4.3 Frequency Shift for the Noise due
to Unsteady Propeller Torque Force ................................25
2.5 Free Surface Effect........................26
2.5.1 General Discussion...............26
2.5.2 The Simulation of a Free Surface.28

3 A Time-Domain Iteration Method for Acoustic
Scattering Problems.............................36
3.1 Theoretical Formulations...................36
3.2 Numerical Implementation...................38
3.2.1 The Incident and Scattering
Potential.......................39
3.2.2 Equation for Iterations in Time
Domain..........................39
3.2.3 Time Marching Process...........41
3.3 Numerical Validation of the Present Method.43
3.3.1 Time Step Test..................44
3.3.2 High Frequency test.............45
3.3.3 Multi-Frequency Incident Wave
................................46
3.3.4 Comparison of Computational
Efficiency......................47

4 Computational Results...........................59
4.1 Associated Data for the Propeller..........59
4.2 The Strength of the Noise Sources..........60
4.3 Propeller Radiated Noise...................61
4.3.1 Results Without Free Surface
Effect..........................61
4.3.2 Results With Free Surface Effect ................................64
4.4 Scattering From the Ship Hull..............68
4.4.1 Iteration Scheme and Panel
Distribution....................68
4.4.2 Comparison Between Computational
Result and Experimental Measurement
for Ship Hull Pressure Fluctuation
..................................69
4.4.3 Scattering Effect in the Field
.................................71

5 Conclusion and Future Research Works ...........102

References...............................................107

Appendix
A Boundary Integral Equation............................114
B Derivation of Helmholtz Integral Equation in the Total
Potential Scheme .....................................116
C Hyperboloidal Panel Formulations......................118

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