Study on Added Resistance Using Unsteady Waves Analysis

Transcription

1 Study on Added Resistance Using Unsteady Waves Analysis Kenta Yamamoto, Tomoki Wakabayashi and Masashi Kashiwagi Department of Naval Architecture and Ocean Engineering, Osaka University

2 Background The resistance due to ship s unsteady wave making is the main component of the added resistance. The added resistance is estimated by Maruo s formula including Kochin function. In most of the past work, the computed values by the potential-flow theory for wave-making component have been compared with the total values of the added resistance measured directly by a dynamometer. The hydrodynamic relation between the added resistance and unsteady waves is unclear.

3 Purpose To investigate the hydrodynamic relation between the added resistance and unsteady waves, the added resistance was estimated with unsteady wave analysis. To check the amplitude effect on the estimation of the added resistance, the experiment was performed in the different amplitude of incident wave. To confirm the linearity in unsteady wave, the linear superposed wave was obtained. To see the degree of contribution from the components of different wavenumbers, the unsteady wave was decomposed.

4 Maruo s Formula In head wave where k k k 4 U k

5 Unsteady Wave Analysis where Fourier transform Substituting into Maruo s formula Computing the added resistance with unsteady waves

6 Ship Model Modified Wigley Model where Principal dimensions Value (unit) Ship length L. [m] Ship breadth B. [m] Draft d.5 [m] Displacement V.45 [m ] Height of the center of gravity KG.44 [m] Radius of Gyration κ yy /L.48

7 Method for Measuring Waves where Transforming coordinate system X and Y is space fixed system of coordinates. x and y is body fixed system of coordinates.

8 Method for Measuring Waves trigger Modified Wigley model Vessel speed Capacitance type wave height meter Incident wave

9 Experimental Condition Motion free problem and Diffraction problem Item Wavelength of incident wave λ/l Small amplitude of incident wave A Condition.<λ/L<. A=. [cm] Large amplitude of incident wave A A/λ=/ (.<λ/l<.7) and A=.5(.8<λ/L<.) Froude number Fn. Radiation problem (heave and pitch) Item Wavenumber KL Forced heave amplitude ξ Forced pitch amplitude ξ 5 Condition 5<KL< [cm].6 [deg.] Froude number Fn.

10 Superposed Wave heave pitch

11 Comparison of Added Resistance R AW / ρga (B /L) The results 6 by a dynamometer agree 5with the results by EUT 4 Dynamometer (A=.cm) (a=.cm) Wave Wave Analysis (A=.cm) (a=.cm) EUT EUT.5.5 λ/l Large discrepancy between results by a dynamometer and unsteady wave analysis are seen near the peak

12 Comparison of Added Resistance R AW / ρga (B /L) The 6tendency of the results at A=.5cm 5 is similar to the results at A=.cm 4 Dynamometer (A=.cm) (a=.cm) Dynamometer (A=.5cm) (a=.5cm) Wave Wave Analysis (A=.cm) (a=.cm) Wave Wave Analysis (A=.5cm) (a=.5cm) EUT EUT.5.5 λ/l The discrepancy between the results by a dynamometer and unsteady wave analysis at A=.5cm is larger than A=.cm

13 Comparison of Added Resistance R AW / ρga (B /L) Dynamometer (A=.cm) (a=.cm) Dynamometer (A=.5cm) (a=.5cm) Wave Wave Analysis (A=.cm) (a=.cm) Wave Wave Analysis (A=.5cm) (a=.5cm) Superposed Superposee Wave Wave EUT EUT.5.5 λ/l The results obtained from linearly superposed waves agree very well with a dynamometer and EUT

14 Comparison of Unsteady Waves (a) Superposed Wave Superposed Wave Cos: Superposed Sin: Superposed - - Measured (b) Measured Wave in Motion Wave Free in (amax=.cm) Motion Free (A=. cm) The wave profile measured at A=.cm The wave profile measured at is similar to superpose A=.5cm is slightly different in wave. - the fore-front part from - superposed wave. (c) Measured Wave in Motion Free (A=.5 cm) Measured Wave in Motion Free (amax=.5cm)

15 Comparison of Unsteady Waves (a) Superposed Wave Cos: Superposed Sin: Superposed wave and A=.5cm - is - (b) Measured Wave in Motion Free (A=. cm) Wave profile measured at A=.cm is different Short-wavelength component in the fore-front part can be seen clearly in from the superposed superposed waves but cannot in the measured waves at more different than A=.5cm - - A=.cm. (c) Measured Wave in Motion Free (A=.5 cm)

16 Decomposed Unsteady Waves Fourier transform of unsteady waves Inverse Fourier transform where The range of wavenumber of unsteady waves extracted

17 Decomposed Unsteady Waves The range of the wavenumber of unsteady waves decomposed The case of

18 Decomposed Unsteady Waves (a) Superposed Wave (<k<k ) - - Superposed wave - (b) Superposed Wave (k <k<) - The fore-front part of - - the wave contains of - various wavenumber (c) Superposed Wave (<k<k c ) components - - Large wavenumber components play an important role in accounting for larger magnitude of the wave in the wave in the fore-front part. - - (d) Superposed Wave (k c <k<5)

19 Decomposed Unsteady Waves (a) Measured Wave in Motion Free(<k<k A=.5cm) - - (b) Measured Wave in Motion Free(k <k< A=.5cm) - - Measured wave at A=.5cm - The components of - large wavenumbers cannot be seen in the fore-front part. (c) Measured Wave in Motion Free(<k<k c A=.5cm) Disappearance of large wavenumber components is influential in discrepancy of the estimation of the added resistance. (d)measured Wave in Motion Free(k c <k<5 A=.5cm)

20 Conclusions Validity of linear superposition of the wave was confirmed. When the ship motions become large near the resonance, a large discrepancy between results of the added resistance obtained by a dynamometer and through unsteady wave analysis are seen. The discrepancy increases as amplitude of incident wave is large, which implies that the nonlinearity with respect to the amplitude of incident wave exists. The difference in the fore-front part of wave profiles is influential in the discrepancy of the estimation of the added resistance. The fore-front part of the wave consists of various wavenumber components. Large wavenumber components play an important role in accounting for larger magnitude of the wave in the fore-front part. Large wavenumber components is key to accurate estimation of the added resistance.

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22 Comparison of Steady Waves.4 Kelvin Wave Measured Steady Wave in Motion free a=. cm Measured Steady Wave in Motion free a=.5 cm

23 Comparison of Steady Waves.4 Kelvin Wave Measured Steady Wave in Motion free a=. cm Measured Steady Wave in Motion free a=.5 cm

24 Comparison of Unsteady Waves (a) Superposed Wave Cos: Superposed Sin: Superposed (b) Measured Wave in Motion Free (a=. cm) - - (c) Measured Wave in Motion Free (a=.5 cm)

25 Comparison of Unsteady Waves (a) Superposed Wave Superposed Wave Cos: Superposed Sin: Superposed (b) Measured Wave in Motion Free (a=. cm) Measured Wave in Motion Free (amax=.cm) - - Measured Wave in Motion Free (amax=.5cm) (c) Measured Wave in Motion Free (a=.5 cm)

26 Decomposed Unsteady Waves K K K K

27 Decomposed Unsteady Waves (a) Measured Wave in Motion Free(a=.cm K) - - (b) Measured Wave in Motion Free(a=.cm K) (c) Measured Wave in Motion Free(a=.cm K) (d)measured Wave in Motion Free(a=.cm K4)

28 Surge a max =.cm a max =.5cm Heave a max =.cm a max =.5cm Pitch a max =.cm a max =.5cm ξ /a ξ /a ξ 5 /k a λ/l.5.5 λ/l.5.5 λ/l ε ε ε λ/l λ/l λ/l