Validation of propeller-induced pressure pulses on a ship hull
6.2 Pressure pulses induced by P1356 propeller in non-uniform inow on a ship hullnon-uniform inow on a ship hull
In this section the pressure pulses induced by the propeller P1356 on a part of the ship hull located above the propeller are analysed. The propeller flow is simulated subject to a non-uniform inflow. For this two different ship wake fields are used, namely the model wake field DM40M and the full scale wake field DM40S (s. Figure 5.27). The different wake fields are used in order to detect their influence on the magnitude of the pressure pulses.
The surface of the ship hull is discretised by 990 equilateral panels and the pressure pulses are evaluated on five monitoring points on the hull (s. Figure 6.7). The pressure values are observed on the panels of the hull that are arranged at the nearest position to the co-ordinates of the monitoring points in the experiments (s. Table 6.3). For points 1, 2 and 5 no panels are located directly on the centre line. Instead, the average value of the two nearest panels is calculated (s. Figure 6.7).
Figure 6.7: Location of the monitoring points on the ship hull
Nr. x [m] y [m] z [m]
1 0.055 0 0.177
2 0.0 0 0.182
3 0.0 0.051 0.187 4 0.0 -0.051 0.187
5 -0.055 0 0.191
Table 6.3: Coordinates of the monitoring points on the ship hull
The input data used in the simulations is summarised in Table 6.4. The flow is simulated in model scale under non-cavitating and cavitating conditions. For both wake fields the same rotational speed and cavitation numbers are used. The ship speedVship is adjusted
Chapter 6. Validation of propeller-induced pressure pulses on a ship hull
in the simulations in such a way that the mean thrust coefficient ¯kt measured in experi-ments for the non-cavitating case is obtained. The wake is aligned according to the axial wake alignment model since the wake deformation of a propeller subject to a non-uniform inflow has a significant influence on the magnitude of the pressure fluctuations.
Characteristics Notation DM40M DM40S Unit
Rotation speed nmodel 30 30 1/s
Thrust coecient ¯kt 0.170 0.168
-Cavitation number σn0.8R 1.783/1.486/1.382 1.783/1.486/1.382 -Table 6.4: Input data for the pressure pulses calculations with P1356 propeller in inhomogeneous inow
Firstly, the results of the non-cavitating propeller flow are presented. Figures 6.8 and 6.9 show the first, second and third harmonics obtained by the Fourier analysis of the pres-sure pulses for the monitoring points 1 to 5. The ith harmonic of the pressure pulses is given in the unit kPa and is denoted byp[i]. The bars in the graphs illustrate the measured data taken from the report (s. Heinke and Jaksic, 2003) and the results calculated by the numerical methodpanMARE with the model and full scale wake field.
All values on the bar diagrams are presented in model scale. No significant influence of the different wake fields can be identified. Independent of the wake field, the ampli-tudes of the second and third harmonics are very low. The amplitude of the first harmonic reaches its maximal value in front and above the propeller centre (points 1 and 2) and achieve approximately 0.74kPa with the wake field DM40M and 0.68kPa with the wake field DM40S. The calculated results are in good agreement with the measured values for all orders. Only the amplitude obtained with the wake field DM40M for the fifth point is considerably underestimated bypanMARE compared to the measurements.
0
Point1 Point2 Point5
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003))panMARE, non-cavitating
0
Point3 Point2 Point4
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003))panMARE, non-cavitating
Figure 6.8: Pressure pulses calculated for the non-cavitating case with ship wake eld DM40M
Chapter 6. Validation of propeller-induced pressure pulses on a ship hull
0 0.2 0.4 0.6 0.8 1 1.2
p[i][kPa]
Point1 Point2 Point5
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003))panMARE, non-cavitating
0 0.2 0.4 0.6 0.8 1 1.2
p[i][kPa]
Point3 Point2 Point4
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003))panMARE, non-cavitating
Figure 6.9: Pressure pulses calculated for the non-cavitating case with ship wake eld DM40S
σn= 1.783 σn= 1.486 σn= 1.382
Figure 6.10: Sheet cavity extents at the angular position θ = 0◦ calculated by panMARE with dierent cavitation numbers with the ship wake eld DM40M
σn = 1.783 σn= 1.486 σn = 1.382
Figure 6.11: Sheet cavity extents at the angular position θ = 0◦ calculated by panMARE with dierent cavitation numbers with the ship wake eld DM40S
Now the results of the cavitating propeller flow with three different cavitation numbers are demonstrated. Figures 6.10 and 6.11 show the sheet cavity shapes on the key blade of the propeller calculated with the model and full scale wake field, respectively. The
Chapter 6. Validation of propeller-induced pressure pulses on a ship hull
Point1 Point2 Point5
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.486 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.783= 1.486= 1.783
0
Point3 Point2 Point4
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.486 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.783= 1.486= 1.783
Figure 6.12: Pressure pulses calculated for the cavitation numbers σn0.8R = 1.486 and σn0.8R = 1.783 with the ship wake eld DM40M
0
Point1 Point2 Point5
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.382 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.486= 1.382= 1.486
0
Point3 Point2 Point4
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.382 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.486= 1.382= 1.486
Figure 6.13: Pressure pulses calculated for the cavitation numbers σn0.8R = 1.382 and σn0.8R = 1.486 with the ship wake eld DM40M
key blade is illustrated at the angular position of zero degree. It can be observed that the cavitation number has a significant impact on the sheet cavity extent and thickness on the blade. With the wake field DM40M a more extensive cavity thickness and length can be observed than with the wake field DM40S.
Figures 6.12 and 6.13 illustrate the first, second and third harmonics obtained by the Fourier analysis of the pressure pulses for the monitoring points 1 to 5 with the wake field DM40M. The values are presented in model scale and show the results for all three cavitation numbers. The pressure pulses rise significantly with the occurrence of sheet cavitation. For the cavitation number σn = 1.382 the first harmonic is 4.2 times higher than that obtained in the non-cavitating case. By reducing the cavitation number (which is equivalent to an increase of the cavity thickness and volume) the first harmonic increases.
Chapter 6. Validation of propeller-induced pressure pulses on a ship hull
Point1 Point2 Point5
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.486 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.783= 1.486= 1.783
0
Point3 Point2 Point4
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.486 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.783= 1.486= 1.783
Figure 6.14: Pressure pulses calculated for the cavitation numbers σn0.8R = 1.486 and σn0.8R= 1.783 with the ship wake eld DM40S
0
Point1 Point2 Point5
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.382 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.486= 1.382= 1.486
0
Point3 Point2 Point4
i= 1 i= 2 i= 3 i= 1 i= 2 i= 3 i= 1 i= 2 i= 3
measurements (from Heinke and Jaksis (2003)),σn= 1.382 measurements (from Heinke and Jaksis (2003)),panMARE,panMARE,σσσnnn= 1.486= 1.382= 1.486
Figure 6.15: Pressure pulses calculated for the cavitation numbers σn0.8R = 1.382 and σn0.8R= 1.486 with the ship wake eld DM40S
The measurements with the model wake field DM40M show a very high first harmonic.
The maximal amplitudes occur above the propeller (point 2), at the star board side (point 4) and behind the propeller (point 5). The measured values show that cavitation also has a considerable influence on the second and third harmonics. In contrast to the first har-monics, a decrease of the cavitation number does not significantly increase the second and third harmonics. The simulation results coincide very well with the measured values for the first harmonic for the points 1-4. As for the non-cavitating case, the first harmonic cal-culated for the fifth point is underestimated. The influence of the cavitation number on the magnitude of the pressure pulses is well reproduced by the simulation tool. However, the calculated second and third harmonics are underestimated compared to the measurements.
This can be explained by the fact that the tangential and radial velocity components of the
Chapter 6. Validation of propeller-induced pressure pulses on a ship hull
wake fields were neglected in the simulations. Additionally, tip vortex cavitation is said to be relevant for the determination of the pressure pulses and is observed in experiments with both wake fields (s. Heinke and Jaksic, 2003, p. 1.36). In the simulations tip vortex cavitation was not calculated.
Figures 6.14 and 6.15 illustrate the calculated and measured first, second and third har-monics of the pressure fluctuations obtained with the full scale wake field DM40S. The measurements show very high second and third harmonics, which result from the strong unsteady cavitation patterns. According to Heinke and Jaksic (2003, p. 1.33), sheet cav-itation is more extensive with the wake field DM40M but it fluctuates stronger with the wake field DM40S, which leads to higher second and third harmonics. The higher fluctua-tion of cavitafluctua-tion is a consequence of the tangential and radial velocity components of the wake field DM40S (s. Heinke and Jaksic, 2003, p. 1.33). In the simulations these velocity components were neglected. Thus, the second and third harmonics are underestimated by panMARE. Nevertheless, the qualitative tendencies of the second and third harmon-ics are captured correctly. In presence of sheet cavitation the magnitude of the pressure fluctuations increases. For monitoring point 2 and cavitation numbers σn = 1.783 and σn = 1.486the calculated first harmonics are overestimated. For the remaining points the agreement of the calculated and measured first harmonics is satisfying. The magnitude of the first harmonic with the wake field DM40M is higher than that obtained with the wake field DM40S. This observation applies to measured and calculated data. The higher amplitudes of the first order can be explained by the wider wake peak of the model wake field, which results in a higher sheet cavity thickness (s. Figures 6.10 and 6.11).
This simulation study indicates that the influence of the non-uniform inflow to the pro-peller is low when no cavitation occurs on the blades. When cavitation occurs, the influ-ence of the non-uniform inflow increases. The pulsation of cavitation directly correlates with the heterogeneity of the wake field, which leads to higher pressure pulses. The first harmonic of the pressure pulses can be reproduced by the underlying numerical method with a satisfying level of accuracy. The second and third harmonics of the pressure pulses differ quantitatively from the experimental data, even though the qualitative tendencies are captured correctly. In future studies the effect of the tangential and radial velocity components of the wake field on the sheet cavitation patterns and on the magnitude of the second and higher harmonics should be examined. Additionally, the influence of tip vortex cavitation should be included in the analysis.