NUMERICAL PREDICTION ON VIBRATION AND NOISE REDUCTION EFFECTS OF PROPELLER BOSS CAP FINS ON A PROPULSION SYSTEM

To investigate the vibration and noise reduction effects of Propeller Boss Cap Fins (PBCF), the Large Eddy Simulation (LES) method has been employed in the noise performance estimation of a propeller-rudder system. The hydrodynamic performance of the propulsion system is predicted after the grid independence analysis, then further compared with the result of cavitation tunnel experiment. The acoustic simulation is performed based on Ffowcs Williams and Hawkings (FW-H) equation. After the observation of the hydrodynamic noise performance changes, the forces of propulsion systems and noise reduction effects of PBCF are analyzed. It’s indicated from the research results that PBCF can not only improve the propulsion efficiency, but also reduce the radiation noise intensity significantly. Meanwhile, the lateral force fluctuation of hub cap can be decreased by suppressing the vibration of propeller shaft. In addition, the time-averaged value of the rudder lateral force has been decreased by about 15.5%. It has been well known that the radiation of propulsion noise is directional. Accordingly, it is found that the noise reduction effects due to PBCF are also directional, which is the most noticeable in the axial direction.


Introduction
Plenty of ship Energy Saving Devices (ESDs) can reduce the propulsion vibration and noise. In 1988, Ouchi first introduced the Propeller Boss Cap Fins (PBCF) to recovery the rotational energy from the hub vortex and increase the propulsive efficiency. PBCF can produce a torque behind the propeller blades, which offsets a part of the propeller torque. The hub vortex intensity is reduced, and the cavitation performance is improved [1,2].
There are some earlier researches about PBCF. Ouchi and Tamashima [3] carried out some systematic investigations on PBCF. The results showed that PBCF was an excellent ESD which could reduce the hub vortex and increase the propulsive efficiency with a minor improvement. Then Ouchi et al. [4] carried out an experimental research on the noise reduction effect of PBCF under the cavitation pattern. PBCF could reduce the propulsive Sound Pressure 3 force are observed with and without PBCF, and the influence on the whole propulsion system is analyzed according to the change of the flow field. Finally, the noise and vibration reduction mechanism of PBCF has been studied.

Turbulence model
Motion-compliant continuity and momentum conservation equations of the LES method for incompressible Newtonian fluid motion are as follows.
where ui and uj are the time-average values (i, j = 1,2,3) of the velocity component, p is the time-average pressure, the overline represents the physical quantity after filtering, ρ is the fluid density which is a fixed value, ν is the kinematical viscosity coefficient, and [24,25,26]. This study applied LES method to predict the hydrodynamic performance. The boxy filtering function was employed in all the simulations. Firstly, SST K-ω model was applied to the steady performance simulation until the iteration convergence. Then the turbulence model was replaced as LES with the Smargorinsky-Lily mode, and the unsteady force and flow field were simulated [27,28,29]. In all the simulations which were run by using the Pressure-Based solver [30,31], the SIMPLEC algorithm was applied for Pressure-Velocity Coupling, with Least Squares Cell Based for gradient discretization, with PRESTO for pressure discretization, and with Bounded Central Differencing for momentum discretization. Sliding mesh technique was applied to the rotation motion simulation. To observe the noise performance, the time step was set as 10 -5 s and 20 iterations were proceeded in each step [32,33].

Hydrodynamic performance coefficients
The hydrodynamic coefficients of the propulsion system were calculated according to the following equations.
where Ka, Kt and Kr are the thrust coefficients of entire propulsion system, propeller with or without PBCF and rudder, Kq is the torque coefficient of propeller, η and ηa are the efficiencies of propulsion systems without rudder and with rudder, TP and TR represent the thrust generated by propeller with or without PBCF and rudder, Q is the torque of propeller, ρ is the fluid density, Va is the flow speed in the tunnel, n is propeller rotational speed, D is the diameter of propeller disk, and J is the advance coefficient. The fluid in the tunnel is incompressible, and ρ is a fixed value.

Acoustic model
After completion of the flow field calculation, Ffowcs Williams and Hawkings (FW-H) equation based on LES is added into the acoustic simulation [33,34], of which the reference Where c0 and ρ0 are the reference sound speed and medium density, ρ is fluid density under turbulence, p' = p-p0 is sound pressure of disturbed flow field,  ij represents Kronecker product function, δ (f) and H (f) represent Dirac delta function and Heaviside function, f represents wall function, un stands for flow velocity component in xi direction, vn stands for normal velocity component on the wall, and Tij is the Lighthill stress tensor.
In addition, SPL distance attenuation formula is as follows [35].
where L0 and r0 are the total SPL and the sound source distance of the known position respectively, L and r are the total SPL and the sound source distance of the calculation position.   Hence there is no blockage effect to be worried. The flow velocity range in the tunnel is from 3m/s to 20 m/s, and the turbulence intensity in present tunnel is less than 2%. The propulsive thrust and torque are measured by the rotary dynamometer, and the rudder force is obtained by the force balance showed in Fig.1 (c).

Introduction to cavitation tunnel
3.2 Major model parameters and test conditions A propulsion system model of a certain container ship is shown in Fig.2. The system includes a 5-blade propeller, a 5-blade PBCF and a rudder. The diameter of the propeller and PBCF is 250mm and 70mm, respectively. The pitch ratio of the propeller is 0.9510. The section of the rudder is NACA0018, and the distance between the rudder shaft and the hub end is 140mm. Experimental pictures are given in Fig.3. The propulsion system without PBCF was installed. The hydrodynamic forces were measured, which included propulsive thrust and torque. The force on the rudder was obtained separately by a force balance. Under atmospheric pressure, the advance coefficient J of the propulsion ranged from 0.45 to 1.00, which increased 0.05 in each test. The flow speed Va in the tunnel was fixed 4m/s. J was changed by the propeller rotational speed increase. After all the above tests finished, the hub cap was replaced by PBCF and the former measurements were repeated exactly.

Numerical modelling
The hydrodynamic performance predictions were proceeded by applying the FLUENT (Version 19.2) solution technique. The establishment process of the numerical model is described as below.
The computational flow field of the propulsion was divided into three parts by two cylinders, and the propeller disk center was placed at the coordinate origin. The division of domains is shown in Fig.4a. Domain 1 and Domain 2 were where the propeller and rudder are Yu Sun, Tiecheng Wu, Numerical Prediction on Vibration and Noise Reduction Effects Yumin Su, Huanghua Peng of Propeller Boss Cap Fins on a Propulsion System 6 located. The grids in the two domains were unstructured tetrahedral ones and the grids of thin edges were refined. Domain 3 involved the rest of the flow field and was filled with structured hexahedral grids. The diameter of the cylinder field was 3.2 times propeller disk diameter D.
The distances from the propeller disk to the inlet and the outlet were 3.2D and 8D, separately. Therefore, the flow field could be fully developed. The fluid velocity Va and the advance coefficient J were set according to the experimental scheme. At high Reynolds numbers, layer meshes are needed for turbulence prediction [36,37]. Therefore, adaptive grids with prismatic layer mesh are generated in this work. To make sure y + values less than 1, the thickness of the layer mesh stick to the model was 10 -5 D with a stretching factor of 1.10. The coarse, medium and fine meshing schemes were created to validate the grid independence. The grid numbers of the three schemes were 4.95 million, 8.23 million and 13.01 million, respectively. The medium meshing scheme is shown in Fig.4. The results of three meshing schemes given in Table 1 coincide reasonably well, so the increased mesh density had little impact on the propulsive efficiency results. Therefore, the scheme of the medium grid was applied to the hydrodynamic predictions.

Validation of acoustic model
According to the FW-H equation, the acoustic simulation is carried out on the basis of flow field distribution [38]. The investigation on the flow field of NACA airfoil are very systematic. Therefore, the hydrodynamic noise performance is verified by the NACA0018 airfoil simulation [32]. According to the computational model [32], the domain and mesh were established. The airfoil chord length was C (0.08m), and its span length was 2C. To make sure the flow field fully developed, the distance between the inlet and the leading edge was 5C, the distance between the inlet and the leading edge was 10C, the distance between the upper and lower sides was 5C，and the distance between the right and left sides was as much as the span length. The settings of boundary conditions are shown in Fig.5. The inlet was set as the velocity inlet, and the velocity of flow field was 30m/s. The outlet was set as pressure outlet, the right and left sides were set as the periodic boundary, and the rest surfaces and boundaries were set as the wall. At this time, the Reynolds number was 1.6×10 5 . To keep the y + under 1, the thickness of the first prismatic layer mesh was set to 10 -5 m with a stretching factor of 1.10. The reference sound pressure is 2×10 -5 Pa and the sound speed is 340m/s in the air. The rest settings were as same as the calculation model of the propulsion system. After the simulations, the pressure distributions can be obtained. According to Equation 6, the pressure coefficient Cp along the chord direction is calculated and compared with the reference result.
where P is the pressure on the airfoil surface, ρair is the air density, V is the flow speed.  The pressure distribution and the flow separation position at attack angles of 3° and 6° are given in Fig.6 and Table 2. According to the contrast result, the flow field prediction is considered reliable. Depending on the way of noise performance calculation [32], the SPL 10m away from the airfoil was calculated. Then the data was transformed to the SPL 0.095m away from the airfoil by noise attenuation formula. The contrast result is given in Fig.7. It is indicated that the radiated noise intensity of NACA0018 airfoil is directional, of which the SPL in the chord direction is the smallest, and the SPL perpendicular to the chord direction is the largest. The total SPLs at different angles are in the shape of "8". The calculation result of sound field distribution agrees well with that in the literature. Meanwhile, the error is within the acceptable range. Therefore, the reliability of the noise prediction method is verified.

Hydrodynamic performance coefficients
The calculated and experimental values of Ka, KQ and ηa are plotted and compared. The results are presented in Fig.8. In the following figures, the suffixes "EFD" and "CFD" stand for experimental values and calculated values separately, "A" and "B" represent the propellerrudder system and the propeller-PBCF-rudder system. According to the comparison results, the error of hydrodynamic performance coefficients at J=0.8 is within 3%, and the calculation models of this work are considered reliable. The calculation results indicate that the propulsion

Lateral forces with and without PBCF
The pressure fluctuation on the blade, fin and rudder surface can cause the vibration of the propeller shaft and the rudder shaft. By observing the fluctuation of lateral force Fz, the vibration reduction effect of PBCF is analyzed. The lateral force direction is shown in Fig.9.  Fig. 10. It is found that there is basically no influence of PBCF on the blade and hub parts. By contrast, a significant change of the lateral force fluctuation on fins and hub cap has taken place. With the PBCF installed, the fluctuation amplitude of the hub cap is reduced, and the force period on the hub and fins becomes short. This weakened fluctuation intensity is beneficial to the vibration reduction of the propeller shaft. Meanwhile, due to the asymmetry along the rudder shaft, the rudder lateral force of the upper half is greater than the lower half. Therefore, there is a nonnegligible resultant force in the Z direction. In many cases, the ship's course will be maintained by adjusting the rudder angle during the voyage, and it will cause partial sacrifice of the propulsion efficiency. After the installation of PBCF, there is no obvious change of the lateral force fluctuation, but the average force reduces from -9.7N to -8.2N. With the lateral force reduced by 15.5%.

Noise reduction effect analysis of PBCF
After the contrast result of hydrodynamic performance obtained, the noise performance (J=0.8) of the two systems is contrasted. The SPL of different angles at r=10m as shown in Fig.11 is monitored, which are in the horizontal plane passing through the origin of the propeller disk. The consequence of noise performance is given in Fig.12 and Table 3. In the following results, 0°and 180°are located in the downstream and upstream directions.  The contrast results indicate that the SPL in the axial direction is about 2.2dB higher than that in the radial direction. Accordingly, the noise reduction effect is also directional. The noise reduction effect in the axial direction is more significant, where the SPL can be reduced by more 0.56dB. The SPL spectrums (J=0.8) in the axial and radial directions are displayed in Fig.12.  The result of SPL spectrums shows that the SPL in the axial direction is as most as 20dB greater than that in the radial direction in the frequency range of less than 1000Hz. Then the gap between them is gradually disappeared beyond that range. After the installation of PBCF, SPL of the propulsion system is reduced. While there is little impact of PBCF on the SPL peaks Yu Sun, Tiecheng Wu, Numerical Prediction on Vibration and Noise Reduction Effects Yumin Su, Huanghua Peng of Propeller Boss Cap Fins on a Propulsion System 12 at high frequencies, and the low frequency noise in the axial direction accounts for a larger proportion of the total SPL. Therefore, the noise reduction effect of PBCF in the axial direction is more obvious. In addition, the propeller wake flows around the rudder, and the accelerated rotation wake enhances its turbulent intensity. The changing flow field makes the SPL increased at high frequencies. The noise intensity of rudder becomes the major part of the total noise intensity at high frequencies. Therefore, the SPL spectrum of the propeller-rudder system is different from the propeller SPL spectrum.

Flow field analysis
The visual output of the CFD method is shown from Fig.13 to Fig.17. According to the flow field change of propulsion systems, the vibration and noise reduction mechanism of PBCF is analyzed in this section.  The velocity distribution (J=0.8) behind the propeller is illustrated in Fig.13, in which the contours show the axial velocity magnitudes. It is indicated that the velocity distribution at the centre of the section changes significantly. After the installation of PBCF, the axial velocity magnitude of the propeller wake increases. The magnitude of circumferential velocity behind PBCF reduces accordingly. The change of the flow field makes the energy of the hub vortex recycled. Therefore, the propulsive efficiency is enhanced. What's more, the wake velocity variation weakens the rudder lateral force magnitude due to the asymmetry and increases the course stability of a ship.  The vortex structures (Q=5000) generated by the rotation of the propeller and PBCF are shown in Fig.14. In the tunnel, there is no cavitation at atmospheric pressure, and the cavitation grows by depressurizing the fluid pressure. The cavitation only represents the vortex intensity distribution in the tests. In the simulation cases, the vortex intensity at atmospheric pressure is analyzed. All the noises and pulsations are caused by the vortex intensity change. By contrast, it is found that the existence of PBCF has little effect on the tip vortex intensity of the propeller blades. Meanwhile the vortex behind the hub cap is reduced significantly, which makes the hub vortex weakened and accelerates the diffusion. In addition, a small amount of the tip vortex is generated by PBCF, but the influence on the propulsion system is not obvious. The fin tip vortex goes disappeared with the development of the wake.
In order to examine the flow field distribution of propulsion system, two planes are intercepted at different positions. The plane A (x=0.3D) is located before the rudder, and the plane B (x= 1.2D) is located behind the rudder. The axial positions of the planes are given in Fig.15. The vorticity distribution of the propulsion systems is shown in Fig. 16 and Fig.17. At the Plane A, the hub vortex intensity is reduced significantly by PBCF, and the vortex intensity of fin tips increases slightly. After the flow arriving at the Plane B, the contours of hub vortex expand and the intensity decreases, which means the vortex diffusion accelerated. The acoustic performance is related to the vortex distribution. The large-scale and small-scale vortex reductions result in the low and high frequency noise decreases, respectively. Thus, the flow wake change is coincided with the noise reduction effect of the PBCF.

Conclusions
The noise and vibration reduction effects of PBCF have been numerically investigated based on LES method and the FW-H equation. The numerical model is firstly verified by the grid convergence study, and further validated by the experimental data.
At the design advance coefficient (J=0.8), the efficiency error is less than 3%, which is within an acceptable range. Therefore, the numerical model is appropriate to evaluate the hydrodynamic performance of the propulsion systems. The calculation results show that the propulsion efficiency with PBCF is higher. The improvement of propulsive efficiency of PBCF is about 1.47% when J=0. 8. In addition, the installation of PBCF can also reduce the lateral force fluctuation of the propeller shaft. By comparison, there is no significant change of the lateral force fluctuation amplitude of the rudder shaft, while the average value of lateral force is reduced by 15.5%.
The installation of PBCF can reduce the hub vortex intensity, and this can help to accelerate its diffusion. The changes of the flow field make the SPL of the propulsion system reduced by as much as 1.51 dB. What's more, the sound pressure level in the axial direction is about 2.2 dB higher than that in the radial direction. Accordingly, the noise reduction effect of PBCF is also directional, and the sound pressure level in the axial direction can be decreased by more 0.56 dB. Overall, it can be seen that PBCF is more than an energy saving device. Its function of noise reduction should be also very attractive. Since it is difficult to design and conduct such an experiment to measure the noise level, only the hydrodynamic performance experiment has been carried out in the cavitation tunnel. The future work may focus on how to design a scheme of the noise performance measurement.