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Experimental and numerical study on underwater radiated noise of AUV
Ocean Engineering 201 (2020) 107111
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Experimental and numerical study on underwater radiated noise of AUV Changli Yu a, b, Renzhi Wang b, Xingming Zhang b, *, Yueming Li a a b
Science and Technology on Underwater Vehicle Technology, Harbin Engineering University, Harbin, No. 145, Nantong Street, Harbin, 150001, PR China School of Naval Architecture and Ocean Engineering, Harbin Institute of Technology, Weihai, No.2 West Wenhua Road, Weihai, 264200, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: AUV Lighthill equation Propeller CFD Underwater radiated noise
The wide range use of marine equipment has greatly increased the underwater radiated noise (URN) level, creating more threat to marine life. Autonomous underwater vehicle is one of the solutions to reduce the use of large marine equipment and then decrease the noise. Aiming at the noise control of AUV, this study conducted a far field noise measurement experiment on an AUV working on 10 different conditions, which is rarely measured. The hybrid method, predicting the noise with Lighthill equation based on unsteady flow field data from CFD calculation, is adopted. The results from experiment and simulation indicates that the simulative results are in good agreements with experimental results and the propeller will still generate noise due to the irregular vi bration of the propeller, which is about 3–5 dB. With the occurrence of cavitation, the sound pressure level (SPL) increases sharply, and there will be a wide gap between experimental and simulative noise data, owing to the single phase considered in the Lighthill equation. The analysis of the experimental and simulative results highlights the existence of structure excitation noise, ranging from 300 to 500 Hz and the shortcoming of noise prediction of the hybrid method under cavitation stage.
1. Introduction The increasing scale of general shipping activities and one of the emissions, underwater radiated noise (URN), have been under the spotlight (Hildebrand, 2009). Due to the increasing scale of marine equipment, noise level in seas, especially near harbors, has increased constantly and interfered with the daily life of mammals, including the communication, hunting and breeding (Merchant et al., 2014; Madsen, 2005). Recent studies have shown that noise also influences fish and invertebrates when courting and laying eggs (Julia et al., 2016; Matthew et al., 2013). In addition to the protection of marine life, marine equipment used in military itself has stricter requirements for noise control. Classifying the sonar target based on its acoustic signal char acteristics is considered to be an effective sonar application method. On the one hand, oceanography (Carral et al., 2018; Martinelli et al., 2016), sonar modeling and engineering (Mohammad and Hassan, 2019; �s et al., 2017; Abraham, 2008) and also statistical processing (Hurto Miles et al., 2006) are taken into account to improve the accuracy of classification. On the other hand, random methods, including artificial intelligence (AI) methods (Najafzadeh et al., 2016a; Najafzadeh et al., 2016b; Najafzadeh and Sarkamaryan, 2018), have resulted in significant improvements in classification efficiency. More and more advanced
sonar technology poses a more serious challenge to the survivability of autonomous underwater vehicles in the execution of missions. There fore, the URN control for marine equipment should be put on the agenda as soon as possible, considering both military and ecological aspects. The noise measurement of ship propeller, as an indicator of noise prediction accuracy, is the basis of noise analysis. There has been a field noise measurement to an LNG carrier under the speed of 9 and 19knots (Kellett et al., 2013). The comparison between experimental and simu lative results revealed that while providing more generally accurate results, the rotating mesh didn’t provide the same realistic details of the spectral levels as the moving frame of reference method. Although the field noise test can capture the real noise of ship, the test costs a lot and there have been many interference factors. In order to provide invalu able underwater radiated noise (URN) data of a full-scale vessel, extrapolated URN data based on the tunnel tests was compared with the data obtained from the full-scale trials with The Princess Royal (Batuhan et al., 2016). The research proves that the medium size facilities using dummy-hull models with wake screens can still provide a very useful means for the URN investigations. The noise of ship is made up of structural noise, hydrodynamic noise and propeller noise. As for AUV, motor drivers and relatively low speeds makes that propeller noise has a higher proportion. The noise
* Corresponding author. E-mail address: [email protected] (X. Zhang). https://doi.org/10.1016/j.oceaneng.2020.107111 Received 7 October 2019; Received in revised form 17 December 2019; Accepted 10 February 2020 Available online 5 March 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved.
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the flow field simulation. The simulation combining Reynolds Average Navier-Stokes (RANS) turbulence model with the turbulence viscosity correction and the Zwart cavitation model captured periodic cavitation development (Wu et al., 2018). There has also been the simulation using DES simulation and FW-H equation on a normal Pumpjet propulsor (PJP) model and a PJP model with the sawtooth duct (Denghui et al, 2019). The research predicted the spectrum form 10 Hz–5000 Hz. The hybrid method of noise prediction has been adopted in this study to enable the numerical prediction of radiated underwater noise from the AUV under investigation. As stated above, existing simulation and experiment tend to measure and predict the noise of ship and propeller separately, in terms of high cost and model size. At present, there is no scientific prediction method for AUV underwater noise that has considered the influence of hull, and there is no corresponding experiment to provide reference. The study aims to design a numerical noise prediction model for an AUV in design stage and conducted an open water test in a comprehensive test pool for reference. Applying the field noise measurement equipment, 10 rota tional speed conditions were tested and recorded for the noise data, which were also simulated through acoustic analogy theory. Since nu merical investigations on high frequency continuous spectrum are not taken into account, only low frequency spectrum will be analyzed. This paper intends to demonstrate results from field test and simulation.
Fig. 1. Layout of the comprehensive test pool.
2. Experiment validation data
Table 1 Parameters of AUV and propeller. AUV
The noise measurements in this study was carried out in a compre hensive test pool (30 m � 50 m � 11 m) of the Key Laboratory of Un derwater Robotics in Harbin Engineering University (HEU). The measured acoustic spectra were then used for validating the numerically predicted values, as well as to indicate the relative accuracy of different rotational speeds. The large-scale comprehensive test pool was design for model test research on ship-wave resistance and maneuverability, maneuverability in waves, marine engineering. The test pool was upgraded for the noise measurements maintaining the ability of wave elimination, as shown in Fig. 1. The test area is rectangular and spans a small crane above. The hydrophone, Bruel and Kjaer Type 8100, was installed in the far field of the pool, 20 m away from the AUV and 5 m away from the pool wall and the pool bottom. The hydrophone is tied by a rope and immersed in water. Virtual receivers are located in the numerical model to corre spond with the Closest Point of Approach (CPA) locations seen in the field trials. The water temperature and speed of sound values used within the model is an average taken from the measured values. The field acoustic spectra were then used for validating the numerically predicted values, as well as to indicate the relative accuracy of different modelling variations. The AUV and propeller are made up of carbon fiber, which aims to work under water 2000m. The main design data is summarized in Table 1 and shape of propeller is shown in Fig. 2. The two ends of the AUV parallel middle body are equipped with two hooks for crane lifting. The AUV, combined with the propeller, is located in the center of the pool, with a depth of 5 m. The background noise was recorded at first in order to compare the exact noise while AUV is working. Both the background noise and signal from working AUV were processed using the fast Fourier transform (FFT) technique and then the signal ampli tudes on corresponding frequencies were derived. This experiment is different from previous experiments using similar laws and an AUV with a depth of 2000m was tested. For the experiment performed in cavitation tunnel or circulating water channel, the back ground noise includes environmental and electrical signal noise, ma chine noise, noise caused by impellers driving water, noise from power meters and shafting, noise from the flow field, and noise caused by back pressure changing. In this experiment, no inflow was set and rotation speeds for the propeller were controlled by electronic motor. To get as much data as possible, the rotational speed of propeller varies from 100
Propeller
Essential factor
value
Essential factor
value
Length molded breadth molded depth Working depth Design speed
5.235 m 0.41 m 0.82 m 2000m 7kn
Direction Diameter (D) Blade number Design speed Hub diameter ratio
Right 0.475 m 2 1200RPM 0.294
measurement especially for propeller usually take place in cavitation tunnel in order to investigate its performance. There have been many experiments on the standard propellers under non-cavitation and cavi tation condition. The Meridian Standard propeller was tested in the Emerson Cavitation Tunnel and the flow field was filmed with high speed cameras, acquiring obvious cavitation photos (Batuhan et al., 2018). The recorded data revealed the importance of the observed instantaneous cavitation dynamics on the time pressure signals and their consequent impact in the frequency domain. With the model and pro totype noise data provide by Samsung Heavy Industries (SHI), the novel scaling law has better agreement with the prototype TVC noise mea surement than the prototype TVC noise level predicted by the modified ITTC noise estimation rule (Jisoo and Seong, 2017). In addition to the noise measurement on propellers, the comparison between ECT (Emerson Cavitation Tunnel) and UNIGE(University of Genoa) cavita tion tunnel was conducted firstly by University of Genoa, in terms of measured sound pressure levels, propeller open water performance, cavitation observations and cavitation inception characteristics (Giorgio et al., 2017). In the area of noise prediction of ship and propeller, a significant amount of recent work in this field has been focused on the application of acoustic analogy theory. The acoustic analogy theory was originally developed by Lighthill in 1952, which is called Lighthill’s Acoustic Analogy using to predict the aerodynamic noise generated by rotating bodies such as helicopter rotors and fan blades. The lighthill equation was proceeded by Ffowcs-Williams and Hawkings and developed the Ffowcs-Williams Hawkings (FW-H) equation, which considered moving boundary influence in the flow field and extend it to hydroacoustic problems. The accuracy of noise prediction of ship and propeller lays on 2
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Fig. 2. Propeller dimensions.
Fig. 3. Comprehensive test pool and Bruel & Kjae equipment.
to 1000RPM, at the step of 100RPM, making it 10 working conditions. The acquisition of background noise should be started one month before experiment. It is worth noting that when measuring the noise of ten working conditions, they are also in different time periods, so after determining the half-hour test window period of one working condition, the background noise must be in the same test window period. After the noise measurement experiment is over, firstly average the background noise measurement results during the experiment window period. Next, subtract the background noise from the noise measurement results measured in the experiment. The result is the true propeller radiated noise. The photos taken during the test are shown in the Fig. 3.
between the CFD mesh and the acoustic mesh. The last step includes the simulation of the acoustic wave propagation using the Lighthill’s acoustic analogy theory with commercial software ACTRAN that has been used in acoustic simulation (Sandboge et al., 2006; Carton de Wiart et al., 2009; Carton de Wiart et al., 2010; D�etry et al., 2010; Herrin et al., 2012, Liu et al., 2013). 3.1. Discussion of grid convergence The shear stress transport model (Menter, 1994) is employed to simulate a strong adverse pressure gradient flow field by considering the effect of wall shear in the prediction of the rotate flow. This model combines the advantages of the k and ω models and can be used to compute the flow separation region. It is one of the most advanced two-equation turbulence models, and is superior in its calculation of the viscous ambient flow field. It has also been suggested that the accuracy of results in such work might benefit form coupling with a more complex hydrodynamic solver such as the Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) solvers as opposed to a RANS-based solver.
3. Methodology The radiated noise is analyzed in three main steps and the flow di agram is shown in Fig. 4. In the first step, the flow field information, such as velocity and pressure fluctuations, are obtained through k-ω SST model (Shear Stress Transfer) with the CFD mesh. Then, noise sources are computed from the flow field information with the interpolation 3
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Fig. 4. Flow-induced noise simulation process.
Fig. 5. Blade mesh (Coarse, Medium and Fine).
Fig. 6. Dimensionless thrust and torque coefficient.
Nevertheless, providing promising results, investigation into coupling DES, LES models with the acoustic analogy equation requires finer grid and computational time. In this study, a pressure-based coupled solver is used for the governing equations of the numerical computation. Spatial discretization of the convection term is performed using a second-order upwind scheme and discretization of the dissipative term is performed
using a second-order central difference scheme (Weiss and Smith, 1995). In solving the governing equation of turbulence model above, prism layer will significantly affect the accuracy of hydrodynamic results. Therefore, for the purposes of this work, where accuracy must be balanced against run time and complexity, the k-ω based SST model is adopted and a resolution of the boundary layer of over 10 points is 4
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� 1 ∂k ∂ω ; 10 CDkω ¼ max 2ρω2 ω ∂xj ∂xj
� 10
(4)
And, μt, named eddy viscosity, is computed by:
μt ¼
ρa1 k maxða1 ω; ΩF2 Þ "
F2 ¼ tanh max
required. In order to estimate the grid convergence, three grid levels including Coarse, Medium and Fine grids validate the mesh indepen dence. The dimensionless torque coefficient and thrust coefficient of the propeller are chosen as convergence criterion. For the reason that the tested propeller is low-skew, the propeller AU5-50 is selected to perform the study of grid convergence. The comparison of CFD results between open water characteristics of propeller AU5-50 calculated by three grids are shown in Fig. 5. The results of open water characteristics calculated by the grids for propeller AU5-50 at J ¼ 0.4 is shown in Fig. 6. It can be observed from the figure that the difference between computational and standard values is small in the whole simulation range. Overall, the solution with Medium grids shows best convergence.
3.3. Lighthill’s acoustic analogy theory The sound features of the flow field is acquired through Lighthill’s acoustic analogy theory, which is derived from N-S equations (NavierStokes equations). Due to the nonlinearity and the coupling of flow and acoustics, the sound field is divided into near field and far field. The near field is the source area and the far field is the radiation area. This study assumes that flow in the radiation area has no effect on the sound feature. In this assumption, the continuity equation and the mo mentum equation are simplified and used to get the Lighthill’s acoustic analogy equation:
3.2. Governing equation
0
0
∂ρ ∂t2
The SST k-ω turbulence model solves two transport equations, one for the turbulent kinetic energy, k, and one for the turbulent frequency, ω. The stress tensor is computed from the eddy-viscosity concept. The corresponding equations of k (the turbulence kinetic energy) and ω (the specific dissipation rate) are: � � � ∂ðρkÞ ∂ ρuj k ∂ ∂k ðμ þ σk μt Þ (1) ¼ Pk β* ρωk þ þ ∂xj ∂t ∂xj ∂xj �
βρω2 þ 2ð1
F1 Þ
(6)
Where, d is the distance to the nearest wall, and Ω is the vorticity magnitude. The default values of the constants in the Eq. (5) and Eq. (6) are usually defined as follows: σk ¼ 1.0, σω2 ¼ 0.85616, β* ¼ 0.09, a1 ¼ 0.31.
Fig. 7. CFD grid.
∂ðρωÞ ∂ ρuj ω ργ ¼ Pk þ ∂t ∂xj μt � � ∂ ∂k þ ðμ þ σ k μt Þ ∂xj ∂xj
!# pffiffi 2 k 500v ; β* ωd d2 ω
(5)
0
c20 r2 ρ ¼
∂Tij ∂xi ∂xj
Where is the Lighthill’s stress tensor, which can be written as: � � 0 Tij ¼ ρvi vj τij þ δij ðp p0 Þ c20 ðρ ρ0 Þ
(7)
(8)
In resolving the equation, some assumptions are made. On the one hand, the small stress tensor is ignored according to the actual flow conditions. On the other hand, the interaction between flow and sound is ignored, so that there is no interaction between them in this paper. Ignoring the fluctuation of fluid density and pressure, the Lighthill’s 0 stress tensor is simplified as Tij ¼ ρvi vj .
ρσω2 ∂k ∂ω ω ∂xj ∂xj (2)
4. Numerical modelling set-up
Where, F1 is a harmonic function, which is written as the following formulas: ! #)4 ( " pffiffi k 500v 4ρσω2 k ; F1 ¼ tanh min max * ; 2 (3) β ωd d ω CDkω d2
4.1. CFD model setup The CFD simulation for the AUV and its underwater noise is carried out in full scale, an approach which is rarely taken. The enclosing rectangular domain, of size 30 � 50 � 10 m3 surrounds the 5.235 m hull and propeller. The centroid of the AUV coincides with that of the
Fig. 8. Acoustic analogy setting. 5
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Fig. 9. Thrust curve.
6
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Fig. 9. (continued).
stationary and rotating region. The surrounding and under surfaces are set to wall condition and up surface is set to opening condition. Mesh generation was carried out using the automatic meshing tool in ICEM CFD, resulting in a computation mesh of approximately 6.4 million cells in total; a typical Medium density grid. There is a gradually encryption of grid in the area around the hull and propeller, especially the region where the complex flow properties are appropriately captured. The grid in the aft section of the AUV and the propeller is shown in Fig. 7. The frequency ranges from 80 to 1200hz is the focus of this study. In order to ensure that results up to this value are obtained with a sufficient level of accuracy, a time-step of 0.0004 is used throughout. The maximum run-time is set to 5s and the number iteration of inner itera tions per each full iteration is limited to 10. It equates to around 125000 iterations in per simulation. A 2nd-order implicit unsteady simulation has been used, with a k-ω SST turbulence model. Thrust and torque values are also monitored for comparison. Once the unsteady calculation is over, flow field value is export for acoustic analogy calculation.
Table 2 Vapor-Water volume fraction. RPM 100 200 300 400 500 600 700 800 900 1000
Volume fraction of water
Volume fraction of vapor
Max
Min
Max
Min
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 0.96375 0.81538 0.66814 0.52202
0 0 0 0 0 0 0.03625 0.18462 0.33186 0.47798
0 0 0 0 0 0 0 0 0 0
domain. The stationary region included all elements except the propeller and enclosing cylinder which were included in the rotating region. The forward and aft faces of the enclosing cylinder, as well as its circum ference, are selected as the fluid-fluid interface, which located between 7
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Fig. 10. Noise spectrum curve.
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Fig. 10. (continued).
4.2. Acoustic analogy model setup
fmin ¼ Δf ¼
The acoustic calculation region is the same size as stated in section 2. In this study, a permeable source surface, which encloses the AUV, is placed within the flow and is used as the radiating surface for the acoustic model, rather than the propeller and hull surfaces used previ ously. The permeable surface is selected as surface source and the region surrounded by it is selected as volume source. This surface will then allow for the monopole and dipole sources from the hull and propeller surfaces to be captured, as well as the quadrupole sources within the flow, such as those arising from turbulence. The permeable surface takes the form of a cuboid, which encloses the entirety of the AUV and part of the flow. Previous study on the optimum location of the surface reveals that the location and size will not affect the results significantly. The far field of the acoustic calculation region is selected as the radiation area. The frequency range is as follows. 1 fmax ¼ 2Δt
1 NΔt
(10)
This study focuses on the range of 80–1200 Hz. According to the time step as stated in section 4.1, the maximum frequency can be predicted is 1250 Hz. In ACTRAN, the element of acoustic grid needs to satisfy the requirement that there should be at least 6 nodes in each acoustic wavelength, making the maximum size of the acoustic grid element 200 mm. The surrounding and down boundaries are selected as wall boundary and up boundary is selected as acoustic infinite boundary condition. The condition setting is shown in Fig. 8. In the noise simu lation, the boundary has been as concrete material aiming at the simu lation of reverberation. 5. Results and discussion The following sections outline the acoustic results achieved from the simulations and experiment based on different rotational speeds, and discuss the significance of these results in the context of general
(9)
9
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Fig. 11. Noise 1/3 octave curve.
recommendations for hydroacoustic modelling. The machinery noise contribution is also not accounted for in these results.
5.2. Narrowband spectral noise In Fig. 10, the blue characteristics correspond to the simulative re sults and the orange characteristics correspond to the experimental re sults. Experimental and numerical results are comparable from 80 to 1200 Hz. The results in Fig. 9 above, show that the spectral curves are close to each other between simulative and experimental results between 100–600RPM rotational speeds. At the lower frequencies, from 300 to 500 Hz, curves from experiment gives higher noise results. This may due to that low frequencies noise produced from propeller and hull vibra tion. Looking more specifically at the variations for simulation and experiment results between 100–600RPM rotational speeds, although on the frequency band the results agree well, it can be seen that there are no tonal peaks which is present in experiment results shown in simu lation results and do not replicate the spectra seen in the fields mea surements as accurately. With the rotational speed rise to 700RPM, the discrepancy between
5.1. Flow filed discussion Fig. 9 above only intercepts the stable part of the thrust curve, which includes at least 2 pulsating thrust cycle. It should be noted that there are 2 similar pulsating curves in each cycle of the thrust curve, one of which has a peak value greater than the other. This phenomenon differs from the feature of open water simulation of propeller as the research before. It indicates that there will be irregular vibration noise of pro peller in the field test and simulation. It can be seen form Table 2 that, with rotational speed rising to 700 RPM, cavitation occurs. Due to the large size of the test pool, the speed of the propeller was not clearly observed. It is foreseeable that when the speed reached 700 RPM, the feature of the spectra from experiment will be different.
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Fig. 11. (continued).
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simulative and experimental results increase. This gap in results be tween field and modelled data can be contributed to lack of represen tation of cavitation noise, as well as difficulties in recreating an accurate representation of real conditions in a mathematical model. When the governing equations switched into the governing equations for multiphase mixture and applying cavitation model, the volume fraction of vapor rises while that of liquid drops. While there is single one fluid medium considered in the calculation of the acoustic equation, which is the reason for 20–25 dB gap. In the four examples where the rotation speed is higher than 700 RPM, at higher frequencies, the spectrum curve of numerical simulation has a downward trend, but the measurement curves do not. In addition to the effects of cavitation noise, the effects of the acoustic grid scale as introduced in Section 4.2 should also be considered. Noise measurement experiments are performed under reverberation conditions, so the acoustic grid requirements for numerical simulations under the same boundary conditions are more stringent than CFD grids. From an engi neering perspective, it is necessary and economical to use the infinite element method to reduce the size of the computational domain for numerical simulation of noise. However, in this paper, the method of reducing the calculation domain is not adopted, which also brings a compromise on the size of the grid, that is, in the numerical simulation, the length of the grid is slightly increased to reduce the requirements for computer performance.
Credit author statement Changli Yu: Conceptualization, Writing - Review & Editing, Super vision, Funding acquisition. Renzhi Wang: Methodology, Software, Validation, Formal analysis, Writing - Original Draft. Xingming Zhang: Project administration, Investigation. Yueming Li: Resources, Data Curation. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The study is supported by the Research Fund from Science and Technology on Underwater Vehicle Technology (Grant No. SXJQR2017KFJJ02) and the Shandong Provincial Key Research and Development Plan (Grant No. 2019GHZ011) and (Grant No. 2017CXGC0922). The authors would like to acknowledge the projects support. References
5.3. 1/3 octave noise
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In Fig. 11, the blue characteristics correspond to the simulative re sults and the orange characteristics correspond to the experimental re sults. Experimental and numerical results are comparable up to the central frequency of 1000 Hz, with overall sound pressure level (OSPL) listed and compared. Both the shape of hydroacoustic curves is similar. Between the rotational speed in 100–600RPM, the trend of simulation results is close to experiment results. In the range of center frequency from 250 to 500HZ, experiment results are larger than simulation results clearly. The gap as mentioned indicates the influence of structure noise. When the cavitation occurs, the sound pressure level rises from high frequency to low frequency. The trend indicates that cavitation noise affects largely in high frequency and with cavitation growing, cavitation contributes largely to low frequency noise. Above a frequency of about 100 Hz the discrepancy of both results is significant, higher frequency value higher discrepancy. 6. Conclusion This study conducts a constrain model test of AUV to measure the far field noise. Meanwhile, a CFD simulation and acoustic analogy simula tion on the model of AUV under the same boundary condition is carried out. The hydrodynamic performance of AUV and the diversity between simulative and experimental results is discussed. The spectrum curve is the focus of the study. The thrust curve is selected as the main reference index of the flow field in CFD calculation. There are two thrust fluctuation curves in each cycle of the propeller, and the peak of one cycle is larger. The irregular small peaks present in each cycle mean that the propeller thus generates vibration. A noise prediction of the AUV was performed using a hybrid approach, and the noise data was included in the spectrogram, including a 1/3 octave transform. The comparison between the results of experi ment and simulation under no-cavitation conditions indicates that there is vibration noise rising from propeller and hull irregular vibration. The hybrid method shows less accuracy when the cavitation occurs, resulting from the single medium in Lighthill’s equation. Further investigation is recommended to predict the vibration noise of propeller and hull. Other than the vibration noise, the cavitation noise need to be paid more attention in the future. 12
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Ocean Engineering 201 (2020) 107111 GEP models. J. Hydroinf. 18 (5), 867–884. https://doi.org/10.2166/ hydro.2016.212. Mohammad, K., Hassan, M., 2019. Passive sonar target classification using multi-layer perceptron trained by salp swarm algorithm. Ocean Eng. 181, 98–108. https://doi. org/10.1016/j.oceaneng.2019.04.013. In press. Najafzadeh, Mohammad, Etemad-Shahidi, Amir, Lim, Siow Yong, 2016b. Scour prediction in long contractions using ANFIS and SVM. Ocean. Eng. 111, 128–135. https://doi.org/10.1016/j.oceaneng.2015.10.053. Najafzadeh, M., Sarkamaryan, S., 2018. Extraction of optimal equations for evaluation of pipeline scour depth due to currents. Proceedings of the Institution of Civil Engineers – Maritime Engineering 1–34 d. Sandboge, R., Caro, S., Ploumhans, P., Ambs, R., Schillemeit, B., Washburn, K.B., Shakib, F., 2006. Validation of a CAA formulation based on Lighthill’s Analogy using AcuSolve and ACTRAN/LA on an Idealized Automotive HVAC Blower and on an axial fan. In: 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference). https://doi.org/10.2514/6.2006-2692. Weiss, J., Smith, W., 1995. Preconditioning Applied to Variable and Constant Density Flows. Aiaa Journal 33, 2050–2057. https://doi.org/10.2514/3.12946. Wu, Qin, Huang, Biao, Wang, Guoyu, Cao, Shuliang, Zhu, Mingming, 2018. Numerical modelling of unsteady cavitation and induced noise around a marine propeller. Ocean. Eng. 160 (April), 143–155. https://doi.org/10.1016/j. oceaneng.2018.04.028.
Liu, Jiming, Zhang, Tao, Zhang, Yong’ou, 2013. Numerical study on flow-induced noise for a steam stop-valve using large eddy simulation. J. Mar. Sci. Appl. 12 (3), 351–360. https://doi.org/10.1007/s11804-013-1195-9. Madsen, P.T., 2005. Marine mammals and noise: problems with root mean square sound pressure levels for transients. J. Acoust. Soc. Am. 117 (6), 3952–3957. https://doi. org/10.1121/1.1921508. Martinelli, M., Guicciardi, S., Penna, P., Belardinelli, A., Croci, C., Domenichetti, F., Santojanni, A., Sparnocchia, S., 2016. Evaluation of the oceanographic measurement accuracy of different commercial sensors to Be used on fishing gears. Ocean. Eng. 111, 22–33. https://doi.org/10.1016/j.oceaneng.2015.10.037. Matthew, Wale A., Simpson, Stephen D., Radford, Andrew N., 2013. Noise negatively affects foraging and antipredator behaviour in shore crabs. Anim. Behav. 86 (1), 111–118. https://doi.org/10.1016/j.anbehav.2013.05.001. Menter, F.R., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 1598–1605. https://doi.org/10.2514/3.12149. Merchant, Nathan D., Pirotta, Enrico, Barton, Tim R., Thompson, Paul M., 2014. Monitoring ship noise to assess the impact of coastal developments on marine mammals. Mar. Pollut. Bull. 78 (1–2), 85–95. https://doi.org/10.1016/j. marpolbul.2013.10.058. Miles, David A., Kirk, David, Clarke, Timothy, 2006. A statistical analysis of the detection performance of a broadband splitbeam passive sonar. IEEE J. Ocean. Eng. 31 (4), 986–996. https://doi.org/10.1109/JOE.2006.880393. Najafzadeh, Mohammad, Rezaie Balf, Mohammad, Rashedi, Esmat, 2016a. Prediction of maximum scour depth around piers with debris accumulation using EPR, MT, and
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental and numerical study on underwater radiated noise of AUV Changli Yu a, b, Renzhi Wang b, Xingming Zhang b, *, Yueming Li a a b
Science and Technology on Underwater Vehicle Technology, Harbin Engineering University, Harbin, No. 145, Nantong Street, Harbin, 150001, PR China School of Naval Architecture and Ocean Engineering, Harbin Institute of Technology, Weihai, No.2 West Wenhua Road, Weihai, 264200, PR China
A R T I C L E I N F O
A B S T R A C T
Keywords: AUV Lighthill equation Propeller CFD Underwater radiated noise
The wide range use of marine equipment has greatly increased the underwater radiated noise (URN) level, creating more threat to marine life. Autonomous underwater vehicle is one of the solutions to reduce the use of large marine equipment and then decrease the noise. Aiming at the noise control of AUV, this study conducted a far field noise measurement experiment on an AUV working on 10 different conditions, which is rarely measured. The hybrid method, predicting the noise with Lighthill equation based on unsteady flow field data from CFD calculation, is adopted. The results from experiment and simulation indicates that the simulative results are in good agreements with experimental results and the propeller will still generate noise due to the irregular vi bration of the propeller, which is about 3–5 dB. With the occurrence of cavitation, the sound pressure level (SPL) increases sharply, and there will be a wide gap between experimental and simulative noise data, owing to the single phase considered in the Lighthill equation. The analysis of the experimental and simulative results highlights the existence of structure excitation noise, ranging from 300 to 500 Hz and the shortcoming of noise prediction of the hybrid method under cavitation stage.
1. Introduction The increasing scale of general shipping activities and one of the emissions, underwater radiated noise (URN), have been under the spotlight (Hildebrand, 2009). Due to the increasing scale of marine equipment, noise level in seas, especially near harbors, has increased constantly and interfered with the daily life of mammals, including the communication, hunting and breeding (Merchant et al., 2014; Madsen, 2005). Recent studies have shown that noise also influences fish and invertebrates when courting and laying eggs (Julia et al., 2016; Matthew et al., 2013). In addition to the protection of marine life, marine equipment used in military itself has stricter requirements for noise control. Classifying the sonar target based on its acoustic signal char acteristics is considered to be an effective sonar application method. On the one hand, oceanography (Carral et al., 2018; Martinelli et al., 2016), sonar modeling and engineering (Mohammad and Hassan, 2019; �s et al., 2017; Abraham, 2008) and also statistical processing (Hurto Miles et al., 2006) are taken into account to improve the accuracy of classification. On the other hand, random methods, including artificial intelligence (AI) methods (Najafzadeh et al., 2016a; Najafzadeh et al., 2016b; Najafzadeh and Sarkamaryan, 2018), have resulted in significant improvements in classification efficiency. More and more advanced
sonar technology poses a more serious challenge to the survivability of autonomous underwater vehicles in the execution of missions. There fore, the URN control for marine equipment should be put on the agenda as soon as possible, considering both military and ecological aspects. The noise measurement of ship propeller, as an indicator of noise prediction accuracy, is the basis of noise analysis. There has been a field noise measurement to an LNG carrier under the speed of 9 and 19knots (Kellett et al., 2013). The comparison between experimental and simu lative results revealed that while providing more generally accurate results, the rotating mesh didn’t provide the same realistic details of the spectral levels as the moving frame of reference method. Although the field noise test can capture the real noise of ship, the test costs a lot and there have been many interference factors. In order to provide invalu able underwater radiated noise (URN) data of a full-scale vessel, extrapolated URN data based on the tunnel tests was compared with the data obtained from the full-scale trials with The Princess Royal (Batuhan et al., 2016). The research proves that the medium size facilities using dummy-hull models with wake screens can still provide a very useful means for the URN investigations. The noise of ship is made up of structural noise, hydrodynamic noise and propeller noise. As for AUV, motor drivers and relatively low speeds makes that propeller noise has a higher proportion. The noise
* Corresponding author. E-mail address: [email protected] (X. Zhang). https://doi.org/10.1016/j.oceaneng.2020.107111 Received 7 October 2019; Received in revised form 17 December 2019; Accepted 10 February 2020 Available online 5 March 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved.
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the flow field simulation. The simulation combining Reynolds Average Navier-Stokes (RANS) turbulence model with the turbulence viscosity correction and the Zwart cavitation model captured periodic cavitation development (Wu et al., 2018). There has also been the simulation using DES simulation and FW-H equation on a normal Pumpjet propulsor (PJP) model and a PJP model with the sawtooth duct (Denghui et al, 2019). The research predicted the spectrum form 10 Hz–5000 Hz. The hybrid method of noise prediction has been adopted in this study to enable the numerical prediction of radiated underwater noise from the AUV under investigation. As stated above, existing simulation and experiment tend to measure and predict the noise of ship and propeller separately, in terms of high cost and model size. At present, there is no scientific prediction method for AUV underwater noise that has considered the influence of hull, and there is no corresponding experiment to provide reference. The study aims to design a numerical noise prediction model for an AUV in design stage and conducted an open water test in a comprehensive test pool for reference. Applying the field noise measurement equipment, 10 rota tional speed conditions were tested and recorded for the noise data, which were also simulated through acoustic analogy theory. Since nu merical investigations on high frequency continuous spectrum are not taken into account, only low frequency spectrum will be analyzed. This paper intends to demonstrate results from field test and simulation.
Fig. 1. Layout of the comprehensive test pool.
2. Experiment validation data
Table 1 Parameters of AUV and propeller. AUV
The noise measurements in this study was carried out in a compre hensive test pool (30 m � 50 m � 11 m) of the Key Laboratory of Un derwater Robotics in Harbin Engineering University (HEU). The measured acoustic spectra were then used for validating the numerically predicted values, as well as to indicate the relative accuracy of different rotational speeds. The large-scale comprehensive test pool was design for model test research on ship-wave resistance and maneuverability, maneuverability in waves, marine engineering. The test pool was upgraded for the noise measurements maintaining the ability of wave elimination, as shown in Fig. 1. The test area is rectangular and spans a small crane above. The hydrophone, Bruel and Kjaer Type 8100, was installed in the far field of the pool, 20 m away from the AUV and 5 m away from the pool wall and the pool bottom. The hydrophone is tied by a rope and immersed in water. Virtual receivers are located in the numerical model to corre spond with the Closest Point of Approach (CPA) locations seen in the field trials. The water temperature and speed of sound values used within the model is an average taken from the measured values. The field acoustic spectra were then used for validating the numerically predicted values, as well as to indicate the relative accuracy of different modelling variations. The AUV and propeller are made up of carbon fiber, which aims to work under water 2000m. The main design data is summarized in Table 1 and shape of propeller is shown in Fig. 2. The two ends of the AUV parallel middle body are equipped with two hooks for crane lifting. The AUV, combined with the propeller, is located in the center of the pool, with a depth of 5 m. The background noise was recorded at first in order to compare the exact noise while AUV is working. Both the background noise and signal from working AUV were processed using the fast Fourier transform (FFT) technique and then the signal ampli tudes on corresponding frequencies were derived. This experiment is different from previous experiments using similar laws and an AUV with a depth of 2000m was tested. For the experiment performed in cavitation tunnel or circulating water channel, the back ground noise includes environmental and electrical signal noise, ma chine noise, noise caused by impellers driving water, noise from power meters and shafting, noise from the flow field, and noise caused by back pressure changing. In this experiment, no inflow was set and rotation speeds for the propeller were controlled by electronic motor. To get as much data as possible, the rotational speed of propeller varies from 100
Propeller
Essential factor
value
Essential factor
value
Length molded breadth molded depth Working depth Design speed
5.235 m 0.41 m 0.82 m 2000m 7kn
Direction Diameter (D) Blade number Design speed Hub diameter ratio
Right 0.475 m 2 1200RPM 0.294
measurement especially for propeller usually take place in cavitation tunnel in order to investigate its performance. There have been many experiments on the standard propellers under non-cavitation and cavi tation condition. The Meridian Standard propeller was tested in the Emerson Cavitation Tunnel and the flow field was filmed with high speed cameras, acquiring obvious cavitation photos (Batuhan et al., 2018). The recorded data revealed the importance of the observed instantaneous cavitation dynamics on the time pressure signals and their consequent impact in the frequency domain. With the model and pro totype noise data provide by Samsung Heavy Industries (SHI), the novel scaling law has better agreement with the prototype TVC noise mea surement than the prototype TVC noise level predicted by the modified ITTC noise estimation rule (Jisoo and Seong, 2017). In addition to the noise measurement on propellers, the comparison between ECT (Emerson Cavitation Tunnel) and UNIGE(University of Genoa) cavita tion tunnel was conducted firstly by University of Genoa, in terms of measured sound pressure levels, propeller open water performance, cavitation observations and cavitation inception characteristics (Giorgio et al., 2017). In the area of noise prediction of ship and propeller, a significant amount of recent work in this field has been focused on the application of acoustic analogy theory. The acoustic analogy theory was originally developed by Lighthill in 1952, which is called Lighthill’s Acoustic Analogy using to predict the aerodynamic noise generated by rotating bodies such as helicopter rotors and fan blades. The lighthill equation was proceeded by Ffowcs-Williams and Hawkings and developed the Ffowcs-Williams Hawkings (FW-H) equation, which considered moving boundary influence in the flow field and extend it to hydroacoustic problems. The accuracy of noise prediction of ship and propeller lays on 2
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Fig. 2. Propeller dimensions.
Fig. 3. Comprehensive test pool and Bruel & Kjae equipment.
to 1000RPM, at the step of 100RPM, making it 10 working conditions. The acquisition of background noise should be started one month before experiment. It is worth noting that when measuring the noise of ten working conditions, they are also in different time periods, so after determining the half-hour test window period of one working condition, the background noise must be in the same test window period. After the noise measurement experiment is over, firstly average the background noise measurement results during the experiment window period. Next, subtract the background noise from the noise measurement results measured in the experiment. The result is the true propeller radiated noise. The photos taken during the test are shown in the Fig. 3.
between the CFD mesh and the acoustic mesh. The last step includes the simulation of the acoustic wave propagation using the Lighthill’s acoustic analogy theory with commercial software ACTRAN that has been used in acoustic simulation (Sandboge et al., 2006; Carton de Wiart et al., 2009; Carton de Wiart et al., 2010; D�etry et al., 2010; Herrin et al., 2012, Liu et al., 2013). 3.1. Discussion of grid convergence The shear stress transport model (Menter, 1994) is employed to simulate a strong adverse pressure gradient flow field by considering the effect of wall shear in the prediction of the rotate flow. This model combines the advantages of the k and ω models and can be used to compute the flow separation region. It is one of the most advanced two-equation turbulence models, and is superior in its calculation of the viscous ambient flow field. It has also been suggested that the accuracy of results in such work might benefit form coupling with a more complex hydrodynamic solver such as the Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) solvers as opposed to a RANS-based solver.
3. Methodology The radiated noise is analyzed in three main steps and the flow di agram is shown in Fig. 4. In the first step, the flow field information, such as velocity and pressure fluctuations, are obtained through k-ω SST model (Shear Stress Transfer) with the CFD mesh. Then, noise sources are computed from the flow field information with the interpolation 3
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Fig. 4. Flow-induced noise simulation process.
Fig. 5. Blade mesh (Coarse, Medium and Fine).
Fig. 6. Dimensionless thrust and torque coefficient.
Nevertheless, providing promising results, investigation into coupling DES, LES models with the acoustic analogy equation requires finer grid and computational time. In this study, a pressure-based coupled solver is used for the governing equations of the numerical computation. Spatial discretization of the convection term is performed using a second-order upwind scheme and discretization of the dissipative term is performed
using a second-order central difference scheme (Weiss and Smith, 1995). In solving the governing equation of turbulence model above, prism layer will significantly affect the accuracy of hydrodynamic results. Therefore, for the purposes of this work, where accuracy must be balanced against run time and complexity, the k-ω based SST model is adopted and a resolution of the boundary layer of over 10 points is 4
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� 1 ∂k ∂ω ; 10 CDkω ¼ max 2ρω2 ω ∂xj ∂xj
� 10
(4)
And, μt, named eddy viscosity, is computed by:
μt ¼
ρa1 k maxða1 ω; ΩF2 Þ "
F2 ¼ tanh max
required. In order to estimate the grid convergence, three grid levels including Coarse, Medium and Fine grids validate the mesh indepen dence. The dimensionless torque coefficient and thrust coefficient of the propeller are chosen as convergence criterion. For the reason that the tested propeller is low-skew, the propeller AU5-50 is selected to perform the study of grid convergence. The comparison of CFD results between open water characteristics of propeller AU5-50 calculated by three grids are shown in Fig. 5. The results of open water characteristics calculated by the grids for propeller AU5-50 at J ¼ 0.4 is shown in Fig. 6. It can be observed from the figure that the difference between computational and standard values is small in the whole simulation range. Overall, the solution with Medium grids shows best convergence.
3.3. Lighthill’s acoustic analogy theory The sound features of the flow field is acquired through Lighthill’s acoustic analogy theory, which is derived from N-S equations (NavierStokes equations). Due to the nonlinearity and the coupling of flow and acoustics, the sound field is divided into near field and far field. The near field is the source area and the far field is the radiation area. This study assumes that flow in the radiation area has no effect on the sound feature. In this assumption, the continuity equation and the mo mentum equation are simplified and used to get the Lighthill’s acoustic analogy equation:
3.2. Governing equation
0
0
∂ρ ∂t2
The SST k-ω turbulence model solves two transport equations, one for the turbulent kinetic energy, k, and one for the turbulent frequency, ω. The stress tensor is computed from the eddy-viscosity concept. The corresponding equations of k (the turbulence kinetic energy) and ω (the specific dissipation rate) are: � � � ∂ðρkÞ ∂ ρuj k ∂ ∂k ðμ þ σk μt Þ (1) ¼ Pk β* ρωk þ þ ∂xj ∂t ∂xj ∂xj �
βρω2 þ 2ð1
F1 Þ
(6)
Where, d is the distance to the nearest wall, and Ω is the vorticity magnitude. The default values of the constants in the Eq. (5) and Eq. (6) are usually defined as follows: σk ¼ 1.0, σω2 ¼ 0.85616, β* ¼ 0.09, a1 ¼ 0.31.
Fig. 7. CFD grid.
∂ðρωÞ ∂ ρuj ω ργ ¼ Pk þ ∂t ∂xj μt � � ∂ ∂k þ ðμ þ σ k μt Þ ∂xj ∂xj
!# pffiffi 2 k 500v ; β* ωd d2 ω
(5)
0
c20 r2 ρ ¼
∂Tij ∂xi ∂xj
Where is the Lighthill’s stress tensor, which can be written as: � � 0 Tij ¼ ρvi vj τij þ δij ðp p0 Þ c20 ðρ ρ0 Þ
(7)
(8)
In resolving the equation, some assumptions are made. On the one hand, the small stress tensor is ignored according to the actual flow conditions. On the other hand, the interaction between flow and sound is ignored, so that there is no interaction between them in this paper. Ignoring the fluctuation of fluid density and pressure, the Lighthill’s 0 stress tensor is simplified as Tij ¼ ρvi vj .
ρσω2 ∂k ∂ω ω ∂xj ∂xj (2)
4. Numerical modelling set-up
Where, F1 is a harmonic function, which is written as the following formulas: ! #)4 ( " pffiffi k 500v 4ρσω2 k ; F1 ¼ tanh min max * ; 2 (3) β ωd d ω CDkω d2
4.1. CFD model setup The CFD simulation for the AUV and its underwater noise is carried out in full scale, an approach which is rarely taken. The enclosing rectangular domain, of size 30 � 50 � 10 m3 surrounds the 5.235 m hull and propeller. The centroid of the AUV coincides with that of the
Fig. 8. Acoustic analogy setting. 5
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Fig. 9. Thrust curve.
6
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Fig. 9. (continued).
stationary and rotating region. The surrounding and under surfaces are set to wall condition and up surface is set to opening condition. Mesh generation was carried out using the automatic meshing tool in ICEM CFD, resulting in a computation mesh of approximately 6.4 million cells in total; a typical Medium density grid. There is a gradually encryption of grid in the area around the hull and propeller, especially the region where the complex flow properties are appropriately captured. The grid in the aft section of the AUV and the propeller is shown in Fig. 7. The frequency ranges from 80 to 1200hz is the focus of this study. In order to ensure that results up to this value are obtained with a sufficient level of accuracy, a time-step of 0.0004 is used throughout. The maximum run-time is set to 5s and the number iteration of inner itera tions per each full iteration is limited to 10. It equates to around 125000 iterations in per simulation. A 2nd-order implicit unsteady simulation has been used, with a k-ω SST turbulence model. Thrust and torque values are also monitored for comparison. Once the unsteady calculation is over, flow field value is export for acoustic analogy calculation.
Table 2 Vapor-Water volume fraction. RPM 100 200 300 400 500 600 700 800 900 1000
Volume fraction of water
Volume fraction of vapor
Max
Min
Max
Min
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 0.96375 0.81538 0.66814 0.52202
0 0 0 0 0 0 0.03625 0.18462 0.33186 0.47798
0 0 0 0 0 0 0 0 0 0
domain. The stationary region included all elements except the propeller and enclosing cylinder which were included in the rotating region. The forward and aft faces of the enclosing cylinder, as well as its circum ference, are selected as the fluid-fluid interface, which located between 7
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Fig. 10. Noise spectrum curve.
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Fig. 10. (continued).
4.2. Acoustic analogy model setup
fmin ¼ Δf ¼
The acoustic calculation region is the same size as stated in section 2. In this study, a permeable source surface, which encloses the AUV, is placed within the flow and is used as the radiating surface for the acoustic model, rather than the propeller and hull surfaces used previ ously. The permeable surface is selected as surface source and the region surrounded by it is selected as volume source. This surface will then allow for the monopole and dipole sources from the hull and propeller surfaces to be captured, as well as the quadrupole sources within the flow, such as those arising from turbulence. The permeable surface takes the form of a cuboid, which encloses the entirety of the AUV and part of the flow. Previous study on the optimum location of the surface reveals that the location and size will not affect the results significantly. The far field of the acoustic calculation region is selected as the radiation area. The frequency range is as follows. 1 fmax ¼ 2Δt
1 NΔt
(10)
This study focuses on the range of 80–1200 Hz. According to the time step as stated in section 4.1, the maximum frequency can be predicted is 1250 Hz. In ACTRAN, the element of acoustic grid needs to satisfy the requirement that there should be at least 6 nodes in each acoustic wavelength, making the maximum size of the acoustic grid element 200 mm. The surrounding and down boundaries are selected as wall boundary and up boundary is selected as acoustic infinite boundary condition. The condition setting is shown in Fig. 8. In the noise simu lation, the boundary has been as concrete material aiming at the simu lation of reverberation. 5. Results and discussion The following sections outline the acoustic results achieved from the simulations and experiment based on different rotational speeds, and discuss the significance of these results in the context of general
(9)
9
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Fig. 11. Noise 1/3 octave curve.
recommendations for hydroacoustic modelling. The machinery noise contribution is also not accounted for in these results.
5.2. Narrowband spectral noise In Fig. 10, the blue characteristics correspond to the simulative re sults and the orange characteristics correspond to the experimental re sults. Experimental and numerical results are comparable from 80 to 1200 Hz. The results in Fig. 9 above, show that the spectral curves are close to each other between simulative and experimental results between 100–600RPM rotational speeds. At the lower frequencies, from 300 to 500 Hz, curves from experiment gives higher noise results. This may due to that low frequencies noise produced from propeller and hull vibra tion. Looking more specifically at the variations for simulation and experiment results between 100–600RPM rotational speeds, although on the frequency band the results agree well, it can be seen that there are no tonal peaks which is present in experiment results shown in simu lation results and do not replicate the spectra seen in the fields mea surements as accurately. With the rotational speed rise to 700RPM, the discrepancy between
5.1. Flow filed discussion Fig. 9 above only intercepts the stable part of the thrust curve, which includes at least 2 pulsating thrust cycle. It should be noted that there are 2 similar pulsating curves in each cycle of the thrust curve, one of which has a peak value greater than the other. This phenomenon differs from the feature of open water simulation of propeller as the research before. It indicates that there will be irregular vibration noise of pro peller in the field test and simulation. It can be seen form Table 2 that, with rotational speed rising to 700 RPM, cavitation occurs. Due to the large size of the test pool, the speed of the propeller was not clearly observed. It is foreseeable that when the speed reached 700 RPM, the feature of the spectra from experiment will be different.
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Fig. 11. (continued).
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simulative and experimental results increase. This gap in results be tween field and modelled data can be contributed to lack of represen tation of cavitation noise, as well as difficulties in recreating an accurate representation of real conditions in a mathematical model. When the governing equations switched into the governing equations for multiphase mixture and applying cavitation model, the volume fraction of vapor rises while that of liquid drops. While there is single one fluid medium considered in the calculation of the acoustic equation, which is the reason for 20–25 dB gap. In the four examples where the rotation speed is higher than 700 RPM, at higher frequencies, the spectrum curve of numerical simulation has a downward trend, but the measurement curves do not. In addition to the effects of cavitation noise, the effects of the acoustic grid scale as introduced in Section 4.2 should also be considered. Noise measurement experiments are performed under reverberation conditions, so the acoustic grid requirements for numerical simulations under the same boundary conditions are more stringent than CFD grids. From an engi neering perspective, it is necessary and economical to use the infinite element method to reduce the size of the computational domain for numerical simulation of noise. However, in this paper, the method of reducing the calculation domain is not adopted, which also brings a compromise on the size of the grid, that is, in the numerical simulation, the length of the grid is slightly increased to reduce the requirements for computer performance.
Credit author statement Changli Yu: Conceptualization, Writing - Review & Editing, Super vision, Funding acquisition. Renzhi Wang: Methodology, Software, Validation, Formal analysis, Writing - Original Draft. Xingming Zhang: Project administration, Investigation. Yueming Li: Resources, Data Curation. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The study is supported by the Research Fund from Science and Technology on Underwater Vehicle Technology (Grant No. SXJQR2017KFJJ02) and the Shandong Provincial Key Research and Development Plan (Grant No. 2019GHZ011) and (Grant No. 2017CXGC0922). The authors would like to acknowledge the projects support. References
5.3. 1/3 octave noise
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In Fig. 11, the blue characteristics correspond to the simulative re sults and the orange characteristics correspond to the experimental re sults. Experimental and numerical results are comparable up to the central frequency of 1000 Hz, with overall sound pressure level (OSPL) listed and compared. Both the shape of hydroacoustic curves is similar. Between the rotational speed in 100–600RPM, the trend of simulation results is close to experiment results. In the range of center frequency from 250 to 500HZ, experiment results are larger than simulation results clearly. The gap as mentioned indicates the influence of structure noise. When the cavitation occurs, the sound pressure level rises from high frequency to low frequency. The trend indicates that cavitation noise affects largely in high frequency and with cavitation growing, cavitation contributes largely to low frequency noise. Above a frequency of about 100 Hz the discrepancy of both results is significant, higher frequency value higher discrepancy. 6. Conclusion This study conducts a constrain model test of AUV to measure the far field noise. Meanwhile, a CFD simulation and acoustic analogy simula tion on the model of AUV under the same boundary condition is carried out. The hydrodynamic performance of AUV and the diversity between simulative and experimental results is discussed. The spectrum curve is the focus of the study. The thrust curve is selected as the main reference index of the flow field in CFD calculation. There are two thrust fluctuation curves in each cycle of the propeller, and the peak of one cycle is larger. The irregular small peaks present in each cycle mean that the propeller thus generates vibration. A noise prediction of the AUV was performed using a hybrid approach, and the noise data was included in the spectrogram, including a 1/3 octave transform. The comparison between the results of experi ment and simulation under no-cavitation conditions indicates that there is vibration noise rising from propeller and hull irregular vibration. The hybrid method shows less accuracy when the cavitation occurs, resulting from the single medium in Lighthill’s equation. Further investigation is recommended to predict the vibration noise of propeller and hull. Other than the vibration noise, the cavitation noise need to be paid more attention in the future. 12
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