# Suppression of the Hydrodynamic Noise Induced by the Horseshoe Vortex through Mechanical Vortex Generators

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## Abstract

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## Featured Application

**The proposed method can be used to reduce the hydrodynamic noise from underwater vehicles at low frequency.**

## Abstract

## 1. Introduction

## 2. The Theory of Numerical Simulation

#### 2.1. LES Method

#### 2.2. Theory of Vibration and Sound Radiation by the Flow-Induced Force

- (1)
- The turbulent pressure field is spatially uniform and static relative to time. That is, the time–space correlation of wall pressure fluctuation only depends on the spatial distance and time interval.
- (2)
- The sound radiation from the vibration of the model is under the excitation of turbulent fluctuation pressure, while that from the turbulent fluctuation pressure itself is ignored.
- (3)
- The properties of the model are isotropic and obey the theory of elasticity.

#### 2.3. The Accuracy Validation of the Numerical Simulation

## 3. The Description of the Model in Numerical Simulation

#### 3.1. The Research Model

#### 3.2. The Parameters of Numerical Simulation

^{+}≈ 35, Re = 1.6 × 10

^{7}. The mesh thickness of the first boundary layer, namely, $\Delta $y

_{p}was 0.0001 m, which was obtained from Equation (21):

^{6}, 1.5 × 10

^{6}, 2 × 10

^{6}, 2.5 × 10

^{6}, 3 × 10

^{6}, 3.5 × 10

^{6}, and 4 × 10

^{6}. Through the comparison, we found that the grid number of 3 × 10

^{6}could obtain the appropriate resistance. Therefore, the grid number of the flow field calculation was 3 × 10

^{6}. The transient simulation of the flow field was performed by the dynamic sub-lattice model in the LES.

^{−4}s according to Equation (22). The number of samples was selected as 800 time steps to calculate the sound field.

## 4. The Flow Field of the Model

## 5. The Shape Selection of Mechanical VGs

## 6. The Optimized Angle of Mechanical VGs to the Flow Direction

_{t}is the Strouhal number, U is the incoming flow velocity, and C is the feature length of the model. According to Equation (24), the frequency of the tail vortex shedding was 595 Hz, just as the black dotted line in Figure 11 indicates. This phenomenon indicated that the triangular VGs also changed the formation of the tail vortex shedding.

## 7. The Mechanism of Noise Reduction by Triangular VGs

## 8. The Optimized Distance between the VGs and the Sail Hull

## 9. The Experimental Validation

#### 9.1. The Theory of Reverberation Method

_{0}is the radiated sound power, P

_{e}is the effective sound pressure, ${\rho}_{0}$ is the density, and c

_{0}is the velocity of the sound waves.

_{60}is the reverberation time, and V is the whole reverberation tank’s volume.

#### 9.2. The Description of the Experimental Measurement

## 10. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Yu, M.; Wu, Y.; Pang, Y. A review of progress for hydrodynamic noise of ships. J. Ship Mech.
**2007**, 11, 152–158. [Google Scholar] - Li, D.Q.; Hallander, J.; Johansson, T. Predicting underwater radiated noise of a full scale ship with model testing and numerical methods. Ocean Eng.
**2018**, 161, 121–135. [Google Scholar] [CrossRef] - Fouatih, O.M.; Medale, M.; Imine, O.; Imine, B. Design optimization of the aerodynamic passive flow control on NACA 4415 airfoil using vortex generators. Eur. J. Mech. B/Fluids
**2016**, 56, 82–96. [Google Scholar] [CrossRef] - Tao, S.; Tang, A.; Xin, D.; Liu, K.; Zhang, H. Vortex-induced vibration suppression of a circular cylinder with vortex generators. Shock Vib.
**2016**, 1–10. [Google Scholar] [CrossRef] - Kuya, Y.; Takeda, K.; Zhang, X. Computational investigation of a race car wing with vortex generators in ground effect. J. Fluids Eng.
**2010**, 132, 1–8. [Google Scholar] [CrossRef] - Lin, J.C. Review of research on low-profile vortex generators to control boundary-layer separation. Prog. Aerosp. Sci.
**2002**, 38, 389–420. [Google Scholar] [CrossRef] - Brüderlin, M.; Zimmer, M.; Hosters, N.; Behr, M. Numerical simulation of vortex generators on a winglet control surface. Aerosp. Sci. Technol.
**2017**, 71, 651–660. [Google Scholar] [CrossRef] - Titchener, N.; Babinsky, H. A review of the use of vortex generators for mitigating shock-induced separation. Shock Waves
**2015**, 25, 473–494. [Google Scholar] [CrossRef] - Rybalko, M. Aerodynamic impact of vortex generators on a relaxed-compression low-boom inlet. AIAA J.
**2015**, 53, 3700–3711. [Google Scholar] [CrossRef] - Boniface, J.-C. A computational framework for helicopter fuselage drag reduction using vortex generators. J. Am. Helicopter Soc.
**2016**, 61, 1–13. [Google Scholar] [CrossRef] - Hoffmann, F.; Schmidt, Ha.; Nayeri, C.; Paschereit, O. Drag reduction using base flaps combined with vortex generators and fluidic oscillators on a bluff body. Int. J. Commer. Veh.
**2015**, 8, 705–712. [Google Scholar] [CrossRef] - Gao, L.; Zhang, H.; Liu, Y.; Han, S. Effects of vortex generators on a blunt trailing-edge airfoil for wind turbines. Renew. Energy
**2015**, 76, 303–311. [Google Scholar] [CrossRef] - Verma, S.B.; Manisankar, C.; Raju, C. Control of shock unsteadiness in shock boundary-layer interaction on a compression corner using mechanical vortex generators. Shock Waves
**2012**, 22, 327–339. [Google Scholar] [CrossRef] - Lee, S.; Loth, E. Supersonic boundary-layer interactions with various micro-vortex generator geometries. Aeronaut. J.
**2009**, 113, 683–697. [Google Scholar] [CrossRef] - Verma, S.B.; Chidambaranathan, M. Transition control of Mach to regular reflection induced interaction using an array of micro ramp vane-type vortex generators. Phys. Fluids
**2015**, 27, 1–23. [Google Scholar] [CrossRef] - Godard, G.; Stanislas, M. Control of a decelerating boundary layer. Part 1: Optimization of passive vortex generators. Aerosp. Sci. Technol.
**2006**, 10, 181–191. [Google Scholar] [CrossRef] - Lo, K.H.; Kontis, K. Flow characteristics over a tractor-trailer model with and without vane-type vortex generator installed. J. Wind Eng. Ind. Aerodyn.
**2016**, 159, 110–122. [Google Scholar] [CrossRef] - Zhang, Y.; Hu, S.; Zhang, Xu.; Benner, M.; Mahallati, A.; Vlasic, E. Flow control in an aggressive interturbine transition duct using low profile vortex generators. J. Eng. Gas Turbines Power
**2014**, 136, 1–8. [Google Scholar] [CrossRef] - Lengani, D.; Simoni, D.; Ubaldi, M.; Zunino, P.; Bertini, F. Turbulent boundary layer separation control and loss evaluation of low profile vortex generators. Exp. Therm. Fluid Sci.
**2011**, 35, 1505–1513. [Google Scholar] [CrossRef] - Törnblom, O.; Johansson, A.V. A Reynolds stress closure description of separation control with vortex generators in a plane asymmetric diffuser. Phys. Fluids
**2007**, 19, 1–15. [Google Scholar] - De Tavernier, D.; Baldacchino, D.; Ferreira, C. An integral boundary layer engineering model for vortex generators implemented in XFOIL. Wind Energy
**2018**, 21, 906–921. [Google Scholar] [CrossRef] - Li, Q.; Liu, C. Declining angle effects of the trailing edge of a microramp vortex generator. J. Aircr.
**2010**, 47, 2086–2095. [Google Scholar] [CrossRef] - Wang, H.; Zhang, B.; Qiu, Q.; Xu, X. Flow control on the NREL S809 wind turbine airfoil using vortex generators. Energy
**2017**, 118, 1210–1221. [Google Scholar] [CrossRef] - Jirasek, A. Vortex generator model and its application to flow control. J. Aircr.
**2005**, 42, 1486–1491. [Google Scholar] [CrossRef] - Joubert, G.; le Pape, A.; Heine, B.; Huberson, S. Vortical interactions behind deployable vortex generator for airfoil static stall control. AIAA J.
**2013**, 51, 240–252. [Google Scholar] [CrossRef] - Yan, Y.; Chen, L.; Li, Q.; Liu, C. Numerical study of micro-ramp vortex generator for supersonic ramp flow control at Mach 2.5. Shock Waves
**2017**, 27, 79–96. [Google Scholar] [CrossRef] - Bao, D.; Jia, Q.; Zhang, Z. Effect of vortex generator on flow field quality in 3/4 open jet automotive wind tunnel. SAE Int. J. Passeng. Cars Mech. Syst.
**2017**, 10, 224–234. [Google Scholar] [CrossRef] - Von stillfried, F.; Wallin, S.; Johansson, A.V. Evaluation of a vortex generator model in adverse pressure gradient boundary layers. AIAA J.
**2011**, 49, 982–993. [Google Scholar] [CrossRef] - Giepman, R.H.M.; Schrijer, F.F.J.; van Oudheusden, B.W. Flow control of an oblique shock wave reflection with micro-ramp vortex generators, effects of location and size. Phys. Fluids
**2014**, 26, 1–16. [Google Scholar] [CrossRef] - Zhang, B.; Zhao, Q.; Xiang, X.; Xu, J. An improved micro-vortex generator in supersonic flows. Aerosp. Sci. Technol.
**2015**, 47, 210–215. [Google Scholar] [CrossRef] - Suarez, J.M.; Flaszynski, P.; Doerffer, P. Application of rod vortex generators for flow separation reduction on wind turbine rotor. Wind Energy
**2018**, 21, 1202–1215. [Google Scholar] [CrossRef] - Součková, N.; Kuklová, J.; Popelka, L.; Matějka, M. Visualization of flow separation and control by vortex generators on an single flap in landing configuration. EPJ Web Conf.
**2012**, 25, 1–12. [Google Scholar] - Martinez-filgueira, P.; Fernandez-Gamiz, U.; Zulueta, E.; Errasti, I.; Fernandez-Gauna, B. Parametric study of low-profile vortex generators. Int. J. Hydrogen Energy
**2017**, 42, 17700–17712. [Google Scholar] [CrossRef] - Kaltenbacher, M.; Escobar, M.; Becker, S.; Ali, I. Numerical simulation of flow-induced noise using LES/SAS and Lighthill’s acoustic analogy. Int. J. Numer. Methods Fluids
**2010**, 63, 1103–1122. [Google Scholar] [CrossRef] - Germano, M.; Piomelli, U.; Moin, P. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids
**1991**, 3, 1760–1765. [Google Scholar] [CrossRef] - Heatwole, C.M.; Franchek, M.A.; Bernhard, R.J. A robust feedback controller implementation for flow induced structural radiation of sound. In Proceedings of the INTER-NOISE and NOISE-CON Congress and Conference, Seattle WA, USA, 29 September 1996; Institute of Noise Control Engineering: Reston, VA, USA, 1996. [Google Scholar]
- Zhang, N.; Xie, H.; Wang, X.; Wu, B. Computation of votical flow and flow induced noise by large eddy simulation with FW-H acoustic analogy and Powell vortex sound theory. J. Hydrodyn.
**2016**, 28, 255–266. [Google Scholar] [CrossRef]

**Figure 1.**The comparison curve between the numerical simulation and the experimental test. The dark line denotes the preliminary test, and the red line denotes the numerical calculation. The frequency is in the range from 0 to 1000 Hz. The reference sound pressure level is 20 uPa.

**Figure 2.**The diagram of the model. The model is a whole sail hull with part of the body. The dimension is scaled from the SUBOFF model. The length (L) of the sail hull is 184 cm. The height (H) of the sail hull is 10 cm. The chord length (c) is 18.4 cm.

**Figure 3.**The diagram of the planes. Plane A is in the longitudinal direction, Plane B is in the longitudinal direction, and Plane C is in the transversal direction.

**Figure 4.**The pressure contour at the leading edge of Plane A and Plane B. The pressure is from 5000 Pa to 35,000 Pa, when the points are approaching to the leading edge. (

**a**) Plane A; (

**b**) Plane B.

**Figure 7.**The mechanical vortex generators (VGs) on the model: (

**a**) triangular; (

**b**) trapezoidal; (

**c**) semi-circular.

**Figure 8.**The radiated sound power from the original model and the models with three shapes of mechanical VGs.

**Figure 9.**The comparison curve of radiated sound power from the original model and the model with triangular VGs at different angles to the flow direction. ‘The 0° VG’ means that the triangular VGs are at the angle of 0° to the flow direction. The other meanings are the same as ‘The 0° VG’.

**Figure 10.**The comparison curve of radiated sound power between the original model and the model with triangular VGs at the angle of 0° to the flow direction.

**Figure 11.**The curve of radiated sound power from the original model and the model with triangular VGs at the angle of 30° to the flow direction.

**Figure 12.**The wake flow field of the two models. (

**a**) The original model; (

**b**) the model with the mechanical VGs.

**Figure 13.**The pressure gradient of the leading edge at Plane B of the model with triangular VGs. Two eddies from the triangular VGs can be clearly observed.

**Figure 14.**The streamline near the leading edge of Plane B between the original model and the model with triangular VGs. (

**a**) The original model; (

**b**) the model with triangular VGs.

**Figure 15.**The local streamline of Plane C between the original model and the model with triangular VGs. (

**a**) The original model; (

**b**) the model with triangular VGs.

**Figure 18.**The contour map at the leading edge of Plane B of the model with triangular VGs at different distances. (

**a**) 0.1c; (

**b**) 0.15c; (

**c**) 0.2c.

**Figure 19.**The streamline of Plane B between the original model and the model with triangular VGs at different distances. (

**a**) The original model; (

**b**) VGs at 0.1c; (

**c**) VGs at 0.15c; (

**d**) VGs at 0.2c.

**Figure 20.**The streamline of Plane C between the original model and the model with triangular VGs. (

**a**) The original model; (

**b**) the VGs at 0.1c.

**Figure 21.**The vortex quanta from the model with triangular VGs at a distance of 0.1c from the leading edge of the sail hull.

**Figure 22.**The comparison curve of radiated sound power from the original model and the models with triangular VGs at different distances. The black line denotes the radiated sound power from the original model. The blue dot line denotes the radiated sound power from the model with triangular VGs at the leading edge of the sail hull. The green line denotes the radiated sound power from the model with triangular VGs at a distance of 0.2c from the leading edge of the sail hull. The pink line denotes the radiated sound power from the model with triangular VGs at a distance of 0.15c from the leading edge of the sail hull. The yellow line denotes the radiated sound power from the model with triangular VGs at a distance of 0.1c from the leading edge of the sail hull.

**Figure 23.**The directivity of the sound field of the two models at different frequencies. (

**a**) f = 45 Hz; (

**b**) f = 500 Hz; (

**c**) f = 1200 Hz; (

**d**) f = 1800 Hz.

**Figure 24.**The gravity water tunnel and the reverberation tank. (

**a**) The whole water tunnel; (

**b**) The reverberation water tank

**Figure 26.**The diagram of the experimental measurement. (

**a**) The composition of the vertical hydrophone array; (

**b**) the spatial average method.

**Figure 27.**The turbulent fluctuation pressure measured by the fluctuation pressure sensor at different flow velocities: (

**a**) 4.62 m/s; (

**b**) 8.68 m/s.

**Figure 28.**The radiated sound power measured by the vertical hydrophone array in the reverberation tank at different flow velocities: (

**a**) 4.62 m/s; (

**b**) 8.68 m/s.

**Table 1.**The level of radiated sound power from the original model and the models with triangular VGs (vortex generators), trapezoidal VGs, and semi-circular VGs.

Model | Total Level of Radiated Sound Power/dB ^{1} | Noise Reduction/dB ^{1} |
---|---|---|

Original | 113.51 | 0 |

With triangular VGs | 108.23 | 5.28 |

With trapezoidal VGs | 110.88 | 2.63 |

With semi-circular VGs | 126.46 | −12.95 |

^{1}dB The reference is 0.67 × 10

^{−18}.

**Table 2.**The total level of radiated sound power from the original model and the models with triangular VGs at different angles.

Model | Total Level of Radiated Sound Power/dB ^{1} | Noise Reduction/dB ^{1} |
---|---|---|

Original | 113.51 | 0 |

0° VGs | 130.54 | −17.03 |

15° VGs | 111.44 | 2.07 |

30° VGs | 108.23 | 5.23 |

45° VGs | 112.03 | 1.48 |

60° VGs | 119.71 | −6.20 |

^{1}dB The reference is 0.67 × 10

^{−}

^{18}.

Model | Total Level of Radiated Sound Power/dB ^{1} | Noise Reduction/dB ^{1} |
---|---|---|

Original | 113.51 | 0 |

VGs at the leading edge | 108.23 | 5.28 |

VGs at the distance of 0.1c | 104.58 | 8.93 |

VGs at the distance of 0.15c | 106.98 | 6.53 |

VGs at the distance of 0.2c | 104.63 | 8.88 |

^{1}dB The reference is 0.67 × 10

^{−18}.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Jiang, H.; Li, Y.; Shang, D.
Suppression of the Hydrodynamic Noise Induced by the Horseshoe Vortex through Mechanical Vortex Generators. *Appl. Sci.* **2019**, *9*, 737.
https://doi.org/10.3390/app9040737

**AMA Style**

Liu Y, Jiang H, Li Y, Shang D.
Suppression of the Hydrodynamic Noise Induced by the Horseshoe Vortex through Mechanical Vortex Generators. *Applied Sciences*. 2019; 9(4):737.
https://doi.org/10.3390/app9040737

**Chicago/Turabian Style**

Liu, Yongwei, Hongxu Jiang, Yalin Li, and Dejiang Shang.
2019. "Suppression of the Hydrodynamic Noise Induced by the Horseshoe Vortex through Mechanical Vortex Generators" *Applied Sciences* 9, no. 4: 737.
https://doi.org/10.3390/app9040737