A Review of the Hydrodynamic Damping Characteristics of Blade-like Structures: Focus on the Quantitative Identification Methods and Key Influencing Parameters

Abstract

cean energy has progressively gained considerable interest due to its sufficient potential to meet the world’s energy demand, and the blade is the core component in electricity generation from the ocean current. However, the widened hydraulic excitation frequency may satisfy the blade resonance due to the time variation in the velocity and angle of attack of the ocean current, even resulting in blade fatigue and destructively interfering with grid stability. A key parameter that determines the resonance amplitude of the blade is the hydrodynamic damping ratio (HDR). However, HDR is difficult to obtain due to the complex fluid–structure interaction (FSI). Therefore, a literature review was conducted on the hydrodynamic damping characteristics of blade-like structures. The experimental and simulation methods used to identify and obtain the HDR quantitatively were described, placing emphasis on the experimental processes and simulation setups. Moreover, the accuracy and efficiency of different simulation methods were compared, and the modal work approach was recommended. The effects of key typical parameters, including flow velocity, angle of attack, gap, rotational speed, and cavitation, on the HDR were then summarized, and the suggestions on operating conditions were presented from the perspective of increasing the HDR. Subsequently, considering multiple flow parameters, several theoretical derivations and semi-empirical prediction formulas for HDR were introduced, and the accuracy and application were discussed. Based on the shortcomings of the existing research, the direction of future research was finally determined. The current work offers a clear understanding of the HDR of blade-like structures, which could improve the evaluation accuracy of flow-induced vibration in the design stage.

Keywords

Blade fatigue / Hydrodynamic damping ratio / Identification method / Affecting factors / Prediction formula

References

[1] Anthony D, Simon F. Accuracy and robustness of four basic single degree of freedom methods for determining the modal parameters of non-lightly damped systems. Journal of Sound and Vibration, 2012, 331(24): 5191-5208

[2] Aquelet N, Souli M (2003) Damping effect in fluid-structure interaction: Application to slamming problem. ASME Pressure Vessels and Piping Conference, Cleveland

[3] Ausoni P. Turbulent vortex shedding from a blunt trailing edge hydrofoil, 2009, Lausanne: Swiss Federal Institute of Technology Lausanne

[4] Bahrami M, Cervantes M, Raisee M, Nourbakhsh A. Hydrodynamic damping in laminar, transient and turbulent regimes: Analytical and computational study. Ocean Engineering, 2023, 289: 116277

[5] Bai X, Li B, Xu X, Xiao Y. A review of current research and advances in unmanned surface vehicles. Journal of Marine Science and Application, 2022, 21(2): 47-58

[6] Bergan C, Solemslie B, Østby P, Dahlhaug O. Hydrodynamic damping of a fluttering hydrofoil in high-speed flows. International Journal of Fluid Machinery and Systems, 2018, 11(2): 146-153

[7] Bergan C, Tengs E, Solemslie B, Dahlhaug O. An experimental investigation of the hydrodynamic damping of vibrating hydrofoils. IOP Conference Series: Earth and Environmental Science, 2018, 240(6): 062008

[8] Bergan C, Tengs E, Solemslie B, Dahlhaug O. Damping measurements on a multi-blade cascade with multiple degrees of freedom: a francis-99 test case. Journal of Physics Conference Series, 2019, 1296: 012003

[9] Blake W. On the damping of transverse motion of free-free beams in dense stagnant fluids. Shock and Vibration Bulletin, 1972, 42(4): 41-55

[10] Blake W, Maga L. Vibration dynamics of flow-excited structs in water, 1973, Bethesda: Naval Ship Research and Development Center, Report

[11] Bulatovic R. On the critical damping in multi-degree-of-freedom systems. Mechanics Research Communications, 2002, 29(5): 315-319

[12] Cha Y, Chae W, Kim H, Walcott H, Peterson S, Porfiri M. Energy harvesting from a piezoelectric biomimetic fish tail. Renewable Energy, 2016, 86: 449-458

[13] Chaplin J, Subbiah K. Hydrodynamic damping of a cylinder in still water and in a transverse current. Applied Ocean Research, 1998, 20(4): 251-259

[14] Chaplin JR. Hydrodynamic damping of a cylinder at β ≈ 10⁶. Journal of Fluids and Structures, 2000, 14(8): 1101-1117

[15] Chen H, Aït-Ahmed N, Zaïm E, Machmoum M (2012) Marine tidal current systems: state of the art. 2012 IEEE International Symposium on Industrial Electronics, 1431–1437. DOI: https://doi.org/10.1109/ISIE.2012.6237301

[16] Chen H, Tang T, Aït-Ahmed N, Benbouzid M, Machmoum M, Zaïm M. Attraction, challenge and current status of marine current energy. IEEE Access, 2018, 6: 12665-12685

[17] Chen H, Tong X, He Z, Chen Y. Numerical and experimental studies on the hydrodynamic damping of a zero-thrust propeller. Journal of Fluids and Structures, 2020, 94: 102957

[18] Chen P, Chen J, Hu Z. Review of experimental-numerical methodologies and challenges for floating offshore wind turbines. Journal of Marine Science and Application, 2020, 19: 339-361

[19] Chen S, Jendrzejczyk J. Flow velocity dependence of damping in tube arrays subjected to liquid cross-flow. Journal of Fluids Engineering, 1981, 103(5): 130-135

[20] Chin C, Lau M. Modeling and testing of hydrodynamic damping model for a complex-shaped remotely-operated vehicle for control. Journal of Marine Science and Application, 2012, 11: 150-163

[21] Coutu A, Seeley C, Monette C, Nennemann B, Marmont H. Damping measurements in flowing water. IOP Conference Series: Earth and Environmental Science, 2012, 15(4): 062060

[22] Crandall S. The role of damping in vibration theory. Journal of Sound and Vibration, 1970, 11(1): 3-18

[23] Čupr P, Štefan D, Habán V, Rudolf P. FSI analysis of francis-99 hydrofoil employing SBES model to adequately predict vortex shedding. Journal of Physics: Conference Series, 2019, 1296: 012002

[24] Dehkharqani A, Aidanpää J, Engström F, Cervantes M. A review of available methods for the assessment of fluid added mass, damping, and stiffness with an emphasis on hydraulic turbines. Applied Mechanics Reviews, 2018, 70(5): 050801

[25] Ducoin A, Astolfi J, Deniset F, Sigrist J. Computational and experimental investigation of flow over a transient pitching hydrofoil. European Journal of Mechanics-B/Fluids, 2009, 28(6): 728-743

[26] Ducoin A, Astolfi J, Gobert M. An experimental study of boundary-layer transition induced vibrations on a hydrofoil. Journal of Fluids and Structures, 2012, 32: 37-51

[27] Fraenkel P. Power from marine currents. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2002, 216(1): 1-14

[28] Gaschler M, Abdel-Maksoud M. Computation of hydrodynamic mass and damping coefficients for a cavitating marine propeller flow using a panel method. Journal of Fluids and Structures, 2014, 49: 574-593

[29] Gauthier J, Giroux A, Etienne S, Gosselin F. A numerical method for the determination of flow-induced damping in hydroelectric turbines. Journal of Fluids and Structures, 2017, 69: 341-354

[30] Harrison C, Tavernier E, Vancauwenberghe O. On the response of a resonating plate in a liquid near a solid wall. Sensors and Actuators A: Physical, 2007, 134(2): 414-426

[31] He L, Wang Z, Kurosawa S, Nakahara Y. Resonance investigation of pump-turbine during startup process. IOP Conference Series: Earth and Environmental Science, 2014, 22(3): 032024

[32] He L, Zhou L, Ahn S, Wang Z, Nakahara Y, Kurosawa S. Evaluation of gap influence on the dynamic response behavior of pump-turbine runner. Engineering Computations, 2019, 36(2): 491-508

[33] Jacobson K, Kiviaho J, Kennedy G, Smith M. Evaluation of time-domain damping identification methods for flutter-constrained optimization. Journal of Fluids and Structures, 2019, 87: 174-188

[34] Kaminer A, Kavitskii B. Experimental investigation of hydrodynamic damping during bending oscillations of blade profiles in water flow. Strength of Materials, 1976, 8(1): 25-2

[35] Kohtanen E, Davis R. Hydroelastic damping of low aspect ratio cantilevered plates. Journal of Fluids and Structures, 2019, 90: 315-333

[36] Liaghat T, Guibault F, Allenbach L, Nennemann B (2014) Two-way fluid-structure coupling in vibration and damping analysis of an oscillating hydrofoil. Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, Quebec

[37] Liang Q, Rodriguez C, Egusquiza E, Escaler X, Farhat M, Avellan F. Numerical simulation of fluid added mass effect on a francis turbine runner. Computing Fluids, 2007, 36(6): 1106-1118

[38] Liu X, Luo Y, Karney B, Wang Z, Zhai L. Virtual testing for modal and damping ratio identification of submerged structures using the PolyMAX algorithm with two-way fluid–structure Interactions. Journal of Fluids and Structures, 2015, 54: 548-565

[39] Liu X, Zhou L, Escaler X, Wang Z, Luo Y, Torre O. Numerical simulation of added mass effects on a hydrofoil in cavitating flow using acoustic fluid-structure interaction. Journal of Fluids Engineering, 2017, 139(4): 041301

[40] Liu Y, Berger T, Huang B, Wu Q, Farhat M. Vortex shedding from a composite hydrofoil: Experimental evidence of a novel “partial lock-in”. Physics of Fluids, 2023, 35(12): 125132

[41] Louyot M, Nennemann B, Monette C, Gosselin F. Modal analysis of a spinning disk in a dense fluid as a model for high head hydraulic turbines. Journal of Fluids and Structures, 2020, 94: 102965

[42] Maung P, Prusty B, Shamsuddoha M, Phillips A, St John N. Static and dynamic response of a carbon composite full-scale hydrofoil manufactured using automated fibre placement. Composites Part C: Open Access, 2021, 6: 100218

[43] Monette C, Nennemann B, Seeley C, Coutu A, Marmont H. Hydrodynamic damping theory in flowing water. IOP Conference Series: Earth and Environmental Science, 2014, 22(3): 032044

[44] Nachtane M, Tarfaoui M, Goda I, Rouway M. A review on the technologies, design considerations and numerical models of tidal current turbines. Renewable Energy, 2020, 157: 1274-1288

[45] Naik T, Longmire E, Mantell S. Dynamic response of a cantilever in liquid near a solid wall. Sensors and Actuators A: Physical, 2003, 102(3): 240-254

[46] Nennemann B, Monette C, Chamberland-lauzon J. Hydrodynamic damping and stiffness prediction in Francis turbine runners using CFD. IOP Conference Series: Earth and Environmental Science, 2016, 49(7): 072006

[47] Nicholls-Lee R, Turnock S, Boyd S (2011) A method for analysing fluid structure interactions on a horizontal axis tidal turbine. 9th European Wave and Tidal Energy Conference, Southampton

[48] Pernod L, Ducoin A, Le Sourne H, Astolfi J, Casari P. Experimental and numerical investigation of the fluid-structure interaction on a flexible composite hydrofoil under viscous flows. Ocean Engineering, 2019, 194: 106647

[49] Presas A, Egusquiza E, Valero C, Valentin D, Seidel U. Feasibility of using PZT actuators to study the dynamic behavior of a rotating disk due to rotor-stator interaction. Sensors, 2014, 14(7): 11919-11942

[50] Presas A, Valentin D, Egusquiza E, Valero C, Egusquiza M, Bossio M. Accurate determination of the frequency response function of submerged and confined structures by using PZT-patches. Sensors, 2017, 17(3): 660

[51] Presas A, Valentin D, Egusquiza E, Valero C, Seidel U. Influence of the rotation on the natural frequencies of a submerged-confined disk in water. Journal of Sound and Vibration, 2015, 337: 161-180

[52] Presas A, Valentin D, Egusquiza E, Valero C, Seidel U. Dynamic response of a rotating disk submerged and confined. Influence of the axial gap. Journal of Fluids and Structures, 2016, 62: 332-349

[53] Presas A, Valentin D, Valero C, Egusquiza M, Egusquiza E. Experimental measurements of the natural frequencies and mode shapes of rotating disk-blades-disk assemblies from the stationary frame. Applied Sciences, 2019, 9(18): 3864

[54] Qiao F, Sun Y, Zhu D, Fang M, Zhang F, Tao R, Xiao R. Analysis of stress–strain characteristics and signal coherence of low-specific-speed impeller based on fluid - structure interaction. Journal of Marine Science and Engineering, 2023, 12(1): 2

[55] Rankl C, Pastushenko V, Kienberger F, Stroh C, Hinterdorfer P. Hydrodynamic damping of a magnetically oscillated cantilever close to a surface. Ultramicroscopy, 2004, 100(4): 301-308

[56] Reese M. Vibration and damping of hydrofoils in uniform flow, 2010, Pennsylvania: The Pennsylvania State University

[57] Rodriguez C, Flores P, Pierart F, Contzen L, Egusquiza E. Capability of structural–acoustical FSI numerical model to predict natural frequencies of submerged structures with nearby rigid surfaces. Computers & Fluids, 2012, 64: 117-126

[58] Roig R, Chen J, Torre O, Escaler X. Understanding the influence of wake cavitation on the dynamic response of hydraulic profiles under lock-in conditions. Energies, 2021, 14(19): 6033

[59] Roth S. Fluid-structure coupling effects on the dynamic response of pump-turbine guide vanes, 2012, Lausanne: Swiss Federal Institute of Technology Lausanne

[60] Roth S, Calmon M, Farhat M, Münch C, Bjoern H, Avellan F (2009) Hydrodynamic damping identification from an impulse response of a vibration blade. 3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Brno

[61] Santo F. Added mass and hydrodynamic damping of perforated plates vibrating in water. Journal of Pressure Vessel Technology, 1981, 103(2): 175-182

[62] Seeley C, Coutu A, Monette C, Nennemann B, Marmont H. Characterization of hydrofoil damping due to fluid-structure interaction using piezocomposite actuators. Smart Materials and Structures, 2012, 21(3): 035027

[63] Silva D. Vibration: fundamentals and practice, 2000, Boca Raton: CRC Press

[64] Sun Y, Yao Z, Wen H, Zhong Q, Wang F. Cavitation bubble collapse in a vicinity of a rigid wall with a gas entrapping hole. Physics of Fluids, 2022, 34(7): 073314

[65] Tengs E. Numerical simulation of fluid-structure Interaction in high head Francis turbines, 2019, Trondheim: Norwegian University of Science and Technology

[66] Tengs E, Bergan C, Jakobsen K, Storli P. Numerical simulation of the hydrodynamic damping of a vibrating hydrofoil. IOP Conference Series: Earth and Environmental Science, 2019, 240(6): 062002

[67] Tita V, Carvalho J, Lirani J. A procedure to estimate the dynamic damped behavior of fiber reinforced composite beams submitted to flexural vibrations. Materials Research, 2001, 4: 315-321

[68] Torre O, Escaler X, Egusquiza E, Farhat M. Experimental investigation of added mass effects on a hydrofoil under cavitation conditions. Journal of Fluids and Structures, 2013, 39: 173-187

[69] Torre O, Escaler X, Egusquiza E, Farhat M. Numerical and experimental study of a nearby solid boundary and partial submergence effects on hydrofoil added mass. Computers & Fluids, 2014, 91: 1-9

[70] Trivedi C. A review on fluid structure interaction in hydraulic turbines: A focus on hydrodynamic damping. Engineering Failure Analysis, 2017, 77: 1-22

[71] Valentin D, Presas A, Egusquiza E, Valero C. Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement. Journal of Fluids and Structures, 2014, 50: 1-17

[72] Vandiver J, Chung T. Hydrodynamic damping on flexible cylinders in sheared flow. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1989, 115(2): 154-171

[73] Wang J, Wan D. Application progress of computational fluid dynamic techniques for complex viscous flows in ship and ocean engineering. Journal of Marine Science and Application, 2020, 19: 1-16

[74] Wang W. Effect of cavitation on the dynamic characteristics of hydraulic machinery structures, 2020, Beijing: China Agricultural University

[75] Wang W, Zhou L, Xia X, Tao R. Analysis of the hydrodynamic damping characteristics on a symmetrical hydrofoil. Renewable Energy, 2021, 178: 821-829

[76] Wang Y, Niu W, Yu X, Yang S, Zhang L. Quantitative evaluation of motion performances of underwater gliders considering ocean currents. Ocean Engineering, 2021, 236: 109501

[77] Weder M, Horisberger B, Monette C, Sick M, Dual J. Experimental modal analysis of disk-like rotor-stator system coupled by viscous liquid. Journal of Fluids and Structures, 2019, 88: 198-215

[78] Wen H, Yao Z, Wu Q, Sun Y, Yang C, Zhong Q. Investigation of cavitation erosion caused by laser-induced single bubble collapse near alloy coating surface. Journal of Hydrodynamics, 2023, 35: 876-886

[79] Wen H, Yao Z, Zhong Q, Tian Y, Sun Y, Wang F. Energy partitioning in laser-induced millimeter-sized spherical cavitation up to the fourth oscillation. Ultrasonics Sonochemistry, 2023, 95: 106391

[80] Wu J, Liu Y, Zhang D, Cao Z, Guo Z. Numerical investigation of vortex shedding from a 5: 1 rectangular cylinder at different angles of attack. Journal of Marine Science and Engineering, 2022, 10(12): 1913

[81] Xie T, Wang T, He Q, Diallo D, Claramunt C. A review of current issues of marine current turbine blade fault detection. Ocean Engineering, 2020, 218: 108194

[82] Xiu H, Davis R, Romeo R. Edge clearance effects on the added mass and damping of beams submerged in viscous fluids. Journal of Fluids and Structures, 2018, 83: 194-217

[83] Xu Y, Tan L, Liu Y, Cao S. Pressure fluctuation and flow pattern of a mixed-flow pump with different blade tip clearances under cavitation condition. Advances in Mechanical Engineering, 2017, 9(4): 1-12

[84] Yang J, Marks C, Jiang J, Chen D, Elahi A, Tsai W. Determination of fluid damping using random excitation. Journal of Energy Resources Technology, 1985, 107(2): 220

[85] Yao Z, Wang F, Dreyer M, Farhat M. Effect of trailing edge shape on hydrodynamic damping for a hydrofoil. Journal of Fluids and Structures, 2014, 51: 189-198

[86] Younes M, Younes Y, El-Madah M, Ibrahim I, El-Dannanh E. An experimental investigation of hydrodynamic damping due to vertical baffle arrangements in a rectangular tank. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 2007, 221(3): 115-123

[87] Zeng Y, Qi X, Bai M, Zhou L, Yao Z. How the radial gap affects the runner’s hydrodynamic damping characteristic of a pump-turbine: A physical experiment on a rotating disc. Journal of Hydrodynamics, 2023, 35(4): 736-745

[88] Zeng Y, Qi X, Shu L, Yao Z, Zhou L, Wang F. Fluid-structure interaction effects of a partially immersed, cantilevered hydrofoil. Journal of Fluids Engineering, 2022, 144(2): 021202

[89] Zeng Y, Qi X, Yao Z, Wang F, Wang Y, Wang F. Experimental investigation on damping characteristics of a vibrating hydrofoil in low-order modes. Journal of Mechanical Engineering, 2022, 58(5): 108-118 in Chinese)

[90] Zeng Y, Wang C, Huang B, Wang F, Xiao R, Yao Z. A comprehensive empirical equation for the hydrodynamic damping of vibrating blade-like structures. Ocean Engineering, 2023, 270: 113721

[91] Zeng Y, Yao Z, Gao J, Hong Y, Wang F, Zhang F. Numerical investigation of added mass and hydrodynamic damping on a blunt trailing edge hydrofoil. Journal of Fluids Engineering, 2019, 141(8): 081108

[92] Zeng Y, Yao Z, Huang B, Wu Q, Wang F. Experimental investigation of the hydrodynamic damping of a vibrating hydrofoil in cavitating flow. Ocean Engineering, 2022, 266: 112734

[93] Zeng Y, Yao Z, Hong Y, Wang F. Research on numerical prediction methods of hydrodynamic damping ratio for a hydrofoil based on one-way and two-way fluid-structure interactions. Journal of Hydraulic Engineering, 2020, 51(11): 1432-1439 (in Chinese)

[94] Zeng Y, Yao Z, Zhang S, Wang F, Xiao R. Influence of Tip clearance on the hydrodynamic damping characteristics of a hydrofoil. Journal of Fluids Engineering, 2021, 143(6): 061202

[95] Zeng Y, Yao Z, Zhou P, Wang F, Hong Y. Numerical investigation into the effect of the trailing edge shape on added mass and hydrodynamic damping for a hydrofoil. Journal of Fluids and Structures, 2019, 88: 167-184

[96] Zeng Y, Zhang M, Du Y, Yao Z, Wu Q, Wang F. Influence of attack angle on the hydrodynamic damping characteristic of a hydrofoil. Ocean Engineering, 2021, 238: 109692

[97] Zhang A, Li S, Cui P, Li S, Liu Y. A unified theory for bubble dynamics. Physics of Fluids, 2023, 35(3): 033323

[98] Zhang M, Mbango-Ngoma P, Xiao Z, Qing G. Numerical investigation of the trailing edge shape on the added damping of a Kaplan turbine runner. Mathematical Problems in Engineering, 2021, 2021: 1-11

[99] Zhou J, Si Y, Chen Y. A review of subsea AUV technology. Journal of Marine Science and Engineering, 2023, 11(6): 1119

[100] Zhu D, Tao R, Lu Z, Wu Y, Xiao R. Optimization design of the internal structural support of marine turbine blade for weight reduction: A preliminary study. Ocean Engineering, 2022, 260: 111989

[101] Zobeiri A. Effect of hydrofoil trailing edge geometry on the wake dynamic, 2012, Lausanne, Switzerland: Swiss Federal Institute of Technology Lausanne

[102] Zobeiri A, Ausoni P, Avellan F, Farhat M. How oblique trailing edge of a hydrofoil reduces the vortex-induced vibration. Journal of Fluids and Structures, 2012, 32: 78-89

[103] Zrayka A, Mucchi E. A comparison among modal parameter extraction methods. Applied Sciences, 2019, 1: 1-11