Investigation of the Hydrodynamic Performance of Separated Undulating Fins in Heave Motion

Abstract

Due to their distinctive hydrodynamic characteristics, undulating fins have become a research hotspot in the field of underwater vehicles. However, conventional undulating fins exhibit significant limitations in heave motion, which severely restrict their applicability in underwater environments. Inspired by biomimetic principles, a novel undulating fin configuration is proposed in this study to overcome deficiencies associated with heave performance. Numerical simulations are conducted to investigate the effects of undulation patterns, swing angles, and other parameters on the hydrodynamic responses during heave motion. The results indicate that variations in the swing angle exert a pronounced influence on the hydrodynamic forces in the Y direction. Specifically, the hydrodynamic response in the Y direction generated by an undulating fin with a swing angle of 30° is approximately three times that produced by a fin with a swing angle of 10°, demonstrating that larger swing angles enable more effective heave motion. The underlying mechanisms of these influencing factors are further elucidated through flow field analyses. The results show that, under different undulation modes, the vortices generated by the separated undulating fins either diverge or cancel each other. Nevertheless, none of the undulation patterns produces a significant impact on the overall hydrodynamic response of the undulating fins, thereby ensuring the stability of the heave motion of the separated undulating fin system. Overall, the proposed approach effectively enhances the maneuverability of underwater vehicles and compensates for the insufficient heave performance of conventional undulating fins.

Keywords

Biomimetics / Undulating fin / Hydrodynamic performance / Flow field analysis

References

[1] Clark RP, Smits AJ. Thrust production and wake structure of a batoid-inspired oscillating fin. Journal of Fluid Mechanics, 2006, 562: 415-429

[2] Hu QQ, Yu YL. The hydrodynamic effects of undulating patterns on propulsion and braking performances of long-based fin. AIP Advances, 2022, 12: 035319

[3] Li Y, Chen L, Wang Y, Ren C. Design and experimental evaluation of the novel undulatory propulsors for biomimetic underwater robots. Bioinspiration & Biomimetics, 2021, 16(5): 056005

[4] Li G, Liu G, Ma P, Li G, Fang X. Study on stable thrust of separated undulating fins. Ocean Engineering, 2024, 306: 118046

[5] Li G, Ma P, Fang X, Li G, Liu G, Cheng H. Study on thrust increase characteristics of separated undulating fins. Ocean Engineering, 2024, 313: 119292 Part 1

[6] Li S, Hu Q, Zhang T, Shi X, Zeng Y, Chen L, Wei H, Zhang J, Guo C. Bionic parallel undulating fins: Influence of unsteady coupling effect on robot propulsion performance. Ocean Engineering, 2024, 312: 119075

[7] Li G, Ma P, Fang X, Li G, Liu G, Liu X. Hydrodynamic response of separated undulating fins based on numerical simulation and orthogonal experiment: Analysis and optimization of thrust influencing factors. Ocean Engineering, 2025, 328: 121094

[8] Liu C, Zhang X, Wang C. Hydrodynamic performance of two-dimensional undulating fins under flow excitation near the free surface in three-dimensional numerical tank. Physics of Fluids, 2025, 37: 015158

[9] Liu F, Lee KM, Yang CJ. Hydrodynamics of an undulating fin for a wave-like locomotion system design. IEEE/ASME Transactions on Mechatronics, 2011, 17(3): 554-562

[10] Low KH. Modelling and parametric study of modular undulating fin rays for fish robots. Mechanism and Machine Theory, 2009, 44(3): 615-632

[11] Neveln ID, Bale R, Bhalla APS, Curet OM, Patankar NA, MacIver MA. Undulating fins produce off-axis thrust and flow structures. Journal of Experimental Biology, 2014, 217(2): 201-213

[12] Nygaard TF, Martin CP, Torresen J, Glette K, Howard D. Real-world embodied AI through a morphologically adaptive quadruped robot. Nature Machine Intelligence, 2021, 3: 410-419

[13] Pang S, Qin F, Shang W, Cong S, Zhang S. Optimized design and investigation about propulsion of bionic Tandem undulating fins I: Effect of phase difference. Ocean Engineering, 2021, 239: 109842

[14] Peng J, Xie Y, Yang Q, Jia Y, Huang W, Xie G. Multi-environment robotic locomotion through integrated pectoral and caudal fin propulsion. Ocean Engineering, 2025, 328: 120982

[15] Ren K, Yu J. Research status of bionic amphibious robots: A review. Ocean Engineering, 2021, 227: 108862

[16] Rafeeq M, Toha SF, Ahmad S, Razib MA. Locomotion strategies for amphibious robots-A review. IEEE Access, 2021, 9: 26323-26342

[17] Sfakiotakis M, Lane DM, Davies JBC. Review of fish swimming modes for aquatic locomotion. IEEE Journal of Oceanic Engineering, 1999, 24(2): 237-252

[18] Shi X, Chen Z, Zhang T, Li S, Zeng Y, Chen L, Hu Q. Hydrodynamic performance of a biomimetic undulating fin robot under different water conditions. Ocean Engineering, 2023, 288: 116068 Part 1

[19] Shi G, Xiao Q. Numerical investigation of a bio-inspired underwater robot with skeleton-reinforced undulating fins. European Journal of Mechanics-B/Fluids, 2021, 87: 75-91

[20] Su Z, Shen X, Han W, Zhu B, Wang Q, Li W. Dynamic analysis of symmetric oscillation and turning characteristics of a flexible fin underwater robot propelled by double fins. Physics of Fluids, 2023, 35(3): 13

[21] Sun G, Wang Z, Ling H, Dou P, Yan Y. Investigation on the propulsive efficiency of undulating fin propulsor. Ocean Engineering, 2024, 312: 119113 Part 2

[22] Wang C, Liu Q, Yang J, Guo C. Numerical and experimental study of a hydrodynamic analysis of the periodical fluctuation of bio-inspired banded fins. Journal of Marine Science and Engineering, 2025, 13(2): id.462

[23] Wei C, Li S, Hu Q. Hydrodynamic performance analysis of formations of dual three-dimensional undulating fins. Ocean Engineering, 2024, 305: 117939

[24] Wei QP, Wang S, Dong X, Shang LJ, Tan M. Design and kinetic analysis of a biomimetic underwater vehicle with two undulating long-fins. Acta Automatica Sinica, 2013, 39(8): 1330-1338

[25] Wei C, Hu Q, Li S, Zhang T, Shi X. Hydrodynamic performance analysis of undulating fin propulsion. Physics of Fluids, 2023, 35: 091906

[26] Xia M, Wang H, Yin Q, Shang J, Luo Z, Zhu Q. Design and mechanics of a composite wave-driven soft robotic fin for biomimetic amphibious robot. Journal of Bionic Engineering, 2023, 20: 934-952

[27] Zeng Y, Hu Q, Zhang T, Li S, Shi X, Sun L, Jiang C, Zhang J, Guo C. Dynamic modeling and performance analysis of the undulating fin considering flexible deformation and fluid-fin interactions. Ocean Engineering, 2025, 320: 120281

[28] Zhang J, Bai Y, Zhai S, Gao D. Numerical study on vortex structure of undulating fins in stationary water. Ocean Engineering, 2019, 187: 106166

[29] Zhang D, Pan G, Chao L, Zhang Y. Effects of Reynolds number and thickness on an undulatory self-propelled foil. Physics of Fluids, 2018, 30: 071902

[30] Zhou J, Yu N, Liu S, Xin L, Liu Y, Gao G, Na Z, Hou X. Inspired by the Black Ghost Knifefish: Bionic design of undulatory fin with 2-DOF rays and its propulsion performance. Applied Bionics and Biomechanics, 2023, 2023: 7831175

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Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature