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Research Papers: Flows in Complex Systems

Optimization of Biomimetic Propulsive Kinematics of a Flexible Foil Using Integrated Computational Fluid Dynamics–Computational Structural Dynamics Simulations

[+] Author and Article Information
Jiho You, Jinmo Lee

Department of Mechanical Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213

Seungpyo Hong

Department of Mechanical Engineering,
Pohang University of Science and Technology,
Pohang 37673, Gyeongbuk, South Korea

Donghyun You

Associate Professor
Department of Mechanical Engineering,
Pohang University of Science and Technology,
Pohang 37673, Gyeongbuk, South Korea
e-mail: dhyou@postech.ac.kr

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 6, 2018; final manuscript received September 12, 2018; published online December 24, 2018. Assoc. Editor: Shawn Aram.

J. Fluids Eng 141(6), 061106 (Dec 24, 2018) (11 pages) Paper No: FE-18-1246; doi: 10.1115/1.4041879 History: Received April 06, 2018; Revised September 12, 2018

A computational methodology, which combines a computational fluid dynamics (CFD) technique and a computational structural dynamics (CSD) technique, is employed to design a deformable foil whose kinematics is inspired by the propulsive motion of the fin or the tail of a fish or a cetacean. The unsteady incompressible Navier–Stokes equations are solved using a second-order accurate finite difference method and an immersed-boundary method to effectively impose boundary conditions on complex moving boundaries. A finite element-based structural dynamics solver is employed to compute the deformation of the foil due to interaction with fluid. The integrated CFD–CSD simulation capability is coupled with a surrogate management framework (SMF) for nongradient-based multivariable optimization in order to optimize flapping kinematics and flexibility of the foil. The flapping kinematics is manipulated for a rigid nondeforming foil through the pitching amplitude and the phase angle between heaving and pitching motions. The flexibility is additionally controlled for a flexible deforming foil through the selection of material with a range of Young's modulus. A parametric analysis with respect to pitching amplitude, phase angle, and Young's modulus on propulsion efficiency is presented at Reynolds number of 1100 for the NACA 0012 airfoil.

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References

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Figures

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Fig. 1

Computational configuration of a pitching-heaving hydrofoil

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Fig. 2

Computational domain and boundary conditions

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Fig. 3

Grid lines in the domain and around the hydrofoil

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Fig. 4

Finite element discretization of a foil

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Fig. 5

Coupling of fluid and structure solver

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Fig. 6

Latin hypercube sampling in a two-dimensional case

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Fig. 7

Procedure of surrogate management framework. Note that dots with a circle inside denote optimal points and dots with a cross inside denote space-filling points, respectively: (a) Latin hypercube sampling, (b) kriging interpolation, (c) estimate optimal point and add more samples, and (d) after the solution converges.

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Fig. 8

A contour plot of J in two-parameter optimization (phase angle versus pitching amplitude): (a) α = 0.6, (b) α = 0.7, and (c) α = 0.8

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Fig. 9

The thrust coefficient and the power input of the optimal kinematic case (—) and the best thrust case (- - -) for α = 0.7: (a) thrust coefficient CT and power input CP

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Fig. 10

Spanwise vorticity contours during a period (T) of the optimal kinematic motion of a rigid foil for α = 0.7: (a) t = 0.000T, (b) t = 0.125T, (c) t = 0.250T, (d) t = 0.375T, (e) t = 0.500T, (f) t = 0.625T, (g) t = 0.750T, and (h) t = 0.875T

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Fig. 11

Spanwise vorticity contours during a period (T) of the optimal kinematic motion of a rigid foil for α = 0.6: (a) t = 0.000T, (b) t = 0.125T, (c) t = 0.250T, (d) t = 0.375T, (e) t = 0.500T, (f) t = 0.625T, (g) t = 0.750T, and (h) t = 0.875T

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Fig. 12

Spanwise vorticity contours during a period (T) of the optimal kinematic motion of a rigid foil for α = 0.8: (a) t = 0.000T, (b) t = 0.125T, (c) t = 0.250T, (d) t = 0.375T, (e) t = 0.500T, (f) t = 0.625T, (g) t = 0.750T, and (h) t = 0.875T

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Fig. 13

A contour plot of Γ in three-parameter optimization (α = 0.7): (a) Young's modulus versus phase angle, (b) Young's modulus versus pitching amplitude, and (c) phase angle versus pitching amplitude

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Fig. 14

The thrust coefficient and the power input of the optimal kinematics for α = 0.7 with a flexible foil (—) and with a rigid foil (- - -): (a) thrust coefficient CT and power input CP

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Fig. 15

Spanwise vorticity contours during a period (T) of the optimal kinematic motion of a flexible foil for α = 0.7: (a) t = 0.000T, (b) t = 0.125T, (c) t = 0.250T, (d) t = 0.375T, (e) t = 0.500T, (f) t = 0.625T, (g) t = 0.750T, and (h) t = 0.875T

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