Research Papers: Flows in Complex Systems

Effect of Nonuniform Flexibility on Hydrodynamic Performance of Pitching Propulsors

[+] Author and Article Information
Samane Zeyghami

Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015
e-mail: saz316@lehigh.edu

Keith W. Moored

Department of Mechanical
Engineering and Mechanics,
Lehigh University,
Bethlehem, PA 18015
e-mail: kmoored@lehigh.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 5, 2018; final manuscript received November 2, 2018; published online February 8, 2019. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 141(4), 041108 (Feb 08, 2019) (7 pages) Paper No: FE-18-1081; doi: 10.1115/1.4041976 History: Received February 05, 2018; Revised November 02, 2018

Many aquatic animals propel themselves efficiently through the water by oscillating flexible fins. These fins are, however, not homogeneously flexible, but instead their flexural stiffness varies along their chord and span. Here, we develop a simple model of these functionally graded materials where the chordwise flexibility of the foil is modeled by one or two torsional springs along the chord line. The torsional spring structural model is then strongly coupled to a boundary element fluid model to simulate the fluid–structure interactions. We show that the effective flexibility of the combined fluid–structure system scales with the ratio of the added mass forces acting on the passive portion of the foil and the elastic forces defined by the torsional spring hinge. Importantly, by considering this new scaling of the effective flexibility, the propulsive performance is then detailed for a foil with a flexible hinge that is actively pitching about its leading edge. The scaling allows for the resonance frequency of the fluid–structure system and the bending pattern of the propulsor to be independently varied by altering the effective flexibility and the location of a single torsional spring along the chord, respectively. It is shown that increasing the flexion ratio, by moving the spring away from the leading edge, leads to enhanced propulsive efficiency, but compromises the thrust production. Proper combination of two flexible hinges, however, can result in a gain in both the thrust production and propulsive efficiency.

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Grahic Jump Location
Fig. 1

Schematic of the model for a single spring

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Fig. 2

Propulsive efficiency as a function of (a) number of time steps and (b) number of body panels

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Fig. 3

Analytical solutions for thrust and power coefficient as a function of reduced frequency, for two different nondimensional spring stiffnesses, are shown with solid lines. These solutions are taken from Ref. [26]. Closed circles are the solutions calculated by the present numerical method.

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Fig. 4

(a) Trailing edge amplitude, (b) thrust coefficient, (c) power coefficient, and (d) efficiency as a function of Πk

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Fig. 5

Variation of thrust (a) and power (b) coefficients, C′t and C′p, defined by Eq. (3) with Πk. Contours of C′t and C′p in λ–Πk plane. Dotted lines are the contours of propulsive efficiency.

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Fig. 6

(a) Trailing edge amplitude, (b) thrust coefficient, (c) power coefficient, and (d) efficiency as a function of Πk for two flexible hinge configuration

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Fig. 7

Change in the relative orientation of the solid elements versus time, within one cycle. The line representing θ0 shows the prescribed pitching motion of the leading edge. The lines representing θ1 and θ2, respectively, show the deflection angles of the second and the third element. The deflection angles are measured relative to the preceding element. The angles are shown for three different Πk values of 0.2, 0.35, and 0.5.



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