Research Papers: Flows in Complex Systems

Fluid–Structure Interaction Simulation on Energy Harvesting From Vortical Flows by a Passive Heaving Foil

[+] Author and Article Information
Zhenglun Alan Wei

Department of Aerospace Engineering,
University of Kansas,
1530 W 15th Street,
Lawrence, KS 66045-7621
e-mail: alan.zlwei@gmail.com

Zhongquan Charlie Zheng

Fellow ASME,
Department of Aerospace Engineering,
University of Kansas,
1530 W 15th Street,
Lawrence, KS 66045-7621
e-mail: zzheng@ku.edu

1Present address: Georgia Institute of Technology, 387 Technology Circle, Suite 234, Atlanta, GA 30313.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 26, 2017; final manuscript received July 31, 2017; published online September 20, 2017. Assoc. Editor: Ioannis K. Nikolos.

J. Fluids Eng 140(1), 011105 (Sep 20, 2017) (10 pages) Paper No: FE-17-1187; doi: 10.1115/1.4037661 History: Received March 26, 2017; Revised July 31, 2017

This study investigates energy harvesting of a two-dimensional foil in the wake downstream of a cylinder. The foil is passively mobile in the transverse direction. An immersed boundary (IB) method with a fluid–structure interaction (FSI) model is validated and employed to carry out the numerical simulation. For improving numerical stability, this study incorporates a modified low-storage first-order Runge–Kutta scheme for time integration and demonstrates the performance of this temporal scheme on reducing spurious pressure oscillations of the IB method. The simulation shows the foil emerged in a vortical wake achieves better energy harvesting performance than that in a uniform flow. The types of the dynamic response of the energy harvester are identified, and the periodic response is desired for optimal energy harvesting performance. Last, the properties of vortical wakes are found to be of pivotal importance in obtaining this desired periodic response.

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Grahic Jump Location
Fig. 4

Time-periodic variation of the lift coefficient between three RK3 schemes. “RK3—all three stages”: the flow quantities for forcing points were interpolated by Eq. (20) with Vk= Vn for all three stages of the RK3 scheme; “RK3—first two stages”: the flow quantities for the forcing points were interpolated by Eq. (20) with Vk= Vn for the first two stages of the RK3 scheme; “RK3—first stage”: the RK3 scheme proposed in the current study (the same as Fig. 3).

Grahic Jump Location
Fig. 2

Cp on the top surface of a stationary cylinder at Re = 40. Compare the current result with δt = 256−1 to the results from Ref. [31].

Grahic Jump Location
Fig. 3

Time-periodic variation of the lift coefficient between two RK3 schemes. “RK3—three-sublocation implementation”: the Vk in Eq. (20) was reconstructed as intermediate physical velocities corresponding to the substep physical positions, based on the effective time step, αkδt; “RK3—first stage”: It was proposed by the current paper, e.g., see Eqs. (21) and (22), which only applied the momentum equation with nonzero forcing terms for forcing points at the first stage of the RK3 scheme.

Grahic Jump Location
Fig. 5

Time-periodic variation of the lift coefficient between three RK3 schemes. “First-order time marching”: the time marching scheme follows [31], which obtained an overall first order temporal accuracy; “RK3—first stage”: the RK3 scheme proposed in the current study, which is the same as Figs. 3 and 4 and used δt = 256−1; “RK3—first stage—2δt”: the RK3 scheme proposed in the current study with 2δt = 128−1.

Grahic Jump Location
Fig. 6

The variation of the response amplitude with the reduced velocity for a single vortex induced vibrating cylinder and its comparison with previous studies [35,46,47]. (y/D)max is the maximum vertical displacement of the cylinder.

Grahic Jump Location
Fig. 7

Sketch of the configuration of the system of a D-cylinder and an elliptical foil

Grahic Jump Location
Fig. 8

Vorticity contours for the case with hc = 0.25 and (a) L = 4, (b) L = 5, (c) L = 6, and (d) L = 7 when the airfoil is down-stroking and Ya is about zero

Grahic Jump Location
Fig. 1

Sketch of the configuration of the system involving only one cylinder

Grahic Jump Location
Fig. 9

Histories of vertical positions for all the cases of L = 5 and 7 with variable hc: (a) hc=0.1, (b) hc=0.25, (c) hc=0.4, (d) hc=0.55, and (e) hc=0.7

Grahic Jump Location
Fig. 10

Fourier transform of the Ya histories for different cases with (a) L = 5 and (b) L = 7

Grahic Jump Location
Fig. 11

Comparison of (a) energy harvesting efficiency and (b) extracted power between all the cases

Grahic Jump Location
Fig. 12

The history of approximate foil positions and vorticity contours over an oscillating cycle of the foil for the case with hc = 0.25 and L = 7

Grahic Jump Location
Fig. 13

The history of approximate foil positions and vorticity contours over an oscillating cycle of the foil for the case with hc = 0.4 and L = 7

Grahic Jump Location
Fig. 14

The history of approximate foil positions and vorticity contours over an oscillating cycle of the foil for the case with hc = 0.1 and L = 7



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