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Research Papers: Flows in Complex Systems

Numerical Investigation of the Effects of Nonsinusoidal Motion Trajectory on the Propulsion Mechanisms of a Flapping Airfoil

[+] Author and Article Information
A. Boudis

LTSE,
Faculty of Physics,
University of Science and Technology
Houari Boumediene (USTHB),
BP 32 El-Alia,
Algiers 16111, Algeria
e-mail: aboudis@usthb.dz

A. C. Bayeul-Lainé

LMFL,
Arts et Métiers ParisTech,
8 Boulevard Louis XIV,
Lille 59046, France

A. Benzaoui

LTSE,
Faculty of Physics,
University of Science and Technology
Houari Boumediene (USTHB),
BP 32 El-Alia,
Algiers 16111, Algeria

H. Oualli

LMF,
Ecole Militaire Polytechnique,
BP 17 Bordj-el-Bahri,
Algiers 16046, Algeria

O. Guerri

Centre de Développement des
EnergiesRenouvelables, CDER,
BP 62, Route de l'Observatoire,
Bouzareah,
Algiers 16340, Algeria

O. Coutier-Delgosha

Virginia Tech,
Kevin T. Crofton Department of
Aerospace and Ocean Engineering,
Blacksburg, VA 24061

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 15, 2018; final manuscript received November 30, 2018; published online January 8, 2019. Assoc. Editor: Philipp Epple.

J. Fluids Eng 141(4), 041106 (Jan 08, 2019) (18 pages) Paper No: FE-18-1102; doi: 10.1115/1.4042175 History: Received February 15, 2018; Revised November 30, 2018

The effect of nonsinusoidal trajectory on the propulsive performances and the vortex shedding process behind a flapping airfoil is investigated in this study. A movement of a rigid NACA0012 airfoil undergoing a combined heaving and pitching motions at low Reynolds number (Re = 11,000) is considered. An elliptic function with an adjustable parameter S (flattening parameter) is used to realize various nonsinusoidal trajectories of both motions. The two-dimensional (2D) unsteady and incompressible Navier–Stokes equation governing the flow over the flapping airfoil are resolved using the commercial software starccm+. It is shown that the nonsinusoidal flapping motion has a major effect on the propulsive performances of the flapping airfoil. Although the maximum propulsive efficiency is always achievable with sinusoidal trajectories, nonsinusoidal trajectories are found to considerably improve performance: a 110% increase of the thrust force was obtained in the best studied case. This improvement is mainly related to the modification of the heaving motion, more specifically the increase of the heaving speed at maximum pitching angle of the foil. The analysis of the flow vorticity and wake structure also enables to explain the drop of the propulsive efficiency for nonsinusoidal trajectories.

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Figures

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Fig. 1

Vortical patterns in the wake of a flapping airfoil [5]: (a) drag-indicative wake and (b) thrust-indicative wake

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Fig. 2

Main kinematic parameters of a flapping airfoil (Adapted from Ref. [37])

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Fig. 3

Flapping trajectories according to different values of the flattening parameter S

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Fig. 4

Computational domain and boundary conditions

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Fig. 5

Grid independence study

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Fig. 6

Time-step independence study

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Fig. 7

Variation of Ct¯, Cp¯, and η with StTE

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Fig. 8

Effect of nonsinusoidal heaving, case 1

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Fig. 9

Effect of nonsinusoidal pitching, case 2

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Fig. 10

Effect of nonsinusoidal heaving and pitching motions, case 3

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Fig. 11

Effect of the flapping trajectory on the propulsion performances

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Fig. 12

Effect of the flapping trajectory on the kinematic angle of attack

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Fig. 13

Time variation of CD and CL under the effect of nonsinusoidal motion

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Fig. 14

The 2S vortex shedding mode

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Fig. 15

Modes of vortex shedding and the wake pattern, case 1

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Fig. 16

Modes of vortex shedding and the wake pattern, case 2

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Fig. 17

Modes of vortex shedding and the wake pattern, case 3

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Fig. 18

Pressure distribution on the foil at t = 0, 2T/8, 4T/8, and 6T/8 for Sh = 0.25, 1, and 2

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Fig. 19

Pressure distribution: (a) at t = 0 and t = 4T/8 for Sh = 0.25 (left) and Sh = 1 (right) and (b) at t = 2t/8 and t = 6T/8 for Sh = 1 (left) and Sh = 2 (right)

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Fig. 20

Relative velocity for Sh = 2

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Fig. 21

Evolution of the foil load between t = 13T/64 and 17T/64, for Sh = 2

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Fig. 22

Position and orientation of the foil during one flapping cycle for Sh = 0.25, Sh = 1 and Sh = 2

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Fig. 23

(a) velocity and (b) acceleration of the foil during one flapping cycle for Sh = 0.25, Sh = 1 and Sh = 2

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Fig. 24

Flow vorticity and relative velocity fields at t = T/8 for Sh = 0.25 (left), Sh = 1 (middle) and Sh = 2 (right)

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Fig. 25

Velocity profile in the wake of the foil at t = t/8, 2T/8, and 3T/8

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