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Recurrence Perspective of Forces Generated by Flapping Wing Under Different Frontal Inflow Conditions

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Advances in Engineering Design and Simulation

Part of the book series: Lecture Notes on Multidisciplinary Industrial Engineering ((LNMUINEN))

Abstract

Qualitative and quantitative recurrence paradigms have been frequently used to study the stability of dynamic systems. In the present work, Global Recurrence Plots (GRPs) and Windowed Recurrence Quantification Analysis (WRQA) were employed to analyse the force patterns of a flapping wing in 3D reference frame for Re = 150. The wing followed a canonical form of asymmetrica 1DoF flapping. Force patterns were numerically estimated for four different frontal inflow conditions viz. uniform inflow profile, shear inflow profile, temporally oscillating uniform inflow profile and spatiotemporally varying inflow profile. User-defined functions (UDFs) were developed to specify these frontal inflow conditions. The flapping kinematics of wing was simulated by dynamic meshing technique and UDFs. 3D unsteady Navier–Stokes equations were solved using finite volume formulation, assuming incompressible and laminar flow. Mass and momentum equations were solved in a fixed inertial reference frame by the Arbitrary Lagrangian–Eulerian (ALE) formulation. Spatial discretization was second-order upwind and temporal discretization was second-order implicit. PISO scheme was used for pressure–velocity coupling. The finite volume formulation based commercial CFD code ANSYS Fluent was used. Force patterns were qualitatively evaluated using GRPs and quantitatively by evaluating the WRQA of eight parameters viz. recurrence rate (RR), determinism (DET), laminarity (LAM), trapping time (TT), ratio (RATIO), entropy (ENTR), maximum line (Lmax) and trend (TREND). From these recurrence studies, it was observed that shear inflow condition influenced the forces and moment pattern more than the other primary inflow conditions for the chosen wing kinematics.

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Abbreviations

c :

Wing chord length, m

f g :

Gust frequency, Hz

f w :

Wing flapping frequency, Hz

l :

Diagonal line

l min :

Minimum threshold diagonal line

m:

Dimensional phase space trajectory

t :

Time, sec

v :

Length of vertical structures in recurrence plot

v min :

Minimum threshold vertical line

\(\vec{u}\) :

Flow velocity, m/s

\(\overrightarrow {{u_{g} }}\) :

Velocity of the moving mesh, m/s

C H :

Coefficient of horizontal force

C M :

Coefficient of moment

C V :

Coefficient of vertical force

Lmax:

Maximum diagonal structure of the recurrence plot

N :

Length of data series

\(P^{\varepsilon } \left( l \right)\) :

Frequency distribution of the diagonal lengths l

\(P^{\varepsilon } \left( v \right)\) :

Frequency distribution of vertical length, v

\(R_{i,j}^{m,\varepsilon }\) :

Recurrence matrix of an m-dimensional phase space trajectory and a neighbourhoods radius ε

Re:

Reynolds number

\({\text{S}}_{\phi }\) :

Source term

T :

Period of flapping, sec

T g :

Period of gust, sec

U g :

Gust amplitude, m/s

U w :

Root mean square average flapping velocity at the tip of the wing, m/s

U G :

Gust velocity, m/s

U ∞ :

Mean free stream velocity, m/s

V :

Arbitrary control volume

ϒ:

Elliptical flow domain around the wing

ε :

Threshold distance

ø :

Any scalar quantity

ρ :

Fluid density, kg/m3

Γ :

Diffusion coefficient

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Author information

Authors and Affiliations

  1. CSIR-National Aerospace Laboratories, CSMST, Bengaluru, India

    M. De Manabendra

  2. CSIR-National Aerospace Laboratories, CTFD, Bengaluru, India

    J. S. Mathur

  3. Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India

    S. Vengadesan

Authors
  1. M. De Manabendra
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  2. J. S. Mathur
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  3. S. Vengadesan
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Corresponding author

Correspondence to M. De Manabendra .

Editor information

Editors and Affiliations

  1. Swansea University, Swansea, UK

    Chenfeng Li

  2. Vel Tech Dr. RR & Dr. SR Technical University, Chennai, Tamil Nadu, India

    U. Chandrasekhar

  3. Sheridan College, Oakville, ON, Canada

    Godfrey Onwubolu

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De Manabendra, M., Mathur, J.S., Vengadesan, S. (2020). Recurrence Perspective of Forces Generated by Flapping Wing Under Different Frontal Inflow Conditions. In: Li, C., Chandrasekhar, U., Onwubolu, G. (eds) Advances in Engineering Design and Simulation. Lecture Notes on Multidisciplinary Industrial Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-8468-4_16

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  • DOI: https://doi.org/10.1007/978-981-13-8468-4_16

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-8467-7

  • Online ISBN: 978-981-13-8468-4

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