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PIV-based investigations of animal flight

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Abstract

An overview is presented of the principles of estimation of fluid forces exerted upon solid bodies, based upon whole-field velocity measurements such as provided by PIV. The focus will be on the range of length and velocity scales characterised by the flight of large insects, birds, bats and small unmanned air vehicles, so that while viscous terms in the Navier–Stokes equations can many times be ignored in the quantitative analysis, understanding and measuring boundary-layer flows, separation and instability will ultimately be critical to predicting and controlling the fluid motions. When properly applied, PIV methods can make accurate estimates of time-averaged and unsteady forces, although even ostensibly simple cases with uncomplicated geometries can prove challenging in detail. Most PIV-based force estimates are embedded in some analytical model of the fluid–structure interaction, and examples of these with varying degrees of complexity are given. In any event, the performance and accuracy of the PIV method in use must be well understood as part of both the overall uncertainty analysis and the initial experimental design.

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Abbreviations

A :

tip-to-tip flapping amplitude (m)

AR :

aspect ratio (AR = b/c)

b :

wingspan (m)

c :

mean chord (m)

C L, C D :

lift and drag coefficients (C x = F x/qS)

C D,pro :

profile drag coefficient of wing

C D,i :

induced drag coefficient of wing

C F :

laminar skin friction coefficient

D :

image displacement (pix)

D :

drag, force parallel to U 0 (N)

D′:

drag per unit span (N/m)

f :

flapping frequency (/s)

F x :

force component in the x direction (N)

g :

acceleration due to gravity (m/s2)

I :

impulse (kg m/s)

l :

length scale (m)

L :

lift, force normal to U 0 (N)

p :

pressure (N/m2)

p 0 :

freestream pressure (N/m2)

q :

dynamic pressure \( \left( {q = \frac{1}{2}\rho U^{2} ,\;{\text{N}}/{\text{m}}^{2} } \right) \)

Re :

Reynolds number (Re x based on length scale x)

r 0 :

vortex radius (m)

R :

general, resultant force vector (N)

R wv :

wake vortex ratio

S :

control surface (m2)

S :

shear deformation (dx/x, dimensionless)

S :

wing planform area (S = bc, m2)

St :

Strouhal number (St = fA/U)

t :

time (s)

T :

wingbeat period (s)

u :

velocity vector field (m/s)

u, v, w :

velocity components in x, y, z (m/s)

u 1 :

upstream uniform streamwise velocity (m/s)

u 2 :

downstream,disturbed streamwise velocity (m/s)

U 0 :

mean, undisturbed uniform streamwise velocity (m/s)

U :

mean flow speed or mean flight speed (m/s)

V :

control volume (m3)

w i :

induced velocity (due to wing lift) (m/s)

W :

body weight (N)

x :

position vector (m)

x, y, z :

Cartesian coordinates in streamwise (flightwise), spanwise and vertical directions (m)

α :

angle of attack (deg)

α i :

induced angle of attack—the decrease in α caused by w i (deg)

δt :

exposure time between two PIV images (typically μs)

ϕ :

velocity potential (m2/s)

Γ:

circulation (m2/s)

Γ0 :

circulation at wing centreline (m2/s)

μ :

viscosity (kg/m/s)

ν :

kinematic viscosity (ν = μ/ρ, m2/s)

θ :

momentum integral (m)

ρ :

fluid density (kg/m3)

\(\varvec{\upomega}\) :

vorticity vector (/s)

ω x :

vorticity component in the x direction (normal to the yz plane) (/s)

CIV:

Correlation Imaging Velocimetry

DLE:

Direct Lyapunov Exponent

DNS:

Direct Numerical Simulation

ENOB:

Effective Number of Bits

LCS:

Lagrangian Coherent Structure

LEV:

Leading Edge Vortex

PIV:

Particle Image Velocimetry

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Acknowledgments

This work is a review based in part on work done at the University of Southern California and at Lund University. Significant contributors to this effort at USC include John McArthur and Mikael Rosen, and Florian Muijres, Christoffer Johansson and Per Henningsson at LU. We are most grateful to the Swedish Research Council and the Knut and Alice Wallenberg Foundation for support in LU. The Air Force Office of Scientific Research provided partial support for JMcA at USC.

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  1. Geoffrey R. Spedding

    Present address: Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, 0002, South Africa

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, USA

    Geoffrey R. Spedding

  2. Department of Theoretical Ecology, Lund University, Ecology Building, 223 62, Lund, Sweden

    Anders Hedenström

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Correspondence to Geoffrey R. Spedding.

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Spedding, G.R., Hedenström, A. PIV-based investigations of animal flight. Exp Fluids 46, 749–763 (2009). https://doi.org/10.1007/s00348-008-0597-y

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