Experiments in Fluids

, Volume 46, Issue 5, pp 749–763

PIV-based investigations of animal flight

Research Article

DOI: 10.1007/s00348-008-0597-y

Cite this article as:
Spedding, G.R. & Hedenström, A. Exp Fluids (2009) 46: 749. doi:10.1007/s00348-008-0597-y

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.

List of symbols

A

tip-to-tip flapping amplitude (m)

AR

aspect ratio (AR = b/c)

b

wingspan (m)

c

mean chord (m)

CL,CD

lift and drag coefficients (Cx = Fx/qS)

CD,pro

profile drag coefficient of wing

CD,i

induced drag coefficient of wing

CF

laminar skin friction coefficient

D

image displacement (pix)

D

drag, force parallel to U0 (N)

D

drag per unit span (N/m)

f

flapping frequency (/s)

Fx

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 U0 (N)

p

pressure (N/m2)

p0

freestream pressure (N/m2)

q

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

Re

Reynolds number (Rex based on length scale x)

r0

vortex radius (m)

R

general, resultant force vector (N)

Rwv

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)

u1

upstream uniform streamwise velocity (m/s)

u2

downstream,disturbed streamwise velocity (m/s)

U0

mean, undisturbed uniform streamwise velocity (m/s)

U

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

V

control volume (m3)

wi

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)

αi

induced angle of attack—the decrease in α caused by wi (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)

ωx

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

Abbreviations

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

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Mechanical and Aeronautical EngineeringUniversity of PretoriaPretoriaSouth Africa
  3. 3.Department of Theoretical EcologyLund UniversityLundSweden