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Advances in Fluid Mechanics Measurements pp 263–321Cite as

The Measurement of Vorticity in Transitional and Fully Developed Turbulent Flows

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Part of the book series: Lecture Notes in Engineering ((LNENG,volume 45))

Abstract

The significance of vorticity and the importance of its temporally and spatially resolved measurement in turbulent flows is discussed. The measurement methods are categorized as those which use multipoint measurements of velocity to determine the required velocity gradients or circulation and those which sense these gradients directly. The characteristics and performance of these vorticity measurement methods are evaluated. Where available, measurements of some vorticity field statistics by two or more methods are compared.

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Abbreviations

A:

area

B:

the magnetic field intensity

C:

closed contour defining the circulation (see equation 2a)

h:

hot-wire probe prong spacing

n:

outward normal to surface

p:

(static) pressure

t:

time

ui :

velocity vector (cartesian tensor notation)

\(\overrightarrow v\) :

velocity vector (vector notation)

α:

hot-wire sensor angle to cross-stream plane

δ:

distance around a closed contour (see equation 2a)

∈xy :

strain-rate component

⌽:

potential of the electric field

Г:

circulation (see equation 2)

γxy :

hot-wire probe pitch angle in the xy plane

η:

Kolmogorov dissipation length scale

ν:

kinematic viscosity

Ω:

vorticity (\([\overrightarrow \Omega\) vector notation, Ωi cartesian tensor notation; see equation 1)

ωx,ωy,ωz :

cartesian vorticity components in an x,y,z reference frame

ρ:

density

aI :

the summation of the accelerative effects that permits the absolute acceleration A to be expressed as the sum of the acceleration in the local reference frame plus the Coriolis acceleration (2Ω × V), the centripetal acceleration (Ω × Ω × R) and the unsteady effect (dΩ/dt × R), (see equation 6).

S:

a portion of C that borders a physical surface (see equation 7)

u,v,w:

Cartesian velocity components in an x,y,z, reference frame

Uc :

convection velocity used in Taylor’s hypothesis

ur,vθ,w:

cylindrical coordinate (r,θ,z) velocity components

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Authors and Affiliations

  1. Michigan State University, East Lansing, MI, 48824, USA

    John F. Foss

  2. The University of Maryland, College Park, MD, 20742, USA

    James M. Wallace

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  1. Dept. of Aerospace & Mechanical Engineering, University of Notre Dame, 46556, Notre Dame, IN, USA

    Mohamed Gad-el-Hak

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Foss, J.F., Wallace, J.M. (1989). The Measurement of Vorticity in Transitional and Fully Developed Turbulent Flows. In: Gad-el-Hak, M. (eds) Advances in Fluid Mechanics Measurements. Lecture Notes in Engineering, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83787-6_7

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