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Convection velocity measurements in a cylinder wake

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Abstract

The convection velocity of vortices in the wake of a circular cylinder has been obtained by two different approaches. The first, implemented in a wind tunnel using an array of X-wires, consists in determining the velocity at the location of maximum spanwise vorticity. Four variants of the second method, which estimates the transit time of vortices tagged by heat or dye, were used in wind and water tunnels over a relatively large Reynolds number range. Results from the two methods are in good agreement with each other. Along the most probable vortex trajectory, there is only a small streamwise increase in the convection velocity for laminar conditions and a more substantial variation when the wake is turbulent. The convection velocity is generally greater than the local mean velocity and does not depend significantly on the Reynolds number.

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Abbreviations

d :

diameter of circular cylinder

f :

frequency in spectrum analysis

f v :

average vortex frequency

r v :

vortex radius

Re :

Reynolds number ≡ U o d/v

t :

time

Th ω, Th Γ, Th r :

thresholds for ω zp, Γ, and r v respectively

U o :

free stream velocity

U 1 :

maximum value of (U o − U)

U c :

convection velocity of the vortex, as obtained either by Eq. (1) or Eq. (2)

U co :

convection velocity used in Eq. (3) U cd, U cu average convection velocities of downstream and up-stream regions respectively of the vortex

U cv :

the value of U c at y = 0.5 δ

u, v :

the velocity fluctuations in x and y directions respectively

U, V :

mean velocity components in x and y directions respectively

U,V :

U = U + u, V = V + v

x, y, z :

co-ordinate axes, defined in Fig. 1

Γ :

circulation

δ :

mean velocity half-width

Δx :

spacing between two cold wires or grid spacing

θ 1, θ 2 :

temperature signals from upstream and downstream cold wires respectively

v :

kinematic viscosity

τ c :

transit time for a vortex to travel a distance Δx

φ :

phase in the cross-spectrum of θ 1 and θ 2

ω z :

instantaneous spanwise vorticity

ω zc :

cut-off vorticity used in determining the vortex size

ω zp :

peak value of ω z

〈〉a:

denotes conditional average, defined in Eq. (12)

′a:

prime denoting rms value

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, University of Newcastle, 2308, N.S.W., Australia

    Y. Zhou & R. A. Antonia

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  1. Y. Zhou
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  2. R. A. Antonia
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Zhou, Y., Antonia, R.A. Convection velocity measurements in a cylinder wake. Experiments in Fluids 13, 63–70 (1992). https://doi.org/10.1007/BF00208077

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  • DOI: https://doi.org/10.1007/BF00208077

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