======Plane Wake after a Circular Cylinder======
=====Experiments by Antonia and Browne=====

----

====Description====

Plane turbulent wake downstream of a heated circular cylinder.
A 2D flow with temperature as passive scalar.

===Geometry and Flow Characteristics====

The wake-generating body is a stainless steel tube
of \(d = 2.67\) mm outer diameter. It is mounted horizontally
in the mid-plane of the working section of the wind tunnel, with
its axis located at \(x = 0\) and \(y = 0\). Electrical heating of 
the cylinder provides the temperature as a passive marker of the flow
in the self-preserving region, and a zero longitudinal
pressure gradient prevents free-stream velocity variations.

For computations, it is suggested that uniform inlet conditions are
applied upstream of the cylinder at around \(x/d=-10\), and the domain
should extend to at least \(x/d = 420\), where measurements are provided, as
shown in <imgref fig3-geom>.
  
<imgcaption fig3-geom| Flow geometry>{{  figs:case003:case03-geom.png  | Flow geometry}}</imgcaption>


===Flow Parameters===

Air with:
  * Kinematic viscosity: \(\nu =1.53 \times 10^{-5}\) m<sup>2</sup>/s.
  * Free-stream velocity: \(U_e = 6.70\) m/s.
  * Reynolds number based on \(d\): \(Re_d = 1170\).

At station \(x/d = 420\):
  * Mean-velocity defect half-width:  \(L = 12.3\) mm
  * Centreline mean-velocity defect:  \(U_o = 0.36\) m/s
  * Relative mean-temperature excess: \(T_o = 0.82\)<sup>o</sup>C

Constant power supplied for the electrical heating of the cylinder: 100 W.

===Inflow Conditions===

At station \(x/d\) = -10, constant velocity \(U_e\) and temperature.
Turbulent quantities corresponding to a free-stream turbulence level of 0.08%.

====Experimental Details====

Velocity measurements were taken using either single hot wires and single X-wires, or two
single hot wires or two X-wires, in order to obtain various turbulence quantities.

Temperature measurements were made using cold-wire probes.

===Measurement Errors===

  * \(\delta(\overline{vt}/(U_oT_o)) = 12\)%
  * \(\delta(\text{positions}) = \pm 0.02\) m


====Available Measurements====

===Velocity Measurements:===

At station \(x/d = 420\), profiles for \(\eta = y/L\) ranging from 0 to 2.2 of:

  * First order moment: \(U/U_o\) and \((U_e-U)/U_o\)
  * Reynolds stresses: \(\overline{u^2}/U_o^2\), \(\overline{v^2}/U_o^2\), \(\overline{w^2}/U_o^2\)
  * Turbulent kinetic energy: \(k/U_o^2\)
  * Turbulent kinetic energy dissipation rates: \(\varepsilon L/U_o^3\), \(\varepsilon_{homogeneous} L/U_o^3\)
  * Third order moment: Part of the diffusion term of the \(k\) transport equation: \(d(\overline{u_ku_kv}/2)/d\eta\)

===Temperature Measurements===

At station \(x/d=420\), profiles for \(\eta = y/L\) from 0 to 2.5 of:

  * First order moment: \((T-T_e)/T_o\)
  * Second order moments: \(\overline{t^2}/T_o^2\), \(\overline{vt}/(U_oT_o)\)
  * Dissipation rate: \(\varepsilon_{t} L/(U_oT_o^2)\)
  * Third order moment: Part of the diffusion term of the \(\overline{t^2}\) transport equation: \(d(\overline{vt^2}/2)/d\eta\)

[[case003-plots|Sample plots]] of some of these quantities are available.

The data can be downloaded as compressed archive files from the links below, or as individual files.

  * {{cdata:case003:pwc-allfiles.zip|pwc-allfiles.zip}}
  * {{cdata:case003:pwc-allfiles.tar.gz|pwc-allfiles.tar.gz}}

The individual files provided are:
  * Dynamic field profiles, contained in the file {{cdata:case003:dynamic-field-data.dat|dynamic-field-data.dat}}
  * Thermal field profiles, contained in the file {{cdata:case003:thermal-field-data.dat|thermal-field-data.dat}}
  * Additional notes in {{cdata:case003:readme.txt|readme.txt}}


====Main References====


  - Browne, L.W.B., Antonia, R.A., Shah, D.A. (1987). [[https://doi.org/10.1017/S002211208700154X|Turbulent energy dissipation in a wake]]. //J. Fluid Mech.//, Vol. 179, pp. 307-326.
  - Antonia, R.A., Browne, L.W.B. (1986). [[https://doi.org/10.1017/S0022112086002343|Anisotropy of the temperature dissipation in a turbulent wakei]]. //J. Fluid Mech.//, Vol. 163, pp. 393-403.
  - Antonia, R.A., Browne, L.W.B. (1986). [[https://doi.org/10.1016/0017-9310(86)90073-6|Heat transport in a turbulent plane wake]]. //Int. J. Heat Mass Transfer//, Vol. 29, pp. 1585-1592.
  - Antonia, R.A., Browne, L.W.B., Fulachier, L. (1987). [[https://doi.org/10.1007/BF00277708|Average wavelength of organised structures in the turbulent far wake of a cylinder]]. //Expts. in Fluids//, Vol. 5, pp. 298-304.

----

Indexed data:
<data dbcase flow_around_body free_flow>
case       : 003
title      : Plane Wake after a Circular Cylinder
author*    : Antonia, Browne
year       : 1985
type       : EXP
flow_tag*  : wake, scalar
</data>