Plane Wake after a Circular Cylinder

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

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 figure 1.

Fig. 1: Flow geometry

Air with:

• Kinematic viscosity: \(\nu =1.53 \times 10^{-5}\) m²/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: \(T_o = 0.82\)^oC

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

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

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.

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

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: \(d(\overline{u_ku_kv}/2)/d\eta\)

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: \(d(\overline{vt^2}/2)/d\eta\)

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.

• pwc-allfiles.zip
• pwc-allfiles.tar.gz

The individual files provided are:

• Dynamic field profiles, contained in the file dynamic-field-data.dat
• Thermal field profiles, contained in the file thermal-field-data.dat
• Additional notes in readme.txt

1. Browne, L.W.B., Antonia, R.A., Shah, D.A. (1987). Turbulent energy dissipation in a wake. J. Fluid Mech., Vol. 179, pp. 307-326.
2. Antonia, R.A., Browne, L.W.B. (1986). Anisotropy of the temperature dissipation in a turbulent wakei. J. Fluid Mech., Vol. 163, pp. 393-403.
3. Antonia, R.A., Browne, L.W.B. (1986). Heat transport in a turbulent plane wake. Int. J. Heat Mass Transfer, Vol. 29, pp. 1585-1592.
4. Antonia, R.A., Browne, L.W.B., Fulachier, L. (1987). Average wavelength of organised structures in the turbulent far wake of a cylinder. Expts. in Fluids, Vol. 5, pp. 298-304.

Indexed data: