cases:case003

# Plane Wake after a Circular Cylinder

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 figure 1.

Fig. 1: Flow geometry

#### Flow Parameters

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.

#### 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%.

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

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

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.

The individual files provided are:

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:

case003 (dbcase, flow_around_body, free_flow)
case003
titlePlane Wake after a Circular Cylinder
authorAntonia, Browne
year1985
typeEXP
flow_tagwake, scalar