cases:case036

# Couette Flow with Plane Fixed Wall

Flow in a channel, between a plane fixed wall and a plane moving wall as shown in figure 1. The distance between the two walls is $h = 2\delta = 29.7$ mm and the length of the domain is $L = 1.38$ m.

Fig. 1: Flow geometry and configuration

#### Flow Characteristics

The channel flow develops from a pure Poiseuille flow (fixed bottom wall) in the upstream region to an established state over the moving bottom wall section. Experimental data are available in both the developing and developed flow regions.

Three cases are considered, with different moving wall velocities. In the lowest velocity case the developed flow is of Poiseuille type; in the highest case it is of Couette type, and in the third case of intermediate type, with $\partial U/\partial y$ close to zero at the moving wall (see figure 2). Measurements of the pure Poiseuille flow upstream of the moving wall region are also available.

Fig. 2: Mean velocity profile sketches of the cases considered

#### Flow Parameters

• Air with kinematic viscosity: $\nu = 1.5 \times 10^5$ m2/s.
• Wall velocity: $U_w$.
• Flow rate velocity: $U_q$.
• Friction velocity on fixed wall: $u_{\tau f}$.
• Friction velocity on moving wall: $u_{\tau m}$.

Conditions for the three cases are summarized in the table below.

Pure Poiseuille Poiseuille-type Intermediate-type Couette-type
$Re_q = U_qh/\nu$ 5100 5080 5020 4800
$Re_w = U_wh/\nu$ 0 3960 5940 9900
$U_w$ (m/s) 0 2 3 5
$u_{\tau m}$ (m/s) 0.162 0.083 0.036 0.116
$u_{\tau f}$ (m/s) 0.162 0.145 0.141 0.116

Measurements are reported at five streamwise locations, given in the table below. Station 1 is upstream of the moving wall region; Stations 2 and 3 are in the flow development region, and Stations 4 and 5 in the developed flow region. The origin $x=0$ corresponds to the start of the moving wall region.

Measurement Station Location
Station 1 -0.235 m
Station 2 0.165 m
Station 3 0.265 m
Station 4 1.165 m
Station 5 1.265 m

#### Inflow Conditions

Measurements are provided at station 1, $x = -0.235$ m, upstream of the part of the channel where the bottom wall is moving, for a pure Poiseuille flow (fixed bottom wall). They can be used to calculate the developing flow.

The file poispur1.dat contains profiles of:

• First order moments: $U/U_q$, $V/U_q$, $W/U_q$
• Second order moments: $u'/u_{\tau f}$, $v'/u_{\tau f}$, $w'/u_{\tau f}$, $\overline{uv}/u_{\tau f}^2$, $\overline{uw}/u_{\tau f}^2$
• Hot wire velocity measurements have been carried out using single-wire and X-wire probes of boundary layer type.
• Wall friction velocity $u_{\tau f}$ has been deduced from the $\overline{uv}$ profile close to the fixed wall.

Measurements available include:

• Profiles of mean and rms streamwise velocity, $U/U_q$, $u'/U_q$, at the five measurement locations.
• Profiles of mean velocity and Reynolds stress components, $U/U_q$, $V/U_q$, $W/U_q$, $u'/u_{\tau f}$, $v'/u_{\tau f}$, $w'/u_{\tau f}$, $\overline{uv}/u_{\tau f}^2$, $\overline{uw}/u_{\tau f}^2$, at the downstream measurement location(s).
• 1-D spectra of the streamwise velocity at selected cross-stream positions at the downstream measurement location.

The file readme.txt contains a brief description of the data files and notation used in them.

The file poispur1.dat contains profiles of mean velocity and Reynolds stresses for the pure Poiseuille flow upstream of the moving wall.

The following files provide profiles of the streamwise mean and rms fluctuating velocities, $U$ \nd $u'$, at the five measurement locations ($x=-0.235$, $0.165$, $0.265$, $1.165$ and $1.265$ m from the start of the moving wall region).

Case File
Poiseuille-type case ($U_w=2$ m/s) etabtp.dat
Intermediate-type case ($U_w=3$ m/s) etabti.dat
Couette-type case ($U_w=5$ m/s) etabtc.dat

The following files provide profiles at the downstream measurement locations of mean velocity and Reynolds stress components.

Case Location File
Poiseuille-type case ($U_w=2$ m/s) Station 5 typpoi5.dat
Intermediate-type case ($U_w=3$ m/s) Station 5 typint5.dat
Couette-type case ($U_w=5$ m/s) Station 4 typcou4.dat
Station 5 typcou5.dat

The following files provide 1-D spectra of the streamwise velocity, at various cross-stream locations.

Case $y/h=0.04$ $y/h=0.5$ $y/h=0.75$ $y/h=0.95$
Pure Poiseuille flow spepo050.dat spepo075.dat spepo095.dat
Poiseuille-type case, Station 5 spetp004.dat spetp050.dat spetp095.dat
Intermediate-type case, Station 5 speti004.dat speti050.dat speti095.dat
Couette-type case, Station 5 spetc004.dat spetc050.dat spetc095.dat

Sample plots of selected quantities are available.

1. Corenflos, K. (1993). Etude experimentale d'ecoulements de Couette-Poiseuille turbulents a faible nombre de Reynolds. PhD Thesis, L'Universite des Sciences et Technologies de Lille.
2. Corenflos, K., Rida, S., Monnier, J.C., Dupont, P., Dang Tran, K., Stanislas, M. (1993). Experimental and numerical study of a plane Couette-Poiseuille flow as a test case for turbulence modeling. Proc. 5th Int. Symp. on refined flow modelling and turbulence measurements, Paris.

Indexed data:

case036 (dbcase, confined_flow)
case036
titleCouette Flow with Plane Fixed Wall
authorCorenflos, Rida, Monnier, Dupont, Dang Tran, Stanislas
year1993
typeEXP
flow_tagconstant_cross_section, channel_flow