cases:case046

# Couette Flow with Plane Fixed Wall

Couette-Poiseuille flow in a channel, between a plane fixed wall and a plane moving wall. The mean shear rate on one wall is varied by changing the relative wall velocities and the streamwise pressure gradient, allowing the turbulence statistics and structures under different wall shear rates to be investigated.

#### Flow Characteristics

Schematic pictures of the type of flow simulated are shown in figure 1. The top wall is at rest, while the bottom wall is moving at a constant speed, $U_w$.

Fig. 1: Flow configuration schematics

Data for the case of stationary lower wall (plane channel flow) is available elsewhere (including case032, case044 and case045 in this database). The parameters for the three cases reported here were chosen in order to give different shear stresses at the bottom wall (up to nearly the case of zero wall shear stress), whilst maintaining almost the same wall shear stress on the top wall.

The flow parameters and conditions for the three cases are summarized below:

• Air with a 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: $U_{\tau m}$
• Channel half-width: $\delta$
• Non-dimensional pressure gradient: $a = -(\delta/(\rho U_w^2)) \partial P/\partial x$
 Case $U_w\delta/\nu$ $a$ $U_{\tau f}\delta/\nu$ $U_{\tau m}\delta/\nu$ CP1 1800 0.00434 148 79.0 CP2 2640 0.00186 152 49.0 CP3 3000 0.00133 154 17.7

Referring to the numerical procedure used by Kim et al. (1987), a fourth-order partial differential equation for $v$, a second-order partial differential equation for the wall-normal component of vorticity $\omega_y$ and the continuity equation were used to solve the flow field.

A spectral method with Fourier series in the $x$ and $z$ directions and a Chebyshev polynomial expansion in the wall-normal direction were used. The computational periods were chosen to be $5\pi\delta$, $2\delta$ and $2\pi\delta$ in the $x$, $y$ and $z$ directions, respectively. $128 \times 128$ Fourier modes and Chebyshev polynomials up to the order 96 in wave number space were used in order to resolve all essential turbulent scales on the computation grid. The collocation grid used to compute the nonlinear terms in physical space had 1.5 times finer resolution in each direction to remove aliasing errors.

For time integration, the second-order Adams-Bashforth and Crank-Nicolson schemes were adopted for the nonlinear and viscous terms, respectively.

Data are non-dimensionalized by wall variables, i.e. $U_{\tau f}$ and $\nu$.

The data available includes:

• Mean velocity and Reynolds stress profiles across the channel
• Skewness and flatness factors
• Budgets of Reynolds stresses, turbulent kinetic energy and its dissipation rate
• One dimensional energy spectra at selected $y^+$ locations
• Two-point correlations at selected $y^+$ locations

Sample plots of selected quantities are available.

 Case Datafile PC1 pc12_pg_wl1.dat PC2 pc12_pg_wl2.dat PC3 pc12_pg_wl3.dat
1. Kim, J., Moin, P., Moser, R. (1987). Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech., Vol. 177, pp. 133-166.
2. Kuroda, A., Kasagi, N., Hirata, M. (1993). A direct numerical simulation of turbulent plane Couette-Poiseuille flows: effect of near stream on the near wall turbulence structures. Proc. 9th Turbulent Shear Flows Symposium, Kyoto, Japan.
3. Kuroda, A. (1990). Direct numerical simulation of Couette-Poiseuille flows. Dr. Eng. Thesis, the University of Tokyo.

Indexed data:

case046 (dbcase, confined_flow)
case046
titleCouette Flow with Plane Fixed Wall
authorKuroda, Kasagi, Hirata
year1993
typeDNS
flow_tagconstant_cross_section, channel_flow