The case considered is fully developed flow in a channel rotating in orthogonal mode as shown in the figure. The flow is at a low Reynolds number and direct numerical simulation data is available for a range of rotation rates.
The Reynolds number Reb=Ubh/
, based on bulk velocity Ub
and channel half-width h is around 2900. Data is available at rotation numbers Ro=2
h/Ub of 0,
0.01, 0.05, 0.1, 0.15, 0.2 and 0.5.
The Navier-Stokes equations were solved using a finite difference technique on a 128 x
128 x 128 mesh. The computational domain extended to 4
h and 2h in the streamwise (x) and spanwise (z) directions
respectively, and periodic boundary conditions were applied in both of these homogeneous
directions
The fully developed flow in a 1-dimensional domain -h<y<h is to be
considered, with a solid wall boundary condition applied at y=±h. In this
case, the mean streamwise momentum equation reduces to
where the effective pressure P*=P - 1/2
2r2
and r is the radial distance of any point from the rotation axis.
The simulations were performed for a fixed Reynolds number Retau = ut
h/ of 194, where the friction
velocity ut is defined as
.
This means that the bulk Reynolds number varies slightly with rotation number, although
the data below (taken from Kristoffersen & Andersson 1993) show that the differences
are fairly small.
| Ro | Ub/ut |
| 0.0 | 15.06 |
| 0.01 | 15.03 |
| 0.05 | 15.57 |
| 0.10 | 15.60 |
| 0.15 | 15.41 |
| 0.20 | 15.23 |
| 0.50 | 15.25 |
Computations should be carried out for the above range of rotation numbers.
We plan to compare mean velocity and Reynolds stress profiles at each rotation number, together with the wall shear stresses on the pressure and suction sides of the channel.
Mean velocity, turbulent kinetic energy profiles and some budget data:
case7_1.tar.gz (for gunzip)
case7_1.tar.Z (for uncompress)
Reynolds stress profiles:
case7_1a.tar.gz (for gunzip)
case7_1a.tar.Z (for uncompress)
Andersson, H.I., Kristoffersen, R. 1995 "Turbulence statistics of rotating channel flow" in Turbulent Shear Flows-9, (ed. Durst et al), Springer.
Kristoffersen, R., Andersson, H.I. 1993 "Direct simulations of low-Reynolds-number turbulent flow in a rotating channel" J. Fluid Mech., 256, 163-197.