Couette flow with fixed wavy wall -- Experiments by Nakabayashi

Description

Experimental work has been performed to investigate turbulent Couette- type flow with repeated longditudinal pressure gradients that are realized in a channel consisting of a wavy fixed wall on one side and a moving wall on the other.
This type of flow simulates the flow in high speed journal bearings operating in turbulent conditions.
2D flow with constant temperature.

Geometry

figure

The channel has its lower wall moving and its upper wall wavy and fixed.
The test section is L=1.4 m long (one wavelength) with a mean height (distance between the two walls) of: 2overline(h)=15 mm.
Equation of the fixed wavy wall: y=2overline(h)-e cos(2pi x/L) with e=4.5 mm

Flow Characteristics / Flow Parameters

figure

The figure shown above describes the test channel and co-ordinate system used. The measurements have been carried out in the middle part of the channel (total length of 3.5 times the wavelength) in order to minimize upstream and downstream effects. The pressure has been found to be the same at the inlet and outlet of the considered one wavelength-long portion. Moreover the longitudinal pressure gradient is also found to be periodic.
The mean velocity distributions and turbulent intensities are measured at various streamwise positions of x/l for Reynolds number of Re=5000 and 8000. Non-dimensional pressure gradient parameters

figure

can be seen in the table below.

figure

Inflow Conditions

Channel flow at x=0. Velocity measurements stored in file couette.prn
Profiles from fixed wall to moving wall of:

  1. First order moments
    overline(U) /U_b , overline(V) /U_b , overline(U) /U_star
  2. Second order moments
  3. Reynolds stresses:
    overline(u'^2') , overline(v'^2') , overline(u'^2')/U_star²

Measurement Techniques

All velocity measurements were made using hot-wire anemometer.
Reynolds shear stresses were measured by hot-wire anemometer.

Measurement Errors

Measurement errors are not published in any English language paper.

Available Measurements

  1. Velocity measurements stored in file couette.prn
    1. Profiles at x= .175, .35, .525, .7, .875, 1.05, 1.225 m of:
    2. First order moments
      overline(U) /U_b , overline(V) /U_b , overline(U) /U_star
    3. Second order moments
    4. Reynolds stresses:
      overline(u'^2') , overline(v'^2') , overline(u'^2')/U_star²
    5. Friction velocity along the wavy wall at x= 0., .175, .35, .525, .7, .875, 1.05, 1.225 m
      U_star
  2. Pressure measurements available only in the literature.
    1. Longitudinal pressure gradient at x= 0., .175, .35, .525, .7, .875, 1.05, 1.225 m
      doverline(p)/dx

Instructions for Calculations

Inlet and outlet conditions

Ideally the calculation of the channel flow should be performed using periodicity conditions for both velocities and pressure gradient (doverline(p) (x+L)/dx=doverline(p)(x)/dx).
Nevertheless it is also possible to start at x=0 prescribing the experimental values provided as inlet conditions and assume zero gradients for the flow variables at outlet. In this case the flow periodicity has to be checked.

Presentation of the results

The following results should be plotted and compared with the data:

References

  1. NAKABAYASHI, K., KITOH, O. & IWATA, H. (1991). Turbulent Couette type flow with an alternating pressure gradient. Presented at 8th Symposium on Turbulent Shear Flows, Munich, poster no. I-13, (category No. 48.0: wavy fixed wall, b91-0433).
  2. EL TELBANY, M.M.M. & REYNOLDS, A.J. (1980) J. Fluid Mech. 100, 1-29.
  3. HUFFMAN, G.D. & BRADSHAW P. (1972) J. Fluid Mech. 53, Pt.1, 45-60.
  4. TOWNSEND, A.A. (1961) J. Fluid Mech. 11, 97-120

WWW ERCOFTAC Database
last updated 21/07/99