All calculations were made with FLUENT 5.0, using a laminar
The following results are ranked with increasing Taylor numbers.
The aim of this serie of simulations was to locate the critical Taylor number, at which Taylor-Couette instabilities may appear.
At a low Taylor number, we observe a purely azimuthal flow, which is solution of Couette's flow between two cylinders.
The next simulation ran with a rotation speed of the inner cylinder corresponding to a Taylor number equal to its theorical critical value. The predicted instability and apparition of rolls didn't appear, even if the image shows little gradients of non-azimuthal velocities. Those gradients can be neglected, compared with the average azimuthal flow.
Some simulations showed that the Taylor number needed to be raised until around 5000, to obtain the first significant instabilities. Two series of rolls can then be observed in radial planes. Let's remark that the theorical wave number predicted well that kind of rolls configuration.
The experimental critical Taylor number may be then fixed
Over the critical Taylor number, instabilities still remain, as expected. Nevertheless, the radial and vertical parts of the global flow are still unsignificant. The azimuthal part of the flow begin to be affected by the instabilities with a Taylor number about 9000, as shown on figure below.