(195i) Instabilities in the Flow Around a Rotating Finite-Size Disk

A rotating disk is the ”gold-standard” experiment for measuring surface reactions rates in geochemical and electrochemical systems. In ideal circumstances, described first by Von Karman, the flow around the disk is laminar. However, more recent theoretical and numerical work, as well as some laboratory experiments, show that there are instabilities in the flow at much smaller Reynolds numbers (Re ≈ 10⁴ ) than the expected transition to turbulence
(Re ≈ 10⁵ ). The critical Reynolds number for the onset of an instability depends on geometry; it is higher for a single disk in a half space than a pair of disks with the fluid confined between them (a ”rotor-stator” geometry). Our numerical simulations show that the critical Re for a finite-size disk within a larger container of solution is below 1000, which is much smaller than in a ”rotor-stator” geometry. Here, starting at Re ≈ 800, the instability is initiated at the edge of the disk and propagates to the core of the fluid, with the formation of coherent structures in the flow.

Our simulations are finite volume based, using the OpenFOAM toolkit. Our code was validated in a rotor-stator geometry, by comparing with self similar solutions at low Re and with spectral solutions above the critical Re. I will present preliminary results for the flow field in a ”finite-disk” geometry.

Figure 1: Time dependent oscillations of the axial velocity (Uz) are shown at 9 different probe positions; the probes are in the lower half of the container, between a spinning disk of radius R and the base of the container (at z = -R). The first row of points is placed at an axial distance of 0.05R from the base of the disk, while the points in rows 2 and 3 are 0.5R and 0.9R from the disk. Points in column A lie close to the boundary of the container at r = 3.9R, while points in columns B and C are at R and 0.05R respectively.