Concentric cylinders Taylor number

When the shear rate reaches a critical value, secondary flows occur. In the concentric cylinder, a stable secondary flow is set up with a rotational axis perpendicular to both the shear gradient direction and the vorticity axis, i.e. a rotation occurs around a streamline. Thus a series of rolling toroidal flow patterns occur in the annulus of the Couette. This of course enhances the energy dissipation and we see an increase in the stress over what we might expect. The critical value of the angular velocity of the moving cylinder, Qc, gives the Taylor number ... 

Smith, G. P., and A. A. Townsend. 1982. Turbulent Couette flow between concentric cylinders at large Taylor numbers. J. Fluid Mechanics 123 187-217. 

Many studies have been devoted to the Taylor-Couette problem (flow between two concentric cylinders with radii R and R2, Ri < R2, of infinite length, and rotating with angular velocities fij and 02 repectively). For instance Zielinska and Demay [74] consider the general Maxwell models with —1 <0 < 1. They show that the axisymmetric steady flow (the Couette flow) does not exist for 2dl values of parameters where the steady state exists moreover all models, except for a very close to —1, predict stabilization of the Couette flow in the spectral sense, for small enough values of the Weissenberg number. (See also [55].)... 

The Couette-Taylor flow reactor consists of two concentric cylinders in which the outer one is fixed and jacketed, while the inner one rotates. Under some particular conditions, a flow pattern characterized by counter-rotating toroidal vortices is formed. This Couette-Taylor flow makes the RTD in this reactor similar to that of a train of CSTRs [74]. However, because viscosity may change substantially as polymerization proceeds (along the reactor), it is difficult to maintain the required Taylor number in the whole reactor. The use of a conical outer cylinder may counteract the viscosity increase [75]. However, no example of the production of a commercial-like latex (i.e., high solids content) has been reported. 

The critical Taylor number T for the onset of Taylor vortices can be predicted by examining the stability of snail amplitude disturbances when superimposed on the basic Couette flow. The use of this linear stability analysis for concentric cylinders has been extensively reviewed by Chandrasekhar (1) and Stuart (2). All such analyses assune that the cylinders are infinitely long. In addition to T they predict an initial Taylor vortex celf axial length, . ... 

For low-viscosity liquids flowing in concentric cylinders, with the inner cylinder rotating at high velocities, we see the appearance inertia-driven secondary flow cells called Taylor vortices, see figure 8. The onset of these vorhces is controlled by the Taylor number which is given by... 

---