Couette flow

Couette flow and Taylor - Couette flow refers to the laminar flow of an incompressible viscous fluid in the space between two coaxial rotating cylinders relative to one another, or between two relatively moving, infinitely long and wide plates (plane Couette flow ), is located. The resulting flow between the cylinders is not only dependent on the rotation speed, but also on whether the inner or the outer cylinder is rotated. Is the relative velocity of the cylinder is low ( see below) and the gap between the two cylinders is small compared with the diameter of the cylinder, the flow to be treated as a flat Couette flow. Here, a plate as fixed and the others are considered to be moved. The flow was named after Maurice Couette, who has the end of the 19th century constructed the first functioning rotational viscometer.

Development of the flow and vortex formation

Rotate only the outer cylinder, the flow behaves according to the naive expectation. It forms a uniform laminar flow between the two cylinders. Even when the inner cylinder rotates slowly, the intuitively accessible image is preserved. At higher speeds of the inner cylinder, however, breaks the flow into strips, as accelerated by the centrifugal force pushes liquid outwards to the inner cylinder; this creates vortices, which are perpendicular to the axis of rotation ( Taylor vortices ). These vortices are Strictly speaking, induced in the finite system of the upper and lower cover plates by so-called Ekman - vortex and go continuously from the laminar flow forth. With a further increase of the rotation speed of the inner cylinder, the lines arranged in a waveform, which also starts to rotate around the cylinder.

Mathematical formulation

Rotating cylinder

The instability occurs when the resistance of the centrifugal force can no longer balance:

With

Plane Couette flow

Speed

With

Example of use

Sludge dewatering is a step in industrial and municipal wastewater treatment plants. For optimum drainage in the drainage aggregates flocculation of the sludge components is via the addition of flocculants a precondition. The forming flakes are not very shear stable. To improve the shear stability is a method of using the physical basis of the Taylor - Couette flow. The spiked with flocculent sludge passes through a unit which is called a " mechanical floc formers ". The gap width between the stationary and rotating cylinder adapted to the specific type of sludge, the cylinder is designed as a cone. This adjustability is an innovation over previous systems which operate with a fixed gap width. The rotational speed is adjustable.

The resulting Taylor vortices in the system ensure a constant rolling of the flakes, the result for a pelletizing the still soft flakes on the walls of the rotating inner cone and the static outer wall. The subsequent dehydration unit can perform the separation process faster and with better selectivity. In addition, even Feinstschwebstoffe be committed in the pellets and go with the solids from. The outgoing water is clearer. The addition of flocculants occurs more economical, the efficiency is higher because of the longer mixing time in the floc formers. Improvements up to 30 % are possible, depending on the type of sludge.