Symmetry breaking in a Taylor–Couette flow with fractal outer wall

The Taylor–Couette device is an important tool commonly used to measure the fluid viscosity. Here, we consider three modified versions of this device, where the first three fractal generations and the triadic square Koch curve (TSKC) are used to reshape the outer cylindric wall. This way it becomes possible to follow the influence of wall irregularities on the flow and on itself and on the shear stress on the surface of the inner cylinder. The device operates in the usual way, keeping the inner wall at rest and rotating the outer wall in the anticlockwise direction. The three-dimensional flow within this device was investigated through computational fluid dynamics simulations, while the results are discussed in terms of the shear stress in the inner wall as well as by observing the flow patterns inside the cavities created by the TSKC. It is shown that the perturbations created by the fractal wall strongly influence the shear stress at the inner wall, and that this effect depends in a nonlinear way on the Reynolds number Re. It has been also observed that the shear stress decreases with the increase in the number of the cavities.