Numerical investigation of the onset of axisymmetric and wavy Taylor-Couette flows between combinations of cylinders and spherocylinders

The Taylor-Couette flow, which is the flow that occurs between two rotating bodies, has become fundamental to the study of instability and nonlinear behaviour. Many modifications can be made to the Taylor-Couette flow resulting in much more complex flow structures, either by geometrical changes, or by combining different geometries. The main goal of this work is to numerically investigate the effect of the cylinders-spheres combinations on the onset of different instabilities of a fluid confined between two concentric bodies. The modelling strategy was developed by studying three types of flow configurations: cylindrical Taylor-Couette flow (with fixed endcaps), flow between two concentric cylinders with hemispheres on the lower end wall, and flow between two coaxial spherocylinders (cylinders with hemispheres on the upper and lower end surfaces). The inner element rotates while the outer one is at rest. The numerical calculations were carried out to determine the transition zone from a laminar Couette flow to the onset of Taylor vortices and wavy vortex flow. The parameter that determines the flow regimes is the Reynolds number based on the angular velocity of the inner element. The fluid dynamic behaviours for different flow configurations are characterized by the wall shear stress and the skin friction coefficient. Laminar, axisymmetric and wavy Taylor-Couette flows are predicted for different configurations. It is established that the different combinations deeply affect the flow behaviour and the appearance of the instabilities. The transition from LCF to TVF and then to WVF in the combined flow systems is substantially retarded compared to the cylindrical Taylor-Couette flow system.