No abstract

The aim of this work is to highlight the critical thresholds corresponding to the onset of different instabilities considered in the flow between two vertical coaxial cones with and without free surface. The inner cone is rotating and the outer one is maintained at rest. Both cones have the same apex angle Φ =12° giving a constant annular gap δ =d/R1max. The height of the fluid column is H=155mm and It can be progressively decreased for each studied case of the flow system. Two kinds of configurations are studied, small and large gap. The working fluid is assumed as Newtonian and having constant properties like density and viscosity within the range of the required experimental conditions. By means of visualization technique of the flow we have been able to show the different transition modes occurring in the conical flow system according to the aspect ratio and then the induced action of the free surface which introduces a delay in the onset of different instability modes. The obtained results in term of features and stability of the flow are compared to those of Wimmer and Noui-Mehidi.

The flow between rotating cones have been investigated experimentally and numerically by several authors. There are a few analytical studies concerning the so called flow system. The flow is defined by an incompressible viscous fluid characterized by constant physical properties (density and kinematic viscosity) between two coaxial cones. The cones have the same apex angle, giving a constant radial gap. The inner cone rotates with an angular velocity Ω and the outer one is maintained at rest. Furthermore, the basic flow between rotating coaxial cones is fully three-dimensional resulting from the balance between centrifugal and viscous forces. The present work focuses in analytical and numerical approach to establish the mean velocity profiles characterizing the basic flow. For that purpose, a particular curvilinear coordinate system is used to establish the governing equation corresponding to the conical Taylor-Couette flow system. The obtained results indicate that the flow is dominated mainly by the tangential velocity component.

Abstract. The present work is intended to experimentally study the Taylor-Couette flow between coaxial cones. The inner cone is rotated and the outer cone is maintained fixed. Both cones have the same apex angle ĭ =12°, giving a constant annular gap į =0.12. The height of the fluid column is H=155 mm. The working fluid is assumed as Newtonian and has constant properties (as density and viscosity) within the range of the required experimental conditions. By means of visualization techniques, the critical thresholds related to the onset of various instabilities have been obtained and the corresponding flow modes have been identified. Using images processing, spatio-temporal diagrams have also been calculated, showing the characteristics (wavelength, drift velocity) of the downward helical motion. The results obtained for these transition regimes are compared to those of Wimmer et al. [1][2][3].

The present work is concerned with an experimental study of free surface effect on the onset of the Taylor-Dean instability. The experimental device consists of two horizontal coaxial truncated cones, the inner cone is rotating and the outer one is at rest. The cones have the same apex angle giving a constant radial gap. The rotational speed variation occurs in a quasi-static mode. This is to highlight the occurrence conditions of the Taylor-Dean instability in this kind of flow system by using two photometry techniques (transmission and reflexion of natural light). Therefore, by varying the aspect ratio Γ=H/d in the range 6.71 ≤ Γ ≤ 13.95 we examine the interaction of free surface on the appearance of TaylorDean instability in laminar-turbulent transition. In each case, one measures the features of the associated structures in vicinity of the critical points of their appearance. The obtained results are compared with the classical cylindrical Taylor-Dean flow system. The main result is to find that the occurrence of the instabilities is only limited to the primary mode in the conical flow system. The triplet mode is not observed in our case.