Innocent Mutabazi

Gap size effects on centrifugally and rotationally driven instabilities

The rotation effects on centrifugally driven instabilities in curved channel flow with a finite gap are investigated. An inviscid criterion of stability is formulated to explain the behavior of the flow when rotation and curvature effects compete to either stabilize or destabilize the flow. The stability of curved Poiseuille flow with finite gap size is studied, and it is shown that the asymmetry between the directions of rotation is enhanced when the gap size increases.

Experimental study of inertioelastic Couette–Taylor instability modes in dilute and semidilute polymer solutions

Instabilities appearing in the circular Couette flow with a dilute or semidilute solution of high molecular weight polyethyleneoxide in water have been investigated when the outer cylinder is kept at rest. The shear-thinning behavior of solutions was determined through low shear viscosity measurements. We have found that, depending on concentration, different flow structures can appear at the onset of instability. For dilute concentrations, the critical mode is the stationary and axisymmetric Taylor vortex flow, which bifurcates to time periodic wavy vortex flow for a higher shear rate. The oscillation amplitude of wavy vortex flow decreased with the increasing shear rate. For sufficiently semidilute solutions, the critical mode occurs in the form of standing waves, the frequency of which decreases with the shear rate. The critical Taylor number increases for solutions without a shear-thinning effect and decreases for solutions exhibiting shear thinning.

Dielectrophoretic force-driven thermal convection in annular geometry

The thermal convection driven by the dielectrophoretic force is investigated in annular geometry under microgravity conditions. A radial temperature gradient and a radial alternating electric field are imposed on a dielectric fluid that fills the gap of two concentric infinite-length cylinders. The resulting dielectric force is regarded as thermal buoyancy with a radial effective gravity. This electric gravity varies in space and may change its sign depending on the temperature gradient and the cylinder radius ratio. The linear stability problem is solved by a spectral-collocation method. The critical mode is stationary and non-axisymmetric. The critical Rayleigh number and wavenumbers depend sensitively on the electric gravity and the radius ratio. The mechanism behind the instability is examined from an energetic viewpoint. The instability in wide gap annuli is an exact analogue to the gravity-driven thermal instability.

Transition to turbulence in a tall annulus submitted to a radial temperature gradient

We have investigated the transition to turbulence in a water flow confined inside a tall vertical cylindrical annulus submitted to a radial temperature gradient using the space-time diagrams technique. As soon as a small radial temperature gradient is applied to the annular flow, the radial stratification of density induces a torque that produces a large convection cell. The first instability of this flow occurs via a supercritical bifurcation and gives rise to axisymmetric rolls localized in the middle of the system. Just above the onset, the pattern contains spatiotemporal defects. For large values of the control parameter, we have observed a coexistence of turbulent bursts and laminar domains. We have measured the turbulent fraction and have performed a statistical analysis of the laminar and turbulent zones, and have found that they bear the main characteristics of spatiotemporal intermittency.

Instability of the vertical annular flow with a radial heating and rotating inner cylinder

A linear stability analysis of the flow confined in a differentially rotating cylindrical annulus with a radial temperature gradient has been performed. Depending on values of control parameters (the Taylor number, the Grashof number, and the Froude number), it has shown flow destabilization to axisymmetric or non-axisymmetric modes. Analysis of different terms involved in the evolution rate of the perturbation kinetic energy has allowed us to isolate the dominant terms (centrifugal force or buoyancy force) in the destabilization process. We have shown that the centrifugal buoyancy can induce the asymmetry of the temperature gradient on critical states.

Nonlinear analysis of instability modes in the Taylor–Dean system

The linear and weakly nonlinear stability of flow in the Taylor–Dean system is investigated. The base flow far from the boundaries, is a superposition of circular Couette and curved channel Poiseuille flows. The computations provide for a finite gap system, critical values of Taylor numbers, wave numbers and wave speeds for the primary transitions. Moreover, comparisons are made with results obtained in the small gap approximation. It is shown that the occurrence of oscillatory nonaxisymmetric modes depends on the ‘‘anisotropy’’ coefficient in the dispersion relation, and that the critical Taylor number changes slightly with the azimuthal wave number for large absolute values of rotation ratio. The weakly nonlinear analysis is made in the framework of the Ginzburg–Landau equations for anisotropic systems. The primary bifurcation towards stationary or traveling rolls is supercritical when Poiseuille component of the base flow is produced by a partial filling. An external pumping can induce a subcritical bi...

Numerical investigation of the heat transfer in cylindrical annulus with a dielectric fluid under microgravity

Three-dimensional (3D) flow driven by thermal convection in a dielectric liquid confined in the gap between two coaxial cylinders is investigated by direct numerical simulations. The inner surface is warmer than the outer one and a high frequency alternating electric tension is applied to the cylinders. The fluid is therefore subjected to a radial dielectrophoretic force which plays the role of a buoyancy force that can generate a thermal convection. We have performed 3D simulations using periodic boundary conditions. The transition from the base state to convective flow occurs via a supercritical bifurcation and leads to helicoidal stationary vortices. The behavior of the heat transfer by convective flow is investigated for different values of the radius ratio, Prandtl number, and electric Rayleigh number.

Secondary structures in a one-dimensional complex Ginzburg-Landau equation with homogeneous boundary conditions

Experiments in extended systems, such as the counter-rotating Couette–Taylor flow or the Taylor–Dean flow system, have shown that patterns with vanishing amplitude may exhibit periodic spatio-temporal defects for some range of control parameters. These observations could not be interpreted by the complex Ginzburg–Landau equation (CGLE) with periodic boundary conditions. We have investigated the one-dimensional CGLE with homogeneous boundary conditions. We found that, in the ‘Benjamin–Feir stable’ region, the basic wave train bifurcates to state with periodic spatio-temporal defects. The numerical results match the observations quite well. We have built a new state diagram in the parameter plane spanned by the criticality (or equivalently the linear group velocity) and the nonlinear frequency detuning.

Flow regimes in a vertical Taylor-Couette system with a radial thermal gradient

A rich variety of flow regimes in a Newtonian fluid inside a vertical large-aspect ratio and a wide-gap Taylor-Couette system with a radial temperature gradient has been determined in experiments and in direct numerical simulations (DNSs). Compared to previous experiments and numerical studies, a wider range of temperature differences (i.e., of the Grashof number Gr) and of the rotation rate (the Taylor number Ta) has been covered. The combined effect of rotation and of the radial temperature gradient is the occurrence of helicoidal vortices or modulated waves at the onset. Stationary axisymmetric vortices are found for very weak temperature differences. A good agreement was found for critical states between results from experiments, linear stability analysis, and DNS. Higher instability modes have been determined for a wide range of parameters and a state diagram of observable flow regimes has been established in the plane spanned by Gr and Ta. Some higher states observed in experiments were retrieved in...

Coriolis Force And Centrifugal Force Induced Flow Instabilities

Coriolis force and centrifugal force acting on flow induce longitudinal vortices in the main direction of the base flow. They couple either to give rise to oscillatory modes or to stabilize the flow when one of the forces is dominant with respect to the other. A comparative description of rotation and curvature effects is performed using the generalized Rayleigh criterion and linear stability theory.