Weak temperature gradient effect on the stability of the circular Couette flow (original) (raw)
Related papers
Computers & Fluids, 2014
From 28 high-order DNS computations, one investigates the formation of instabilities due to the strong competition between an azimuthal flow induced by rotation and an axial flow due to convection in a tall Taylor-Couette apparatus (C ¼ 80; g ¼ 0:8) submitted to a radial temperature gradient. One explores the richness of the transition diagram that reports seven different flow patterns appearing either as spiral rolls, wavy vortices or a combination of both depending on the Taylor and Rayleigh numbers. The partial spiral regime observed experimentally by Guillerm is not recovered at very low Rayleigh numbers. The spatio-temporal properties of the different spirals close to the threshold of the primary instability are fairly predicted and a new insight on the flow and thermal structures of the instabilities is gained from this study. Finally, the distributions of the Nusselt number against the Taylor number are established for various Rayleigh numbers.
Linear stability of cylindrical Couette flow in the convection regime
Physics of Fluids, 2005
The instability of steady circular Couette flow with radial heating across a vertically oriented annulus with a rotating inner cylinder and a stationary outer cylinder is investigated using a linear stability analysis. The convection regime base flow is developed for an infinite aspect ratio geometry and constant fluid properties with buoyancy included through the Boussinesq approximation. The base flow is characterized by a dimensionless stratification parameter ␥ that is proportional to the vertical temperature gradient. Critical stability boundaries are calculated for this assumed base flow with respect to both toroidal and helical disturbances. The numerical investigation is primarily restricted to a radius ratio of 0.6 at a Prandtl number of 100. Critical stability boundaries in Taylor-Grashof number space are presented for two values of the stratification parameter ␥ ͑4 and 13͒. The results follow the development of critical stability from Taylor cells at small Grashof numbers up to a maximum Grashof number used in this calculation of 20 000 and 80 000 for ␥ = 4 and 13, respectively. Results show that increasing the stratification parameter stabilizes the isothermal Taylor vortices, followed by a destabilization at higher azimuthal mode numbers ͑n Ͼ 0͒. The results also show that for ␥ =4 ͑close to the conduction regime͒, two modes are obtained: one is axisymmetric and the other is nonaxisymmetric. However, for the convection regime ͑large ␥͒ six asymmetric modes are obtained. Finally, the disturbance wavelength, phase speed, and spiral inclination angle are presented as a function of the critical Grashof number for the stratification parameters considered in this work.
Flow regimes in a vertical Taylor-Couette system with a radial thermal gradient
Physics of Fluids, 2015
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 (DNS). 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 DNS.
Direct numerical simulation of Taylor-Couette flow subjected to a radial temperature gradient
Physics of Fluids, 2015
Direct numerical simulations have been performed to study the Taylor-Couette (TC) flow between two rotating, coaxial cylinders in the presence of a radial temperature gradient. Specifically, the influence of the buoyant force and the outer cylinder rotation on the turbulent TC flow system with the radius ratio η = 0.912 was examined. For the co-rotating TC flows with Re i (inner cylinder) = 1000 and Re o (outer cylinder) = 100, a transition pathway to highly turbulent flows is realized by increasing σ, a parameter signifying the ratio of buoyant to inertial force. This nonlinear flow transition involves four intriguing states that emerge in sequence as chaotic wavy vortex flow for σ = 0, wavy interpenetrating spiral flows for σ = 0.02 and 0.05, intermittent turbulent spirals for σ = 0.1 and 0.2, and turbulent spirals for σ = 0.4. Overall, the fluid motion changes from a centrifugally driven flow regime characterized by large-scale wavy Taylor vortices (TVs) to a buoyancy-dominated flow regime characterized by small-scale turbulent vortices. Commensurate changes in turbulence statistics and heat transfer are seen as a result of the weakening of large-scale TV circulations and enhancement of turbulent motions. Additionally, the influence of variation of the outer cylinder rotation, −500 < Re o < 500 in presence of buoyancy (σ = 0.1) with Re i = 1000, has been considered. Specifically, it is demonstrated that this variation strongly influences the azimuthal and axial mean flows with a weaker influence on the fluctuating fluid motions. Of special interest, here are the turbulent dynamics near the outer wall where a marked decrease of turbulence intensity and a sign inversion of the Reynolds stress R r z are observed for the strongly counter-rotating regimes (Re o = −300 and −500). To this end, it has been shown that the underlying flow physics for this drastic modification are associated with the modification of the correlation between the radial and axial fluctuating motions. In turn, the intriguing effects of this modification on the mean axial flow, turbulent statistics, force balance, and dynamic processes such as turbulence production and dissipation are discussed.
Thermoelectric instabilities in a circular Couette flow
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
The stability of a non-isothermal circular Couette flow is analyzed when subjected to a dielectrophoretic force field. Outward and inward heating configurations are considered when the inner cylinder is rotating and the outer cylinder is at rest. In addition, an alternating voltage is applied between the two cylinders to induce a radial electric buoyancy that acts on the dielectric fluid. The linear stability analysis provides the threshold for the first transition to instability, as well as the corresponding wavenumber and frequency of the modes. This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.
Stability of Rayleigh-stable Couette flow between two differentially heated cylinders
Physical review fluids, 2021
The stability of the circular Couette flow with two differentially heated cylinders is studied in the special cases of hydrodynamically stable rotation regimes. A one-dimensional model is developed to derive the condition of flow stability. This condition combines the curvature of the cylinders, the applied temperature difference between the two cylinders, and the diffusion properties of the fluid. The three-dimensional analysis is performed for two different rotation regimes: the Keplerian regime and the regime where the inner cylinder is stationary. The main results of this analysis is that, for a given radius ratio of the two cylinders, a single parameter combining the Prandtl number and the thermal expansion parameter can describe the critical state of the system. The description is in good agreement with the result of the one-dimensional model. An energy analysis shows a subtle role played by the shear stress in these two rotation regimes.
Radial buoyancy effects on momentum and heat transfer in a circular Couette flow
Physical Review Fluids
The numerical investigation of a circular Couette flow with a radial temperature gradient is performed to elucidate the influence of the radial buoyancy on flow and heat transfer for different values of the Prandtl number when the gravitational acceleration is neglected. We consider an infinite-length cylindrical annulus of radius ratio 0.8 with the inner rotating cylinder and the outer stationary cylinder. The flow is stabilized with the outward heating while it is destabilized with the inward heating. A weakly nonlinear analysis shows that the transition to stationary axisymmetric modes is supercritical while the oscillatory axisymmetric modes occur via a subcritical bifurcation. The effect of the centrifugal buoyancy on the transfer of angular momentum (i.e., torque) is quite weak while the effect on the heat transfer is significant.
Absolute and convective instability of cylindrical Couette flow with axial and radial flows
Physics of Fluids, 2009
Imposing axial flow in the annulus and/or radial flow through the cylindrical walls in a Taylor-Couette system alters the stability of the flow. Theoretical methods and numerical simulations were used to determine the impact of imposed axial and radial flows, homogeneous in the axial direction, on the first transition of Taylor-Couette flow in the framework of convective and absolute instabilities. At low axial Reynolds numbers the convective instability is axisymmetric, but convective helical modes with an increasing number of helices having a helicity opposite that of the base flow dominate as the axial flow increases. The number of helices and the critical Taylor number are affected only slightly by the radial flow. The flow becomes absolutely unstable at higher Taylor numbers. Absolutely unstable axisymmetric modes occur for inward radial flows, while helical absolute instability modes having a helicity identical to that of the base flow occur at high enough axial Reynolds numbers for outward radial flow.