Linear Stability of Taylor-Couette Flows with Axial Heat Buoyancy

The linear stability is studied of flows confined between two concentric cylinders, in which the radial temperature gradient and axial gravity are considered for an incompressible Newtonian fluid. Numerical method based on the Petrov-Galerkin scheme is developed to deal with the buoyancy term in momentum equations and an additional temperature perturbation equation. Computations of the neutral stability curves are performed for different rotation cases. It is found that the flow instability is influenced by both centrifugal and axial shear instabilities, and the two instability mechanisms interact with each other. The outer cylinder rotation plays dual roles of stabilizer and destabilizer under different rotating stages with the inner cylinder at rest. For the heat buoyancyinduced axial flow, spiral structures are found in the instability modes.     

中等半径比反向旋转圆Couette系统流动稳定性的实验和数值研究

圆Couette系统已成为研究从层流转捩为湍流以及有限几何尺寸对图案选择影响的范例.本文以实验和计算机模拟方法研究中等半径比圆Couette系统的稳定性.考察同轴独立旋转圆筒之间的粘性不可压缩流体运动，推广了经典的Rayleigh离心不稳定性理论，导出稳定性判据，用来定量地确定稳定界限.实验采用了流动显示和激光散射技术.仪器有半径比η=0.699，形状比Γ=18.流动状态相图中的显著特征是新的首次失稳态：当外筒静止或反向旋转时，首次失稳出现具有非零方位角波数的螺旋涡流，在轴向和方位角方向为行进波，而并非与时间无关的Taylor涡.初步实验所得的转捩Reynolds数与数值计算结果一致.实验室和数值实验显示出半径比对图案形成和转捩序列的影响. 关键词：     

Three-dimensional simulations of instabilities in a Marangoni-driven, low Prandtl number liquid bridge with magnetic stabilization to verify linear stability theory

The Full-Zone model of a liquid bridge encountered in crystal growth is analyzed via linear stability analysis and three-dimensional spectral element simulations, neglecting gravitational forces, for Prandtl number 0.02. The base state is axisymmetric and steady state. Linear stability predicts the character of flow transitions and the value of Re _FZ , the thermocapillary Reynolds number, at which instabilities occur. Previous linear stability findings show that application of a steady, axial magnetic field stabilizes the base state. Previous three-dimensional simulations with no magnetic field predict a first transition that agrees well with linear stability theory. However, these simulations also demonstrated that continued time integration at just slightly higher Re _FZ leads to what appears to be periodic flow. Closer inspection and comparison with linear stability theory revealed that this apparent periodicity was actually competition between two steady modes with different axial symmetries. Here an axial magnetic field is applied in three-dimensional simulations and it is verified that the magnetic field does have the intended effect of stabilizing the flow and removing modal competition. The azimuthal flow shows excellent agreement with eigenvectors predicted by linear stability theory.     

旋转环形浅液池内双组分溶液耦合热-溶质毛细对流渐近解

为了了解水平温度梯度作用下旋转环形浅液池内耦合热-溶质毛细对流基本特征, 采用匹配渐近展开法对旋转环形浅液池内耦合热-溶质毛细对流过程进行了求解, 获得了中心区域的速度、温度和浓度分布,分析了旋转、Soret效应、浮力、溶质扩散 系数和液池的几何尺寸对流动结构的影响.将所得到的渐近解和文献中的已有结果进行对比,证明了所求结果的正确性;在浅液池内,耦合热-溶质毛细力对流体流动起主导作用, 旋转和浮力对流动的影响较小,溶质扩散系数和几何尺寸有较明显影响;当各种耦合的 驱动力作用方向相同时,流动增强;否则, 流动减弱. 关键词： 旋转 环形浅液池 耦合热-溶质毛细对流 渐近解     

Pinch instability of a cylindrical couette flow in a nonuniform axial magnetic field

The paper addresses the linear stability to axisymmetric perturbations of an incompressible nonideal fluid between two rotating coaxial infinitely long cylinders in a nonuniform axial magnetic field. For conducting cylinders, the results for uniform and nonuniform magnetic fields are qualitatively identical. This is also observed for nonconducting cylinders in a magnetic field with a constant direction. Instability appears for nonconducting cylinders in a magnetic field with a varying direction, whose magnitude exceeds a certain critical value. This new instability also exists in the absence of rotation and, hence, is independent of its parameters. In addition, the critical magnetic field is independent of the magnetic Prandtl number, which facilitates experimental observation of the new instability.     

Existence of dual solutions and three-dimensional instability in helical pipe flow

Three-dimensional (3D) direct numerical simulations (DNS) of the viscous incompressible fluid flow through a helical pipe with circular cross section were performed. The flow is governed by three parameters: the Dean number (or the Reynolds number), curvature, and torsion. First, we obtained steady solutions by steady 3D calculations, where dual solutions were found, one was uniform in the pipe axial direction and the other varied very slowly, if torsion exceeded a critical value. Then, the instability of the steady solutions obtained was studied by unsteady 3D calculations. We obtained critical Reynolds numbers of steady to unsteady transition by observing the behaviors of the unsteady solutions. The present results of the critical Reynolds number nearly agreed with those by the 2D linear stability analysis (Yamamoto et al. [9]) except for the lowest critical Reynolds number region, where the present study gave the critical Reynolds number much less than that obtained by the 2D linear stability analysis. We found the vortical structures in the form of a standing wave slightly above the marginal instability state, which is a trigger of explosive 3D instability.     

Analysis of radiation in a suspension of nanoparticles and gyrotactic microorganism for rotating disk of variable thickness

Here heat, concentration and motile microorganism transfer rates in radiative flow of nanofluid are investigated. Variable thicked surface of rotating disk is examined. Concept of microorganisms suspended nanoparticles is stabilized through bioconvection which has been induced by combined effects of magnetic field and buoyancy forces. For obtained nonlinear differential systems the convergent series solutions are derived. Fluid flow, temperature, concentration and motile density behaviors for different parameters are analyzed through graphs. Skin friction and Nusselt number are analyzed numerically. Clearly temperature and concentration have opposite behavior for larger Brownian motion parameter. Motile density reduces for bioconvection Peclet number and bioconvection Lewis number.     

On the stability of superfluid helium between rotating concentric cylinders

The stability of the flow of pure superfluid helium between two rotating concentric cylinders is considered. In contrast to the case of classical rotating Couette flow we find that non-axisymmetric disturbances are more important than axisymmetric disturbances. We also find that linear instability can occur when the outer cylinder rotates and the inner cylinder is at rest, a situation which is linearly stable in the classical fluid case.     

Observation of a free-Shercliff-layer instability in cylindrical geometry

We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, Re～10(3)-10(6). The free Shercliff layer is formed by imposing a sufficiently strong axial magnetic field across a pair of differentially rotating axial end cap rings. This layer is destabilized by a hydrodynamic Kelvin-Helmholtz-type instability, characterized by velocity fluctuations in the r-θ plane. The instability appears with an Elsasser number above unity, and saturates with an azimuthal mode number m which increases with the Elsasser number. Measurements of the structure agree well with 2D global linear mode analyses and 3D global nonlinear simulations. These observations have implications for a range of rotating MHD systems in which similar shear layers may be produced.     

The Brunt–Väisälä frequency of rotating tokamak plasmas

The continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt–Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.     

Mechanism on oscillating lifted flames in nonpremixed laminar coflow jets

The oscillating lifted flame in a laminar nonpremixed nitrogen-diluted fuel jet is known to be a result of buoyancy, though the detailed physical mechanism of the initiation has not yet been properly addressed. We designed a systematic experiment to test the hypothesis that the oscillation is driven by competition between the positive buoyancy of flame and the negative buoyancy of a fuel stream heavier than the ambient air. The positive buoyancy was examined with various flame temperatures by changing fuel mole fraction, and the negative buoyancy was investigated with various fuel densities. The density of the coflow was also varied within a certain range by adding either helium or carbon dioxide to air, to study how it affected the positive and negative buoyancies at the same time. As a result, we found that the range of oscillation was well-correlated with the positive and the negative buoyancies; the former stabilized the oscillation while the latter triggered instability and became a source of the oscillation. Further measurements of the flow fields and OH radicals evidenced the important role of the negative buoyancy on the oscillation, detailing a periodic variation in the unburned flow velocity that affected the displacement of the flame.     

Order parameter equation and model equation for high Prandtl number. Rayleigh-Bénard convection in a rotating large aspect ratio system

We derive the order parameter equation which describes the evolution of spatio-temporal patterns close to the Bénard instability in a rotating large aspect ratio system for high Prandtl number fluids. Since this order parameter equation contains rather complicated nonlinear terms we present a model equation which can be obtained from the order parameter equation by suitable simplification of the nonlinearity. For this model equation we calculate the family of roll solutions and investigate their stability with respect to long scale instabilities and examine the onset of the Küppers-Lortz instability. Then we present spatiotemporal patterns which are obtained from a numerical evaluation of the model equation.     

气流对电弧螺旋不稳定性的影响

采用与时间有关的线性微扰理论,研究了气流作用下电弧等离子体的螺旋不稳定性,导出了相应方程和满足的边界条件,给出了临界Maecker’s数和不稳定性增长率等定量结果.计算结果表明,轴向气流对电弧稳定性起重要作用     

A Nonlinear Azimuthal Instability of Hydromgantic Rigid-Rotating Column

This work examines a new approach to studying the nonlinear azimuthal instability analysis. The system consists of two rotating fluids through porous media in the influence of a uniform azimuthal magnetic field. For gullibility, the problem is assumed in a planar configuration. The boundary-value problem reveals a differential equation of nonlinearity nature which controls the surface deflection of the interface. The investigation of this equation is based mainly on the homotopy perturbation technique. The linear and nonlinear stability criteria are conducted. Besides, the profile of the surface deflection is theoretically achievable. The numerical calculations are done to display the effect of the several physical parameters on the stability profile. It is found that the ratio of the densities between the two fluid columns plays an interesting role in the stability picture in linear as well as the nonlinear approaches. For instance; a dual role of the density ratio occurs when the density of the inner column is greater than that of the outer one. Furthermore, the azimuthal wavenumber, like the axial wavenumber, plays a stabilizing influence.     

Competition of Brazil nut effect,buoyancy, and inelasticity induced segregation in a granular mixture

It has been recently reported that a granular mixture in which grains differ in their restitution coefficients presents segregation: the more inelastic particles sink to the bottom. When other segregation mechanisms as buoyancy and the Brazil nut effect are present, the inelasticity induced segregation can compete with them. First, a detailed analysis, based on numerical simulations of two dimensional systems, of the competition between buoyancy and the inelasticity induced segregation is presented, finding that there is a transition line in the parameter space that determines which mechanism is dominant. In the case of neutrally buoyant particles having different sizes the inelasticity induced segregation can compete with the Brazil nut effect (BNE). Reverse Brazil nut effect (RBNE) could be obtained at large inelasticities of the intruder. At intermediate values, BNE and RBNE coexist and large inelastic particles are found both near the bottom and at the top of the system.     

Impact of the gravity field on stability of premixed flames propagating between two closely spaced parallel plates

The stability of a planar flame front propagating between two parallel adiabatic plates inclined at an arbitrary angle is investigated in the frame of narrow-channel approximation. It is demonstrated that buoyancy forces can suppress the hydrodynamic (Darrieus–Landau) and cellular (diffusive-thermal) instabilities for sufficiently large value of the gravity parameter for the case of downward-propagating flames. The stability analysis reveals that in the case of oscillatory diffusive-thermal instability, the flame front cannot be stabilized in the similar way. Finally, the stability results are compared satisfactorily with unsteady numerical simulations.     

Visualization of sudden-start flow between two concentric rotating cylinders with finite length

Numerical simulation and visualization are performed to investigate the developing processes of flows between two concentric rotating cylinders. The length of the cylinders is finite and the end walls are fixed. Initially the fluid is at rest, and the inner cylinder suddenly begins to rotate. Various flow modes appear in this flow. Developments of the flow to these modes are examined and the physical explanation for the transient process is presented. The processes are classified into some types. At low Reynolds numbers, vortices begin to grow on end walls. When the Reynolds number is higher, the centrifugal instability brings first vortices around the mid-plane in the axial direction. Some final modes are established via an intermediate mode, and some other modes are attained after merging and vanishing of vortices.     

MHD swirling flow and heat transfer in Maxwell fluid driven by two coaxially rotating disks with variable thermal conductivity

We develop a mathematical modeling for an electrically conducting non-Newtonian Maxwell fluid flow occurring between two coaxially parallel stretchable rotating disks at constant distant apart. The pressure and heat transfer analysis is carried out subject to the effects of axial magnetic field and temperature dependent thermal conductivity. The stretching and rotating rates of both disks are assumed different from each other. The two diverse phenomena, such as, when both disks are rotating with different angular velocities in the same as well as in the opposite directions are discussed. The similarity procedure adopted by von Kármán is utilized to reduce the governing momentum and energy equations into nonlinear ordinary differential equations. The solution of the governing problem is obtained numerically using bvp4c scheme in Matlab. The effects of active parameters including stretching rates, Deborah number, magnetic number, Prandtl number, thermal conductivity parameter and Reynolds number are examined for same as well as opposite rotation direction for radial, azimuthal, and axial flows, pressure and temperature fields. The classical flow pattern happening between the disks is significantly altered by the stretching action which is a main physical significances of this study. The azimuthal flow is observed higher for the same direction of disks rotation as compared to opposite disks rotation. The pressure field drops near the lower disk with increasing values of Reynolds number. The role of thermal conductivity parameter is quite useful to enhance the fluid temperature.     

Experimental analysis of the stratorotational instability in a cylindrical Couette flow

This study is devoted to the experimental analysis of the stratorotational instability (SRI). This instability affects the classical cylindrical Couette flow when the fluid is stably stratified in the axial direction. In agreement with recent theoretical and numerical analyses, we describe for the first time in detail the destabilization of the stratified flow below the Rayleigh line (i.e., the stability threshold without stratification). We confirm that the unstable modes of the SRI are nonaxisymmetric, oscillatory, and take place as soon as the azimuthal linear velocity decreases along the radial direction. This new instability is relevant for accretion disks.     

Numerical investigation of incompressible fluid flow and heat transfer around a rotating circular cylinder

The heat transfer and air flow around an unconfined heated rotating circular cylinder is investigated numerically for varying rotation rates (α = 0–6) in the Reynolds number range of 20–200. The numerical calculations are carried out by using a finite volume method based commercial computational fluid dynamics solver FLUENT. The successive changes in the flow pattern are studied as a function of the rotation rate. Suppression of vortex shedding occurs as the rotation rate increases (α > 2). A second kind of instability appears for higher rotation speed where a series of counter-clockwise vortices is shed in the upper shear layer. The rotation attenuates the secondary instability and increases the critical Reynolds number for the appearance of this instability. Besides, time-averaged (lift and drag coefficients and Nusselt number) results are obtained and compared with the literature data. A good agreement has been obtained for both the local and averaged values.