Stability Analysis of a Vertical Curved Channel Flow with a Radial Temperature Gradient

The linear stability analysis of a Newtonian incompressible fluid in a vertical curved channel formed by two coaxial cylindrical surfaces with a radial temperature gradient and an azimuthal pressure gradient shows that critical modes are oscillatory and non-axisymmetric. We have derived a generalized Rayleigh discriminant which includes both the curvature and buoyancy effects. Centrifugal buoyancy induces weak asymmetry of the dependence of the control parameter critical values on the sign of the temperature gradient. The critical parameters depend on the temperature gradient, the radius ratio and the nature of the fluid. For a wide curvature channel flow, there are two critical modes: oscillatory Dean modes for small temperature gradients and oscillatory centrifugal-thermal modes for relatively large temperature gradients. Received 14 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 Communicated by H.J.S. Fernando     

Experimental study on radial temperature gradient effect of a Taylor-Couette flow with axial wall slits

The flow between two concentric cylinders with the inner cylinder rotating and an imposed radial temperature gradient was studied using a digital particle image velocimetry method. The flow transition process under both a positive and negative temperature gradient with four different models of a stationary outer cylinder without and with differing numbers of slits (6, 9 and 18) was studied. The results showed that the buoyant force due to the temperature gradient clearly generated a helical flow when the rotating Reynolds number was small. For the plain and 6-slit models, the transition to a turbulent Taylor vortex flow was not affected by the temperature gradient considered in this study. In addition, the transition process of a larger number of slits (9-, 18-slit models) was accelerated due to the slit wall. As the temperature gradient became larger, the critical Reynolds number of the transition process decreased.     

Non-linear Oberbeck-electroconvection in a poorly conducting fluid through a vertical channel in the presence of an electric field

Non-linear Oberbeck-electroconvection (OBEC) in a poorly electrically conducting fluid through a vertical channel, when the walls are held at different temperatures with temperature difference perpendicular to gravity, is studied using the modified Navier stokes equation in the presence of both induced and an applied electric field. Both analytical and numerical solutions for the non-linear coupled equations governing the motion are obtained and found that analytical solutions agree well with numerical solutions for values of the buoyancy parameter N<1. It is shown that OBEC can be controlled by maintaining the temperature difference either in the same direction or opposing the potential difference with a suitable value of electric number W. The effect of W on velocity, temperature, rate of heat transfer, skin friction and mass flow rate are computed and the results are depicted graphically. We found that analytical results agree well with numerical results for small values of N. We also found that an increase in W accelerates the flow and hence increases linearly the skin friction and mass flow rate.     

电场作用下导电射流稳定性的理论与实验研究

建立导电射流在径向电场作用下的线性稳定性粘性模型,通过正则模方法,推导了轴对称和非轴对称模态下的色散关系,通过计算求得增长率随波数及电欧拉数的变化,并在理论上预测了最有可能波长.选用酒精和酒精甘油混合物作实验液体,观察了径向电场对射流不稳定性行为的影响规律,并测量射流表面波的波长.实验结果和理论结果在定性方面取得了较好的一致.但通过与实验比较,理论预测的最有可能波长在非轴对称模态出现较大偏差,普遍比实验结果小.而且,实验表明,最大增长率并不是判断主导模态的好标准,因为在非轴对称的最大增长率小于轴对称的最大增长率情况下,实验显示非轴对称模态要比轴对称模态明显了.因此,对于非轴对称的不稳定机理,需要进一步研究.对轴对称模态,理论给出了较好的预测.     

电场作用下无黏聚焦射流的时间不稳定性研究

基于电场作用下的流动聚焦实验建立了简化的理论模型,开展了带电同轴液气射流的时间不稳定性分析.在无黏假设下,得到了扰动在时间域内发展演化的解析形式的色散关系,分析了主要控制参数对不稳定模态的影响.结果表明,只有轴对称扰动和第一类非轴对称扰动在时间域内是增长的;液气界面的表面张力对轴对称扰动有着双重影响而对非轴对称扰动起抑制作用;外层气体的流速以及密度的增加均能促进射流的失稳.这些结论与实验结果是定性一致的.结果也表明,在不考虑初始界面电荷密度时,单一的轴向电场能抑制射流的失稳.      

A glance on the effects of temperature on axisymmetric dynamic behavior of multiwall carbon nanotubes

In this paper the effects of temperature on theradial breathing modes(RBMs) and radial wave propagation in multiwall carbon nanotubes(MWCNTs) are investigated using a continuum model of multiple elastic isotropicshells.The van der Waals forces between tubes are simulatedas a nonlinear function of interlayer spacing of MWCNTs.The governing equations are solved using a finite elementmethod.A wide range of innermost radius-to-thickness ratioof MWCNTs is considered to enhance the investigation.Thepresented solution is verified by comparing the results withthose reported in the literature.The effects of temperature onthe van der Waals interaction coefficient between layers ofMWCNTs are examined.It is found that the variation of thevan der Waals interaction coefficient at high temperature issensible.Subsequently,variations of RBM frequencies andradial wave propagation in MWCNTs with temperatures upto 1 600 K are illustrated.It is shown that the thick MWCNTs are more sensible to temperature than the thin ones.     

Double-diffusive convection for a heated cylinder submerged in a salt-stratified fluid layer

Double-diffusive convection due to a cylindrical source submerged in a salt-stratified solution is numerically investigated in this study. For proper simulation of the vortex generated around the cylinder, a computational domain with irregular shape is employed. Flow conditions depend strongly on the thermal Rayleigh number, Ra _T , and the buoyancy ratio, R _ρ. There are two types of onset of instability existing in the flow field. Both types are due to either the interaction of the upward temperature gradient and downward salinity gradient or the interaction of the lateral temperature gradient and downward salinity gradient. The onset of layer instability due to plume convection is due to the former, whereas, the onset of layer instability of layers around the cylinder is due to the latter. Both types can be found in the flow field. The transport mechanism of layers at the top of the basic plume belongs to former while that due to basic plume and layer around the cylinder are the latter. The increase in Ra _T reinforces the plume convection and reduces the layer numbers generated around the cylinder for the same buoyancy ratio. For the same Ra _T , the increase of R _ρ suppresses the plume convection but reinforces the layers generated around the cylinder. The profiles of local Nusselt number reflects the heat transfer characteristics of plume convection and layered structure. The profiles of averaged Nusselt number are between the pure conduction and natural convection modes and the variation is due to the evolution of layers. Received on 13 September 1996     

Forces acting on water droplets falling in oil under the influence of an electric field: numerical predictions versus experimental observations

The combination of an electric field and a moderate turbulent flow is a promising technique for separating stable water–oil emulsions. Field-induced charges on the water droplets will cause adjacent droplets to align with the field and attract each other. The present work describes the forces that influence the kinematics of droplets falling in oil when exposed to an electric field. Mathematical models for these forces are presented and discussed with respect to a possible implementation in a multi-droplet Lagrangian framework. The droplet motion is mainly due to buoyancy, drag, film-drainage, and dipole–dipole forces. Attention is paid to internal circulations, non-ideal dipoles, and the effects of surface tension gradients.Experiments are performed to observe the behavior of a droplet falling onto a stationary one. The droplet is exposed to an electric field parallel to the direction of the droplet motion. The behavior of two falling water droplets exposed to an electric field perpendicular to the direction of their motion is also investigated until droplet coalescence. The droplet motion is recorded with a high-speed CMOS camera. The optical observations are compared with the results from numerical simulations where the governing equations for the droplet motion are solved by the RK45 (Runge Kutta) Fehlberg method with step-size control and low tolerances. Results, using different models, are compared and discussed in detail. A framework is otlined to describe the kinematics of both a falling rigid spherical particle and a fluid droplet under the influence of an electric field.     

实践十号卫星项目——热毛细对流振荡特征的地面研究

上部开口环形液池在水平径向温度梯度作用下会出现内部温度和自由面的振荡,本文研究了二者发生的临界条件.环形液池内柱加热外壁制冷,以0.5℃/min的速率线性升温得到水平径向温差,T型热电偶测量液层内部单点温度,高精度激光位移传感器测量液层自由面某点形变.随两端温差增加,当超过某一临界温度△T_(cr)时,开始出现振荡.实验结果表明,对同一种硅油,两种振荡的临界条件随液层厚度具有相同的变化趋势.对不同普朗特(Prandtl)数(Pr)的硅油,振荡临界条件临界马兰哥尼数(Ma_(cr))随着邦德数(Bo)的增加而变大.本文工作是中国科学院科学先导专项SJ-10返回式科学实验卫星项目-热毛细对流表面波空间实验研究的地面研究结果,该工作为空间实验提供前期的基础科学研究数据和实验保障.     

Instability of fully developed mixed convection with viscous dissipation in a vertical porous channel

Flow driven by an externally imposed pressure gradient in a vertical porous channel is analysed. The combined effects of viscous dissipation and thermal buoyancy are taken into account. These effects yield a basic mixed convection regime given by dual flow branches. Duality of flow emerges for a given vertical pressure gradient. In the case of downward pressure gradient, i.e. upward mean flow, dual solutions coincide when the intensity of the downward pressure gradient attains a maximum. Above this maximum no stationary and parallel flow solution exists. A nonlinear stability analysis of the dual solution branches is carried out limited to parallel flow perturbations. This analysis is sufficient to prove that one of the dual solution branches is unstable. The evolution in time of a solution in the unstable branch is also studied by a direct numerical solution of the governing equation.     

The effect of magnetic fields on low frequency oscillating natural convection with pressure gradient

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Effects of a.c. Electric Field and Rotation on Bénard–Marangoni Convection

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stability of a plane-parallel convective flow of a liquid in a horizontal layer

We consider the stationary plane-parallel convective flow, studied in [1], which appears in a two-dimensional horizontal layer of a liquid in the presence of a longitudinal temperature gradient. In the present paper we examine the stability of this flow relative to small perturbations. To solve the spectral amplitude problem and to determine the stability boundaries we apply a version of the Galerkin method, which was used earlier for studying the stability of convective flows in vertical and inclined layers in the presence of a transverse temperature difference or of internal heat sources (see [2]). A horizontal plane-parallel flow is found to be unstable relative to two critical modes of perturbations. For small Prandtl numbers the instability has a hydrodynamic character and is associated with the development of vortices on the boundary of counterflows. For moderate and for large Prandtl numbers the instability has a Rayleigh character and is due to a thermal stratification arising in the stationary flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 95–100, January–February, 1974.     

Similarity solutions of mixed convection heat and mass transfer in combined stagnation and rotation-induced flows over a rotating disk

The objective of the present study is to develop a novel similarity model for analysis of mixed convection heat and mas transfer in combined stagnation and rotation-induced flows over a rotating disk. Thermal and concentration (solutal) buoyancy effects stemmed from temperature and concentration gradients in rotational as well as gravitational forces fields are all taken into account. The influences of the forced flow, disk rotation, thermal buoyancy, buoyancy ratio and the fluid properties, i.e. Prandtl and Schmidt numbers, on the flow, temperature and concentration fields and the associated friction factors, heat and mass transfer rates are investigated. The present results reveal the effects of various buoyancy modes with combined forces on the transport phenomena in rotating-disk flows, and the analysis is also useful in understanding the mechanisms of mixed convection in the class of rotating fluids. Received on 30 December 1997     

Non-axisymmetric thermal stress of a functionally graded coated circular inclusion in an infinite matrix

This paper is to study the non-axisymmetric two-dimensional problem of thermal stresses in an infinite matrix with a functionally graded coated circular inclusion based on complex variable method. With using the method of piece-wise homogeneous layers, the general solution for the functionally graded coating having radial arbitrary elastic properties is derived when the matrix is subjected to uniform heat flux at infinity, and then numerical results are presented for several special examples. It is found that the existence of the functionally graded coating can change interfacial thermal stresses, and choosing proper change ways of the radial elastic properties in the coating can obviously reduce the thermal stresses.     

TEMPORAL STABILITY OF FLOW THROUGH VISCOELASTIC TUBES

The stability of the Hagen–Poiseuille flow of a Newtonian fluid in an incompressible, viscoelastic tube contained within a rigid, hollow cylinder is determined using linear stability analysis. The stability of the system subjected to infinitesimal axisymmetric or non-axisymmetric disturbances is considered. The fluid and wall inertia terms are retained in their respective equations of motion. A novel numerical strategy is introduced to study the stability of the coupled fluid–structure system. The strategy alleviates the need for aninitial guess and thus ensures that all the unstable modes within a given closed region in the complex eigenvalue plane will be found. It is found that the system is unstable to both axisymmetric and non-axisymmetric disturbances. Moreover, depending on the values of the control parameters, the first unstable mode can be either an axisymmetric mode with the azimuthal wavenumber n=0 or a non-axisymmetric mode withn =1. For a given azimuthal wavenumber, it is found that there are no more than two unstable modes within the closed region considered here in the complex plane. For both the axisymmetric and non-axisymmetric instabilities, one mode is a solid-based, flow-induced surface instability, while the other one is a fluid-based instability that asymptotes to the least-damped rigid-wall mode as the thickness of the compliant wall tends to zero. All four modes are stabilized, to different degrees, by the solid viscosity.     

Dynamics of electroconvective structures in a weakly conducting liquid

The finite-amplitude evolution of electroconvective structures in a weakly conducting liquid with an electroconductive charge formation mechanism is examined. The liquid is in the electrostatic field of a horizontally placed capacitor and is heated from below, and the electric charge time constant is much shorter than the characteristic hydrodynamic time. The interaction between the electroconductive convection and thermogravitational convection is considered. The evolution of the supercritical structures is investigated by direct numerical simulation using the finite-difference method. The bifurcations leading to the formation of stationary and wave liquid flows are analyzed. Nonlinear modes of stationary convection and traveling waves with different space-time patterns are identified and investigated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 20–27, May–June, 2008.     

Adverse and favorable mixed convection heat transfer in a two-side heated square channel

Experimental heat transfer measurements and analysis for mixed convection in a vertical square channel are presented. Water flow directions are selected such that buoyancy assists or opposes the bulk flow pressure gradient. Unlike most previous experiments with symmetrically heated circular tubes, the present configuration uses an asymmetric heating condition (two sides heated and two sides insulated) and shows significant increase in the Nusselt number for both assisted and opposed flow conditions. Observed heat transfer coefficient distributions are different from the symmetrically heated channels; and this difference in heat transfer coefficient is attributed to the formation of buoyancy driven large-scale flow structures. In general, opposed flow shows higher heat transfer coefficients, and the Nusselt number ratio is observed to increase as Gr/Re or Gr/Re² ratios increase for both assisted and opposed flow conditions. A correlation based on the buoyancy parameter predicts the heat transfer pattern well in both assisted and opposed mixed convection. The range of Reynolds numbers discussed (Re=400–10,000) is of importance for direct numerical simulations and the details provided here can serve as the benchmark data required for complicated buoyancy affected turbulence simulations.     

Simultaneous PIV and thermography measurements of partially blocked flow in a differentially heated rotating annulus

A radial barrier has been mounted in a differentially heated rotating annulus that partially blocks the azimuthal flow component. The experiment can be seen as an analog to geophysical flows with constrictions, e.g., the Antarctic Circumpolar Current. However, the experiment has been carried out without a particular natural flow in mind. The main interest was to observe a baroclinic annulus flow that does not become saturated. Hence, in contrast to the annulus flow without a barrier, the partially blocked flow remains transient and surface heat fluxes associated with baroclinic life cycles can be studied. The annulus can be subdivided into the upstream half of the barrier, where waves amplify, and the downstream half of the barrier, where waves decay. In the upstream half, the azimuthal mean flow is moderate but with a significant positive eddy radial heat flux. In the downstream half, we find a strong jet in the mean azimuthal flow and furthermore an increased radial mean temperature gradient. The latter points to a weakened or even reversed radial eddy heat flux in the lee side of the barrier. Temperature anomalies appear as large bulges in the outer part of the annulus. Moreover, an outward shift of vortex centers can be observed with respect to centers of temperature anomalies. This phase shift between pressure and temperature anomalies differs from that of classical Eady modes of baroclinic instability.     

Effect of temperature gradient within a solid particle on the rotation and oscillation modes in solid-dispersed two-phase flows

Liquid–solid two-phase flow with heat transfer is simulated, and the effect of temperature gradient within a solid particle on the particle behaviour and heat transfer is studied. The interaction between fluid and particles is considered with our original immersed solid approach on a rectangular grid system. The local heat flux at the fluid–solid interface is described with an anisotropic heat conductivity matrix, and the governing equation of temperature is time-updated with an implicit treatment for the diffusion term. The method is applied to a 2-D natural convection flow of a relatively low Rayleigh number including multiple particles. Heat transfer and particle behaviours are studied for different solid heat conductivities (ratio to the fluid conductivity ranging between 10⁻³ and 10³) and solid volume fractions. Under a condition of relatively low heat conductivity ratio, the particles show a simple circulating flow. By increasing the heat conductivity ratio, a transition of the particulate flow is observed to oscillation mode around the domain centre due to the buoyancy force as a restitution force. The oscillation period is found to vary with the heat conductivity ratio, and it is related to the time scales for the heat transfer via fluid and solid.