Steady hydromagnetic flow between two porous concentric circular cylinders

The problem considered here is to study the MHD effects on the steady flow of an incompressibe viscous conducting fluid through two concentric porous non-conducting infinite circular cylinders, rotating in various ways with uniform angular velocities in presence of a radial magnetic field. It is supposed that the rate of suction at the inner cylinder is equal to the rate of injection at the outer.     

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.     

Ultrasonic scattering by two concentric cylinders

A series solution for scattering from two concentric, fluid cylinders of different speeds and densities has been employed to compute the scattered pressure for a range of frequencies, material parameters, and emitter and detector functions. This range includes the nominal parameters of measurements that were made at a frequency of 1.0 MHz and a radius of 150 mm on a gel model with an outer radius of 25.00 mm and an inner radius of 9.52 mm. The nominal parameters correspond to a ka of 626.2 for the measurement radius, a ka of 106.0 for the outer cylinder, and a ka of 39.8 for the inner cylinder. Scattering was calculated for frequencies for 10 kHz to 10 MHz which resulted in ka values from 6.26 to 6262 for the measurement radius, from 1.06 to 1060 for the outer cylinder, and from 0.398 to 398 for the inner cylinder. The effects on scattering of changes in speed and density parameters of the concentric cylinders are presented. First, the speed of the outer cylinder was raised by a factor of 10 from the nominal while the density of the outer cylinder and the speeds and densities of the inner cylinder and the surrounding medium were held fixed. Next, the density of the outer cylinder was raised while its speed was fixed at nominal, as were the speeds and densities of the inner cylinder and the medium. Finally, the speed first and then the density of the inner cylinder was raised while the parameters of the outer cylinder and of the medium were held fixed at nominal.(ABSTRACT TRUNCATED AT 250 WORDS)     

Couette flow of two immiscible liquids between two concentric cylinders: the formation of toroidal drops and liquid sheaths

We describe the direct observation of deforming water drops in oil undergoing shear flow in a horizontal annular Couette cell. The drops assume a wide variety of highly reproducible structures depending on drop size, rotation speed, and flow history. These structures include toroidal rings of water around the rotating shaft and water sheaths, which, depending on experimental conditions, can either expand to press against the inner walls of the outer stationary cylinder or contract to hug the outside of the rotating shaft.     

On near-wall effects in hard disk packing between two concentric cylinders

Monodisperse packing of disks in confined geometries is rarely addressed in the literature. We present some theoretical aspects of the microstructural properties of 2D static packing of disks between two concentric cylinders. In the core of the geometry, the packing is intact, while it is dilated in the vicinity of the walls as a result of the removal of overlapping disks. We have derived the formula for average packing density in concentric cylinders geometry with given ratio of the particle diameter to the gap between cylinders. It is verified and analyzed further by constructing ordered and disordered packs of monodisperse disks in computer. In this context, Voronoi tessellation is performed for the resulting packs to demonstrate the thickness of the static boundary layer where the packing is influenced by the presence of cylindrical walls.     

两个同心旋转球之间流动的谱方法

利用Stokes算子的特征函数作为基函数,用谱Galerkin方法对两个同心球之间的粘性不可压缩流动进行了研究,并作了数值模拟,并且利用谱方法得到了一个Lorenz型方程,分析了它的稳定性,证明了其吸引子的存在性。     

Stability of hydromagnetic Dean flow between two arbitrarily spaced concentric circular cylinders in the presence of a uniform axial magnetic field

The effect of a uniform axial magnetic field on the stability of the flow of an incompressible viscous electrically conducting fluid between two arbitrarily spaced concentric circular cylinders driven by a constant azimuthal pressure gradient is studied. The linearized stability equations for steady axisymmetric disturbances form an eigenvalue problem, which are solved by using a classical Runge–Kutta scheme combined with a shooting method, termed unit disturbance method. It is observed that for fixed gap width, the magnetic field has a stabilizing influence on the flow for both perfectly conducting and nonconducting walls. It is also found that for a given value of magnetic parameter, stabilization is more as the gap width increases. Further the electrically nonconducting walls are found to be more destabilizing than the perfectly conducting walls. The critical value of the radii ratio (0<η<1) beyond which the first unstable mode becomes nonaxisymmetric is determined for various values of the magnetic parameter.     

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.     

Two-dimensional radiative equilibrium of a gray medium between concentric cylinders

A method for calculating radiative equilibrium temperature and surface heat-flux distributions is developed for an absorbing-emitting medium between concentric cylinders. The cylinder walls are assumed to be gray diffuse absorbers and emitters and have arbitrary temperature distributions along their peripheries. Heat generation may take place within the medium. As a first approximation, the problem is solved for optically-thick systems by using the differential approximation. To obtain accurate results also for the optically-thin and intermediate regimes, the differential approximation is subsequently improved by a number of geometric parameters, as has been discussed in a previous paper. As examples, two cares are presented in detail: (1) a hollow cylinder with uniform internal heat generation and uniform surface temperature and (2) a hollow cylinder with a cosine temperature distribution imposed on the wall, with no internal heat generation. Comparison with some numerical results generated by Hottel's zonal method shows excellent agreement.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

同心旋转圆柱间隙流场中纤维取向的动态模拟

本文对两同心旋转圆柱间隙形成的流场以及处于流场中的纤维运动和取向进行了数值研究. 在贴体坐标网格下求解了流场控制方程, 得到了流场中的速度、压力等物理量. 研究了两同心圆柱同速反向旋转以及仅内层圆柱旋转这两种情况下的纤维运动和取向状态. 得到了处于这两种情况下的纤维在流场中从静止到开始运动和取向直至最终达到稳定状态的动态详细过程. 结果表明, 当两个圆柱同速反向旋转时, 纤维运动与取向也相应的呈现两层结构; 而仅内圆柱旋转时, 纤维运动与取向呈单层结构. 在两种情况下, 纤维均沿流线方向运动和取向. 讨论了纤维长径比对纤维取向的影响, 结果表明随着纤维长径比的增加, 纤维沿流线取向的取向度逐渐增强.     

The capillary interaction between two vertical cylinders

Particles floating at the surface of a liquid generally deform the liquid surface. Minimizing the energetic cost of these deformations results in an inter-particle force which is usually attractive and causes floating particles to aggregate and form surface clusters. Here we present a numerical method for determining the three-dimensional meniscus around a pair of vertical circular cylinders. This involves the numerical solution of the fully nonlinear Laplace-Young equation using a mesh-free finite difference method. Inter-particle force-separation curves for pairs of vertical cylinders are then calculated for different radii and contact angles. These results are compared with previously published asymptotic and experimental results. For large inter-particle separations and conditions such that the meniscus slope remains small everywhere, good agreement is found between all three approaches (numerical, asymptotic and experimental). This is as expected since the asymptotic results were derived using the linearized Laplace-Young equation. For steeper menisci and smaller inter-particle separations, however, the numerical simulation resolves discrepancies between existing asymptotic and experimental results, demonstrating that this discrepancy was due to the nonlinearity of the Laplace-Young equation.     

Free convection effects on HMD horizontal channel flow with Hallcurrents

An exact solution of MHD channel flow between two horizontal parallel plates taking into account free convection currents and the Hall currents is presented. Solutions for the primary and secondary velocity, the induced magnetic field, the skin friction, and the temperature are derived. The velocity field and magnetic field are shown on graphs, and the values of the skin friction and the rate of heat transfer are indicated on tables. The results are discussed in terms of the hall parameter, the Hartmann number, and the Grashof number     

Free axisymmetric vibration of a circular plate elastically supported along two concentric circles

This letter deals with the vibration of homogeneous circular plates resting on linear and torsion spring supports along the outside periphery and along a circle of arbitrary radius. The solution includes two special cases. In the first, the intermediate elastic support becomes rigid and in the second the elastic coefficient goes to zero thereby removing the intermediate support. Results are shown in the form of graphs. These graphs also include results for classical conditions at the outer periphery which are found to be in excellent agreement with the available results.     

Mathematical modeling and simulation for the flow of magneto-Powell-Eyring fluid in an annulus with concentric rotating cylinders

The rheological fluid flows through concentric rotating cylinders have wide range of applications in many machinary parts such as axles and shafts to spinning projectiles. Whenever, the rotating motion connected with the discs, the proximity of a surface may be remarkably change the structure of the flow. The main purpose of this study is to discuss the motion of Powell-Eyring fluid between two concentric rotating cylinders. We formulated the problem in cylindrical coordinate system with suitable boundary conditions. The existence and uniqueness of the solution for the equation governing the flow is provided with the help of Schauder’s fixed point theorem. The velocity distribution is obtained by Mathematica software. The numerical results are presented for the sundry parameters through graphical representations. It is depicted from our analysis that, the velocity is an increasing function of rotation parameter and Powell-Eyring fluid parameter. The present analysis has wide range of applications in engineering sciences.     

Pattern formation and bistability in flow between counterrotating cylinders

In the Taykor-Coutte experiment on fluid flow counterrotating cylinders, there is a bicritical point where the onset of instabilities to Taylor vortex flow (a steady-state bifurcation) and spiral vortex flow (a Hopf bifurcation) meet. The nonlinear mode interactions near this bicritical point are analyzed, exploiting the role of symmetry in the bifurcation theory, and with emphasis of the relevance to experiments, for a range of raduis ratios 0.43 ≤η≤0.98. The mechanism of the pattern formation is elucidated, and several new flow patterns and transitions are predicted, including wavy vortices, bistability, hysteresis, and up to 7 quasiperiodic flows.