Numerical study of a laminar melt flow driven by a rotating magnetic field in enclosed cylinders with different aspect ratios

Summary This paper is devoted to the numerical study of axisymmetric rotating flow in enclosed cylinders with aspect ratios R (diameter divided by height) equal to 0.25, 0.33, 0.5, 1, 2, 3 and 4. The steady motion of the liquid is caused by the action of a low-frequency, low-induction rotating magnetic field with magnetic Taylor numbers lying in the range from 0.0025 · Ta _cr to 0.9 · Ta _cr , where Ta _cr refers to the critical magnetic Taylor number. We found that the ratio between global meridional to global azimuthal flow velocity passes a distinct maximum which depends on the aspect ratio. It marks the transition from the viscous to the inertial regime. Their characteristic features are examined by analysis of the angular velocity and the torques exerted by the boundaries, in dependence on Ta and the aspect ratio.     

Stability of ferrofluid flow between concentric rotating cylinders with an axial magnetic field

A linear stability analysis for the ferrofluid flow between two concentric rotating cylinders in the presence of an axial magnetic field is implemented in this study. Both of the wide-gap and small-gap cases are considered and the governing equations with respect to three-dimensional disturbances including axisymmetric and non-axisymmetric modes are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of ?, the volume fraction of colloidal particles; ξ, the strength of axial magnetic field; μ, the ratio of angular velocity of the outer cylinder to that of the inner cylinder; and ε, the ratio of radius of the inner cylinder to that of the outer cylinder, is conducted. Results show that the stability characteristics depend heavily on these factors. It is found that the increases of ? and ξ, and decrease of ε tend to stabilize the basic flow for an assigned value of μ. The variations of the onset mode with these parameters are discussed in detail. An example for the practical application of present results is given to help the understanding of stability behaviour of this flow.     

On the flow between two rotating disks enclosed by a cylinder

Summary The flow field inside a cylindrical container caused by the impulsively started constant co-rotation or counter rotation of the top-bottom endwalls with fixed sidewall is described. After a transient phase from an initial state at rest a steady flow situation is reached. The unsteady axisymmetric Navier-Stokes equations describing the transient flow are expressed in vorticity-stream function form. For large values of Reynolds number (based on angular velocity on the lower endwall) an upwind differencing in the spatial derivatives for the convective terms is used. A fourth-order accurate compact difference scheme is applied to solve the Poisson equation. The results show that the slight co-rotation of the topbottom endwalls induces a breakdown bubble at a critical value of the Reynolds number which is much smaller than the value of the Reynolds number for the onset of vortex breakdown in a flow due to rotation either of the top or bottom end wall. On the other hand, a weak counter-rotation of top-bottom endwalls suppresses the vortex breakdown. The question of whether the similarity solutions are locally useful in describing the flow between finite disks is also addressed.     

Streamlining of a cylinder with an electric arc rotating in a magnetic field

Streamlining of a circular cylinder with a localized heat source modeling an MHD actuator in which the plasma arc channel moves along the cylinder surface under the action of the Lorentz force in a radial magnetic field is studied experimentally and simulated numerically. It is shown that the presence of a moving heat release region leads to a break in the symmetry in cylinder streamlining by the external flow and the appearance of a nonzero lift force and circulation.     

轴向磁场下分离结晶熔体内热毛细对流的数值模拟

为研究轴向磁场对分离结晶Bridgman法生长CdZnTe晶体熔体热毛细对流的影响,采用有限差分法进行了三维数值模拟。结果表明轴向磁场能有效抑制熔体内的热毛细对流;轴向磁场对熔体内部温度分布也有较大的影响,能使等温线分布变得平缓;当磁场强度不变时,随着狭缝宽度的增大熔体内部的流动减弱。     

NMR and axial magnetic field textures in stationary and rotating superfluid3He-B

We have performed NMR measurements on the flare-out texture of superfluid³He-B in a cylindrical container of 5 mm diameter in axial magnetic fields of 28.4 and 56.9 mT. The transverse cw NMR spectra have been analyzed both with respect to their overall shape and the spin-wave absorption peaks close to the Larmor frequency. Our analysis of the stationary state spectra, based on texture computations, yields the longitudinal resonance frequency v _L (T), the magnetic healing length _H (T), and the dipolar length _D (T), which we report for pressures below 29 bar. A lattice of quantized vortex lines appears in the rotating state, and two additional textural free energy terms have to be included in the analysis. One of the terms is linear in the applied magnetic field and arises from the spontaneous magnetization of the vortex cores. The second term is quadratic in magnetic field; it is generated both by the superflow field v _s (r) about the vortex core and the difference in the induced magnetizations of the vortex-core and the bulk superfluids. The rotational orienting effects have been studied for rotation speeds up to 2red/sec.     

部分失速工况下轴流压气机转子受力特性的研究

首次将轴流压气机的受力特性与工况相结合,分析压气机转子的速度变化和受力特性。首先从理论角度阐述了轴流压气机的失速原理及过程,然后对压气机在正常运行工况和部分失速工况下的受力表达式进行理论推导,通过仿真得出轴流压气机在部分失速工况下的受力特性,最后将仿真结果与理论推导部分相对比。论文通过仿真验证了理论分析的可行性,并得出了失速工况下轴流压气机的速度变化与受力特性,为后续转子的振动分析以及转子的结构优化设计提供有益参考。     

Numerical simulation of the screw shape of an electric arc in an external axial magnetic field

The characteristics of an electric arc of a direct current, burning in a cylindrical channel in a uniform external axial field, are numerically computed within a nonstationary three-dimensional mathematical model at partial local thermodynamic equilibrium. A method for the numeric modeling of the screw shape of an arc in this field is suggested. This approach is in addition to the “network” analogue of fluctuations for the temperature of electrons, which increases weak numeric asymmetry of electron temperature distribution that occurs randomly during computation. This asymmetry can be “picked up” by an external magnetic field and continue to increase up to a certain value, which is enough to form an arc column screw structure. If there are no fluctuations in the computation algorithm of fluctuations, the arc column in an external axial magnetic field maintains cylindrical axial symmetry and the arc screw shape is not observed.     

Source-sink flow in a rotating cylinder

Summary This paper describes the axisymmetric source-sink flow in a rapidly rotating cylinder. Relative fluid motion is induced by the presence of a sink in the bottom corner and a ring source located somewhere in the fluid, at some distance from the solid boundaries. In order to neglect nonlinear effects the volumetric flow rates are assumed to be small, i.e. O(E ^1/2), with E the Ekman number of the flow. The transport from the source to the sink is carried by Ekman layers at the end caps, and a Stewartson layer at the sidewall. At the ring source a free Stewartson layer arises, in which the injected fluid is transported towards the Ekman layers. This Stewartson layer consists of layers of thicknesses E ^1/4 and E ^1/3, which both contribute to the vertical O(E ^1/2) transport. The ring source is enveloped by a ring-shaped region of cross-sectional dimensions O(E ^1/2 × E ^1/2), in which the injected fluid is rearranged before erupting into the E ^1/3 layer. As E ^1/2 E ^1/3, this region appears as an isolated singularity in the E ^1/3 layer; in fact it consists of a combination of an upward and a downward directed source, the strengths of which can be determined by transport arguments. The paper presents an analysis of the E ^1/3-layer structure on the basis of a linear theory; it also describes how the analysis can be extended to the situation in which fluid is injected through an array of sources at different heights.     

An effect of sudden circumferential strain on the laminar boundary layer on a rotating cylinder in an axial flow

Summary The laminar boundary layer which develops on a rotating thin cylinder fitted with an aft-section rotating with an angular velocity different from that of a fore-section is examined numerically. This problem concerns a relaxation process of the boundary layer subjected to a sudden circumferential rate of strain. Two methods are adopted: one is to regard the flow on the aft-cylinder as perturbations of that on the fore-section, and the other is to approximate the discontinuous change in the angular velocity by the cumulative normal distribution function. It is shown that the flow fields are largely influenced by the degree of favorable pressure gradient produced in the boundary layer. Especially, in case of flow passing onto the aft-section with a smaller angular velocity, adverse pressure gradient is induced immediately after the junction between two cylinders, and when the degree of the discontinuity is increased, flow separation can be provoken.With 11 Figures     

Laminar flow of a liquid in a rotating cylinder in a gravitational field

The laminar flow of a viscous liquid in a vertical rotating cylinder is studied.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 2, pp. 198–202, February, 1988.     

Numerical simulation of a viscous separation flow around a rotating circular cylinder

Results of numerical solution of Navier-Stokes equations in stream function-vortex variables for a nonstationary laminar flow around a circular cylinder with a rotational degree of freedom are presented. The cases of definite, free, and inertial rotation of the indicated cylinder were considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 3, pp. 75–81, May–June, 2006.     

Experimental investigation of axial dispersion in a horizontal rotating cylinder

This work reports experimental measurements of the dispersion of particles during rotation in a horizontal cylinder. The axial dispersion of a pulse of approximately monodisperse black glass ballotini into a bed of clear glass ballotini of the same size is analysed. This is done using a sectioning technique, where the concentration is determined throughout the cylinder for a given rotation time and speed. The concentration profile is fitted to an appropriate solution of Fick’s second law to determine the dispersion coefficient. The dispersion coefficient is compared for various drum rotation rates and glass ballotini sizes. The cylinder was filled to 35 % by volume and rotated at a range of speeds between 5 and 20 rpm. The particle sizes vary from 1.14 to 3.15 mm. The dispersion coefficient was found to be dependent on both particle size and rotation speed. As the rotation speed, \(\omega \), was increased the dispersion coefficient increased proportionally to \(\omega ^{0.8}\). As the particle diameter, \(d_p\), was increased the dispersion coefficient increased proportionally to \(d_p^{1.84}\). These results are compared with previous experimental and simulation data, in particular the simulations of Third et al. (Powder Technol 203:510, 2010). Strong agreement was found between the simulations of Third et al. and the experimental results.

     

On compressible flow in a rotating cylinder

Summary Axisymmetric steady flow of a perfect gas in a rotating cylinder is studied by applying a linearised analysis to a small perturbation about isothermal rigid body rotation. Motivated by present day gas centrifuges, special attention is focussed on the effect of a length-to-radius ratio which increases from unit magnitude to infinity and on the effect of a strong radial density gradient associated with the isothermal rigid body rotation. The Ekman number E _*based on the small radial density scale and the density at the cylinder wall is taken to be small. It appears that the flow outside Ekman boundary layers at the end caps consists of three types. These correspond to 1 L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} L _*, E _* ^–1 andE _* ^–1 L _* where L _*is the ratio of the cylinder-length to the radial density scale. For 1 L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} an inviscid flow in a region of limited thickness near the cylinder wall is found. Due to the strong decrease of the density, radial diffusion is not confined to Stewartson boundary layers at the wall (typical for incompressible flow) but extends in the core. This finds expression in two layers in the centre of the cylinder, parallel to the rotation axis, having a structure similar to both Stewartson layers and adjusting the inviscid flow near the wall to a flow dominated by radial diffusion near the rotation axis. For L _* E _* ^{% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% qaaSqaaiaaigdaaeaacaaIYaaaaaaa!386D!\[ - \tfrac{1}{2}\]} and L _* E _* ^–1 both Stewartson layers become successively of the same thickness as the density scale. At the same time the corresponding layers in the core go to the wall and join. As a result, for L _* E _* ^–1 radial diffusive processes are significant in the entire cylinder, a situation also known from studies of flows in semi-infinite gas centrifuges.     

Ferrofluid flow under the influence of rotating magnetic fields

Experimental data are presented concerning the physical mechanism of the electromagnetically induced macroscopic rotation of ferrofluids. The rotating velocity distributions, determined using a DISA anemometer equipment and a tensometric transducer system, showed a very different behaviour of ferrofluids in a low frequency (0 + 10 Hz) rotating magnetic field in comparison with that observed in the higher frequency region ( >15 Hz). The data are compared with other experimental and theoretical results.     

A nonlinear magnetoelastic tube under extension and inflation in an axial magnetic field: numerical solution

In the context of nonlinear magnetoelasticity theory very few boundary-value problems have been solved. The main problem that arises when a magnetic field is present, as compared with the purely elastic situation, is the difficulty of meeting the magnetic boundary conditions for bodies with finite geometry. In general, the extent of the edge effects is unknown a priori, and this makes it difficult to interpret experimental results in relation to the theory. However, it is important to make the connection between theory and experiment in order to develop forms of the magnetoelastic constitutive law that are capable of correlating with the data and can be used for making quantitative predictions. In this paper the basic problem of a circular cylindrical tube of finite length that is deformed by a combination of axial compression (or extension) and radial expansion (or contraction) and then subjected to an axial magnetic field is examined. Such a field cannot be uniform throughout, since the boundary conditions on the ends and the lateral surfaces of the tube would be incompatible in such circumstances. The resulting axisymmetric boundary-value problem is formulated and then solved numerically for the case (for simplicity of illustration) in which the deformation is not altered by the application of the magnetic field. The distribution of the magnetic-field components throughout the body and the surrounding space is determined in order to quantify the extent of the edge effects for both extension and compression of the tube.     

Numerical study of plane couette flow in a rotating framework

Summary A numerical study of laminar plane Couette flow subjected to a steady spanwise rotation is conducted. The full nonlinear Navier-Stokes equations in a steadily rotating framework are solved by a finite difference method for a long, large-aspect-ratio rectangular channel where the outer wall moves at a constant velocity. In this manner, nonlinear and wall end effects which are present in any real laboratory Couette flow experiment are taken into account. The computations demonstrate the existence of a roll instability, at intermediate rotation rates, when the Reynolds number exceeds a critical value of 42. The associated secondary flow in the form of longitudinal rolls is shown to have a severe distortional effect on the primary axial velocity in the interior of the channel which is not linear like its counterpart in an inertial framework. Comparisons are made with previously conducted linear stability analyses as well as with other analogous numerical and experimental studies.With 15 Figures     

Numerical simulation of planar shear flow passing a rotating cylinder at low Reynolds numbers

Two-dimensional shear flow over a rotating circular cylinder is investigated using lattice Boltzmann method. Simulations are performed at a fixed blockage ratio (B = 0.1) while the Reynolds number, nondimensional shear rate (K) and absolute rotational speed range as 80 ≤ Re ≤ 180, 0 ≤ K ≤ 0.2 and −2 ≤ β ≤ 2, respectively. To verify the simulation, the results are compared to previous experimental and numerical data. Quantitative information about the flow variables such as drag and lift coefficients, pressure coefficient and vorticity distributions on the cylinders is highlighted. It is found that, generally, with the increment in |β|, the absolute value of time average lift coefficient increases and time average drag coefficient decreases, and beyond a certain magnitude of β, the vortex shedding vanishes. It is also revealed that the drag coefficient decreases as the Reynolds number increases while the effect of the Reynolds number on lift is almost negligible. At the end, correlations for drag and lift coefficients ([`(C<sub>D</sub> )] ,[`(C_L )]){(\overline {C_D } ,\overline {C_L })} are extracted from the numerical data.