Rotating Inclined Cylinder and the Effect of the Tilt Angle on Vortices

We study numerically some possible vortex configurations in a rotating cylinder that is tilted with respect to the rotation axis and where different numbers of vortices can be present at given rotation velocity. In a long cylinder at small tilt angles the vortices tend to align along the cylinder axis and not along the rotation axis. We also show that the axial flow along the cylinder axis, caused by the tilt, will result in the Ostermeier-Glaberson instability above some critical tilt angle. When the vortices become unstable the final state often appears to be a dynamical steady state, which may contain turbulent regions where new vortices are constantly created. These new vortices push other vortices in regions with laminar flow towards the top and bottom ends of the cylinder where they finally annihilate. Experimentally the inclined cylinder could be a convenient environment to create long lasting turbulence with a polarization which can be adjusted with the tilt angle.     

The impact of cylinder vortex stabilizer on fluctuating turbulence characteristics of a cyclone separator based on Large Eddy Simulation

The main purpose of present study is to comprehensively clarify the impact of cylinder vortex stabilizer on fluctuating turbulence structure of a Stairmand cyclone separator on basis of Large Eddy Simulation. The cylinder vortex stabilizer is easy and could be applied to any existing cyclone model without any major replacement. This novel modification in cyclone body is considered to alleviate the negative effect of entrainment of particles from the ash hopper and swing of the vortex end in swirling flow. The numerical simulations were conducted based on Stairmand cyclone separator and three new models with variation of vortex stabilizer length and diameter. The results showed that the cylinder vortex stabilizer could enhance flow instability and improve fluctuating turbulence structure to some extent. It is confirmed that cylinder vortex stabilizer could significantly reduce the tangential velocity in the inner quasi-forced vortex region of the cyclones. Comparing with Stairmand cyclone, the swirling first and second peak frequency of cyclone model with vortex stabilizer (Length L/D: 6.5, diameter d/D: 0.12) have been confirmed to get considerable reduction of 11.54% and 10.86%, respectively. This modified cyclone model is comparatively better for enhancement of flow stability, providing about 18.4% maximum reduction of normalized flow angle, 24.8% of rotational kinetic energy in dust collector and 14.2% in the main body of cyclone.     

Electro-magnetic collapse of thick-walled cylinders to investigate spontaneous shear localization

We present an electro-magnetic (EM) setup in order to collapse thick-walled cylinders, for the investigation of spontaneous formation of multiple adiabatic shear bands. The EM setup is based on a pulsed current generator using a capacitor bank system. The cylindrical specimen is part of an assembly of coaxial cylinders, where the inner and outer cylinders, each attached to an opposite pole, are short-circuited. Upon capacitor discharge, a high current flows through the cylinders, in opposite directions, creating repulsive magnetic forces between them. The outer cylinder is driven outwards and the inner cylinder is driven inwards - in a collapsing manner. This work presents the design procedure of the specimens’ geometry using numerical simulations, and some preliminary experimental results for SS304L steel specimens. The spatial distribution of the multiple adiabatic shear bands in these specimens is in good agreement with that reported in the literature for explosively driven experiments with the same material. Our numerical simulations of the collapsing cylinder show good agreement with the experimental results for both global behavior and shear band distribution.     

Numerical solution of Stokes flow generated by vortices: part 2, inside an elliptical cylinder

In this second part paper, the two-dimensional flow inside an elliptical cylinder is studied in the presence of no-slip boundary conditions. For simplicity, line vortices are assumed to be parallel to the elliptical cylinder axis, all axes in the same plane. The interior boundary value problem is solved in terms of a stream function. Numerical solutions for the flow field are obtained by application of the boundary element method. The streamline patterns are sketched for a number of special cases where the elliptical cylinder is either stationary or rotating about its own axis. In particular, some interesting flow patterns are observed in the parameter space which may have potential significance in studies of various flows. We also investigate the change in streamline topologies as the parameters are varied. Eddies of various sizes and shapes appear depending on the primary vortices and their locations. The results presented may be relevant for a variety of applications including vortex mixing. The analytical closed-form expressions for the single vortex inside an elliptical cylinder and double vortices inside circular a cylinder are found.     

Film depth and concentration banding in free-surface Couette flow of a suspension

The film depth of a free-surface suspension flowing in a partially filled horizontal concentric-cylinder, or Couette, device has been studied in order to assess its role in the axial concentration banding observed in this flow. The flow is driven by rotation of the inner cylinder. The banding phenomenon is characterized by particle-rich bands which under flow appear as elevated regions at the free surface separated axially by regions dilute relative to the mean concentration. The concentric cylinders studied had outer radius R(o) = 2.22 cm and inner radii R(i) = 0.64, 0.95 and 1.27 cm; the suspension, of bulk particle volume fraction phi = 0.2 in all experiments described, was composed of particles of either 250-300 microm diameter or less than 106 microm diameter, with the suspending fluid an equal density liquid of viscosity 160 P. The ratio of the maximum to the minimum particle volume fraction along the axis in the segregated condition varies from O(1) to infinite. The latter case implies complete segregation, with bands of clear fluid separating the concentrated bands. The film depth has been varied through variation of the filled fraction, f, of the annular gap between the cylinders and through the rotation rate. Film depth was analysed by edge detection of video images of the free surface under flow, and the time required for band formation was determined for all conditions at which film depth was studied. The film depth increases roughly as the square root of rotation speed for f = 0.5. Band formation is more rapid for thicker films associated with more rapid rotation rates at f = 0.5, whereas slower formation rates are observed with thicker films caused by large f, f > 0.65. It is observed that the film depth over the inner cylinder grows prior to onset of banding, for as yet unknown reasons. A mechanism for segregation of particles and liquid in film flows based upon 'differential drainage' of the particle and liquid phase in the gravity-driven flow within the film over the inner cylinder is formulated to describe the onset of concentration fluctuations. This model predicts that suspension drainage flows lead to growth of fluctuations in phi under regions of negative surface curvature.     

Effects on vortex breakdown due to an abrupt change in the rotation of endwall in a disk-cylinder system

Summary The transient flow in a cylindrical enclosure with fixed sidewall is studied numerically. The initial motion due to uniform rotation of the lower endwall is disturbed by setting the top endwall to corotate impulsively with a small angular velocity. The flow parameter values are chosen so as to induce a vortex breakdown in the initial steady state. The unsteady rotationally-symmetric Navier-Stokes equations are solved iteratively using a combination of second-order and fourth order compact difference schemes. At higher values of the Reynolds number, upwind differencing is used in the convective terms. The breakdown bubble in the initial steady state occurs between the stationary top end wall and the mid-plane. The numerical soulution shows that at the early stage of the transient flow the breakdown bubble enlarges in size, and in subsequent time the bubble occurs between the mid-plane and the faster rotating endwall. The role of the azimuthal component of vorticity in the breakdown phenomena is analysed. The torque on the lower endwall is obtained at several values of non-dimensional time during the transient flow.     

Numerical solution of Stokes flow generated by vortices: part 1: around an elliptical cylinder

In this paper, the Stokes flow outside a two-dimensional elliptical cylinder is considered for a highly viscous, incompressible fluid flow, driven by a pair of vortices placed at different positions. Relating the coefficients of some of the terms in the asymptotic expansion of the stream function to the force components and the torque on the combined system, together with the imposition of integral constraints, enables the boundary element method to provide a closed system of equations. It is found that excellent agreement is obtained between the numerical results for a single vortex and all the previous analytical expressions. Some new results relating to forces and torques on the elliptical cylinder are presented. The analytical closed-form expression for the single vortex is provided.     

VORTEX SHEDDING FROM FIXED AND OSCILLATING RECTANGULAR PRISMS IN SHEAR FLOWS

ABSTRACT

The main focus of this paper is to study the results of experiments on six different rectangular prisms with varied side ratios, with and without forced oscillation, displaced in two shear free streams and one uniform flow. The setting of free stream shear parameters β=dU/dyxD/Uc are 0.024 and 0.032. With respect to vortex shedding phenomena, a comparison between shear flows and uniform flows is also part of the focus.

Experimental results indicate that disturbance on the two-dimensional vortex shedding of the uniform flow is caused by the longitudinal vortex of the shear flow gradient. As a result, a spanwise distribution of cells among the vortex shedding frequencies is created. Increases in the side ratios of the rectangular prisms can cause a shifting of cell boundaries toward the high-speed end. As shear parameters for the same prism increase, the cell boundaries move toward the low-speed end. During oscillation, differences arise between the vorticity structures of cells, and the vortices of each cell are more unified, with improvements in correlation.     

A Direct Forcing Immersed Boundary Method Based Lattice Boltzmann Method to Simulate Flows with Complex Geometry

In the present study, a lattice Boltzmann method based new immersed boundary technique is proposed for simulating two-dimensional viscous incompressible flows interacting with stationary and moving solid boundaries. The lattice Boltzmann method with known force field is used to simulate the flow where the complex geometry is immersed inside the computational domain. This is achieved via direct-momentum forcing on a Cartesian grid by combining "solid-body forcing" at solid nodes and interpolation on neighboring fluid nodes. The proposed method is examined by simulating decaying vortex, 2D flow over an asymmetrically placed cylinder, and in-line oscillating cylinder in a fluid at rest. Numerical simulations indicate that this method is second order accurate, and all the numerical results are compatible with the benchmark solutions.     

Existence of extra vortex and twin vortex of anomalous mode in Taylor vortex flow with a small aspect ratio

Summary This experimental work on Taylor vortex flow in a gap with a small aspect ratio is concerned with two extra vortices and a twin vortex system, each of which depends on an anomalous cell of the anomalous mode. Extra vortices are smaller than other vortices such as defined cells. At any Reynolds number and aspect ratio extra vortices can be found at the corner of the end plate and inner rotating cylinder and at the corner of the end plate and outer stationary cylinder. For a one-cell flow (anomalous one-cell mode) in a symmetric system, an outer extra vortex develops and grows to the same size as the main cell, only in an aspect ratio of less than one. A twin vortex is observed to form when two vortices are aligned in the direction of the radius. There are three flow fields on the end plate; two are extra vortex flows and the other is the main cell flow. The flow direction of the anomalous cell is from the inner cylinder to the outer one, at the end plate opposite of the flow direction of the normal cell.Nomenclature R ₁ Radius of inner cylinder (2R ₁=40.19±0.006 mm) - R ₂ Radius of outer cylinder (2R ₂=60.11±0.024 mm) - R _r Radius ratio (R ₁/R ₂=0.669) - d Clearance between cylinders (R ₂–R ₁=9.96±0.025 mm) - L Height of working fluid - Aspect ratio=L/d - Rotational angular speed - Kinematic viscosity - Re Reynolds number=R ₁ d/ Other nomenclature is defined as it appears     

Inertial Waves and Steady Flows in a Liquid Filled Librating Cylinder

The fluid flow in a non-uniformly rotating (librating) cylinder about a horizontal axis is experimentally studied. In the absence of librations the fluid performs a solid-body rotation together with the cavity. Librations lead to the appearance of steady zonal flow in the whole cylinder and the intensive steady toroidal flows near the cavity corners. If the frequency of librations is twice lower than the mean rotation rate the inertial waves are excited. The oscillating motion associated with the propagation of inertial wave in the fluid bulk leads to the appearance of an additional steady flow in the Stokes boundary layers on the cavity side wall. In this case the heavy particles of the visualizer are assembled on the side wall into ring structures. The patterns are determined by the structure of steady flow, which in turn depends on the number of reflections of inertial wave beams from the cavity side wall. For some frequencies, inertial waves experience spatial resonance, resulting in inertial modes, which are eigenmodes of the cavity geometry. The resonance of the inertial modes modifies the steady flow structure close to the boundary layer that is manifested in the direct rebuilding of patterns. It is shown that the intensity of zonal flow, as well as the intensity of steady flows excited by inertial waves, is proportional to the square of the amplitude of librations.     

Dissipation and Phase Slip in Confined Superfluid 4He

We give a brief summary of some results that are to appear elswhere. We have studied a vortex-related mechanism for the non-vanishing thermal resistance well below the bulk lambda point of liquid ⁴He confined in a long cylinder. Here we outline the main concept of the proposed physical mechanism. It involves the non-equilibrium distribution of vortices in the steady state when a small heat current flows along the cylinder axis. We have found that the probability of the saddle-point vortex configuration, which depends exponentially on the length of the vortex, scaled in units of the superfluid correlation length, is the dominant factor in the thermal resistance.     

Hydrodynamic stability of viscous flow between curved porous channel with radial flow

A linear stability analysis has been presented for the flow between long concentric stationary porous cylinders driven by constant azimuthal pressure gradient, when a radial flow through the permeable walls of the cylinders is present. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius is varied from −100 to 30. The linearized stability equations form an eigenvalue problem which are solved using a numerical technique based on classical Runge-Kutta scheme combined with a shooting method, termed as unit disturbance method. It is observed that radially outward flow and strong inward flow have a stabilizing effect, while weak inward flow has a destabilizing effect on the stability. Profiles of the relative amplitude of the perturbed radial velocities show that radially outward flow shifts the vortices toward the outer cylinder, while radially inward flow shifts the vortices toward the inner cylinder.     

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios ofU _m toU ₀ are ofO(10⁻¹),O(1) andO(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re=10², 10³ and 3×10³ are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Kármán vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method. This study was supported by the National Natural Science Foundation of China and the Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, as well as by the National Basic Research project “Nonlinear Science”.     

Experimental study on the particle accumulation phenomenon in seeded flows around a near-bottom-wall horizontal cylinder

In experiments of flows around a cylinder in a water channel, an interesting phenomenon is that a particle accumulation line obviously forms on the bottom of the channel. The present paper focuses on this phenomenon, and the formation mechanism of the particle accumulation line is in detail investigated experimentally with particle image velocimetry (PIV). The circular cylinder was set in a fully developed turbulent boundary layer with 12 gap ratios S/D ranging from 0 to 1.5 under two Reynolds numbers (1371 and 902) based on the momentum loss thickness. The possible mechanism of this phenomenon has been demonstrated with the experimental results: the separation takes place due to the interaction between the wake of the cylinder and the boundary layer of the plane wall, the gap flow separates from the wall downstream of the cylinder and causes an attachment vortex of low velocity area at about 1 to 2 cylinder diameters from the cylinder, where the particle accumulation line forms steadily.     

Organised structures in wall turbulence as deduced from stability theory-based methods

In earlier work, we have explored the relevance of hydrodynamic stability theory to fully developed turbulent wall flows. Using an extended Orr-Sommerfeld Equation, based on an anisotropic eddy-viscosity model, it was shown that there exists a wide range of unstable wave numbers (wall modes), which mimic some of the key features of turbulent wall flows. Here we present experimental confirmation for the same. There is good qualitative and quantitative agreement between theory and experiment. Once the dominant coherent structure is obtained from stability theory, control of turbulence would be the next logical step. As shown, the use of a compliant wall shows considerable promise. We also present some theoretical work for bypass transition (Klebanoff/K-modes), wherein the receptivity of a laminar boundary layer to a vortex sheet in the freestream has been studied. Further, it is shown that triadic interaction between K-modes, 2D TS waves and 3D TS waves can lead to rapid algebraic growth. A similar mechanism seems to carry over to inner wall structures in wall turbulence and perhaps this is the “root cause” for sustenance of turbulence.     

Study and optimization of flow field in a novel cyclone separator with inner cylinder

This paper presents a study of gas-solid flow in a novel cyclone separator with inner cylinder, compared with that in a conventional cyclone. The Reynolds stress model (RSM) is used to simulate fluid flow, and the discrete phase model (DPM) is selected to describe the motion behavior of particles. The experimental data measured by particle image velocimetry (PIV) is used to verify the reliability of the numerical model. The results show that in the novel cyclone, the cleaned gas can be quickly discharged from the vortex finder, the movement distance and residence time of fine particles are prolonged, the short-circuit flow and vertical vortex under the vortex finder are eliminated, the mutual interference between upflow and downflow in the cylinder is eliminated, and the region of quasi-free vortex in the cone is enlarged. Compared with the conventional cyclone, the novel cyclone has higher collection efficiency and lower pressure drop.     

Vortex Tangle Polarized by Rotation

Almost all studies of vortex states in superfluid ⁴He have been concerned with either ordered vortex arrays driven by rotation or disordered vortex tangles driven, for example, by thermal counterfiow. In this work we study numerically what happens to vortices in the presence of both effects. We find that a rotating vortex array becomes unstable, exciting Kelvin waves when it is subject to a counterfiow which is parallel to the rotation axis and which is sufficiently large. After the initial growth of the instability, the vortices enter a new, statistically steady, turbulent state, in which the vortex tangle is polarized along the rotational axis. We determine the polarization of the tangle as a function of the rotation frequency and the counterfiow velocity.     

Nonlinear stability analysis of thin Newtonian film flowing down on the inner surface of a rotating vertical cylinder

Summary The paper presents both of the linear and nonlinear stability theories for characterization of Newtonian film flows down on the inner surface of a rotating in.nite vertical cylinder. After showing the insufficiency of the linear model in characterizing certain flow behaviors, a generalized nonlinear kinematic model is then derived to represent the physical system. The model is solved by the long wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, an elaborated nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The modeling results indicate that by increasing the rotation speed, X, and the radius of cylinder, R, the film flow will make the flow system more stable.