Fluid Rotation Research Articles

Extraction of gold in a centrifugal field of fluid rotation

With the samples of the gold-antimony ore processing products of the Sentachan deposit, flotation experiments were carried out on a laboratory centrifugal flotation machine with peripheral concentrate discharge (CFM) and on a laboratory mechanical flotation machine (FM). The selectivity of falling of mineral particles from the flotation mineralized foam flowing along the inclined plane after flotation under different modes (with and without the use of a collector) was investigated; it was shown that the use of a collector can regulate the intensity and selectivity of the falling of material from the foam layer. It was found that the combination of the effect of the centrifugal force of fluid rotation and the hydrophobic properties of minerals makes it possible to enhance the selectivity of the separation of minerals; during flotation in a centrifugal flotation machine, it is possible to carry out cleaning operations in order to improve the quality of the concentrate.

Transportation of heat generation/absorption and radiative heat flux in homogeneous–heterogeneous catalytic reactions of non-Newtonian fluid (Oldroyd-B model)

BackgroundThis study addresses the three-dimensional (3D) stagnation point flow of non-Newtonian material (Oldroyd-B) with magnetohydrodynamics. Furthermore, Ohmic heating and radiative flux are used in the modeling of energy expression. The surface is convectively heated. Equal strengths of diffusions for homogeneous and heterogeneous reactions are counted. Results are computed and presented graphically. Heat transfer rate is numerically discussed through table. MethodHere the nonlinear differential system first converted into ordinary differential equation through implementation of appropriate similarity variables. The obtained ordinary system is tackled through homotopy technique for convergent solutions. The outcomes are presented through different graphs and discussed in section six. OutcomesThe remarkable results of the present communication which is obtained from the semi analytical method i.e., “homotopy method” is summarized as(i) Opposite impact is noticed for velocity components i.e., (f′(ξ), g(ξ)) for rising fluid parameter and rotation parameter.(ii) The temperature is direct relation with Biot number and radiative variable.(iii) Heat transfer rate is more versus Biot number and radiation variable.(iv) The concentration field shows opposite impact versus homogeneous and heterogeneous parameters.

Fluid flow in an enclosed cavity of rotational bioreactor for bone tissue engineering

The developed mathematical model was applied for study of fluid dynamics in a rotational bioreactor for bone tissue engineering by in vitro technology. The research goal is finding an optimal mode for rotation ensuring proper cyclic loading from fluid upon the cell-seeded biomaterial. The basis for developing a mathematical model of a bioreactor was a design of rotational type biological reactor used in medical research; the liquid flow is generated through viscosity mechanism due to surface rotation. Mathematical description of flow in a reactor cavity was performed with Navier—Stokes equations. It was assumed that flow regime in the boundary layer is laminar. Numerical algorithm was accomplished using a fluid flow solver “Fluent” in the code package ANSYS-12. Four variants of generating the rotational motion in the reactor cavity were considered. A series of parametric computations was performed for the rotation frequency f in the range 0.05 ≤ f ≤ 0.25 Hz. The paper offers visualization of velocity fields in the vertical plane. The distributions for shear stress and pressure in the working zone of reactor were calculated and analyzed. Simulations demonstrated that a method of fluid rotation by driving the outer cylinder with an offset axis is the best for arranging a cyclic pressure and cyclic shear stress on the biological material.

Stokes waves with constant vorticity: folds, gaps and fluid bubbles

The Stokes wave problem in a constant vorticity flow is formulated, by virtue of conformal mapping techniques, as a nonlinear pseudodifferential equation, involving the periodic Hilbert transform, which becomes the Babenko equation in the irrotational flow setting. The associated linearized operator is self-adjoint, whereby the modified Babenko equation is efficiently solved by the Newton-conjugate gradient method. For strong positive vorticity, a ‘fold’ appears in the wave speed versus amplitude plane, and a ‘gap’ as the vorticity strength increases, bounded by two touching waves, whose profile contacts with itself at the trough line, enclosing a bubble of air. More folds and gaps follow for stronger vorticity. Touching waves at the beginnings of the lowest gaps tend to the limiting Crapper wave as the vorticity strength increases indefinitely or, equivalently, gravitational acceleration vanishes, while the profile encloses a circular bubble of fluid in rigid body rotation at the ends of the gaps. Touching waves at the beginnings of the second gaps tend to the circular vortex wave on top of the limiting Crapper wave in the infinite vorticity limit, or the zero gravity limit, and the circular vortex wave on top of itself at the ends of the gaps. Touching waves for higher gaps accommodate more circular bubbles of fluid.

Transient flows and reorientations of large-scale convection in a cubic cell

The transient processes of a turbulent large-scale convective circulation (LSC) in a cubic cell are investigated using large-eddy simulations for Rayleigh number Ra = 108 and Prandtl number Pr = 0.7. For the first time, we have explicitly shown that LSC is accompanied by large-scale azimuthal flows with non-zero total angular momentum. It is also shown that solid-body rotation of the entire fluid is not realized. It is found that correlation between rotation of LSC plane and the mean azimuthal motion is high during quasiperiodic oscillations of LSC near the diagonal plane and relatively weak during LSC reorientations. We propose a new plausible scenario for the reorientations of the LSC in a cube that does not involve a mean azimuthal flow. Instead of a single-roll, we introduce the superposition of a pair of large-scale orthogonal quasi-two-dimensional (Q2D) rolls and the reorientation of the LSC occurs as a result of the cessation of one of the Q2D rolls. This scenario is consistent with all known experimental and numerical data.

An explicit expression for the calculation of the Rortex vector

Recently, a vector called Rortex was proposed and successfully applied to identify the local fluid rotation with both the rotation axis and strength. The first implementation relies on the real Schur decomposition of the velocity gradient tensor, resulting in a relatively long computational time. Subsequently, a mathematically equivalent eigenvector-based definition of Rortex was introduced with an improved implementation. Unfortunately, this definition still tends to be an algorithmic description rather than an explicit one and involves two successive cumbersome coordinate rotations. In this paper, a simple and explicit expression for the calculation of the Rortex vector, which is based on a special (transposed) Schur form of the velocity gradient tensor, is presented. The explicit expression is consistent with the previous definition but avoids the explicit calculation of the coordinate rotation, and thus can significantly simplify the implementation. According to the explicit expression, a new implementation is proposed and validated by a large eddy simulation of the flow transition around a NACA0012 airfoil and a direct numerical simulation of the boundary layer transition on a flat plate.

Numerical modelling of melt-conditioned direct-chill casting

Melt conditioned direct-chill (MC-DC) casting is a novel technology which combines direct-chill (DC) casting with a high shear device directly immersed in the sump for in situ microstructural control. A numerical model of melt-conditioned direct-chill casting (MC-DC) is presented in this paper. This model is based on a finite volume continuum model using a moving reference frame (MRF) to enforce fluid rotation inside the rotor-stator region and is numerically stable within the range of processing conditions. The boundary conditions for the heat transfer include the effects of the hot-top, the aluminium mould, and the direct chill. This model is applied to the casting of two alloys: aluminium-based A6060 and magnesium-based AZ31. Results show that MC-DC casting modifies the temperature profile in the sump, resulting in a larger temperature gradient at the solidification front and a shorter local solidification time. The increased heat extraction rate due to forced convection in the sump is expected to contribute to a finer, more uniform grain structure in the as-cast billet.

Explicit expressions for Rortex tensor and velocity gradient tensor decomposition

The introduction of Rortex provides a new perspective to investigate the local properties of vortical structures in transitional and turbulent flows, as Rortex offers a new and systematic description of the local fluid rotation, including scalar, vector and tensor forms. Unfortunately, the previous definition of Rortex is not straightforward, which requires the explicit calculation of somewhat cumbersome coordinate rotation. In this letter, a new explicit tensor form of Rortex and the relevant explicit velocity gradient tensor decomposition are presented, based on an explicit formula of the Rortex vector. The explicit tensor form represents the real local rotational part of the velocity gradient tensor in the original coordinate system. The explicit calculation of coordinate rotations can be totally avoided, which indicates an important improvement of Rortex based velocity gradient tensor decomposition.

Mapping spheroid rotation modes in turbulent channel flow: effects of shear, turbulence and particle inertia

The rotational behaviour of non-spherical particles in turbulent channel flow is studied by Lagrangian tracking of spheroidal point particles in a directly simulated flow. The focus is on the complex rotation modes of the spheroidal particles, in which the back reaction on the flow field is ignored. This study is a sequel to the letter by Zhao et al. (Phys. Rev. Lett., vol. 115, 2015, 244501), in which only selected results in the near-wall buffer region and the almost-isotropic channel centre were presented. Now, particle dynamics all across the channel is explored to provide a complete picture of the orientational and rotational behaviour with consideration of the effects of particle aspect ratio ranging from 0.1 to 10 and particle Stokes number from 0 (inertialess) to 30. The rotational dynamics in the innermost part of the logarithmic wall layer is particularly complex and affected not only by modest mean shear, but also by particle inertia and turbulent vorticity. While inertial disks exhibit modest preferential orientation in either the wall-normal or cross-stream direction, inertial rods show neither preferential tumbling nor spinning. Examination of the co-variances between particle orientation, particle rotation and fluid rotation vectors explains the qualitatively different ‘wall mode’ rotation and ‘centre mode’ rotation. Inertialess spheroids transition between the two modes within a narrow zone ($15<z^{+}<35$) in the buffer region. If the spheroids have inertia, the transition zone between the two modes shifts to the inner part of the logarithmic layer, i.e. $z^{+}\geqslant 40$. We ascribe the transition of inertialess spheroids from the ‘wall mode’ to the ‘centre mode’ rotation to the changeover between the time scales associated with mean shear and small-scale turbulence. Inertial spheroids, however, transition between the two rotational modes when the Kolmogorov time scale becomes comparable to the time scale for particle rotation, i.e. the effective Stokes number is of order unity. The aforementioned findings reveal, in addition to the effects of particle shape and alignment, the importance of the characteristic local time scale of fluid flow for the rotation of both tracer and inertial spheroids in turbulent channel flows.

Diagnostic tools of particle rotation anisotropy

Anisotropies of rotation of inertia-free spheroidal particles have been studied by means of invariants of a rotation correlation tensor. Anisotropy invariant maps (AIMs), supplemented by flatness and axisymmetry parameters F and A, represent a new approach to characterize rotations of non-spherical particles. To demonstrate the attractive features of these diagnostic tools we examined the rotation of spheroidal point-particles suspended in an asymmetric turbulent channel flow with typical mean shear at one side and shear-free conditions at the other side. The AIMs showed that spheroidal particles rotate differently from the local fluid rotation even in the absence of inertia and also that prolate and oblate spheroids rotate differently. The particles generally achieve different modes of rotation near the sheared and shear-free walls. The most aspherical particles, however, exhibited the same pancake-shaped mode (A=−1) of axisymmetric rotation at both sides. Next to the shear-free wall, particles with similar magnitude of asphericity, be it disks or rods, attained the same mode of rotation. The present results suggest that AIMs, supplemented by the axisymmetry measure A, can serve as a versatile tool to characterize the complex rotation modes of non-spherical particles embedded in a turbulent flow. Although the present study was concerned only with inertia-free spheroids, exactly the same approach can be used for inertial spheroids or tri-axial ellipsoidal particles.

The decay of isotropic turbulence carrying non-spherical finite-size particles

Direct particle–fluid simulations of heavy spheres and ellipsoids interacting with decaying isotropic turbulence are conducted. This is the rigorous extension of the spherical particle analysis in Schneiders et al. (J. Fluid Mech., vol. 819, 2017, pp. 188–227) to $O(10^{4})$ non-spherical particles. To the best of the authors’ knowledge, this represents the first particle-resolved study on turbulence modulation by non-spherical particles of near-Kolmogorov-scale size. The modulation of the turbulent flow is precisely captured by explicitly resolving the stresses acting on the fluid–particle interfaces. The decay rates of the fluid and particle kinetic energy are found to increase with the particle aspect ratio. This is due to the particle-induced dissipation rate and the direct transfer of kinetic energy, both of which can be substantially larger than for spherical particles depending on the particle orientation. The extra dissipation rate resulting from the translational and rotational particle motion is quantified to detail the impact of the particles on the fluid kinetic energy budget and the influence of the particle shape. It is demonstrated that the previously derived analytical model for the particle-induced dissipation rate of smaller particles is valid for the present cases albeit these involve significant finite-size effects. This generic expression allows us to assess the impact of individual inertial particles on the local energy balance independent of the particle shape and to quantify the share of the rotational particle motion in the kinetic energy budget. To enable the examination of this mechanistic model in particle-resolved simulations, a method is proposed to reconstruct the so-called undisturbed fluid velocity and fluid rotation rate close to a particle. The accuracy and robustness of the scheme are corroborated via a parameter study. The subsequent discussion emphasizes the necessity to account for the orientation-dependent drag and torque in Lagrangian point-particle models, including corrections for finite particle Reynolds numbers, to reproduce the local and global energy balance of the multiphase system.

Method and system for the centrifugal fabrication of low cost, polymeric, parabolic lenses.

A method for low-cost, rapid production of aspheric polymeric lenses using fluid rotation is presented. The system utilizes a cylindrical chamber to hold and cure a polymer while spinning. This system is capable of producing lenses with parabolic planar-concave, planar-convex, and meniscus geometries with tunable radii of curvature and focal lengths. Examples are demonstrated for lenses of 25 mm diameter. System models, performance, and components are described in detail, and lens variability is assessed for surface profile, surface roughness, radius of curvature, and single-lens resolution limit. Results show excellent RMS surface roughness for a low-cost lens production technique.

Topology-based characterization of compressibility effects in mixing layers

Direct numerical simulations of high-speed mixing layers are used to characterize the effects of compressibility on the basis of local streamline topology and vortical structure. Temporal simulations of the mixing layers are performed using a finite volume gas-kinetic scheme for convective Mach numbers ranging from $M_{c}=0.2$ to $M_{c}=1.2$. The focus of the study is on the transient development and the main objectives are to (i) investigate and characterize the turbulence suppression mechanism conditioned upon local streamline topology; and (ii) examine changes in the vortex vector field – distribution, magnitude and orientation – as a function of Mach number. We first reaffirm that kinetic energy suppression with increasing Mach number is due to a decrease in pressure–strain redistribution. Then, we examine the suppression mechanism conditioned upon topology and vortex structure. Conditional statistics indicate that (i) at a given Mach number, shear-dominated topologies generally exhibit more effective pressure–strain redistribution than vortical topologies; and (ii) for a given topology, the level of pressure–strain correlation mostly decreases with increasing Mach number. At each topology, with increasing Mach number, there is a corresponding decrease in turbulent shear stress and production leading to reduced kinetic energy. Further, as $M_{c}$ increases, the proportion of vortex-dominated regions in the flow increases, leading to further reduction in the turbulent kinetic energy of the flow. Then, the orientation of vortical structures and direction of fluid rotation are examined using the vortex vector approach of Tian et al. (J. Fluid Mech., vol. 849, 2018, pp. 312–339). At higher $M_{c}$, the vortex vectors tend to be more aligned in the streamwise direction in contrast to low $M_{c}$ wherein larger angles with streamwise direction are preferred. The connection between vortex orientation and kinetic energy production is also investigated. The findings lead to improved insight into turbulence suppression dynamics in high Mach number turbulent flows.

On the plane-parallel motion of self-gravitating and rotating incompressible fluid with a free boundary

Abstract In this paper, we study a plane-parallel flow of the homogeneous inviscid incompressible fluid. The close attention is paid to the free boundary deformation under the forces of self-gravitation and fluid rotation. The problem is studied numerically, i.e., we propose the numerical algorithm for the free boundary calculation. The algorithm is based on the boundary element method. Algorithm applications include calculation of thin cumulative jets. The second point of interest is numerical results validation. The computational accuracy is controlled through the conservation laws. In this paper, we provide the derivation of conservation laws of energy and angular momentum for the case of rotating flows. In addition, we analytically investigate dynamics of two-dimensional near-equilibrium shapes and check the consistency of the analytical and numerical results.

Two-phase modeling of nanofluid forced convection in different arrangements of elliptical tube banks

PurposeThe purpose of this study is two phase modeling of Water/Cu nanofluid forced convection in different arrangements of elliptical tube banks in a two-dimensional space.Design/methodology/approachThe arrangements of tube banks have been regarded as equal spacing triangle (ES), equilateral triangle (ET) and the rotated square (RS). The obtained results indicate that, among the investigated arrangements, the RS arrangement has the maximum value of heat transfer with cooling fluid. Also, the changes of Nusselt number and the local friction factor are under the influence of three main factors including volume fraction of slid nanoparticles, the changes of fluid velocity parameters on the curved surface of tube and flow separation after crossing from a specified angle of fluid rotation.FindingsIn Reynolds number of 250 and in all arrangements of the tube banks, the behavior of Nusselt number is almost the same and the separation of flow happens in almost 155-165 degrees from fluid rotation on surface. In RS arrangement, due to the strength of vortexes after fluid separation, better mixture is created and because of this reason, after the separation zone, the level of local Nusselt number graph enhances significantly.Originality/valueIn this research, the laminar and two-phase flow of Water/Cu nanofluid in tube banks with elliptical cross section has been numerically investigated in a two-dimensional space with different longitudinal arrangements. In this study, the effects of using nanofluid, different arrangements of tube banks and the elliptical cross section on heat transfer and cooling fluid flow among the tube banks of heat exchanger have been numerically simulated by using finite volume method.

Rotational stabilisation of the Rayleigh–Taylor instability at the inner surface of an imploding liquid shell

A number of applications utilise the energy focussing potential of imploding shells to dynamically compress matter or magnetic fields, including magnetised target fusion schemes in which a plasma is compressed by the collapse of a liquid metal surface. This paper examines the effect of fluid rotation on the Rayleigh–Taylor (RT) driven growth of perturbations at the inner surface of an imploding cylindrical liquid shell which compresses a gas-filled cavity. The shell was formed by rotating water such that it was in solid body rotation prior to the piston-driven implosion, which was propelled by a modest external gas pressure. The fast rise in pressure in the gas-filled cavity at the point of maximum convergence results in an RT unstable configuration where the cavity surface accelerates in the direction of the density gradient at the gas–liquid interface. The experimental arrangement allowed for visualisation of the cavity surface during the implosion using high-speed videography, while offering the possibility to provide geometrically similar implosions over a wide range of initial angular velocities such that the effect of rotation on the interface stability could be quantified. A model developed for the growth of perturbations on the inner surface of a rotating shell indicated that the RT instability may be suppressed by rotating the liquid shell at a sufficient angular velocity so that the net surface acceleration remains opposite to the interface density gradient throughout the implosion. Rotational stabilisation of high-mode-number perturbation growth was examined by collapsing nominally smooth cavities and demonstrating the suppression of small spray-like perturbations that otherwise appear on RT unstable cavity surfaces. Experiments observing the evolution of low-mode-number perturbations, prescribed using a mode-6 obstacle plate, showed that the RT-driven growth was suppressed by rotation, while geometric growth remained present along with significant nonlinear distortion of the perturbations near final convergence.

Study on the breakup of liquid jet in a coaxial swirling compressible gas flow

The breakup length and position of liquid jet are the important parameters to determine the atomization quality. The nonlinear dispersion equation is used to study the breakup length and position of liquid jet with cavitation bubbles in a coaxial swirling compressible gas flow. First, the comparison of the jet breakup characteristics under linear and nonlinear stability theories is made, and then the effects of swirling gas, fluid compressibility and cavitation bubbles on jet breakup length are analyzed. The results show that the second-order perturbation may accelerate the breakup of liquid jet and may also inhibit the jet breakup when nonlinear stability theory is taken. In addition, the breakup position of liquid jet may appear after the main droplet and also appear after the satellite droplet. With the increase in gas rotational strengths, fluid compressibility and bubble volume fractions, the breakup length decreases, which indicates that swirling gas, fluid compressibility and cavitation bubbles can accelerate the jet breakup to a certain extent. In general, the effect of fluid compressibility on jet breakup length is the most obvious.

Left ventricular vortex formation in preterm infants assessed by blood speckle imaging.

A vortex is a rotational fluid structure formed by shearing of fluid layers. It forms during diastole in the left ventricle (LV) and helps redirect flow to the LV outflow tract for ejection, optimizing energy conservation. The aim of this study was to demonstrate the feasibility of detecting and analyzing LV vortices using a new ultrasound technique known as blood speckle imaging (BSI). Conventional and BSI parameters were acquired in preterm infants referred for echocardiography. BSI feasibility and reliability were explored using highest frequency settings and optimized Nyquist limits. Vortex area was determined by tracing the outer vortex ring at maximum area. Peak vortex formation time (PVFT) was determined at time of maximum vortex area relative to the R-wave, and vortex duration from frame-by-frame analysis of first appearance to vortex degradation. Left ventricle vortices were detected in 49 of the 50 preterm infants (weight 500-2020g) with excellent intra- and inter-observer reliability. Mean vortex area indexed to LV area was 0.19 (0.08). Peak vortex formation time was at 87 (7)% of the cardiac cycle, and vortex duration lasted 13 (4)% of the cardiac cycle. Vortex area correlated positively with LV length, end-diastolic dimension, end-diastolic volume, mitral annular (R +0.42, +0.50, +0.47, +0.50, all P<0.01), and transmitral Vti (R +0.37, P<0.01). PVFT correlated negatively with E, EA, and Ee' (R -0.42, -0.47, -0.47, all P<0.01). Left ventricle vortex formation can be analyzed with two-dimensional BSI and has the potential to complement existing parameters of cardiac health.

An objective version of the Rortex vector for vortex identification

Vortices are a ubiquitous natural phenomenon, and their structure, shape, and characteristics should be independent of the observer, which implies that the vortex identification method or vortex definition should maintain its objectivity. Currently, most of the vortex identification methods rely on velocity gradient tensors. The calculation of the velocity gradient tensor is based on the reference frame of the observer, and the velocity gradient tensor will vary with the observer’s motion. By these vortex identification methods, very different vortex structures could be visualized and described in a moving reference frame. Recently, a mathematical definition of the Rortex vortex vector was proposed to represent the local fluid rotation. The definition used velocity gradient tensor to derive the local rigid rotation axis and strength. However, the original definition of the Rortex vector is nonobjective. In order to obtain the objectivity, in this paper, by a definition of a net velocity gradient tensor, an objective Rortex vortex vector is defined which uses a spatially averaged vorticity to offset the impact of the motion frame. Some typical numerical examples, such as an implicit large-eddy simulation result for shock and boundary layer interaction and a direct numerical simulation for boundary layer transition, are provided to show the objectivity of the developed method.

Kinematics of local entrainment and detrainment in a turbulent jet

In this paper we investigate the continuous, local exchange of fluid elements as they are entrained and detrained across the turbulent/non-turbulent interface (TNTI) in a high Reynolds number axisymmetric jet. To elucidate characteristic kinematic features of local entrainment and detrainment processes, simultaneous high-speed particle image velocimetry and planar laser-induced fluorescence measurements were undertaken. Using an interface-tracking technique, we evaluate and analyse the conditional dependence of local entrainment velocity in a frame of reference moving with the TNTI in terms of the interface geometry and the local flow field. We find that the local entrainment velocity is intermittent with a characteristic length scale of the order of the Taylor micro-scale and that the contribution to the net entrainment rate arises from the imbalance between local entrainment and detrainment rates that occurs with a ratio of two parts of entrainment to one part detrainment. On average, an increase in local entrainment is correlated with excursions of the TNTI towards jet centreline into regions of higher streamwise momentum, convex surface curvature facing the turbulent side of the jet and along the leading edges of the interface. In contrast, detrainment is correlated with excursions of the TNTI away from the jet centreline into regions of lower streamwise momentum, concave surface curvature and along the trailing edge. We find that strong entrainment is characterised by a local counterflow velocity field in the frame of reference moving with the TNTI which enhances the transport of rotational and irrotational fluid elements. On the other hand, detrainment is characterised by locally uniform flow fields with the local fluid velocity on either side of the TNTI advecting in the same direction. These local flow patterns and the strength of entrainment or detrainment rates are also observed to be strongly influenced by the presence and relative strength of vortical structures which are of the order of the Taylor micro-scale that populate the turbulent region along the jet boundary.