Fluid Rotation Research Articles

Spontaneous rotation in the exact solution of magnetohydrodynamic equations for flow between two stationary impermeable disks

Magnetohydrodynamic (MHD) flow of a viscous electrically conducting incompressible fluid between two stationary impermeable disks is considered. A homogeneous electric current density vector normal to the surface is specified on the upper disk, and the lower disk is nonconducting. The exact von Karman solution of the complete system of MHD equations is studied in which the axial velocity and the magnetic field depend only on the axial coordinate. The problem contains two dimensionless parameters: the electric current density on the upper plate Y and the Batchelor number (magnetic Prandtl number). It is assumed that there is no external source that produces an axial magnetic field. The problem is solved for a Batchelor number of 0–2. Fluid flow is caused by the electric current. It is shown that for small values of Y, the fluid velocity vector has only axial and radial components. The velocity of motion increases with increasing Y, and at a critical value of Y, there is a bifurcation of the new steady flow regime with fluid rotation, while the flow without rotation becomes unstable. A feature of the obtained new exact solution is the absence of an axial magnetic field necessary for the occurrence of an azimuthal component of the ponderomotive force, as is the case in the MHD dynamo. A new mechanism for the bifurcation of rotation in MHD flow is found.

Asymptotically based self-similarity solution of the Navier–Stokes equations for a porous tube with a non-circular cross-section

This work introduces a similarity solution to the problem of a viscous, incompressible and rotational fluid in a right-cylindrical chamber with uniformly porous walls and a non-circular cross-section. The attendant idealization may be used to model the non-reactive internal flow field of a solid rocket motor with a star-shaped grain configuration. By mapping the radial domain to a circular pipe flow, the Navier–Stokes equations are converted to a fourth-order differential equation that is reminiscent of Berman’s classic expression. Then assuming a small radial deviation from a fixed chamber radius, asymptotic expansions of the three-component velocity and pressure fields are systematically pursued to the second order in the radial deviation amplitude. This enables us to derive a set of ordinary differential relations that can be readily solved for the mean flow variables. In the process of characterizing the ensuing flow motion, the axial, radial and tangential velocities are compared and shown to agree favourably with the simulation results of a finite-volume Navier–Stokes solver at different cross-flow Reynolds numbers, deviation amplitudes and circular wavenumbers.

Viscorotational shear instability of Keplerian granular flows.

The linear stability of viscous Keplerian flow around a gravitating center is studied using the rheological granular fluid model. The linear rheological instability triggered by the interplay of the shear rheology and Keplerian differential rotation of incompressible dense granular fluids is found. Instability sets in in granular fluids, where the viscosity parameter grows faster than the square of the local shear rate (strain rate) at constant pressure. Found instability can play a crucial role in the dynamics of dense planetary rings and granular flows in protoplanetary disks.

On the swirling Trkalian mean flow field in solid rocket motors

In this work, an exact Euler solution is derived under the fundamental contingencies of axisymmetric, steady, rotational, incompressible, single-phase, non-reactive and inviscid fluid, which also stand behind the ubiquitously used mean flow profile named ‘Taylor–Culick.’ In comparison with the latter, which proves to be complex lamellar, the present model is derived in the context of a Trkalian flow field, and hence is capable of generating a non-zero swirl component that increases linearly in the streamwise direction. This enables us to provide an essential mathematical representation that is appropriate for flow configurations where the bulk gaseous motion is driven to swirl. From a procedural standpoint, the new Trkalian solution is deduced directly from the Bragg–Hawthorne equation, which has been repeatedly shown to possess sufficient latitude to reproduce several existing profiles such as Taylor–Culick’s as special cases. Throughout this study, the fundamental properties of the present model are considered and discussed in the light of existing flow approximations. Consistent with the original Taylor–Culick mean flow motion, the Trkalian velocity is seen to exhibit both axial and tangential components that increase linearly with the distance from the headwall, and a radial component that remains axially invariant. Furthermore, the Trkalian model is shown to form a subset of the Beltramian class of solutions for which the velocity and vorticity vectors are not only parallel but also directly proportional. This characteristic feature is interesting, as it stands in sharp contrast to the complex-lamellar nature of the Taylor–Culick motion, where the velocity and vorticity vectors remain orthogonal. By way of verification, a numerical simulation is carried out using a finite-volume solver, thus leading to a favourable agreement between theoretical and numerical predictions.

Chemical reaction effects on MHD rotating fluid over a vertical plate embedded in porous medium with heat source

Several boundary layer flowswith heat and mass transfer problems do arise from a pebble bed nuclear reactor system. In this study, we examine the combined effects of variable thermal conductivity, thermal diffusion, diffusion thermo, heat source, chemical reaction and fluid rotation on hydromagnetic mixed convective flow with heat and mass transfer over a vertical plate embedded in porous medium. The governing partial differential equations have been transformed into a system of ordinary differential equations by employing the similarity transformation and solved numerically using the Runge–Kutta–Fehlberg method with a shooting technique. Pertinent results obtained are presented graphically and in tabular form with respect to variation in various thermophysical parameters. A comparison of the special case of this study with the previously published work shows excellent agreement.

Intracycle angular velocity control of cross-flow turbines

Cross-flow turbines, also known as vertical-axis turbines, are attractive for power generation from wind and water currents. Some cross-flow turbine designs optimize unsteady fluid forces and maximize power output by controlling blade kinematics within one rotation. One established method is to dynamically pitch the blades. Here we introduce a mechanically simpler alternative: optimize the turbine rotation rate as a function of angular blade position. We demonstrate experimentally that this approach results in a 59% increase in power output over standard control methods. Analysis of fluid forcing and blade kinematics suggest that power increase is achieved through modification of the local flow conditions and alignment of fluid force and rotation rate extrema. The result is a low-speed, structurally robust turbine that achieves high efficiency and could enable a new generation of environmentally benign turbines for renewable power generation. Unlike ubiquitous axial-flow turbines, cross-flow turbines have rotation axes perpendicular to the flow they sit in. This study presents a control scheme that optimizes blade angular velocity as a function of blade position with no extra degrees of freedom, yielding a 59% increase in power output.

Severe Remote Cerebellar Hemorrhage with Intracerebral Hemorrhage after Burr-Hole Evacuation for Chronic Subdural Hematoma

Since remote cerebellar hemorrhage, with intracerebral hemorrhage after supratentorial neurosurgery, is rare, its pathophysiology remains elusive. Here, we report a 64-year-old man who had severe bilateral symmetric remote cerebellar hemorrhage with frontal lobe hemorrhage following burr-hole evacuation for supratentorial chronic subdural hematoma. Computed tomography venography showed undeveloped left internal jugular vein and sigmoid sinus. He received 3 weeks of conservative treatment and fully recovered. Overdrainage of cerebrospinal fluid and head rotation with undeveloped internal jugular vein may have resulted in this complication. This case is the first case in the literature with this event sequence and has some significance for revealing the mechanism of remote cerebellar hemorrhage occurrence after other supratentorial surgeries.

Um modelo de usina hidrelétrica como ferramenta no ensino de Física

http://dx.doi.org/10.5007/2175-7941.2017v34n1p248No atual contexto da sustentabilidade e do uso consciente de energia elétrica, preocupações com quedas no suprimento de energia e manifestações ambientais contra a construção de usinas cujo impacto ambiental é iminente, discussões sobre a produção de energia limpa e sustentável se tornam comuns nas escolas de ensino básico do país. Além disso, o conhecimento sobre a matriz energética no Brasil tem se intensificado sobretudo nas escolas de Ensino Básico, sem, contudo, propor uma discussão dos conceitos físicos importantes para a conservação de energia ocorrida nestes tipos de usinas. Muitos materiais impressos, como livros didáticos e apostilas, trazem discussões mais consistentes sobre os conceitos de eletromagnetismo, esquecendo-se de outros como de hidrodinâmica e energia mecânica. Este trabalho tem como objetivo apresentar uma proposta de construção de um modelo interativo de usina hidroelétrica com materiais recicláveis e de baixo custo, que pode ser utilizado para trabalhar vários conceitos de mecânica rotacional, mecânica dos fluidos e eletromagnetismo em uma classe de Ensino Fundamental e Médio, de forma qualitativa, evidenciando os conceitos físicos envolvidos, seus fundamentos e interpretações.

Overdense plasma generation in a compact ion source

Electron cyclotron resonance ion sources (ECRIS) are widely used plasma based machines for the production of intense ion beams in science and industry. The performance of modern devices is limited by the presence of the density cut-off, above which electromagnetic (EM) waves sustaining the plasma are reflected. We hereby discuss the systematic data analysis of electrostatic wave generation in an ECR prototype operating at 3.75 GHz–0.1 THz. In particular, electron Bernstein waves (EBW) have been excited. EBW have already been generated in large-scale plasma devices for thermonuclear fusion purposes. In ion sources where Lc ∼ λRF (Lc being the plasma chamber size and λRF the pumping wave wavelength) the EM field assumes a modal behaviour; thus both plasma and EM field self-organize so that no optical-like wave launching is possible (i.e. the cavity effect dominates on the optical path). The collected data, however, supported by 3D full-wave simulations, actually demonstrate that a Budden-type X-B conversion scenario can be established above some critical RF power thresholds, operating in an off-ECR regime. The generation and absorption of the EBW has been demonstrated by the presence of three peculiar signatures: along with the establishment of an overdense plasma, generation of supra-thermal electrons and modification (non-linear broadening) of the EM spectrum measured within the plasma have been observed. At the threshold establishing such a heating regime, the collected data provide evidence for a fast rotation of the electron fluid.

Abrasion erosion modeling in particulate flow

Solid particle erosion is of great importance to many industries including oil and gas production, drilling, process and transportation of minerals including oil sands. The particles that may cause erosion are of various sizes, shapes and hardnesses. These particles may impact the surface at various speeds and angles, and the influence of these parameters is characterized to some extent in the literature. Experimental and numerical studies have shown that when particles are transported by liquid (e.g. slurry transport in the pipe) or dense gas, the particle impact angles are very low. The impact angles in these cases are sometimes less than the smallest value that can be obtained in a direct impingement erosion test in gas. In this work, the mechanistic erosion equation developed previously is extended to near zero impact angles for sharp particles. The abrasion erosion equation is developed by introducing an initial penetration of the sharp particle in the equation of the motion. This initial penetration may be attributed to the sharp particle rotation and/or turbulent flow fluctuations of the carrier fluid near the wall. The empirical constants are obtained from submerged erosion experiments in liquid. The equation has been implemented in a commercially available Computational Fluid Dynamics (CFD) code (ANSYS FLUENT) to calculate erosion for a submerged impingement jet geometry, and the result is compared with the experiment. It is shown that by neglecting the abrasive term in the erosion equation, the specimen mass loss does not match the experimental measured mass loss. While by including the abrasive term, the total mass loss of the specimen agrees well with the experimental data. Moreover, the erosion pattern becomes closer to the experimentally measured pattern especially farther from the center of the highly eroded area where abrasive wear is expected to dominate.

Numerical simulation of water waves generated by seabed movement

This paper investigates the processes involving the generation and evolution of water waves induced by seafloor movements, focusing on the conditions for the occurrence of nonlinear wave and the effects of the nonlinear terms in the basic equations of fluid dynamics. The Reynolds-averaged Navier-Stokes (RANS) equations were incorporated into a k−ε turbulence model and applied to simulate the generation of water waves by treating the seafloor as a moving boundary. The simulation results were analyzed and compared with theoretical and experimental results from the literature. The analysis shows that nonlinear effects are not apparent for either of the following two conditions: a) if both the non-dimensional time scale for the bottom movements and the amplitude of seafloor uplift to water depth ratio are well below unity; b) if the non-dimensional time scale for the bottom movement is well above unity. However, the nonlinearity cannot be neglected when neither of these conditions is satisfied, largely due to the effects of fluid rotation, and to a certain degree, because Reynolds shear stresses are no longer insignificant. The occurrence of the maximum wave rise is determined by the frequency of the bottom movement and its amplitude relative to the water depth. The linear potential flow model may underestimate the maximum wave surface elevation for cases with high frequency or high amplitude seabed movements.

Rotating‐Electric‐Field‐Induced Carbon‐Nanotube‐Based Nanomotor in Water: A Molecular Dynamics Study

Using molecular dynamics simulations, it is shown that a carbon nanotube (CNT) suspended in water and subjected to a rotating electric field of proper magnitude and angular speed can be rotated with the aid of water dipole orientations. Based on this principle, a rotational nanomotor structure is designed and the system is simulated in water. Use of the fast responsiveness of electric-field-induced CNT orientation in water is employed and its operation at ultrahigh-speed (over 1011 r.p.m.) is shown. To explain the basic mechanism, the behavior of the rotational actuation, originated from the water dipole orientation, is also analyzed . The proposed nanomotor is capable of rotating an attached load (such as CNT) at a precise angle as well as nanogear-based complex structures. The findings suggest a potential way of using the electric-field-induced CNT rotation in polarizable fluids as a novel tool to operate nanodevices and systems.

Exact Steady Azimuthal Internal Waves in the f-Plane

We present an explicit exact solution of the nonlinear governing equations with Coriolis and centripetal terms in the f-plane approximation for internal geophysical trapped waves with a uniform current near the equator. This solution describes in the Lagrangian framework azimuthal equatorial internal waves propagating westward in a stratified rotational fluid.

Severe remote cerebellar hemorrhage with intracerebral hemorrhage after burr-hole evacuation for chronic subdural hematoma

Since remote cerebellar hemorrhage, with intracerebral hemorrhage after supratentorial neurosurgery, is rare, its pathophysiology remains elusive.Here, we report a 64-year-old man who had severe bilateral symmetric remote cerebellar hemorrhage with frontal lobe hemorrhage following burr-hole evacuation for supratentorial chronic subdural hematoma.Computed tomography venography showed undeveloped left internal jugular vein and sigmoid sinus.He received 3 weeks of conservative treatment and fully recovered.Overdrainage of cerebrospinal fluid and head rotation with undeveloped internal jugular vein may have resulted in this complication.This case is the first case in the literature with this event sequence and has some significance for revealing the mechanism of remote cerebellar hemorrhage occurrence after other supratentorial surgeries.

Thermal Conduction in Higher-Dimensional Sphere and Application to Fluid Rotation

Thermal Conduction in Higher-Dimensional Sphere and Application to Fluid Rotation

Numerical analysis of the wake of a 10kW HAWT

With the rising of wind power industry and the ever-growing scale of wind farm, the research for the wake performance of wind turbine has an important guiding significance for the overall arrangement of wind turbines in the large wind farm. The wake simulation model of 10kW horizontal-axis wind turbine is presented on the basis of Averaged Navier-Stokes (RANS) equations and the RNG k-ε turbulence model for applying to the rotational fluid flow. The sliding mesh technique in ANSYS CFX software is used to solve the coupling equation of velocity and pressure. The characters of the average velocity in the wake zone under rated inlet wind speed and different rotor rotational speeds have been investigated. Based on the analysis results, it is proposed that the horizontal spacing between the wind turbines is less than two times radius of rotor, and its longitudinal spacing is less than five times of radius. And other results have also been obtained, which are of great importance for large wind farms.

Instability of cylinder wake under open-loop active control

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimens- ional control input created by an electromagnetic actuator located on the cylinder surface, adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number repre- senting the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926D and 0.822D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation. All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force.

Heat Transfer on MHD Peristaltic Rotating Flow of a Jeffrey Fluid in an Asymmetric Channel

This paper addresses heat transfer and rotation effects on MHD peristaltic flow of a Jeffrey fluid in an asymmetric channel with partial slip. Mathematical modeling is carried out by utilizing long wavelength and small Reynolds number assumptions. The analytical solution has been computed for the stream function, velocity and temperature distribution. The expression for pressure rise is carried out using numerical integration. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. The axial velocity depresses with increasing of Hartmann number, Jeffrey fluid parameter and slip parameter. The size of trapping bolus enhances when an increase in Hartmann number, Jeffrey fluid parameter and rotation parameter. The temperature diminishes as the larger values of slip parameter. A comparison of a special case of our results with the one previously reported in the literature shows a very good agreement.

Nonlinear interaction and wave breaking with a submerged porous structure

Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ε turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold “clockwise” and “anticlockwise” rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.

Orientation and rotation dynamics of triaxial ellipsoidal tracers in wall turbulence

The rotational dynamics of triaxial ellipsoidal particles in turbulent channel flow have been explored. The non-inertial particles were tracked in a Lagrangian approach in an Eulerian flow field that resulted from a direct numerical simulation. Although the tracer particles translated along with the local fluid, they did not adhere to the local fluid rotation. The triaxial ellipsoids were characterized by two independent shape parameters that both were varied from 0.1 to 10. In spite of the anisotropic velocity field in the channel center, the tumbling of the particles closely resembled earlier results in homogeneous isotropic turbulence. The orientation of the particles varied substantially from the center to the near-wall region where triaxial particles tended to align their major axis in the mean flow direction and their minor axis in the wall-normal direction. These preferential alignments caused the ellipsoid to tumble as a rod about the major axis and like a disk about the minor axis. These observations show the dual nature of triaxial ellipsoids embedded in real turbulence.