Steady Rotation Research Articles

Global attraction of steady motions of a gimbal-mounted asynchronous gyroscope

The subject of consideration is a gyroscope mounted in the gimbal (Cardan) suspension and placed on the immovable foundation in the field of gravity. Dissipative and control torques on the axes of gimbals are supposed to be absent, but the fast rotating rotor is under the action of the frictional torque, and so the device is supplied with the asynchronous electric motor that forms a driving torque acting about the axis of rotation of the rotor in the inner gimbal. The inner gimbal serves as the stator of the motor. This device has a family of steady motions, which are steady precessions of the rotor about the outer gimbal axis and steady rotations of the rotor about its axis of rotation in the inner gimbal. In the paper, the global attraction property is proved for the set of steady motions. This means that every motion of the device tends to one of its steady motions as time tends to infinity. Outcomes of numerical simulation are presented to give a demonstration of this property.

On rotational dynamics of inertial disks in creeping shear flow

Abstract The rotational motion of an inertial disk-like particle in a creeping linear shear flow is investigated. A disk-like particle in a linear shear flow tends to rotate in the velocity-gradient plane as do rod-like particles. Unlike prolate spheroids, however, oblate spheroids always attain the same steady rotation in the shear plane irrespective of their initial orientation. The drift of the orientation of the rotation axis towards the vorticity vector consists of two qualitatively different stages. First, the wobbling drift towards rotation in the velocity-gradient plane becomes slower with increasing particle inertia, except for the least inertial spheroids. The duration of the second stage, during which the spheroid spins up to match the angular fluid velocity, becomes independent of the aspect ratio for relatively flat particles, provided that a new shape-dependent Stokes number is used.

Dynamics of single, non-spherical ellipsoidal particles in a turbulent channel flow

Using disk, spherical and needle-like particles with equal equivalent volume diameters, the orientational dynamics of non-spherical particles is studied in a turbulent channel flow. An Eulerian–Lagrangian approach based on large eddy simulation with a dynamic sub-grid scale model is used to predict a fully developed gas–solid flow at a shear Reynolds number Reτ=300. Particle shape and orientation are accounted for by the coupling between Newton׳s law of translational motion and Euler׳s law of rotational motion, both in a Lagrangian framework. The particle shapes are simulated using the super-quadrics form, with the dynamically relevant parameters being the particle aspect ratio, equivalent volume diameter and response time. The translational and orientational behaviour of single particles initially released at three different locations in the wall-normal direction are monitored, with analysis showing a clear distinction between the behaviour of the different particle shapes. The results show that turbulent dispersion forces non-spherical particles to have a broad orientation distribution. The orientational states observed include periodic, steady rotation, tumbling, precessing and nutating. Velocity gradient, aspect ratio and particle inertia all have an effect on the alignment of the particle principal axis to the inertial axes. Unlike spherical particles, the disk and needle-like particles display a transition from one orientational state to another, especially when their initial position is in the near-wall region, with the frequency of this transition highest for the disk-like particle. Overall, this study leads to an improved understanding of the significance of shape on particle behaviour which is of relevance to many practical flows.

Numerical Study of Single-Mode Interface Shape on Rotary Motion Instability

Using the method of numerical simulations to study fluid dynamic characteristic of underwater vehicle rotary motion, using the N-S equation turbulence model description of the steady rotation of the vehicle, this paper studies the numerical calculation method of aircraft rotating derivative underwater, using UDF programming to produce a stable pressure rotation the flow field, set up an numerical turning basin. Then based on the simulation analysis the influence of the different radius of gyration and different angle of attack on the vehicle motion.

Role of viscous friction in the reverse rotation of a disk.

The mechanical response of a circularly driven disk in a dissipative medium is considered. We focus on the role played by viscous friction in the spinning motion of the disk, especially on the effect called reverse rotation, where the intrinsic and orbital rotations are antiparallel. Contrary to what happens in the frictionless case, where steady reverse rotations are possible, we find that this dynamical behavior may exist only as a transient when dissipation is considered. Whether or not reverse rotations in fact occur depends on the initial conditions and on two parameters, one related to dragging, inertia, and driving, the other associated with the geometric configuration of the system. The critical value of this geometric parameter (separating the regions where reverse rotation is possible from those where it is forbidden) as a function of viscosity is well adjusted by a q-exponential function.

Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion

We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object's scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified, and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating back-reaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object's angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced in the first part to simplify the technicalities and ease the conceptual complexities; a detailed discussion of quantum electrodynamics is presented in the second part.

Intensified heat transfer in modulated rotating Rayleigh–Bénard convection

Heat transfer in a Rayleigh-Bénard configuration consisting of a vertical cylinder, which is rotating about its axis, can be intensified considerably when the rotation rate is modulated harmonically in time. Such time-dependent rotation introduces an Euler force into the governing equations which leads to a particular modification of the flow that is shown to support a Nusselt number (Nu) that is considerably higher than in case of constant rotation. We use direct numerical simulation of the incompressible Navier–Stokes equations to perform a comprehensive parameter study of the flow-structuring and associated heat transfer investigating primarily the effect of variations in the frequency with which the rotation rate varies. We consider flow in an upright cylinder of unit aspect ratio which is heated from below and cooled at the top. At sufficiently strong Euler forces the temporal variation of Nu shows a striking dynamics with periods of gradual increase in Nu with more rapid oscillations superimposed, next to rather catastrophic events in which the entire flow-structure that supported high levels of Nu collapses entirely and it returns to a value more similar to that attained at steady rotation. During periods of oscillatory build-up of Nu, high levels of turbulence gradually become more pronounced from the outer cylinder wall inward and a gradually stronger thermal column arises along the centreline of the cylinder. This flow structure can support Nu up to 250% larger than without rotation, a value otherwise achievable only by employing phase transition.

The magnetic flywheel flow meter: Theoretical and experimental contributions

The development of contactless flow meters is an important issue for monitoring and controlling of processes in different application fields, like metallurgy, liquid metal casting, or cooling systems for nuclear reactors and transmutation machines. Shercliff described in his book “The Theory of Electromagnetic Flow Measurement, Cambridge University Press, 1962” a simple and robust device for contact-less measurements of liquid metal flow rates which is known as magnetic flywheel. The sensor consists of several permanent magnets attached on a rotatable soft iron plate. This arrangement will be placed closely to the liquid metal flow to be measured, so that the field of the permanent magnets penetrates into the fluid volume. The flywheel will be accelerated by a Lorentz force arising from the interaction between the magnetic field and the moving liquid. Steady rotation rates of the flywheel can be taken as a measure for the mean flow rate inside the fluid channel. The present paper provides a detailed theoretical description of the sensor in order to gain a better insight into the functional principle of the magnetic flywheel. Theoretical predictions are confirmed by corresponding laboratory experiments. For that purpose, a laboratory model of such a flow meter was built and tested on a GaInSn-loop under various test conditions.

Numerical simulation of flow and structure in nematic liquid crystalline materials between eccentric cylinders

In this paper the time transient isothermal flow of lyotropic nematic liquid crystals (LC) between two eccentric cylinders was studied numerically by applying the Landau-de Gennes (LdG) theory. The start-up flow induced by the steady rotation of the inner cylinder was used to model the lubrication problem inside a journal bearing. The ability of liquid crystalline materials to form ordered boundary layers with good load-carrying capacity, outstanding lubricating properties, has been widely demonstrated. The LdG theory for the microstructure of the molecules along with continuity and momentum equations were solved simultaneously using General PDE and Laminar Flow packages of the COMSOL Multiphysics. Flow properties and structure were investigated as a function of simulation time, the Reynolds number and the Energy ratio, R. Interconnection and impact of the texture and defects formation/evolution on velocity profile and pressure distribution was observed; nucleation and evolution of disclination line and defect points were detected and pursued over the simulation time. For high Reynolds numbers, the flow reached quasi-stationary condition while the microstructure evolution was at unsteady state. The influence of the Energy ratio and the Reynolds number on the formation and evolution of polydomains was studied. Indeed, it was found that coupling the evolution of liquid crystalline microstructure with the hydrodynamics has a quantitative and qualitative impact on the macro-scale attributes of the flow and on the structure. The standard procedure to classify defects has been applied, oblate and isotropic defects have been identified.

The long‐term steady motion of Saturn's hexagon and the stability of its enclosed jet stream under seasonal changes

AbstractWe investigate the long‐term motion of Saturn's north pole hexagon and the structure of its associated eastward jet, using Cassini imaging science system and ground‐based images from 2008 to 2014. We show that both are persistent features that have survived the long polar night, the jet profile remaining essentially unchanged. During those years, the hexagon vertices showed a steady rotation period of 10 h 39 min 23.01 ± 0.01 s. The analysis of Voyager 1 and 2 (1980–1981) and Hubble Space Telescope and ground‐based (1990–1991) images shows a period shorter by 3.5 s due to the presence at the time of a large anticyclone. We interpret the hexagon as a manifestation of a vertically trapped Rossby wave on the polar jet and, because of their survival and unchanged properties under the strong seasonal variations in insolation, we propose that both hexagon and jet are deep‐rooted atmospheric features that could reveal the true rotation of the planet Saturn.

Growth of multiparticle aggregates in sedimenting suspensions

AbstractThe process of multiparticle aggregation in a dilute sedimenting suspension is rigorously simulated, with precise hydrodynamical interactions. The primary particles are monodisperse non-Brownian spheres at zero Reynolds number, with short-range molecular attractions. The rigid aggregates grow, as they settle downwards, by sequential particle addition – a valid assumption for dilute suspensions during the initial stages. The growth starts from doublet–particle interaction, but the indeterminate initial doublet concentration does not affect the results for cluster geometry and settling velocity. A new particle is generated far below a cluster with uniform probability density, and many trial particle–cluster relative trajectories are computed with high accuracy until a collision is found. The new cluster is then assumed to be rigid and allowed to reach a steady sedimentation regime (which is a spiral motion around the axis of steady rotation, ASR) before another particle is added, and so on. The ASR is typically far away from the cluster centre of mass. The Stokes flow solution algorithm for particle–cluster interaction works very efficiently with high-order multipoles (to order 100) and is extended to arbitrarily small particle–cluster separations by a geometry perturbation adapted from the conductivity simulations of Zinchenko (Phil. Trans. R. Soc. Lond. A, 1998, vol. 356, pp. 2953–2998). Clusters are generated to $N=100$ spheres, with extensive averaging over many growth realizations. The fractal scaling $\sim N^{0.48}$ for the cluster settling speed is quickly attained once $N\geq 25$, and the exponent 0.48 is practically independent of the strength of molecular forces. The cluster fractal dimension is predicted to be $d_f=1.91\pm 0.02$ (in contrast to the existing views that sequential addition can only produce high-$d_f$ clusters). Several average characteristics of the cluster size are also computed. The theoretical settling speed has no adjustable parameters and agrees reasonably well with prior experiments for a moderately polydisperse system in a broad range of cluster sizes.

Electromagnetic drag on a magnetic dipole caused by a translating and rotating conducting cylinder

We report an analytical and numerical investigation of the forces and torques on a magnetic point dipole due to the presence of a moving electrically conducting cylinder. The kinematic induction problem is formulated in the quasistatic approximation that is appropriate for low magnetic Reynolds numbers. The motion of the cylinder is either a steady translation along its axis or a steady rotation about it. We find different power laws for the dependence of the force on the distance between dipole and cylinder when it is either small or large compared with the cylinder radius. The power laws for large distances are derived systematically by a long-wave expansion in the axial coordinate. For rotation, the case of a finite cylinder is studied by means of a dipole approximation.

Full-f gyrokinetic simulation over a confinement time

A long time ion temperature gradient driven turbulence simulation over a confinement time is performed using the full-f gyrokinetic Eulerian code GT5D. The convergence of steady temperature and rotation profiles is examined, and it is shown that the profile relaxation can be significantly accelerated when the simulation is initialized with linearly unstable temperature profiles. In the steady state, the temperature profile and the ion heat diffusivity are self-consistently determined by the power balance condition, while the intrinsic rotation profile is sustained by complicated momentum transport processes without momentum input. The steady turbulent momentum transport is characterized by bursty non-diffusive fluxes, and the resulting turbulent residual stress is consistent with the profile shear stress theory [Y. Camenen et al., “Consequences of profile shearing on toroidal momentum transport,” Nucl. Fusion 51, 073039 (2011)] in which the residual stress depends not only on the profile shear and the radial electric field shear but also on the radial electric field itself. Based on the toroidal angular momentum conservation, it is found that in the steady null momentum transport state, the turbulent residual stress is cancelled by the neoclassical counterpart, which is greatly enhanced in the presence of turbulent fluctuations.

Investigations on synthesis, growth and physical characterization of lithium selenoindate single crystals

Crack free LiInSe2 single crystal with bottom dimension of 8mm diameter and 10mm length and top dimension of 12mm diameter and 22mm length was grown using modified vertical Bridgman–Stockbarger method with steady ampoule rotation. The grown LiInSe2 crystal was characterized by X-ray diffraction pattern, Rutherford backscattering spectroscopy (RBS) analysis, Thermogravimetric-Differential thermal (TG-DTA) analysis, optical transmission and microhardness measurements. X-ray diffraction pattern gives the orientation of the crystal as 〈002〉. RBS analysis confirms that the composition of the grown crystal is Li0.8In1.16Se2.04. TG-DTA analysis confirms that the melting point of the grown crystal is 897.5°C. Optical behavior has been assessed by ultraviolet–visible–near infrared spectroscopy and Fourier transform infrared analysis. LiInSe2 optical band gap energy is 2.72eV and the cut off wavelength is 450nm. Mechanical behavior has been studied using Vickers Microhardness measurements.

A comprehensive and densely sampled map of shear-wave azimuthal anisotropy in the Aegean–Anatolia region

A better understanding of what drives surface motion in the rapidly deforming Aegean–Anatolia region requires the comparison of mantle circulation models with reliable and densely spaced seismic anisotropy data. We present a new set of 4279 high-quality splitting data of core-refracted shear waves measured at 216 permanent and temporary broadband seismic stations in Turkey and Greece, and their neighboring countries. When combined with previously published observations, our dataset provides unprecedented dense spatial coverage of the area. The delay time between the fast and slow shear waves is highest in the northern Aegean Sea and northwestern Anatolia (average, 1.5±0.4 s) and lowest in the southern Aegean Sea (average, 0.6±0.4 s). The fast-wave polarization axes are oriented NE–SW over most of Anatolia and the northern Aegean Sea. These show steady counterclockwise rotation of 1° per degree of longitude from eastern Anatolia to the northern Aegean. The only exceptions to this uniform pattern are NNW–SSE to NW–SE orientations in mainland Greece, and NW–SE orientations in the southwestern corner of Anatolia. The overall anisotropy pattern can be explained by instantaneous density–driven mantle flow with additional local effects, such as slab rollback in the Aegean Sea and a slab window beneath southwestern Anatolia.

Asymptotic properties of the motions of a heavy gyroscope with internal dissipation

The limiting motions of a heavy gyroscope, simulated by a system of rigid bodies, are considered when there is internal friction. The whole set of limiting motions is determined and the nature of their stability is studied in detail for cases when the carried body of the gyroscope has a) three degrees and b) one degree of freedom with respect to the supporting body. The results of an analysis of case a are extended to the motion of a gyroscope with a fluid filling. For case b, the values of the parameters are determined for which the gyroscope, apart from steady rotations, has unsteady limiting motions that are integrable motions in the special Bobylev-Steklov case.

The effect of fluorine oligomer coatings on the tribocontacts of a piezoelectric actuator

The tribological study of the parameters of piezoactuator when switching over contacts a trib- ocouple deals with of rotation of piezoactuator steady during 500 m when the rotor from polished steel C45 (HRC 50, R a = 2 μm) is used. Often the rotation speed leaps up to 16-18 min-1. The coating with fluoroli- gomeric material stabilizes the rotation and continuous operation of piezoactuator. The steady rotation speed starts from a 50-m run (350 rotor revolutions, i.e., cycles of repeating impacts on the surface). The lower dam- age of the friction surface takes place after a 500-m run when the rotor is coated with fluoroligomeric mate- rial. Scratch tests show that steel surface with the fluoroligomeric layer has a lower hardness and 20% higher elasticity compared to a noncoated surface.

Investigations on synthesis, growth, electrical and defect studies of lithium selenoindate single crystals

LiInSe2 polycrystalline material was successfully synthesized from melt and temperature oscillation method (MTOM). The crystalline phase was confirmed by powder X-ray diffraction pattern. Crack free LiInSe2 single crystal of size 12mm diameter and 32mm length was grown using two zone tubular resistive heated furnace by modified vertical Bridgman–Stockbarger method with steady ampoule rotation. The grown LiInSe2 crystal was subjected to single crystal XRD, inductively coupled plasma-optical emission spectroscopy (ICP-OES), positron annihilation spectroscopy (PAS), Hall effect and dielectric measurements. Single crystal XRD measurement confirms the orthorhombic crystal system. ICP-OES analysis gives the crystal composition as Li0.81In1.01Se2.18. The average lifetime 278.03ps in PAS measurements corresponds to vacancy clusters present in LiInSe2 crystal. Hall effect measurement confirms the n-type semiconductor nature. The dielectric permittivity and dielectric loss were obtained to be 9.8 and 0.108 respectively by capacitance measurements at room temperature for the frequency of 2MHz.

Laminar mixing performances of baffling, shaft eccentricity and unsteady mixing in a cylindrical vessel

The laminar mixing performance in a cylindrical vessel agitated by a plate impeller is investigated. Several mixing enhancement strategies such as baffling, shaft eccentricity and angularly-oscillating impeller (unsteady mixing) are considered. The flow equations are solved numerically via a Lagrangian particle method based on the Moving Particle Semi-implicit (MPS) technique. It is observed that radial mixing is poor in an unbaffled vessel agitated by a concentric impeller undergoing steady rotation. In general, baffling has marginally improved the radial momentum exchange between the near-wall and inner fluid particles. This shortcoming can be alleviated by introducing the shaft eccentricity and the unsteady mixing procedure. In general, the unsteady mixing procedure with the smaller oscillating amplitude outperforms all the mixing enhancement strategies considered in the current study.

Rotational Stabilization of Cargo Container Slung Loads

The stabilization of “difficult” loads that become aerodynamically unstable at airspeeds well below the power-limited speed of the helicopter-load configuration has been studied since the 1960s. This paper looks at the possibility of stabilizing slung loads in forward flight by imposing a slow steady rotation in yaw (spin stabilization). Slow rotations of 100–150 deg/s suffice to suppress the pendulum motions of the load. A swivel is required at the hook, and only a few foot-pounds of yaw moment are needed to overcome swivel friction and impose the desired yaw rate. The approach is limited to single-point suspensions. A stabilizer design consisting of a one-shaft anemometer-like device with hemispherical cups at the ends was developed in wind tunnel tests. The shaft angle can be controlled to vary the applied yaw moment and allow feedback regulation of the load yaw rate. Flight tests with two cargo containers demonstrated that a simple linear control law with fixed gains was effective in maintaining the desired yaw rate in forward flight over the range of configurations of the test loads. Wind tunnel data were obtained at all stages of the development and testing and proved to be an accurate source of design data and an accurate predictor of performance in flight.