Uniform Rotation Research Articles

Frequency characteristic of a uniformly rotating laser gyro in exact and polynomial forms

In some inertial navigation systems of a carousel type, laser gyros operate in regime of uniform rotation. For development of such systems and computer simulation of their work, one needs to have the “exact” (in wide range of angular velocities ) analytical expression for counterpropagating waves beat frequency of uniformly rotating device. This expression may be obtained by solving the well-known system of laser gyro dynamic equations with accuracy to second order in parameters of counterpropagating waves linear coupling. But before use of such non-dithered laser gyros in the named inertial system, their metrological parameters (scale factors and null shifts) must be preliminary calibrated. For synthesis and qualitative analysis of methodical errors of the procedure of such calibration on a quickly rotating platform of a single-axis stand, one needs also to have the approximate analytical expression for counterpropagating waves beat frequency in the form of polynomial
 with coefficients , ..., which involve parameters of the exact expression for . As analysis of the literature shows, the known expression for and the known relations for some of coefficients of polynomial are not complete and, therefore, must be modified. In the paper, the result of such modification is presented.

The thermophysical flow of viscous fluid toward a permeable rotating disk with the Hall current and the Maxwell-Cattaneo law

The phenomenon of fluid flow through rotating surfaces has been a topic of vast interest among the research community due to its industrial applications such as spinning disk electrodes, evaporators, centrifuges, power engineering, and microclimate systems. Inspired by such developments, the ongoing study investigates the swirl flow of viscous fluid about a permeable disk. The disk experiences a uniform rotation and undergoes shrinking or stretching in its own plane. Hall’s current effects are also featured in the flow model. The energy equation is demonstrated by the Maxwell-Cattaneo law. This law holds the main feature of thermal inertia due to which the relaxation time initiates the steady-state heat conduction. Therefore, such a law overcomes the paradox of heat conduction in Fourier’s law. The traditional Von Karman approach of similarity functions is implemented to convert the governing flow equations into a self-similar form. The resultant flow system is then solved by the Runge–Kutta-Fehlberg (RKF) procedure with the shooting technique. For the exactness of the numerical computations, the results are compared with the available data for the limiting case of the physical flow configuration. The physical quantities are elaborated through graphical descriptions.

Mechanical properties of functionally graded rotating lattice structures fabricated with SLM process

Triply periodic minimal surface (TPMS) based sheet lattice structure, especially the Diamond sheet structure, has higher strength than traditional TPMS network lattice structure. However, the mechanical properties of sheet lattice structures with rotating orientation should be further investigated to utilize the unique properties of lattice structure fully. In this paper, the structure with a graded rotation angle from 0° to 45° (DGRS) is designed and manufactured by selective laser melting (SLM). Then, the mechanical properties of DGRS are compared with that of other lattice samples, namely, non-rotating structure (DNS) and the structure with a uniform rotation angle of 45° along the x- axis (DRS). The experimental results demonstrate that DGRS has the highest plateau stress and more stable stress variation at the post-yield stage than other samples. The numerical simulation exhibits dispersive equivalent stress distribution in DGRS, which could alleviate the local stress concentration in the joint area of the lattice structure. Additionally, DGRS shows superior energy absorption capability.

Thermodinamically-consistent dynamic continualization of block-lattice materials

Lattice-like materials featuring periodic planar tessellation of regular rigid blocks connected by linear elastic interfaces and chiral or achiral properties are considered. The chirality results from a uniform rotation of the blocks with respect to their centroidal joining line and leads to interesting auxetic and dispersive acoustic behaviors. The governing equations of the discrete Lagrangian model are properly manipulated via the novel enhanced continualization scheme in such a way to obtain equivalent non-local integral and gradient-type higher-order continua. Based on the formal Taylor series expansion of the integral kernels or the corresponding pseudo-differential functions accounting for shift operators and proper pseudo-differential downscaling laws, the proposed enhanced continualization technique allows formulating homogeneous non-local continuum models of increasing orders, analytically featured by characteristic non-local constitutive and inertial terms. The enhanced continualization shows thermodynamic consistency in the definition of the overall non-local constitutive tensors, as well as qualitative agreement and quantitative convergent matching of the actual complex frequency band structure. The theoretical findings are successfully verified though the study of wave dispersion and attenuation properties as referred to a representative tetrachiral geometry.

Dynamics of water conveying iron oxide and graphene nanoparticles subject to stretching/spiraling surface: An asymptotic approach

The applications of hybrid nanofluids due to its heat transfer characteristics has piqued the interest of many researchers. Inspired by this, in this article, hybrid nanofluid flow is considered, where the fluid is flowing normally over a disk that is exhibiting rotation and linear stretching in the stagnation region. The energy transport and irreversibility analysis are conducted with Ohmic heating, thermal radiation, and heat source/sink. Homann’s problem is modified with simultaneous effects of the linear radial stretchiness of the disk, uniform rotation, and magnetohydrodynamic, which contributes to the spiral motion. It is noted that the surface velocity is generated as a spiral logarithm because of rotation and linear stretching of the disk. Two types of nanoparticles are considered, i.e., ferrous oxide and graphene immersed in water. Furthermore, ordinary differential equations are generated by applying appropriate similarity ansatz. The problem is studied numerically and illustrated graphically for both hybrid nanofluid and conventional nanofluid profiles in MATLAB (bvp4c). The influence of pertinent parameters on the radial and azimuthal velocities and temperature are discussed. The comparison of asymptotic values of wall stress parameters is made, and the results obtained are in impeccable agreement with the ones mentioned in the literature. The impact of the Prandtl number is provided, which represents that the thermal transport phenomenon is a decreasing function of the Prandtl number. Entropy generation and Bejan number are magnified because of thermal radiation. Entropy generation signifies the feasibility of a reaction and how the energy is lost or degraded in a system. It is also noted that the inclusion of a hybrid nanofluid causes the thermal conductivity of the system to incline.

Dynamic Induction Heating Temperature Field Analysis of Spiral Bevel Gears

Combining tooth surface induction heating and shot peening is an efficient method to improve tooth surface performance. Reasonable designs of the induction coil structure and parameters are essential for achieving uniform and efficient tooth surface heating. In this work, to precisely control the tooth surface temperature field and improve the heat uniformity across the tooth surface, a transverse coil (TC) and a longitudinal coil (LC) were designed, and the gear was set to rotate at a constant speed of 20 r/min, dividing the tooth surface is into a shot-peening area and heating area. Further, dynamic numerical simulations were performed using COMSOL Multiphysics in combination with the uniform rotation of gears to investigate the effect of the coil structure on the temperature field of the outer surface of gears. The results of the analyses combining the effects of different electrical parameters revealed that the gear surface temperature under LC heating was more uniformly distributed in the axial and circumferential directions, the tooth surface temperature fluctuations were smaller, the temperature difference between the root and top of the tooth was smaller, an coil heating was more efficient. Thus, the LC was deemed suitable for use as the spiral bevel gear induction heating coil. Finally, heating experiments were conducted using the LC to validate the simulation model. The results show that the use of LC heating can achieve the research goals of uniform temperature field distribution on the tooth surface and efficient temperature rise, providing the prerequisite for shot peening.

Power spectrum of domain-wall network, and its implications for isotropic and anisotropic cosmic birefringence

Recently, based on a novel analysis of the Planck satellite data, a hint of a uniform rotation of the polarization of cosmic microwave background photons, called isotropic cosmic birefringence, has been reported. The suggested rotation angle of polarization of about 0.2–0.4 degrees is close to the fine-structure constant, α ≃ 1/137 rad ≃ 0.42 deg. Interestingly, this coincidence can be naturally explained over a very wide parameter range by the domain walls of axion-like particles. Furthermore, the axion-like particle domain walls predict not only isotropic cosmic birefringence but also anisotropic one that reflects the spatial distribution of the axion-like particle field on the last scattering surface. In this paper, we perform lattice simulations of the formation and evolution of domain walls in the expanding universe and obtain for the first time the two-point correlation function and power spectrum of the scalar field that constitutes the domain walls. We find that for initial fluctuations at subhorizon scales, the power spectrum is roughly consistent with analytical predictions based on random wall distributions. However, there is some excess at scales corresponding to the Hubble radius. Applying our results to the anisotropic cosmic birefringence, we predict the power spectrum of the rotation angles induced by the axion-like particle domain walls for the similar initial condition, and show that it is within reach of future observations of the cosmic microwave background.

YORP Effect on Long-Term Rotational Dynamics of Debris in GEO

The Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect describes the torque induced on space objects produced by solar radiation and thermal re-emission. Previous analyses have demonstrated its influence on long-term rotational dynamics of space debris objects in Geostationary Orbit (GEO), where YORP becomes predominant with respect to other external perturbations (e.g., atmospheric drag, gravity gradient, eddy current torque), leading to a wide variety of possible behaviors. The capability of forecasting time windows of slow uniform rotation, if any, would bring significant advantages in operations of Active Debris Removal and on-orbit servicing, especially in the detumbling phase. Also, a non-negligible impact of the End-of-Life configuration, in terms of movable surfaces orientation and center of mass location, could lead to guidelines for future satellites to be easier targets in the disposal phase. In this work, a previously derived semi-analytical tumbling-averaged YORP rotational dynamics model is leveraged. Exploiting an averaged model, computational time is strongly reduced while maintaining sufficient accuracy compared to propagation of Euler’s equations of motion. First, a satellite of the Geostationary Operational Environmental Satellite (GOES) family is analyzed and compared to previous studies to verify the correct implementation of the model. A wider analysis is performed on simple geometric models, such as a box-wing satellite, a 3U CubeSat, and a rocket body. The impact of object size, surface optical properties, and center of mass position on long-term rotational behavior is investigated, providing a general insight into these phenomena with a possible future application to existing objects in GEO.

Quasi-stationary sequences of hyper-massive neutron stars with exotic equations of state

In this work, we study the effect of differential rotation, finite temperature and strangeness on the quasi stationary sequences of hyper massive neutron stars (HMNS). We generate constant rest mass sequences of differentially rotating and uniformly rotating stars. The nucleonic matter relevant to the star interior is described within the framework of the relativistic mean field model with the DD2 parameter set. We also consider the strange $\Lambda$ hyperons using the BHB$\Lambda\phi$ equation of state (EoS). Additionally, we probe the behaviour of neutron stars (NS) with these compositions at different temperatures. We report that the addition of hyperons to the EoS produces a significant boost to the spin-up phenomenon. Moreover, increasing the temperature can make the spin-up more robust. We also study the impact of strangeness and thermal effects on the T/W instability. Finally, we analyse equilibrium sequences of a NS following a stable transition from differential rotation to uniform rotation. The decrease in frequency relative to angular momentum loss during this transition is significantly smaller for EoS containing hyperons, compared to nucleonic EoS.

EHD stability of two horizontal finite conducting rotating viscous fluids: Effects of energy and concentration distributions

The objective of the present study tackles the Electrohydrodynamics (EHD) stability of two superposed horizontal liquids, where the upper layer is occupied by a perfect gas and the lower one by a viscous liquid. The structure is saturated in porous media and is subjected to a uniform rotation around its normal axis, so both centrifugal and Coriolis forces are considered. Additionally, the system is affected by a uniform, normal electric field. The novelty of the proposed mathematical model is supplemented with the impacts of temperature and concentration distributions. Therefore, for more accuracy, apart from Hsieh’s simplified modulation Hsieh (1972), energy and concentration equations are incorporated. The boundary-value problem is examined using regular mode modeling; hereafter a linear stability analysis is attained. The analysis reveals in more depth a set of non-dimensional physical numbers. Consequently, this procedure reveals an extremely difficult dispersion relationship. After performing the numerical calculations, the comparison between the outcomes and the existingliterature gives satisfactoryfindings. Furthermore, the electric field destabilizes the system. Nevertheless, based on the proportion of fluids permittivities and conductivities, the field has a dual role in leaky dielectrics.

Biomechanical responses of human lumbar spine and pelvis according to the Roussouly classification

BackgroundFew studies have analyzed the different biomechanical properties of the lumbar with various morphological parameters, which play an important role in injury and degeneration. This study aims to preliminarily investigate biomechanical characteristics of the spine with different sagittal alignment morphotypes by using finite element (FE) simulation and in-vitro testing.MethodsAccording to the lumbar-pelvic radiographic parameters of the Chinese population, the parametric FE models (L1-S1-pelvis) of Roussouly’s type (1–4) were validated and developed based on the in-vitro biomechanical testing. A pure moment of 7.5 Nm was applied in the three anatomical planes to simulate the physiological activities of flexion, extension, left-right lateral bending and left-right axial rotation.ResultsThe sagittal configuration of four Roussouly’s type models had a strong effect on the biomechanical responses in flexion and extension. The apex of the lumbar lordosis is a critical position where the segment has the lowest range of motion among all the models. In flexion-extension, type 3 and 4 models with a good lordosis shape had a more uniform rotation distribution at each motor function segment, however, type 1 and 2 models with a straighter spine had a larger proportion of rotation at the L5-S1 level. In addition, type 1 and 2 models had higher intradiscal pressures (IDPs) at the L4-5 segment in flexion, while type 4 model had larger matrix and fiber stresses at the L5-S1 segment in extension.ConclusionThe well-marched lordotic type 3 lumbar had greater stability, however, a straighter spine (type 1 and 2) had poor balance and load-bearing capacity. The hypolordotic type 4 model showed larger annulus fiber stress. Therefore, the sagittal alignment of Roussouly’s type models had different kinetic and biomechanical responses under various loading conditions, leading to different clinical manifestations of the lumbar disease.

Energy transport near Homann stagnation point flow over a spiraling disk with Cattaneo–Christov theory

In this paper, axisymmetric magnetohydrodynamic (MHD) Homann flow is studied normally over a stretching and spiraling disk in the stagnation region. Homann’s problem is modified with simultaneous effects of the radial linear stretching and uniform rotation of the disk. The magnetic field is applied perpendicular to the motion of the flow. The energy and mass distribution phenomena are analyzed by using Cattaneo–Christov (CC) double diffusion model, heat sink/source and chemical reaction effects. The main purpose of this study is to highlight the significance of CC theory on Homann problem along with asymptotic behavior. Similarly, ansatzes are utilized to transform the partial differential equations into ordinary differential equations. The solutions are computed numerically by a built-in scheme, namely, bvp4c in MATLAB. Moreover, it is concluded that the surface velocity is produced in the form of a spiral logarithm because of the continual activity of radial stretching and uniform rotation of the disk. The outcomes of magnetic field, rotation and stretching parameters are discussed graphically for coefficients of skin friction. The coefficient of skin friction along the [Formula: see text]-axis is enhanced, whereas along [Formula: see text]-axis, it is decreased by varying stretching and rotating parameters. The impact of thermal and solutal relaxation time coefficients reveals that they reduce the heat and mass transfer rates, respectively.

General Tumbling-Averaged Rotational Dynamics for Defunct Satellites

Understanding and predicting the long-term spin state evolution of defunct satellites and rocket bodies is important for solar radiation pressure modeling, space domain awareness, and active debris removal (ADR). Dynamical modeling and observations indicate that defunct geosynchronous satellite spin states are primarily driven by solar radiation torques via the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. In our two recent papers, we uncovered dynamically rich YORP-driven behavior including cycling between uniform rotation and non-principal axis tumbling, angular momentum sun tracking, and tumbling period resonances. These papers only considered the YORP effect. However, tumbling satellites are also subject to energy dissipation from residual fuel slosh and flexure. Gravitational torques and other environmental perturbations may affect long-term evolution as well. In this paper, the third in our series, we develop semi-analytical tumbling-averaged models for internal energy dissipation and gravity gradient torques and combine them with the earlier YORP models. Accounting for YORP and dissipation, we find asymptotically stable tumbling states with constant angular momentum and kinetic energy and a pole fixed in the rotating sun-satellite orbit frame. With gravity gradients, these asymptotic states become stable limit cycles with yearly periodicity. We discuss the implications of these findings for the space debris population, ADR, and satellite decommission procedures.

Enhanced control of the turbulent flow past a circular cylinder with rotating rods inspired by an inviscid solution

This paper examines an active mechanism of wake control for a turbulent flow regime of Reynolds number 1000 through finite volume, three-dimensional DES simulations. Eight peripheral rods equally spaced about a central body are forced to spin around their axes in two arrangements: case 0, with uniform rotation speed and case 1, with rotation rates inspired by the solution of the potential flow around the body. The two cases were constrained to the same input kinetic energy for every set of rotations. We have found case 1 to be more effective to control the wake, eliminate turbulent structures, and attenuate mean drag and fluctuating lift. The interference of the rods in the flow past the main body resulted in a steady wake in both cases, provided enough rotation was supplied to the system. This result was previously achieved only in laminar regime. Novel to such a system, rotations midway between a vortex wake and a steady wake led streamwise vortices to show a mode-B-like mechanism of vorticity transfer. Case 1 generally suppressed vortex shedding with lower input kinetic energy and required less power than case 0, thus resulting in a more efficient configuration to suppress vortices in the wake.

Convection in Compressible Dusty Fluids

The aim of the present research was to study the thermosolutal convection in compressible fluids with suspended particles in permeable media. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, it is found that that stable solute gradient introduces oscillatory modes which were non-existent in its absence. For the case of stationary convection, it is found that medium permeability and suspended particles have destabilizing effects whereas the stable solute gradient has a stabilizing effect on the system. This problem was further extended to include uniform rotation. In this case for stationary convection, the suspended particles are found to have destabilizing effect whereas stable solute gradient, rotation and compressibility have stabilizing effect on the system. The medium permeability has a destabilizing effect in the absence of rotation but has both stabilizing and destabilizing effects in the presence of rotation.

ПРО СТІЙКІСТЬ РІВНОМІРНОГО ОБЕРТАННЯ У СЕРЕДОВИЩІ З ОПОРОМ НЕСИМЕТРИЧНОГО ТВЕРДОГО ТІЛА ПІД ДІЄЮ ПОСТІЙНОГО МОМЕНТУ У ІНЕРЦІАЛЬНІЙ СИСТЕМІ ВІДЛІКУ

Assuming that the center of mass of a rigid asymmetric body is on the third main axis of inertia of a rigid body, the conditions for the asymptotic stability of uniform rotation of a dynamically asymmetric solid rigid body with a fixed point are obtained. These conditions are obtained in the form of a system of three inequalities based on the Lénard-Shipar test, written in innormal form. The rigid body is under the action of gravity, dissipative moment and constant moment in the inertial frame of reference. The rotation of a rigid asymmetric body around the center of mass is studied. Uniform rotation around the center of mass of a rigid asymmetric body will be unstable in the absence of a constant moment. Cases of absence of dynamic or dissipative asymmetry are considered. It is shown that the equilibrium position of a rigid body will be stable only under the action of the reducing moment. Dynamic asymmetry has a more significant effect on the stability of rotation of an asymmetric rigid body than dissipative asymmetry. Stability conditions have been studied for various limiting cases of small or large values of restoring, overturning, or constant moments. It is noted that for sufficiently large values of the modulus of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. If the axial moment of inertia is the greatest or the smallest moment of inertia, then at sufficiently large values of angular velocity, both under the action of the overturning moment and under the action of the reducing moment, the rotation of the asymmetric solid will be asymptomatically stable. Analytical studies of the influence of dissipative, constant, overturning and restorative moments on the stability of uniform rotations of asymmetric and symmetric solids have been carried out. It is shown that in the absence of dynamic and dissipative symmetries, the obtained stability conditions coincide with the known ones.

Linear and weakly non-linear stability analysis of oscillatory convection in rotating ferrofluid layer

In the present paper, the problem of ferroconvection in the presence of uniform vertical rotation is considered to investigate the linear and weakly non-linear oscillatory stability. Two-dimensional convective roll instability is discussed with finite-amplitude disturbances. For linear stability, as a first-order problem, the expressions for Rayleigh numbers for stationary and oscillatory convection are derived and the effects of Coriolis force and magnetic parameters on the onset of ferromagnetic convection are studied, numerically. In weakly nonlinear oscillatory analysis, the second-order and third-order stability problems are discussed and the complex Ginzburg-Landau equation describing the amplitude of convection cell in rotating ferrofluid is derived and consequently, the expression for Nusselt number representing the heat transfer rate is obtained. From the present analysis, we observed that the rotation has the usual stabilizing effect on the linear stability in ferroconvection, however, the magnetic number (M1) and the measure of nonlinearity of magnetization (M3) both have a destabilizing effect on the onset of linear instability. Also, we found that for non-linear convection, the heat transfer rate (the Nusselt number) increases with increasing values of Taylor number, magnetic number, and the measure of nonlinearity of magnetization.

Goldstone States as Non-Local Hidden Variables

We consider the theory of spinor fields in polar form, where the spinorial true degrees of freedom are isolated from their Goldstone states, and we show that these carry information about the frames which is not related to gravitation, so that their propagation is not restricted to be either causal or local: we use them to build a model of entangled spins where a singlet possesses a uniform rotation that can be made to collapse for both states simultaneously regardless their spatial distance. Models of entangled polarizations with similar properties are also sketched. An analogy with the double-slit experiment is also presented. General comments on features of Goldstone states are given.

Structure of the twist-bend nematic phase with respect to the orientational molecular order of the thioether-linked dimers.

An analysis of the IR absorbance for the segmented functional groups of liquid crystal dimers mesogen and linker enabled the orientation order to be determined and information about the dipole interactions in the nematic and twist-bend nematic phases to be obtained. The long axis orientational order increases as the temperature decreases in the nematic phase, although much more slowly than for the classical nematics, and then reverses this trend in the twist-bend nematic phase due to the tilt of the molecules. In the nematic phase, the short axis of the molecule performs an isotropic uniform rotation and has a uniaxial alignment. In the twist-bend nematic phase, however, biaxial ordering occurs and grows significantly in accordance with the helical deformation of the director. Changes in the mean absorbance in the twist-bend nematic phase were observed: a decrease for the longitudinal dipole at the nematic-twist-bend nematic phase transition, thus emphasizing the antiparallel axial interaction of the dipoles, while the absorbance of the transverse dipoles remains unchanged up to 340 K, and then the latter become parallelly correlated.

Stable Hydrogen-burning Limits in Rapidly Rotating Very Low Mass Objects

We present novel effects of uniform rapid stellar rotation on the minimum mass of stable hydrogen burning in very low mass stars, using an analytic model and relaxing the assumption of spherical symmetry. We obtain an analytic formula for the minimum mass of hydrogen burning as a function of the angular speed of stellar rotation. Further, we show the existence of a maximum mass of stable hydrogen burning in such stars, which is purely an artifact of rapid rotation. The existence of this extremum in mass results in a minimum admissible value of the stellar rotation period of ∼22 minutes, below which a very low mass object does not reach the main sequence, within the ambit of our model. For a given angular speed, we predict a mass range beyond which such an object will not evolve into a main-sequence star.