Angular Velocity Of Fluid Research Articles

Spirographic motion in a vortex

The present study investigates the dynamics of an inertialess rigid dumbbell in a steady two-dimensional vortex. This system goes beyond the point-particle approximation but remains analytically solvable. For any vortex, the dynamics of the dumbbell follows from the existence of a constant of motion that is independent of the form of the vortex. In particular, if the fluid angular velocity decreases with the radial distance, the dumbbell performs spirographic trajectories around the vortex center, the shape of which is highly sensitive to the initial position and orientation of the dumbbell.

A statistical analysis of velocity and acceleration fluctuations of inertial particles in particle-laden turbulent Couette flow

Dynamics of the particle phase in a particle-laden turbulent flow is strongly influenced by the fluctuating velocity and vorticity field of the fluid phase. The present work mainly focuses on exploring the statistics of velocity and acceleration of the particle phase in a particle-laden turbulent Couette flow. Direct numerical simulations have been performed for particle-laden turbulent Couette flow with two different Reynolds numbers, Reδ=750 and 1300, in the presence of sub-Kolmogorov sized inertial particles for multiple Stokes numbers (Stokes number ≫1). The inter-particle and wall-particle interactions have also been considered to be elastic. We report the distribution functions for the linear and rotational velocities and accelerations in the presence of particle roughness. From the particle equation of rotational motion, we arrive at the expression where the fluctuating angular acceleration αi′ of the particle is expressed as the ratio of a linear combination of fluctuating rotational velocities of particle (ωi′) and fluid angular velocity (Ωi′) to the particle rotational relaxation time τr. The analysis is done using probability density function plots and Jensen–Shannon divergence-based method to assess the similarity between the particle net rotational acceleration distributions f(αi′), with (i) the distributions of particle acceleration component arises from fluctuating fluid angular velocity computed in the particle-Lagrangian frame f((Ω′i/τr)pl), (ii) fluctuating particle angular velocity f(ω′i/τr), and (iii) the fluid angular velocity f((Ω′i/τr)e) computed in the fluid Eulerian grids. The analysis leads to the conclusion that for a wide range of Reynolds and Stokes numbers, f(αi′) can be represented with a Gaussian white noise with a pre-estimated strength that can be calculated from the temporal decorrelation correlation of fluid-phase angular velocity fluctuations at Eulerian grid (Ω′i/τr)e.

Sloshing of Fluid Between Rotating Inner Vertical Shaft and Stationary Outer Casing

Abstract Unsteady behaviors of free surface around a rotating vertical shaft in cylindrical stationary casing were investigated. Experiments were carried out with various rotating frequency of the shaft at two initial water levels. An axi-symmetrical free surface oscillation took place when the rotational speed of the shaft became larger than a certain value. The frequency of the free surface oscillation decreased as the rotating frequency increased. A theoretical model was developed, and the mechanisms of the free surface oscillation were clarified. The oscillation was found to be a sloshing mode excited by the change of fluid angular velocity, caused by the change of wetted areas on the inner rotating shaft and outer stationary casing, associated with the change in free surface height.

Modeling heat transfer in fluid flow near a decelerating rotating disk with variable fluid properties

Present work formulates the unsteadily revolving fluid flow caused by a rotating porous disk in a variable viscosity fluid. Following an existing paper, the disk angular velocity is assumed to exhibit an inversely linear time dependency. Moreover, temperature dependency in fluid viscosity is incorporated in the analysis. Two different numerical approaches namely, a modified finite difference scheme and the collocation method based MATLAB package bvp4c, are employed to find self-similar solutions. Subtle fluid mechanics concepts such as radial wall stress, torque required, volumetric flow rate and heat transfer rate are analyzed for full range of unsteadiness parameter S, measuring the decay rate of disk angular velocity. There exists a particular value of S designated as S∗ which corresponds to zero torque (G′(0) = 0) illustrating the situation of freely rotating disk. Beyond this value of S, that is S < S∗, G ′ (0) has a negative sign signaling that fluid's angular velocity becomes higher than that of the disk. Our emphasis is to seek how the said flow model is affected by variable fluid properties. It should be remarked here that variable viscosity/thermal conductivity considerably alters the overall drag coefficient as well as heat transfer rate.

Unsteady oscillatory MHD boundary layer flow past a moving plate with mass transfer and binary chemical reaction

In this work, we have studied analytically the heat and mass transfer of unsteady MHD natural convective flow past a motioning plate with binary chemical reaction. The flow surface spontaneously moves with unvaried velocity in the flow direction or opposite under the influence of magnetic field. We studied both frequency-dependent effects and “long-time” effects that would require non-practically long channels to be observed in steady flow. We also explored mathematically the important aspects of reactive fluid flow, especially the residence time flow behaviour, scale-up and scale-down procedures. From the present study, it is seen amongst others that temperature is enhanced as the fluid angular velocity rises which leads to maximum temperature in the body of the liquid. It is discovered that mean velocity decrease with a rise in the species reaction and reaction order. The graphical results representing the governing flow parameters effect were presented and discussed. The flow conditions at the wall were also investigated, presented and described.

Spectral Quasi-Linearization Method for Non-Darcy Porous Medium with Convective Boundary Condition

The boundary layer micropolar fluid over a horizontal plate embedded in a non-Darcy porous medium is investigated in this study. This paper is solely focused on contributions oriented towards the application of micropolar fluid flow over a stretching sheet. The prime equations are renewed to ordinary differential equations with the assistance of similarity transformation; they are then subsequently solved numerically using the spectral quasi-linearization method (SQLM) for direct Taylor series expansions that can be applied to non-linear terms in order to linearize them. The spectral collocation approach is then applied to solve the resulting linearized system of equations. The paper acquires realistic numerical explanations for rapidly convergent solutions using the spectral quasi-linearization method. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The validity of our model is established using error analysis. The impact of different geometric parameters on angular velocity, temperature, and entropy generation numbers are presented in graphs. The results show that the entropy generation number decelerates with an increase in Reynolds number and Brinkmann number. The velocity profile increases with the increasing material parameter. The results indicate that the fluid angular velocity decreases throughout the boundary layer for increasing values of the material parameter.

Design of Attitude Control Servomechanisms with Fluid Ring and CMG for Rigid Satellite

Satellites cover a wide range of space missions as remote sensing. Accomplishment of the mission depends on satellite’s stability maintenance and direction. The main task of the attitude control system is to provide stability to the satellite against external disturbances. Such perturbations are caused due to aerodynamic drag, solar radiation and magnetic field. The attitude dynamics model and the development of a controller to stabilize the three degrees of freedom rotational angles are quite important steps in the design of satellites. Although there are several actuators to provide attitude determination and control, a novel type is considered in this paper. This new actuator is the fluid contained inside one or more rings and fluid flow supplied by pump. The required torque control made by change of angular velocity of fluid. In this paper, the satellite is considered rigid and nonlinear dynamics equations were written. Because of the importance of satellite mission, the failure of the pyramid-shaped satellite with an additional ring fluid will be discussed. Satellite attitude control is carried out with an Euler angle errors control law. The performance of this actuator is compared with moment control gyro and their advantages on to each other have been described.

Comparing fluid ring and CMG servomechanisms for active control of rigid satellites

Purpose This paper aims to describe a novel type of attitude control system (ACS) in different configurations. This servomechanism is compared with control moment gyro (CMG) in significant parameters of performance for ACS of rigid satellite. Design/methodology/approach This new actuator is the fluid containing one or more rings and fluid flow is supplied by pump. The required torque control is obtained by managing fluid angular velocity. The cube-shaped satellite with three rings of fluid in the principle axes is considered for modeling. The satellite is considered rigid and nonlinear dynamics equation is used for it. In addition, the failure of the pyramid-shaped satellite with an additional ring fluid is discussed. Findings The controller model for four fluid rings has more complexity than for three fluid rings. The simulation results illustrated that four fluid rings need less energy for stabilization than three fluid rings. The performance of this type of actuator is compared with CMG. At last, it is demonstrated that performance parameters are improved with fluid ring actuator. Research limitations/implications Fluid ring actuator can be affected by environmental pressure and temperature. Therefore, freezing and boiling temperature of the fluid should be considered in system designation. Practical implications Fluid ring servomechanism can be used as ACS in rigid satellites. This actuator is compared by CMG, the prevalent actuator. It has less displacement attitude maneuver. Originality/value The results provide the feasibility and advantages of using fluid rings as satellite ACS. The quaternion error controller is used for this model to enhance its performance.

Fluid dynamics during Random Positioning Machine micro-gravity experiments

A Random Positioning Machine (RPM) is a device used to study the role of gravity on biological systems. This is accomplished through continuous reorientation of the sample such that the net influence of gravity is randomized over time. The aim of this study is to predict fluid flow behavior during such RPM simulated microgravity studies, which may explain differences found between RPM and space flight experiments. An analytical solution is given for a cylinder as a model for an experimental container. Then, a dual-axis rotating frame is used to mimic the motion characteristics of an RPM with sinusoidal rotation frequencies of 0.2Hz and 0.1Hz while Particle Image Velocimetry is used to measure the velocity field inside a flask. To reproduce the same experiment numerically, a Direct Numerical Simulation model is used. The analytical model predicts that an increase in the Womersley number leads to higher shear stresses at the cylinder wall and decrease in fluid angular velocity inside the cylinder. The experimental results show that periodic single-axis rotation induces a fluid motion parallel to the wall and that a complex flow is observed for two-axis rotation with a maximum wall shear stress of 8.0mPa (80mdyne/cm2). The experimental and numerical results show that oscillatory motion inside an RPM induces flow motion that can, depending on the experimental samples, reduce the quality of the simulated microgravity. Thus, it is crucial to determine the appropriate oscillatory frequency of the axes to design biological experiments.

Drift of spheres in a rotating fluid

The drift of spheres in a rotating fluid is investigated. The problem is studied experimentally and numerically using the Galerkin method. It is shown that for small angular velocities of the fluid Ω the drift velocity of the spheres is almost independent of Ω, but once a certain threshold value Ω* is attained the drift velocity rapidly decreases. The experimental dependence of the translational velocity of the sphere on the fluid angular velocity is explained on the basis of a theoretical analysis.

Particle spin in a turbulent shear flow

The translational and rotational motions of small spherical particles dilutely suspended in a turbulent channel flow have been investigated. Three different particle classes were studied in an Eulerian-Lagrangian framework to examine the effect of the response times on the particle statistics. The results for the fluctuating particle velocities were consistent with earlier observations. The mean particle spin exceeded the mean fluid angular velocity in a region close to the channel walls. The fluctuating components of the particle spin were consistently lower than the corresponding fluid angular velocities for the heaviest particles.

Transient rotating flow over a moving surface with a magnetic field

The transient flow and heat transfer on a moving surface in a rotating fluid in the presence of a magnetic field have been investigated. The unsteadiness in the flow field has been introduced by the sudden change in the surface velocity or the fluid angular velocity. The parabolic partial differential equations governing the unsteady flow and heat transfer have been solved by using an implicit finite-difference scheme in combination with the quasilinearization technique. The computations have been carried out from the initial steady state to the final steady state. The effects of the sudden change in the surface velocity on the flow and heat transfer are found to be more significant than those of the impulsive change in the angular velocity of the fluid. When the surface velocity is suddenly reduced, the surface shear stress is found to vanish in a small time interval after the start of the impulsive motion, but it does not imply flow separation. The surface shear stress for the primary flow increases with the magnetic field and the fluid angular velocity, but the surface heat transfer decreases. The surface shear stress for the secondary flow increases with the angular velocity of the fluid, but decreases with increasing magnetic field.

On the effect of the Boussinesq–Basset force on the radial migration of a Stokes particle in a vortex

The trajectory of an isolated solid particle dropped in the core of a vertical vortex is investigated theoretically and experimentally, in order to analyze the effect of the history force on the radial migration of the inclusion. Both the Stokes number (based on the particle radius and the fluid angular velocity) and the particle Reynolds number are small. The particle is heavier than the fluid, and is therefore expelled from the center of the vortex. An experimental device using spherical particles injected in a rotating cylindrical tank filled with silicone oil has been built. Experimental trajectories are compared to analytical solutions of the motion equations, which are obtained by making use of classical Laplace transforms. The analytical expression of the history force and the ejection rate are carried out. This force does not vanish, but increases exponentially and has to be taken into account for efficient predictions. In particular, calculations without history force overestimate particle ejection. The relative difference between the ejection rate with and without history force scales like the square root of the Stokes number, so that differences of the order of 10% are visible as soon as the Stokes number is of the order of 0.01. Also, agreement between experimental and theoretical trajectories is observed only if the acceleration term in the history integral involves the time derivative of the fluid velocity following the particle, rather than the acceleration of fluid points at the particle location, even for small particle Reynolds numbers. Finally, analytical calculations show that the particle ejection rate is more sensitive to the Boussinesq–Basset force than to Saffman’s lift.

Relativistic stars in differential rotation: bounds on the dragging rate and on the rotational energy

For general relativistic equilibrium stellar models (stationary axisymmetric asymptotically flat and convection-free) with differential rotation, it is shown that for a wide class of rotation laws the distribution of angular velocity of the fluid has a sign, say “positive,” and then both the dragging rate and the angular momentum density are positive. In addition, the “mean value” (with respect to an intrinsic density) of the dragging rate is shown to be less than the mean value of the fluid angular velocity (in full general, without having to restrict the rotation law, nor the uniformity in sign of the fluid angular velocity); this inequality yields the positivity and an upper bound of the total rotational energy.

Large-scale features of rotating forced turbulence.

Large-scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity, we find two types of modifications to the fluid equation of motion. The first correction transforms the molecular shear viscosity into a (rotation independent) effective viscosity. The second perturbative correction leads to a new large scale nondissipative force proportional to the fluid angular velocity in the slow rotation regime. This effective force does no net work and alters the dispersion relation of inertial waves propagating in the fluid. Both dynamically generated corrections can be identified with certain components of the most general axisymmetric "viscosity tensor" for a Newtonian fluid.

Core dynamics of a strained vortex: instability and transition

We study the instability of a laminar vortex column (in an external orthogonal strain field) to an axisymmetric core size perturbation, and the resulting transition to fine-scale turbulence. The perturbation, which evolves as a standing wave oscillation (i.e. core dynamics, CD), is inviscidly amplified by the external strain. Analysis of a weakly strained Rankine vortex explains the physical mechanism of instability: resonant interaction between the perturbation – the azimuthal wavenumber m = 0 wave – and m = ±2 waves. The CD instability (CDI) – a type of elliptic instability – experiences the fastest growth when the CD oscillation frequency equals vortex column's fluid angular velocity, such matching occurring only at specific discrete values of the axial wavenumber k. At this resonant frequency, the net effect of the swirl-induced tilting of perturbation vorticity and the CD-induced tilting of base flow vorticity is such that perturbation vorticity is continually aligned with the stretching direction of the external strain. Such strain–vorticity locking occurs for all m; hence all waves are unstable, the instability oscillation frequency being dependent on m. In a viscous Gaussian-like vortex, CDI has low-strain, low-Re and high-k cutoffs – consequences of the competing effects of inviscid amplification and viscous damping. Direct numerical simulation reveals two physical-space mechanisms of transition: (i) formation of a thin annular vortex sheath surrounding a low-enstrophy ‘bubble’ (similar to axisymmetric vortex breakdown) and the sheath's subsequent roll-up into smaller ‘vortexlets’; and (ii) folding and reconnection of core vortex filaments giving rise to additional fine-grained random vorticity within the bubble – both mechanisms caused by CD-induced intense axial flow within the vortex column. The resulting finer tubular vortices (similar to ‘worms’) have in turn their own CD, and thus this transition scenario suggests a physical-space cascade process in developed turbulence (as well as a concomitant anti-cascade process during the bubble's collapse phase). Additionally, we show that bending waves, in spite of their faster growth, effect surprisingly much slower transfer of energy into fine scales than CDI does, and hence are less effective than CDI in vortex transition and in turbulence cascade.

Mechanics of inner core super‐rotation

A mechanism is proposed to explain the seismologically‐inferred prograde rotation of the Earth's solid inner core in terms of the structure of convection in the fluid outer core. Numerical calculations of convection and dynamo action in the outer core exhibit excess temperatures inside the tangent cylinder surrounding the inner core. We show that this temperature difference generates a prograde thermal wind and a strong azimuthal magnetic field inside the tangent cylinder. Electromagnetic torques on the inner core derived from induced azimuthal magnetic fields and the ambient poloidal field equilibrate when the inner core angular velocity lags the nearby tangent cylinder fluid angular velocity by approximately 14%. The inferred prograde rotation of the inner core (1.1–3°/year relative to the mantle) can be produced by a very small (⋍ 0.001 K) temperature anomaly within the tangent cylinder and indicates strong toroidal magnetic fields with peak intensities of 24–66 mT in that region of the core.

Vorticity meter calibration using a cross-wires survey

A vorticity meter of the vane-type has been used in this study for direct and quantitative measurements of vertical flows. The vane calibration procedure is carried out by using measurements deduced from a preliminary cross-wires survey of the flow-field generated in the wake of a half wing set at incidence in the wind tunnel. Emphasis is placed on the resulting calibration law which relates the vane rotational speed to the fluid angular velocity. Specially it is shown that this calibration law can be obtained as a linear expression by taking into account the minimum threshold rotational speed necessary for vane rotation. When comparing vorticity distributions obtained through the vortical wing wake by the indirect cross-wires technique, good agreements are found with the corresponding vorticity distributions as deduced from the so calibrated vorticity meter.

Boundary-layer separation on a sphere in a rotating flow

The velocity just outside the boundary layer and upstream of the separation ring on a sphere moving along the axis of a slightly viscous, rotating fluid is calculated through a least-squares approximation on the hypothesis of no upstream influence. A reverse flow is found in the neighbourhood of the forward stagnation point fork≡ 2Ωa/U&gt;k= 2·20 (Ω = angular velocity of fluid,U= translational velocity of sphere,a= radius of sphere) and is accompanied by a forwardseparation bubble, such as that observed by Maxworthy (1970) fork[gsim ] 1. Rotation also induces a downstream shift of the peak velocity; the estimated shift of the separation ring in the absence of forward separation increases withkto a maximum of 24°, in qualitative agreement with Maxworthy's observations.The least-squares formulation is compared with that given by Stewartson (1958) for unseparated flow (Stewartson did not consider separation). Both formulations require truncation of an infinite set of simultaneous equations, but Stewartson's formulation yields a non-positive-definite matrix that may exhibit spurious singularities. The least-squares formulation yields a positive-definite matrix, albeit at the expense of slower convergence for fixedk, and is especially well suited for automatic computation.Anad hocincorporation of a cylindrical wave of strength [Uscr ], such that the maximum upstream axial velocity is [Uscr ]U, is considered in an appendix. It is found thatkdecreases monotonically from 2·2 to 0 as [Uscr ] increases from 0 to 1.

An Empirical Method for Calculating Radial Pressure Distribution on Rotating Disks

This paper presents the results of an investigation conducted to develop more accurate equations for predicting the radial pressure distribution on enclosed rotating disks with or without blades and with radial outward or inward throughflow. Variables that affect pressure distribution, such as blade height, number of blades, axial blade top-to-housing clearance, flow rate, and rotor speed, were investigated. The results are applicable to the design for turbomachinery and, in particular, centrifugal pumps. The investigation was divided into two phases, the first of which used water as the test fluid and the second, liquid hydrogen. The results of the water tests were presented at the ASME Aviation and Space Conference, March, 1965. This paper presents the results of the tests conducted with liquid hydrogen. Empirical equations were derived from the test data relating the fluid angular velocity ratio to the significant variables by using a statistical regression-analysis method programmed for the IBM 7090. A comparison is made of the results obtained from the two fluids, water and liquid hydrogen.