Angular Velocity Profiles Research Articles

Periodic magnetohydrodynamic natural convection flow of a micropolar fluid with radiation

This article is concerned with the problem of periodic magnetohydrodynamic (MHD) natural convection boundary-layer flow of a radiating micropolar fluid near a vertical surface. Such type of problems are posed by induction electromagnetic pumps and generators. The governing equations are reduced to a convenient form by the introduction of stream function formulations and are simulated by the implicit finite difference method along with the Keller-box scheme. The results of the surface shear stress, rate of heat transfer, distribution of couple stress, velocity profile, temperature profile and angular velocity profile are shown graphically for a range of parameters. Excellent agreement is found when present solutions are compared with the previous studies. It is shown that the heat transfer rate remains insensitive when magnetic field parameter, micropolar parameter and micro-inertia density parameter increases. Further, the micropolar parameter, K, has dominant effect on skin friction coefficient and couple stress coefficient.

Brain strain uncertainty due to shape variation in and simplification of head angular velocity profiles.

Head angular velocity, instead of acceleration, is more predictive of brain strains. Surprisingly, no study exists that investigates how shape variation in angular velocity profiles affects brain strains, beyond characteristics such as peak magnitude and impulse duration. In this study, we evaluated brain strain uncertainty due to variation in angular velocity profiles and further compared with that resulting from simplifying the profiles into idealized shapes. To do so, we used reconstructed head impacts from American National Football League for shape extraction and simulated head uniaxial coronal rotations from onset to full stop. The velocity profiles were scaled to maintain an identical peak velocity magnitude and duration in order to isolate the shape for investigation. Element-wise peak maximum principal strains from 44 selected impacts were obtained. We found that the shape of angular velocity profile could significantly affect brain strain magnitude (e.g., percentage difference of 4.29-17.89% in the whole brain relative to the group average, with cumulative strain damage measure (CSDM) uncertainty range of 23.9%) but not pattern (correlation coefficient of 0.94-0.99). Strain differences resulting from simplifying angular velocity profiles into idealized shapes were largely within the range due to shape variation, in both percentage difference and CSDM (signed difference of 3.91% on average, with a typical range of 0-6%). These findings provide important insight into the uncertainty or confidence in the performance of kinematics-based injury metrics. More importantly, they suggest the feasibility to simplify head angular velocity profiles into idealized shapes, at least within the confinements of the profiles evaluated, to enable real-time strain estimation via pre-computation in the future.

Efficient batch-mode mixing and flow patterns in a microfluidic centrifugal platform: a numerical and experimental study

During recent years centrifugal-based microfluidic devices known as Lab-on-a-CD have attracted a lot of attentions. Applications of these CD-based platforms are ubiquitous in numerous biological analyses and chemical syntheses. Mixing of different species in microscale is one of the essential operations in biochemical applications where this seemingly simple task remains a major obstruction. Application of centrifugal force, however, may significantly improve the flow agitation and mixing, especially when it is combined with the Coriolis force which acts perpendicular to centrifugal force. In this study, mixing process in minichambers located on a rotating platform under a periodic acceleration and deceleration angular velocity profile is investigated both numerically and experimentally. We have incorporated various arrangements of obstacles and baffles, which are usually used in stationary mixers, within a batch-mode rotating mixing chamber. Subsequently, the effect of these obstacles on flow field and mixing process has been studied, and among these arrangements four cases have been selected for further experimental analysis. Experimental studies have been performed on a multi-layer CD platform fabricated in polycarbonate plates, and subsequently mixing has been investigated in these minichambers. The quantitative mixing data were obtained after a set of image analyses on the captured images of mixing chamber during the process and the results were compared with the simulation. The results indicate a good resemblance between the two studies both qualitatively and quantitatively. Furthermore, it has been shown that the application of obstacles and baffles together in chamber results in reducing the mixing time more than 50 % as compared to a chamber without any obstacle and/or baffle configuration. Obtaining mixing times less than 10 s in both studies, makes these CD-based platforms an appropriate device for many applications in which a cost-effective device as well as low mixing time is required.

Influence of fish swimming on the flow pattern of circular tanks

The effect of swimming fish on the average velocity and velocity profile of a circular tank was studied. Working with different inlet diameters and flow rates, nine different impulse forces (configurations) were evaluated. Each configuration was tested with and without fish, and the effects of two different fish sizes were compared.The velocity profiles in experiments with fish presented a considerable reduction in velocity in the centre of the tank near the outlet, which was a consequence of the increase in the kinematic eddy viscosity due to the turbulence introduced by fish swimming. A flattening of the angular velocity profile was observed in the central area of the tank, which had a radius of about 0.3m (18% of the total volume of the tank).A previous model proposed by Oca and Masaló (2013) was modified in order to better describe the distribution of velocities in the central volume of a tank with swimming fish. The proposed modification was based on Burgers⿿ proposal for a bathtub vortex, which implies the determination of the parameter (1⿿e⿿αr2), where r is the radius and the α values were experimentally obtained for each tank configuration, in which they increased with the impulse force.The average velocities in the tank were proportional to the square root of the impulse force in experiments with and without fish. Experiments with fish presented lower average velocities, which imply higher tank resistance coefficients. At similar stocking densities (14.6kg/m3), the increase in the tank resistance coefficients obtained with small fish sizes (154g) were slightly higher than those obtained with bigger fish sizes (330g).

RETRACTED: Characteristics of recursive backstepping algorithm and active damping of oscillations in feedback linearization for electromechanical system with extended stability analysis and perturbation rejection

In this paper, a technique for estimation of state variables and control of a class of electromechanical system is proposed. Initially, an attempt is made on rudimentary pole placement technique for the control of rotor position and angular velocity profiles of Permanent Magnet Stepper Motor. Later, an alternative approach is analyzed using feedback linearization method to reduce the error in tracking performances. A damping control scheme was additionally incorporated into the feedback linearization system in order to nullify the persistent oscillations present in the system. Furthermore, a robust backstepping controller with high efficacy is put forth to enhance the overall performance and to carry out disturbance rejection. The predominant advantage of this control technique is that it does not require the DQ Transformation of the motor dynamics. A Lyapunov candidate was employed to ensure global asymptotical stability criterion. Also, a nonlinear observer is presented to estimate the unknown states namely load torque and rotor angular velocity, even under load uncertainty conditions. Finally, the performances of all the aforementioned control schemes and estimation techniques are compared and analyzed extensively through simulation.

Taylor–Couette turbulence at radius ratio : scaling, flow structures and plumes

Using high-resolution particle image velocimetry, we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor–Couette flow for a radius ratio of 0.5 and Taylor number of up to $6.2\times 10^{9}$. The extracted angular velocity profiles follow a log law more closely than the azimuthal velocity profiles due to the strong curvature of this ${\it\eta}=0.5$ set-up. The scaling of the wind Reynolds number with the Taylor number agrees with the theoretically predicted $3/7$ scaling for the classical turbulent regime, which is much more pronounced than for the well-explored ${\it\eta}=0.71$ case, for which the ultimate regime sets in at much lower Taylor number. By measuring at varying axial positions, roll structures are found for counter-rotation while no clear coherent structures are seen for pure inner cylinder rotation. In addition, turbulent plumes coming from the inner and outer cylinders are investigated. For pure inner cylinder rotation, the plumes in the radial velocity move away from the inner cylinder, while the plumes in the azimuthal velocity mainly move away from the outer cylinder. For counter-rotation, the mean radial flow in the roll structures strongly affects the direction and intensity of the turbulent plumes. Furthermore, it is experimentally confirmed that, in regions where plumes are emitted, boundary layer profiles with a logarithmic signature are created.

Kinematical evolution of tidally limited star clusters: the role of retrograde stellar orbits

The presence of an external tidal field often induces significant dynamical evolutionary effects on the internal kinematics of star clusters. Previous studies investigating the restricted three-body problem with applications to star cluster dynamics have shown that unbound stars on retrograde orbits (with respect to the direction of the cluster's orbit) are more stable against escape than prograde orbits, and predicted that a star cluster might acquire retrograde rotation through preferential escape of stars on prograde orbits. In this study we present evidence of this prediction, but we also illustrate that there are additional effects that cannot be accounted for by the preferential escape of prograde orbits alone. Specifically, in the early evolution, initially underfilling models increase their fraction of retrograde stars without losing significant mass, and acquire a retrograde angular velocity. We attribute this effect to the development of preferentially eccentric/radial orbits in the outer regions of star clusters as they are expanding into their tidal limitation. We explore the implications of the evolution of the fraction of prograde and retrograde stars for the evolution of the cluster internal rotation, and its dependence on the initial structural properties. Although all the systems studied here evolve towards an approximately solid-body internal rotation with angular velocity equal to about half of the angular velocity of the cluster orbital motion around the host galaxy, the evolutionary history of the radial profile of the cluster internal angular velocity depends on the cluster initial structure.

Motion-based nearest vector metric for reference frame selection in the perception of motion.

We investigated how the visual system selects a reference frame for the perception of motion. Two concentric arcs underwent circular motion around the center of the display, where observers fixated. The outer (target) arc's angular velocity profile was modulated by a sine wave midflight whereas the inner (reference) arc moved at a constant angular speed. The task was to report whether the target reversed its direction of motion at any point during its motion. We investigated the effects of spatial and figural factors by systematically varying the radial and angular distances between the arcs, and their relative sizes. We found that the effectiveness of the reference frame decreases with increasing radial- and angular-distance measures. Drastic changes in the relative sizes of the arcs did not influence motion reversal thresholds, suggesting no influence of stimulus form on perceived motion. We also investigated the effect of common velocity by introducing velocity fluctuations to the reference arc as well. We found no effect of whether or not a reference frame has a constant motion. We examined several form- and motion-based metrics, which could potentially unify our findings. We found that a motion-based nearest vector metric can fully account for all the data reported here. These findings suggest that the selection of reference frames for motion processing does not result from a winner-take-all process, but instead, can be explained by a field whose strength decreases with the distance between the nearest motion vectors regardless of the form of the moving objects.

New code for equilibriums and quasiequilibrium initial data of compact objects. III. Axisymmetric and triaxial rotating stars

We introduce new code for stationary and axisymmetric equilibriums, as well as for triaxial quasiequilibrium initial data, of single rotating relativistic stars. The new code is developed as a part of our versatile initial data code for compact objects, Compact Object CALculator (cocal). In computing strong gravitational fields, the waveless formulation is incorporated into the cocal code on top of the previously developed Isenberg-Wilson-Mathews formulation (conformally flat thin-sandwich formulation). Also introduced is a new differential rotation law that contains two parameters to control an angular velocity profile and a transition from uniform to differential rotation. We present convergence tests and solution sequences for both uniformly and differentially rotating equilibriums of stationary axisymmetric compact stars, as well as for quasiequilibrium initial data of uniformly rotating triaxial (nonaxisymmetric) compact stars. We also show comparisons of uniformly rotating axisymmetric solutions computed with three different codes: cocal, lorene, and the RNS code.

Homotopy Analysis of MHD Free Convective Micropolar Fluid Flow along a Vertical Surface Embedded in Non-Darcian Thermally-Stratified Medium

The dynamics of steady, two-dimensional magnetohydrodynamics (MHD) free convective flow of micropolar fluid along a vertical porous surface embedded in a thermally stratified medium is investigated. The ratio of pressure drop caused by liquid-solid interactions to that of pressure drop caused by viscous resistance are equal; hence, the non-Darcy effect is properly accounted for in the momentum equation. The temperature at the wall and at the free stream which best accounts for thermal stratification are adopted. Similarity transformations are used to convert the nonlinear partial differential equation to a system of coupled non-linear ordinary differential equation and also to parameterize the governing equations. The approximate analytical solution of the corresponding BVP are obtained using Homotopy Analysis Method (HAM). The effects of stratification parameter, thermal radiation and other pertinent parameters on velocity, angular velocity and temperature profiles are shown graphically. It is observed that increase in the stratification parameter leads to decrease in both velocity and temperature distribution and also makes the microrotation distribution to increase near the plate and decrease away from the plate. The influence of both thermal stratification and exponential space dependent internal heat source on velocity, micro-rotation and temperature profiles are presented. The comparison of the solutions obtained using analytical techniques (HAM) and MATLAB package (bvp4c) is shown and a good agreement is observed.

Velocity profiles and energy fluctuations in simple shear granular flows

Rheology analysis of granular flows is important for predicting geophysical hazards and designing industrial processes. Using a discrete element method, we simulate simple shear flows in 3D under a constant confining pressure of 10kPa. The inertial number proposed by the GDR MiDi group in France is adopted to distinguish rheology regimes. Both translational and angular velocity profiles are investigated, and both fluid-like and solid-like behavior modes are observed in the flows. The maximum angular velocity occurs near the localized deformation area. We also investigate the energy characteristics of the flows and find that at very small shearing speed, the mean kinetic energy density ek is close to zero, while the mean elastic energy density ec is much greater. At large shearing speed, ek increases. The fluctuating parts of the two types of energy increase with increasing shear speed. Thus, the mean energy density ratio ek/ec can be used in addition to the inertial number to distinguish flow regimes. These results provide insights from energetics into the rheological properties of granular flows.

Dynamics of Vortex Rossby Waves in Tropical Cyclones, Part 1: Linear Time‐Dependent Evolution on an f‐Plane

Analyses of observational data on hurricanes in the tropical atmosphere indicate the existence of spiral rainbands which propagate outward from the eye and affect the structure and intensity of the hurricane. These disturbances may be described as vortex Rossby waves. This paper describes the evolution of barotropic vortex Rossby waves in a cyclonic vortex in a two‐dimensional configuration where the variation of the Coriolis force with latitude is ignored. The waves are forced by a constant‐amplitude boundary condition at a fixed radius from the center of the vortex and propagate outward. The mean flow angular velocity profile is taken to be a quadratic function of the radial distance from the center of the vortex and there is a critical radius at which it is equal to the phase speed of the waves. For the case of waves with steady amplitude, an exact solution is derived for the steady linearized equations in terms of hypergeometric functions; this solution is valid in the outer region away from the critical radius. For the case of waves with time‐dependent amplitude, asymptotic solutions of the linearized equations, valid for late time, are obtained in the outer and inner regions. It is found that there are strong qualitative similarities between the conclusions on the evolution of the vortex waves in this configuration and those obtained in the case of Rossby waves in a rectangular configuration where the latitudinal gradient of the Coriolis parameter is taken into account. In particular, the amplitude of the steady‐state outer solution is greatly attenuated and there is a phase change of across the critical radius, and in the linear time‐dependent configuration, the outer solution approaches a steady state in the limit of infinite time, while the amplitude of the inner solution grows on a logarithmic time scale and the width of the critical layer approaches zero.

Experimental study on the heat transfer of heat sink with bio-mimetic oscillating foil

This paper experimentally investigates the heat transfer performance and characteristics of a heat sink with bio-mimetic oscillating foil. The oscillating foil is driven by a novel mechanism of grooved cam with linkage. The air flow is drawn into a rectangular duct through the motion of the bio-mimetic oscillating foil. Various heat sinks were set at the outlet of the duct to study the thermal performance. Two types of grooved cams were designed to obtain different angular velocity profiles for the oscillating foils. The angular velocity was specified as fast forward/slow backward and sinusoidal patterns. Foils with three flexural stiffness values were utilized in the study. The averaged velocity at the inlet was measured to estimate the Reynolds number and Strouhal number. The effects of configuration of heat sink design with oscillating foil were also under investigation. The junction temperature of the heat sink was measured to obtain the effective thermal resistance. Results show that the angular velocity profile and flexural stiffness of the oscillating foil have a significant effect on the thermal performance of the heat sink.

Transition of accretion flow from Keplerian phase to advective phase as a dynamical system

A model for the transition of Keplerian accretion flow to advective phase is proposed. The advective fluid particle in the Keplerian accretion background is modelled using two-phase hydrodynamics. The hydrodynamic equations for the advective phase is reduced to a non-linear dynamical system. For small fluctuation of advective nature for sufficiently small time, a linearized dynamical system in density and radial velocity is obtained. The fluctuation is found to be linearly growing for suitable choice of the values of free parameters. The linear growth is studied as a function of the angular Mach number of the background Keplerian accretion flow. The other parameters of the dynamical system are the radial Mach number of the Keplerian accretion flow, viscosity parameters and gas constants of the Keplerian phase as well as the advective phase and the angular velocity profile of the advective fluid particle. The location of the transition region between Keplerian accretion flow and advective accretion flow is parametrized by the radial Mach number and the angular Mach number of the Keplerian accretion flow. The Keplerian accretion flow is found to be linearly unstable against transition to advective phase only if the radial Mach number greater than or of the order of 10−3. Since radial velocity has no dynamical relevance in Keplerian accretion flow (radial Mach number is very small, and the radial velocity comes only as a drift velocity in the equation of continuity), this means that such a transition is possible only at much inner part of the accretion disc. Appreciable linear growth of the advective fluctuation is possible only if the viscosity parameter of the advective phase has high or intermediate value. This could severely restrict the plausible branches of global solution of the inner advective accretion disc.

Novel method to form adaptive internal impedance profiles in walkers.

This paper proposes a novel approach to improve walking in prosthetics, orthotics and robotics without closed loop controllers. The approach requires impedance profiles to be formed in a walker and uses state feedback to update the profiles in real-time via a simple policy. This approach is open loop and inherently copes with the challenge of uncertain environment. In application it could be used either online for a walker to adjust its impedance profiles in real-time to compensate for environmental changes, or offline to learn suitable profiles for specific environments. So far we have conducted simulations and experiments to investigate the transient and steady state gaits obtained using two simple update policies to form damping profiles in a passive dynamic walker known as the rimless wheel (RW). The damping profiles are formed in the motor that moves the RW vertically along a rail, analogous to a knee joint, and the two update equations were designed to a) control the angular velocity profile and b) minimise peak collision forces. Simulation results show that the velocity update equation works within limits and can cope with varying ground conditions. Experiment results show the angular velocity average reaching the target as well as the peak force update equation reducing peak collision forces in real-time.

ROTATION OF GIANT STARS

The internal rotation of post-main sequence stars is investigated, in response to the convective pumping of angular momentum toward the stellar core, combined with a tight magnetic coupling between core and envelope. The spin evolution is calculated using model stars of initial mass 1, 1.5 and $5\,M_\odot$, taking into account mass loss on the giant branches. We also include the deposition of orbital angular momentum from a sub-stellar companion, as influenced by tidal drag along with the excitation of orbital eccentricity by a fluctuating gravitational quadrupole moment. A range of angular velocity profiles $\Omega(r)$ is considered in the envelope, extending from solid rotation to constant specific angular momentum. We focus on the back reaction of the Coriolis force, and the threshold for dynamo action in the inner envelope. Quantitative agreement with measurements of core rotation in subgiants and post-He core flash stars by Kepler is obtained with a two-layer angular velocity profile: uniform specific angular momentum where the Coriolis parameter ${\rm Co} \equiv \Omega \tau_{\rm con} \lesssim 1$ (here $\tau_{\rm con}$ is the convective time); and $\Omega(r) \propto r^{-1}$ where ${\rm Co} \gtrsim 1$. The inner profile is interpreted in terms of a balance between the Coriolis force and angular pressure gradients driven by radially extended convective plumes. Inward angular momentum pumping reduces the surface rotation of subgiants, and the need for a rejuvenated magnetic wind torque. The co-evolution of internal magnetic fields and rotation is considered in Kissin & Thompson, along with the breaking of the rotational coupling between core and envelope due to heavy mass loss.

Mechanical Implementation of Kinematic Synergy for Continual Grasping Generation of Anthropomorphic Hand

The synergy-based motion generation of current anthropomorphic hands generally employ the static posture synergy, which is extracted from quantities of joint trajectory, to design the mechanism or control strategy. Under this framework, the temporal weight sequences of each synergy from pregrasp phase to grasp phase are required for reproducing any grasping task. Moreover, the zero-offset posture has to be preset before starting any grasp. Thus, the whole grasp phase appears to be unlike natural human grasp. Up until now, no work in the literature addresses these issues toward simplifying the continual grasp by only inputting the grasp pattern. In this paper, the kinematic synergies observed in angular velocity profile are employed to design the motion generation mechanism. The kinematic synergy extracted from quantities of grasp tasks is implemented by the proposed eigen cam group in tendon space. The completely continual grasp from the fully extending posture only require averagely rotating the two eigen cam groups one cycle. The change of grasp pattern only depends on respecifying transmission ratio pair for the two eigen cam groups. An illustrated hand prototype is developed based on the proposed design principle and the grasping experiments demonstrate the feasibility of the design method. The potential applications include the prosthetic hand that is controlled by the classified pattern from the bio-signal.

Shoulder kinematics and spatial pattern of trapezius electromyographic activity in real and virtual environments.

The design of an industrial workstation tends to include ergonomic assessment steps based on a digital mock-up and a virtual reality setup. Lack of interaction and system fidelity is often reported as a main issue in such virtual reality applications. This limitation is a crucial issue as thorough ergonomic analysis is required for an investigation of the biomechanics. In the current study, we investigated the biomechanical responses of the shoulder joint in a simulated assembly task for comparison with the biomechanical responses in virtual environments. Sixteen male healthy novice subjects performed the task on three different platforms: real (RE), virtual (VE), and virtual environment with force feedback (VEF) with low and high precision demands. The subjects repeated the task 12 times (i.e., 12 cycles). High density electromyography from the upper trapezius and rotation angles of the shoulder joint were recorded and split into the cycles. The angular trajectories and velocity profiles of the shoulder joint angles over a cycle were computed in 3D. The inter-subject similarity in terms of normalized mutual information on kinematics and electromyography was investigated. Compared with RE the task in VE and VEF was characterized by lower kinematic maxima. The inter-subject similarity in RE compared with intra-subject similarity across the platforms was lower in terms of movement trajectories and greater in terms of trapezius muscle activation. The precision demand resulted in lower inter- and intra-subject similarity across platforms. The proposed approach identifies biomechanical differences in the shoulder joint in both VE and VEF compared with the RE platform, but these differences are less marked in VE mostly due to technical limitations of co-localizing the force feedback system in the VEF platform.

Multicolor particle shadow accelerometry

This paper describes the extension of multicolor particle shadow velocimetry (CPSV) to the measurement of local acceleration in an Eulerian frame of reference. A validation experiment was conducted on a pendulous disk undergoing unsteady rigid body rotation. Angular velocity and acceleration profiles by CPSA are presented along with a comparison to recordings by an accelerometer mounted on the pendulum. CPSA is also demonstrated in a fully-developed turbulent pipe flow. Profiles of standard deviation of the local acceleration in the near wall region are compared to similar measurements by Christensen and Adrian. A favorable comparison is found between CPSA and particle image accelerometry (PIA). The effect of acceleration time delay, or the time between two velocity estimates, on local acceleration estimates is discussed.

Unsteady coupled heat and mass transfer by mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface in the presence of radiation and chemical reaction

The effects of radiation and chemical reaction on coupled heat and mass transfer by unsteady mixed convection boundary-layer flow of a micropolar fluid near the region of the stagnation point on a double-infinite vertical flat plate are studied. The free stream velocity and the surface temperature and concentration are assumed to vary linearly with the distance along the surface. The flow is impulsively set into motion and both of the temperature and concentration at the surface are also suddenly changed from that of the ambient fluid. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. A representative set of numerical results for the velocity, angular velocity, temperature and concentration profiles as well as the skin-friction coefficient, wall couple stress, Nusselt number and the Sherwood number is presented graphically for various parametric conditions and discussed.