High Rotation Rates Research Articles

Instability and sensitivity of the flow around a rotating circular cylinder

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a role of ‘wavemaker’ in the excitation of the global instability is identified by considering the structural sensitivity of the unstable mode. This approach is compared with the analysis of the perturbation kinetic energy production, a classic approach in linear stability analysis. Multiple steady-state solutions are found at high rotation rates, explaining the quenching of the second shedding mode. Turning points in phase space are associated with the movement of the flow stagnation point. In addition, a method to examine which structural variation of the base flow has the largest impact on the instability features is proposed. This has relevant implications for the passive control of instabilities. Finally, numerical simulations of the flow are performed to verify that the structural sensitivity analysis is able to provide correct indications on where to position passive control devices, e.g. small obstacles, in order to suppress the shedding modes.

An overview of Boeing flywheel energy storage systems with high-temperaturesuperconducting bearings

An overview summary of recent Boeing work on high-temperature superconducting (HTS)bearings is presented. A design is presented for a small flywheel energy storage system thatis deployable in a field installation. The flywheel is suspended by a HTS bearing whosestator is conduction cooled by connection to a cryocooler. At full speed, the flywheel has5 kW h of kinetic energy, and it can deliver 3 kW of three-phase 208 V power to anelectrical load. The entire system, which includes a containment structure, iscompatible with transportation by forklift or crane. Laboratory measurements of thebearing loss are combined with the parasitic loads to estimate the efficiency ofthe system. Improvements in structural composites are expected to enable theoperation of flywheels with very high rim velocities. Small versions of such flywheelswill be capable of very high rotational rates and will likely require the low lossinherent in HTS bearings to achieve these speeds. We present results of experimentswith small-diameter rotors that use HTS bearings for levitation and rotate invacuum at kHz rates. Bearing losses are presented as a function of rotor speed.

A New Sobolev Gradient Method for Direct Minimization of the Gross–Pitaevskii Energy with Rotation

In this paper we improve traditional steepest descent methods for the direct minimization of the Gross–Pitaevskii (GP) energy with rotation at two levels. We first define a new inner product to equip the Sobolev space $H^1$ and derive the corresponding gradient. Second, for the treatment of the mass conservation constraint, we use a projection method that avoids more complicated approaches based on modified energy functionals or traditional normalization methods. The descent method with these two new ingredients is studied theoretically in a Hilbert space setting, and we give a proof of the global existence and convergence in the asymptotic limit to a minimizer of the GP energy. The new method is implemented in both finite difference and finite element two-dimensional settings and is used to compute various complex configurations with vortices of rotating Bose–Einstein condensates. The new Sobolev gradient method shows better numerical performances compared to classical $L^2$ or $H^1$ gradient methods, especially when high rotation rates are considered.

Characterization of the drag force in an air-moderated granular bed

We measure the torque acting on a rod rotated perpendicular to its axis in a granular bed, through which an upflow of gas is utilized to tune the hydrostatic loading between grains. At low rotation rates the torque is independent of speed, but scales quadratically with rod-length and linearly with depth; the proportionality approaches zero linearly as the upflow of gas is increased towards a critical value above which the grains are fluidized. At high rotation rates the torque exhibits quadratic rate-dependence and scales as the rod's length to the 4th power. The torque has no dependence on either depth or airflow at these higher rates. A model used to describe the stopping force experienced by a projectile impacting a granular bed can be shown to predict these behaviors for our system's geometry, indicating that the same mechanics dictate both steady-state and transient drag forces in granular systems, regardless of geometry or material properties of the grains.

Out-of-plane librations of spinning tethered satellite systems

We analyze the out-of-plane librations of a tethered satellite system that is nominally rotating in the orbit plane. To isolate the librational dynamics, the system is modeled as two point masses connected by a rigid rod with the system mass center constrained to an unperturbed circular orbit. For small out-of-plane librations, the in-plane motion is unaffected by the out-of-plane librations and a solution for the in-plane motion is determined in terms of Jacobi elliptic functions. This solution is used in the linearized equation for the out-of-plane librations, resulting in a Hill’s equation. Floquet theory is used to analyze the Hill’s equation, and we show that the out-of-plane librations are unstable for certain ranges of in-plane spin rate. For relatively high in-plane spin rates, the out-of-plane librations are stable, and the Hill’s equation can be approximated by a Mathieu’s equation. Approximate solutions to the Mathieu’s equation are determined, and we analyze the dominant characteristics of the out-of-plane librations for high in-plane spin rates. The results obtained from the analysis of the linearized equations of motion are compared to numerical simulations of the nonlinear equations of motion, as well as numerical simulations of a more realistic system model that accounts for tether flexibility. The instabilities discovered from the linear analysis are present in both the nonlinear system and the more realistic system model. The approximate solutions for the out-of-plane librations compare well to the nonlinear system for relatively high in-plane rotation rates, and also capture the significant qualitative behavior of the flexible system.

Explicit algebraic subgrid stress models with application to rotating channel flow

New explicit subgrid stress models are proposed involving the strain rate and rotation rate tensor, which can account for rotation in a natural way. The new models are based on the same methodology that leads to the explicit algebraic Reynolds stress model formulation for Reynolds-averaged Navier–Stokes simulations. One dynamic model and one non-dynamic model are proposed. The non-dynamic model represents a computationally efficient subgrid scale (SGS) stress model, whereas the dynamic model is the most accurate. The models are validated through large eddy simulations (LESs) of spanwise and streamwise rotating channel flow and are compared with the standard and dynamic Smagorinsky models. The proposed explicit dependence on the system rotation improves the description of the mean velocity profiles and the turbulent kinetic energy at high rotation rates. Comparison with the dynamic Smagorinsky model shows that not using the eddy-viscosity assumption improves the description of both the Reynolds stress anisotropy and the SGS stress anisotropy. LESs of rotating channel flow at Reτ = 950 have been carried out as well. These reveal some significant Reynolds number influences on the turbulence statistics. LESs of non-rotating turbulent channel flow at Reτ = 950 show that the new explicit model especially at coarse resolutions significantly better predicts the mean velocity, wall shear and Reynolds stresses than the dynamic Smagorinsky model, which is probably the result of a better prediction of the anisotropy of the subgrid dissipation.

Relativistic g-modes in rapidly rotating neutron stars

We study the g-modes of fast rotating stratified neutron stars in the general relativistic Cowling approximation, where we neglect metric perturbations and where the background models take into account the buoyant force due to composition gradients. This is the first paper studying this problem in a general relativistic framework. In a recent paper by Passamonti et al.(2009), a similar study was performed within the Newtonian framework, where the authors presented results about the onset of CFS-unstable g-modes and the close connection between inertial- and gravity-modes for sufficiently high rotation rates and small composition gradients. This correlation arises from the interplay between the buoyant force which is the restoring force for g-modes and the Coriolis force which is responsible for the existence of inertial modes. In our relativistic treatment of the problem, we find an excellent qualitatively agreement with respect to the Newtonian results.

High abnormal rotation rates of sunspots and flare productivity

Solar activity, such as flares and CMEs, affect the interplanetary medium, and Earth’s atmosphere. Therefore, to understand the Space Weather, we need to understand the mechanisms of solar activity. Towards this end, we use 1135 events of solar H α flares and the positional data of sunspots from the archive of Solar Geophysical Data (SGD) for the period January–April, 2000 and compute the abnormal rotation rates that lead to high flare productivity. We report that the occurrence of 5 or more flares in a day in association with a given sunspot group can be defined as high flare productivity and the sunspots that have an abnormal rotation rates of ∼4–10 deg day −1 trigger high flare productivity. Further, in order to compare the flare productivity expressed as the strength of the flux emitted, especially the soft X-ray (SXR) flares in the frequency range of 1–8 Å, we compute the flare index of SXR flares and find that 8 out of 28 active regions used in this study satisfy the requirement for being flare productive. This enables us to conclude that the high rotation rates of sunspots are an important mechanism to understand the flare productivity, especially numerical flare productivity that includes flares of all class.

Equilibrium states in homogeneous turbulence with baroclinic instability

The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ∂U i /∂x j = S δ i1 δ j3, a system rotation about the vertical axis with rate Ω, Ω i = Ωδ i3, and uniform buoyancy gradients in the spanwise $${(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)}$$ and vertical $${(\partial B{/}\partial x_3\,{=}\,N_v^2)}$$ directions. Computations based on the rapid distortion theory (RDT) are performed for several values of the rotation number R = 2Ω/S and the Richardson number $${R_i\,{=}\,N_v^2/S^2 <1 }$$ . It is shown that, during an initial phase, the energies and the buoyancy fluxes are sensitive to the effects of pressure and viscosity. At large time, the ratios of energies, as well as the normalized fluxes, evolve to an asymptotically constant value, while the pressure–strain correlation scaled with the product of the turbulent kinetic energy by the shear rate approaches zero. Accordingly, an analytical parametric study based on the “pressure-less” approach (PLA) is also presented. The analytical study indicates that, when R i < 1, there is an exponential instability and equilibrium states of turbulence, in agreement with RDT. The energies and the buoyancy fluxes grow exponentially for large times with the same rate (γ in St units). The asymptotic value of the ratios of energies yielded by RDT is well described by its PLA counterpart derived analytically. At R i = 0, the asymptotic value of γ increases with increasing R approaching 2 for high rotation rates. At low rotation rates, an important contribution to the kinetic energy comes from the streamwise kinetic energy, whereas, at high rotation rates, the contribution of the vertical kinetic energy is dominant. When 0 < R i < 1 and $${R\ne 0}$$ , the asymptotic value of γ decreases as R i increases so as it becomes zero at R i = 1.

On the stabilizing effect of the Coriolis force on the turbulent wake of a normal flat plate

The turbulent Karman vortex street behind a flat plate in a rotating fluid is explored by means of direct numerical simulations. The effect of the Coriolis force is often said to be stabilizing on the cyclonic side of the wake and destabilizing on the anticyclonic side. The present computer experiments reveal a more subtle influence of the system rotation. The turbulence is suppressed at the cyclonic side of the wake at Rossby numbers of about unity whereas the cyclonic Karman roller eddies persist. The anticyclonic vortex cells which are blurred by the enhanced turbulence level are scarcely visible. The Strouhal number of this asymmetric vortex shedding is slightly higher than in the absence of rotation. At even higher rotation rates, the three-dimensional turbulence is suppressed also along the anticyclonic side of the wake and a nearly symmetric vortex street is observed at Rossby number of 0.16 with the Strouhal number significantly lower than for the nonrotating wake. At this rotation rate, the anticyclonically shed cells appeared as high-pressure zones. At even lower Rossby numbers, not only the turbulence but also the periodic vortex shedding is suppressed, in accordance with the demarcation line in a Rossby–Ekman number flow regime map.

YELLOW SUPERGIANTS IN THE ANDROMEDA GALAXY (M31)

The yellow supergiant content of nearby galaxies can provide a critical test of stellar evolution theory, bridging the gap between the hot, massive stars and the cool red supergiants. But, this region of the color-magnitude diagram is dominated by foreground contamination, requiring membership to somehow be determined. Fortunately, the large negative systemic velocity of M31, coupled to its high rotation rate, provides the means for separating the contaminating foreground dwarfs from the bona fide yellow supergiants within M31. Using the MMT, we obtained spectra of about 2900 stars, selected using the color and magnitude range to be yellow supergiants. Comparing the velocities to that of M31's rotation curve, we identified 54 certain, and 66 probable yellow supergiants from among the sea of foreground dwarfs. We find excellent agreement between the location of yellow supergiants in the H-R diagram and that predicted by the latest Geneva evolutionary tracks which include rotation. However, the relative number of yellow supergiants seen as a function of mass varies from that predicted by the models by a factor of more than 10, in the sense that more high mass yellow supergiants are predicted than are actually observed. Comparing the total number of yellow supergiants with masses above 20Mo with the estimated number of unevolved O stars indicates that the duration of the yellow supergiant phase is about 3000 years. This is consistent with what the 12Mo and 15Mo evolutionary tracks predict, but disagrees with the 20,000-80,000 year time scales predicted by the models for higher masses.

New Dissipative Leapfrog Finite Difference Scheme for Elastodynamic Simulation in Noninertial Frames

A new approach to numerically solving problems of the elastodynamics of arbitrarily shaped bodies with nonuniform material properties in rotation has been proposed in the present study. The present approach is based on first principles and is well suited to the study of problems of fluid-structure interaction and wave-based structural health monitoring. The governing hyperbolic partial differential equations of elastodynamics are cast in strong conservation form in the noninertial frame of reference and in generalized curvilinear coordinates. The results are obtained directly in the time domain. No special boundary treatment is required at material interfaces, and predictions can be made with and without material damage in a given structure for damage detection of the structure. The effect on the dynamics of a rotating annulus due to centrifugal force and, additionally, Coriolis force at high rates of rotation is studied. The partial differential equations are solved using a new dissipative time-centered leapfrog scheme presented here. A one-dimensional theoretical analysis of the numerical scheme shows that the new scheme has well-defined stability and dissipation characteristics. A comparison of the new scheme with a conventional dissipative time-centered leapfrog scheme shows that much larger time steps can be taken with the new scheme than allowed by the existing scheme. A dissipation-dependence study demonstrates that as the dissipation parameter is decreased, the steady-state solution uniformly approaches the exact solution. For larger values of this parameter, although the natural frequency of the system is not altered, the system vibrations damp too quickly, and the steady-state solution deviates from the exact steady-state solution. The larger the dissipation parameter, the larger this deviation from the exact steady state. The present scheme is very simple to incorporate in a finite difference simulation of elastodynamics in generalized curvilinear coordinates, and it has been used in the software FiDDLE, which solves the velocity-stress system of elastodynamic partial differential equations. It will be used in simulating fluid-elastodynamic interaction of the Mars Science Laboratory canopies and other decelerators such as inflatable aerodynamic devices as well as in wave-based structural health monitoring of these systems. Other applications include elastodynamics of turbomachinery blades, computer disk drive, and cutting-tool industry applications.

The reduction of the misfit dislocation in non-doped AlAs/GaAs DBRs

The non-doped AlAs/GaAs distributed Bragg reflectors (DBRs) with density of misfit dislocation (MD) close to zero had been obtained. The reduction of MD density was achieved by increasing temperature distribution homogeneity on the growing crystal in consequence of higher rotation rate of the wafer. Two structures of DBR were crystallized using molecular beam epitaxy (MBE) under the same optimal growth condition. The growth runs differ only in the rotation rate of the wafers. X-ray topograph showed no residual MDs in case of faster rotation. The DBR structure with residual MD density is still highly strained. No additional relaxation process has occurred, what was confirmed by an angular position of DBR zeroth-order peak on high-resolution X-ray diffractometry (HRXRD) rocking curve.

Influence of process conditions on the separation behaviour of starch–gluten systems

Separation of wheat flour into its constituents starch and gluten was studied using a cone-cone shearing device, with emphasis on the effect of rotation rate, processing time, temperature and water content. This study confirms the two step mechanism previously proposed for the gluten migration: aggregation of gluten protein into gluten domains that subsequently migrate to the apex of the cone. The results show that optimal process conditions for gluten migration are different from the process conditions for gluten aggregation. While gluten agglomeration (step 1) benefits from high temperature, low rotation rate and high water content, gluten migration (step 2) is positively influenced by a high dough viscosity and higher rotation rate.

The effect of rotation on the stability of nuclear burning in accreting neutron stars

Hydrogen and/or helium accreted by a neutron star from a binary companion may undergo thermonuclear fusion. At different mass accretion rates different burning regimes are discerned. Theoretical models predict helium fusion to proceed as a thermonuclear runaway for accretion rates below the Eddington limit and as stable burning above this limit. Observations, however, place the boundary close to 10% of the Eddington limit. We study the effect of rotationally induced transport processes on the stability of helium burning. For the first time detailed calculations of thin helium shell burning on neutron stars are performed using a hydrodynamic stellar evolution code including rotation and rotationally induced magnetic fields. We find that in most cases the instabilities from the magnetic field provide the dominant contribution to the chemical mixing, while Eddington-Sweet circulations become important at high rotation rates. As helium is diffused to greater depths, the stability of the burning is increased, such that the critical accretion rate for stable helium burning is found to be lower. Combined with a higher heat flux from the crust, as suggested by recent studies, turbulent mixing could explain the observed critical accretion rate. Furthermore, close to this boundary we find oscillatory burning, which previous studies have linked to mHz QPOs. In models where we continuously lower the heat flux from the crust, the period of the oscillations increases by up to several tens of percents, similar to the observed frequency drift, suggesting that this drift could be caused by the cooling of deeper layers.

ROTATIONAL STABILIZATION OF MAGNETICALLY COLLIMATED JETS

We investigate the launching and stability of extragalactic jets through nonlinear magnetohydrodynamic (MHD) simulation and linear eigenmode analysis. In the simulations of jet evolution, a small-scale equilibrium magnetic arcade is twisted by a differentially rotating accretion disk. These simulations produce a collimated outflow which is unstable to the current driven m=1 kink mode for low rotational velocities of the accretion disk relative to the Alfven speed of the coronal plasma. The growth rate of the kink mode in the jet is shown to be inversely related to the rotation rate of the disk, and the jet is stable for high rotation rates. Linear MHD calculations investigate the effect of rigid rotation on the kink mode in a cylindrical plasma. These calculations show that the Coriolis force distorts the m=1 kink eigenmode and stabilizes it at rotation frequencies such that the rotation period is longer than a few Alfven times.

Bubble Pinch-Off in a Rotating Flow

We create air bubbles at the tip of a "bathtub vortex" which reaches to a finite depth. The bathtub vortex is formed by letting water drain through a small hole at the bottom of a rotating cylindrical container. The tip of the needlelike surface dip is unstable at high rotation rates and releases bubbles which are carried down by the flow. Using high-speed imaging we find that the minimal neck radius of the unstable tip decreases in time as a power law with an exponent close to 1/3. This exponent was found by Gordillo et al. [Phys. Rev. Lett. 95, 194501 (2005)10.1103/PhysRevLett.95.194501] to govern gas flow driven pinch-off, and indeed we find that the volume oscillations of the tip creates a considerable air flow through the neck. We argue that the Bernoulli pressure reduction caused by this air flow can become sufficient to overcome the centrifugal forces and cause the final pinch-off.

Reduction of Scratch on Brush Scrubbing in Post CMP Cleaning by Analyzing Contact Kinetics on Ultra Low-k Dielectric

Damage reduction during planarization is strongly required to avoid scratch generation leading to yield loss in an integrated circuit fabrication especially after implementation of ultra low-k dielectrics in Cu damascene structure. By analyzing contact characteristic on the advanced non-porous ultra low-k dielectric, fluorocarbon film, brush scrubbing at high rotation rate and low down pressure is proposed to satisfy both particle removal efficiency and scratch reduction in post CMP cleaning. Shear force increases with increasing in brush rotation rate because of enlargement of pressured area which is generated by fluid flow. Enhancement of contribution of fluid flow by increasing brush rotation rate with lowering down force to particle removable efficiency can be direction for future low-k compatible process.

Effect of Rotation on Thermal Convection in an Anisotropic Porous Medium with Temperature-dependent Viscosity

A linear stability analysis is performed for mono-diffusive convection in an anisotropic rotating porous medium with temperature-dependent viscosity. The Galerkin variant of the weighted residual technique is used to obtain the eigen value of the problem. The effect of Taylor–Vadasz number and the other parameters of the problem are considered for stationary convection in the absence or presence of rotation. Oscillatory convection seems highly improbable. Some new results on the parameters’ influence on convection in the presence of rotation, for both high and low rotation rates, are presented.

Kinetic analysis of the rotation rate of light-driven unidirectional molecular motors

The combination of a photochemical and a thermal equilibrium in overcrowded alkenes, which is the basis for unidirectional rotation of light-driven molecular rotary motors, is analysed in relation to the actual average rotation rates of such structures. Experimental parameters such as temperature, concentration and irradiation intensity could be related directly to the effective rates of rotation that are achieved in solution by means of photochemical and thermal reaction rate theory. It is found that molecular properties, including absorption characteristics and photochemical quantum yields, are of less importance to the overall rate of rotation than the experimental parameters. This analysis holds considerable implications in the design of experimental conditions for functional molecular systems that will rely on high rates of rotation, and shows that average rotation rates comparable to ATPase or flagella motors are within reach assuming common experimental parameters.