Solid-body Rotation Research Articles

A flux-corrected RBF-FD method for convection dominated problems in domains and on manifolds

Abstract In this work, we present a Flux-Corrected Transport (FCT) algorithm for enforcing discrete maximum principles in Radial Basis Function (RBF) generalized Finite Difference (FD) methods for convection-dominated problems. The algorithm is constructed to guarantee mass conservation and to preserve positivity of the solution for irregular data nodes. The method can be applied both for problems defined in a domain or if equipped with level set techniques, on a stationary manifold. We demonstrate the numerical behavior of the method by performing numerical tests for the solid-body rotation benchmark in a unit square and for a transport problem along a curve implicitly prescribed by a level set function. Extension of the proposed method to higher dimensions is straightforward and easily realizable.

Rotational stabilisation of the Rayleigh–Taylor instability at the inner surface of an imploding liquid shell

A number of applications utilise the energy focussing potential of imploding shells to dynamically compress matter or magnetic fields, including magnetised target fusion schemes in which a plasma is compressed by the collapse of a liquid metal surface. This paper examines the effect of fluid rotation on the Rayleigh–Taylor (RT) driven growth of perturbations at the inner surface of an imploding cylindrical liquid shell which compresses a gas-filled cavity. The shell was formed by rotating water such that it was in solid body rotation prior to the piston-driven implosion, which was propelled by a modest external gas pressure. The fast rise in pressure in the gas-filled cavity at the point of maximum convergence results in an RT unstable configuration where the cavity surface accelerates in the direction of the density gradient at the gas–liquid interface. The experimental arrangement allowed for visualisation of the cavity surface during the implosion using high-speed videography, while offering the possibility to provide geometrically similar implosions over a wide range of initial angular velocities such that the effect of rotation on the interface stability could be quantified. A model developed for the growth of perturbations on the inner surface of a rotating shell indicated that the RT instability may be suppressed by rotating the liquid shell at a sufficient angular velocity so that the net surface acceleration remains opposite to the interface density gradient throughout the implosion. Rotational stabilisation of high-mode-number perturbation growth was examined by collapsing nominally smooth cavities and demonstrating the suppression of small spray-like perturbations that otherwise appear on RT unstable cavity surfaces. Experiments observing the evolution of low-mode-number perturbations, prescribed using a mode-6 obstacle plate, showed that the RT-driven growth was suppressed by rotation, while geometric growth remained present along with significant nonlinear distortion of the perturbations near final convergence.

Rotating-field-driven ensembles of magnetic particles.

Vortex patterns in ensembles of magnetic particles driven by a rotating field are studied. The driving arises due to the lubrication forces between the rotating particles acting in the direction perpendicular to the radius vector between the particles. Since the lubrication forces cannot be equilibrated by the radial forces due to the dipolar attraction and steric repulsion, the ensemble is in a nonequilibrium state. Different regimes are found for the dynamics of the driven ensembles-solid-body rotation at low frequency of the rotating field and stick-slip motion of the external layers of the aggregate with respect to the internal structure as the frequency is increased. The relation obtained for describing the angular velocity of the solid-body rotation is in good agreement with existing experimental data.

The effects of surface fossil magnetic fields on massive star evolution: I. Magnetic field evolution, mass-loss quenching, and magnetic braking

Abstract Surface magnetic fields have a strong impact on stellar mass loss and rotation and, as a consequence, on the evolution of massive stars. In this work, we study the influence of an evolving dipolar surface fossil magnetic field with an initial field strength of 4 kG on the characteristics of 15 M⊙ solar metallicity models using the Geneva stellar evolution code. Non-rotating and rotating models considering two different scenarios for internal angular momentum transport are computed, including magnetic field evolution, mass-loss quenching, and magnetic braking. Magnetic field evolution results in weakening the initially strong magnetic field; however, in our models, an observable magnetic field is still maintained as the star evolves towards the red supergiant phase. At the given initial mass of the models, mass-loss quenching is modest. Magnetic braking greatly enhances chemical element mixing if radial differential rotation is allowed for; on the other hand, the inclusion of surface magnetic fields yields a lower surface enrichment in the case of near solid-body rotation. Models including surface magnetic fields show notably different trends on the Hunter diagram (plotting nitrogen abundance versus vsin i) compared to those that do not. The magnetic models agree qualitatively with the anomalous ‘Group 2 stars’, showing slow surface rotation and high surface nitrogen enhancement on the main sequence.

Heat transfer due to revolving flow of Reiner-Rivlin fluid over a stretchable surface

The interaction of rotating flow and a stationary stretchable surface is discussed for a non-Newtonian Reiner-Rivlin fluid. The radial variation of the disk’s surface temperature follows a power law. Similarity solutions of the governing partial differential equations are obtained for the case of the outer flow in solid-body rotation. The resulting coupled and highly nonlinear system of equations are solved numerically. The solutions indicate that the disk stretching has prominent effects on both momentum and thermal boundary layers. The strength of the induced secondary flow in the boundary layer decreases significantly with an increase in the stretching parameter. Stretching dominates the oscillatory nature of the velocity profiles. As a result of reduction in the momentum boundary layer, the thermal boundary layer thickness decreases significantly with an increase in the radial stretching. On the other hand, shrinking of the disk has opposite effects on the boundary layers. An asymptotic analysis has also been carried out to support the obtained numerical results.

Instability of precession driven Kelvin modes: Evidence of a detuning effect

We report an experimental study of the instability of a nearly-resonant Kelvin mode forced by precession in a cylindrical vessel. The instability is detected above a critical precession ratio via the appearance of peaks in the temporal power spectrum of pressure fluctuations measured at the end-walls of the cylinder. The corresponding frequencies can be grouped into frequency sets satisfying resonance conditions with the forced Kelvin mode. We show that one triad is associated with a parametric resonance of Kelvin modes. For the first time, we observe a significant frequency variation of the unstable modes with the precession ratio. We explain this frequency modification by considering a detuning mechanism due to the slowdown of the background flow. By introducing a semi-analytical model, we show that the departure of the flow from the solid body rotation leads to a modification of the dispersion relation of Kelvin modes and to a detuning of the resonance condition. Our calculations reproduce the features of experimental measurements. We also show that a second frequency set, including one very low frequency as observed in the experiment, does not exhibit the properties of a parametric resonance between Kelvin modes. Our observations suggest that it may correspond to the instability of a geostrophic mode.

Experimental lateral wall boundary layer behavior of a differentially rotating split-cylinder flow.

The cylindrical wall boundary layer of a closed cylinder split in two halves at the equator is studied experimentally. When these two parts rotate in exact corotation the internal flow is essentially in solid-body rotation at the angular velocity of both halves. When a slight difference between the rotation frequencies is established a secondary flow is created due to the differential rotation between both sides and restricted to the boundary layer. This behavior of the boundary layer is compared with theoretical and numerical results finding the "sandwich" structure of a Stewartson boundary layer. Time-dependent waves are observed near the cylindrical wall. Their behavior for different values of the control parameters are presented. Finally, a global recirculation mode is also found due to a symmetry-breaking induced between sides that appears because of a slight misalignment of the experimental setup, whose characteristics are compatible with the behavior of a precessing cylinder.

Time-dependent lift and drag on a rigid body in a viscous steady linear flow

We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid-body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow.

Multicomponent Kinematics in a Massive Filamentary Infrared Dark Cloud

Abstract To probe the initial conditions for high-mass star and cluster formation, we investigate the properties of dense filaments within the infrared dark cloud (IRDC) G035.39–00.33 (G035.39) in a combined Very Large Array and Green Bank Telescope mosaic tracing the NH3 (1, 1) and (2, 2) emission down to 0.08 pc scales. Using agglomerative hierarchical clustering on multiple line-of-sight velocity component fitting results, we identify seven extended velocity-coherent components in our data, likely representing spatially coherent physical structures, some exhibiting complex gas motions. The velocity gradient magnitude distribution peaks at its mode of 0.35 and has a long tail extending into higher values of 1.5–2 , and it is generally consistent with those found toward the same cloud in other molecular tracers and with the values found toward nearby low-mass dense cloud cores at the same scales. Contrary to observational and theoretical expectations, we find the nonthermal ammonia line widths to be systematically narrower (by about 20%) than those of N2H+ (1–0) line transition observed with similar resolution. If the observed ordered velocity gradients represent the core envelope solid-body rotation, we estimate the specific angular momentum to be about 2 × 1021 cm2 s−1, similar to the low-mass star-forming cores. Together with the previous finding of subsonic motions in G035.39, our results demonstrate high levels of similarity between kinematics of a high-mass star-forming IRDC and the low-mass star formation regime.

Helical vortex core dynamics and flame interaction in turbulent premixed swirl combustion: A combined experimental and large eddy simulation investigation

In this study, a combined experimental and Large Eddy Simulation (LES) investigation is performed to identify the vortical structures, their dynamics, and interaction with a turbulent premixed flame in a swirl-stabilized combustor. Our non-reacting flow experiment shows the existence of large scale precessing motion, commonly observed for such flows. This off-axis precessing dynamics disappears with combustion but only above a critical equivalence ratio at which the flame attaches to the swirler centerbody and vortex breakdown changes from a cone to a bubble type. For compact flames stabilized along the inner shear layer (ISL), no precessing is seen, but large scale vortices along the ISL are observed; these structures interact with the ISL-stabilized flame and contribute to its wrinkling as revealed by laser-induced fluorescence data. After validating the LES results in terms of low order statistics and point temperature measurements in relevant areas of the flow, we show that it can capture the precessing motion in the non-reacting flow and its suppression with combustion. The simulations show that the ISL vortices in the reacting case originate from a vortex core that is formed at the swirler’s centerbody. This vortex core has a conical helical shape that interacts—as it winds out—with the ISL and the flame stabilized along it. The simulated helical vortex core (HVC) exists in both reacting and non-reacting flows; in the latter, it is dominated by the off-axis motion, whereas in the reacting case, that motion is damped and only remains the cork-screw type solid body rotation of the HVC.

Simulation of Wingtip Vortex Flows with Reynolds-Averaged Navier–Stokes and Scale-Resolving Simulation Methods

The simulation of wingtip vortex flows is investigated with Reynolds-averaged Navier–Stokes (RANS) equations and scale-resolving simulation (SRS) models. These range from turbulent viscosity and Reynolds-stress model (RSM) RANS closures, to hybrid and bridging SRS methods. The objective of the study was threefold: assess the relevance of replicating the experimental flow conditions, evaluate the numerical requisites of each mathematical model, and determine their modeling accuracy in prediction of a representative wingtip vortex flow. The selected problem is the flow around a NACA 0012 wing at 10 deg of angle of attack and Reynolds number of . The results confirm the relevance of reproducing the experimental flow conditions, in particular at the inlet boundary where the flow is not uniform. For this reason, the evaluation of modeling errors using the available measurements requires the specification of the experimental inlet conditions. On the other hand, the quantification of the modeling error indicates that solely RANS–RSM can achieve an accurate representation of the flow dynamics. Whereas the well-recognized limitations of turbulent viscosity RANS closures to deal with solid-body rotation lead to the overprediction of turbulence and consequent rapid diffusion of the wingtip vortex, the predictive use of SRS methods may reveal excessively complex and demanding.

Flow attenuation due to the addition of rigid rod-like particles

Interactions between fluid flow, in particular, turbulent flow, and solid particles are complex because many parameters control the interactions. In experiments of particle-laden turbulent flow, it is difficult to identify the scale of vortices which interacts strongly with the particles, since vortices of various scales coexist in turbulence. We, therefore, focus on the effect of the addition of solid particles to a single-scale vertical flow. More concretely, in our experiments, we use a container with a spherical cavity of 180 mm diameter. The container is filled with water and many rigid rod-like particles (the length is 12 mm and the diameter is 2 mm) are laden. We rotate the container at a constant angular velocity to create a swirling flow. This flow would be the solid-body rotation if the particles were not added. Our experiments show that the flow velocity in a central region of the cavity is drastically reduced when we add particles with a density slightly higher than that of the working fluid. We aim to explore the physical mechanism of this suppression phenomenon. For this purpose, we quantify the suppression rate by using particle tracking velocimetry (PTV) and reveal the condition when the addition of rod-like particles suppresses the swirling flow.

Parameters of the Link between the Optical and Radio Frames from Gaia DR2 Data and VLBI Measurements

Based on published data, we have assembled a sample of 88 radio stars for which there are both trigonometric parallax and proper motion measurements in the Gaia DR2 catalogue and VLBI measurements. A new estimate of the systematic offset between the optical and radio frames has been obtained by analyzing the GaiaDR2-VLBI trigonometric parallax differences: $\Delta\pi=-0.038\pm0.046$ mas (with a dispersion of 0.156 mas). This means that the Gaia DR2 parallaxes should be increased by this correction. The parallax scale factor is shown to be always very close to unity within $\sim$3 kpc of the Sun: $b=1.002\pm0.007.$ Our analysis of the proper motion differences for the radio stars based on the model of solid-body mutual rotation has revealed no rotation components differing significantly from zero: $(\omega_x,\omega_y,\omega_z)=(-0.14,0.03,-0.33)\pm(0.15,0.22,0.16)$ mas yr$^{-1}.$

Axisymmetric rotating flow with free surface in a cylindrical tank

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

Evolution of Hubble wedges in episodic protostellar outflows

Young low-mass protostars undergo short phases of high accretion and outburst activity leading to lumpy outflows. Recent observations have shown that the position-velocity and mass-velocity diagrams of such outflows exhibit individual bullet-like features; some of these bullets subscribe to a `Hubble Law' velocity relation, and others are manifest as `Hubble wedges'. In order to explore the origin of these features, we have developed a new episodic outflow model for the SPH code {\sc gandalf}, which mimics the accretion and ejection behaviour of FU Ori type stars. We apply this model to simulations of star formation, invoking two types of initial conditions: spherically symmetric cores in solid-body rotation with $\rho\propto r^{-2}$, and spherically symmetric turbulent cores with density proportional to the density of a Bonnor-Ebert sphere. For a wide range of model parameters, we find that episodic outflows lead to self-regulation of the ejected mass and momentum, and we achieve acceptable results, even with relatively low resolution. Using this model, we find that recently ejected outflow bullets produce a `Hubble wedge' in the position-velocity relation. However, once such a bullet hits the leading shock front, it decelerates and aligns with older bullets to form a `Hubble-law'. Bullets can be identified as bumps in the mass-velocity relation, which can be fit with a power-law, $dM/d\upsilon_{_{\rm RAD}}\propto\upsilon_{_{\rm RAD}}^{-1.5}$.

FRANCIS G. PEASE AND THE FIRST GALACTIC ROTATION CURVES (1916‒1922)

With the 60-inch reflector at Mount Wilson Observatory, Francis G. Pease obtained the first measurements of the rotation curves of two nearly edge-on spiral galaxies, NGC 4594 (the Sombrero Galaxy) and NGC 224 (the Andromeda Galaxy) in 1916 and 1918, respectively. Pease aligned the spectrograph's slit with the major axes of the galaxies' foreshortened elliptical figures and obtained direct measurements of the Doppler-induced radial velocity components along their axes. This technique originally had been applied in 1895 by James E. Keeler to a rotational analysis of the rings of Saturn. By subtracting out the radial velocities of their centers, Pease obtained their rotational velocities as a function of distance away from the centers. This enabled him to determine that linear relationships existed in both cases, whereby these objects appeared to show evidence of solid-body rotations out to (and beyond) the limits that could be observed spectroscopically (about 2.5 arcminutes from their centers). These relationships contradicted the behaviors of planets that orbited our Sun, and indicated that the objects' mass distributions likewise increased in direct proportion away from the centers. Pease's dynamical results were applied in two independent cases (by Ernst J. Öpik and Knut Lundmark) to a greater understanding of the distance and nature of the 'spiral nebulae' in the aftermath of the 'Great Debate'. Yet, the remaining questions posed by Pease's data were not effectively answered for two decades (or more) until Horace W. Babcock extended spectroscopic investigations into the disk region of the Andromeda Galaxy and showed that those stellar velocities were largely independent of their distances from the center. Along with many other examples, this finding was later confirmed by Vera Rubin and her colleagues and has become one of the leading forms of evidence for the existence of dark matter in galaxies.

Lyman α photons through rotating outflows

Outflows and rotation are two ubiquitous kinematic features in the gas kinematics of galaxies. Here we introduce a semi-analytic model to quantify how rotating outflows impact the morphology of the Lyman-$\alpha$ emission line. The model is contrasted against Monte Carlo radiative transfer simulations of outflowing gas with additional solid body rotation. We explore a range of neutral Hydrogen optical depth of $10^5 \leq \tau_{\mathrm{H}} \leq10^7$, rotational velocity $0 \leq v_{\mathrm{rot}}/\mathrm{km\ s}^{-1} \leq 100$ and outflow velocity $0\leq v_{\mathrm{out}}/\mathrm{km\ s}^{-1} \leq 50$. We find three consequences of rotation. First, it introduces a dependency with viewing angle; second it broadens the line and third it increases the flux at the line's center. For all viewing angles, the semi-analytic model reproduces the radiative transfer results for the line width and flux change at the line's center within a $7\%$ and $50\%$ precision for an optical depth of $\tau_{\mathrm{H}}=10^5$, respectively, and within $2\%$ and $1\%$ for an optical depth of $\tau_{\mathrm{H}}=10^7$. Using this model we also show that the peaks of integrated spectra taken from opposite sides of an edge-on rotating gas distribution should have a separation of $\frac{1}{2}v_{\mathrm{rot}}$. The semi-analytic model presented here is a convenient tool to introduce rotational kinematics as a post-processing step of idealized Monte Carlo simulations; it provides a framework to interpret \lya spectra in systems where rotation is expected or directly measured through kinematic maps.

A dynamic simplified Lund model for large-eddy simulation and its application to a centrifugal pump

PurposeConstruct a new sub-grid scale (SGS) model which can improve the efficiency and maintain comparative accuracy comparing to the existing dynamic cubic non-linear SGS model (DCNM).Design/methodology/approachThe polynomial constitutive relation between the SGS stress tensor and both strain and rotation rate is selected as a basement. Simplification is achieved by eliminating the solid-body rotation term and adopting the assumption proposed by Kosovic. A dynamic procedure is applied to calculate three model coefficients in the new model. The new model (named dynamic simplified Lund model) and DCNM are applied to the rotating channel flow and the internal flow in a centrifugal pump impeller to examine the performance.FindingsThe new model is as accurate as DCNM but decreases 25 per cent computational resources. The ability of capturing rotation effect and reflecting backscatter is verified through cases. In addition, good numerical stability is shown during the calculation.Research limitations/implicationsMore benchmark and engineering cases should be used to get further confidence on the new model.Practical implicationsThe new model is promising in industrial application with the advantage of both accuracy and efficiency. For the flow with large-scale separation or more complicate phenomenon, the model is thought to give accurate flow structure.Originality/valueA new non-linear SGS model is proposed in this paper. The accuracy, numerical stability and efficiency are validated for this model. Therefore, it is promising in the prediction of the flow structure in centrifugal pumps.

Vortex-induced vibration of finite-length circular cylinders with spanwise free-ends: Broadening the lock-in envelope

The unsteady response of finite-length rigid circular cylinders with spanwise free-ends undergoing vortex-induced vibration (VIV) has been experimentally investigated in a large-scale wind tunnel. The model consists of a cylinder mounted on the upstream tip of an elastic cantilever beam, thus allowing the investigation of the effects of the aspect-ratio on the VIV dynamic response of the system. Models with different aspect-ratios have been tested, and the time dependent oscillation amplitude of the cylinder has been determined from the analysis of images obtained with a high-speed camera. The solid body rotation of the vibrating cylinder and the vorticity flux generated by this moving boundary, entering the flow field, are associated with the formation of large vortical structures and increased forcing on the cylinder. Surprisingly, the results show an unexpected broadening of the lock-in envelope by about 200% as the aspect-ratio decreases from 28.8 to 5 and an almost 230% increase in the peak oscillation amplitude. The reduced damping parameter known as the Skop-Griffin parameter has been used to interpret these novel results. The Griffin plot shows a reasonably good agreement between the present experimental data of different aspect-ratio cylinders and those of other investigators.

The ESO Multi-instrument Kinematic Survey (MIKiS) of Galactic Globular Clusters: Solid-body Rotation and Anomalous Velocity Dispersion Profile in NGC 5986∗

Abstract As part of the ESO-VLT Multi-Instrument Kinematic Survey of Galactic globular clusters (GCs), we present a detailed investigation of the internal kinematics of NGC 5986. The analysis is based on about 300 individual radial velocities of stars located at various distances from the cluster center, up to 300″ (about four half-mass radii). Our analysis reveals the presence of a solid-body rotation extending from the cluster center to the outermost regions probed by the data, and a velocity dispersion profile initially declining with the distance from the cluster’s center, but flattening and staying constant at ∼5 km s−1 for distances larger than about one half-mass radius. This is the first GC for which evidence of the joint presence of solid-body rotation and flattening in the outer velocity dispersion profile has been found. The combination of these two kinematical features provides a unique opportunity to shed light on fundamental aspects of GC dynamics and to probe the extent to which internal relaxation, star escape, angular momentum transport and loss, and the interaction with the Galaxy tidal field can affect a cluster’s dynamical evolution and determine its current kinematical properties. We present the results of a series of N-body simulations illustrating the possible dynamical paths leading to kinematic features like those observed in this cluster and the fundamental dynamical processes that underpin them.