Critical Rotation Research Articles

Rotating asymmetric solitons in competing nonlinear media

We predict a novel family of off-center localized nonlinear modes in a rotating optical system. The whispering-gallery-like solitons bifurcate out from the symmetric fundamental solitons through a symmetry breaking. They can appear as localized spots, nearly flat-top beams and crescent-like patterns extending over the entire range of polar angles. At critical rotation frequency, asymmetric solitons transform into vortex solitons, whose topological charge gradually increases with the growth of the propagation constant. Asymmetric solitons rotate around the origin persistently during propagation and preserve their shape over arbitrary distance in almost the whole existence domain. Thus, we put forward the first example of stable asymmetric intermediate states in optical systems that bridge the symmetric fundamental solitons and the symmetric vortex solitons with different topological charges, through the variance of the propagation constant and rotation frequency.

Displacement flows in rotating pipes

<h2>Abstract</h2> Displacement flows frequently occur in natural phenomena and industrial applications, e.g., in lung airways, oil well cementing, coating and cleaning of processing machinery. We study experimentally and numerically the effects of a pipe axial rotation on buoyant miscible flows in inclined pipes, while considering three cases of progressively increasing complexity: (i) Newtonian exchange flows (Lyu et al., 2020), (ii) Newtonian displacement flows (Lyu & Taghavi, 2018), and (iii) viscoplastic displacement flows (Lyu & Taghavi, 2020). We show how the flow dynamics is governed by an elegant balance among the characteristic velocities of the flow. We demonstrate that increasing the pipe rotation speed induces transverse mixing and results in a complete removal of the displaced fluid by the displacing fluid, above a critical rotation speed. Our findings offer insights on how to improve displacement efficiency using rotational motion.

Stellar labels for hot stars from low-resolution spectra

We set out to determine stellar labels from low-resolution survey spectra of hot stars, specifically OBA stars with Teff ≳ 7500 K. This fills a gap in the scientific analysis of large spectroscopic stellar surveys such as LAMOST, which offers spectra for millions of stars at R ~ 1800 and covers 3800 Å ≤ λ ≤ 9000 Å. We first explore the theoretical information content of such spectra to determine stellar labels via the Cramér-Rao bound. We show that in the limit of perfect model spectra and observed spectra with signal-to-noise ratio ~50–100, precise estimates are possible for a wide range of stellar labels: not only the effective temperature, Teff, surface gravity, log g, and projected rotation velocity, vsin i, but also the micro-turbulence velocity,vmic, helium abundance, NHe/Ntot, and the elemental abundances [C/H], [N/H], [O/H], [Si/H], [S/H], and [Fe/H]. Our analysis illustrates that the temperature regime of Teff ~ 9500 K is challenging as the dominant Balmer and Paschen line strengths vary little with Teff. We implement the simultaneous fitting of these 11 stellar labels to LAMOST hot-star spectra using the Payne approach, drawing on Kurucz’s ATLAS12/SYNTHE local thermodynamic equilibrium spectra as the underlying models. We then obtain stellar parameter estimates for a sample of about 330 000 hot stars with LAMOST spectra, an increase by about two orders of magnitude in sample size. Among them, about 260 000 have good Gaia parallaxes (ω/σω &gt; 5), and their luminosities imply that ≳95% of them are luminous stars, mostly on the main sequence; the rest are evolved lower luminosity stars, such as hot subdwarfs and white dwarfs. We show that the fidelity of the results, particularly for the abundance estimates, is limited by the systematics of the underlying models as they do not account for nonlocal thermodynamic equilibrium effects. Finally, we show the detailed distribution of vsin i of stars with 8000–15 000 K, illustrating that it extends to a sharp cutoff at the critical rotation velocity, vcrit, across a wide range of temperatures.

SIMULATION OF FATIGUE CRACK GROWTH DURING TRANSVERSE VIBRATIONS OF A TURBINE SHAFT

In real operational conditions structural elements of steam turbines are subjected to a wide range of thermal and mechanical loading. Even substantial reserve of static and dynamic strength, laid down at the stage of turbine design, can not prevent the appearance of fatigue cracks in structural elements, which lead to catastrophic failures. One of the reasons of damage in structural elements of turbine is technological operations used in the process of manufacture (forging, turning, and milling, heat treatment), since they are accompanied with plastic deformation of material, which is the physical basis of the so-called distributed fatigue damage. It accumulates during long-term cyclic deformation and turns into local damage of a fatigue crack type. In addition, the appearance of cracks in turbine shafts is caused by complex geometry, that is, by the presence of fillets and grooves, which are stress concentrators and, therefore, potential areas of initiation and growth of fatigue cracks. The high pressure rotor of the K-200-130 steam turbine was used to simulate the process of crack growth at forced transverse vibrations of the rotor when it passes through the first critical speed. At this the amplitude-dependent energy dissipation typical for metallic materials was taken into account. There was estimated the maximum stresses arising in the rotor when it passed through the critical speed rotation and the number of loading cycles leading to the crack growth. It was assumed that a crack with a depth of about 1 mm has formed on the surface of the rotor, which is the maximum permissible depth according to the instructions for safe operation of the turbine. The growth rate of this crack is predicted based on the fracture mechanics approaches through the determined maximum stresses in the section with a crack and experimental dependences of the crack growth rate on the stress intensity factor range. Based on the model, the crack growth time is predicted until the rotor loses its bearing ability. Predictions are made for different scenarios of loading and mechanical properties of rotor steel.

Fermi bubbles: the collimated outburst needed to explain forward-shock edges

ABSTRACT The bipolar, non-thermal, high-latitude lobes known as the Fermi bubbles (FBs) are thought to originate from a massive energy release near the Galactic Centre (GC). We constrain the FB engine and the circumgalactic medium (CGM) by analytically and numerically modelling the FB edges as strong forward shocks, as inferred from recent observations. A non-directed energy release produces shocks too spherical to account for observations even for a maximally massive Galactic disc, critical CGM rotation, or injection effectively offset from the GC. In contrast, collimated injection nearly perpendicular to the disc can account for observations in both ballistic (free expansion) and slowdown regimes, as we show using a simple stratified evolution model verified by hydrodynamic simulations. FBs still in their ballistic regime require injection (at z ≃ 100 pc heights in our model) with a half-opening angle θ ≃ 4°, a normalized velocity β−2 ≡ v/(0.01c) ≳ 0.4, and an energy $E\gtrsim 2\beta _{-2}^2\times 10^{55}$ erg, launched $\mathbb {T}\simeq 3.3\beta _{-2}^{-1}$ Myr ago, showing a distinctive low-pressure region behind the bubble head. Slowing-down (mass accumulated) FBs require a faster injection, a thinner jet, a smaller E/(β−2θ)2, and a comparable $\mathbb {T}$, and follow a ballistic stage that must reach a height zs ≳ 5 kpc.

Properties of the Be-type stars in 30 Doradus

ABSTRACTThe evolutionary status of Be-type stars remains unclear, with both single-star and binary pathways having been proposed. Here, VFTS spectroscopy of 73 Be-type stars, in the spectral-type range, B0–B3, is analysed to estimate projected rotational velocities, radial velocities, and stellar parameters. They are found to be rotating faster than the corresponding VFTS B-type sample but simulations imply that their projected rotational velocities are inconsistent with them all rotating at near critical velocities. The de-convolution of the projected rotational velocities estimates leads to a mean rotational velocity estimate of 320–350 km s−1, approximately 100 km s−1 larger than that for the corresponding B-type sample. There is a dearth of targets with rotational velocities less than 0.4 of the critical velocity, with a broad distribution reaching up to critical rotation. Our best estimate for the mean or median of the rotational velocity is 0.68 of the critical velocity. Rapidly rotating B-type stars are more numerous than their Be-type counterparts, whilst the observed frequency of Be-type stars identified as binary systems is significantly lower than that for normal B-type stars, consistent with their respective radial-velocity dispersions. The semi-amplitudes for the Be-type binaries are also smaller. Similar results are found for a Small Magellanic Cloud Be-type sample centred on NGC 346 with no significant differences being found between the two samples. These results are compared with the predictions of single and binary stellar evolutionary models for Be-type stars. Assuming that a single mechanism dominated the production of classical Be-type stars, our comparison would favour a binary evolutionary history.

The vibration modal characteristics of drillstring in compound drilling

The compound drilling plays an important role in improving borehole quality. The modal analysis model of drillstring is established to analyze the modal of longitudinal vibration, lateral vibration and torsional vibration, respectively. Compared with longitudinal and torsional vibrations, the intrinsic frequency range of lateral vibration are smaller, and it is harder to prevent resonance by adjusting critical rotation speed in case of lateral vibration. The intrinsic frequency of drillstring decreases as drillstring length increases. The longer drillstring is, the larger the increase and the smaller the interval range between the intrinsic frequencies of orders will be. It is easier to cause resonance when the frequency of exciting forces changes. As the number of order increases, the intrinsic frequency of the three vibrations increases and their increase amplitude is: longitudinal vibration > torsional vibration > lateral vibration. The results are benefit for the drillstring design and improving the wellbore quality.

Automatic algorithm to obtain v sin i values via Fourier transform in the BeSOS database

ABSTRACT Be stars are found to rotate close to their critical rotation and therefore they are considered an important laboratory for the study of stellar rotation. In this context, we obtain the projected rotational velocity of a sample of classical Be southern stars in the BeSOS database via Fourier transforms in an automated way for several absorption lines at different epochs. A Gaussian profile is fitted to eight observed photospheric He i lines in order to select automatically from the profile the spectral signal given by areas under the curve of 95.45, 98.75, and 99.83 per cent, to obtain vsin i via the Fourier transform technique. The values obtained are in global agreement with the literature. Analysing only one line is not enough to set the vsin i value: depending on the line, the value in most cases is underestimated with respect to λ4471. When gravity-darkening effects are included, apparent values increase by ∼10 per cent. The resolution of the instrument Pontificia Universidad Catolica High Echelle Resolution Optical Spectrograph (PUCHEROS) used for BeSOS spectra ($R \sim 17\, 000$) constrains the theoretical lower bound possible to vsin i ∼ 100 km s−1. The procedure has limitations, using a linear limb-darkening function with ε = 0.6 for classical Be stars rotating close to the break-up velocity without gravity-darkening corrections, which cannot be negligible. Previous works measure vsin i values using just one spectral line and here we demonstrate that with more lines the results can vary. This could be due to the photospheric distribution of atomic transitions in classical Be stars.

Water modelling on particle dispersion during KR desulphurization process

ABSTRACT In the current study, a 1:7 scaled water model was established to investigate the dispersion of desulphurizer particles during the Kanbara Reactor (KR) desulphurization process. The concentration, movement, and dispersion of the particle in the liquid were visualized and analysed. The influence of the impeller rotation speed, immersion depth, particle density and addition amount, and ladle wall baffle on the particle dispersion were systematically studied. The minimum critical rotation speed at which particles began to disperse into the liquid under different parameters was obtained. A regression equation for the influence of the impeller immersion depth and particle mass proportion on the critical rotation speed was proposed. Particles were easier to be driven into the liquid by the stirring impeller due to the higher particle additions. The area proportion of dispersed particles using the baffle was increased by three times compared with the case without the baffle.

Electron scattering emission in the light curves of stars with centrifugal magnetospheres

ABSTRACT Strongly magnetic, rapidly rotating B-type stars with relatively weak winds form centrifugal magnetospheres (CMs), as the stellar wind becomes magnetically confined above the Kepler co-rotation radius. Approximating the magnetic field as a dipole tilted by an angle β with respect to the rotation axis, the CM plasma is concentrated in clouds at and above the Kepler radius along the intersection of the rotational and magnetic equatorial planes. Stellar rotation can bring such clouds in front of the stellar disc, leading to absorption of the order of 0.1 mag ($\sim 10 {{\ \rm per\ cent}}$ of continuum flux). However, some stars with prominent CMs, such as σ Ori E, show an emission bump in addition to absorption dips, which has been so far unexplained. We show that emission can occur from electron scattering towards the observer when CM clouds are projected off the stellar limb. Using the rigidly rotating magnetosphere model, modified with a centrifugal breakout density scaling, we present a model grid of photometric light curves spanning parameter space in observer inclination angle i, magnetic obliquity angle β, critical rotation fraction W, and optical depth at the Kepler radius τK. We show that τK of order unity can produce emission bumps of the magnitude ∼0.05 seen in σ Ori E. We discuss the implications for modelling the light curves of CM stars, as well as future work for applying the radiative transfer model developed here to 3D magnetohydrodynamic simulations of CMs.

Dynamical Tidal Love Numbers of Rapidly Rotating Planets and Stars

Abstract Tidal interactions play an important role in many astrophysical systems, but uncertainties regarding the tides of rapidly rotating, centrifugally distorted stars and gaseous planets remain. We have developed a precise method for computing the dynamical, nondissipative tidal response of rotating planets and stars, based on summation over contributions from normal modes driven by the tidal potential. We calculate the normal modes of isentropic polytropes rotating at up to ≃90% of their critical breakup rotation rates, and tabulate fits to mode frequencies and tidal overlap coefficients that can be used to compute the frequency-dependent, nondissipative tidal response (via potential Love numbers k ℓm ). Although fundamental modes (f-modes) possess dominant tidal overlap coefficients at (nearly) all rotation rates, we find that the strong coupling of retrograde inertial modes (i-modes) to tesseral (ℓ &gt; ∣m∣) components of the tidal potential produces resonances that may be relevant to gas giants like Jupiter and Saturn. The coupling of f-modes in rapid rotators to multiple components of both the driving tidal potential and the induced gravitational field also affect the tesseral response, leading to significant deviations from treatments of rotation that neglect centrifugal distortion and high-order corrections. For very rapid rotation rates (≳70% of breakup), mixing between prograde f-modes and i-modes significantly enhances the sectoral (ℓ = ∣m∣) tidal overlap of the latter. The tidal response of very rapidly rotating, centrifugally distorted planets or stars can also be modified by resonant sectoral f-modes that are secularly unstable via the Chandrasekhar–Friedman–Schutz mechanism.

Investigation of the direct utilization possibility of methane fermentation residue sludge as liquid fertilizer by micronization

ABSTRACT For establishing a sustainable society, it is crucial to reuse the organic waste as a material resource. Therefore, herein, we aim to pulverize the methane fermentation residue sludge by ball milling and high-speed agitation to directly utilize it as a liquid fertilizer. The solid particles in the sludge can be below 100 µm, corresponding to the nozzle diameter of the boom sprayer by both ball milling and high-speed agitation; when ball milling was carried out for at least 1 h, the ratio of coarse particles larger than 100 µm decreased by less than 10%. In addition, the phosphate-ion concentration in the sludge increased with a decrease in the particle size of solid in the sludge mainly due to increase in its specific surface area. Furthermore, we investigated the effects of various experimental conditions for ball milling on the pulverization efficiency. Results suggests that for grinding the soft solid particles in the sludge by ball milling, the volume ratio of the total medium balls and sludge, total volumes of the balls and sludge, and inner pot volume should be larger, while the ratio of the rotation speed to the critical rotation speed should be almost the same as those reported previously in the reports on grinding of inorganic particles to attain an effective pulverization.

SENSITIVITY OF STRENGTH, RIGID AND DYNAMIC CHARACTERISTICS OF THE CONSOLE ROTOR TO VARIATION OF DESIGN PARAMETERS

The analysis sensitivity of strength, rigid and dynamic characteristics of the console rotor to variation of design parameters in paper describes The speed of rotation of the shaft, the material of the impeller vary. The dependences of radial and axial displacements on the angular velocities of rotation and the modulus of elasticity of the impeller material are established. For objects of the type of rotary systems with a cantilever arrangement of the impeller, not one, but a set of criteria has been introduced into consideration, which should be taken into account in the research of this type of objects. The tendencies of change of the first and second critical rotational speeds from the modulus of elasticity, rotor rotational frequencies and density of the impeller material are also determined. On this basis, recommendations have been developed for determining the design parameters of the rotor part of the air blower with a cantilevered impeller. Keywords: air blower; critical rotation speed; natural vibration frequency; rotary system; stress-strain state

Damage analysis of rotation speed on corrosion film of 3Cr steel in the CO2 environment with silty sand

The 3Cr steel used as the tubing has serious corrosion damage in a flowing CO2 environment with silty sand. Hence, the investigation for the influence of flow velocity on the corrosion behavior of 3Cr steel has an important and practical significance. It could not only unveil the corrosion damage mechanism of the steel under dynamic conditions, but also provide a theoretical basis for the corrosion protection of the tubing. In this paper, the effect of flow velocity on the corrosion film of 3Cr steel in a CO2 environment with silty sand was investigated by adjusting rotation speed. The results revealed that the corrosion resistance of 3Cr steel was first reduced, followed by enhancing and then reduced as the rotation speed increased. There was a critical rotation speed for the transformation of corrosion mechanism of 3Cr steel, i.e., 600 r/min. When the rotation speed was lower than the critical speed, the mass transfer process of corrosive medium dominated the corrosion resistance of 3Cr steel, and silty sand participated in the formation of corrosion film. The increasing rotation speed accelerated the mass transfer process, which first reduced and then improved the corrosion resistance. When the rotation speed was higher than the critical speed, the shear stress of silty sand played a predominant role. At the same time, silty sand impinged on the corrosion film, and then destroyed the stability of the film, leading to a significant decrease of the corrosion resistance. Silty sand changed from participating in the corrosion film to destroying the corrosion film with increasing rotation speed.

Relationship between Critical Shoulder Angle and Rotator Cuff Tears in Patients with Non-Traumatic Shoulder Pain

Relationship between Critical Shoulder Angle and Rotator Cuff Tears in Patients with Non-Traumatic Shoulder Pain

Balancing high-speed rotors at low speed using optimized parametric excitation and tuned nonlinear feedback

The paper presents an improved slow-speed mass balancing procedure capable of reducing high-speed related imbalance. Parametric excitation is used to project the small imbalance forces onto a chosen mode of vibration, corresponding to a high critical rotation speed. The method employs two kinds of parametric excitation leading to combination and principal parametric resonances. The former projects the imbalance forces onto a selected vibration mode, and the latter significantly amplifies the dynamic response due to imbalance. In addition to the parametric excitations, specially tuned nonlinear feedback forces are applied to limit the response to desired vibration levels and achieve a pseudo-linear behavior. In situ proper tuning of the nonlinear terms, and parametric excitations, enables to increase both amplification and sensitivity to the imbalance forces without having to compromise between the two. The latter includes digital, nonlinear feedback that enhances the sensitivity to imbalance forces, while limiting the level of vibration. This method allows to identify the projection of the imbalance on any desired mode, and therefore to cancel them by adding or removing mass. An experimental realization of the method validates the theory with good accuracy.

Fragmenting Active Asteroid 331P/Gibbs

Abstract We describe active asteroid 331P/Gibbs (2012 F5) using archival Hubble Space Telescope (HST) data taken between 2015 and 2018. 331P is an outer main belt active asteroid with a long-lived debris trail that formed in 2011. Embedded in the debris trail we identify 19 fragments with radii between 0.04 and 0.11 km (albedo 0.05 assumed) containing about 1% of the mass of the primary nucleus. The largest shows a photometric range (∼1.5 mag), a V-shaped minimum, and a two-peaked lightcurve period near 9 hr, consistent with a symmetric contact binary. Less convincing explanations are that 331P-A is a monolithic, elongated splinter or that its surface shows hemispheric 4:1 albedo variations. The debris trail is composed of centimeter-sized and larger particles ejected with characteristic 10 cm s−1 speeds following a size distribution with index q = 3.7 ± 0.1 to 4.1 ± 0.2. The HST data show that earlier, ground-based measurements of the nucleus were contaminated by near-nucleus debris, which cleared by 2015. We find that the primary nucleus has effective radius 0.8 ± 0.1 km and is in rapid rotation (3.26 ± 0.01 hr), with a lightcurve range of 0.25 mag and a minimum density of 1600 kg m−3 if strengthless. The properties of 331P are consistent with (1) formation about 1.5 Myr ago by impact shattering of a precursor body, (2) spin-up by radiation torques to critical rotation, (3) ejection of about 1% of the nucleus mass in mid 2011 by rotational instability, and (4) subsequent evolution of the fragments and dispersal of the debris by radiation pressure.

Analytical simulation of influential parameters affecting grooved wet clutches performance underdisengagement condition

Innovating new approaches and effective methods to improve the efficiency of mechanical systems in terms of energy losses and environmental effects serve as an attractive domain for researchers and industries. Wet clutches are widely used in power transmission systems in automotive and other tribological mechanisms. The wet clutch has two functional modes; under the engaged state, in which two disks come into contact to each other, and under disengagement the plates are located at a very short distance from each other, and oil flows between them. In disengaged state, the differential speed of driving and driven units causes oil shearing within the clearance which leads to transmission of certain amount of drag torque from the driving to the output shaft. This transferred drag torque is distinguished as power loss in form of heat. The governing physical relation based on continuity equation and Navier–Stokes equations reveals that in a certain rotational velocity, the pressure gradient at the outer radius of the clutch becomes null, and, in this circumstance, aeration occurs that is known as critical rotation speed. Experimental findings provide evidence that geometry manipulation and considering grooves over the frictional disk, reduces the critical rotational speed. But there is a shortage of physical analytical relations to predict the pressure gradient in grooved wet clutches. Therefore, this article is aimed to introduce analytical model to evaluate grooved wet clutches performance in terms of drag torque and critical rotational speed under single-phase flow condition.

Influence of PDC bit cutter layout on stick–slip vibrations of deep drilling systems

This paper extends the class of two degrees-of-freedom (2 DOF) models that simulate the self-excited vibrations of a rotary drilling system, by considering PDC bits equipped with round cutters and a realistic cutter layout. The extension requires an elaborate bit/rock interaction model that involves bit characterization, cutter projection and correlating the bit/rock engagement with the bit motion history. The governing equations are state-dependent delay differential inclusions with two major sources of nonlinearities: the regenerative effect in both cutting and frictional components of the drilling force and the unilateral nature of the frictional force. To solve for the state variables, the technical challenges involve a search of many delays and a fast and accurate geometric computation, which are respectively resolved with a modified inverse algorithm and the polygon clipping technique. The linear stability analysis is formulated based on the geometric variations of the bit/rock engagement surfaces, which result in critical rotation speeds that separate various stability regions of the decoupled axial dynamics. Determined by the bit design, the resulting stability boundaries are defined in terms of the rotation speed and the nominal bit penetration per revolution. With the time simulation, it is verified that the stability map, in conjunction with the exact location of unstable axial poles, can be used to predict the occurrence of axial stick–slip oscillations in the coupled dynamics, which eventually lead to sustained torsional stick–slip oscillations.

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

In the Sun and Sun-like stars, it is believed that cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helicity in the plasma flows in their convection zones (CZs). Hence, it is expected that for each star, there is a critical dynamo number for the operation of a large-scale dynamo. As a star slows down, it is expected that the large-scale dynamo ceases to operate above a critical rotation period. In our study, we explore the possibility of the operation of the dynamo in the subcritical region using the Babcock–Leighton type kinematic dynamo model. In some parameter regimes, we find that the dynamo shows hysteresis behavior, i.e., two dynamo solutions are possible depending on the initial parameters—decaying solution if starting with weak field and strong oscillatory solution (subcritical dynamo) when starting with a strong field. However, under large fluctuations in the dynamo parameter, the subcritical dynamo mode is unstable in some parameter regimes. Therefore, our study supports the possible existence of subcritical dynamo in some stars which was previously demonstrated in a mean-field dynamo model with distributed α and MHD turbulent dynamo simulations.