Viscous Torque Research Articles

Dependence of the resonant magnetic perturbation penetration threshold on plasma parameters and ions in helical plasmas

We investigate the penetration threshold of resonant magnetic perturbation (RMP) by the external coils in the Large Helical Device (LHD) for various plasma aspect ratio configurations. The qualitative dependence on the collisionality is opposite to that in a high plasma aspect configuration; this is a quite unique property first found in the LHD. We also investigate the threshold dependence on the ion species, and find that the threshold in deuterium discharges is much smaller than that in hydrogen discharges. In all cases the thresholds are higher as the poloidal rotation becomes faster, which shows that poloidal rotation is the dominant driver to the RMP shielding. This is qualitatively consistent with the torque balance model between the electromagnetic and poloidal viscous torques. In a configuration of the LHD, the dependence of the threshold on the density is qualitatively similar to that in Ohmic tokamak plasmas, but the beta dependence is opposite to that of tokamaks. The difference arises from the cause of the viscous torque.

Effects of groove orientation on transmission characteristics of hydro-viscous film in the parallel-disk system

The disk groove can greatly influence the hydrodynamic behaviors of the rotating film, especially on the cooling performance and the transmission efficiency. In the present work, the effects of groove orientation on the hydro-viscous transmission of the parallel-disk system are investigated. The Reynolds equation and thermal equation, considering tangential Coriolis effect and temperature–viscosity dependency, are derived and solved. The effects of the groove orientation on the shear stress, load-carrying capacity, viscous torque, and transmission efficiency are analyzed. The results reveal that the Coriolis resisting torque can be restrained but the load-carrying capacity declines if the groove orientation is consistent with the rotating direction, and the variation of the transmission efficiency can even be inverted at the turning point of the groove orientation. Therefore, the effects of groove orientation must be paid more attention in the hydro-viscous transmission.

Trajectories of magnetically-actuated helical swimmers in cylindrical channels at low Reynolds numbers

Artificial microswimmers have a huge potential in various microfluidic and medical applications. Most of the swimming scenarios involve some kind of confinement such as arteries or microchannels for both natural and artificial swimmers. It is shown both experimentally and numerically that confinement influences the swimmer trajectories significantly at low Reynolds numbers. Magnetically-actuated helical microswimmers follow helical or straight trajectories depending on whether the tail is pushing or pulling the swimmer. To improve the understanding of this behavior, we use a direct numerical approach that couples a simple kinematic model with a computational fluid dynamics (CFD) model to solve steady Stokes equations for low Reynolds number swimming. The kinematic model updates the position and the orientation of the swimmer by using the linear and angular velocities from the CFD model at each instant. In addition to the viscous force, the external magnetic torque, the gravity force and the normal contact force on the swimmer are also considered in the CFD model. Simulations are used to study the effects of the Mason number, which is the ratio of viscous and magnetic torques, the diameter ratio of the swimmer and the channel, the tail length and the channel flow. In addition to improving the fundamental understanding, these results bear strong relevance to the development of control systems for microswimming robots.

The end of runaway: how gap opening limits the final masses of gas giants

Gas giants are thought to form by runaway accretion: an instability driven by the self-gravity of growing atmospheres that causes accretion rates to rise super-linearly with planet mass. Why runaway should stop at a Jupiter or any other mass is unknown. We consider the proposal that final masses are controlled by circumstellar disc gaps (cavities) opened by planetary gravitational torques. We develop a fully time-dependent theory of gap formation and couple it self-consistently to planetary growth rates. When gaps first open, planetary torques overwhelm viscous torques, and gas depletes as if it were inviscid. In low-viscosity discs, of the kind motivated by recent observations and theory, gaps stay predominantly in this inviscid phase and planet masses finalize at $M_{\rm final}/M_\star\sim(\Omega t_{\rm disc})^{0.07}(H/a)^{2.73}(G\rho_0/\Omega^2)^{1/3}$, with $M_\star$ the host stellar mass, $\Omega$ the planet's orbital angular velocity, $t_{\rm disc}$ the gas disc's lifetime, $H/a$ its aspect ratio, and $\rho_0$ its unperturbed density. This final mass is independent of the dimensionless viscosity $\alpha$ and applies to large orbital distances, typically beyond $\sim$10 AU, where disc scale heights exceed planet radii. It evaluates to a few Jupiter masses at 10-100 AU, increasing gradually with distance as gaps become harder to open.

The coupling between inertial and rotational eigenmodes in planets with liquid cores

The Earth is a rapidly rotating body. The centrifugal pull makes its shape resemble a flattened ellipsoid and Coriolis forces support waves in its fluid core, known as inertial waves. These waves can lead to global oscillations, or modes, of the fluid. Periodic variations of the Earth's rotation axis (nutations) can lead to an exchange of angular momentum between the mantle and the fluid core and excite these inertial modes. In addition to viscous torques that exist regardless of the shape of the boundaries, the small flattening of the core-mantle boundary (CMB) allows inertial modes to exert pressure torques on the mantle. These torques effectively couple the rigid-body dynamics of the Earth with the fluid dynamics of the fluid core. Here we present the first high resolution numerical model that solves simultaneously the rigid body dynamics of the mantle and the Navier-Stokes equation for the liquid core. This method takes naturally into account dissipative processes in the fluid that are ignored in current nutation models. We find that the Free Core Nutation (FCN) mode, mostly a toroidal fluid flow if the mantle has a large moment of inertia, enters into resonance with nearby modes if the mantle's moment of inertia is reduced. These mode interactions seem to be completely analogous to the ones discovered by Schmitt (2006) in a uniformly rotating ellipsoid with varying flattening.

Non-linear interplay between edge localized infernal mode and plasma flow

Non-linear interaction between the edge localized infernal mode (ELIM) and the plasma toroidal flow is numerically investigated, by solving the initial value problem for the n = 1 ELIM, where n is the toroidal mode number. The linear results show that the ELIM instability is strongly affected by a close-fitting resistive wall. The presence of a resistive wall can fully stabilize an otherwise flow-shear destabilized ELIM. The computed toroidal torques based on linear ELIM eigenfunctions show different radial distributions: neoclassical toroidal viscous torque has a global distribution, whilst the torques associated with the Maxwell and Reynolds stresses largely peak near rational surfaces. The non-linear interplay between the unstable ELIM and the plasma flow tends to push the mode towards a more stable domain, no matter where the instability starts. This may help to understand some of the underlying physics for the experimentally observed edge harmonic oscillations in tokamak H-mode plasmas.

Modeling of a Chaotic Gyrostat System and Mechanism Analysis of Dynamics Using Force and Energy

Incorporating both viscous friction torque and external torque, a mathematical model of a gyrostat system consisting of three rotors and a fixed outer frame is configured. This model is transformed into a Kolmogorov‐type system for force analysis. The force field in the gyrostat system includes four different torques—inertial, internal, dissipative, and external. Correspondingly, four different energies are identified and the interconversion of energies is analyzed. The Casimir power being equivalent to the error power between the supplied power and the dissipative power is found and used to analyze the mechanism underlying the different dynamical behaviors. A four‐wing chaotic attractor is found when the gyrostat is subject to a combination of inertial, internal, and dissipative torques as well as the addition of an external torque. The bifurcation of the Casimir power and leaps in Casimir energy level are used as indicators of the different definitive dynamics, which is demonstrated to be identical to that appearing in the state bifurcation and the Lyapunov exponent spectrum.

Fluid transportation and heat transfer analysis of PP/TiO2 nanocomposites in an internal mixer

The internal mixer is an important devise for processing the polymer nanocomposites acting as a chemical reactor. In this article, based on the computational fluid dynamics method, the fluid transportation and heat transfer analysis of sol–gel reaction processing for Polypropylene (PP)/TiO2 nanocomposites in the internal batch mixers with single-winged and two-winged Cam rotors were simulated. First, the Lagrangian coherent structure analysis was used to understand the fluid transport properties in the mixers. Then the effect of rotational speeds (ratios) and barrel temperatures on the heat transfer characteristics in the mixers with different rotors was analyzed. Also, the changes of viscous heating and torques of rotors with different thermal conditions in the mixers were discussed. Especially, the relationship between the fluid transportation and heat transfer characteristics was explored. The results show that a big rotor speed ratio can induce great fluid transportation in the left and right mixer chambers based on the Lagrangian coherent structure analysis, and the fluid near the horseshoe map has great folding effect and temperature magnitude. The viscous dissipation, viscous heat generation, and rotor torques in the mixers increase with increasing the rotational speeds and decrease with increasing the barrel temperatures. The mixer with two-winged rotors has higher average temperature, viscous dissipation, viscous heat generation and the torques of rotors values of reactive fluid than that with single-winged rotors.

Moment of Inertia and Friction Torque Coefficient Identification in a Servo Drive System

This paper proposes a new method to identify the mechanical parameters of a servo drive system, such as the moment of inertia and friction torque coefficients. Identification of the moment of inertia is essential for the design of a high-performance speed and position controller. Furthermore, the mechanical friction torque coefficients, such as the viscous and Coulomb friction torque coefficients, can be used to reduce the speed and position error without resorting to the use of a high gain for the speed controller. To simultaneously identify the moment of inertia and the friction torque coefficients, the proposed method uses the fact that the sinusoidal speed is in phase with the friction torque and out of phase with the torque for the moment of inertia. The proposed method is based on the speed control loop and the moment of inertia, and friction torque coefficients can be exactly obtained from a half-period integration of the torque reference of the low frequency sinusoidal speed control. Using computer simulations and experiments employing 600-W servo drive systems, the feasibility of the proposed method was verified.

A Composite Neoclassical Toroidal Viscosity Model Incorporating Torques from both Axisymmetric and Nonaxisymmetric Tokamak Magnetic Fields

This paper combines the older neoclassical gyroviscous model for toroidal viscosity in the plasma core, which is based on an axisymmetric magnetic field and obtains reasonable agreement with experiment for toroidal rotation in the plasma core but not in edge plasma, with recent models for neoclassical toroidal viscosity (NTV) based on nonaxisymmetric “perturbation” magnetic field components present primarily in the edge plasma to obtain a composite toroidal viscosity model for toroidal velocity calculations in the tokamak core and edge plasma. This combination is facilitated by the fact that the same form of “drag frequency” representation of the viscous torque used in many of the new (NTV) torque models arising from toroidally nonaxisymmetric perturbation magnetic fields that are present mostly in the plasma edge can also be used to represent the old neoclassical toroidal viscous torques arising from toroidally axisymmetric magnetic fields.

Hydrodynamic Flows in Microsized Liquid Crystal Cells with Orientational Defects

The effect of the orientational defect (OD) on the formation process of a vortical flow v(t, r), emerging in a microsized liquid crystal (LC) cell under the action of a focused laser radiation, was studied within the nonlinear generalization of the classical Ericksen–Leslie theory by numerical methods, considering the thermomechanical contributions to both the stress tensor and viscous torque, that acts on the unit volume of the liquid crystal phase (LC phase). The analysis of the obtained results showed that the vortical flow, rotating clockwise, is generated in a “defect” LC cell close to the OD, with the OD, placed on the lower bounding surface, on which the laser radiation was focused. The rotational velocity of this flow is two orders of magnitude greater than the rotational velocity of the vortex, which is generated in a “pure” LC cell at the same conditions and rotates anticlockwise.

Toroidal modeling of interaction between internal kink mode and plasma flow

Non-linear interaction between the internal kink mode and toroidal plasma rotation is numerically studied using the MARS-Q code [Liu et al., Phys. Plasmas 20, 042503 (2013)]. Simulation results show core plasma flow damping due to various toroidal torques, generated by a weakly stable internal kink mode. The 3-D field perturbation induced torques, including the neoclassical toroidal viscous (NTV) torque, as well as that produced by the Maxwell and Reynolds stresses, act as sink terms in the toroidal momentum balance model. The NTV torque is found to play a dominant role in the flow damping in all cases considered in this study. The modification to the internal kink mode structure is observed during the flow damping. Whilst a steady state can be achieved in the coupled mode-flow evolution with a uniform initial flow, a sheared initial flow affects the linear stability of the mode and consequently changes the non-linear evolution. For cases where the steady state solution is achieved, the saturated plasma flow speed critically depends on the initial flow condition as well as the initial amplitude of the internal kink mode but is less sensitive to the on-axis safety factor q0, as long as the latter stays above 1.

Simulation and experiment of viscous torque for disengaged wet clutches of tracked vehicle

In order to predict the viscous drag loss for tracked vehicles, the drag torque of the friction pair with different grooves was investigated in this paper. The traditional computation method is difficult to adapt for the new kinds of friction plates with complex grooves. A numerical method with the help of CFD models is adopted to simulate the fluid flow status in the grooves and the drag torque was obtained by the accumulation of the discrete viscous force. The simulation results implied that the plates with different kinds grooves were provided with various characteristics of viscous torque and these characteristics could be affected by the rotation direction for the plate with spiral grooves, which are proved in experiment. Meanwhile, it was also found that the two kinds of plates with double arc or spiral grooves, which have different sensitive parameters in drag dissipation, have to perform accurate flow control and clearance design respectively. The simulations and experiments showed that the ‘positive spiral grooves’ friction plates had minimum drag torque in regular heavy-duty conditions. It can be used in transmission system with requirements of limited space and high mobility, which can lead to better heat dissipation and less power loss.

The effect of AGN feedback on the migration time-scale of supermassive black holes binaries

The gravitational interaction at parsec to sub-parsec scales between a circumbinary gas disc and a super massive black hole binary (SMBHB) is a promising mechanism to drive the migration of SMBHBs toward coalescence. The typical dynamical evolution can be separated in two main regimes: I) Slow migration ($T_{\rm mig}$ $\sim$ $10^{3-4}\times T_{\rm orb}$), where viscous torques are not efficient enough to redistribute the extracted angular momentum from the binary, leading to the formation of a low density cavity around the binary. II) Fast migration ($T_{\rm mig}$ $\sim$ $10^{1-2} \times T_{\rm orb}$), in which the redistribution of angular momentum is efficient and no low density cavity is formed in the circumbinary disc. Using N-Body/SPH simulations we study the effect of AGN feedback in this phase of a SMBHB evolution. We implement an AGN feedback model in the SPH code Gadget-3 that includes momentum feedback from winds, X-ray heating/radial-momentum and Eddington force. Using this implementation we run a set of simulations of SMBHB+disc in the two main shrinking regimes. From these simulations we conclude that the effect of the AGN mechanical feedback is negligible for SMBHBs in the slowly shrinking regime. However, in the fast shrinking regime the AGN wind excavate a "feedback cavity" leaving the SMBHB almost naked, thus stalling the orbital decay of the binary.

The life cycles of Be viscous decretion discs: The case of ω CMa

We analyzed V-band photometry of the Be star {\omega} CMa, obtained during the last four decades, during which the star went through four complete cycles of disc formation and dissipation. The data were simulated by hydrodynamic models based on a time-dependent implementation of the viscous decretion disc (VDD) paradigm, in which a disc around a fast-spinning Be star is formed by material ejected by the star and driven to progressively larger orbits by means of viscous torques. Our simulations offer a good description of the photometric variability during phases of disc formation and dissipation, which suggests that the VDD model adequately describes the structural evolution of the disc. Furthermore, our analysis allowed us to determine the viscosity parameter {\alpha}, as well as the net mass and angular momentum (AM) loss rates. We find that {\alpha} is variable, ranging from 0.1 to 1.0, not only from cycle to cycle but also within a given cycle. Additionally, build-up phases usually have larger values of {\alpha} than the dissipation phases. Furthermore, during dissipation the outward AM flux is not necessarily zero, meaning that {\omega} CMa does not experience a true quiescence but, instead, switches between a high to a low AM loss rate during which the disc quickly assumes an overall lower density but never zero. We confront the average AM loss rate with predictions from stellar evolution models for fast-rotating stars, and find that our measurements are smaller by more than one order of magnitude.

Effects of Pressure Boundary on Dynamic Torque Behavior of Hydroviscous Drive

The object of this work is to investigate the effect of the change of film pressure resulting from axial squeeze-film motion between driving and driven disks on the performance of hydroviscous drive (HVD). A simplified mathematical model of the steady and laminar flow between parallel disks is established with consideration of three kinds of pressure boundary conditions. Some analytical solutions of film thickness, rotate speed of driven disk, viscous torque, and total torque are obtained. The numerical results show that the torque response depends on the relationship between the inlet pressure and the outlet pressure when considering the Dirichlet boundary conditions. The soft-start under Dirichlet boundary conditions and Mixed boundary conditions reflects the constant-torque startup and torque control startup, respectively. Compared with the two boundary conditions above, the soft-start under pressure profile boundary from Neumann boundary conditions has advantages for speed regulation. The effects of the ratio of inner and outer radius on the torque profiles and soft-start time are mainly related to Dirichlet boundary conditions and pressure profile boundary from Neumann boundary conditions.

Deep and wide gaps by super Earths in low-viscosity discs

Planets can open cavities (gaps) in the protoplanetary gaseous discs in which they are born by exerting gravitational torques. Viscosity counters these torques and limits the depletion of the gaps. We present a simple one-dimensional scheme to calculate the gas density profile inside gaps by balancing the gravitational and viscous torques. By generalizing the results of Goodman & Rafikov (2001), our scheme properly accounts for the propagation of angular momentum by density waves. This method allows us to easily study low-viscosity discs, which are challenging for full hydrodynamical simulations. We complement our numerical integration by analytical equations for the gap's steady-state depth and width as a function of the planet's to star's mass ratio $\mu$, the gas disc's aspect ratio $h$, and its Shakura & Sunyaev viscosity parameter $\alpha$. Specifically, we focus on low-mass planets ($\mu<\mu_{\rm th}\equiv h^3$) and identify a new low-viscosity regime, $\alpha<h(\mu/\mu_{\rm th})^5$, in which the classical analytical scaling relations are invalid. Equivalently, this low-viscosity regime applies to every gap that is depleted by more than a factor of $(\mu_{\rm th}/\mu)^3$ relative to the unperturbed density. We show that such gaps are significantly deeper and wider than previously thought, and consequently take a longer time to reach equilibrium.

The Structure of a Quasi-Keplerian Accretion Disk around Magnetized Stars

Abstract In this paper, we present the complete structure of a quasi-Keplerian thin accretion disk with an internal dynamo around a magnetized neutron star. We assume a full quasi-Keplerian disk with the azimuthal velocity deviating from the Keplerian fashion by a factor of ξ (0 &lt; ξ &lt; 2). In our approach, we vertically integrate the radial component of the momentum equation to obtain the radial pressure gradient equation for a thin quasi-Keplerian accretion disk. Our results show that, at large radial distance, the accretion disk behaves in a Keplerian fashion. However, close to the neutron star, pressure gradient force (PGF) largely modifies the disk structure, resulting into sudden dynamical changes in the accretion disk. The corotation radius is shifted inward (outward) for ξ &gt; 1 (for ξ &lt; 1), and the position of the inner edge with respect to the new corotation radius is also relocated accordingly, as compared to the Keplerian model. The resulting PGF torque couples with viscous torque (when ξ &lt; 1) to provide a spin-down torque and a spin-up torque (when ξ &gt; 1) while in the advective state. Therefore, neglecting the PGF, as has been the case in previous models, is a glaring omission. Our result has the potential to explain the observable dynamic consequences of accretion disks around magnetized neutron stars.

Linear stability of thermal-bioconvection in a suspension of gyrotactic micro-organisms

By utilizing a randomly swimming model, a linear stability analysis is applied to investigate the stability of bioconvection in a horizontal suspension layer of motile gyrotactic micro-organisms with heated from below. The micro-organisms under consideration are orientated by a balance between a gravitational torque, due to them being bottom heavy, and viscous torque arising from local fluid velocity gradients. The obtained eigenvalue problem containing thermal Rayleigh number and bioconvection Rayleigh number is solved numerically using one-term Galerkin method. The case of non-oscillatory instability is analyzed, the relationship among thermal Rayleigh number, bioconvection Rayleigh number, Lewis number, critical wavenumber and the shape of microorganisms are discussed. We point out that the heating from below makes the layer more unstable. When increasing the value of thermal Rayleigh number to 1750, the suspension becomes unstable itself, which imply that bioconvection Rayleigh number has nothing to do with the stability of this system. We also find that Lewis number has no effect on critical value of thermal Rayleigh number, but has a great influence on critical bioconvection Rayleigh number. The increasing cell eccentricity enlarges the critical value of bioconvection Rayleigh number, which means that the suspension is more stable.

Mechanical parameter identification of two-mass drive system based on variable forgetting factor recursive least squares method

Alternating current (AC) motor drive systems are widely used and their performances are greatly affected by motor parameters and load disturbances, so it is necessary to identify and observe their moment of inertia, the viscous friction coefficient and load torque. This paper presents an identification method combined a Luenberger observer and the variable forgetting factor recursive least squares method (FFRLSM), which does not require the torque sensor but a position encoder and can identify the moment of inertia of the drive system, the viscous friction coefficient, and the load torque, simultaneously. The Luenberger observer takes the position and the actual current to estimate speed and angular position. This information, together with variable FFRLSM is used to identify the moment of inertia, viscous friction coefficient and load torque. The identified moment of inertia of the system is substituted into the Luenberger observer model to correct the error of the system model. According to a probability density function of a normal distribution, the proposed method estimates the identification target in a short time, with stable and high identification precision. Finally, a comparison is made between the proposed algorithm and the FFRLSM. Results show that the proposed identification method achieves intended purpose and promise application values with its short consuming-time and high identification accuracy.