Fluid Moment Research Articles

An Analysis of Baffles Designs for Limiting Fluid Slosh in Partly Filled Tank Trucks~!2009-10-29~!2010-04-21~!2010-07-23~!

This study presents an analysis of effectiveness of different designs of baffles, including the conventional, partial and oblique, in limiting the manoeuvre-induced transient as well as steady-state fluid slosh forces and moments in a partly-filled tank truck. The effect of an alternating arrangement of partial baffles is also explored. A three-dimensional computational fluid dynamics model of a partly-filled tank is developed to study the relative anti-slosh properties of different baffles designs and layouts under combined idealized longitudinal and lateral acceleration fields and different cargo loads. The analyses are also performed for a cleanbore tank, which is validated using the widely-used quasi-static slosh model. The results suggest that the conventional transverse baffles offer important resistance to fluid slosh under braking manoeuvres, while the obliquely placed baffles could help limit the longitudinal as well as lateral fluid slosh under combined lateral and longitudinal acceleration excitations.

The effect of heat flux on pressure evolution in the magnetosheath

An analysis of anisotropic pressure ( p ⊥ ≠ p ∥ ) evolution in the quasi-perpendicular magnetosheath is carried out based on a two-dimensional hybrid code simulation. The validity of different fluid models is evaluated by comparing the prediction of the models with the values of pressure observed in the hybrid code simulation. The Double Adiabatic model, the bounded anisotropy model, which incorporates local energy exchange from p ⊥ to p ∥ to model the effects of ion cyclotron waves, and a two way local energy exchange model have all been tested with and without including the effect of the heat flux terms q ∥ and q ⊥ (the third velocity moment). The heat flux terms yield a flow of perpendicular or parallel heat along magnetic field lines due to particle velocity distributions that are asymmetric with respect to the direction along the magnetic field and non-Maxwellian with respect to the parallel velocity. The two way energy exchange with heat flux terms does the best job of accounting for the pressure evolution in the hybrid code simulation. An attempt to model the parallel heat flux q ∥ using lower fluid moments was made, but this was not successful. These results show the inadequacy of fluid equations to model the hybrid code results. However, the effects we have examined here may not be as significant in the real magnetosheath, because the specific hybrid simulation examined here does not have a realistic separation of time scales of interest.

Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

The gauge invariant electromagnetic Wigner equation is taken as the basis of a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge-dependent Wigner function is shown to produce inconsistencies if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and it is shown to be in agreement with the kinetic theory in the long-wavelength approximation, provided that an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.

Spin Kinetic Theory—Quantum Kinetic Theory in Extended Phase Space

The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar quasi-distribution function. In contrast to the proper Wigner transformation technique, for which we expect the corresponding quasi-distribution function to be a complex matrix, we introduce a spin projection operator for the density matrix in order to obtain the aforementioned scalar quasi-distribution function. There is a close correspondence between this projection operator and the Husimi (or Q) function used extensively in quantum optics. Such a function is based on a Gaussian smearing of a Wigner function, giving a positive definite distribution function. Thus, our approach gives a Wigner-Husimi quasi-distribution function in extended phase space, for which the reduced distribution function on the Bloch sphere is strictly positive. We also discuss the gauge issue and the fluid moment hierarchy based on such a quantum kinetic theory.

Rotordynamic Instabilities Caused by the Fluid Force Moments on the Backshroud of a Francis Turbine Runner

Severe flexural vibration of the rotor shaft of a Francis turbine runner was experienced in the past. It was shown that the vibration was caused by the fluid forces and moments on the backshroud of the runner associated with the leakage flow through the back chamber. The aim of the present paper is to study the self-excited rotor vibration caused by the fluid force moments on the backshroud of a Francis turbine runner. The rotor vibration includes two fundamental motions, one is a whirling motion which only has a linear displacement and the other is a precession motion which only has an angular displacement. Accordingly, two types of fluid force moment are exerted on the rotor, the moment due to whirl and the moment due to precession. The main focus of the present paper is to clarify the contribution of each moment to the self-excited vibration of an overhung rotor. The runner was modeled by a disk and the whirl and the precession moments on the backshroud of the runner caused by the leakage flow were evaluated from the results of model tests conducted before. A lumped parameter model of a cantilevered rotor was used for the vibration analysis. By examining the frequency, the damping rate, the amplitude ratio of lateral and angular displacements for the cases with longer and shorter overhung rotor, it was found that the precession moment is more important for smaller overhung rotors and the whirl moment is more important for larger overhung rotors, although both types of moment due to the leakage flow can cause self-excited vibration of an overhung rotor.

Fluid simulation of the collisionless plasma sheath surrounding an electric dipole antenna in the inner magnetosphere

[1] The electrostatic sheath formation surrounding an electric dipole antenna at very low frequencies (VLF) in a magnetoplasma is examined through numerical simulation. In this paper, a hydrodynamic approach is used to solve for the nonlinear sheath dynamics of antennas located in plasmas similar to that which exists in the plasmasphere between L = 2 and L = 3 in the geomagnetic equatorial plane. The plasma environment at this location is assumed to be fully ionized and collisionless consisting of electrons and protons. Poisson's equation is used to close the system, providing the quasi-electrostatic fields within the sheath region. Sheath characteristics are given as a function of antenna drive frequency and voltage with results that are compared with existing theory. Capacitance and resistance values are given to reflect the sheath's contribution to the input impedance of the antenna. Finally, the importance of ion motion and the nonlinear sheath effects on the current, charge collection and bias voltage for the transmitting antenna are shown. The primary assumptions underlying the closure mechanisms for the infinite set of fluid moments are examined through theoretical observations and simulated comparisons of the truncation schemes. This paper constitutes one of the first works on the subject of high-voltage transmitting dipole antenna in a space plasma using a three-dimensional nonlinear formulation.

Fluid moment hierarchy equations derived from quantum kinetic theory

A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm–Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm–de Broglie–Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.

Toroidal flow and radial particle flux in tokamak plasmas

Many effects influence toroidal flow evolution in tokamak plasmas. Momentum sources and radial plasma transport due to collisional processes and microturbulence-induced anomalous transport are usually considered. In addition, toroidal flow can be affected by nonaxisymmetric magnetic fields; resonant components cause localized electromagnetic toroidal torques near rational surfaces in flowing plasmas and nonresonant components induce “global” toroidal flow damping torque throughout the plasma. Also, poloidal magnetic field transients on the magnetic field diffusion time scale can influence plasma transport. Many of these processes can also produce momentum pinch and intrinsic flow effects. This paper presents a comprehensive and self-consistent description of all these effects within a fluid moment context. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfvén waves (Grad–Shafranov equilibrium and ion radial force balance), sound waves (pressure constant along a field line and incompressible flows within a flux surface), and ion collisions (damping of poloidal flow). Finally, plasma transport across magnetic flux surfaces is induced by the many second order (in the small gyroradius expansion) toroidal torque effects indicated above. Nonambipolar components of the induced particle transport fluxes produce radial plasma currents. Setting the flux surface average of the net radial current induced by all these effects to zero yields the transport-time-scale equation for evolution of the plasma toroidal flow. It includes a combination of global toroidal flow damping and resonant torques induced by nonaxisymmetric magnetic field components, poloidal magnetic field transients, and momentum source effects, as well as the usual collision- and microturbulence-induced transport. On the transport time scale, the plasma toroidal rotation determines the radial electric field for net ambipolar particle transport. The ultimate radial particle transport is composed of intrinsically ambipolar fluxes plus nonambipolar fluxes evaluated at this toroidal-rotation-determined radial electric field.

Praying for power: Dispositions and discipline in the Azusa Street Revival's Apostolic Faith

The Azusa Street Revival in 1906 introduced new theological and practical challenges for believers: namely the Baptism of the Holy Spirit with the evidence of tongues and divine healing. Apostolic Faith, the revival's popular periodical, both implicitly and explicitly taught believers how to “pray through” to receive baptism for the soul and to utter the “prayer of faith” to accept divine healing for the body. Acknowledging the prescriptive nature of the text, this paper examines the dispositions and disciplines readers were encouraged to develop in this rather fluid moment in American religious history. The prayerful encounter among believer, Holy Spirit, and God, affords an opportunity to explore several conceptualizations of human agency. The most effective model goes beyond those conceptualizations that feature the submission and subversion of norms to consider agency in terms of the dispositions and skills necessary to effect specific actions in light of the historically specific disciplines through which subjects are formed.

Numerical and experimental study of the fluid dynamics of a flapping wing with low order flexibility

A simple canonical problem for understanding the role of flexibility in flapping wing flight is investigated numerically and experimentally. The problem consists of a two-dimensional two-component wing structure connected by a single hinge with a damped torsion spring. One component of the wing is driven with hovering flapping wing kinematics, while the other component responds passively to the fluid dynamic and inertial/elastic forces. Numerical simulations are carried out with the viscous vortex particle method with strongly coupled body dynamics. The experiments are conducted in a water tank with suspended particles for flow visualization. The system is analyzed in several different kinematic test cases that are designed to span a broad parametric range of flapping. Hinge deflection is used as the primary metric for comparison; the agreement between computation and experiment is very good in all cases. The trajectories of shed vortices are also compared, again with favorable agreement. Fluid forces and moments are computed in the numerical simulation at two different Reynolds numbers. It is found that the rate and timing of wing rotation primarily controls the generation of lift; in contrast, the translational acceleration has little effect. Likewise, kinematics with rotation transition well separated from translation transition are captured utilizing rotation-only kinematics. Reynolds number has little effect on the wing deflection but does influence the mean lift generated by the wing.

A potential-flow, deformable-body model for fluid–structure interactions with compact vorticity: application to animal swimming measurements

This paper presents an approach to quantify the unsteady fluid forces, moments and mass transport generated by swimming animals, based on measurements of the surrounding flow field. These goals are accomplished within a framework that is independent of the vorticity field, making it unnecessary to directly resolve boundary layers on the animal, body–vortex interactions, or interactions among vortex lines in the wake. Instead, the method identifies Lagrangian coherent structures in the flow, whose dynamics in flows with compact vorticity are shown to be well approximated by potential flow concepts, especially the Kirchhoff and deformation potentials from deformable body theory. Examples of the application of these methods are given for pectoral fin locomotion of the bluegill sunfish and undulatory swimming of jellyfish, and the methods are validated by analysis of a canonical starting vortex ring flow. The transition to a Lagrangian approach toward animal swimming measurements suggests the possibility of implementing recently developed particle tracking (vis-a-vis DPIV) techniques for fully three-dimensional measurements of animal swimming.

LIGKA: A linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks

In a plasma with a population of super-thermal particles generated by heating or fusion processes, kinetic effects can lead to the additional destabilisation of MHD modes or even to additional energetic particle modes. In order to describe these modes, a new linear gyrokinetic MHD code has been developed and tested, LIGKA (linear gyrokinetic shear Alfvén physics) [Ph. Lauber, Linear gyrokinetic description of fast particle effects on the MHD stability in tokamaks, Ph.D. Thesis, TU München, 2003; Ph. Lauber, S. Günter, S.D. Pinches, Phys. Plasmas 12 (2005) 122501], based on a gyrokinetic model [H. Qin, Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks, Ph.D. Thesis, Princeton University, 1998]. A finite Larmor radius expansion together with the construction of some fluid moments and specification to the shear Alfvén regime results in a self-consistent, electromagnetic, non-perturbative model, that allows not only for growing or damped eigenvalues but also for a change in mode-structure of the magnetic perturbation due to the energetic particles and background kinetic effects. Compared to previous implementations [H. Qin, mentioned above], this model is coded in a more general and comprehensive way. LIGKA uses a Fourier decomposition in the poloidal coordinate and a finite element discretisation in the radial direction. Both analytical and numerical equilibria can be treated. Integration over the unperturbed particle orbits is performed with the drift-kinetic HAGIS code [S.D. Pinches, Ph.D. Thesis, The University of Nottingham, 1996; S.D. Pinches et al., CPC 111 (1998) 131] which accurately describes the particles’ trajectories. This allows finite-banana-width effects to be implemented in a rigorous way since the linear formulation of the model allows the exchange of the unperturbed orbit integration and the discretisation of the perturbed potentials in the radial direction. Successful benchmarks for toroidal Alfvén eigenmodes (TAEs) and kinetic Alfvén waves (KAWs) with analytical results, ideal MHD codes, drift-kinetic codes and other codes based on kinetic models are reported.

Exact linearized Coulomb collision operator in the moment expansion

In the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integro-differential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collision operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Useful forms involving the small mass-ratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.

Bootstrap Current in Quasi-Symmetric Stellarators

This work examines bootstrap current in quasi-symmetric stellarators with a focus on the impact of bootstrap current on the equilibrium properties of stellarator configurations. In the design of the Quasi-Poloidal Stellarator (QPS), a code was used to predict the bootstrap current based on a calculation in an asymptotically collisionless limit. This calculation is believed to be a good approximation of the bootstrap current for low-collisionality plasmas but is expected to be higher than the actual bootstrap current for more collisional plasmas. A fluid moments approach has been developed to self-consistently calculate viscosities and neoclassical transport coefficients. The viscosities and transport coefficients can be used to calculate the bootstrap current for arbitrary collisionality and magnetic geometry. The bootstrap current calculations from the two codes were done for low-density, electron cyclotron–heated (ECH) plasmas and high-density, ion cyclotron–heated (ICH) plasmas for a range of configurations, and provide a benchmark for the moments code and a test of the range of validity of the collisionless code. In the configurations examined here, namely, QPS, the National Compact Stellarator Experiment, the Helically Symmetric Experiment, the Large Helical Device, and the Wendelstein-7X Stellarator, the bootstrap currents predicted from the two codes agree qualitatively for both ICH and ECH profiles.

Linear and nonlinear analyses of sheet flutter induced by leakage flow

This paper deals with both linear and nonlinear analyses of sheet flutter in a narrow passage caused by fluid–structure interaction. The sheet is considered as a combination of massless beam elements, springs and discrete mass particles, in which the mass of each particle and spring coefficients are calculated based on the beam model. In the linear analysis, equations of motion of the system are obtained by formulating fluid dynamic forces and moments acting on each sheet element, yielding an eigenvalue problem. To show the validity of the proposed method, calculated results were compared with previously reported experimental ones. In the nonlinear analysis, nonlinear fluid dynamic forces are introduced to simulate the behavior of the sheet, showing the appearance of limit-cycle vibration in high flow speed.

Fluid formalism for collisionless magnetized plasmas

A comprehensive analysis of the finite-Larmor-radius (FLR) fluid moment equations for collisionless magnetized plasmas is presented. It is based on perturbative but otherwise general solutions for the second and third rank fluid moments (the stress and stress flux tensors), with closure conditions still to be specified on the fourth rank moment. The single expansion parameter is the ratio between the largest among the gyroradii and any other characteristic length, which is assumed to be small but finite in a magnetized medium. This formalism allows a complete account of the gyroviscous stress, the pressure anisotropy, and the anisotropic heat fluxes, and is valid for arbitrary magnetic geometry, arbitrary plasma pressure, and fully electromagnetic nonlinear dynamics. As the result, very general yet notably compact perturbative systems of FLR collisionless fluid equations, applicable to either fast (sonic or Alfvénic) or slow (diamagnetic) motions, are obtained.

Kinetic investigation of a collisionless scrape-off layer with a source of poloidal momentum

The influence of a source of poloidal momentum on the collisionless tokamak scrape-off layer (SOL) is investigated. The solutions of the kinetic equation for ion flow and the corresponding system of fluid equations assuming zero ion heat flux are compared. The two models agree quite well for small poloidal Mach numbers of the momentum source, and for larger Mach numbers near the target towards which the drift is directed. At the other target the agreement is poor because the kinetic heat flux dominates energy transport near the stagnation point. The kinetic model yields smooth solutions for any value of poloidal drift. The fluid model breaks down at a particular supersonic poloidal Mach number due to the appearance of a singularity on the domain. The failure of the fluid model does not represent a real detachment, but is simply a mathematical artefact caused by the truncation of the series of fluid moment equations.

102 ヘリングボーン溝付気体軸受の並進,傾き運動を考慮した動的挙動と安定解析

In this paper, the dynamic stability of gas-lubricated journal bearing with Herring-bone groove are investigated. The pressure distribution which is generated in compressible fluid at the gap in the bearing is calculated. The equation of motion is derived using the fluid force and fluid moment acting on journal which is calculated from the pressure distribution. On the basis of the derived equation, the numerical simulation of the dynamic behavior of the journal is performed. The vibrational mode and the stability of the behavior of the journal are investigated. Finally parameter studies are discussed.

1411 ヘリングボーン溝付気体軸受の並進,回転達成振動解析(GS-10 回転機,研究発表講演)

The dynamic stability of gas-lubricated journal bearing with Herring-bone groove are investigated. The pressure distribution which is generated in compressible fluid at the gap in the bearing is caluculated. The equation of motion is derived using the fluid force and fluid moment acting on journal which is caluculated from the pressure distribution. On the basis of the derived equation, the numerical simulation of the dynamic behavior of the journal is performed. The vibrational mode and the stability of the behavior of the journal are investigated. Finally parameter studies are discussed.

Transient and Quasi-Steady Computational Fluid Dynamics Study of a Left Ventricular Assist Device

The HeartQuest continuous flow left ventricle assist device (LVAD) with a magnetically levitated impeller operates under highly transient flow conditions. Due to insertion of the in-flow cannula into the apex of the left ventricle, the inlet flow rate is transient because of ventricular contraction, and the pump's asymmetric circumferential configuration with five rotating blades forces blood intermittently through the pump to the great arteries. These two transient conditions correspond to time varying boundary conditions and transient rotational sliding interfaces in computational fluid dynamics (CFD). CFD was used to investigate the pump's performance under these dynamic flow conditions. A quasi-steady analysis was also conducted to evaluate the difference between the steady and transient analyses and demonstrate the significance of transient analysis, especially for transient rotational sliding interfaces transient simulations. This transient flow analysis can be applied generally in the design process of LVADs; it provides more reliable fluid forces and moments on the impeller for successful design of the magnetic suspension system and motor.