Random Velocity Component Research Articles

Dissipation Mechanisms for Fluids and Objects in Relative Motion Described by the Navier-Stokes Equation.

This work demonstrates that an additional resistance term should be included in the Navier–Stokes equation when fluids and objects are in relative motion. This is based on an observation that the effect of the microscopic molecular random velocity component parallel to the macroscopic flow direction is neglected. The two components of the random velocity perpendicular to the local mean flow direction are accounted for by the viscous resistance, e.g., by Stokes’ law for spherical objects. The relationship between the mean- and the random velocity in the longitudinal direction induces differences in molecular collision velocities and collision frequency rates on the up- and downstream surface areas of the object. This asymmetry therefore induces flow resistance and energy dissipation. The flow resistance resulting from the longitudinal momentum transfer mode is referred to as thermal resistance and is quantified by calculating the net difference in pressure up- and downstream the surface areas of a sphere using a particle velocity distribution that obeys Boltzmann’s transport equation. It depends on the relative velocity between the fluid and the object, the number density and the molecular fluctuation statistics of the fluid, and the area of the object and the square root of the absolute temperature. Results show that thermal resistance is dominant compared to viscous resistance considering water and air in slow relative motion to spherical objects larger than nanometer-size at ambient temperature and pressure conditions. Including the thermal resistance term in the conventional expression for the terminal velocity of spherical objects falling through liquids, the Stokes–Einstein relationship and Darcy’s law, corroborates its presence, as modified versions of these equations fit observed data much more closely than the conventional expressions. The thermal resistance term can alternatively resolve d’Alembert’s paradox as a finite flow resistance is predicted at both low and high relative fluid–object velocities in the limit of vanishing fluid viscosity.

A quasar microlensing light-curve generator for LSST

ABSTRACT We present a tool to generate mock quasar microlensing light curves and sample them according to any observing strategy. An updated treatment of the fixed and random velocity components of observer, lens, and source is used, together with a proper alignment with the external shear defining the magnification map caustic orientation. Our tool produces quantitative results on high magnification events and caustic crossings, which we use to study three lensed quasars known to display microlensing, viz. RX J1131–1231, HE 0230–2130, and Q 2237+0305, as they would be monitored by The Rubin Observatory Legacy Survey of Space and Time (LSST). We conclude that depending on the location on the sky, the lens and source redshift, and the caustic network density, the microlensing variability may deviate significantly than the expected ∼20-yr average time-scale (Mosquera & Kochanek 2011). We estimate that ∼300 high magnification events with Δmag>1 mag could potentially be observed by LSST each year. The duration of the majority of high magnification events is between 10 and 100 d, requiring a very high cadence to capture and resolve them. Uniform LSST observing strategies perform the best in recovering microlensing high magnification events. Our web tool can be extended to any instrument and observing strategy, and is freely available as a service at http://gerlumph.swin.edu.au/tools/lsst_generator/, along with all the related code.

Bluff body boundary-layer modification and its effect on the near-wake topology

Boundary-layer modification over a bullet-shaped body has been accomplished using wall suction and its effect on the near-wake topology is reported. Two-dimensional velocity fields in the Reynolds number range 6.7×103−5.5×104 are acquired by means of particle image velocimetry and the mean, periodic, and random velocity components are analyzed. Wall suction reduces the boundary-layer thickness and increases the wall-normal velocity gradient. When the boundary layer is laminar up to the point of separation, the modification of the boundary layer leads to a vortex formation region that is up to 19% shorter compared with the case without wall suction. The modification of the boundary layer is accompanied by an increase of the Reynolds normal and shear stresses, which corresponds to larger forces acting on a fictive control area enclosing the mean recirculation region. The increase in Reynolds normal and shear stresses is due to an increase of the random fluctuation component, while the contribution of the periodic fluctuation component remains constant. The altered topology of the vortex formation region is accompanied by a significant change of the vortex shedding frequency and the base pressure. Empirical relations between the wake inlet conditions and the wake characteristics are reported, which hold for both laminar and turbulent boundary layers. The curvature of the streamlines enclosing the rear part of the body was also quantified and found to be proportional to the base pressure.

Application of particle image velocimetry (PIV) to vibrational finishing

Vibrational finishing processes are finding increased application in the finishing of high end components. Despite the growing popularity of vibrational finishing, and due to limited suitable process instrumentation, understanding of underlying physical processes remains largely anecdotal and empirical, and system-independent process control remains unrealized. In this paper, particle image velocimetry (PIV) is proposed as a versatile, non-intrusive, readily available diagnostic for both studying fundamental features associated with vibrational finishing, as well as for developing system-independent control strategies. With regard to fundamental processes, PIV is used to measure surface media velocity fields and find that in our experimental system, the media flow field consists of: (i) a weak, random component having repeatable statistical properties which are sensitive to, and indicative of, changing process parameters and media selection, superposed on, (ii) a dominant, non-random component which is insensitive to changes in process parameters. Importantly, from a potential process control standpoint, it is shown that a filtered version of the random velocity component offers a system-independent, parameter-sensitive indicator of process conditions.

Random drift particle swarm optimization algorithm: convergence analysis and parameter selection

The random drift particle swarm optimization (RDPSO) algorithm is a PSO variant inspired by the free electron model in metal conductors placed in an external electric field. Based on the preliminary work on the RDPSO algorithm, this paper makes systematical analyses and empirical studies of the algorithm. Firstly, the motivation of the RDPSO algorithm is presented and the design of the particle's velocity equation is described in detail. Secondly, a comprehensive analysis of the algorithm is made in order to gain a deep insight into how the RDPSO algorithm works. It involves a theoretical analysis and the simulation of the stochastic dynamical behavior of a single particle in the RDPSO algorithm. The search behavior of the algorithm itself is also investigated in detail, by analyzing the interaction among the particles. Then, some variants of the RDPSO algorithm are presented by incorporating different random velocity components with different neighborhood topologies. Finally, empirical studies of the RDPSO algorithm are performed by using a set of benchmark functions from the CEC2005 benchmark suite. Based on the theoretical analysis of the particle's behavior, two methods of controlling the algorithmic parameters are employed, followed by an experimental analysis on how to select the parameter values, in order to obtain a satisfactory overall performance of the RDPSO algorithm and its variants in real-world applications. A further performance comparison between the RDPSO algorithm and other variants of PSO is made to prove the effectiveness of the RDPSO.

Coherent structure and sound production in the helical mode of a screeching axisymmetric jet

AbstractThe structure of a screeching axisymmetric jet in the helical C mode at a nozzle pressure ratio of 3.4 issuing from a convergent nozzle is studied using high-resolution particle image velocimetry. Proper orthogonal decomposition (POD) is used to extract the dominant coherent structures within the jet. The first two modes produced by the POD are used to reconstruct a phase-averaged data sequence. A triple decomposition into mean, coherent and random velocity components is performed. The embedded shock structures within the jet are shown to strongly modulate the coherent axial stresses within the shear layer and to weakly modulate the random axial stresses. Analysis of the third and fourth moments of the velocity probability density function is used as an indicator of possible regions of shock–vortex interaction and thus screech tone generation. Peaks of kurtosis (flatness) occur at the second, third and fourth shock–boundary intersection points, with the radial position shifting towards the centreline with increasing downstream distance. Analysis of the coherent component of vorticity shows that the largest fluctuations in coherent vorticity occur at the high-speed side of the shear layer in an area extending from the second to the fourth shock cell. With reference to prior literature, the argument is made that it is this increased magnitude of coherent vorticity fluctuation that is the primary factor in the determination of which shock cells act as dominant screech sources.

TurbSeed—A model for wind dispersal of seeds in turbulent currents based on publicly available climate data

A numerical model (TurbSeed) is described which calculates explicitly the dispersal of plant seeds by wind, especially the fraction of seeds, which are transported more than 100m starting at the inflorescence. Such rare events are called here long-distance dispersal. The framework of TurbSeed includes three main modules:(1)A turbulence model (TM) for a specified location and time period using meteorological parameters from publicly available mesoscale weather models or simulated climate data.(2)A Lagrangian model (LM) which calculates the seed transport in the turbulent boundary layer and(3)A module which considers the effect of weather conditions on release of seeds (RS).In this approach the turbulent field is prescribed by a coarse wind field derived from the mesoscale climate simulations superimposed by a random velocity component. Similar approaches are known as Eulerian–Lagrangian approaches. The main difference in this new approach (TM) lies in the construction of the turbulent structure of the wind field. The introduction of such a random velocity component uses the Monin–Obukhov similarity theory. An inverse random phase Fast-Fourier-Transformation reconstructs the time structure of turbulence using a parameterized power spectrum of turbulence which is accepted as standard in micro meteorology.In the LM module Monte-Carlo-Simulations for numerous trajectories are used to incorporate the effects of turbulence. The RS module takes into account various conditions of release of plant seeds, such as the date of maturity of the seeds and the effect of wind speed on the release of seeds.This model can be driven not only with data from observed weather conditions, but also with output of mesoscale climate scenarios. Thus, TurbSeed can study the effect of climate change on wind dispersal of seeds.

RODOS meteorological pre-processor and atmospheric dispersion model DIPCOT: a model suite for radionuclides dispersion in complex terrain

The Meteorological Pre-Processor (MPP) of the Decision Support System RODOS acts as interface between the incoming meteorological data from stations and/or prognostic models and the Atmospheric Dispersion Models (ADMs) used for predicting the spread of the accidentally emitted radionuclides. The MPP includes a diagnostic Wind Field Model (WFM) to ensure mass conservation of the calculated wind field. Its output is usable by simple and complex ADMs and it is applicable for highly complex topography and from micro- to meso-scales. The MPP has been tested for both real and artificial flow fields and it has been optimized to function with very short execution times and to give the most reasonable results under all terrain complexity and atmospheric stability conditions. DIPCOT (DIsPersion over COmplex Terrain) is a Lagrangian Puff / Particle model that has been implemented in RODOS to simulate radionuclides atmospheric dispersion over complicated terrain. For this purpose, it uses a certain number of fictitious puffs/particles which are assumed to move with the mean wind flow plus a random velocity component to simulate turbulent diffusion. The calculation of the gamma radiation dose rates in air due to the radioactive plume is calculated by a very fast method that takes into account the inhomogeneous 3-dimensional cloud shape. DIPCOT has been evaluated by comparisons to widely used real-scale experimental data sets: Copenhagen, Prairie Grass, Indianapolis and Mol. The integration of the above models greatly enhances the applicability of the RODOS system.

R fluids

A theory of collisionless fluids is developed in a unified picture, where nonrotating (?f1 = ?f2 = ?f3 = 0) figures with some given random velocity component distributions, and rotating (?f1 = ?f2 = ?f3 ) figures with a different random velocity component distributions, make adjoint configurations to the same system. R fluids are defined as ideal, self-gravitating fluids satisfying the virial theorem assumptions, in presence of systematic rotation around each of the principal axes of inertia. To this aim, mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The figure rotation is defined as the mean angular velocity, weighted on the moment of inertia, with respect to a selected axis. The generalized tensor virial equations (Caimmi and Marmo 2005) are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general hypotheses, by reversing the sign of tangential or axial velocity components of an assigned fraction of particles, leaving the distribution function and other parameters unchanged (Meza 2002). The application of the reversion process to tangential velocity components is found to imply the conversion of random motion rotation kinetic energy into systematic motion rotation kinetic energy. The application of the reversion process to axial velocity components is found to imply the conversion of random motion translation kinetic energy into systematic motion translation kinetic energy, and the loss related to a change of reference frame is expressed in terms of systematic motion (imaginary) rotation kinetic energy. A number of special situations are investigated in greater detail. It is found that an R fluid always admits an adjoint configuration where figure rotation occurs around only one principal axis of inertia (R3 fluid), which implies that all the results related to R3 fluids (Caimmi 2007) may be ex- tended to R fluids. Finally, a procedure is sketched for deriving the spin parameter distribution (including imaginary rotation) from a sample of observed or simulated large-scale collisionless fluids i.e. galaxies and galaxy clusters.

Properties of the particle velocity field in gas-solid turbulent channel flow

Spatial characteristics of the particle velocity field are investigated using numerical simulations of gas-solid turbulent channel flow. The carrier phase is resolved using large eddy simulation (LES) of the incompressible Navier-Stokes equations. The dispersed phase is computed using Lagrangian tracking in which particle motion is governed by the drag force. Predictions of dispersed phase transport are obtained for three particle response times in simulations with and without interparticle collisions. Spatial correlations of the particle velocity field are measured in planes parallel to the wall and exhibit a discontinuity at the origin. The discontinuity in the spatial correlations is consistent with recent work by Fevrier et al. [J. Fluid Mech., 533, 1 (2005)] that shows the velocity of a particle is comprised of a contribution from a continuous field, shared by all the particles, and a random velocity component that is not spatially correlated. Analysis of the simulation database shows that the random component of the particle velocity increases with increasing particle response time. The influence of interparticle collisions leads to a changes in the partitioning of the particle velocity, with a greater fraction residing in the uncorrelated component compared to the correlated part.

Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study

The velocity distribution of dilute suspensions of heavy particles in gas–solid turbulent flows is investigated. A statistical approach – the mesoscopic Eulerian formalism (MEF) – is developed in which an average conditioned on a realization of the turbulent carrier flow is introduced and enables a decomposition of the instantaneous particle velocity into two contributions. The first is a contribution from an underlying continuous turbulent velocity field shared by all the particles – the mesoscopic Eulerian particle velocity field (MEPVF) – that accounts for all particle–particle and fluid–particle two-point correlations. The second contribution corresponds to a distribution – the quasi-Brownian velocity distribution (QBVD) – that represents a random velocity component satisfying the molecular chaos assumption that is not spatially correlated and identified with each particle of the system. The MEF is used to investigate properties of statistically stationary particle-laden isotropic turbulence. The carrier flow is computed using direct numerical simulation (DNS) or large-eddy simulation (LES) with discrete particle tracking employed for the dispersed phase. Particle material densities are much larger than that of the fluid and the force of the fluid on the particle is assumed to reduce to the drag contribution. Computations are performed in the dilute regime for which the influences of inter-particle collisions and fluid-turbulence modulation are neglected. The simulations show that increases in particle inertia increase the contribution of the quasi-Brownian component to the particle velocity. The particle velocity field is correlated at larger length scales than the fluid, with the integral length scales of the MEPVF also increasing with particle inertia. Consistent with the previous work of Abrahamson (1975), the MEF shows that in the limiting case of large inertia, particle motion becomes stochastically equivalent to a Brownian motion with a random spatial distribution of positions and velocities. For the current system of statistically stationary isotropic turbulence, both the DNS and LES show that the fraction of the kinetic energy residing in the mesoscopic field decreases with particle inertia as the square root of the ratio of the total particulate-phase kinetic energy to that of the fluid.

Noninvasive quantitation of blood flow turbulence in patients with aortic valve disease using online digital computer analysis of Doppler velocity data

Previous experimental studies have demonstrated that aortic valve disease is associated with significant downstream turbulence (T). In this study, we developed a noninvasive method on the basis of Doppler velocity recording for quantitating aortic blood flow T in patients with aortic valve disease. The instantaneous blood velocity at a point in the aorta is equal to the sum of a mean periodic velocity component with a random or turbulent velocity component. According to the ensemble average method, time mean absolute T intensity is the root-mean-square value of turbulent velocity averaged over time and T is better quantitated by the relative T intensity (TIr), which is the ratio of absolute T intensity to the ensemble average velocity averaged over time. We computed TIr in 18 patients with mild to severe aortic stenosis and in 13 healthy volunteers from instantaneous modal velocities of 70 cycle length–matched heart beats recorded in the proximal part of the descending aorta by pulsed Doppler using an ultrasound system with an output port for online digital data transfer into a microcomputer. TIr was greater in patients with aortic valve disease (18.4 ± 5.1%, range 11.2%-28.9%) than in control patients (7.9 ± 1.9%, range 4.8%-9.8%; P = .0001). In patients with aortic valve disease, TIr was better linearly related to the ratio of postvalvular aorta to valvular orifice cross-sectional areas ( r = 0.89, P = .0001) than to other parameters of valve restriction: transvalvular pressure gradient ( r = 0.78, P = .0001); valve area ( r = −0.56, P = .01); and valve resistance ( r = 0.72, P = .0002). Thus, T that can be computed noninvasively from direct digital transfer of Doppler velocity data appears to be linearly related to indices of aortic valve restriction. Our data support the concept of the postvalvular aorta to valvular orifice cross-sectional areas ratio as a new important hemodynamic parameter in patients with aortic valve disease.

Eulerian/Lagrangian Analysis for the Prediction of Cavitation Inception

An Eulerian/Lagrangian computational procedure was developed for the prediction of cavitation inception by event rate. The carrier-phase flow field was computed using an Eulerian Reynolds-averaged Navier-Stokes (RANS) solver. The Lagrangian analysis was one-way coupled to the RANS solution, since at inception, the contributions of mass, momentum, and energy of the microbubbles to the carrier flow are negligible. The trajectories were computed using Newton’s second law with models for various forces acting on the bubble. The growth was modeled using the Rayleigh-Plesset equation. The important effect of turbulence was included by adding a random velocity component to the mean flow velocity and by reducing the local static pressure. Simulation results for the Schiebe body indicate agreement with experimentally observed trends and a significant event rate at cavitation indices above visual inception.

Coherent global motion in the absence of coherent velocity signals.

It is widely believed that form and motion are analysed separately in mammalian visual systems. Form is confined within a stream that projects ventrally from V1 to the inferotemporal cortex, and motion within a stream that projects more dorsally, to the posterior parietal cortex [1] [2] [3] [4] [5] [6] [7]. Current descriptions suggest that there is little contact between the two streams until the products of their separate analyses are bound together at a late (and still unidentified) stage in perception [3] [8] [9] [10]. There are, however, indications that form and motion signals may interact [11], and that form signals, streaks derived from motion, may assist in the analysis of its direction [12]. Lennie [13] proposes that all image attributes, form and motion included, remain intimately coupled within the same retinotopic map at all stages of visual analysis. Here we show that form, independent of motion, can give coherence to incoherent motion. Sequences of Glass patterns [14] built to a common global rule are devoid of coherent motion signals, but they produce motion consistent with the global rule for form, not with the random velocity components of the pattern sequence.

A random simulation of droplet distribution in nozzle and plume flows

A simple entrainment model is used to estimate droplet streamlines, velocity and mass flux in rocket exhaust plumes. Since droplet mass flux constitutes only about 1% of the exhaust mass flux, the effect of droplet entrainment on the gas flow is neglected. The novelty of the present model is in obtaining the droplet distribution within the nozzle by assuming a small radial random velocity component for droplets at the throat. Gas flow in the nozzle is approximated as isentropic plus a correction for the boundary layer. The computed distribution of droplet mass flux is found to be in good agreement with experimental data.

The effects of a random off-axis velocity component on the penetration achieved by long rod kinetic energy penetrators and shaped charge jets

The impact of long rod kinetic energy penetrators and shaped charge jets on homogeneous targets is investigated. In particular the effects of a random off-axis velocity component on the penetration achieved are analyzed. The aim of this study is to consider the case where the off-axis velocity component takes a uniform value W along the rod or jet. It is assumed that penetration takes place according to the classical hydrodynamic penetration law, and that it continues either until the projectile material is exhausted or until a side wall collision occurs. The penetration is evaluated as a function of a reference coordinate q defined along the projectile, and the corresponding crater radius distribution R(q) calculated, on the assumption that W is zero. The locus of the penetration stagnation point S corresponding to the true value of W is then determined as a function of q and a revised crater profile is calculated with radius R(q), centred on S. We determine whether a side-wall collision occurs, and calculate the final penetration, P. The probability that P exceeds a given value P o is found. We then determine the expected value of P and investigate parameter variations to maximize this value.

Inverse kinematic problem for a random gradient medium in geometric optics approximation

Scattering at random inhomogeneities in a gradient medium results in systematic deviations of the rays and travel times of refracted body waves from those corresponding to the deterministic velocity component. The character of the difference depends on the parameters of the deterministic and random velocity component. However, at great distances to the source, independently of the velocity parameters (weakly or strongly inhomogeneous medium), the most probable depth of the ray turning point is smaller than that corresponding to the deterministic velocity component, the most probable travel times also being lower. The relative uncertainty in the deterministic velocity component, derived from the mean travel times using methods developed for laterally homogeneous media (for instance, the Herglotz-Wiechert method), is systematic in character, but does not exceed the contrast of velocity inhomogeneities by magnitude. The gradient of the deterministic velocity component has a significant effect on the travel-time fluctuations. The variance at great distances to the source is mainly controlled by shallow inhomogeneities. The travel-time flucutations are studied only for weakly inhomogeneous media.

Fabry-Perot Interferogram Profiles in λ5303 in Relation to Coronal Structures: 1980 and 1983 Eclipses

Fringe profiles of Fabry-Perot interferograms taken in the λ 5303 line during the total solar eclipses of 1980 and 1983 are studied in relation to coronal structures observed in white-light pictures. Evidence for doppler-shifted discrete components and large random velocity components in specific regions is presented here.

Long‐term cluster growth modeling

The growth of particle clusters is modeled by allowing the particles to be moved by the atmospheric winds and a random velocity component. The dispersion of the cluster is followed for 432 hours. The results from many model runs using wind fields during a 2‐year period indicate that clusters grow with a time‐varying exponent. The growth between 40 and 150 hours is exponential in time. The rapid growth can be explained as resulting from horizontal wind shear.

Frequency-modulation detection of particle diffusion from heterodyne quasi-elastic light scattering

The Brownian/diffusive motion of micrometer-sized, suspended particles has been observed by using heterodyne light scattering with frequency-modulation (FM) detection and signal processing. The FM output is linear in the coherent velocity of the particles, with the random diffusive velocity component giving rise to background noise in the FM output. Experimental measurements of polystyrene latex spheres in water corroborate the predicted result for the signal-to-noise ratio. The noise component of the FM output was found to be independent of the particle number and, within the instrumental bandwidth, to be flat. Good quantitative agreement between the predicted and measured noise backgrounds was obtained for particle diameters from 0.5 to 50 μm.