scholarly journals Tracer particle momentum effects in vortex flows

2013 ◽  
Vol 723 ◽  
pp. 665-691 ◽  
Author(s):  
David M. Birch ◽  
Nicholas Martin
Keyword(s):  
Particle Transport ◽  
Tracer Particle ◽  
Classical Model ◽  
Tracking Error ◽  
Selection Criterion ◽  
Tangential Velocity ◽  
Stokes Number ◽  
Radial Component ◽  
Vortex Flows ◽  
Tracer Particles

AbstractThe measurement of vortex flows with particle-image velocimetry (PIV) is particularly susceptible to error arising from the finite mass of the tracer particles, owing to the high velocities and accelerations typically experienced. A classical model of Stokes-flow particle transport is adopted, and an approximate solution for the case of particle transport within an axisymmetric, quasi-two-dimensional Batchelor $q$-vortex is presented. A generalized expression for the maximum particle tracking error is proposed for each of the velocity components, and the importance of finite particle size distributions is discussed. The results indicate that the tangential velocity component is significantly less sensitive to tracking error than the radial component, and that the conventional particle selection criterion (based on the particle Stokes number) may result in either over- or under-sized particles for a specified allowable error bound. Results were demonstrated by means of PIV measurements carried out in air and water using particles with very different properties.

Tracer trajectories and displacement due to a micro-swimmer near a surface

2015 ◽  
Vol 773 ◽  
pp. 498-519 ◽  
Author(s):  
A. J. T. M. Mathijssen ◽  
D. O. Pushkin ◽  
J. M. Yeomans
Keyword(s):  
Particle Transport ◽  
Numerical Study ◽  
Tracer Particle ◽  
Persistence Length ◽  
Theoretical Work ◽  
Solid Boundary ◽  
Tracer Transport ◽  
Tracer Particles ◽  
Recent Theoretical Work ◽  
Run And Tumble

We study tracer particle transport due to flows created by a self-propelled micro-swimmer, such as a swimming bacterium, alga or a microscopic artificial swimmer. Recent theoretical work has shown that as a swimmer moves in the fluid bulk along an infinite straight path, tracer particles far from its path perform closed loops, whereas those close to the swimmer are entrained by its motion. However, in biologically and technologically important cases tracer transport is significantly altered for swimmers that move in a run-and-tumble fashion with a finite persistence length, and/or in the presence of a free surface or a solid boundary. Here we present a systematic analytical and numerical study exploring the resultant regimes and their crossovers. Our focus is on describing qualitative features of the tracer particle transport and developing quantitative tools for its analysis. Our work is a step towards understanding the ecological effects of flows created by swimming organisms, such as enhanced fluid mixing and biofilm formation.

TRACER TIME DISTRIBUTION OF PARTICLES IN POROUS MEDIA

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 1075-1079
Author(s):  
MARIELA ARAUJO
Keyword(s):  
Porous Medium ◽  
Transit Time ◽  
Power Law ◽  
Time Distribution ◽  
Tracer Particle ◽  
Power Law Distribution ◽  
Low Velocity ◽  
Constant Flow Rate ◽  
Variable Permeability ◽  
Tracer Particles

We study the transit time distributions of tracer particles in a porous medium through which a constant flow rate is established. Our model assumes that non-Gaussian dispersion is due to the presence of low velocity zones or channels in parallel with a faster flow path. Each channel is represented as a trap and simulates the existence of variable permeability blocks inside the porous medium. The time the tracer particle spends inside each channel is related to the heterogeneity of the sample, and is assumed here to have a power-law distribution. We compare the transit time distribution of these particles for the case in which the traps are Poisson distributed with the one in which the trap distribution is a power-law function.

scholarly journals Disk Structure in U Geminorum

1977 ◽  
Vol 42 ◽  
pp. 313-321
Author(s):  
J. Madej ◽  
B. Paczyński
Keyword(s):  
Angular Momentum ◽  
Hot Spot ◽  
Outer Part ◽  
Tangential Velocity ◽  
Radial Component ◽  
Small Radius ◽  
Large Radius ◽  
Disk Structure ◽  
Orbital Periods ◽  
The Difference

AbstractA hot spot at the outer rim of the accretion disk dominates the light of U Geminorum at minimum light. We take this as evidence that there is no accretion from the disk onto the white dwarf between the eruptions, and we assume there is no viscosity in the disk at that time. The hot spot is produced by dissipation of the radial component of velocity of stream falling from the inner Lagrangian point. Angular momentum per unit massis smaller in the stream than it is in the outer parts of the disk. This leads to angular momentum redistribution in the outer part of the disk. The difference of tangential velocity between the stream and the disk is dissipated in few orbital periods. These processes make the outer parts of the disk look like a torus. We calculated the structure of the torus in U Geminorum between the eruptions and we obtained the following oarameters: mass of the torus: 10-9 - 10-8 M⊙ (assumed), its optical thickness: 106, the large radius (i.e. the radius of the disk): 0.5 R⊙ (assumed), the small radius (i.e. the half thickness of the outer parts of the disk): 0.05 R⊙. Conditions at the surface of the torus are similar as on the solar surface.

An Investigation of Droplet Diffusion in Isotropic Turbulence With Digital Holographic PIV

Volume 3 ◽  
2004 ◽  
Author(s):  
Edwin Malkiel ◽  
Jian Sheng ◽  
David Garber ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
Isotropic Turbulence ◽  
Diffusion Rate ◽  
Density Ratio ◽  
Digital Camera ◽  
Stokes Number ◽  
Sample Volume ◽  
Tracer Particles ◽  
Fluid Velocities ◽  
Digital Holograms

In-line digital holography is utilized to measure the Lagrangian trajectory of droplets in locally isotropic turbulence. The objective of these measurements is to determine the diffusion rate of these droplets as a function of density ratio between the continuous and dispersed phases, Stokes number and turbulence level relative to the quiescent settling/rise velocity of the droplets. The present experiments are conducted using diesel fuel with diameters of 0.5–2 mm, specific gravity of 0.85 and Stokes number in the 0.2 to 5 range. The droplets are injected into a 50 × 50 × 50 mm sample volume located in the center of a 160 1 tank. The turbulence is generated by four spinning grids, located symmetrically in the corners of the tank. Planar PIV has been used to characterize the turbulence prior to the experiments. A time series of in-line digital holograms is recorded at 2000 frames per second using a 1000×1000 pixel digital camera by back illuminating the sample volume with a collimated laser beam. Numerical reconstruction generates a time series of high-resolution images of the droplets and tracer particles throughout the sample volume. Subsequent analysis is used to obtain the velocity along the droplet trajectory. Lagrangian correlations can then be used for calculating the diffusion rate of these droplets. In a smaller sample volume, with a 15×15 mm cross section, and by using localized seeding, we can also simultaneously measure the droplet velocity along with the velocity of the fluid in the vicinity of this droplet. The results provide statistics on the correlations between the droplet and fluid velocities.

The stability of unsteady axisymmetric incompressible pipe flow close to a piston. Part 2. Experimental investigation and comparison with computation

1971 ◽  
Vol 50 (4) ◽  
pp. 645-655 ◽  
Author(s):  
M. D. Hughes ◽  
J. H. Gerrard
Keyword(s):  
Free Surface ◽  
Pipe Flow ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Radial Component ◽  
Tube Diameter ◽  
Ring Vortex ◽  
Tracer Particles ◽  
The Stability ◽  
Cylindrical Reservoir

Flow visualization has been used quantitatively to determine the flow relative to a piston and a free surface started from rest. The discharge of water from a cylindrical reservoir was investigated. Flow with a free surface started from rest was found to have a critical Reynolds number (based on tube diameter and surface speed) of about 450 above which a ring vortex was produced just below the surface.Measurements at Reynolds numbers of 525 and 1200 were compared with computations made by the methods described in Part 1. The computed drift of tracer particles agreed well with observed values. The largest discrepancies occurred in the radial component of the drift in the early stages of the motion and amounted to 2½% of the tube diameter.

Trajectories of charged tracer particles around a charged sphere in a simple shear flow

1994 ◽  
Vol 263 ◽  
pp. 185-206 ◽  
Author(s):  
A. S. Dukhin ◽  
T. G. M. Van De Ven
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Tracer Particle ◽  
Simple Shear Flow ◽  
Infinite Length ◽  
Charged Sphere ◽  
Neutral Particles ◽  
Tracer Particles ◽  
Two Parameters ◽  
Limiting Case

The trajectories of electrically charged tracer particles travelling around a charged sphere subjected to a simple shear flow have been calculated. This is a limiting case of the relative trajectories of two unequal-sized spheres when the radius ratio a1/a2 approaches zero. Until now these trajectories have been calculated by assuming the additivity of hydrodynamic and electrostatic forces, while neglecting the electroviscous coupling forces. These electroviscous forces are long range and can significantly alter the relative trajectories of spheres. When a1/a2 → 0, it is found that these trajectories depend on two parameters, α and β, which depend on the surface charge density of the tracer particle and the sphere. The relative trajectories of charged particles are qualitatively different from those of neutral particles. There exist six intervals of α-values for which the trajectories of the tracer particle show different features. Several new types of trajectory appear, besides the open and closed trajectories for neutral particles, which we refer to as uni- and bidirectional infinite length trajectories, uni- and bidirectional finite length trajectories, open returning trajectories, and prolate, oblate and circular closed trajectories. This richness of possible trajectories is the result of three electrokinetic phenomena, affecting particle motion: electro-osmotic slip, electrophoretic and diffusiophoretic motion.

scholarly journals Modelling the Energy Spectra of Radio Relics

Galaxies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 111
Author(s):  
Denis Wittor ◽  
Matthias Hoeft ◽  
Marcus Brüggen
Keyword(s):  
Tracer Particle ◽  
Galaxy Cluster ◽  
Cosmic Ray ◽  
Radio Spectrum ◽  
Adiabatic Compression ◽  
Energy Spectra ◽  
Similar Amount ◽  
Inverse Compton Scattering ◽  
Tracer Particles ◽  
Compression And Expansion

Radio relics are diffuse synchrotron sources that illuminate shock waves in the intracluster medium. In recent years, radio telescopes have provided detailed observations about relics. Consequently, cosmological simulations of radio relics need to provide a similar amount of detail. In this methodological work, we include information on adiabatic compression and expansion, which have been neglected in the past in the modelling of relics. In a cosmological simulation of a merging galaxy cluster, we follow the energy spectra of shock accelerated cosmic-ray electrons using Lagrangian tracer particles. On board of each tracer particle, we compute the temporal evolution of the energy spectrum under the influence of synchrotron radiation, inverse Compton scattering, and adiabatic compression and expansion. Exploratory tests show that the total radio power and, hence, the integrated radio spectrum are not sensitive to the adiabatic processes. This is attributed to small changes in the compression ratio over time.

scholarly journals Portfolio Strategies to Track and Outperform a Benchmark

2020 ◽  
Vol 13 (8) ◽  
pp. 171
Author(s):  
Paskalis Glabadanidis
Keyword(s):  
Factor Model ◽  
Signal To Noise Ratio ◽  
Tracking Error ◽  
Selection Criterion ◽  
Stock Index ◽  
Signal To Noise ◽  
Information Ratio ◽  
Noise Ratio ◽  
Fund Portfolio ◽  
Global Minimum Variance Portfolio

I investigate the question of how to construct a benchmark replicating portfolio consisting of a subset of the benchmark’s components. I consider two approaches: a sequential stepwise regression and another method based on factor models of security returns’ first and second moments. The first approach produces the standard hedge portfolio that has the maximum feasible correlation with the benchmark. The second approach produces weights that are proportional to a “signal-to-noise” ratio of factor beta to idiosyncratic volatility. Using a factor model of securities returns allows the use of a larger number of securities than the number of time periods used to estimate the parameters of the factor model. I also consider a second objective that maximizes expected returns subject to a target tracking error variance. The security selection criterion naturally extends to the product of the information ratio and the signal-to-noise ratio. The optimal tracking portfolio is either a one-fund or a two-fund portfolio rule consisting of the optimal hedging portfolio, the tangent portfolio or the global minimum variance portfolio, depending on what constraints are imposed on the objective function. I construct buy-and-hold replicating portfolios using the algorithms presented in the paper to track a widely followed stock index with very good results both in-sample and out-of-sample.

Effects of Preferential Concentration on Heat Transfer in Particle-Based Solar Receivers

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Hadi Pouransari ◽  
Ali Mani
Keyword(s):  
Heat Transfer ◽  
Turbulent Flows ◽  
Particle Transport ◽  
Three Dimensional ◽  
Stokes Number ◽  
Radiative Heating ◽  
Radiation Absorption ◽  
Order Unity ◽  
Carrier Fluid ◽  
Preferential Concentration

The working principle of particle-based solar receivers is to utilize the absorptivity of a dispersed particle phase in an otherwise optically transparent carrier fluid. In comparison to their traditional counterparts, which use a solid surface for radiation absorption, particle-based receivers offer a number of opportunities for improved efficiency and heat transfer uniformity. The physical phenomena at the core of such receivers involve coupling between particle transport, fluid turbulence, and radiative heat transfer. Previous analyses of particle-based solar receivers ignored delicate aspects associated with this three-way coupling. Namely, these investigations considered the flow fields only in the mean sense and ignored turbulent fluctuations and the consequent particle preferential concentration. In the present work, we have performed three-dimensional direct numerical simulations of turbulent flows coupled with radiative heating and particle transport over a range of particle Stokes numbers. Our study demonstrates that the particle preferential concentration has strong implications on the heat transfer statistics. We demonstrate that “for a typical setting” the preferential concentration of particles reduces the effective heat transfer between particles and the gas by as much as 25%. Therefore, we conclude that a regime with Stokes number of order unity is the least preferred for heat transfer to the carrier fluid. We also provide a 1D model to capture the effect of particle spatial distribution in heat transfer.

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