Analysis of Dispersion of Small Spherical Particles in a Random Velocity Field

1990 ◽  
Vol 112 (1) ◽  
pp. 114-120 ◽  
Author(s):  
H. Ounis ◽  
G. Ahmadi
Keyword(s):  
Particle Velocity ◽  
Digital Simulation ◽  
Density Ratio ◽  
Spherical Particles ◽  
Theoretical Predictions ◽  
The Mean ◽  
Analysis Of Dispersion ◽  
Gradient Effects ◽  
Analytical Expressions ◽  
Good Agreement

The equation of motion of a small spherical rigid particle in a turbulent flow field, including the Stokes drag, the Basset force, and the virtual mass effects, is considered. For an isotropic field, the lift force and the velocity gradient effects are neglected. Using the spectral method, responses of the resulting constant coefficient stochastic integrao-differential equation are studied. Analytical expressions relating the Lagrangian energy spectra of particle velocity to that of the fluid are developed and the results are used to evaluate various response statistics. Variations of the mean-square particle velocity and particle diffusivity with size, density ratio and response time are studied. The theoretical predictions are compared with the digital simulation results and the available data and good agreement is observed.

scholarly journals Sedimentation of finite-size spheres in quiescent and turbulent environments

2016 ◽  
Vol 788 ◽  
pp. 640-669 ◽  
Author(s):  
Walter Fornari ◽  
Francesco Picano ◽  
Luca Brandt
Keyword(s):  
Turbulent Flow ◽  
Settling Velocity ◽  
Solid Phase ◽  
Density Ratio ◽  
Finite Size ◽  
Spherical Particles ◽  
Volume Fractions ◽  
Turbulent Environments ◽  
The Mean ◽  
Quiescent Fluid

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

Beam-foil spectroscopy of oxygen in the wavelength region from 270 to 490 Å

1978 ◽  
Vol 56 (5) ◽  
pp. 508-516 ◽  
Author(s):  
Eric H. Pinnington ◽  
Keith E. Donnelly ◽  
J. Anthony Kernahan ◽  
David J. G. Irwin
Keyword(s):  
Satisfactory Agreement ◽  
Wavelength Region ◽  
Theoretical Predictions ◽  
The Mean ◽  
Theoretical Results ◽  
Beam Foil ◽  
Foil Technique ◽  
Good Agreement

We have used the beam-foil technique to study the spectrum of oxygen between 270 and 490 Å. We have measured the mean lives of the 3d2F, 3d4P, 3d4D, 3d′ 2D, 3d′ 2F, 4d4P, and 4d4D terms of O II, the 3s1P0, 3s3P0, 3S5P, 3s′ 3D, 3d3P, 3d3D, 3d3F, and 3d5P terms of O III, and the 3S2S, 3P2P0, and 3s4P0 terms of O IV. All cascade components are adequately explained. Good agreement is found with previous measurements in most cases, but significant discrepancies are found with some earlier results obtained using branches above 2000 Å. Generally satisfactory agreement is also found with theoretical predictions, although disagreement is found for several members of the 2p3–2p23d array in O II f-Values are computed for 18 individual lines, and compared with other experimental and theoretical results. Finally, we discuss briefly the f-value trends along the 2p23P–2p3s3P0 (O III), 2p21D–2p3s1P0 (O III), 2s2p24P–2s2p(3P0)3s4P0 (O IV), and 2p2P0–3s2S (O IV) isoelectronic sequences.

A Simplified Method of Using Four-Hole Probes to Measure Three-Dimensional Flow Fields

1985 ◽  
Vol 107 (1) ◽  
pp. 31-35 ◽  
Author(s):  
N. Sitaram ◽  
A. L. Treaster
Keyword(s):  
Flat Plate ◽  
Three Dimensional ◽  
Flow Fields ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Application Procedure ◽  
Simplified Method ◽  
Theoretical Predictions ◽  
Gradient Effects ◽  
Good Agreement

A simplified method of using four-hole probes to measure three-dimensional flow-fields is presented. This method is similar to an existing calibration and application procedure used for five-hole probes. The new method is demonstrated for two four-hole probes of different geometry. These four-hole probes and a five-hole probe are used to measure the turbulent boundary layer on a flat plate. The results from the three probes are in good agreement with theoretical predictions. The major discrepancies occur near the surface of the flat plate and are attributed to wall vicinity and velocity gradient effects.

Stochastic Lagrangian model for hydrodynamic acceleration of inertial particles in gas–solid suspensions

2016 ◽  
Vol 788 ◽  
pp. 695-729 ◽  
Author(s):  
Sudheer Tenneti ◽  
Mohammad Mehrabadi ◽  
Shankar Subramaniam
Keyword(s):  
Particle Acceleration ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Granular Temperature ◽  
Solid Flow ◽  
Acceleration Model ◽  
The Mean ◽  
Solid Suspensions

The acceleration of an inertial particle in a gas–solid flow arises from the particle’s interaction with the gas and from interparticle interactions such as collisions. Analytical treatments to derive a particle acceleration model are difficult outside the Stokes flow regime, but for moderate Reynolds numbers (based on the mean slip velocity between gas and particles) particle-resolved direct numerical simulation (PR-DNS) is a viable tool for model development. In this study, PR-DNS of freely-evolving gas–solid suspensions are performed using the particle-resolved uncontaminated-fluid reconcilable immersed-boundary method (PUReIBM) that has been extensively validated in previous studies. Analysis of the particle velocity variance (granular temperature) equation in statistically homogeneous gas–solid flow shows that a straightforward extension of a class of mean particle acceleration models (drag laws) to their corresponding instantaneous versions, by replacing the mean particle velocity with the instantaneous particle velocity, predicts a granular temperature that decays to zero, which is at variance with the steady particle granular temperature that is obtained from PR-DNS. Fluctuations in particle velocity and particle acceleration (and their correlation) are important because the particle acceleration–velocity covariance governs the evolution of the particle velocity variance (characterized by the particle granular temperature), which plays an important role in the prediction of the core annular structure in riser flows. The acceleration–velocity covariance arising from hydrodynamic forces can be decomposed into source and dissipation terms that appear in the granular temperature evolution equation, and these have already been quantified in the Stokes flow regime using a combination of kinetic theory closure and multipole expansion simulations. From PR-DNS data we show that the fluctuations in the particle acceleration that are aligned with fluctuations in the particle velocity give rise to a source term in the granular temperature evolution equation. This approach is used to quantify the hydrodynamic source and dissipation terms of granular temperature from PR-DNS results for freely-evolving gas–solid suspensions that are performed over a wide range of solid volume fraction ($0.1\leqslant {\it\phi}\leqslant 0.4$), Reynolds number based on the slip velocity between the solid and the fluid phase ($10\leqslant \mathit{Re}_{m}\leqslant 100$) and solid-to-fluid density ratio ($100\leqslant {\it\rho}_{p}/{\it\rho}_{f}\leqslant 2000$). The straightforward extension of drag law models does not give rise to any source in the granular temperature due to hydrodynamic effects. This motivates the development of better Lagrangian particle acceleration models that can be used in Lagrangian–Eulerian formulations of gas–solid flow. It is found that a Langevin equation for the increment in the particle velocity reproduces PR-DNS results for the stationary particle velocity autocorrelation in freely-evolving suspensions. Based on the data obtained from the simulations, the functional dependence of the Langevin model coefficients on solid volume fraction, Reynolds number and solid-to-fluid density ratio is obtained. This new Lagrangian particle acceleration model reproduces the correct steady granular temperature and can also be adapted to gas–solid flow computations using Eulerian moment equations.

TAMING CHAOS IN A DRIVEN JOSEPHSON JUNCTION

2001 ◽  
Vol 11 (07) ◽  
pp. 1897-1909 ◽  
Author(s):  
R. CHACÓN ◽  
F. PALMERO ◽  
F. BALIBREA
Keyword(s):  
Josephson Junction ◽  
Phase Difference ◽  
Initial Phase ◽  
Chaotic Dynamics ◽  
Numerical Results ◽  
Initial Phase Difference ◽  
Theoretical Predictions ◽  
Melnikov Analysis ◽  
Analytical Expressions ◽  
Good Agreement

We present analytical and numerical results concerning the inhibition of chaos in a single driven Josephson junction by means of an additional weak resonant perturbation. From Melnikov analysis, we theoretically find parameter-space regions, associated with the chaos-suppressing perturbation, where chaotic states can be suppressed. In particular, we test analytical expressions for the intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated. All the theoretical predictions are in overall good agreement with numerical results obtained by simulation.

Opto-Electrical Modeling of CMOS Buried Quad Junction Photodetector

2014 ◽  
Vol 605 ◽  
pp. 470-473 ◽  
Author(s):  
S. Feruglio ◽  
Thierry Courcier ◽  
A. Karami ◽  
A. Alexandre-Gauthier ◽  
O. Romain ◽  
...  
Keyword(s):  
Spectral Response ◽  
Intrinsic Noise ◽  
Response Prediction ◽  
Cmos Technology ◽  
Device Structure ◽  
Double Junction ◽  
The Mean ◽  
Dark Currents ◽  
Analytical Expressions ◽  
Good Agreement

A Buried Quad Junction (BQJ) PhotoDetector (PD), composed of four vertically-stacked p-n junctions, has recently been implemented and fabricated in CMOS technology. The detector, providing four different spectral responses, has higher spectral discriminating ability than both conventional Buried Double Junction (BDJ) and Buried Triple Junction (BTJ) detectors. For rapid system design integrating of the BQJ PD, we propose a BQJ SPICE-like model based on the physical properties of the device structure. The analytical expressions of the four BQJ photocurrents have been developed. Dark currents as well as intrinsic noise can also be evaluated by computations. Results have been compared with both TCAD simulations and measurements. Our model shows a good agreement with measurements and the mean relative error on spectral response prediction is between 6 % and 17 % in function of the observed junction.

scholarly journals Elasto-capillary coalescence of multiple parallel sheets

2013 ◽  
Vol 723 ◽  
pp. 692-705 ◽  
Author(s):  
A. D. Gat ◽  
M. Gharib
Keyword(s):  
Energy Analysis ◽  
Minimal Energy ◽  
Common Assumption ◽  
Viscous Forces ◽  
Theoretical Predictions ◽  
The Mean ◽  
The Stability ◽  
Elastic Sheets ◽  
Theoretical Results ◽  
Good Agreement

AbstractWe analyse two-dimensional clamped parallel elastic sheets which are partially immersed in liquid as a model for elasto-capillary coalescence. In the existing literature this problem is studied via minimal energy analysis of capillary and elastic energies of the post-coalescence state, yielding the maximal stable post-coalescence bundle size. Utilizing modal stability analysis and asymptotic analysis, we studied the stability of the configuration before the coalescence occurred. Our analysis revealed previously unreported relations between viscous forces, body forces, and the instability yielding the coalescence, thus undermining a common assumption that coalescence will occur as long as it will not create a bundle larger than the maximal stable post-coalesced size. A mathematical description of the process creating the hierarchical coalescence structure was obtained and yielded that the mean number of sheets per coalesced region is limited to the subset ${2}^{N} $ where $N$ is the set of natural numbers. Our theoretical results were illustrated by experiments and good agreement with the theoretical predictions was observed.

Comprehensive Dynamic Cutting Force Model and Its Application to Wave-Removing Processes

1988 ◽  
Vol 110 (2) ◽  
pp. 153-161 ◽  
Author(s):  
D. W. Wu
Keyword(s):  
Cutting Force ◽  
Machining Process ◽  
Plastic Deformation Zone ◽  
Force Model ◽  
Cutting Force Model ◽  
Dynamic Cutting Force ◽  
Theoretical Predictions ◽  
Force Variation ◽  
The Mean ◽  
Good Agreement

A new concept is taken to develop a comprehensive cutting force model for analyzing the dynamic behavior of the machining process. The model is derived based on the principles of the cutting mechanics, and takes into account the fluctuation of the mean factional coefficient on the tool-chip interface as well as the variations of the normal hydrostatic pressure distribution and the shear flow stress along the primary plastic deformation zone. The model has been tested through computer simulation for orthogonal wave-removing processes by reference to an existing experimental evidence. The result indicates a generally good agreement with the theoretical predictions except that the amplitude of the force variation in the feeding direction appears to be underestimated. An explanation is also given.

Sedimentation and sediment flow in settling tanks with inclined walls

1995 ◽  
Vol 290 ◽  
pp. 39-66 ◽  
Author(s):  
B. Kapoor ◽  
A. Acrivos
Keyword(s):  
Layer Thickness ◽  
Particle Velocity ◽  
Slip Velocity ◽  
Laser Doppler Anemometry ◽  
Finite Size ◽  
Velocity Profiles ◽  
Spherical Particles ◽  
Sediment Layer ◽  
Inclined Plate ◽  
Theoretical Predictions

The flow of a sediment layer that forms on an inclined plate as a consequence of the steady sedimentation of spherical particles was investigated theoretically as well as experimentally. The theoretical analysis was based on the model proposed by Nir & Acrivos (1990), modified to include shear-induced diffusion due to gradients in the shear stress as well as a slip velocity along the wall due to the finite size of the particles. The resulting set of partial differential equations, which is amenable to a similarity-type solution both near the leading edge as well as far downstream, was solved numerically using a finite difference scheme thereby yielding theoretical predictions for the particle concentration and velocity profiles, plus the local sediment layer thickness, all along the plate. In addition, a new experimental technique based on laser Doppler anemometry was developed and was used to measure the particle velocity profiles in the highly concentrated sediment layer as well as the corresponding slip coefficient which relates the slip velocity to the velocity gradient adjacent to a wall. The thickness profile of the sediment layer was also measured experimentally by means of video imaging. It was found that the experimental results thus obtained for the particle velocity profile and for the local sediment layer thickness were in very good agreement with the corresponding theoretical predictions especially considering that the latter did not make use of any adjustable parameters.

scholarly journals Laboratory Measurements of Light Scattering by Dust Particles

1996 ◽  
Vol 150 ◽  
pp. 409-413
Author(s):  
Patrick P. Combet ◽  
Philippe L. Lamy
Keyword(s):  
Light Scattering ◽  
Laser Beam ◽  
Mie Theory ◽  
Spherical Particles ◽  
Dust Particles ◽  
Laboratory Measurements ◽  
Scattering Function ◽  
Hene Laser ◽  
Set Up ◽  
Good Agreement

AbstractWe have set up an experimental device to optically study the scattering properties of dust particles. Measurements over the 8 — 174° interval of scattering angles are performed on a continuously flowing dust loaded jet illuminated by a polarized red HeNe laser beam. The scattering is averaged over the population of the dust particles in the jet, which can be determined independently, and give the “volume scattering function” for the two directions of polarization directly. While results for spherical particles are in good agreement with Mie theory, those for arbitrary particles show conspicuous deviations.

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