IL08 NEW UNDERSTANDING OF THE INFLUENCE OF STOKES NUMBER ON PARTICLE-LADEN JETS FROM SIMULTANEOUS PLANAR MEASUREMENTS OF NUMBER DENSITY AND VELOCITY

2013 ◽  
Vol 2013.4 (0) ◽  
pp. _IL08-1_-_IL08-12_
Author(s):  
Lau Timothy C. W. ◽  
Nathan Graham J.
Keyword(s):  
Stokes Number ◽  
Number Density ◽  
Particle Laden Jets

Particle Dispersion in Fine Scales of Homogeneous Isotropic Turbulence

2007 ◽  
Author(s):  
M. Sato ◽  
M. Tanahashi ◽  
T. Miyauchi
Keyword(s):  
Isotropic Turbulence ◽  
Major Axis ◽  
Stokes Number ◽  
High Energy ◽  
Energy Dissipation Rate ◽  
Particle Dispersion ◽  
Fine Scale ◽  
Number Density ◽  
Homogeneous Isotropic Turbulence ◽  
Preferential Concentration

Direct numerical simulations of homogeneous isotropic turbulence laden with particles have been conducted to clarify the relationship between particle dispersion and coherent fine scale eddies in turbulence. Dispersion of 106 particles are analyzed for several particle Stokes numbers. The spatial distributions of particles depend on their Stokes number, and the Stokes number that causes preferential concentration of particles is closely related to the time scale of coherent fine scale eddies in turbulence. On the plane perpendicular to the rotating axes of fine scale eddies, number density of particle with particular Stokes number is low at the center of the fine scale eddy, and high in the regions with high energy dissipation rate around the eddy. The maximum number density can be observed at about 1.5 to 2.0 times the eddy radius on the major axis of the fine scale eddy.

scholarly journals Investigation of the Horizontal Motion of Particle-Laden Jets

Computation ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 23 ◽  
Author(s):  
Tooran Tavangar ◽  
Hesam Tofighian ◽  
Ali Tarokh
Keyword(s):  
Reynolds Number ◽  
Gravitational Force ◽  
Dispersion Model ◽  
Passive Scalar ◽  
Stokes Number ◽  
Industrial Applications ◽  
Horizontal Motion ◽  
Jet Flows ◽  
Mass Loading ◽  
Particle Laden Jets

Particle-laden jet flows can be observed in many industrial applications. In this investigation, the horizontal motion of particle laden jets is simulated using the Eulerian–Lagrangian framework. The two-way coupling is applied to the model to simulate the interaction between discrete and continuum phase. In order to track the continuum phase, a passive scalar equation is added to the solver. Eddy Life Time (ELT) is employed as a dispersion model. The influences of different non-dimensional parameters, such as Stokes number, Jet Reynolds number and mass loading ratio on the flow characteristics, are studied. The results of the simulations are verified with the available experimental data. It is revealed that more gravitational force is exerted on the jet as a result of the increase in mass loading, which deflects it more. Moreover, with an increase in the Reynolds number, the speed of the jet rises, and consequently, the gravitational force becomes less capable of deviating the jet. In addition, it is observed that by increasing the Stokes number, the particles leave the jet at higher speed, which causes a lower deviation of the jet.

Preferential concentration driven instability of sheared gas–solid suspensions

2015 ◽  
Vol 770 ◽  
pp. 85-123 ◽  
Author(s):  
M. Houssem Kasbaoui ◽  
Donald L. Koch ◽  
Ganesh Subramanian ◽  
Olivier Desjardins
Keyword(s):  
Turning Point ◽  
Fluid Velocity ◽  
Density Wave ◽  
Multiple Scale ◽  
Stokes Number ◽  
Particle Number Density ◽  
Simple Shear Flow ◽  
Number Density ◽  
Preferential Concentration ◽  
Algebraic Instability

We examine the linear stability of a homogeneous gas–solid suspension of small Stokes number particles, with a moderate mass loading, subject to a simple shear flow. The modulation of the gravitational force exerted on the suspension, due to preferential concentration of particles in regions of low vorticity, in response to an imposed velocity perturbation, can lead to an algebraic instability. Since the fastest growing modes have wavelengths small compared with the characteristic length scale ($U_{g}/{\it\Gamma}$) and oscillate with frequencies large compared with ${\it\Gamma}$, $U_{g}$ being the settling velocity and ${\it\Gamma}$ the shear rate, we apply the WKB method, a multiple scale technique. This analysis reveals the existence of a number density mode which travels due to the settling of the particles and a momentum mode which travels due to the cross-streamline momentum transport caused by settling. These modes are coupled at a turning point which occurs when the wavevector is nearly horizontal and the most amplified perturbations are those in which a momentum wave upstream of the turning point creates a downstream number density wave. The particle number density perturbations reach a finite, but large amplitude that persists after the wave becomes aligned with the velocity gradient. The growth of the amplitude of particle concentration and fluid velocity disturbances is characterised as a function of the wavenumber and Reynolds number ($\mathit{Re}=U_{g}^{2}/{\it\Gamma}{\it\nu}$) using both asymptotic theory and a numerical solution of the linearised equations.

scholarly journals Influence of Stokes number on the velocity and concentration distributions in particle-laden jets

2014 ◽  
Vol 757 ◽  
pp. 432-457 ◽  
Author(s):  
Timothy C. W. Lau ◽  
Graham J. Nathan
Keyword(s):  
Particle Image Velocimetry ◽  
High Resolution ◽  
Particle Concentration ◽  
Particle Image ◽  
Stokes Number ◽  
Exit Plane ◽  
Optical Attenuation ◽  
Image Velocimetry ◽  
Particle Laden Jets

AbstractThe first measurement of the influence of the Stokes number on the distributions of particle concentration and velocity at the exit of a long pipe are reported, together with the subsequent influence on the downstream evolution of these distributions through a particle-laden jet in co-flow. The data were obtained by simultaneous particle image velocimetry (PIV) and planar nephelometry (PN), using four cameras to provide high resolution through the first 30 jet diameters and also correction for optical attenuation. These data provide much more detailed information than is available from previous measurements. From them, a new understanding is obtained of how the Stokes number influences the flow at the jet exit plane and how this influence propagates throughout the jet.

scholarly journals Influence of Microscale Turbulent Droplet Clustering on Radar Cloud Observations

2014 ◽  
Vol 71 (10) ◽  
pp. 3569-3582 ◽  
Author(s):  
Keigo Matsuda ◽  
Ryo Onishi ◽  
Masaaki Hirahara ◽  
Ryoichi Kurose ◽  
Keiko Takahashi ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Stokes Number ◽  
Number Density ◽  
Model Estimate ◽  
Density Spectrum ◽  
Radar Observations ◽  
Wavenumber Range ◽  
Proposed Model ◽  
Wide Range ◽  
Clustering Data

Abstract This study investigates the influence of microscale turbulent clustering of cloud droplets on the radar reflectivity factor and proposes a new parameterization to account for it. A three-dimensional direct numerical simulation of particle-laden isotropic turbulence is performed to obtain turbulent clustering data. The clustering data are then used to calculate the power spectra of droplet number density fluctuations, which show a dependence on the Taylor microscale-based Reynolds number (Reλ) and the Stokes number (St). First, the Reynolds number dependency of the turbulent clustering influence is investigated for 127 < Reλ < 531. The spectra for this wide range of Reλ values reveal that Reλ = 204 is sufficiently large to be representative of the whole wavenumber range relevant for radar observations of atmospheric clouds. The authors then investigate the Stokes number dependency for Reλ = 204 and propose an empirical model for the turbulent clustering influence assuming power laws for the number density spectrum. For Stokes numbers less than 2, the proposed model can estimate the influence of turbulence on the spectrum with an RMS error less than 1 dB when calculated over the wavenumber range relevant for radar observations. For larger Stokes number droplets, the model estimate has larger errors, but the influence of turbulence is likely negligible in typical clouds. Applications of the proposed model to two idealized cloud observing scenarios reveal that microscale turbulent clustering can cause a significant error in estimating cloud droplet amounts from radar observations with microwave frequencies less than 13.8 GHz.

Particle motion in the stagnation zone of an impinging air jet

1995 ◽  
Vol 299 ◽  
pp. 333-366 ◽  
Author(s):  
Steven L. Anderson ◽  
Ellen K. Longmire
Keyword(s):  
Particle Motion ◽  
Small Mass ◽  
Stokes Number ◽  
Forced Flow ◽  
Stagnation Zone ◽  
Number Density ◽  
Mean Flow ◽  
Plate Spacing ◽  
Air Jet ◽  
The Mean

This study investigated particle behaviour in the stagnation zone of natural and forced round impinging air jets using flow visualization, image analysis, and particle image velocimetry. The jet Reynolds number was 21000, and the nozzle to plate spacing was five diameters. Small mass loadings of glass beads with inertial time constants τp of 1.7 and 7 ms were examined. The Stokes number associated with the mean flow Stm = τpU0/D ranged from 0.6 to 2.4, and the Stokes number associated with vortices in the forced flow St′ = τpf ranged from 0.3 to 1.25 where f is the vortex passage frequency. Particle velocities near the wall deviated strongly from fluid velocities, resulting in rebound and non-Stokesian effects (i.e. significant particle Reynolds numbers Rep). The deceleration associated with rebounding caused long particle residence times in the stagnation zone and significant increases in particle number density above the plate. Rebound height and the height of the region of particle accumulation were well correlated and increased with Stm. Particles associated with lower Stm were accelerated in the radial direction more quickly, not only because of their decreased inertia, but also because of the larger fluid velocties encountered. Shear layer vortices produced spatial variations in particle concentration in the free jet which caused number density near the plate to fluctuate with time. The vortices had little effect on particle motion near the stagnation point, however. Only particles in the vicinity of vortex cores felt the influence of the vortex-induced velocity field. Hence, particle motion in the stagnation zone was most dependent on the mean flow (and thus Stm).

scholarly journals A multiphase buoyancy-drag model for the study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in dusty gases

2011 ◽  
Vol 29 (2) ◽  
pp. 201-217 ◽  
Author(s):  
Kaushik Balakrishnan ◽  
Suresh Menon
Keyword(s):  
Particle Size ◽  
Particle Number ◽  
Stokes Number ◽  
Particle Number Density ◽  
Future Research ◽  
Number Density ◽  
Drag Model ◽  
Class 1 ◽  
Multi Mode ◽  
Atwood Number

AbstractA new multiphase buoyancy-drag model is developed for the study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in dusty gases, extending on a counterpart single-phase model developed in the past by Srebro et al. (2003). This model is applied to single- and multi-mode perturbations in dusty gases and both Rayleigh-Taylor and Richtmyer-Meshkov instabilities are investigated. The amplitude for Rayleigh-Taylor growth is observed to be contained within a band, which lies within limits identified by a multiphase Atwood number that is a function of the fluid densities, particle size, and a Stokes number. The amplitude growth is subdued with (1) an increase in particle size for a fixed particle number density and with (2) an increase in particle number density for a fixed particle size. The power law index for Richtmyer-Meshkov growth under multi-mode conditions also shows dependence to the multiphase Atwood number, with the index for the bubble front linearly decreasing and then remaining constant, and increasing non-linearly for the spike front. Four new classes of problems are identified and are investigated for Rayleigh-Taylor growth under multi-mode conditions for a hybrid version of the model: (1) bubbles in a pure gas rising into a region of particles; (2) spikes in a pure gas falling into a region of particles; (3) bubbles in a region of particles rising into a pure gas; and (4) spikes in a region of particles falling into a pure gas. Whereas the bubbles accelerate for class (1) and the spikes for class (4), for classes (2) and (3), the spikes and bubbles, respectively, oscillate in a gravity wave-like phenomenon due to the buoyancy term changing sign alternatively. The spike or bubble front, as the case may be, penetrates different amounts into the dusty or pure gas for every subsequent penetration, due to drag effects. Finally, some extensions to the presently developed multiphase buoyancy-drag model are proposed for future research.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

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