Scaling laws for migrating cloud of low-Reynolds-number particles with Coulomb repulsion

2017 ◽  
Vol 835 ◽  
pp. 880-897 ◽  
Author(s):  
Sheng Chen ◽  
Wenwei Liu ◽  
Shuiqing Li
Keyword(s):  
Reynolds Number ◽  
Scaling Laws ◽  
Particle Number ◽  
Coulomb Repulsion ◽  
Particle Number Density ◽  
Particle Size Ratio ◽  
Wide Range ◽  
Self Similar ◽  
Charge Parameter ◽  
Strong Repulsion

We investigate the evolution of spherical clouds of charged particles that migrate under the action of a uniform external electrostatic field. Hydrodynamic interactions are modelled by Oseen equations and the Coulomb repulsion is calculated through pairwise summation. It is shown that strong long-range Coulomb repulsion can prevent the breakup of the clouds covering a wide range of particle Reynolds number $Re_{p}$ and cloud-to-particle size ratio $R_{0}/r_{p}$. A dimensionless charge parameter $\unicode[STIX]{x1D705}_{q}$ is constructed to quantify the effect of the repulsion, and a critical value $\unicode[STIX]{x1D705}_{q,t}$ is deduced, which successfully captures the transition of a cloud from hydrodynamically controlled regime to repulsion-controlled regime. Our results also reveal that, with sufficiently strong repulsion, the cloud undergoes a universal self-similar expansion. Scaling laws of cloud radius $R_{cl}$ and particle number density $n$ are obtained by solving a continuum convection equation.

scholarly journals Spectral analysis of the transition to turbulence from a dipole in stratified fluid

2012 ◽  
Vol 713 ◽  
pp. 86-108 ◽  
Author(s):  
Pierre Augier ◽  
Jean-Marc Chomaz ◽  
Paul Billant
Keyword(s):  
Reynolds Number ◽  
Spectral Analysis ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Scaling Laws ◽  
Stratified Fluid ◽  
Shear Instability ◽  
Transition To Turbulence ◽  
Small Scale ◽  
Wide Range

AbstractWe investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb–Chaplygin dipole in a stratified fluid for a high Reynolds number $Re= 28\hspace{0.167em} 000$ and a wide range of horizontal Froude number ${F}_{h} \in [0. 0225~0. 135] $ and buoyancy Reynolds number $\mathscr{R}= Re{{F}_{h} }^{2} \in [14~510] $. The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale ${L}_{b} = U/ N$, where $U$ is the characteristic horizontal velocity of the dipole and $N$ the Brunt–Väisälä frequency; second, the destabilization of the Kelvin–Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits a ${{\varepsilon }_{K} }^{2/ 3} { k}_{h}^{\ensuremath{-} 5/ 3} $ power law (where ${k}_{h} $ is the horizontal wavenumber and ${\varepsilon }_{K} $ is the dissipation rate of kinetic energy) from ${k}_{b} = 2\lrm{\pi} / {L}_{b} $ to the dissipative scales, with an energy deficit between the integral scale and ${k}_{b} $ and an excess around ${k}_{b} $. The vertical spectrum of kinetic energy can be expressed as $E({k}_{z} )= {C}_{N} {N}^{2} { k}_{z}^{\ensuremath{-} 3} + C{{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ where ${C}_{N} $ and $C$ are two constants of order unity and ${k}_{z} $ is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ shape and approaches the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum for ${k}_{z} \gt {k}_{o} $, ${k}_{o} $ being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ spectrum is associated with large horizontal scales $\vert {\mathbi{k}}_{h} \vert \lt {k}_{b} $ and the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum with the scales $\vert {\mathbi{k}}_{h} \vert \gt {k}_{b} $.

Reynolds number effects on lipid vesicles

2012 ◽  
Vol 711 ◽  
pp. 122-146 ◽  
Author(s):  
David Salac ◽  
Michael J. Miksis
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Scaling Laws ◽  
Circulatory System ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Fluid Viscosity ◽  
Maximum Tension ◽  
Wide Range ◽  
Human Circulatory System

AbstractVesicles exposed to the human circulatory system experience a wide range of flows and Reynolds numbers. Previous investigations of vesicles in fluid flow have focused on the Stokes flow regime. In this work the influence of inertia on the dynamics of a vesicle in a shearing flow is investigated using a novel level-set computational method in two dimensions. A detailed analysis of the behaviour of a single vesicle at finite Reynolds number is presented. At low Reynolds numbers the results recover vesicle behaviour previously observed for Stokes flow. At moderate Reynolds numbers the classical tumbling behaviour of highly viscous vesicles is no longer observed. Instead, the vesicle is observed to tank-tread, with an equilibrium angle dependent on the Reynolds number and the reduced area of the vesicle. It is shown that a vesicle with an inner/outer fluid viscosity ratio as high as 200 will not tumble if the Reynolds number is as low as 10. A new damped tank-treading behaviour, where the vesicle will briefly oscillate about the equilibrium inclination angle, is also observed. This behaviour is explained by an investigation on the torque acting on a vesicle in shear flow. Scaling laws for vesicles in inertial flows have also been determined. It is observed that quantities such as vesicle tumbling period follow square-root scaling with respect to the Reynolds number. Finally, the maximum tension as a function of the Reynolds number is also determined. It is observed that, as the Reynolds number increases, the maximum tension on the vesicle membrane also increases. This could play a role in the creation of stable pores in vesicle membranes or for the premature destruction of vesicles exposed to the human circulatory system.

scholarly journals Numerical validation of novel scaling laws for air entrainment in water

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Daniele Catucci ◽  
Riccardo Briganti ◽  
Valentin Heller
Keyword(s):  
Scaling Laws ◽  
Stokes Equations ◽  
Scale Effects ◽  
Air Entrainment ◽  
Navier Stokes ◽  
The Novel ◽  
Water Flows ◽  
Wide Range ◽  
Self Similar ◽  
Flow Variables

The Froude scaling laws have been used to model a wide range of water flows at reduced size for almost a century. In such Froude scale models, significant scale effects for air–water flows (e.g. hydraulic jumps or wave breaking) are typically observed. This study introduces novel scaling laws, excluding scale effects in the modelling of air–water flows. This is achieved by deriving the conditions under which the governing equations are self-similar. The one-parameter Lie group of point-scaling transformations is applied to the Reynolds-averaged Navier–Stokes equations, including surface tension effects. The scaling relationships between variables are derived for the flow variables, fluid properties and initial and boundary conditions. Numerical simulations are conducted to validate the novel scaling laws for (i) a dam break flow interacting with an obstacle and (ii) a vertical plunging water jet. Results for flow variables, void fraction and turbulent kinetic energy are shown to be self-similar at different scales, i.e. they collapse in dimensionless form. Moreover, these results are compared with those obtained using the traditional Froude scaling laws, showing significant scale effects. The novel scaling laws are a more universal and flexible alternative with a genuine potential to improve laboratory modelling of air–water flows.

A shallow-water model for high-Reynolds-number gravity currents for a wide range of density differences and fractional depths

2007 ◽  
Vol 579 ◽  
pp. 373-382 ◽  
Author(s):  
MARIUS UNGARISH
Keyword(s):  
Reynolds Number ◽  
Shallow Water ◽  
Large Time ◽  
Gravity Current ◽  
Water Model ◽  
Wide Range ◽  
Front Condition ◽  
Practical Limit ◽  
Self Similar ◽  
High Reynolds

We consider the propagation of a gravity current of density ρc from a lock of length x0 and height h0 into an ambient fluid of density ρa in a channel of height H. When the Reynolds number is large, the resulting flow is governed by the parameters ρc/ρa and H* = H/h0. We show that the shallow-water one-layer model, combined with a Benjamin-type front condition, provides a versatile formulation for the thickness and speed of the current, without any adjustable constants. The results cover in a continuous manner the range of light ρc/ρa ≪ 1, Boussinesq ρc/ρa ≈ 1, and heavy ρc/ρa ≫ 1 currents in a fairly wide range of depth ratio. We obtain analytical solutions for the initial dam-break or slumping stage of propagation with constant speed, and derive explicitly the trends for small and large values of the governing parameters. This reveals the main features: (a) the heavy current propagates faster and its front is thinner than for the light counterpart; (b) the speed of the heavy current depends little on H*, while that of the light current increases with H*; and (c) in the shallow ambient case (H* close to 1) the light current is choked to move with the thickness of half-channel, while the heavy current typically moves with an unrestricted smaller thickness. These qualitative predictions are in accord with previous observations, and some quantitative comparisons with available experimental and numerical simulations data also show fair agreement. However, given the paucity of the available data, the main deficiency of the model is the unknown practical limit of applicability. For large time, t, a self-similar propagation with t2/3 is feasible for both the heavy and light currents, but the thickness profiles display differences.

Pressure statistics in self-similar freely decaying isotropic turbulence

2013 ◽  
Vol 717 ◽  
Author(s):  
Marcello Meldi ◽  
Pierre Sagaut
Keyword(s):  
Reynolds Number ◽  
Scaling Laws ◽  
Isotropic Turbulence ◽  
Threshold Value ◽  
Time Decay ◽  
Self Similar ◽  
High Reynolds ◽  
Almost All ◽  
Time Decay Rate ◽  
Large Eddies

AbstractThe time evolution of pressure statistics in freely decaying homogeneous isotropic turbulence (HIT) is investigated via eddy-damped quasi-normal Markovian (EDQNM) computations. The present results show that the time decay rate of pressure-based statistical quantities, such as pressure variance and pressure gradient variance, are sensitive to the breakdown of permanence of large eddies. New formulae for the associated time-decay exponents are proposed, which extend previous relations proposed in Lesieur, Ossia & Metais (Phys. Fluids, vol. 11, 1999, p. 1535). Particular attention is paid to finite-Reynolds-number (FRN) effects on the pressure spectrum and pressure statistics. The results also suggest that $R{e}_{\lambda } = O(1{0}^{4} )$ must be considered to observe a one-decade inertial range in the pressure spectrum with Kolmogorov $- 7/ 3$ scaling. This threshold value is larger than almost all existing direct numerical simulation (DNS) and experimental data, justifying the discussion about other possible scaling laws. The $- 5/ 3$ slope reported in some DNS data is also recovered by the EDQNM model, but it is observed to be a low-Reynolds-number effect. Another important result is that FRN effects yield a departure from asymptotic theoretical behaviours which appear similar to some effects attributed to intermittency by most authors. This is exemplified by the ratio between pressure-based and velocity-based Taylor microscales. Therefore, high-Reynolds-number DNS or experiments such that $R{e}_{\lambda } = O(1{0}^{4} )$ would be required in order to remove FRN effects and to analyse pure intermittency effects.

scholarly journals Predicting specific impulse distributions for spherical explosives in the extreme near-field using a Gaussian function

2021 ◽  
pp. 204141962199349
Author(s):  
Jordan J Pannell ◽  
George Panoutsos ◽  
Sam B Cooke ◽  
Dan J Pope ◽  
Sam E Rigby
Keyword(s):  
Scaling Laws ◽  
Near Field ◽  
Specific Impulse ◽  
Gaussian Function ◽  
Data Driven ◽  
Blast Load ◽  
Structural Deformation ◽  
Load Prediction ◽  
Validation Data ◽  
Wide Range

Accurate quantification of the blast load arising from detonation of a high explosive has applications in transport security, infrastructure assessment and defence. In order to design efficient and safe protective systems in such aggressive environments, it is of critical importance to understand the magnitude and distribution of loading on a structural component located close to an explosive charge. In particular, peak specific impulse is the primary parameter that governs structural deformation under short-duration loading. Within this so-called extreme near-field region, existing semi-empirical methods are known to be inaccurate, and high-fidelity numerical schemes are generally hampered by a lack of available experimental validation data. As such, the blast protection community is not currently equipped with a satisfactory fast-running tool for load prediction in the near-field. In this article, a validated computational model is used to develop a suite of numerical near-field blast load distributions, which are shown to follow a similar normalised shape. This forms the basis of the data-driven predictive model developed herein: a Gaussian function is fit to the normalised loading distributions, and a power law is used to calculate the magnitude of the curve according to established scaling laws. The predictive method is rigorously assessed against the existing numerical dataset, and is validated against new test models and available experimental data. High levels of agreement are demonstrated throughout, with typical variations of <5% between experiment/model and prediction. The new approach presented in this article allows the analyst to rapidly compute the distribution of specific impulse across the loaded face of a wide range of target sizes and near-field scaled distances and provides a benchmark for data-driven modelling approaches to capture blast loading phenomena in more complex scenarios.

The Effect of Pulsed Blowing on the Boundary Layer of a Highly Loaded Low Pressure Turbine Blade

2013 ◽  
Author(s):  
Marion Mack ◽  
Roland Brachmanski ◽  
Reinhard Niehuis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Trailing Edge ◽  
Low Pressure Turbine ◽  
Wide Range ◽  
Highly Loaded

The performance of the low pressure turbine (LPT) can vary appreciably, because this component operates under a wide range of Reynolds numbers. At higher Reynolds numbers, mid and aft loaded profiles have the advantage that transition of suction side boundary layer happens further downstream than at front loaded profiles, resulting in lower profile loss. At lower Reynolds numbers, aft loading of the blade can mean that if a suction side separation exists, it may remain open up to the trailing edge. This is especially the case when blade lift is increased via increased pitch to chord ratio. There is a trend in research towards exploring the effect of coupling boundary layer control with highly loaded turbine blades, in order to maximize performance over the full relevant Reynolds number range. In an earlier work, pulsed blowing with fluidic oscillators was shown to be effective in reducing the extent of the separated flow region and to significantly decrease the profile losses caused by separation over a wide range of Reynolds numbers. These experiments were carried out in the High-Speed Cascade Wind Tunnel of the German Federal Armed Forces University Munich, Germany, which allows to capture the effects of pulsed blowing at engine relevant conditions. The assumed control mechanism was the triggering of boundary layer transition by excitation of the Tollmien-Schlichting waves. The current work aims to gain further insight into the effects of pulsed blowing. It investigates the effect of a highly efficient configuration of pulsed blowing at a frequency of 9.5 kHz on the boundary layer at a Reynolds number of 70000 and exit Mach number of 0.6. The boundary layer profiles were measured at five positions between peak Mach number and the trailing edge with hot wire anemometry and pneumatic probes. Experiments were conducted with and without actuation under steady as well as periodically unsteady inflow conditions. The results show the development of the boundary layer and its interaction with incoming wakes. It is shown that pulsed blowing accelerates transition over the separation bubble and drastically reduces the boundary layer thickness.

scholarly journals Airborne measurements of trace gas and aerosol particle emissions from biomass burning in Amazonia

2005 ◽  
Vol 5 (11) ◽  
pp. 2989-3002 ◽  
Author(s):  
P. Guyon ◽  
G. P. Frank ◽  
M. Welling ◽  
D. Chand ◽  
P. Artaxo ◽  
...  
Keyword(s):  
Large Scale ◽  
Particle Number ◽  
Aerosol Particles ◽  
Secondary Growth ◽  
Combustion Efficiency ◽  
Vertical Transport ◽  
Airborne Measurements ◽  
Sampling Campaign ◽  
Wide Range ◽  
Emission Ratios

Abstract. As part of the LBA-SMOCC (Large-Scale Biosphere-Atmosphere Experiment in Amazonia - Smoke, Aerosols, Clouds, Rainfall, and Climate) 2002 campaign, we studied the emission of carbon monoxide (CO), carbon dioxide (CO2), and aerosol particles from Amazonian deforestation fires using an instrumented aircraft. Emission ratios for aerosol number (CN) relative to CO (ERCN/CO) fell in the range 14-32 cm-3 ppb-1 in most of the investigated smoke plumes. Particle number emission ratios have to our knowledge not been previously measured in tropical deforestation fires, but our results are in agreement with values usually found from tropical savanna fires. The number of particles emitted per amount biomass burned was found to be dependent on the fire conditions (combustion efficiency). Variability in ERCN/CO between fires was similar to the variability caused by variations in combustion behavior within each individual fire. This was confirmed by observations of CO-to-CO2 emission ratios (ERCO/CO2), which stretched across the same wide range of values for individual fires as for all the fires observed during the sampling campaign, reflecting the fact that flaming and smoldering phases are present simultaneously in deforestation fires. Emission factors (EF) for CO and aerosol particles were computed and a correction was applied for the residual smoldering combustion (RSC) fraction of emissions that are not sampled by the aircraft, which increased the EF by a factor of 1.5-2.1. Vertical transport of smoke from the boundary layer (BL) to the cloud detrainment layer (CDL) and the free troposphere (FT) was found to be a very common phenomenon. We observed a 20% loss in particle number as a result of this vertical transport and subsequent cloud processing, attributable to in-cloud coagulation. This small loss fraction suggests that this mode of transport is very efficient in terms of particle numbers and occurs mostly via non-precipitating clouds. The detrained aerosol particles released in the CDL and FT were larger than in the unprocessed smoke, mostly due to coagulation and secondary growth, and therefore more efficient at scattering radiation and nucleating cloud droplets. This process may have significant atmospheric implications on a regional and larger scale.

Experimentally determined particle number density statistics in an industrial-scale, pulverized-coal-fired boiler

1993 ◽  
Vol 7 (6) ◽  
pp. 842-851 ◽  
Author(s):  
M. Queiroz ◽  
M. P. Bonin ◽  
J. S. Shirolkar ◽  
R. W. Dawson
Keyword(s):  
Particle Number ◽  
Particle Number Density ◽  
Pulverized Coal ◽  
Industrial Scale ◽  
Number Density

The next step in precipitation polymerization of N-isopropylacrylamide: particle number density control by monochain globule surface charge modulation

2016 ◽  
Vol 7 (32) ◽  
pp. 5123-5131 ◽  
Author(s):  
O. L. J. Virtanen ◽  
M. Brugnoni ◽  
M. Kather ◽  
A. Pich ◽  
W. Richtering
Keyword(s):  
Particle Size ◽  
Robust Control ◽  
Surface Charge ◽  
Particle Number ◽  
Particle Number Density ◽  
Precipitation Polymerization ◽  
Number Density ◽  
Density Control ◽  
Charge Modulation

Many applications of poly(N-isopropylacrylamide) microgels necessitate robust control over particle size.

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