Dense Particle Clouds Research Articles

Instabilities of a circular moderately dense particle cloud impacted by an incident shock

Shock-driven gas-particle flows exist in a wide variety of physical systems, covering the range from dilute to dense regime. There are a lot of fundamental questions remaining to be answered, like the evolutions of flow instability, two-phase interactions, and inter-particle collision effects. In this work, the Eulerian-Lagrangian approach with gas-particle four-way coupling is applied to model two-dimensional shock-driven gas-particle flow under the moderately dense regime. For the gas flow, the formation mechanism of primary and secondary vortexes is discussed. The primary vortex is caused by the roll-up of slip line, while the secondary vortexes are induced by the velocity and density difference between the penetrating flow of particle-laden zone and the outside mainstream. Parametric studies of different Mach numbers, particle diameters and initial volume fractions have been performed to investigate the effects on shock behaviours and slip line instabilities. For the particle phase, a high-volume-fraction compression region forms at the upstream cloud zone, which blocks the penetrating gas, and results in the formation of slip line. The cloud tail is mainly composed of the upstream edge particles. The inter-particle collisions have impact on the particle distributions, and greatly affect the slip line stability at the upstream cloud edge. This work provides valuable insights into the instability mechanism of compressible gas-solid flow and the particle dispersion behaviours. However, it is important to note that our analysis is based on a two-dimensional configuration. In a real three-dimensional context, the generation of vortices is likely to differ, and may affect the particle dynamics to a certain degree.

Radiative transfer simulations for in-situ particle size diagnostic in reactive, particle growing plasmas

When considering particles produced in reactive plasmas, their basic properties, such as refractive index and grain size often need to be known. They can be constrained both ex-situ, e.g. by microscopy, and in-situ by polarimetry, i.e. analyzing the polarization state of scattered light. Polarimetry has the advantage of temporal resolution and real-time measurement, but the analysis is often limited by the assumption of single scattering and thus optically thin dust clouds. This limits the investigation of the growth process typically to grain sizes smaller than about 200 nm. Using 3D polarized radiative transfer simulations, however, it is possible to consider multiple scattering and to analyze the properties of dense particle clouds. We study the impact of various properties of dust clouds on the scattering polarization, namely the optical depth of the cloud, the spatial density distribution of the particles, their refractive index as well as the particle size dispersion. We find that ambiguities can occur regarding optical depth and spatial density distribution as well as regarding refractive index and particle size dispersion. Determining the refractive index correctly is especially important as it has a strong impact on the derived particle sizes. With this knowledge, we are able to design an in-situ diagnostics strategy for the investigation of the particle growth process based on radiative transfer simulations which are used to model the polarization over the whole growth process. The application of this strategy allows us for the first time to analyze the polarization measured during a growth experiment in a reactive argon-acetylene plasma for particle radii up to 280 nm.

A hybrid Eulerian-Eulerian/Eulerian-Lagrangian method for dense-to-dilute dispersed phase flows

Problems involving a transition between dense and dilute dispersed phase regimes often require hybridization of Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) methods for accurate and efficient computational modeling. A hybrid EE-EL formulation is developed in this work from first principles, which asymptotes to well-established EE and EL methods in limiting conditions. A smooth and dynamic transition criterion and a corresponding algorithm for conversion between the two representations of the dispersed phase are developed. To use EE and EL in their respective regions of effectiveness, the transition criterion is designed as a function of local volume fraction and local kinetic energy of random uncorrelated motion of particles. Several one-dimensional numerical tests are conducted to analyze limits of the hybrid EE-EL method in dense (up to 65% volume loading) and dilute conditions, at first, without any conversion between EE and EL, and then the ability of the conversion algorithm to smoothly transition from EE to EL and vice versa is evaluated using prespecified and dynamically computed transition criteria for one- and two-dimensional tests. Particle evolution in two-dimensional frozen turbulence is simulated to evaluate the method's ability to dynamically transition from EE to EL and vice versa in regions of particle trajectory crossing. Finally, the hybrid method is used for simulating dispersion of an initially dense particle cloud in a three-dimensional spherical sector blast.

Dense Particle Clouds in Laboratory Experiments in Context of Drafting and Streaming Instability

Abstract The streaming instability, as an example of instabilities driven by particle feedback on a gas flow, has been proven to have a major role in controlling the formation of planetesimals. These instabilities in protoplanetary disks occur at the transition from being gas-dominated to being dust and ice particle dominated. Here, we present experiments to approach this situation in the laboratory for particles in the Knudsen flow regime. In these experiments, we observe a particle cloud trapped for about 30 s in a rotating system under Earth’s gravity. For average dust-to-gas ratios up to 0.08, particles behave like individual test particles. Their sedimentation speed is identical to that of a single free-falling particle, even in locally denser regions. However, for higher dust-to-gas ratios, the motion of particles becomes sensitive to clumping. Particles in locally denser regions now sediment faster. Their sedimentation speed then depends linearly on the overall dust-to-gas ratio. This clearly shows a transition from tracerlike behavior to collective behavior. Beyond these findings, these types of experiments can now be used as a gauge to test particle feedback models in astrophysical hydrocodes, which are currently used for numerical simulations of streaming instabilities.

The dynamics of dense particle clouds subjected to shock waves. Part 2. Modeling/numerical issues and the way forward

We address a recent extension of the point-particle method to non-dilute clouds dispersed by shock waves and a claim that added mass and viscous unsteady forces remain effective for a significant portion of the transient, “even when the particle-to-gas density ratio is large” (Ling et al, Phys. Fluids, 24, 113301, 2012). We demonstrate that this (Euler-Lagrange) model is prey to numerical instabilities, that the results depend strongly on the method(s) employed to stabilize the computation, and that the claim about the significance of these unsteady forces, for such systems, is unwarranted. Moreover, we show that these problems exist even in the application of this model to dilute dispersions, and that while maintaining the coupling length scales in the calculations yields convergence on grid refinement, the results are not physically meaningful. Further, computations in a fully-Eulerian framework, including a multi-field rendition, exhibit fundamentally similar trends, leading us to suggest that the root-cause is to be found in the (common) Eulerian part of the two modeling frameworks. This is confirmed by first-of-a-kind direct numerical simulations, which in agreement with our experiments, reveal that high-speed flows down steep volume-fraction gradients are naturally dispersive. This clearly-stabilizing mechanism is missed in current models; worse, the behaviors they exhibit are cumulative. Based on the detailed DNS results, we present a plan for the way ahead, as we conclude that contrary to many previous “diagnoses”, and attempted “remedies”, the ill-posedness (name for the catastrophic instabilities discussed) of the mathematical problem is not just an annoying aberration, but rather it is in the very essence of missing these key physics.

On turbulent particle fountains

We describe new experiments in which particle-laden turbulent fountains with source Froude numbers $20>Fr_{0}>6$ are produced when particle-laden fresh water is injected upwards into a reservoir filled with fresh water. We find that the ratio $U$ of the particle fall speed to the characteristic speed of the fountain determines whether the flow is analogous to a single-phase fountain ($U\ll 1$) or becomes a fully separated flow ($U\geqslant 1$). In the single-phase limit, a fountain with momentum flux $M$ and buoyancy flux $B$ oscillates about the mean height, $h_{m}=(1.56\pm 0.04)M^{3/4}B^{-1/2}$, as fluid periodically cascades from the maximum height, $h_{t}=h_{m}+{\rm\Delta}h$, to the base of the tank. Experimental measurements of the speed $u$ and radius $r$ of the fountain at the mean height $h_{m}$, combined with the conservation of buoyancy, suggest that $Fr(h_{m})=u(g^{\prime }r)^{-1/2}\approx 1$. Using these values, we find that the classical scaling for the frequency of the oscillations, ${\it\omega}\sim BM^{-1}$, is equivalent to the scaling $u(h_{m})/r(h_{m})$ for a fountain supplied at $z=h_{m}$ with $Fr=1$ (Burridge & Hunt, J. Fluid Mech., vol. 728, 2013, pp. 91–119). This suggests that the oscillations are controlled in the upper part of the fountain where $Fr\leqslant 1$, and that they may be understood in terms of a balance between the upward supply of a growing dense particle cloud, at the height where $Fr=1$, and the downward flow of this cloud. In contrast, in the separated flow regime, we find that particles do not reach the height at which $Fr=1$: instead, they are transported to the level at which the upward speed of the fountain fluid equals their fall speed. The particles then continuously sediment while the particle-free fountain fluid continues to rise slowly above the height of particle fallout, carried by its momentum.

The dynamics of dense particle clouds subjected to shock waves. Part 1. Experiments and scaling laws

We quantify experimentally the dispersal characteristics of dense particle clouds in high-speed interactions with an atmosphere. Focused on the fundamentals, the experiments, conducted in a large-scale shock tube, involve a well-characterized ‘curtain’ of (falling) particles that fully occupies the cross-sectional area of the expansion section. The particle material (glass) and size (${\sim}$1 mm) are fixed, as is the curtain thickness (${\sim}$30 mm) and the particle volume fractions in it, varying from ${\sim}$58 % at the top of the curtain to ${\sim}$24 % near the bottom. Thus, the principal experimental variable is the impacting shock strength, with Mach numbers varying from 1.2 to 2.6, and flow speeds that cover from subsonic ($M_{IS}\sim 0.3$) to transonic and supersonic ($M_{IS}\sim 1.2$). The peak shock pressure ratio, 7.6, yields a flow speed of ${\sim}\!630~\text{m}~\text{s}^{-1}$, and a curtain expansion rate at ${\sim}$20 000 g. We record visually (high-speed, particle-resolving shadowgraphic method) the reflected/transmitted pressure waves and the transmitted contact wave, as well as the curtain displacements, and we measure the reflected/transmitted pressure transients. Data analysis yields simple rules for the amplitudes of the reflected pressure waves and the rapid cloud expansions observed, and we discover a time scaling that hints at a universal regime for cloud expansion. The data and these data-analysis results can provide the validation basis for numerical simulations meant to enable a deeper understanding of the key physics that drive this rather complex dispersal process.

How to form planetesimals from mm-sized chondrules and chondrule aggregates

The size distribution of asteroids and Kuiper belt objects in the solar system is difficult to reconcile with a bottom-up formation scenario due to the observed scarcity of objects smaller than $\sim$100 km in size. Instead, planetesimals appear to form top-down, with large $100-1000$ km bodies forming from the rapid gravitational collapse of dense clumps of small solid particles. In this paper we investigate the conditions under which solid particles can form dense clumps in a protoplanetary disk. We use a hydrodynamic code to model the interaction between solid particles and the gas inside a shearing box inside the disk, considering particle sizes from sub-millimeter-sized chondrules to meter-sized rocks. We find that particles down to millimeter sizes can form dense particle clouds through the run-away convergence of radial drift known as the streaming instability. We make a map of the range of conditions (strength of turbulence, particle mass-loading, disk mass, and distance to the star) which are prone to producing dense particle clumps. Finally, we estimate the distribution of collision speeds between mm-sized particles. We calculate the rate of sticking collisions and obtain a robust upper limit on the particle growth timescale of $\sim$$10^5$ years. This means that mm-sized chondrule aggregates can grow on a timescale much smaller than the disk accretion timescale ($\sim$$10^6 - 10^7$ years). Our results suggest a pathway from the mm-sized grains found in primitive meteorites to fully formed asteroids. We speculate that asteroids may form from a positive feedback loop in which coagualation leads to particle clumping driven by the streaming instability. This clumping, in turn reduces collision speeds and enhances coagulation.} Future simulations should model coagulation and the streaming instability together to explore this feedback loop further.

Dense particle cloud dispersion by a shock wave

The study of particle cloud dispersion by a shock wave is important to many applications, including multiphase explosives that comprise a condensed explosive surrounded with packed micrometric reactive metal particles. Detonation of the explosive generates a shock wave which accelerates and compacts the particles. The particles are further accelerated from the reflected rarefaction as the shock wave arrives at the free-surface of the particles, leading to their rapid dispersal into the air. Generally speaking, the shock wave initially propagates through a granular particle bed and much later in time the particle cloud is dispersed and the flow becomes a dilute gas-solid flow. Between these two regimes the flow is characterized by a dense gas-solid flow [1]. Reactive multiphase flow models have been used to simulate the acceleration and dispersion of the particle cloud [2]. The fidelity of the simulations is severely limited by the physical drag models that need to take into account the interactions in the dense gas-solid flow [1]. In order to develop an accurate particle drag model that describes particle acceleration in the dense flow regime, representative experimental data need to be generated.While dispersal experiments have been carried out using a spherical multiphase explosive charge [3], controlled shock wave experiments are necessary to gain understanding of the fundamental physics of the dense supersonic gas-solid flow interactions and quantitative data concerning the particle cloud dispersion. Shock tube experiments have been carried out but typically the particle suspension method influences the shock flow [2] and the particle size is not typical of multiphase explosives. This paper reports on shock tube experiments looking at the acceleration and dispersion of 100 micron-sized aluminum oxide particles. The shock wave propagating into the packed particles provides a low-pressure analogy to multiphase explosive dispersal.

Numerical Study of the Drying Process of Different Sized Particles in an Industrial-Scale Spray Dryer

Development of high-performance spray dryers that are more energy efficient and are able to produce high-quality milk powders is very important for the future of the dairy powder industry. Understanding and optimization of the exiting dryers are also of great value. Computational fluid dynamics is a powerful tool to simulate and help understanding the characteristics of spray drying and to introduce potentially improved designs. The present study has concentrated on the multiphase flow in an industrial-scale spray dryer using the CFD package FLUENT. A Eulerian-Lagrangian approach is used in the simulations. A new drying model, REA model, for milk particles has been implemented for the first time in a CFD application. The numerical results match well with the plant data. It is argued that the “reflecting wall” boundary condition produced more physically correct results for normal dryer operation than the “escaping wall” boundary condition. The second one is an oversimplification. The influences of the particle size and particle size distribution, residence time, kinetic energy, and maximum temperature have been analyzed. The initial droplet size range was set to be from 100 to 500 µm with Rosin-Rammler distribution function. One significant result of this study is that rather dense particle clouds of medium-size particles (224–285 µm) are found near the side walls. They are transported upwards along the side wall (conical wall surface) and then are dispersed. It is found the particles with initial diameters of between 225 and 270 µm have the largest residence times.

Ablation dynamics of tin micro-droplet irradiated by double pulse laser used for extreme ultraviolet lithography source

The ablation dynamics of a tin (Sn) micro-droplet by double pulse laser irradiation for the development of an extreme ultraviolet lithography source was investigated. The solid state Sn droplet target with a diameter of 30 µm was irradiated by double laser pulses from a Q-switched Nd : YAG laser and a CO2 laser, and the kinetic behaviour of debris such as Sn atoms, ions and of the dense particles from the droplet was investigated by the laser-induced fluorescence imaging method, Faraday cups and high-speed imaging, respectively. After the pre-pulse irradiation of the Nd : YAG laser, the ions were emitted towards the laser incident direction with an average kinetic energy of 3–6 keV and the dense particle cloud moved in the direction opposite to the laser incident direction with expansion by a reaction force due to the plasma expansion at a speed of approximately 500 m s−1. On the other hand, the Sn atoms were ejected in all directions from the target with a speed as fast as 20 km s−1. The expanding target was subsequently irradiated by the main pulse of the CO2 laser with a delay of 800 ns and the dense cloud almost disappeared due to main-pulse irradiation.

Imaging Diagnostics of Debris from Laser-Produced Tin Plasma with Droplet Target for EUV Light Source

The dynamics of debris from laser-produced tin (Sn) plasma was investigated for a practical extreme ultraviolet (EUV) lithography source. The kinetic behaviors of the Sn atoms and of the dense particles from Sn droplet target irradiated by double pulses from the Nd:YAG laser and the CO2 laser were also investigated by the laser-induced fluorescence imaging method and a high-speed imaging, respectively. After the pre-pulse irradiation of the Nd:YAG laser, the Sn atoms were ejected in all direction from the target with a speed of as fast as 20 km/s and the dense particle cloud expanded by a reaction force due to the plasma expansion with a speed of approximately 500 m/s. The expanding target was subsequently irradiated by the main-pulse of CO2 laser and the dense cloud was almost disappeared by main-pulse irradiation.

An Eulerian–Lagrangian model for dense particle clouds

The interaction of a shock wave with a layer of particles, a topic important for the formation of dust clouds in air, has been analyzed by numerical simulation. The modelling method used are the Eulerian–Lagrangian and the Eulerian–Eulerian approaches, the latter is traditionally used for this type of simulation. Using Eulerian–Lagrangian simulation, it has been possible to include the effects of particle–particle and particle–wall collisions in a realistic and direct manner. Results are mainly shown as snap-shots of particle positions during the simulations and statistics for the particle displacement and collisions. The results show that collisions influence the process of particle cloud formation significantly.

Two-fluid magnetohydrodynamic simulation of confinement of pellet-produced hydrogen clouds in hot magnetized plasmas

The structure of dense particle clouds surrounding ablating hydrogen isotope pellets is investigated, with particular emphasis on the B-perpendicular expansion, ionization, and deceleration dynamics. A time-dependent single-temperature two-fluid one and one-half-dimensional Lagrangian model is used in which the neutral and ionized fluid components are allowed to move with different velocities. The expansion of the Lagrangian cells along the magnetic field lines is also taken into account. For given ablation rates, the confinement radii and the radial distributions of the velocities, particle densities, magnetic field strength, temperature, and other flow and field properties are calculated as functions of the background plasma parameters. The results show that collisional coupling between the neutral and ionized components is strong enough to change the initially spherically symmetric expansion of the neutral particles to a field-aligned, funneled flow pattern, in full agreement with experimental observations. The calculated cloud parameters are compared with measured data and results stemming from earlier single-velocity models.

Expansion of dense particle clouds in magnetically confined plasmas

A single-cell Lagrangian model has been developed for calculating the ionization and expansion dynamics of high-density clouds in magnetic fields or in magnetically confined plasmas. The model was tested by means of data from magnetospheric barium cloud experiments and approximately reproduced such global characteristics as expansion rate, stopping radius, stopping time, and magnetic cavity lifetime. Detailed calculations were performed for hydrogen clouds associated with the injection of frozen hydrogen pellets into tokamak plasmas. The dynamic characteristics of the cloud expansion, such as ionization radius, stopping time, lifetime, oscillation frequencies, and amplitudes, etc., are computed as functions of the magnetic field strength, the background plasma temperature, and the cloud mass. The results are analyzed and compared with experimental observations.