Turbulent Particle Diffusion Research Articles

Numerical Simulation of Turbulent Structure and Particle Deposition in a Three-Dimensional Heat Transfer Pipe with Corrugation

When colloidal particles are deposited in a heat transfer channel, they increase the flow resistance in the channel, resulting in a substantial decrease in heat transfer efficiency. It is critical to have a comprehensive understanding of particle properties in heat transfer channels for practical engineering applications. This study employed the Reynolds stress model (RSM) and the discrete particle model (DPM) to simulate particle deposition in a 3D corrugated rough-walled channel. The turbulent diffusion of particles was modeled with the discrete random walk model (DRW). A user-defined function (UDF) was created for particle–wall contact, and an improved particle bounce deposition model was implemented. The research focused on investigating secondary flow near the corrugated wall, Q-value standards, turbulent kinetic energy distribution, and particle deposition through validation of velocity in the tube and particle deposition modeling. The study analyzed the impact of airflow velocity, particle size, corrugation height, and corrugation period on particle deposition efficiency. The findings suggest that the use of corrugated walls can significantly improve the efficiency of deposition for particles less than 20 μm in size. Specifically, particles with a diameter of 3 μm showed five times higher efficacy of deposition with a corrugation height of 24 mm compared to a smooth surface.

Experimental study of turbulent thermal diffusion of particles in an inhomogeneous forced convective turbulence

We investigate experimentally the phenomenon of turbulent thermal diffusion of micrometer-size solid particles in an inhomogeneous convective turbulence forced by one vertically oriented oscillating grid in an air flow. This effect causes the formation of large-scale inhomogeneities in particle spatial distributions in a temperature-stratified turbulence. We perform detailed comparisons of the experimental results with those obtained in our previous experiments with an inhomogeneous and anisotropic stably stratified turbulence produced by a one oscillating grid in the air flow. Since the buoyancy increases the turbulent kinetic energy for convective turbulence and decreases it for stably stratified turbulence, the measured turbulent velocities for convective turbulence are larger than those for stably stratified turbulence. This tendency is also seen in the measured vertical integral turbulent length scales. Measurements of temperature and particle number density spatial distributions show that particles are accumulated in the vicinity of the minimum of the mean temperature due to the phenomenon of turbulent thermal diffusion. This effect is observed in both convective and stably stratified turbulence, where we find the effective turbulent thermal diffusion coefficient for micrometer-size particles. The obtained experimental results are in agreement with theoretical predictions.

Application of Stress Blended Eddy Simulation to the prediction of clarified layer depth and solids suspension in a draft tube reactor

Predictions of clarified layer depth and solids suspension in a draft tube reactor were investigated at a moderate solids loading of 16% v/v using both a RANS approach (k−ε) and a scale-resolving approach using Stress Blended Eddy Simulation (SBES). The multiphase flow was modelled using an Algebraic Slip model and the impact of drag law, turbulent particle diffusion and number of particle size classes was examined. The inclusion or exclusion of turbulent particle diffusion is found to dominate the RANS results, with resulting poor prediction of clarified layer depth and solids suspension under some conditions. In contrast, the SBES model is found to give good agreement with experimental data and the results show there is no need for a modelled turbulent dispersion force in this system if the large-scale turbulence structures responsible for particle transport are explicitly resolved.

Modeling the thermophoretic impact on nanoparticle production in an enclosed FSP reactor

For the accurate modeling and simulation of the flame spray pyrolysis (FSP) process, all the essential phenomena need to be taken into account. A validated model could then be used for process optimization and design with reasonably reduced costs. In that sense, this work uses a combination of computational fluid dynamics (CFD) and a population balance model (PBM) to investigate the influence of thermophoresis and other parameters (related to sintering and turbulent particle diffusion) in the final produced particle size. This work simulates the flame spray using CFD under an Eulerian–Lagrangian framework. Furthermore, a monodisperse solver for a bivariate PBM is implemented into ANSYS Fluent to simulate the formation and evolution of nanoparticles inside the reactor. We investigate the production of zirconium dioxide (ZrO2) nanoparticles and use experimental data from the literature for model validation. The model produces accurate results for some of the investigated cases.

Simulation of Turbulent Flow Structure and Particle Deposition in a Three-Dimensional Heat Transfer Duct with Convex Dimples

In engineering applications, dust deposition on the heat transfer channel greatly reduces the efficiency of heat transfer. Therefore, it is very significant to study the characteristics of particle deposition for thermal energy engineering applications. In this study, the Reynolds stress model (RSM) and the discrete phrase model (DPM) were used to simulate particle deposition in a 3D convex-dimpled rough channel. A discrete random walk model (DRW) was used for the turbulent diffusion of particles, and user-defined functions were developed for collisions between particles and walls. An improved deposition model of rebound between particles was developed. The flow structure, secondary flow, temperature distribution, Q criterion, and particle deposition distribution in the convex-dimpled rough channel were analyzed after a study of the grid independence and a numerical validation. The results showed that these mechanisms affected the flow structure in the flow field. For tiny particles (dp ≤ 10 μm), the presence of convex dimples promoted their deposition. The rates of particle deposition in the presence of convex dimples were 535, 768, 269, and 2 times higher than in smooth channels (particle sizes of 1, 3, 5, and 10 μm, respectively). However, for large particles (dp > 10 μm), although the presence of convex dimples had a certain effect on the location distribution of particle deposition, it had little effect on the deposition rates of large particles, which were 0.99, 0.98, 0.97 and 0.96 times those in the smooth channel, respectively.

Numerical simulation of turbulent flow and particle deposition in heat transfer channels with concave dimples

The efficiency of heat transfer will be significantly reduced if airborne particles deposit in the heat transfer channel. Better understandings on particle deposition characteristics in heat exchanger channel are crucial for the energy efficiency improvement. In this study, the particle deposition in a three-dimensional dimpled rough channel was simulated using the Reynolds stress model (RSM) and discrete particle model (DPM). For the turbulent diffusion of particles, the random walk model (DRW) was employed, and for the particle–wall contact, user-defined functions(UDF) are developed in this study to achieve motions such as bouncing and deposition of particles. Grid independence testing and numerical verification were followed by an analysis and study of the flow structures, secondary flow, temperature distribution, and particle deposition distribution in the dimpled rough channel. On the turbulent structure and particle deposition characteristics, the impacts of several significant parameters, including particle size, airflow velocity, the ratio of dimple depth to inner diameter (h/d), and the ratio of inner diameter of dimple to distance between dimples (d/s), were examined. The findings demonstrate that the primary mechanisms influencing the deposition characteristics of particles in dimpled channels are gravity deposition, thermophoresis force distribution, turbulence structure, secondary flow, and particle inertia, and the effects of these mechanisms change significantly with particle size. For small particles (dp ≤ 10 μm), the presence of dimples will encourage deposition; however, for large particles (dp > 10 μm), the presence of dimples will only have a little impact on the distribution of where the particles are deposited.

Experimental study of turbulent thermal diffusion of particles in inhomogeneous and anisotropic turbulence

We experimentally studied the turbulent thermal diffusion of small particles in inhomogeneous and anisotropic stably stratified turbulence produced by one oscillating grid in the air flow. The velocity fields have been measured using Particle Image Velocimetry (PIV). We have determined various turbulence characteristics: the mean and turbulent velocities, two-point correlation functions of the velocity field, and an integral scale of turbulence from the measured velocity fields. The temperature field has been measured with a temperature probe equipped with 12 E thermocouples. Spatial distributions of micrometer-sized particles have been determined by a PIV system using the effect of the Mie light scattering by particles in the flow. The experiments have demonstrated that particles are accumulated at the minimum of mean fluid temperature due to the phenomenon of turbulent thermal diffusion. Using measured spatial distributions of particles and temperature fields, we have determined the effective turbulent thermal diffusion coefficient of particles in inhomogeneous temperature-stratified turbulence. This experimental study has clearly detected the phenomenon of turbulent thermal diffusion in inhomogeneous turbulence.

On the interplay between pressure and gravitational forces in coalescing filters

This paper provides insights into processes governing oil–mist filtration in coalescing filters. In particular, it resolves an apparent inconsistency between different published studies regarding the occurrence (or not) of internal gravity-induced flows. As a result of this, it also clarifies whether in industrially-relevant scenarios such as those pertaining to vertical filter cartridges, non-homogeneous vertical saturation patterns are triggered by these internal flows or are just a result of different oil loading rates. To address these issues, we use Eulerian–Lagrangian CFD simulations, which properly account for the effects of turbulent diffusion of liquid aerosol particles, to replicate an experimental setup available in the literature. In order to interpret results data, we introduce a new dimensionless number, termed SM, defined as the ratio between pressure gradient and gravitational forces, which provides a bulk characterization of the flow and allows to assess whether internal gravity-induced flows, in a given cartridge–oil system, should be expected or not. We show that SM explains well the few experimental data available in the literature and identifies specific behaviors associated with limiting SM values being either very large or close to 1.

Resolved and subgrid-scale crossing trajectory effects in Eulerian large eddy simulations of size-dependent droplet transport

We study the dispersion characteristics of slightly buoyant droplets in a turbulent jet using large eddy simulations (LES). The droplet number density fields are represented using an Eulerian approach, with the dispersed phase modelled using the Fast-Eulerian method (Ferry & Balachandar, Intl J. Multiphase Flow, vol. 27, issue 7, pp. 1199–1226, 2001) that includes the droplet rise velocity. Radial concentration profiles and turbulent concentration fluxes for droplets of different sizes are analysed to quantify the ‘trajectory crossing effect’, when relative motions between particles and turbulent eddies tend to reduce turbulent diffusion. For finer LES grid resolutions, the model captures the differential, size-based dispersion characteristics of the droplets with the transverse dispersion of the larger droplet sizes suppressed, since trajectory crossing effects are explicitly resolved in LES. We examine a similarity solution model for the size-dependent radial concentration profiles based on a modified Schmidt number derived from the theory of turbulent diffusion of particles in the atmosphere proposed by Csanady (J. Atmos. Sci., vol. 20, pp. 201–208, 1963). The results are validated with the high resolution LES data and show good agreement. Then the size-dependent Schmidt number model is reformulated as a model for unresolved subgrid-scale trajectory crossing effects and used to calculate the subgrid concentration flux in a coarse LES of a turbulent jet, with slightly buoyant droplets injected at the centreline in the self-similar region of the jet. The results are compared to a simulation with higher grid resolution and a coarse simulation with a constant Schmidt number subgrid-scale model. We find that the subgrid model enhances the prediction accuracy of the concentration profiles and turbulent concentration flux for the coarse LES.

Optimizing the separation characteristics of the waterinjection hydrocyclone using mathematical modelling

Purpose. Although the hydrocyclone separator has many advantages, it still has some limitations which decrease its separation efficiency in many mineral processing applications because of fine particles which are miss separated to the coarse product in the underflow. Water injection in the conical part of the cyclone was recently implemented to solve this problem. The water injection mechanism and the way in which the injected water affects the separation are still not clear and need to be more investigated. Methods. New design of water injection hydrocyclone was tried using a modified conical part with a water injection range consist of five equal distance injection openings open directly on the periphery of the cone part. Findings. This study presents a mechanical mathematical model that simulates the water injection to give a clear indication of the injection mechanism impact on the classification process. It could also predict the dependence of the basic characteristics of the classification on the amount of the injected water and the influence of different operating and design parameters of the hydrocyclone. Originality. The model accounts for the fluid flow, the particle motion, the turbulent particle diffusion, and particle settling. Particle interactions and fine particle entrainment by settling coarse particles are also included in the model. The model was found to predict well the injection effect and agrees with the experimental results. Practical implications. The results showed also that the increase in water injection velocity leads to an increase in both the cut size and the minimal value of the separation curve. It was found also that the hydrocyclone length has an important effect on the injection process, and the separation sharpness is directly proportional to it at higher values of water injection velocity.

Numerical simulation study of oil diffusion at low tide near the port area of Ma’ao, Zhoushan

In this paper, the numerical hydrodynamic simulation has been carried out by using measured topographic data and related tidal information. The oil particle tracking module of MIKE21 is adopted to study the processes of drifting and turbulent diffusion of oil particles on the water surface, where four working conditions, namely, static wind, dominant wind direction, maximum wind direction and most unfavourable wind direction, are applied. Results show that Xiushan Island will be the apparent ‘victim’ in the cases of oil spill in all wind directions. Meanwhile, due to the existence of Changbai Island and Xiushan Island, the diffusion process of oil particles is obviously retarded to impact the protected marine areas.

EDGE2D-EIRENE simulations of the influence of isotope effects and anomalous transport coefficients on near scrape-off layer radial electric field

EDGE2D-EIRENE (the ‘code’) simulations show that radial electric field, Er, in the near scrape-off layer (SOL) of tokamaks can have large variations leading to a strong local E × B shear greatly exceeding that in the core region. This was pointed out in simulations of JET plasmas with varying divertor geometry, where the magnetic configuration with larger predicted near SOL Er was found to have lower H-mode power threshold, suggesting that turbulence suppression in the SOL by local E × B shear can be a player in the L–H transition physics (Delabie et al 2015 42nd EPS Conf. on Plasma Physics (Lisbon, Portugal, 22–26 June 2015) paper O3.113 (http://ocs.ciemat.es/EPS2015PAP/pdf/O3.113.pdf), Chankin et al 2017 Nucl. Mater. Energy 12 273). Further code modeling of JET plasmas by changing hydrogen isotopes (H–D–T) showed that the magnitude of the near SOL Er is lower in H cases in which the H-mode threshold power is higher (Chankin et al 2017 Plasma Phys. Control. Fusion 59 045012). From the experiment it is also known that hydrogen plasmas have poorer particle and energy confinement than deuterium plasmas, consistent with the code simulation results showing larger particle diffusion coefficients at the plasma edge, including SOL, in hydrogen plasmas (Maggi et al 2018 Plasma Phys. Control. Fusion 60 014045). All these experimental observations and code results support the hypothesis that the near SOL E × B shear can have an impact on the plasma confinement. The present work analyzes neutral ionization patterns of JET plasmas with different hydrogen isotopes in L-mode cases with fixed input power and gas puffing rate, and its impact on target electron temperature, Te, and SOL Er. The possibility of a self-feeding mechanism for the increase in the SOL Er via the interplay between poloidal E × B drift and target Te is discussed. It is also shown that reducing anomalous turbulent transport coefficients, particle diffusion and electron and ion heat conductivities, leads to higher peak target Te and larger Er, suggesting the possibility of a positive feedback loop, under an implicitly made assumption that the E × B shear in the SOL is capable of suppressing turbulence.

Coupling a snowmelt model with a snowdrift model for the study of snow distribution on roofs

A coupled model resulting from the coupling of a sub-snowmelt model and a sub-snowdrift model has been proposed to simulate the snow distribution on roofs. Firstly, based on energy and mass balance, a multi-layer roof snowmelt model, in which the snow accumulation, compaction, melting, and refreezing processes can be considered, was developed in this paper. Then, the snowmelt model was coupled to a quasi-steady snowdrift model to predict the snow distribution on building roofs. With the coupled model, the convection and turbulent diffusion of snow particles caused by wind can be predicted through the sub-snowdrift model by Computational fluid dynamics (CFD) simulations. On the other hand, the variations of snow properties, especially the threshold friction velocity, are simulated by the sub-snowmelt model based on mass and energy balance. Finally, three models (the coupled model, the snowmelt model used individually and the snowdrift model used individually) were applied to simulate the snow distribution on a flat roof, respectively. The characteristics of snow distribution simulated by the coupled model was compared with those simulated when the snowdrift model or the snowmelt model was applied individually.

Azimuthal and Vertical Streaming Instability at High Dust-to-gas Ratios and on the Scales of Planetesimal Formation

Abstract The collapse of dust particle clouds directly to kilometer-sized planetesimals is a promising way to explain the formation of planetesimals, asteroids, and comets. In the past, this collapse has been studied in stratified shearing box simulations with super-solar dust-to-gas ratio ϵ, allowing for streaming instability (SI) and gravitational collapse. This paper studies the non-stratified SI under dust-to-gas ratios from up to without self-gravity. The study covers domain sizes of , , and in terms of the gas-disk scale height using the PencilCode. They are performed in radial-azimuthal (2D) and radial-vertical (2.5D) extents. The used particles of and 0.1 mark the upper end of the expected dust growth. SI activity is found up to very high dust-to-gas ratios, providing fluctuations in the local dust-to-gas ratios and turbulent particle diffusion δ. We find an SI-like instability that operates in r–φ, even when vertical modes are suppressed. This new azimuthal streaming instability (aSI) shows similar properties and appearance as the SI. Both, SI and aSI show diffusivity at only to be two orders of magnitude lower than at , suggesting a relation that is shallow around . The (a)SI ability to concentrate particles is found to be uncorrelated with its strength in particle turbulence. Finally, we performed a resolution study to test our findings of the aSI. This paper stresses the importance of properly resolving the (a)SI at high dust-to-gas ratios and planetesimal collapse simulations, leading otherwise to potentially incomplete results.

Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants

The growth of a planetary core by pebble accretion stops at the so-called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. The value of the pebble isolation mass is crucial in determining the final planet mass. If the isolation mass is very low, gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For higher values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here, we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter α. We find that small pebbles, coupled to the gas, with Stokes number τf < 0.005 can drift through the partial gap at pebble isolation mass. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size. We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. Compared to models neglecting the dependence of the pebble isolation mass on the α-viscosity, our models including this effect result in higher core masses for giant planets. These higher core masses are more similar to the core masses of the giant planets in the solar system.

A single-column particle-resolved model for simulating the vertical distribution of aerosol mixing state: WRF-PartMC-MOSAIC-SCM v1.0

Abstract. The PartMC-MOSAIC particle-resolved aerosol model was previously developed to predict the aerosol mixing state as it evolves in the atmosphere. However, the modeling framework was limited to a zero-dimensional box model approach without resolving spatial gradients in aerosol concentrations. This paper presents the development of stochastic particle methods to simulate turbulent diffusion and dry deposition of aerosol particles in a vertical column within the planetary boundary layer. The new model, WRF-PartMC-MOSAIC-SCM, resolves the vertical distribution of aerosol mixing state. We verified the new algorithms with analytical solutions for idealized test cases and illustrate the capabilities with results from a 2-day urban scenario that shows the evolution of black carbon mixing state in a vertical column.

Modeling the Process of Particle Fractionation in a Pneumatic Centrifugal Apparatus

The present investigation pertains to simulation of the aerodynamics of a two-phase nonisothermal twisted turbulent flow in the vortex chamber of an air-centrifugal classifier. The gas phase dynamics was determined with the aid of Reynolds equations whose closure was based on the Wilcox turbulence model. The motion of the solid phase of an ultradisperse powder is simulated by a combination of calculations of the motion trajectories of particular particles in a Lagrangian coordinate system. The influence of turbulent diffusion of particles and of other factors on the efficiency of the segregation of particle fractions by size is shown. The reliability of the results obtained is confirmed by test studies and by comparing numerical results with well-known experimental data.

The Effect of Freestream Turbulence on Deposition for Nozzle Guide Vanes

An evaluation of the effect of freestream turbulence intensity on the rate of deposit accumulation for nozzle guide vanes (NGVs) was performed using the turbine reacting flow rig (TuRFR) accelerated deposition facility. The TuRFR allowed flows up to 1350 K at inlet Mach numbers of 0.1 to be seeded with coal fly ash particulate in order to rapidly evaluate deposit formation on CFM56 NGVs. Hot film and particle image velocimetry (PIV) measurements were taken to assess the freestream turbulence with and without the presence of a grid upstream of the NGVs. It was determined that baseline turbulence levels were approximately half that of the flow exiting typical gas turbine combustors and were reduced by approximately 30% with the grid installed. Deposition tests indicated that the rate of deposition increases as the freestream turbulence is increased, and that this increase depends upon the particle size distribution. For ash with a mass median diameter of 4.63 μm, the increase in capture efficiency was approximately a factor of 1.77, while for ash with a larger median diameter of 6.48 μm, the capture efficiency increased by a factor of 1.84. The increase in capture efficiency is due to the increased diffusion of particles to the vane surface via turbulent diffusion. Based on these results, smaller particles appear to be less susceptible to this mechanism of particle delivery. Overall, the experiments indicate that the reduction of turbulence intensity upstream of NGVs may lead to reduced deposit accumulation, and consequently, increased service life. A computational fluid dynamics (CFD) analysis was performed at turbulence levels equivalent to the experiments to assess the ability of built-in particle tracking models to capture the physics of turbulent diffusion. Impact efficiencies were shown to increase from 21% to 73% as the freestream turbulence was increased from 5.8% to 8.4%. An analysis incorporating the mass of the particles into the impact efficiency resulted in an increase of the mass-based impact efficiency from 17% to 27% with increasing turbulence. Relating these impact efficiencies directly to capture efficiencies, the predicted increase in capture efficiency with higher turbulence is less than that observed in the experiments. In addition, the variation in the impact efficiencies between the two ash sizes was smaller than the capture efficiency difference from experiments. This indicates that the particle tracking models are not capturing all of the relevant physics associated with turbulent diffusion of airborne particles.

Linking the Origin of Asteroids to Planetesimal Formation in the Solar Nebula

AbstractThe asteroids (more precisely: objects of the main asteroid belt) and Kuiper Belt objects (more precisely: objects of the cold classical Kuiper Belt) are leftovers of the building material for our earth and all other planets in our solar system from more than 4.5 billion years ago. At the time of their formation those were typically 100 km large objects. They were called planetesimals, built up from icy and dusty grains. In our current paradigm of planet formation it was turbulent flows and metastable flow patterns, like zonal flows and vortices, that concentrated mm to cm sized icy dust grains in sufficient numbers that a streaming instability followed by a gravitational collapse of these particle clump was triggered. The entire picture is sometimes referred to as gravoturbulent formation of planetesimals. What was missing until recently, was a physically motivated prediction on the typical sizes at which planetesimals should form via this process. Our numerical simulations in the past had only shown a correlation between numerical resolution and planetesimal size and thus no answer was possible (Johansen et al.2011). But with the lastest series of simulations on JUQUEEN (Stephan & Doctor 2015), covering all the length scales down to the physical size of actual planetesimals, we were able to obtain values for the turbulent particle diffusion as a function of the particle load in the gas. Thus, we have all necessary data at hand to feed a 'back of the envelope' calculation that predicts the size of planetesimals as result of a competition between gravitational concentration and turbulent diffusion. Using the diffusion values obtained in the numerical simulations it predicts planetesimal sizes on the order of 100 km, which suprisingly coincides with the measured data from both asteroids (Bottke et al.2005) as well from Kuiper Belt objects (Nesvorny et al.2011).

Spectral diffusion model of heavy inertial particles in a random velocity field of the continuous medium

Based on the spectral expansion of Euler correlation of the carrier medium the authors have obtained a closed system of functional equations for the Lagrange spectra of heavy inertial particles and the velocity fluctuations of the carrier medium on the particle trajectory. To split the fourth moments the approximation of quasinormality and velocity fluctuations of particles is performed by a random Gaussian process. The approximate self-consistent method is proposed for solving the resulting system of functional equations. The spectrum of Euler correlations of medium velocity fluctuations is modeled by Saffman and Karman distributions. The influence of the spatial microstructure of turbulence, the particles inertia and velocity slip on the intensity of chaotic motion and the coefficient of turbulent diffusion of dispersed particles has been studied.