Particle Velocity Fluctuations Research Articles

A mathematical model for type II profile of concentration distribution in turbulent flows

This paper presents a mathematical model to investigate type II profile of suspension concentration distribution (i.e., the concentration profile where the maximum concentration appears at some distance above the bed surface) in a steady, uniform turbulent flow through open-channels. Starting from the mass and momentum conservation equations of two-phase flow, a theoretical model has been derived. The distribution equation is derived considering the effects of fluid lift force, drag force, particle inertia, particle–particle interactions, particle velocity fluctuations and drift diffusion. The equation is solved numerically and is compared with available experimental data as well as with other models existing in the literature. Good agreement between the observed value and computed result, and minimum error in comparison to other models indicate that the present model can be applied in predicting particle concentration distribution for type II profile for a wide range of flow conditions. The proposed model is also able to show the transition from type I profile to type II profile.

Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

Particle-resolved direct numerical simulations of a 3-D liquid–solid fluidized bed experimentally investigated by Aguilar-Corona (2008) have been performed at different fluidization velocities (corresponding to a range of bed solid volume fraction between 0.1 and 0.4), using Implicit Tensorial Penalty Method. Particle Reynolds number and Stokes number are O(100) and O(10), respectively. In this paper, we compare the statistical quantities computed from numerical results with the experimental data obtained with 3-D trajectography and High Frequency PIV. Fluidization law predicted by the numerical simulations is in very good agreement with the experimental curve and the main features of trajectories and Lagrangian velocity signal of the particles are well reproduced by the simulations. The evolution of particle and flow velocity variances as a function of bed solid volume fraction is also well captured by the simulations. In particular, the numerical simulations predict the right level of anisotropy of the dispersed phase fluctuations and its independence of bed solid volume fraction. They also confirm the high value of the ratio between the fluid and the particle phase fluctuating kinetic energy. A quick analysis suggests that the fluid velocity fluctuations are mainly driven by fluid–particle wake interactions (pseudo-turbulence) whereas the particle velocity fluctuations derive essentially from the large scale flow motion (recirculation). Lagrangian autocorrelation function of particle fluctuating velocity exhibits large-scale oscillations, which are not observed in the corresponding experimental curves, a difference probably due to a statistical averaging effect. Evolution as a function of the bed solid volume fraction and the collision frequency based upon transverse component of particle kinetic energy correctly matches the experimental trend and is well fitted by a theoretical expression derived from Kinetic Theory of Granular Flows.

Aspect ratio effect on particle transport in turbulent duct flows

The dynamics of dilute micron-sized spherical inertial particles in turbulent duct flows is studied by means of direct numerical simulations of the carrier phase turbulence with one-way coupled Lagrangian particles. The geometries are a square and a rectangular duct with width-to-height aspect ratio AR of 3 operating at Reτ,c = 360 (based on the centerplane friction velocity and duct half-height). The present study is designed to determine the effect of turbulence-driven secondary motion on the particle dynamics. Our results show that a weak cross-flow secondary motion significantly changes the cross-sectional map of the particle concentration, mean velocity, and fluctuations. As the geometry of the duct is widened from AR = 1 to 3, the secondary vortex on the horizontal wall significantly expands in the spanwise direction, and although the kinetic energy of the secondary flow increases close to the corner, it decays towards the duct centreplane in the AR = 3 case so as the turbulent carrier phase approaches the behavior in spanwise-periodic channel flows, a fact that significantly affects the particle statistics. In the square duct the particle concentration in the viscous sublayer is maximum at the duct centreplane, whereas the maximum is found closer to the corner, at a distance of |z/h| ≈ 1.25 from the centreplane, in the AR = 3 case. Interestingly the centreplane concentration in the rectangular duct is around 3 times lower than that in the square duct. Moreover, a second peak in the accumulation distribution is found right at the corners for both ducts. At this location the concentration increases with particle inertia. The secondary motion changes also the cross-stream map of the particle velocities significantly in comparison to the fluid flow statistics. These directly affect the particle velocity fluctuations such that multiple peaks appear near the duct walls for the particle streamwise and wall-normal velocity fluctuations.

CFD-DEM simulation of flow pattern and particle velocity in a fluidized bed with wet particles

Gas-solid fluidized beds with the presence of a few liquid are applied widely in industry, while agglomeration and poor fluidization could happen as a result of inter-particle cohesiveness. In this paper, a hysteresis contact model is applied to consider energy dissipation resulted from both lubrication and liquid bridge during wet particle collision. The model can predict the particle rebound and adhesion behaviors, under influence of collision velocity, liquid content, liquid viscosity and surface tension. The fluidization characteristics of the wet particles under different conditions in a 2D fluidized bed are simulated and compared. Generally, it is found that with the presence of liquid, the particles begin to be agglomerated and the bubbles become gas channels. By increasing the cohesiveness, the fluctuation of pressure increases first and then decreases, the fluctuation of particle velocity decreases generally and the probability density of particle velocity around zero increases. When the cohesiveness is increased further, the internal recirculation of wet particles is restrained and the gas channels become stable.

Dynamic sound scattering: Field fluctuation spectroscopy with singly scattered ultrasound in the near and far fields.

Dynamic sound scattering (DSS) is a powerful acoustic technique for investigating the motion of particles or other inclusions inside an evolving medium. In DSS, this dynamic information is obtained by measuring the field autocorrelation function of the temporal fluctuations of singly scattered acoustic waves. The technique was initially introduced 15 years ago, but its technical aspects were not adequately discussed then. This paper addresses the need for a more complete account of the method by describing in detail two different implementations of this sound scattering technique, one of which is specifically adapted to a common experimental situation in ultrasonics. The technique is illustrated by the application of DSS to measure the mean square velocity fluctuations of particles in fluidized suspensions, as well as the dynamic velocity correlation length. By explaining the experimental and analytical methods involved in realizing the DSS technique in practice, the use of DSS will be facilitated for future studies of particulate suspension dynamics and particle properties over a wide range of particle sizes and concentrations, from millimeters down to nanometers, where the use of optical techniques is often limited by the opacity of the medium.

CFD simulation and hydrodynamics characterization of solids oscillation behavior in a circulating fluidized bed with sweeping bend return

Solids oscillation circulation is an unstable solids flow behavior exhibited during the start-up process of a circulating fluidized bed (CFB) with sweeping bend return. It results in significant pressure fluctuation and particle loss, further brings about difficulties in establishing a stable solids circulation and blockage of the heat exchanger for recycling gas. However, the oscillation mechanism and hydrodynamic characteristics of the solids oscillation circulation are still far from understanding, since the variation of solids transfer rate, gas flow rate and their complex interactions are still unknown. In this work, the Eulierian-Eulerian method has been employed for the simulation of solids oscillation circulation in a two-dimension (2D) CFB. The results indicate that solids oscillation circulation is triggered by the formation of slugging in the downer, which leads to a decrease of the downer pressure drop and a sharp increase of the riser bypass gas velocity. Besides, intense slugging fluidization is observed in the downer at larger valve opening or higher inlet gas velocity. Moreover, statistical hydrodynamic shows uniform lateral solids volume distributions in the riser and downer. Solids fluctuating energy spectrum is generated to explore the turbulent characteristics, a segment phenomenon is observed in the inertial sub-region. In addition, the deviation of scale index in the inertial region form the Kolmogorov −5/3 scaling law indicates the flow intermittency. According to the wavelet analysis of particle fluctuation velocity, the particle-particle and particle-wall interaction are found to be the main reason for the flow intermittency.

Velocity fluctuations and population distribution in clusters of settling particles at low Reynolds number

A study on the spatial organization and velocity fluctuations of non-Brownian spherical particles settling at low Reynolds number in a vertical Hele-Shaw cell is reported. The particle volume fraction ranged from 0.005 to 0.05, while the distance between cell plates ranged from 5 to 15 times the particle radius. Particle tracking revealed that particles were not uniformly distributed in space but assembled in transient settling clusters. The population distribution of these clusters followed an exponential law. The measured velocity fluctuations are in agreement with that predicted theoretically for spherical clusters, from the balance between the apparent weight and the drag force. This result suggests that particle clustering, more than a spatial distribution of particles derived from random and independent events, is at the origin of the velocity fluctuations.

Numerical studies of the effects of fines on fluidization

Euler‐Lagrange simulations of fluidized beds of Geldart Group A particles containing different levels of fines are performed in periodic domains with various domain‐averaged solid volume fractions. Bubble‐like voids readily form when no fines are added. Introducing fines does not reduce bubble sizes if van der Waals force between particles is not accounted for. In contrast, the addition of van der Waals force produces significant changes. With no fines, bubbles are found to be suppressed at sufficiently high solid volume fractions, corresponding to the expanded bed regime for Group A particles. With the addition of fines, bubbles can be suppressed at lower solid volume fractions. With more fines added, bubbles can be suppressed at even lower solid volume fractions. When bubbles are suppressed, the system is found to be in a stable solid‐like regime. In this regime, forces on each particle are balanced, and the particle velocity fluctuations are dampened. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2271–2281, 2016

Comparison of the structure of computed and measured particle-laden jets for a wide range of Stokes numbers

Turbulent particle-laden jets have been the subject of interest for many years on account of their relevance to several practical devices like engines, combustors and gasifiers. While prior experimental studies have examined particle-laden flows at high Stokes number, experimental data on particle-laden jets with particle Stokes number of the order of one and lower have not been available until recently. This study presents results from computations of particle-laden jets for Stokes number ranging from 0.3 to 500 and their comparison with measured results. The mean gas-phase velocity is found by solving RANS equations with a k–∊ model for turbulence. The particles are solved in a Lagrangian framework with the coupling between the carrier and dispersed phase modeled using a drag coefficient with a high-Reynolds number correction. Particle–turbulence interactions are modeled using a random-walk dispersion model. The influence of Stokes number on the spreading rate of the carrier and dispersed phase is examined. It is shown that for the range of Stokes numbers considered, the computed results agree with measured particle centerline velocities within about 20%. The changes in particle velocities predicted as Stokes number varies are consistent with measured changes in these variables. While no specific trends can be identified in the differences between computed and measured results that would relate the differences to Stokes number, several parametric studies are carried out to investigate the effect of jet inlet gas phase turbulence intensity, fluctuating particle velocity at the jet inlet, turbulence modulation and the dispersion model employed on jet spreading and centerline velocities.

Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics

Simulations of strongly coupled (i.e., high-mass-loading) fluid-particle flows in vertical channels are performed with the purpose of understanding the fundamental physics of wall-bounded multiphase turbulence. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions are presented, and the unclosed terms that are retained in the context of fully developed channel flow are evaluated in an Eulerian–Lagrangian (EL) framework for the first time. A key distinction between the RA formulation presented in the current work and previous derivations of multiphase turbulence models is the partitioning of the particle velocity fluctuations into spatially correlated and uncorrelated components, used to define the components of the particle-phase turbulent kinetic energy (TKE) and granular temperature, respectively. The adaptive spatial filtering technique developed in our previous work for homogeneous flows [J. Capecelatro, O. Desjardins, and R. O. Fox, “Numerical study of collisional particle dynamics in cluster-induced turbulence,” J. Fluid Mech. 747, R2 (2014)] is shown to accurately partition the particle velocity fluctuations at all distances from the wall. Strong segregation in the components of granular energy is observed, with the largest values of particle-phase TKE associated with clusters falling near the channel wall, while maximum granular temperature is observed at the center of the channel. The anisotropy of the Reynolds stresses both near the wall and far away is found to be a crucial component for understanding the distribution of the particle-phase volume fraction. In Part II of this paper, results from the EL simulations are used to validate a multiphase Reynolds-stress turbulence model that correctly predicts the wall-normal distribution of the two-phase turbulence statistics.

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016

Описание флуктуаций скорости броуновской частицы при воздействии пуассоновского случайного процесса

Описание флуктуаций скорости броуновской частицы при воздействии пуассоновского случайного процесса

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

Direct numerical simulations and experiments of a pseudo-2D gas-fluidized bed

This paper reports our study on fluidization of 5000 spherical particles in a pseudo-2D gas-fluidized bed by direct numerical simulations (DNS) and experiments as well. Simulations are performed using an immersed boundary method, together with the methodology developed in our earlier work for accurate prediction of gas–solid interactions at relatively low grid resolutions. This modelling approach provides detailed information on the gas flow and the motion of individual particles, which allows for a priori calculation of the bed hydrodynamics. Experimental measurements of solids mean motion are conducted using a combined technique of Particle Image Velocimetry (PIV) and Digital Image Analysis (DIA). Further, the PIV technique is extended and applied for instantaneous measurements of the particle granular temperature, which is the key characteristics of particle velocity fluctuations. For the first time, this paper reports a direct comparison in great detail between DNS results and experimental data for realistic gas fluidization. The detailed comparison reveals a reasonably good agreement with respect to the time-averaged solids motion and the pressure fluctuations. In addition, the granular temperatures calculated from the simulations agree well with the experimental data, but provide more details with respect to the variations corresponding to bubble formation and eruption. From our investigation, it also becomes clear that attention should be paid on the measurement and interpretation of the granular temperature.

Investigation of particle characteristics, composition and microstructure of LaxCe1−xO2−x/2 thermal barrier coatings during supersonic atmospheric plasma spray using Box–Behnken design

Abstract In this work, Box–Behnken design was used for investigating the influence of the main operating parameters (Argon flow rate: Ar , hydrogen flow rate: H 2 and arc current: I ) on velocity and temperature of La 2 Ce 2 O 7 in-flight particle characteristics (i.e., mean velocity and temperature) during supersonic atmospheric plasma spraying (SAPS). The relationship between the particle characteristics and the composition and the microstructure of LC coating was investigated eventually. During spraying, the particle temperature and velocity were monitored by on-line diagnosis system. The results indicated that the particle velocity linearly increased with the increase of Ar , H 2 and I . I and the interaction between I and Ar and/or H 2 were the most important parameters which influenced the particle temperature. The content of Ce 4 + in the as-sprayed coating rapidly decreased when the particle temperature increased from 2923 to 3036 °C, and then slowly decreased in the range of 3127–3218 °C. When the particle velocity fluctuation was less than 5%, the porosity of as-sprayed coatings decreased with the increase of particle temperature, however, it increased with the increase of particle velocity.

The effect of oscillating flow on a horizontal dilute-phase pneumatic conveying

ABSTRACTA horizontal dilute-phase pneumatic conveying system using vertically oscillating soft fins at the inlet of the gas–particle mixture was studied to reduce the power consumption and conveying velocity in the conveying process. The effect of different fin lengths on horizontal pneumatic conveying was studied in terms of the pressure drop, conveying velocity, power consumption, particle velocity, and intensity of particle fluctuation velocity for the case of a low solid mass flow rate. The conveying pipeline consisted of a horizontal smooth acrylic tube with an inner diameter of 80 mm and a length of approximately 5 m. Two types of polyethylene particles with diameters of 2.3 and 3.3 mm were used as conveying materials. The superficial air velocity was varied from 10 to 17 m/s, and the solid mass flow rates were 0.25 and 0.20 kg/s. Compared with conventional pneumatic conveying, the pressure drop, MPD (minimum pressure drop), critical velocities, and power consumption can be reduced by using soft fins in a lower air velocity range, and the efficiency of fins becomes more evident when increasing the length of fins or touching particles stream by the long fins. The maximum reduction rates of the MPD velocity and power consumption when using soft fins are approximately 15% and 26%, respectively. The magnitude of the vertical particle velocity for different lengths of fins is clearly lower than that of the vertical particle velocity for a non-fin conveying system near the bottom of the pipeline, indicating that the particles are easily suspended. The intensities of particle fluctuation velocity of using fins are larger than that of non-fin. The high particle fluctuation energy implies that particles are easily suspended and are easily conveyed and accelerated.

An effective Euler–Lagrange model for suspended sediment transport by open channel flows

An Euler–Lagrange two-phase flow model is developed to study suspended sediment transport by open-channel flows with an Eddy Interaction Model (EIM) applied to consider the effect of fluid turbulence on sediment diffusion. For the continuous phase, the mean fluid velocity, the turbulent kinetic energy and its dissipation rate are directly estimated by well-established empirical formulas. For the dispersed phase, sediment particles are tracked by solving the equation of motion. The EIM is applied to compute the particle fluctuation velocity. Neglecting the effect of particles on flow turbulence as usually suggested for dilute cases in the literature, the Euler–Lagrange model is applied to simulate suspended sediment transport in open channels. Although the numerical results agree well with those by the well-known random walk particle tracking model (RWM) and with the laboratory data for fine sediment cases, it is clearly shown that such an Euler–Lagrange model underestimates the sediment concentration for the medium-sized and coarse sediment cases. To improve the model, a formula is proposed to consider the local fluid turbulence enhancement around a particle due to vortex shedding in the wake. Numerical results of the modified model then agree very well with laboratory data for not only the fine but also the coarse sediment cases.

CFD prediction of scale-up effect on the hydrodynamic behaviors of a pilot-plant fluidized bed reactor and preliminary exploration of its application for non-pelletizing polyethylene process

This work aims to explore the scale-up effect on the hydrodynamic natures in a pilot-plant gas phase ethylene polymerization fluidized bed reactor (FBR) based on two-dimensional (2D) transient Eulerian model integrating the kinetic theory of granular flow (KTGF). Unlike lab scale FBR, significant differences in the core–annulus structures caused by the scale-up effect are revealed. The core region in pilot-plant scale FBR is much broader, and the distribution is nearly flat for two phases. The annulus structure is thin, and exhibits a very small particle velocity fluctuation. The bed expanding section could reduce the solid velocity and improve the flow patterns of gas and polymer particles. Simulations are also performed to assess the effects of polymer particle size and gas velocity on the hydrodynamics for the non-pelletizing polyethylene process. With the increase of polymer particle diameter (446μm to 1338μm), the superficial gas velocity should be increased from 0.60m/s to 0.90m/s to achieve better steady fluidized state. The results are helpful for understanding how the local mean two phases' velocities and volume fractions vary in pilot-plant reactor for PE production caused by scale-up effect.

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.

Three-component particle velocity measurements in the bottom section of a riser

Abstract Coincident three-component particle velocity measurements are performed in an almost 9 m high cylindrical riser (internal diameter 0.10 m) of a pilot-scale cold-flow Circulating Fluidized Bed set-up, using two Laser Doppler Anemometry (LDA) probes. Experiments are performed with superficial gas velocities of 3.5 m/s and 5.3 m/s near the solids inlet line and with an average solids volume fraction of 0.0002. The particle flow is observed to be highly disturbed due to the asymmetrical position of both the gas and the Y-shaped solids inlet line. A jet-like particle flow and a by-passing streaming gas jet around the particles are formed. Just below the solids inlet line a downward oriented particle velocity is measured. Particles are immediately lifted by the ascending gas and spread over the entire cross-sectional tube area. Near the solids inlet line the axial and radial particle velocity fluctuations are of the same order of magnitude as the corresponding mean particle velocity components, showing that the flow is anisotropic. The radial particle velocity fluctuations decrease fast as the radial inflow of particles is transformed into axial particles flow. The turbulence intensity in the inlet section of the dilute riser flow is found to be extremely high, indicating that the flow is far from being fully developed. The total particle shear stress profiles near the solids inlet line indicate a high momentum transfer from radial to axial particle transport. The particle fluctuation energy values calculated based on experimental data are nearly double than the values corresponding in fully developed flow studied previously.