Dilute Flow Research Articles

The effect of riser end geometry on gas-solid hydrodynamics in a CFB riser operating in the core annular and dilute homogeneous flow regimes

Riser hydrodynamics are a function of the flow rates of gas and solids as well as the exit geometry, particularly when operated above the upper transport velocity. This work compares the exit voidage for multiple geometries and two different solids: Geldart group A glass beads and Geldart group B coke. Geometries were changed by modifying the volume of an abrupt T-shaped exit above the lateral riser exit. This was accomplished by positioning a plunger at various heights above the exit from zero to 0.38m. A dimensionless expression used to predict smooth exit voidage was modified to account for the effect of the depth of the blind-T. The new correlation contains the solids-gas load ratio, solids-to-gas density ratio, bed-to-particle diameter ratio, gas Reynolds Number, as well as a term for the exit geometry. This study also found that there was a minimum riser roof height above the blind-T exit beyond which the riser exit voidage was not affected by the exit geometry. A correlation for this minimum riser roof height has also been developed in this study. This study covered riser superficial gas velocities of 4.35 to 7.7m/s and solids circulation rates of 1.3 to 11.5kg/s.

Numerical Study of the Solid Particle Erosion on H-Type Finned Circular/Elliptic Tube Surface

AbstractIn this paper, numerical simulations of solid particle erosion phenomena on H-type finned circular/elliptic tube surface, which is of great significance to the antiwear design of heat exchanger, are presented. The Eulerian-Lagrangian approach is applied to simulate the dilute gas-solid flow through H-type finned circular/elliptic tubes. A semi-empirical model is adopted to predict the erosion rate. The dynamics behavior of the entrained solid particles in the flow is presented. The geometry of eroded tube surface is changed with the predicted erosion which is taken into account by a UDF and the flow field is re-solved for the eroded tube surface at every time step. The influences of ten parameters (the tube bundle arrangement, particle size, particle concentration, fluid Reynolds number, fin thickness, fin pitch, fin length, fin width, slit width and the transverse tube pitch) on the maximum erosion depth of the H-type circular/elliptic finned tube surface are investigated. Using H-type finned elliptic tube surface can effectively reduce the erosion rate of tube surface comparedwith that using H-type finned circular tube surface. The erosion in in-line arrangement is less severe than that in staggered arrangement. With the increase of particle size, particle concentration and the fluid Reynolds number, the erosion rate of the tube surface rises. The numerically predicted effect of Reynolds number is in good agreement with previous test data. Among the six geometry parameters, the most influential parameter is the transverse tube pitch.

Application of the MP-PIC method for predicting pneumatic conveying characteristics of dilute phase flows

This study investigated the applicability of the multiphase particle-in-cell (MP-PIC) method for predicting pneumatic conveying characteristics. Three-dimensional computational particle fluid dynamics (CPFD) simulations were performed to assess the dilute-phase pneumatic conveying of plastic pellets in a horizontal circular pipe. The pellets were 80–500μm in diameter and 1000kgm−3 in density. The air velocities ranged from 6 to 15ms−1, and the solids-to-air mass flow ratios (solids loading ratios) ranged from 1 to 3. The predicted pressure drops and solids and air velocity profiles were compared with experimental data from the existing literature. A parametric study was carried out to investigate the effects of model collision parameters on pneumatic conveying characteristics. Moreover, the importance of including new collision terms developed by other researchers in the MP-PIC method for the prediction of dilute phase flows was emphasized.

Comparative Study on Occupant Evacuation with Building EXODUS and a Cellular Automaton Model

Building EXODUS software is used to calculate the evacuation times and simulate the evacuation behavior. The results and laws are compared with those from a 2D Cellular Automaton (CA) random evacuation model developed by our group. EXODUS simulation is more reasonable than the CA simulation in the case of evacuation from a simple room, but CA model is more reasonable in the case of evacuation in a long corridor after bottlenecks. As far as the evacuation from a simple room with a single exit is concerned, there is a critical value of exit width. The value of exit width should be bigger than the critical value in order to ensure a dilute pedestrian flow, but the value doesn’t need to be too big. The bigger the original occupant density, the longer the evacuation time is. They can be fitted as a linear relationship. The principle of taking the shortest route is not always useful. If the distribution of occupant density is not uniform at each building part, balancing the use efficiency of each exit should be the main principle in order to improve evacuation efficiency. All the above laws can be obtained both from EXODUS and the CA model.

THE FULLY LAGRANGIAN APPROACH TO THE ANALYSIS OF PARTICLE/DROPLET DYNAMICS: IMPLEMENTATION INTO ANSYS FLUENT AND APPLICATION TO GASOLINE SPRAYS

The fully Lagrangian approach (FLA) to the calculation of the number density of inertial particles in dilute gas-particle flows is implemented into the CFD code ANSYS Fluent. The new version of ANSYS Fluent is applied to modeling dilute gas-particle flow around a cylinder and liquid droplets in a gasoline fuel spray. In a steady-state case, the predictions of the FLA for the flow around a cylinder and those based on the equilibrium Eulerian method (EE) are almost identical for small Stokes number, Stk, and small Reynolds number, Re, (Re = 1, Stk = 0.05). For the larger values of these numbers (Re = 10, 100; Stk = 0.1, 0.2) the FLA predicts higher values of the gradients of particle number densities in front of the cylinder compared with the ones predicted by the EE. For transient flows (Re = 200), both methods predict high values of the number densities between the regions of high vorticity and very low values in the vortex cores. For Stk ≥ 0.1 the maximal values predicted by FLA are shown to be several orders of magnitude higher than those predicted by the EE. An application of FLA to a direct injection gasoline fuel spray has focused on the calculation of the number densities of droplets. Results show good qualitative agreement between the numerical simulation and experimental observations. It is shown that small droplets with diameters dp = 2 μm tend to accumulate in the regions of trajectory intersections more readily, when compared with larger droplets (dp = 10 μm, dp = 20 μm). This leads to the prediction of the regions of high number densities of small droplets.

Normal stress differences and beyond-Navier-Stokes hydrodynamics

A recently proposed beyond-Navier-Stokes order hydrodynamic theory for dry granular fluids is revisited by focussing on the behaviour of the stress tensor and the scaling of related transport coefficients in the dense limit. For the homogeneous shear flow, it is shown that the eigen-directions of the second-moment tensor and those of the shear tensor become co-axial, thus making the first normal stress difference (N 1 ) to zero in the same limit. In contrast, the origin of the second normal stress difference (N 2 ) is tied to the ‘excess’ temperature along the mean-vorticity direction and the imposed shear field, respectively, in the dilute and dense flows. The scaling relations for transport coefficients are suggested based on the present theory.

Transport and deposition of cohesive pharmaceutical powders in human airway

Pharmaceutical powders used in inhalation therapy are in the size range of 1-5 microns and are usually cohesive. Understanding the cohesive behaviour of pharmaceutical powders during their transportation in human airway is significant in optimising aerosol drug delivery and targeting. In this study, the transport and deposition of cohesive pharmaceutical powders in a human airway model is simulated by a well-established numerical model which combines computational fluid dynamics (CFD) and discrete element method (DEM). The van der Waals force, as the dominant cohesive force, is simulated and its influence on particle transport and deposition behaviour is discussed. It is observed that even for dilute particle flow, the local particle concentration in the oral to trachea region can be high and particle aggregation happens due to the van der Waals force of attraction. It is concluded that the deposition mechanism for cohesive pharmaceutical powders, on one hand, is dominated by particle inertial impaction, as proven by previous studies; on the other hand, is significantly affected by particle aggregation induced by van der Waals force. To maximum respiratory drug delivery efficiency, efforts should be made to avoid pharmaceutical powder aggregation in human oral-to-trachea airway.

A hydrodynamic model for granular material flows including segregation effects

The simulation of granular flows including segregation effects in large industrial processes using particle methods is accurate, but very time-consuming. To overcome the long computation times a macroscopic model is a natural choice. Therefore, we couple a mixture theory based segregation model to a hydrodynamic model of Navier-Stokes-type, describing the flow behavior of the granular material. The granular flow model is a hybrid model derived from kinetic theory and a soil mechanical approach to cover the regime of fast dilute flow, as well as slow dense flow, where the density of the granular material is close to the maximum packing density. Originally, the segregation model has been formulated by Thornton and Gray for idealized avalanches. It is modified and adapted to be in the preferred form for the coupling. In the final coupled model the segregation process depends on the local state of the granular system. On the other hand, the granular system changes as differently mixed regions of the granular material differ i.e. in the packing density. For the modeling process the focus lies on dry granular material flows of two particle types differing only in size but can be easily extended to arbitrary granular mixtures of different particle size and density. To solve the coupled system a finite volume approach is used. To test the model the rotational mixing of small and large particles in a tumbler is simulated.

Aerodynamic web forming: process simulation and material properties

In this paper we present a chain of mathematical models that enables the numerical simulation of the airlay process and the investigation of the resulting nonwoven material by means of virtual tensile strength tests. The models range from a highly turbulent dilute fiber suspension flow to stochastic surrogates for fiber lay-down and web formation and further to Cosserat networks with effective material laws. Crucial is the consistent mathematical mapping between the parameters of the process and the material. We illustrate the applicability of the model chain for an industrial scenario, regarding data from computer tomography and experiments. By this proof of concept we show the feasibility of future simulation-based process design and material optimization which are long-term objectives in the technical textile industry.

Experimental and numerical study of particle velocity distribution in the vertical pipe after a 90° elbow

A major problem of utilizing co-firing technique is controllably distributing fuel mixtures of pulverized coal and granular biomass in a common pipeline. This research related into particle velocity distribution in the vertical pipe after a right angle elbow was undertaken using the Laser Doppler Anemometry (LDA) technique and a coupled computational fluid dynamics (CFD)-discrete element method (DEM) simulation. According to the similarity criterion of Stokes Number, three types of glass beads were used to model the dilute gas-solid flow of pulverized coal or biomass pellets. In the vertical pipe after an elbow (R/D=1.3, R is the bend radius as 100mm and D is pipe diameter as 75mm), a horseshoe shape feature has been found on cross-sectional distributions of the axial particle velocity for all three types of glass beads on the first section which is 15mm away from the blend exit. At the further downstream sections, the horseshoe-shaped feature is gradually distorted until it completely disappears. The distance for total disintegration is about 300mm away from the first section for the first type of glass beads, 150mm away for the second type and 75mm away for the third one. As for particle number rate, its cross-sectional distribution on the first section shows that a rope is formed at the pipe outer wall where the maximum particle number rate occurs. On the whole, the rope formed by the first type of glass beads can be still observed at the section which is 450mm away from the first section. For the second type of glass beads, the rope will disintegrate from the section (300mm away) according to the cross-sectional distributions of the dimensional value of particle axial velocity divided by air conveying velocity. Overall, the roping characteristic is not obviously shown in the gas-solid flow of the third type of glass beads after the first section. All of these indicate that ropes formed from larger particles disperse more easily, for reasons perhaps related to their higher inertia. In addition, CFD-DEM analysis was employed to determine the particle characteristics to confirm this assumption. The numerical results indicated that the flow pattern has the highest axial velocity near the elbow to form the ‘horseshoe’ pattern. As the particles with lower Stokes Number were easier to follow the air flow, this is the reason why the horseshoe pattern of smaller particles was more obvious than larger particles.

Emerging Technologies for Measuring Flow Rate and Density of Bulk Flows of Particulate Solids

The operating principles and characteristics of three devices for measuring or monitoring flows of bulk solids are outlined. These are a flowrate meter and a density meter for material in gravity flow, both based on load cell sensors, and a system, based on audio-frequency acoustic sensing, for measuring the flow rate of dilute flows in a pneumatic conveying pipeline. Common features are mechanical simplicity and robustness, ease of calibration, and high precision. These technologies have all been demonstrated under industrial conditions performing reliably and consistently, and are compatible with the wide ranging process requirements of different industrial sectors, including the minerals industry.

A robust two-node, 13 moment quadrature method of moments for dilute particle flows including wall bouncing

For flows where the particle number density is low and the Stokes number is relatively high, as found when sand or ice is ingested into aircraft gas turbine engines, streams of particles can cross each other's path or bounce from a solid surface without being influenced by inter-particle collisions. The aim of this work is to develop an Eulerian method to simulate these types of flow. To this end, a two-node quadrature-based moment method using 13 moments is proposed. In the proposed algorithm thirteen moments of particle velocity, including cross-moments of second order, are used to determine the weights and abscissas of the two nodes and to set up the association between the velocity components in each node. Previous Quadrature Method of Moments (QMOM) algorithms either use more than two nodes, leading to increased computational expense, or are shown here to give incorrect results under some circumstances. This method gives the computational efficiency advantages of only needing two particle phase velocity fields whilst ensuring that a correct combination of weights and abscissas is returned for any arbitrary combination of particle trajectories without the need for any further assumptions. Particle crossing and wall bouncing with arbitrary combinations of angles are demonstrated using the method in a two-dimensional scheme. The ability of the scheme to include the presence of drag from a carrier phase is also demonstrated, as is bouncing off surfaces with inelastic collisions. The method is also applied to the Taylor–Green vortex flow test case and is found to give results superior to the existing two-node QMOM method and is in good agreement with results from Lagrangian modelling of this case.

Evidence of flash floods in Precambrian gravel dominated ephemeral river deposits

Fluvial strata at the base of the Whyte Inlet Formation on Baffin Island, to the west of Sikosak Bay, are predominantly boulder and cobble bearing large pebble conglomerates of braided fluvial origin. Local development of narrow sinuous channels, possibly within the thalwegs of an initially braided bedrock confined system, is indicated by the presence of lateral accretion surfaces, some of which host isolated sub-vertically oriented boulders. These larger boulders were probably emplaced during exceptional flood events involving either hyper-concentrated flows or dilute debris flows, with velocities in the order of 2.2m/s. Isolated ridges of boulders and cobbles are perched on the upper parts of lateral accretion surfaces in mixed sandy-gravelly fluvial intervals. These boulder berms developed down stream from channel bends or bedrock constrictions in response to flow expansion during flash floods, with estimated peak discharge of about 1.4m/s. Associated sandstones on lateral accretion surfaces show evidence of deposition under both upper and lower flow conditions. Similar boulder and cobble berms of this type are known from modern ephemeral and highly seasonal fluvial systems in a wide range of climatic settings, and are a clear indication that highly variable to catastrophic discharge events affected the rivers responsible for deposition of these conglomerates.

Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations

Hybrid particle-continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows. The former handles strong non-equilibrium effects, as they typically occur in the vicinity of solid boundaries, whereas the latter is in charge of the bulk flow, where non-equilibrium can be dealt with perturbatively, i.e. according to Navier-Stokes hydrodynamics. The proposed concurrent multiscale method is applied to the dilute gas Couette flow, showing major computational gains when compared with the full DSMC scenarios. In addition, it is shown that the coupling with LB in the bulk flow can speed up the DSMC treatment of the Knudsen layer with respect to the full DSMC case. In other words, LB acts as a DSMC accelerator.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Bridging the gaps at the physics-chemistry-biology interface.

It is commonly agreed that the most challenging problems in modern science and engineering involve the concurrent and nonlinear interaction of multiple phenomena, acting on a broad and disparate spectrum of scales in space and time. It is also understood that such phenomena lie at the interface

Hydrodynamic modeling strategy for dense to dilute gas–solid fluidized beds

When investigating the hydrodynamic behavior of gas–solid flow systems, there are several options for the drag function, viscosity model, and other parameters. The low accuracy obtained with a random trial and error modeling strategy has led researchers to develop new drag models that are fine-tuned for their specific studies. However, besides the drag functions, an appropriate viscosity model together with radial distribution function have a great impact on the hydrodynamic modeling of fluidized beds. In this study, a detailed validation and verification task is conducted using three different experimental datasets to derive a modeling strategy for predicting hydrodynamic behavior in dense to dilute flow regimes of various fluidized beds. For this purpose, the steady-state Reynolds-averaged Navier–Stokes equations are solved in a finite volume scheme using the twoPhaseEulerFoam solver in the OpenFOAM 2.1.1 software. A comparative study of different drag and viscosity models enables an optimal modeling strategy to be determined for the accurate prediction of the bed pressure drop, bed expansion ratio, time-averaged solid hold-up, and bed height in various dense and dilute flow regimes. Our results show that the modeling strategy prescribed in this study is widely applicable for identifying the hydrodynamic characteristics of various gas–solid fluidized beds with different operating conditions.

Theory and Experiment of Binary Diffusion Coefficient of n-Alkanes in Dilute Gases.

Binary diffusion coefficients were measured for n-pentane, n-hexane, and n-octane in helium and of n-pentane in nitrogen over the temperature range of 300 to 600 K, using reversed-flow gas chromatography. A generalized, analytical theory is proposed for the binary diffusion coefficients of long-chain molecules in simple diluent gases, taking advantage of a recently developed gas-kinetic theory of the transport properties of nanoslender bodies in dilute free-molecular flows. The theory addresses the long-standing question about the applicability of the Chapman-Enskog theory in describing the transport properties of nonspherical molecular structures, or equivalently, the use of isotropic potentials of interaction for a roughly cylindrical molecular structure such as large normal alkanes. An approximate potential energy function is proposed for the intermolecular interaction of long-chain n-alkane with typical bath gases. Using this potential and the analytical theory for nanoslender bodies, we show that the diffusion coefficients of n-alkanes in typical bath gases can be treated by the resulting analytical model accurately, especially for compounds larger than n-butane.

A simple model for electron temperature in dilute plasma flows

In this short note, we present some work on investigating electron temperatures and potentials in steady dilute plasma flows. The analysis is based on the detailed fluid model for electrons. Ionizations, normalized electron number density gradients, and magnetic fields are neglected. The transport properties are assumed as local constants. With these treatments, the partial differential equation for electron temperature degenerates as an ordinary differential equation. Along an electron streamline, two simple formulas for electron temperature and plasma potential are obtained. These formulas offer some insights, e.g., the electron temperature and plasma potential distributions along an electron streamline include two exponential functions, and the one for plasma potential includes an extra linear distribution function.

Natural consolidation characteristics of viscous debris flow deposition

: Pore water pressure and water content are important indicators to both deposition and consolidation of debris flows, enabling a direct assessment of consolidation degree. This article gained a more comprehensive understanding about the entire consolidation process and focused on exploring pore water pressure and volumetric water content variations of the deposit body during natural consolidation under different conditions taking the viscous debris flow mass as a study subject and by flume experiments. The results indicate that, as the color of the debris changed from initial dark green to grayish-white color, the initial deposit thickness declined by 3% and 2.8% over a permeable and impermeable sand bed, respectively. A positive correlation was observed between pore water pressure and depth in the deposit for both scenarios, with deeper depths being related to greater pore water pressure. For the permeable environment, the average dissipation rate of pore water pressure measured at depths of 0.10 m and 0.05 m were 0.0172 Pa/d and 0.0144 Pa/d, respectively, showing a positive changing trend with increasing depth. Under impermeable conditions, the average dissipation rates at different depths were similar, while the volumetric water content in the deposit had a positive correlation with depth. The reduction of water content in the deposit accelerated with depth under impermeable sand bed boundary conditions, but was not considerably correlated with depth under permeable sand bed boundary conditions. However, the amount of discharged water from the deposit was greater and consolidation occurred faster in permeable conditions. This indicates that the permeability of the boundary sand bed has a significant impact on the progress of consolidation. This research demonstrates that pore water and pressure dissipations are present during the entire viscous debris consolidation process. Contrasting with dilute flows, pore pressure dissipation in viscous flows cannot be completed in a matter of minutes or even hours, requiring longer completion time - 3 to 5 days and even more. Additionally, the dissipation of the pore water pressure lagged the reduction of the water content. During the experiment, the dissipation rate fluctuated substantially, indicating a close relationship between the dissipation process and the physical properties of broadly graded soils.

Particle statistics in a two-way coupled turbulent boundary layer flow over a flat plate

In the present study, we investigate heavy solid particle statistics in a spatially developing turbulent boundary layer over a flat plate using the two-way coupled Eulerian-Lagrangian point-particle approach. The particles are much smaller than the Kolmogorov length scale in the dilute gas-solid flow. The simulation results show that the particle streamwise fluctuating velocity exceeds the fluid streamwise fluctuating velocity across the entire boundary layer. In the wall-normal and spanwise directions, however, the velocity fluctuations of the particles generally tend to be lower than those of the fluid. Moreover, the particle wall-normal and spanwise fluctuating velocities decrease monotonically with particle Stokes number and mass loading. In addition, it is found that the spatial evolution of the particle wall concentration along the streamwise direction is similar to that of the mean skin-friction coefficient. These new findings are of great importance in the industrial and environmental applications.