Numerical calculations of erosion in an abrupt pipe contraction of different contraction ratios

Erosion predictions in a pipe with abrupt contraction of different contraction ratios for the special case of two‐phase (liquid and solid) turbulent flow with low particle concentration are presented. A mathematical model based on the time‐averaged governing equations of 2‐D axi‐symmetric turbulent flow is used for the calculations of the fluid velocity field (continuous phase). The particle‐tracking model of the solid particles is based on the solution of the governing equation of each particle motion taking into consideration the effect of particle rebound behaviour. Models of erosion were used to predict the erosion rate in mg/g. The effect of Reynolds number and flow direction with respect to the gravity was investigated for three contraction geometries considering water flow in a carbon steel pipe. The results show that the influence of the contraction ratio on local erosion is very significant. However, this influence becomes insignificant when the average erosion rates over the sudden contraction area are considered. The results also indicate the significant influence of inlet velocity variations. The influence of buoyancy is significant for the cases of low velocity of the continuous flow. A threshold velocity below which erosion may be neglected was indicated. Copyright © 2004 John Wiley & Sons, Ltd.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Coupling Eulerian‐Lagrangian method of air‐particle two‐phase flow with population balance equations to simulate the evolution of vehicle exhaust plume

In this paper, we present a new numerical scheme to describe the dynamic evolution of multiphase polydisperse systems in terms of time, space, and properties by coupling the Eulerian‐Lagrangian method for air‐particle two‐phase flow and population balance equations to describe particle property evolution due to microbehaviors (eg, aggregation, breakage, and growth). This coupling scheme was used to comprehensively simulate the two‐phase flow structure, particle size spectrum, particle number, and volume concentrations. These were characterized by a high‐resolution particle tracking using the Lagrangian approach and the high precision of moments of the particle size spectrum by solving the population balance equation with the quadrature method of moments. The algorithm of the coupling scheme was incorporated into the open source computational fluid dynamics software OpenFOAM to simulate the dynamic evolution of vehicle exhaust plume. The impacts of vehicle velocity, exhaust temperature, and aggregation efficiency on the distribution of auto exhaust particles in space and changes in their properties were analyzed. The results indicate that the particle number concentration, volume concentration, and average diameter of particles in the vehicle exhaust plume could be strongly affected by the plume structure and flow properties.     

A three‐dimensional vortex particle‐in‐cell method for vortex motions in the vicinity of a wall

A new vortex particle‐in‐cell method for the simulation of three‐dimensional unsteady incompressible viscous flow is presented. The projection of the vortex strengths onto the mesh is based on volume interpolation. The convection of vorticity is treated as a Lagrangian move operation but one where the velocity of each particle is interpolated from an Eulerian mesh solution of velocity–Poisson equations. The change in vorticity due to diffusion is also computed on the Eulerian mesh and projected back to the particles. Where diffusive fluxes cause vorticity to enter a cell not already containing any particles new particles are created. The surface vorticity and the cancellation of tangential velocity at the plate are related by the Neumann conditions. The basic framework for implementation of the procedure is also introduced where the solution update comprises a sequence of two fractional steps. The method is applied to a problem where an unsteady boundary layer develops under the impact of a vortex ring and comparison is made with the experimental and numerical literature. Copyright © 2001 John Wiley & Sons, Ltd.     

固-液两相流黑水管道冲蚀磨损的数值模拟研究

煤气化黑水处理系统管道由于其流体介质高含固体颗粒和腐蚀性介质，且工作在高温、高压差环境中，极易受到冲蚀磨损和腐蚀的耦合作用而失效，影响其服役寿命. 采用计算流体力学(CFD)方法数值模拟研究了煤气化黑水处理系统固-液两相流管道的冲蚀磨损行为和机理，以及流体介质速度和固体颗粒粒径对管道冲蚀磨损的影响规律，并分析了盲通管和涡室结构对弯管冲蚀磨损行为的优化改善效果. 研究结果显示，煤气化黑水处理系统管线的冲蚀高危区主要分布在弯管外拱和变径管等结构突变区域；管道冲蚀磨损行为与其内部流体的运动和颗粒冲击特性有关；管道的冲蚀率均随着流体速度的增加而加剧，而粒径对弯管和变径管冲蚀率的影响并非单调关系，这与颗粒受力作用有关；弯管优化分析显示，涡室结构可以降低弯管的最大冲蚀率，减缓弯管的冲蚀磨损.      

No‐slip consistent immersed boundary particle tracking to simulate impaction filtration in porous media

In this paper, we present a new method for simulating the motion of a disperse particle phase in a carrier gas through porous media. We assume a sufficiently dilute particle‐laden flow and compute, independently of the disperse phase, the steady laminar fluid velocity using the immersed boundary method. Given the velocity of the carrier gas, the equations of motion for the particles experiencing the Stokes drag force are solved to determine their trajectories. The ‘no‐slip consistent’ particle tracking algorithm avoids possible numerical filtration of very small particles due to the nonzero velocity field at the solid–fluid interface introduced by the immersed boundary method. This physically consistent tracking allows a reliable estimation of the filtration efficiency of porous filters due to inertial impaction. We illustrate and test our new approach for model porous media consisting of a structured array of aligned rectangular fibers, arranged in line and staggered. In the staggered geometry, the effect of the residual velocity at the solid–fluid interface is significant for particles with low inertia. Without adopting the developed no‐slip consistent numerical method, an artificial numerical filtration is observed, which becomes dominant for small enough particles. For both the in line and the staggered geometries, the filtration rate depends quite strongly and non monotonically on the particle inertia. This is expressed most clearly in the staggered arrangement in which a very strong increase in the filtration efficiency is observed at a well‐defined critical droplet size, corresponding to a qualitative change in the dominant particle paths in the porous medium. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of erosion in a two‐way coupled fluid–particle system

In this study, the effects of flow turbulence intensity, temperature, particle sizes and impinging velocity on erosion by particle impact are demonstrated numerically. Underlying turbulent flow on an Eulerian frame is described by the compressible Reynolds averaged Navier–Stokes equations with a RNG k–ε turbulence model. The particle trajectories and particle–wall interactions are evaluated by a Eulerian–Lagrangian approach in a two‐way coupling system. An erosion model considering material weight removal from surfaces is used to predict erosive wear. Computational validation against measured data is demonstrated satisfactorily. The analysis of erosion shows that the prevention of erosion is enhanced by increasing the effects of flow temperature and turbulence intensity and reducing particle inertial momentum. Copyright © 2001 John Wiley & Sons, Ltd.     

Local heat transfer coefficients around a horizontal heated tube immersed in a gas fluidized bed

The heat transfer characteristics around a single horizontal heated tube immersed in air fluidized bed was investigated, to clarify the mechanism of heat transfer in a fluidized bed heat exchanger. The local heat transfer coefficient around the tube was measured at various fluidization velocities and five different solid particles. The experimental values of the local heat transfer coefficient at the minimum fluidization velocity condition were correlated with the particle size in two empirical equations. The predicted results were in good agreement with the experiment data.     

Theoretical investigation on submicron particle penetration through circular tubes inside a porous medium

The analytical infinite series solution of submicron particle transport in a circular tube bounded by a porous wall, such as a pinhole, is determined under the slip velocity boundary condition, and the solution is verified by using the experimental data in the previous studies for the specific cases. The results show that particle penetration rate increases with the increase of the porous parameter, the axial pressure drop, and the pinhole radius, whereas it decreases with increasing the pinhole length. The penetration rate of nano-particles are more sensitive to the variation of these parameters. However, the differences between the penetrations of particles ranging from 0.3 μm to 1 μm are not evident because the diffusion becomes weak gradually in this size range. In addition, a further comparison is performed between the analytical solution and the existing studies, and approximate expressions are presented for accurate calculation of particle penetration rate through pinholes appearing in porous materials including filter devices and masks.     

Numerical study of short-circuiting flow and particles in a gas cyclone

Short-circuiting flow is an important secondary flow in gas cyclones, which has a negative impact on the separation performance. To improve the understanding of the short-circuiting flow and guide the optimization of gas cyclones, this paper presents a numerical study of a cyclone using computational fluid dynamics. Based on the steady flow field, three methods were adopted to investigate the formation mechanism and characteristics of the short-circuiting flow and particles. The temporal variation of the tracer species concentration distribution reveals that the formation mechanism of the short-circuiting flow is the squeeze between the airflows entering the annular space of the gas cyclone at different times. The short-circuiting flow region, distinguished through the spatial distribution of the moments of age, is characterized by a small mean age and a large coefficient of variation. The proportion of the short-circuiting particles increases with the increase of the inlet velocity only for small particles. But with the increase of particle size, the proportion of the short-circuiting particles decreases faster at higher inlet velocities, resulting in significant differences in collection efficiency curves.     

Coupled Effects of Ionic Strength,Particle Size,and Flow Velocity on Transport and Deposition of Suspended Particles in Saturated Porous Media

In this study, the coupled effect of ionic strength, particle size, and flow velocity on transport and deposition of suspended particles (SP) in saturated sand was undertaken. Three polydispersive SP populations (silt particles with the median of 3.5, 9.5 and 18.3 \(\upmu \)m) were investigated using a pulse injection technique. High ionic strengths were used and vary from 0 to 600 mM (NaCl). Two high velocities were tested: 0.15 and 0.30 cm/s. Suspended particles recovery and deposition kinetics were strongly dependent on the solution chemistry, the hydrodynamics, and the suspended particles size, with greater deposition occurring for increasing ionic strength, lower flow velocity, and larger ratios of the median diameter of the SP to the median sand grain diameter. A shift between the extended Derjaguin–Landau–Verwey–Overbeek theory prediction (the particles and sand grain surfaces are considered chemically and topographically homogeneous) and the experimental results for certain ionic strength was observed. So, as reported in recent literature, effects of surface heterogeneities should be considered. The residence time of the non-captured particles is dependent on ionic strength and hydrodynamic. A relationship between the deposition kinetics, particle and grain sizes, flow velocity, and ionic strength is proposed.     

NUMERICAL SIMULATION OF THREE DIMENSIONAL GAS-PARTICLE FLOW IN A SPIRAL CYCLONE

The three-dimension gas-particle flow in a spiral cyclone is simulated numerically in this paper. The gas flow field was obtained by solving the three-dimension Navier-Stokes equations with Reynolds Stress Model (RSM). It is shown that there are two regions in the cyclone, the steadily tangential flow in the spiral channel and the combined vortex flow in the centre. Numerical results for particles trajectories show that the initial position of the particle at the inlet plane substantially affects its trajectory in the cyclone. The particle collection efficiency curves at different inlet velocities were obtained and the effects of inlet flow rate on the performance of the spiral cyclone were presented. Numerical results also show that the increase of flow rate leads to the increase of particles collection efficiency, but the pressure drop increases sharply.     

Free convection of a dusty‐gas flow along a semi‐infinite vertical cylinder

An analysis is performed to study the free convection of a dusty‐gas flow along a semi‐infinite isothermal vertical cylinder. The governing equations of the flow problem are transformed into non‐dimensional form and the resulting nonlinear, coupled parabolic partial differential equations have been solved numerically using an implicit finite difference scheme of Crank–Nicholson type. The flow variables such as gas–velocity, dust‐particle velocity and temperature, shearing stress and heat transfer coefficients are calculated numerically for various parameters occurring in the problem. It is observed that due to the presence of dust particles, the gas velocity is found to decrease. Copyright © 2009 John Wiley & Sons, Ltd.     

Experimental investigation of cluster properties in dense gas-solid fluidized beds of different diameters

The local solid flow structure of a bubbling fluidized bed of sand particles was investigated m three different columns to characterize the properties of clusters. The experiments were performed using a reflective optical fiber probe. The variations in size, velocity, and void fraction of the clusters due to changes in the superficial gas velocity, particle size, and radial positions were studied. The results indicate that the velocity of the clusters remained unchanged while their size increased as the column diameter increased. In addition, the radial profile of the clusters＇ velocity did not depend on the radial position. The results indicate that larger particles form larger clusters, which move slower.     

Particle deposition due to thermal force in a tube

Particle deposition in a tube with laminar flow is investigated. An analytical procedure is developed for predicting the particle deposition efficiency by incorporating the velocity of thermophoresis in the equation of conservation of particles. Effects of important parameters, such as temperature difference between the inlet gas and the tube wall, particle size and the Lewis number, on the particle precipitation efficiency are examined. Also considered in this work is the assumption of constant temperature gradient as a limiting case. It is found that particle precipitation efficiency predicted by using constant temperature gradient is much optimistic.     

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear‐induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear‐induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse‐flux model. Semi‐implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.     

Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.     

Heat Transfer and Gas Flow through Feed Stream within Horizontal Pipe

In the feeding process, the feed stream forms a moving packed bed of particle from the feedstock in the feed channel. When the feeding is at emergency interruption especially in the case of flooding and uncontrollable discharge, the hot gases from reactor would infiltrate into the feed stream. The high heat penetration into feed stream would affect the feeder performance. In this paper, transient thermal response of feed stream within horizontal pipe is described mathematically with a gas flow and heat transfer model. Influences of varied factors on the thermal penetration into feed stream are examined for different conditions. The temperature of the packed-bed particles and the gas velocity distribution curves are obtained for the feeding service at interruption and at normal operating conditions. The numerical results show that the thermal penetration to the packed-bed particles by the seepage flow fluid is high only in the position near the gas entrance. The thermal penetration depth tends to increase with the seepage flow velocity and decrease with feeding rate. There is no appreciable thermal penetration in the feed stream when the feeding service is at normal running. The operating conditions and the porosity of solid bed have importance effects on the gas velocity and temperature field in the thermal penetration zone. A test system is set up to determine the transient thermal response experimentally for the packed bed of particles within a horizontal pipe. The model results are found to compare favorably with the experimental data.     

Visualization and laser measurements on the flow field and sand movement on sand dunes with porous fences

The installation of windbreak sand fences around sand dunes is one of the most promising methods to suppress windblown sand movement. In the study reported in this paper, we investigated the influence and validity of a small fence mounted on a model sand dune, in order to understand the fence’s suppression mechanism on the sand movement. The flow field around the dune and the process of sand-dune erosion were measured using LDV, PIV, and laser-sheet visualization techniques. A non-porous fence was found to suppress sand movements in its upstream area, but to enhance erosion downstream of the fence. This intensive erosion was caused by separated shear flow from the leading edge of the fence. In this study, four levels of porosity rate of the fence were tested. The fence-porosity dependences of the turbulent flow field and the erosion were discussed. The shapes of eroded sand dunes were found to depend on the porosity rate. The relationship between the sand-dune erosion and the flow field around the dune was illustrated with schematic diagrams. We concluded that the most desirable fence porosity should be 30% in order to avoid dune erosion if installed at a middle height on the stoss surface of a dune. This porosity provides a mean velocity reduction with avoiding a separated flow, although the flow bleeding through the porous fence is accompanied by grid turbulence and induces serious erosion in a narrow space behind the fence. Furthermore, we confirmed that the empirical correlation of the critical friction velocity can be applied to sand movements influenced by a fence.     

Internal flow numerical simulation of a cross‐flow fan in refrigerant operating condition using user‐defined functions

In the paper, a cross‐flow fan in refrigerant operating condition is systematically simulated using user‐defined functions. Three‐dimensional simulations are acquired with Navier–Stokes equations coupled with k–ε turbulence model, and internal flow characteristics of an indoor split‐type air conditioner are obtained, which is mainly composed of cross‐flow fan and heat exchanger. It has systematically been simulated in the isothermal flow condition that the performance of cross‐flow fan may be reduced easily with dry or humid air, and in the refrigerant operating condition in which user‐defined functions are applied to the humid air, considered as a mixture of dry air and vapor. A density‐modulated function is adopted to deal with the condensation of the vapor at the heat‐transfer region approximately. The results show flow mechanism of the two gas‐phase flow, including phase‐vary process. The distribution of the parameters is not uniform at the inlet of the machine, the intensity and position of pressure and velocity vary along the axial direction of the fan, the distribution of vapor volume fraction and turbulent intensity in heat‐transfer region is obtained, and the external characteristic data of the indoor machine are obtained and analyzed. Compared with the experimental data, the calculated characteristic curves and designed parameters are on target. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.