A Numerical Model for Simulating the Motions of Ellipsoidal Fibers Suspended in Low Reynolds Number Shear Flows

A computational model was developed to simulate the motions of ellipsoidal fibers suspended in viscous shear flows. The model incorporates drag, lift, gravity, and hydrodynamic torque acting on ellipsoidal particles. Two numerical experiments were conducted to test the accuracy of the model. First, a single fiber was subjected to a linear shear profile and allowed to rotate without translation. The model's predictions for the fiber rotational period were evaluated and were shown to match well with previously published theoretical and numerical values. Second, fibers were injected into a horizontal tube under different flow conditions and their motions were tracked. Inspection of individual fiber motion showed a tendency to remain aligned with the direction of bulk fluid flow. Fiber aspect ratio, injection location, and flow rate were shown to play important roles in the details of elongated particle motions. The predicted sedimentation efficiencies of fibers matched well with the previously published works. On the basis of the computational model results, an empirical expression for the sedimentation rate of fibers in a horizontal tube with circular cross-section was proposed.     

Fibrous Particle Deposition in a Turbulent Channel Flow—An Experimental Study

The deposition rate of glass cylinders and dust paper fibers in a turbulent duct flow was studied experimentally. The glass fibers with a minimum diameter of 5 μm and the paper fibers with a minimum diameter of 1–20 μm and aspect ratios from 4 to 20 were deposited on a flat gold plate. The particle concentration at the test section was measured with the aid of an isokinetic probe in conjunction with a digital image processing technique. An oil lubricant was used on the plate to reduce the effect of particle bounce from the surface. The experimental data show that the deposition rate increases with an increase in fiber length and size. For a fixed minimum diameter or a fixed equivalent relaxation time, the deposition rate increases rapidly with fiber aspect ratio. When the equivalent spherical particle relaxation time is used, the deposition rate of the fibers was found to increase only slightly with aspect ratio and resemble those of spherical particles. The measured deposition velocities were in good agreement with the empirical model predictions and previous data.     

Respiratory Deposition of Fibers in the Non-Inertial Regime—Development and Application of a Semi-Analytical Model

A semi-analytical model describing the motion of fibrous particles ranging from nano- to micro scale was developed, and some important differences in respiratory tract transport and deposition between fibrous particles of various sizes and shapes were elucidated. The aim of this work was to gain information regarding health risks associated with inhalation exposure to small fibers such as carbon nanotubes. The model, however, is general in the sense that it can be applied to arbitrary flows and geometries at small fiber Stokes and Reynolds numbers. Deposition due to gravitational settling, Brownian motion and interception was considered, and results were presented for steady, laminar, fully developed parabolic flow in straight airways. Regarding particle size, our model shows that decrease in particle size leads to reduced efficiency of sedimentation but increased intensity of Brownian diffusion, as expected. We studied the effects due to particle shape alone by varying the aspect ratios and diameters of the microfibers simultaneously, such that the effect of particle mass does not come into play. Our model suggests that deposition both due to gravitational settling and Brownian diffusion decreases with increased fiber aspect ratio. Regarding the combined effect of fiber size and shape, our results suggest that for particles with elongated shape the probability of reaching the vulnerable gas-exchange region in the deep lung is highest for particles with diameters in the size range 10–100 nm and lengths of several micrometers. Note that the popular multi-walled carbon nanotubes fall into this size-range.     

Transport and Deposition of Angular Fibers in Turbulent Channel Flows

Transport and deposition of angular fibrous particles in turbulent channel flows were studied. The instantaneous fluid velocity field was generated by the direct numerical simulation (DNS) of the Navier-Stokes equation via a pseudo-spectral method. An angular fibers was assumed to consist of two elongated ellipsoids attached at their tips. For a dilute suspension of fibers, a one-way coupling assumption was used in that the flow carries the fibers, but the coupling effect of the fiber on the flow was neglected. The particle equations of motion used included the hydrodynamic forces and torques, the shear-induced lift and the gravitational forces. The hydrodynamic interactions of the high aspect ratio linkage were assumed to be negligibly small. Euler's four parameters (quaternions) were used for describing the time evolution of fiber orientations. Ensembles of fiber trajectories and orientations in turbulent channel flows were generated and statistically analyzed. The results were compared with those for spherical particles and straight fibers and their differences were discussed. Effects of fiber size, aspect ratio, fiber angle, turbulence near wall eddies, and various forces were studied. The DNS predictions were compared with experimental data for straight fibers and a proposed empirical equation model.     

Diffusion of Fibers in a Tubular Flow

Based on an ellipsoidal particle model, the equivalent diameter for the slip correction, diffusion coefficient, and diffusion diameter of fibers were obtained from the adjusted sphere method of Dahneke. The diffusion coefficient calculated for polydisperse crocidolite fibers compared favorably with available experimental data. Deposition of fibers in a tubular flow was then calculated with the use of the derived diffusion coefficient and applied to the human lung airways. The effect of velocity shear on particle orientation was also considered. It was found that the velocity shear had only a small effect on deposition. For a given fiber size, deposition increased in the lung distally, but at the same fiber diameter, the efficiency decreased with increasing aspect ratio.     

Direct Numerical Simulation of Curly Fibers in Turbulent Channel Flow

Wall deposition of rigid-link fibrous aerosols in a turbulent channel flow is studied. The instantaneous turbulent velocity vector field is generated by the direct numerical simulation of the Navier-Stokes equation with the aid of a pseudospectral code. It is assumed that the fiber is composed of five rigidly attached ellipsoidal links. The dynamic behavior of these elongated and irregular shaped particles is markedly different from the spherical ones. The hydrodynamic forces and torques acting on the fiber are evaluated and the equations governing the translational and rotational motions of the fiber are analyzed. Euler's four parameters are used, and motions of fibrous particles in the turbulent channel flow field are studied. Ensembles of 8000 fiber trajectories are generated and are used for evaluating various statistics. Root mean-square fiber velocities and fiber concentrations at different distances from the wall are evaluated and discussed. Empirical models for the deposition rate of curly fibers are also developed. The model predictions are compared with the simulation data and good agreement is observed.     

Clustering in gas-fluidized riser flows of flexible fibers

Clustering of flexible fibers in riser flows is investigated using a hybrid approach of Discrete Element Method and Computational Fluid Dynamics. Unlike spherical particles, the flexible fibers possess elongated shape, undergo significant deformation, and dissipate kinetic energies through rapid fiber deformation. The present studies show that these distinct features have significant impacts on the cluster characteristics of the fibers. A larger fiber aspect ratio leads to larger number and sizes of agglomerates, while it causes a reduction in heterogeneity of solids distribution due to the more dilute clusters with reduced packing densities. As the fibers become more flexible, the heterogeneity increases, and denser clusters are obtained. More significant effects of the fiber flexibility on the clustering are observed for the fibers with larger aspect ratios. The increased energy dissipation through the rapid fiber deformation enhances the clustering by augmenting the number and size of the agglomerates.     

Velocity Profiles of Suspension Flows through an Abrupt Contraction Measured by Magnetic Resonance Imaging

Velocity profiles in steady flows of fluid/particle mixtures through a duct with an abrupt contraction were measured by magnetic resonance imaging. Aqueous solutions of carboxymethyl cellulose containing particles, including spheres, disk‐like particles, and short fibers, at high volume fractions were used. As a result, a plug‐like velocity profile was observed in a straight duct flow for every suspension, but the velocity profile depends on the particle shape at contraction. Disk‐like particles caused an unsteady flow, and short fibers caused a concave shape in the velocity profile near the centerline upstream of the contraction. Spheres did not affect the flow field. The concave profile became obvious with increased volume fraction of fiber. This result is caused by the larger elongational viscosity of the fiber suspension near the centerline of the channel, as compared with that of the sphere suspension.     

A DNS Study of Aerosol Deposition in a Turbulent Square Duct Flow

A particle-laden turbulent flow through a square duct was simulated using a direct numerical solution of the Navier-Stokes equations coupled with Langrangian particle tracking. Computations of particle transport were employed to elucidate the mechanisms by which particles with varying inertia deposit to the walls of a square duct. Gravity was neglected and a one-way coupling was assumed between the particles and the fluid. The computational results demonstrate that, although the aerosol penetration through a square duct is not significantly different than through a circular pipe, there exist differences in the transport and deposition mechanisms. Most notably, the off-axis secondary flows unique to the square duct preferentially deposit higher-inertia particles closer to the corners of the duct. By contrast, the same secondary flows act to suppress the deposition of lower-inertia particles to the duct corners by efficiently transporting them back towards the duct core before deposition can occur.     

Dynamic simulation of microstructure and rheology of fiber suspensions

A numerical simulation method has been developed to predict the motion of fiber suspensions in various flows by using the particle simulation method (PSM), in which a fiber is modeled by an array of spheres. The hydrodynamic interaction among fibers is considered by decomposing into intra-fiber and inter-fiber interactions. For the intra-fiber case, the many-body problem is solved by calculating the mobility matrix for each fiber to obtain the hydrodynamic force and torque exerted on each sphere. For the inter-fiber case, only the near-field lubrication force is considered between spheres belonging to different fibers. The methodology was applied to predicting the microstructure and rheological properties of rigid fiber suspensions in simple shear flow and fiber orientation in two-dimensional diverging flow by combining this method with the finite element method (FEM). In the former, the overshoot of suspension viscosity, due to the transient change of the microstructure, was observed in semi-dilute to concentrated systems. In the latter, the calculated fiber orientations agreed with expectations of theory.     

Discrete particle simulation of gas fluidization of ellipsoidal particles

Fluidization is widely used in industries and has been extensively studied, either experimentally or theoretically, in the past decades. In recent years, a coupled simulation approach of discrete element method (DEM) and computational fluid dynamics (CFD) has been successfully developed to study the gas–solid flow and heat transfer in fluidization at a particle scale. However, to date, such studies mainly deal with spherical particles. The effect of particle shape on fluidization is recognized but not properly quantified. In this paper, the CFD–DEM approach is extended to consider the fluidization of ellipsoidal particles. In the simulation, particles used are either oblate or prolate, with aspect ratios varying from very flat (aspect ratio=0.25) to elongated (aspect ratio=3.5), representing cylinder-type and disk-type shaped particles, respectively. The commonly used correlations to determine the fluid drag force acting on a non-spherical particle are compared first. Then the model is verified in terms of solid flow patterns. The effect of aspect ratio on the flow pattern, the relationship between pressure drop and gas superficial velocity, and microscopic parameters such as coordination number, particle orientation and force structure are investigated. It is shown that particle shape affects bed permeability and the minimum fluidization velocity significantly. The coordination number generally increases with aspect ratio deviating from 1.0. The analysis of particle orientations shows that the bed structures for ellipsoids are not random as that for spheres. Oblate particles prefer facing upward or downward while prolate particles prefer horizontal orientation. Spheres have the largest particle–particle contact force and fluid drag force under the comparable conditions. With aspect ratio deviating from 1.0, particle–particle interaction and fluid drag become relatively weak. The proposed model shows a promising method in examining the effect of particle shape on different flow behaviour in gas fluidization.     

Dilute turbulent gas-solid flow in risers with particle-particle interactions

Earlier work of Sinclair and Jackson that treats the laminar flow of gas-solid suspensions is extended to model dilute turbulent flow. The random particle motion, often exceeding the turbulent flucutations in the gas, is obtained using a model based on the kinetic theory of granular materials. A two-equation low Reynolds number turbulence model is modified to account for the presence of the dilute particle phase. Comparisons of the model predictions with available experimental data for the mean and fluctuating velocity profiles for both phases indicate that the resulting theory captures many of the flow features observed in the pneumatic transport of large particles. THe model predictions did not manifest an exterme sensitivity to the degree of inelasticity in the particle-particle collisions for the range of solid loading ratios investigated.     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

沿同心环面层流流动的气体中颗粒的传热沉积物的预测:发展中的流动和已充分发展的流动的比较

Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium. It has numerous applications, especially in the field of aerosol technology. This study has numerically investigated the thermophoretic deposition efficiency of particles in a laminar gas flow in a concentric annulus using the critical trajectory method. The governing equations are the momentum and energy equations for the gas and the particle equations of motion. The effects of the annulus size, particle diameter, the ratio of inner to outer radius of tube and wall temperature on the deposition efficiency were studied for both developing and fully-developed flows. Simulation results suggest that thermophoretic deposition increases by increasing thermal gradient, deposition distance, and the ratio of inner to outer radius, but decreases with increasing particle size. It has been found that by taking into account the effect of developing flow at the entrance region, higher deposition efficiency was obtained, than fully developed flow.     

Theoretical analysis of fiber motion and loads during flow

A pseudo-analytical model for the forces exerted on fibers during flow that lead to fiber damage is proposed and solved. The fundamental derivations for the forces on fibers moving in suspensions developed by Burgers (1938) were used as a comparison. The cases of the motion of a fiber along its axis and perpendicular to its axis and in shear flow at a −45 degree-angle were investigated for aspect ratios between 10 and 300. The values for the overall forces on the fiber were in good agreement with the results found earlier by Burgers and others. However, the force distribution along the fiber was found to be significantly different from the constant distribution assumed by Burgers. Because of the higher forces on the fiber from the exact solution, the criterion for the onset of buckling in shear flow was revised. The pseudo-analytical solution was also compared to numerical results done with the boundary element method (BEM); the results were in good agreement.     

Dynamic simulation of flow-induced fiber fracture

A dynamic simulation method has been developed of the fracture process of a fiber in a flow field using the particle simulation method proposed i a previous paper. The fiber is modeled with bonded spheres as a fiber model. The flexibility of the fiber model is altered by changing three parameters of the stretching, bending, and twisting constants between adjacent spheres. The stress induced in each bond of the fiber model as a result of deformation is formulated using displacement of the bodn distanc, bond angle, and torsion angle fr each pair of spheres. After deformation, the fiber model fractures at the bond at which the stress surpasses the strength of the fiber. The motion of the fiber model in a flow field is determined by solving the translational and rotational motion equations for individual spheres under the hydrodynamic force and torque exerted on them. The correctness of the method and formulation was verified by comparing the simulated deflection curve of a cantilever beam (with a concentrated load at the end) with the theoretical curve. Good agreement was found in both the deflection and slope of the beam. The fracture process of a fiber after bending deformation in a two-dimensional siimple shear flow was simulated under assumptions of an infinitely dilute system, no hydrodynamic interaction, and a low Reynolds number of a particle. The calculated critical conditions of the flow field for fiber fracture were compared with Forgacs and Mason's theoretical ones. Simulated values of the fracture condition of the fluid shear stress related to the Young's modulus of a fiber agree with theoretical ones over an aspect ratio of 15.     

Lift and drag forces on a sphere attached to a wall in a Blasius boundary layer

Lift and drag forces on a sphere attached to a planar wall, over which a laminar flat plat boundary layer flows, are examined numerically in this study. Particle Reynolds number ranged from 0.1–250, which represents steady, laminar flow about the sphere, and the plate Reynolds number was held constant at 32 400. A finite-volume computational fluid dynamics program was utilised. Simulation results were validated against analytical results for drag and lift in creeping flow and against experimental results available in the literature for lift at higher particle Reynolds number. The model results were curve-fitted and interpolating drag and lift coefficient functions are reported. The lift and drag results are shown to be weakly dependent upon plate Reynolds number. The resulting correlations are expected to be useful in the development of particle impending motion and aerosol entrainment predictions of particles adhering to planar walls.