Fluid Drag Force Research Articles

CFD-DEM modeling of seepage erosion around shield tunnels

When tunnels are built in saturated silty sand, the tunnel leakage can carry fine particles into tunnels and generate seepage erosion process. During this process sand particles are subjected to high confining and hydraulic pressures and then are eroded through the seams of segmental joints. This paper investigates the mechanism of seepage erosion process using Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) coupling simulations. The seepage erosion processes are simulated for loose, medium dense and dense silty sand, respectively. The evolution of the fine particles loss and the volumetric strain are investigated. Results show that the fine particles are eroded in two patterns. The first pattern is induced by axial pressure extruding fine particles through seams without hydraulic pressure. The second pattern is induced by fluid drag force dragging fine particles under hydraulic pressure. Correspondingly, the erosion process is divided into two stages as initial extruding stage and the following eroding stage. Result shows that dense sand is more prone to particle erosion in the first pattern while loose sand are gradually more prone to particle erosion in the second pattern. The quantitative relationship between the fine particles loss, the volumetric strain and the four influencing factors (i.e. time, hydraulic pressure, consolidated stress ratio and void ratio) are investigated using regression analysis based on 81 numerical simulations, respectively. The flow paths of the eroded fine particles are also investigated during the erosion process, which demonstrates that flow paths change alternatively between the blocked state and the opening state and then more flow paths in the model will open as the erosion process carries on.

Development of a mathematical model for submarine granular flows

An Eulerian-Eulerian two-phase model based on a collisional-frictional law for the granular stress is proposed for the description of underwater granular flows and is applied to the collapses of immersed granular columns, which can be viewed as an idealized physical model of submarine landslides. In the mathematical model, the kinetic theory for dry granular flows is extended to take into account the particle-fluid interaction when formulating the collisional stress in the granular material, while the frictional stress is modeled based on an existing relation obtained by statistically averaging the individual contact forces among cohesionless particles. The drag force and the virtual-mass force are considered to represent the inter-phase interaction. The two-phase model is then employed to simulate the laboratory experiments of the collapses of granular columns immersed in an ambient liquid with an emphasis on the effect of the initial packing condition of the granular particles. It has been shown that the computed collapsing process of granular columns is in very good agreement with the experimental observations, and the proposed model can well capture the dynamic features of underwater granular flows. The effects of fluid pressure, drag force, and particle and fluid properties on the granular collapse are also discussed. It is demonstrated that the interstitial fluid flow plays a significant role in the collapsing process.

Active Animations of Reduced Deformable Models with Environment Interactions

We present an efficient spacetime optimization method to automatically generate animations for a general volumetric, elastically deformable body. Our approach can model the interactions between the body and the environment and automatically generate active animations. We model the frictional contact forces using contact invariant optimization and the fluid drag forces using a simplified model. To handle complex objects, we use a reduced deformable model and present a novel hybrid optimizer to search for the local minima efficiently. This allows us to use long-horizon motion planning to automatically generate animations such as walking, jumping, swimming, and rolling. We evaluate the approach on different shapes and animations, including deformable body navigation and combining with an open-loop controller for realtime forward simulation.

Random adhesive loose packings of micron-sized particles under a uniform flow field

The effects of hydrodynamic interactions on random adhesive loose packings of monodisperse spherical micro-particles are investigated via a two-way coupled CFD-DEM approach. It is found out that the packing fraction and coordination number do not follow the regression of the adhesion number, which was proposed recently to well characterize the bulk properties of adhesive packings. Based on the balance between particle adhesion and fluid drag force, we propose a modified fluid adhesion number, Adf, which successfully normalizes the packing fraction and coordination number. Besides, the pressure drop through the packed bed shows a critical behavior, which validates the jamming threshold of fine powders, but occurs at a fixed packing fraction of ϕ ≈ 0.22 under the present protocol. The normalized permeability of the packed bed for different parameters is analyzed, which is in good agreement with the derivation of Kozeny-Carman equation.

A Numerical Procedure Accounting for Fluid Drag Forces and Cable Extensibility for the Static Response of Mooring Cables

An effective numerical method is proposed for the three-dimensional nonlinear analysis of mooring cables using catenary theory. In this method, the mooring line is divided into finite number of catenary elements. In addition to self-weight, each catenary element is subjected to drag force due to steady ocean currents. The proposed procedure is validated by comparing the results with those of the shooting optimization and the finite element methods. Finally, a parametric study is conducted to study the effect of extensibility on the static response of mooring cables. The effects of fluid drag forces and cable extensibility on mooring cable tension, equilibrium configurations, and stressed lengths are illustrated for two- and three-dimensional mooring cable problems. From the numerical results, the method is found to be numerically stable, and it provides a more rational static response for mooring cables.

Approach to design optimization based on CAE and Machine Learning

We are researching to utilize novel machine learning technology and CAE combined for design-estimation and design-optimization in product development. As an example, here is described to verify the fundamental methodology for predicting fluid drag force with a product shape using Deep Learning model which is trained by CFD simulation results.

Particle Removal From Sandbed Deposits in Horizontal Annuli Using Viscoelastic Fluids

SummaryThis paper presents results of an experimental study on how fluid viscoelastic properties would influence the particle removal from the sandbed deposited in horizontal annuli. Water and two different viscoelastic fluids were used for bed-erosion experiments. The particle-image-velocimetry (PIV) technique was used to measure the local fluid velocity at the fluid/sandbed interface, allowing for accurate estimation of the fluid-drag forces and the turbulence stresses.It was found that polymer fluids needed to exert higher level drag forces (than those of water) on the sandbed to start movement of the particles. Results have also shown that, at the critical flow rate of bed erosion, the polymer fluids yielded higher local fluid velocities and turbulent stresses than those of water. Moreover, the local velocity measurements by means of the PIV technique and the resultant bed-shear-stress calculations indicated that enhancing polymer concentration under the constant flow rate should also enhance the drag forces acting on the sandbed. However, these improved fluid hydrodynamic forces did not result in any improvement in the bed erosion. Therefore, the mechanism causing the delay in the bed erosion by polymer additives could not be explained by any decrease in the local fluid velocity and the turbulence.The primary reason for the delayed bed erosion by the polymer fluids was suggested to be linked to their viscoelastic properties. Two possible mechanisms arising from the elastic properties of the polymer fluids that hinder bed erosion were further discussed in the paper. The stress tensor of the viscoelastic-fluid flow was analyzed to determine the normal stress differences and the resultant normal fluid force acting on the particles at the fluid/sandbed interface. The normal force induced by the normal stress differences of the viscoelastic fluid was identified as one of the possible causes of the delayed bed erosion by these types of fluids.

Lattice Boltzmann investigation of the wake effect on the interaction between particle and power-law fluid flow

The wake behind a particle, namely particle wake, affects the interaction between particle and fluid. This effect of either single or two interactive particles is established for Newtonian fluid flow but not clear for non-Newtonian fluid flow. In this study, The particle wake behaviors and related particle-fluid forces in a power-law fluid flow are studied by a parallel three-dimensional lattice Boltzmann (LB) model over wide ranges of Reynolds number (0.1<Re<500) and power-law index (0.6<n<1.4). These ranges are well beyond those reported before. A new calibration model is proposed to reduce the discretization effects on the results analysis to most extents. The validity of the LB model with the calibration step is first examined by comparing the calculated fluid drag forces on a single particle against the measurements for different power-law fluid flows. On this basis, the model is used to study the flow and force characteristics resulting from the interaction of non-Newtonian fluid flow with a single particle or two interactive particles with fixed locations. From the simulation data, a new correlation is formulated to predict the drag coefficient of a single particle in power-law fluid flows. Also, the effect of placement distance between two particles is examined. The numerical results reveal the dynamic characteristics of the particle wake and particle-fluid forces, as well as their dependence on the power-law index, Reynolds number, and particles placement.

Force fields of charged particles in micro-nanofluidic preconcentration systems.

Electrokinetic concentration devices based on the ion concentration polarization (ICP) phenomenon have drawn much attention due to their simple setup, high enrichment factor, and easy integration with many subsequent processes, such as separation, reaction, and extraction etc. Despite significant progress in the experimental research, fundamental understanding and detailed modeling of the preconcentration systems is still lacking. The mechanism of the electrokinetic trapping of charged particles is currently limited to the force balance analysis between the electric force and fluid drag force in an over-simplified one-dimensional (1D) model, which misses many signatures of the actual system. This letter studies the particle trapping phenomena that are not explainable in the 1D model through the calculation of the two-dimensional (2D) force fields. The trapping of charged particles is shown to significantly distort the electric field and fluid flow pattern, which in turn leads to the different trapping behaviors of particles of different sizes. The mechanisms behind the protrusions and instability of the focused band, which are important factors determining overall preconcentration efficiency, are revealed through analyzing the rotating fluxes of particles in the vicinity of the ion-selective membrane. The differences in the enrichment factors of differently sized particles are understood through the interplay between the electric force and convective fluid flow. These results provide insights into the electrokinetic concentration effect, which could facilitate the design and optimization of ICP-based preconcentration systems.

Macro-scale acousto-fluidics using bulk ultrasonic standing waves

Macro-scale acousto-fluidics involves the interaction between acoustic radiation force exerted on a particle by bulk acoustic standing waves spanning many wavelengths, fluid drag force, and the gravitational force of the particle. Parameters are particle size, and ratio of particle to fluid density and particle to fluid compressibility. Different acousto-fluidics configurations can be used to manipulate particles in multiple ways. In cell clarification, the configuration is that of a depth flow filter with the added benefit of separating the cells out of the acoustic field, thereby eliminating any issues with filter clogging or fouling. In perfusion of stirred bioreactors, the configuration resembles that of a tangential flow filter. In a third configuration, the bulk acoustic standing wave is angled relative to the fluid velocity resulting in a label-free fractionation tool. Several underlying theoretical and numerical results of acoustic radiation force and particle trajectory calculations will be presented. A theoretical framework to calculate the acoustic radiation force on spherical, spheroidal, and cylindrical particles has been developed for any particle size relative to wavelength. An analytical solution for particle deflection angle in a planar angled standing wave and uniform flow has been developed. Experimental results will be shown to support the theory.

Understanding the separation of particles in a hydrocyclone by force analysis

The multiphase flow in a hydrocyclone is studied using computational fluid dynamics (CFD). The Reynolds stress model (RSM) is used to describe the turbulent characteristics of the gas-liquid flow. The motions of particles are simulated by the Lagrangian particle tracking model (LPT). By the numerical simulation, the forces on particles are obtained and their spatial and statistical distributions are analyzed. The separation mechanisms of different sized particles are proposed based on the analysis. The results show that for small particles the main force is the fluid drag force. As the particle size increases, the fluid drag force decreases exponentially, while the effects of the centrifugal force and pressure gradient force are enhanced. The fluid drag forces in the axial and tangential directions are both rather random, while with the increase of particle size the randomness of the radial force gradually decreases. The particle motion is governed by the inward pressure gradient force, the outward centrifugal force and the fluid drag force with strong randomness. For different sized particles, the value of the outward centrifugal force is essentially about 2.5 times of the inward pressure gradient force, so that large particles get into the downstream and are collected in the spigot. As particle size decreases, the magnitude of the fluid drag force increases. In addition, the direction of the fluid drag force becomes more random, though it is generally inward. Under the inward drag force, a portion of particles are pushed to the central axis and escape through upstream. When the particle size is smaller than a certain value, the fluid drag force is significantly greater than the centrifugal force and pressure gradient force. In such case, the movements of particles are largely random, and the particles in different directions are uniformly distributed.

Computational simulation of biomolecules transport with multi-physics near microchannel surface for development of biomolecules-detection devices.

The quantitative evaluation of the biomolecules transport with multi-physics in nano/micro scale is demanded in order to optimize the design of microfluidics device for the biomolecules detection with high detection sensitivity and rapid diagnosis. This paper aimed to investigate the effectivity of the computational simulation using the numerical model of the biomolecules transport with multi-physics near a microchannel surface on the development of biomolecules-detection devices. The biomolecules transport with fluid drag force, electric double layer (EDL) force, and van der Waals force was modeled by Newtonian Equation of motion. The model validity was verified in the influence of ion strength and flow velocity on biomolecules distribution near the surface compared with experimental results of previous studies. The influence of acting forces on its distribution near the surface was investigated by the simulation. The trend of its distribution to ion strength and flow velocity was agreement with the experimental result by the combination of all acting forces. Furthermore, EDL force dominantly influenced its distribution near its surface compared with fluid drag force except for the case of high velocity and low ion strength. The knowledges from the simulation might be useful for the design of biomolecules-detection devices and the simulation can be expected to be applied on its development as the design tool for high detection sensitivity and rapid diagnosis in the future.

An investigation on laboratory Knelson Concentrator separation performance: Part 2: Two-component feed separation modelling

In the previous study, a mathematical model was proposed to predict retained mass inside a laboratory Knelson Concentrator bowl. In this part, a model is proposed to describe the particle separation performance of the laboratory Knelson Concentrator. The separation model considers the main forces (fluid drag force, Fd, centrifugal force, Fc, and buoyancy force, Fb) acting on particles inside the concentrating bowl, which are functions of material properties as well as the operating condition parameters. Several materials with different densities including magnetite, zinc, ferromolybdenum, lead, and tungsten were used as valuable components to simulate minerals with the same densities in two-component synthetic feeds with various size fractions. The modelling of component separation in the Knelson Concentrator was performed based on the ratio of Fd/(Fc-Fb). Based on an extensive experimental database, practical and simple models were proposed as predictors of recovered mass of valuable components from tailings and the mass of quartz (as gangue) in the Knelson Concentrator versus the ratio of Fd/(Fc-Fb) for quartz.

An investigation on laboratory Knelson Concentrator separation performance: Part 1: Retained mass modelling

The retained mass of material in the Knelson Concentrator (KC) bowl depends on the main forces—the fluid drag force (Fd), the centrifugal force (Fc), and the buoyancy force (Fb)—which act on the particles in the concentrating bowl. They are functions of the material properties, as well as the operating condition parameters. In this experimental study, the fluid drag force (Fd) experienced by a solid particle in the rotating bowl was estimated by the fluidization water pressure (Pw) multiplied by the projected area (Ap) of a spherical particle hydraulically equivalent to the solid particle, and used in the model fitting. Quartz, magnetite, zinc, copper, and lead powders were used in different sizes as minerals with the same density to investigate and model the retained mass of material in the KC bowl. By defining the new ratio of Fd/(Fc-Fb), the retained volume of the different materials in the KC bowl was modelled, and it was shown to be the same for a given value of Fd/(Fc-Fb) ratio. Based on the developed experimental database consisting of 284 tests, a Weibull model was proposed. It can accurately model the retained mass of material in the KC bowl for particles with various sizes and densities under a given operating condition.

Prediction of dynamic contact angles and bubble departure diameters in pool boiling using equilibrium thermodynamics

A model is proposed for predicting dynamic contact angles and bubble departure diameters in pool boiling based on principles of equilibrium thermodynamics. The method is shown to give good agreement with experimental measurements for pool boiling over a wide range of pressures, liquid superheats and working fluids.The model suggests that for fast-growing bubbles associated with boiling at high Jakob Numbers (>100) the bubble shape is dominated by fluid drag forces rather than surface tension forces, resulting in the bubbles having a predominantly hemispherical shape during growth. For slower-growing bubbles associated with lower Jakob numbers (<50) surface tension forces appear to dominate over fluid drag forces, resulting in the bubbles adopting a spherical cap shape with a contact angle that remains close to the thermodynamic contact angle. This observation is in accordance with experiment.The model implies that in high pressure boiling the thermodynamic contact angle for the system has a controlling influence on bubble departure sizes. Analysis of departure diameters in high pressure boiling of water supports the view that the thermodynamic contact angle is strongly dependent on temperature, and that it is this temperature dependence that is responsible for the small bubble departure sizes observed in high pressure boiling. Previous models of bubble departure have been unable to explain the pressure dependence of bubble departure size. A correlation of the thermodynamic contact angle against temperature for water is proposed.The current model of bubble departure requires a means of calculating the bubble growth rate, as the latter determines the fluid drag forces acting on an attached bubble. A new predictive method for bubble growth is developed for this purpose, based on Scriven’s solution for conduction controlled bubble growth, with corrections to take account of non-uniform liquid superheat, microlayer evaporation, the effect of growth rate on the bubble shape, and the cooling effect of the microlayer on the heated surface. The predictive method gives satisfactory agreement with bubble growth data for a wide range of pool boiling experiments and also with results of microscale CFD simulations of the growth of individual bubbles.

On the adhesive JKR contact and rolling models for reduced particle stiffness discrete element simulations

Discrete Element Method (DEM) simulations are a promising approach to accurately predict agglomeration and deposition of micron-sized adhesive particles. However, the mechanistic models in DEM combined with high particle stiffness for most common materials require time step sizes in the order of nanoseconds, which makes DEM simulations impractical for more complex applications.In this study, analytically derived guidelines on how to reduce computational time by using a reduced particle stiffness are given. The guidelines are validated by comparing simulations of particles with and without reduced particle stiffness to experimental data. Then two well-defined test cases are investigated to show the applicability of the guidelines.When introducing a reduced particle stiffness in DEM simulations by reducing the effective Young's modulus from E to Emod, the surface energy density γ in the adhesive Johnson-Kendall-Roberts (JKR) model by Johnson et al. [1] should be modified as γmod=γ (Emod/E)2/5. Using this relation, the stick/rebound threshold remains the same but the collision process takes place over a longer time period, which allows for a higher time step size. When rolling motion is important, the commonly used adhesive rolling resistance torque model proposed by Dominik and Tielens [2,3], Krijt et al. [4] can be used by modifying the contact radius ratio (a/a0)3/2 to (amod/a0,mod)3/2, while keeping the other terms unaltered in the description of the rolling resistance torque Mr,mod=−4FC (a/a0)3/2ξ. Furthermore, as the particle stiffness is reduced from E to Emod, the time period for collisions (or oscillations when particles stick upon impact) Δtcol is found to vary as Δtcol,mod=Δtcol(E/Emod)2/5. As the collision duration and the collision time step size are directly related, this criterion can be used to estimate how much the time step size can be changed when a reduced particle stiffness is introduced.Introducing particles with a reduced particle stiffness has some limitations when strong external forces are acting to break-up formed agglomerates or re-entrain particles deposited on a surface out into the free stream. Therefore, care should be taken in flows with high local shear to make sure that an external force, such as a fluid drag force, acting to separate agglomerated particles, is several orders of magnitude lower than the critical force required to separate particles.

Experimental investigation of bubble and particle motion behaviors in a gas-solid fluidized bed with side wall liquid spray

Bubble and particle motion behaviors are investigated experimentally in a gas solid fluidized bed with liquid spray on the side wall. The particles used in the experiment are classified as Geldart B particles. The results reveal that when the fluid drag force is less than the liquid bridge force between particles, liquid distribute all over the bed. Bubble size increases as the increase of inter-particle force, then decreases owing to the increase of particle weight with increasing liquid flow rate. When the fluid drag force is greater than the liquid bridge force, liquid mainly distribute in the upper part of the bed. And it is difficult for the wet particles to form agglomerates. Bubble size decreases with increasing liquid flow rate due to the increasing of minimum fluidization velocity. Besides, the acoustic emission (AE) measurements illustrate that the liquid adhesion and evaporation on particles could enhance the particles motion intensity. Consequently, the bubble and particle behaviors change due to the variation in fluidized gas velocity and liquid flow rate should be seriously considered when attempting to successfully design and operate the side wall liquid spray gas solid fluidized bed.

Optimal control theory and the efficiency of the swimming mechanism of the Copepod Zooplankton

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the motion occurs minimizing the energy dissipated by the fluid drag forces in relation with the concept of efficiency of a stroke. The maximum principle is used to compute periodic controls candidates as minimizing controls and is a decisive tool combined with appropriate numerical simulations using indirect optimal control schemes to determine the most efficient stroke compared with standard computations using Stokes theorem and curvature control. Also the concept of graded approximations in SR-geometry is used to evaluate strokes with small amplitudes providing a fixed displacement and minimizing the dissipated energy.

A general solution of the drag force in packed beds of multi-sized particles under creeping fluid flow conditions

Drag correlations for fluid-particles interactions of multi-sized particle systems are important in many industries. Currently such correlations are modelled at particle-scale (Method A) or cell-scale (Method B). However, they are often inconsistent in predicting either the overall fluid-drag force in a packed bed or the individual drag forces for different sized particles in the bed. In this work, a new model is proposed to build up a linkage between the two approaches (Methods A and B) for estimation of the drag forces in packed beds of multi-sized particles under creeping fluid flow conditions. The new model is based on using both the particle-scale parameter, the effective individual porosity, as well as the cell-scale parameter, the effective average diameter. A set of closed equations have been formulated to link these parameters, which can be solved by numerical iterations. The model is shown to be able to satisfactorily predict the overall and individual drag forces. In addition, the predicted effective individual porosity is comparable to the local porosity defined in terms of Voronoi or radical cells, and the effective average diameter reduces to those well-defined ones (such as the harmonic mean and volume-width mean diameters) at different conditions. Then, the model is used to study the effects of overall porosity and particle size distribution on the mean local porosity around a component particle and the effective average diameter. And based on the data predicted by the model, empirical equations are developed to predict the effective average diameter and mean local porosity. Finally, a bridge is established to connect those two approaches for drag force calculation in the literature.

Coupled incompressible Smoothed Particle Hydrodynamics model for continuum-based modelling sediment transport

A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.