Motion Of Fluid Particles Research Articles

A Lagrangian approach for computational acoustics with particle-based method

Although Eulerian approaches are standard in computational acoustics, they are less effective for problems with moving boundaries and multiphase systems like bubble acoustics. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically with particle-based methods. Fluid dynamic equations is divided into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, the smoothed particle hydrodynamics (SPH) method and the corrective smoothed particle (CSP) method are introduced to solve the perturbation equations in Lagrangian form. A hybrid meshfree and finite-difference time-domain boundary treatment technique is utilized to represent acoustic boundaries. Finally, applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP method exhibits accuracy convergence in cases with different background flow. Different acoustic boundary conditions are validated as being effective for benchmark problems in computational acoustics.

Anisotropic dynamics of nanoparticles in clusters at a solid-liquid interface by laser trapping

It is well-recognized that the Brownian motion of particles in fluids is random. Nevertheless, there can be characteristics depending on the specific physical conditions. We analyze the system of nanoparticle clusters formed by the laser trapping force field at the solid-liquid interface, based on the microscopy movie data. Since the laser trapping force field is basically a function of radial distance from the focal point in the two dimension at the liquid-solid interface, we examine the difference of displacement distributions in the radial and circumferential directions. The results show that the basic characteristics in this system depends on the laser power, and there is an anisotropy in the stochastic motion of the nanoparticles.

The motion of rigid particles in the Poiseuille flow of pseudoplastic fluids through straight rectangular microchannels

There has been in the past decade a significantly growing interest in the use of flow-induced lift forces for a passive control of particle motion in microchannels. This nonlinear microfluidic technique can be implemented in both Newtonian and non-Newtonian fluids. The motions of rigid particles in confined flows of viscoelastic fluids with and without shear-thinning effects have each been well studied in the literature. However, a comprehensive understanding of particle motion in inelastic shear-thinning fluids is still lacking. We present herein a systematic experimental study of the motion of rigid particles in the Poiseuille flow of pseudoplastic xanthan gum (XG) solutions through straight rectangular microchannels. We find that the number and location of particle equilibrium positions are both a strong function of channel dimension, particle size and XG concentration. We attempt to explain the experimental observations using the competition of inertial and elastic lift forces acting on particles. Our experimental results imply a potentially high throughput separation of rigid particles by size in XG solutions.

Effect of alternating gradient magnetic field on heat transfer enhancement of magnetoreological fluid flowing through microchannel

To investigate the contribution of transverse velocity pulsation on the heat transfer enhancement of magnetoreological fluid (MRF) flow in microchannel subjected to gradient alternating magnetic field, a doubled-population lattice Boltzmann simulation method is developed, where the magnetic nanoparticles (MPs) are treated as a quasi fluid and a simplified evaluation method for external forces on solid phase lattice points is proposed. Primarily, the effects of the alternating gradient magnetic field on the velocity and temperature distributions under temperature and heat flux boundary conditions are investigated. Simulation results show that, affected by the alternating gradient magnetic field, a considerable transverse velocity component occurs in the flow field. With the increase of pressure difference, the Nusselt number increases while the mean temperature of MRF reduces. The Nusselt number changes fluctuantly when the gradient magnetic field alternates. For the model concerned in this work, the gradient magnetic field induced transverse motion of fluid particles do not affect the heat transfer enhancement significantly. The experimental results indicate that both the heat transfer coefficient and the Nusselt number increase with the increasing Reynolds number, and the increasing magnetic induction intensity results in an obvious increase of heat transfer effect.

Unsteady particle motion in an acoustic standing wave field

The acoustic-based separation has attracted considerable attention in biomedical research, such as sorting of cells and particles. Current design principles used for acoustic systems are based on the steady Stokes theory, equating the Stokes drag with the primary radiation force. However, this approach is not valid for large cells/particles or in the presence of particle–particle interaction. In this work,we analytically examine unsteady inertial affects and particle–particle hydrodynamic interaction on the particle motion in a viscous fluid in the presence of an acoustic standing wave field. Comparing our results to the steady Stokes theory, we find that the unsteady inertial force decreases the particle’s velocity, while particle–particle interaction enhances it. For a particular acoustic-based separation approach ‘tilted-angle standing surface acoustic waves (taSSAW)’, we find that both effects of unsteady inertial force and particle–particle interaction are evident and should be considered for O(10μm) particles or larger. Our study improves the current predictions of particle trajectory in acoustic-based separation devices.

Unsteady flow of chemically reactive Oldroyd-B fluid over oscillatory moving surface with thermo-diffusion and heat absorption/generation effects

This theoretical investigation deals with the magnetohydrodynamic mass and heat transportation of oscillatory Oldroyd-B fluid flow under thermo-diffusion effects. Flow is produced due to periodic motion of sheet. Some interesting effects like heat absorption/generation and chemical reaction are superposed in the energy and mass species equations, respectively. By utilizing apposite variables, independent variables in the model equations are reduced. The set of these equations is solved with help of homotopy analysis method. Reliable results for different physical flow constraints are prepared for the velocity, temperature and concentration profiles. It is noted that the Deborah number in terms of relaxation time resists the motion of fluid particles at various time instants. Both temperature and concentration profiles increase by increasing Deborah number in terms of relaxation time. The presence of Dufour number may enhance the thermal boundary layer effectively. It is also concluded that the species concentration profile is promoted by increasing Hartmann number and Soret number. An excellent accuracy of obtained solution is observed with already reported numerical values as a special case.

Heat transfer analysis in magnetohydrodynamic flow of solid particles in non-Newtonian Ree-Eyring fluid due to peristaltic wave in a channel

In this article, the influence of heat transfer on solid particle motion in MHD Ree-Eyring fluid due to peristaltic wave has been investigated. The governing flow problem is modelled for fluid phase and particle phase with the help of continuity, momentum, and energy equations under the assumption of long wave-length and creeping flow regime. The obtained coupled ODE have been solved analytically and exact solutions have been presented. The influence of all the physical parameters are discussed for Newtonian and non-Newtonian fluid with the help of graphs. In the present analysis, it is observed that due to influence of Hartmann number, the magnitude of the velocity diminishes.

Motion of spheres and cylinders in viscoelastic fluids: Asymptotic behavior

Experiments were conducted to elucidate the effect of fluid elasticity on the motion of single spherical and cylindrical particles in viscoelastic fluids. Aqueous solutions of polyacrylamide in the concentration range of 0.35–0.6% wt./vol. were used as test fluids. The phenomenon of drag enhancement was observed. The maximum drag enhancement occurred at a Weissenberg number (Wi) of 60, beyond which the inertial effects dominate over the viscoelastic effects. In order to signify the relative importance of fluid elasticity and inertia, the results in terms of drag enhancement are represented as a function of elasticity number (E = Wi/Re). The drag enhancement exhibited asymptotic behavior with variation in elasticity number which depicts the dominance of elastic and inertial forces over each other. Based on the observed experimental data, a correlation used to predict drag for the particles falling in viscoelastic fluids has been proposed by incorporating the fluid elasticity and inertia in terms of corrective elasticity number function f(E). Experiments were also conducted to investigate the effect of fluid elasticity on the orientation of cylindrical particles settling in Newtonian, non Newtonian inelastic and viscoelastic fluids. It is found that the tilt angle (with vertical, α), characterizing the orientation of cylinders, decreases with fluid elasticity. However, the reverse behavior is observed with similar particles settling in inelastic fluid with increase in Reynolds number, whereas tilt angle remains constant in Newtonian fluid. Further, an attempt has been made to generate a correlation used to predict the tilt angle as a function of elasticity number and aspect ratio.

Dynamic bridging of proppant particles in a hydraulic fracture

This work is focused on the development of a dynamic criterion for the arching and bridging of spherical particles in a 3D suspension flow through a channel with plane walls. Elasticity of the particles and the channel walls are taken into account, as well as friction between the particles and with the walls. The carrier fluid is viscous, incompressible and Newtonian. Bridging occurs under the balance of the hydrodynamic force exerted from the fluid on the particles and the friction forces exerted from the walls and in between the particles. The 3D motion of particles in fluid is analyzed by means of direct numerical simulation. Various geometrical configurations are considered: three and four particles across the slot, and loose and close packing. Stability of the bridge is studied. The particles behave as a system with jumps (or a system with non-adjacent equilibrium positions), where the transition to the new equilibrium position occurs due to the accumulated elastic energy in the system (when the central particle is pushed through between the side ones). In this sense, the behavior of the grains is similar to the von Mizes truss. The bridging criterion is formulated as a domain on the plane in terms of the two nondimensional parameters: the particle size to channel width ratio and the flow velocity. For each particle-to-width size ratio there is a range of velocities, in which bridging occurs. The dynamic bridging criterion is different from the earlier purely kinematic criteria (e.g., w/d=2.5), which were formulated in terms of the particle-to-channel width ratio only. The bridging criterion is implemented into the 2D width-averaged lubrication model of suspension flow through a fracture, and illustrative simulations are conducted. The proposed model can be further used in the development of proppant transport models for fracture growth simulators, which are used in the oilfield industry for the design of hydraulic fracturing operations.

Molecular dynamics of partially confined Lennard-Jones gases: Velocity autocorrelation function, mean squared displacement, and collective excitations

Particle motion and correlations in fluids within confined domains promise to provide challenges and opportunities for experimental and theoretical studies. We report molecular dynamics simulations of a Lennard-Jones gas mimicking argon under partial confinement for a wide range of densities at a temperature of 300 K. The isotropic behavior of velocity autocorrelation function (VACF) and mean squared displacement (MSD), seen in the bulk, breaks down due to partial confinement. A distinct trend emerges in the VACF-perpendicular and MSD-perpendicular, corresponding to the confined direction, while the trends in VACF-parallel and MSD-parallel, corresponding to the other two unconfined directions are seen to be unaffected by the confinement. VACF-perpendicular displays a minimum, at short timescales, that correlates with the separation between the reflective walls. The effect of partial confinement on MSD-perpendicular is seen to manifest as a transition from diffusive to subdiffusive motion with the transition time correlating with the minimum in the VACF-perpendicular. When compared to the trends shown by MSD and VACF in the bulk, the MSD-perpendicular exhibits subdiffusive behavior and the VACF-perpendicular features rapid decay, suggesting that confinement suppresses the role of thermal fluctuations significantly. Repetitive wall-mediated collisions are identified to give rise to the minima in VACF-perpendicular and in turn a characteristic frequency in its frequency spectrum. The strong linear relation between the minima in VACF-perpendicular and wall-spacing suggests the existence of collective motion propagating at the speed of sound. These numerical experiments can offer interesting possibilities in the study of confined motion with observable consequences.

Zero modes, instantons and fluctuations in the Kraichnan model

Self-similar instanton solutions of the stochastic dynamics of the full passive scalar field in the Kraichnan model of turbulent advection are good candidates for describing the coherent motion of fluid particles leading to the production of strong gradients of the scalar and intermittency properties. By introducing a description of fluid particles in terms of quantum bosons, we show that instantons can be set in correspondence by a Legendre transformation with the so-called zero modes which are known, since the late 90s, to constitute the good mathematical framework for understanding and quantifying anomalous scaling in the Kraichnan model. Sticking to the classical level of approximation in the instanton approach leads clearly to an overestimation of scaling exponents of the structure functions of the scalar. To get further and incorporate the effect of fluctuations, we use the semiclassical instanton solutions as building blocks of more refined trial many-body wave functions for zero modes. One of the proposed approximation schemes gives surprisingly good estimates of scaling exponents even at low statistical orders and points towards a saturation of exponents at high statistical orders, as predicted by many authors either from numerics or analytic investigations in the large d limit.

Numerical Investigation of Two-Phase Mixed Convection Flow of Particulate Oldroyd-B Fluid with Non-Linear Thermal Radiation and Convective Boundary Condition

The present investigation addresses the mixed convection two-phase flow of dusty Oldroyd-B fluid towards a vertical stretching surface in the presence of convective boundary condition and nonlinear thermal radiation. The fluid and dust particles motion is coupled only in the course of drag and heat transfer between them. The Stokes linear drag theory is employed to model the drag force. The numerical solutions based on the Runge-Kutta-Fehlberg 45 scheme with shooting method are presented for both fluid and particle phase velocity and temperature fields. Further, numerical results are obtained for skin friction factor and local Nusselt number of prescribed values of pertinent parameters. The results are presented graphically and the physical aspects of the problem are analyzed. The obtained results are validated with existing results and found to be in good agreement. It is found that the mass concentration of the dust particle parameter plays a key role in controlling flow and thermal behaviour of non-Newtonian fluids.

Simulation of fluid dynamics through complicated networks of channels with cellular automata

To simulate the behavior of a liquid flowing through complicated regions of channels and porous media, we propose to simplify the problem using cellular automata (CA) simulation, in order to study qualitatively the behavior of the fluid dynamics. CA allows us to work with complicated border conditions by simply considering, or not, a particular cell to be part of the fluid flow. The fluid flow in the CA is achieved by setting the following rules of behavior: it is considered that the movement of fluid particles can only be due to gravity (vertically) and/or horizontally (for space availability) using probability values; upward movements can only be due to the balance of hydrostatic pressure outside the framework of CA; also, the particles will not be able to move to spaces already occupied by the fluid or spaces that form the walls of the structure. It was further possible to simulate the simultaneous behavior of two fluids of different density that cannot be mixed due to the programming simplicity of CA. Several case studies are discussed.

Objective Lagrangian Vortex Detection in the Solar Photosphere

Abstract Vortices in the solar photosphere can be linked to a wide range of events, such as small-scale solar eruptions, wave excitation, and heating of the upper part of the solar atmosphere. Despite their importance in solar physics, most of the current studies on photospheric vortices are based on methods that are not invariant under time-dependent translations and rotations of the reference frame and are Eulerian; i.e., they are based on single snapshots of a velocity field and, therefore, do not convey information on the true long-term motion of fluid particles on a time-varying field. Another issue with methods for vortex detection is that typically they provide false identifications in highly compressible flows. This Letter presents a novel criterion that effectively removes wrong detections based on the geometry of the streamlines of the displacement vector of fluid elements and can be readily applied to other astrophysical flows. The new criterion is applied to the Lagrangian-averaged vorticity deviation (LAVD), which is a recently developed frame invariant vortex detection method. The advantage of LAVD is that it delimits the vortices’ outer boundaries precisely by following up the trajectories of fluid elements in space and time. The proposed method is compared with two other techniques using horizontal velocity fields extracted from Hinode satellite data.

Numerical Simulations of a Gas–Solid Two-Phase Impinging Stream Reactor with Dynamic Inlet Flow

Fluid flow characteristics and particle motion behavior of an impinging stream reactor with dynamic inlet flow (both inlet velocity patterns exhibit step variation) are investigated and discussed with the computational fluid dynamics–discrete element method (CFD–DEM). The effect of T (variation period of the dynamic inlet flow) and ∆u (inlet velocity difference) on the motion characteristics of single and multiple particles, as well as the mean particle residence time, are studied and discussed. The research results indicate that, compared with the traditional impinging stream reactor (both inlet velocities are equal and constant) with equal mean inlet velocity (um) within one period, the impinging surface is instantaneously moving and the flow regime is varied with time in the impinging stream reactor with dynamic inlet flow. The impinging stream reactor with dynamic inlet flow provides higher cost performance over the traditional impinging stream reactor, under equal um, in terms of single-particle residence time. Moreover, three new particle motion modes exist in multi-particle motions of the impinging stream reactor with dynamic inlet flow; particles are accelerated by the original or reverse fluid and perform oscillatory motion at least once after an interparticle collision. Whether it is a single particle or multi-particles, the mean particle residence time reaches a maximum value when T/2 is approximately equal to the first particle acceleration time, since the maximum axial kinetic energy increases in every oscillatory motion compared with traditional impinging stream, and the number of oscillatory motions is increasing. The mean residence time of a particle in the impinging stream reactor with a dynamic inlet flow increases with increasing ∆u, since the dynamic inlet conditions and increasing ∆u can continuously supply more energy to particles and thus cause more particles to enter one of the three new modes of particle motion.

Simulations of an asymmetric gas–solid two-phase impinging stream reactor

Fluid flow characteristics and particle motion behaviors of an asymmetric impinging stream are investigated via the computational fluid dynamics-discrete element method at different values of inlet velocity ratio (v), under equal mean inlet velocity. The results indicate that compared with the symmetric impinging stream, the impingement region deviates toward the fluid with lower velocity. A parameter tr is proposed to measure of the particle oscillation time under different conditions of impinging streams. The asymmetric impinging stream provides higher cost performance and tr than the symmetric impinging stream in terms of the single-particle residence time. The asymmetric impinging stream provides enhancement of multi-particle mean residence time over symmetric impinging stream for greater number of oscillatory motion. A critical value of v (v = 0.9 in this work) in multi-particle motions has higher cost performance than symmetric impinging streams in terms of particle residence time and engineering cost.

A Lagrangian-based SPH-DEM model for fluid–solid interaction with free surface flow in two dimensions

• A Lagrangian-based SPH-DEM coupling model is proposed to simulate fluid-solid interaction with free-surface flow. • The coupling mechanism is realised by the decoupling of the force field during the process of fluid-solid interaction. • The proposed model can capture the features of solid movement, deformation and failure with high accuracy and efficiency A Lagrangian-based SPH-DEM coupling model is proposed to study fluid–solid interaction (FSI) problems with free-surface flow. In this model, SPH uses an incompressible divergence-free scheme for simulating complex flow problems. Based on the Mohr–Coulomb criterion with tension cut, the DEM describes the characteristics of solid deformation and failure by means of contact models between particles. The coupling mechanism between SPH and DEM is realised by the decoupling of the force field during the process of fluid–solid interaction. That is, the motions of fluid and solid particles are reflected by the Navier–Stokes equations and interactions among solid particles are determined by Newton's second law in the DEM. To demonstrate the applicability of the SPH-DEM model, three case studies are used to verify the different fluid interaction situations with rigid bodies, deformable objects, and granular assemblies, respectively. The results of the proposed model shows good agreement with experimental data and indicates that it is capable of capturing the features of solid movement, deformation and failure under complex flow conditions with convincing accuracy and high efficiency.

Turbulent Micropolar SPH Fluids with Foam.

In this paper we introduce a novel micropolar material model for the simulation of turbulent inviscid fluids. The governing equations are solved by using the concept of Smoothed Particle Hydrodynamics (SPH). As already investigated in previous works, SPH fluid simulations suffer from numerical diffusion which leads to a lower vorticity, a loss in turbulent details and finally in less realistic results. To solve this problem we propose a micropolar fluid model. The micropolar fluid model is a generalization of the classical Navier-Stokes equations, which are typically used in computer graphics to simulate fluids. In contrast to the classical Navier-Stokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. In addition to the linear velocity field these fluids also have a field of microrotation which represents existing vortices and provides a source for new ones. However, classical micropolar materials are viscous and the translational and the rotational motion are coupled in a dissipative way. Since our goal is to simulate turbulent fluids, we introduce a novel modified micropolar material for inviscid fluids with a non-dissipative coupling. Our model can generate realistic turbulences, is linear and angular momentum conserving, can be easily integrated in existing SPH simulation methods and its computational overhead is negligible. Another important visual feature of turbulent liquids is foam. Therefore, we present a post-processing method which considers microrotation in the foam particle generation. It works completely automatic and requires only one user-defined parameter to control the amount of foam.

Dynamics and rheology of particles in shear-thinning fluids

Particle motion in non-Newtonian fluids can be markedly different than in Newtonian fluids. Here we look at the change in dynamics for a few problems involving rigid spherical particles in shear-thinning fluids in the absence of inertia. We give analytical formulas for sedimenting spheres, obtained by means of the reciprocal theorem, and demonstrate quantitatively the differences in comparison to a Newtonian fluid. We also calculate the first correction to the suspension viscosity, the Einstein viscosity, for a dilute suspension of spheres in a weakly shear-thinning fluid.

Inline motion and hydrodynamic interaction of 2D particles in a viscoplastic fluid

In Stokes flow of a particle settling within a bath of viscoplastic fluid, a critical resistive force must be overcome in order for the particle to move. This leads to a critical ratio of the buoyancy stress to the yield stress: the critical yield number. This translates geometrically to an envelope around the particle in the limit of zero flow that contains both the particle and encapsulated unyielded fluid. Such unyielded envelopes and critical yield numbers are becoming well understood in our previous studies for single (2D) particles as well as the means of calculating. Here we address the case of having multiple particles, which introduces interesting new phenomena. First, plug regions can appear between the particles and connect them together, depending on the proximity and yield number. This can change the yielding behaviour since the combination forms a larger (and heavier) “particle.” Moreover, small particles (that cannot move alone) can be pulled/pushed by larger particles or assembly of particles. Increasing the number of particles leads to interesting chain dynamics, including breaking and reforming.