Fluid-particle Model Research Articles

Smoothed dissipative particle dynamics.

We present a fluid particle model that is both a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and a version of dissipative particle dynamics (DPD), capturing the best of both methods. The model is a discrete version of Navier-Stokes equations, like SPH, and includes thermal fluctuations, like DPD. This model solves some problems with the physical interpretation of the original DPD model.

Far field modeling of the plasma plume of a Hall thruster

Hall thrusters are an attractive form of electric propulsion that are being developed and implemented to replace chemical systems for many in orbit propulsion tasks on communications satellites. One concern in the use of these devices is the possible damage their plumes may cause to the host spacecraft. Computer models of Hall thruster plumes play an important role in integration of these devices onto spacecraft as the space environment is not easily reproduced in ground testing facilities. In this article, a hybrid particle-fluid model of a Hall thruster plume is applied to model the SPT-100 thrusters used on the Russian Express satellites. The emphasis of the article is on making assessment of the model through direct comparison with measurements of ion current density and ion energy distributions taken on board Express spacecraft. A model for simulating atom–ion collisions is described. The sensitivity of the plume simulation results to various aspects of the physical modeling is investigated. The plume model is able to predict many of the most important characteristics of the measured data.

Mesoscopic Dispersion of Colloidal Agglomerate in a Complex Fluid Modelled by a Hybrid Fluid–Particle Model

The dispersion of the agglomerating fluid process involving colloids has been investigated at the mesoscale level by a discrete particle approach—the hybrid fluid–particle model (FPM). Dynamical processes occurring in the granulation of colloidal agglomerate in solvents are severely influenced by coupling between the dispersed microstructures and the global flow. On the mesoscale this coupling is further exacerbated by thermal fluctuations, particle–particle interactions between colloidal beds, and hydrodynamic interactions between colloidal beds and the solvent. Using the method of FPM, we have tackled the problem of dispersion of a colloidal slab being accelerated in a long box filled with a fluid. Our results show that the average size of the agglomerated fragments decreases with increasing shearing rate Γ, according to the power law A·Γk, where k is around 2. For larger values of Γ, the mean size of the agglomerate Savg increases slowly with Γ from the collisions between the aggregates and the longitudinal stretching induced by the flow. The proportionality constant A increases exponentially with the scaling factor of the attractive forces acting between the colloidal particles. The value of A shows a rather weak dependence on the solvent viscosity. But A increases proportionally with the scaling factor of the colloid–solvent dissipative interactions. Similar type of dependence can be found for the mixing induced by Rayleigh–Taylor instabilities involving the colloidal agglomerate and the solvent. Three types of fragmentation structures can be identified, which are called rupture, erosion, and shatter. They generate very complex structures with multiresolution character. The aggregation of colloidal beds is formed by the collisions between aggregates, which are influenced by the flow or by the cohesive forces for small dispersion energies. These results may be applied to enhance our understanding concerning the nonlinear complex interaction occurring in mesoscopic flows such as blood flow in small vessels.

Parallel implementation of the fluid particle model for simulating complex fluids in the mesoscale

AbstractDissipative particle dynamics (DPD) and its generalization—the fluid particle model (FPM)—represent the ‘fluid particle’ approach for simulating fluid‐like behavior in the mesoscale. Unlike particles from the molecular dynamics (MD) method, the ‘fluid particle’ can be viewed as a ‘droplet’ consisting of liquid molecules. In the FPM, ‘fluid particles’ interact by both central and non‐central, short‐range forces with conservative, dissipative and Brownian character. In comparison to MD, the FPM method in three dimensions requires two to three times more memory load and a three times greater communication overhead. Computational load per step per particle is comparable to MD due to the shorter interaction range allowed between ‘fluid particles’ than between MD atoms. The classical linked‐cells technique and decomposing the computational box into strips allow for rapid modifications of the code and for implementing non‐cubic computational boxes. We show that the efficiency of the FPM code depends strongly on the number of particles simulated, the geometry of the box and the computer architecture. We give a few examples from long FPM simulations involving up to 8 million fluid particles and 32 processors. Results from FPM simulations in three dimensions of the phase separation in binary fluid and dispersion of the colloidal slab are presented. A scaling law for symmetric quench in phase separation has been properly reconstructed. We also show that the microstructure of dispersed fluid depends strongly on the contrast between the kinematic viscosities of this fluid phase and the bulk phase. This FPM code can be applied for simulating mesoscopic flow dynamics in capillary pipes or critical flow phenomena in narrow blood vessels. Copyright © 2002 John Wiley & Sons, Ltd.

Mesoscopic dynamics of colloids simulated with dissipative particle dynamics and fluid particle model.

We report results of numerical simulations of complex fluids, using a combination of discrete-particle methods. Our molecular modeling repertoire comprises three simulation techniques: molecular dynamics (MD), dissipative particle dynamics (DPD), and the fluid particle model (FPM). This type of model can depict multi-resolution molecular structures found in complex fluids ranging from single micelle, colloidal crystals, large-scale colloidal aggregates up to the mesoscale processes of hydrodynamical instabilities in the bulk of colloidal suspensions. We can simulate different colloidal structures in which the colloidal beds are of comparable size to the solvent particles. This undertaking is accomplished with a two-level discrete particle model consisting of the MD paradigm with a Lennard-Jones (L-J) type potential for defining the colloidal particle system and DPD or FPM for modeling the solvent. We observe the spontaneous emergence of spherical or rod-like micelles and their crystallization in stable hexagonal or worm-like structures, respectively. The ordered arrays obtained by using the particle model are similar to the 2D colloidal crystals observed in laboratory experiments. The micelle shape and its hydrophobic or hydrophilic character depend on the ratio between the scaling factors of the interactions between colloid-colloid to colloid-solvent. Unlike the miscellar arrays, the colloidal aggregates involve the colloid-solvent interactions prescribed by the DPD forces. Different from the assumption of equilibrium growth, the two-level particle model can display much more realistic molecular physics, which allows for the simulation of aggregation for various types of colloids and solvent liquids over a very broad range of conditions. We discuss the potential prospects of combining MD, DPD, and FPM techniques in a single three-level model. Finally, we present results from large-scale simulation of the Rayleigh-Taylor instability and dispersion of colloidal slab in 2D and 3D. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s00894-001-0068-3.

Electrical characteristics of a RF-GD-OES cell

The purpose of this work is to describe, using a self-consistent two dimensional hybrid fluid-particle model, the electrical characteristics of a discharge operating in a RF-GD-OES cell. We show that, for typical operating conditions at 13.56 MHz, the discharge has a capacitive electrical behavior and that the main current component at the powered electrode is the displacement current. These results are not in agreement with previously published calculations and this point is discussed.

On Two-Dimensional Laminar Hydromagnetic Fluid-Particle Flow Over a Surface in the Presence of a Gravity Field

A continuum two-phase fluid-particle model accounting for particle-phase stresses and a body force due to the presence of a magnetic field is developed and applied to the problem of two-dimensional laminar hydromagnetic flow of a particulate suspension over a horizontal surface in the presence of a gravity field. Analytical solutions for the velocity distributions and the skin-friction coefficients of both phases are reported. Two cases of wall hydrodynamic (velocity) conditions corresponding to stationary and oscillatory velocity distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of the particle-phase stresses and the magnetic field are illustrated through representative results for the horizontal velocity profiles, fluid-phase displacement thickness, and the complete skin-friction coefficient for various combinations of the physical parameters. It is found that the presence of the magnetic field increases the fluid-phase skin-friction coefficient for various particulate volume fraction levels while the presence of the particle-phase viscous stresses reduces it for various particle-to-fluid density ratios.

Effects of heat absorption and thermal radiation on heat transfer in a fluid–particle flow past a surface in the presence of a gravity field

A continuum two-phase fluid–particle model accounting for fluid-phase heat generation or absorption and thermal radiation is developed and applied to the problem of heat transfer in a particulate suspension flow over a horizontal heated surface in the presence of a gravity field. Analytical solutions for the temperature distributions and the wall heat fluxes for both phases are obtained. Two cases of wall thermal conditions corresponding to stationary and periodic temperature distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of heat absorption and thermal radiation are illustrated through representative results for the temperature distributions and heat fluxes of both phases for various fluid–particle suspensions. It is found that heat absorption increases the total heat transfer rate for various particulate volume fraction levels while thermal radiation decreases it.

Fluid particle model

We present a mechanistic model for a Newtonian fluid called fluid particle dynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose an heuristic derivation of a dissipative particle dynamics algorithm that incorporates shear forces between dissipative particles. The inclusion of these non-central shear forces requires the consideration of angular velocities of the dissipative particles in order to comply with the conservation of angular momentum. It is shown that the equilibrium statistical mechanics requirement that the linear and angular velocity fields are Gaussian is sufficient to construct the random thermal forces between dissipative particles. The proposed algorithm is very similar in structure to the (isothermal) smoothed particle dynamics algorithm. In this way, this work represents a generalization of smoothed particle dynamics that incorporates consistently thermal fluctuations and exact angular momentum conservation. It contains also the dissipative particle dynamics algorithm as a special case. Finally, the kinetic theory of the dissipative particles is derived and explicit expressions of the transport coefficients of the fluid in terms of model parameters are obtained. This allows to discuss resolution issues for the model.

The particle fluid model and using Lagrangian representation in two-phase flow modeling

Particle Fluid Model (PFM) is an intermediate method between the numerically intractable local instant model and the fully averaged two-fluid model for simulating transient two-phase flows. PFM uses a Lagrangian description for the dispersed phase and an Eulerian description for the continuous phase. In this paper we report a new way to model bubble lateral transport and the resulting void–fraction profile in bubbly flows simulated by the PFM. This model is based on eddy–bubble interactions. Eddies are generated by two mechanisms namely the wall-shear induced turbulence and the bubble–wake induced turbulence. Fluctuating components of velocity due to both of these effects are obtained separately. A linear superposition of turbulent kinetic energies is performed to obtain the resultant velocity fluctuations. An empirical model is used to determine the eddy size distribution in the pipe. The bubble momentum equation is solved through a succession of eddies to establish the lateral position of that bubble. This paper presents details of our bubble dispersion model and its assessment using experimental data of Serizawa.

Modeling the effect of the cathode geometry in a DC glow discharge ion source for mass spectrometry

A self-consistent, two-dimensional hybrid fluid-particle model is used to study the effect of cathode geometry on the plasma produced in an argon glow discharge for conditions typically of the commercially available glow discharge mass spectrometer system (VG9000 spectrometer and Megacell source). For a given power supply voltage and gas pressure, we show that the spatial distribution of the plasma in the discharge volume is strongly dependent on the cathode geometry. The plasma created in a discharge with a pin cathode tends to form a ring around the cathode, while the plasma in a discharge with a larger diameter, disk cathode is centered on-axis between the cathode face and the anode. The ion current arriving at the entry plane of the mass spectrometer thus depends strongly on the cathode geometry. This suggests that analytical performance can be enhanced by optimization of the cathode (sample) geometry.

Predicted emittance and brightness of the pseudospark electron-beam

The emittance and brightness of the electron beam generated during the hollow cathode phase of pseudospark operation are calculated using the two-dimensional hybrid fluid-particle model previously developed to study the time and space development of the plasma in a pseudospark discharge. Two distinct energy components exist in the electron beam; a high-energy component with an energy equivalent to the full discharge voltage and another, broad, low-energy component. In the 100 ns following breakdown and for the conditions of the calculations, the emittance of the high energy component decreases by an order of magnitude and the brightness of the high energy component reaches almost 10/sup 10/ A/m/sup 2/ rad/sup 2/. This work demonstrates the feasibility of using the model to guide the optimization of the pseudospark electron beam properties and shows that the optimum beam properties are achieved after the plasma has filled the hollow cathode and begun to expand radially in the main gap. >

Governing Equations of Sold-Liquid Two phase Flow and Their Applications

Three types of models, i. e. one fluid model, two fluid model and particlefluid model, are generally applied to investigate the characteristics of two phase flows. In each model, the careful consideration on the structures of governing equations and the constitutive relations employed should be needed. Essential point to be discussed in this paper is how the effects of interactions between two phases are taken into account in these basic equations.

Behavior of Ar plasma formed in a high density plasma source-an ECR reactor

In order to develop the ultra-large scale integration(ULSI), low pressure and high density plasma apparatus are required for etching and deposit of thin films. To understand critical parameters such as the pressure, temperature, electrostatic potential and energy distribution of ions impacting on the wafer, it is necessary to understand how these parameters are influenced by the power input and neutral gas pressure. In the present work, a 2-D hybrid electron fluid-particle ion model has been developed to simulate one of the high density plasma sources-an Electron Cyclotron Resonance (ECR) plasma system with various pressures and power inputs in a non-uniform magnetic field. By means of numerical simulation, the energy distributions of argon ion impacting on the wafer are obtained and the plasma density, electron temperature and plasma electrostatic potential are plotted in 3-D. It is concluded that the plasma density depends mainly on both the power input and neutral gas pressure. However, the plasma potential and electron temperature can hardly be affected by the power input, they seem to be primarily dependent on the neutral gas pressure. The comparison shows that the simulation results are qualitatively in good agreement with the experiment measurements.

Space and time dependence of the electric field and plasma induced emission in transient and steady-state hollow cathode discharges.

We have performed time-resolved observations of the current, optical emission, and electric field profiles in Ar and Ar+1% K hollow cathode discharges. The geometry and pressure are similar to those used in pseudosparks. The discharge was operated with a repetition rate of the order of kHz, an applied voltage in the range 300--600 V and with discharge current up to 1.5 A. Calculations were performed using a 2D, hybrid fluid-particle model developed previously [J. P. Boeuf and L. C. Pitchford, IEEE Trans. Plasma Sci. PS-19, 286 (1991)]. Good agreement is found between the predictions of the model and the experimental results, and, in particular, both show an initial sharp peak (less than 100 ns in width) in the discharge current a short time after application of the voltage which is related to the expansion of the plasma into the hollow cathode. Further, the model shows that the sequence of events leading to the formation of the hollow cathode discharge is the same in the present experiments and in pseudospark switches operating at much higher voltages.

Electron-beam generation during the hollow cathode phase of pseudospark discharges

From calculations using a two-dimensional, hybrid fluid-particle model, the mechanism for the production of the high-current electron beam observed during the hollow cathode phase of pseudospark discharges is identified. The predicted beam properties are in good qualitative agreement with experiments; the onset of the beam current is abrupt and the current in the beam is some 10%–30% of the discharge current. Two distinct components appear in the energy spectrum of the beam. A sizable fraction of the current is carried by electrons with an energy corresponding to the voltage applied to the discharge. A distinct low-energy beam is also predicted with a spread in energy of several 100s of eV.

Two-dimensional, hybrid model of low-pressure glow discharges.

A self-consistent, two-dimensional hybrid fluid-particle model is presented and used to describe the electrical behavior of dc low-pressure discharges in the current range ${10}^{\mathrm{\ensuremath{-}}7}$--${10}^{\mathrm{\ensuremath{-}}2}$ A in argon for products of the gas pressure and the gap spacing (pd) from 1 to 3.3 cm torr. The two-dimensional distributions of the potential, charged particle densities and ionization source term at steady state are shown to illustrate the discharge behavior during the transition from the normal to the abnormal regimes. For the larger values of pd, a positive column region as well as the cathode regions are clearly apparent. The model used here consists of Poisson's equation for the electric field coupled to the continuity equations for the electrons and ions with the important feature that the ionization source term appearing in the continuity equations is nonlocal and determined from a Monte Carlo simulation. This description yields a unified physical picture of discharge behavior in the cathode fall, negative glow, and positive column regions over a wide range of discharge currents.

Alpha-Particle-Driven Alfvén Turbulence and Its Effect on Alpha-Particle Transport

Recent developments in computational and theoretical studies of alpha-particle-driven Alfvén turbulence in both the long (k⊥ρi ≪ 1) and the short (k⊥ρi ≤ 1) wavelength regimes are reported. In the long wavelength regime, a hybrid particle-fluid model is solved numerically as well as analytically in a simple slab geometry. The dominant nonlinear interactions are found to be couplings between two Alfvén waves to generate a zero-frequency electromagnetic convective cell and strong E × B convection of resonant alpha particles, which result in significant changes in plasma equilibria. The fluctuation energies first increase, then saturate and decay. The alpha-particle transport is convective and significant but does not necessarily lead to an appreciable alpha-particle loss. A mode-coupling theory is developed to explain the simulation results. In the short wavelength regime, a reduced turbulence model that describes the coupled nonlinear evolutions of fluctuation spectrum and alpha-particle density profile nα(r,t) in the presence of an alpha-particle source Sα(r, t) is solved numerically. A steady state is achieved. The nonlinear saturation is due to ion Compton scattering-induced energy transfer to higher wave numbers. Alpha-particle transport is significant, and a diffusion coefficient of Dα ≃ 0.5 m2/s for International Thermonuclear Experimental Reactor (ITER)-like parameters is obtained. The effect of anomalous alpha-particle diffusion on alpha-particle power coupling to bulk plasmas is also discussed.

Pseudospark discharges via computer simulation

A hybrid fluid-particle (Monte Carlo) model to describe the initiation of pseudospark discharges has been developed. In this model, time-dependent fluid equations for the electrons and positive ions are solved self-consistently with Poisson's equation for the electric field in a two-dimensional, cylindrically symmetrical geometry. The Monte Carlo simulation is used to determine the ionization source term in the fluid equations. This model has been used to study the evolution of a discharge in helium at 0.5 torr, with an applied voltage of 2 kV and in a typical pseudospark geometry. From the numerical results, the authors have identified a sequence of physical events that lead to the rapid rise in current associated with the onset of the pseudospark discharge mode. They find that there is a maximum in the electron multiplication at the time which corresponds to the onset of the hollow cathode effect, and although the multiplication later decreases, it is always greater than needed for a steady-state discharge. >

Numerical Simulation of Fluid-Particle Flows: Geothermal Drilling Applications

In order to understand how a particulate plug may evolve within the flow of an essentially homogeneous suspension, we have developed a fluid-particle flow model. This theoretical model is based upon a monodisperse collection of rigid, spherical particles suspended in an incompressible, Newtonian liquid. Balance equations of mass and momentum are given for each phase within the context of a continuum mixture theory. The interactions between the phases are dominated by interfacial drag forces and unequilibrated pressure forces. The pressure associated with the solid particles is given by a phenomenological model based upon the flow dynamics. Of primary concern is the calculation of solid particle concentrations within a flow field to indicate the initiation of a particulate plug.