scholarly journals GENERIC-compliant simulations of Brownian multi-particle systems: modeling stochastic lubrication

SeMA Journal ◽  
2022 ◽  
Author(s):  
Adolfo Vázquez-Quesada ◽  
Marco Ellero
Keyword(s):  
Stokes Equations ◽  
Particle System ◽  
Dissipative Particle Dynamics ◽  
Particle Systems ◽  
Lagrangian Model ◽  
Navier Stokes ◽  
Particle Model ◽  
Simple Liquid ◽  
Solvent Model ◽  
Explicit Solvent Model

AbstractA stochastic Lagrangian model for simulating the dynamics and rheology of a Brownian multi-particle system interacting with a simple liquid medium is presented. The discrete particle model is formulated within the GENERIC framework for Non-Equilibrium Thermodynamics and therefore it satisfies discretely the First/Second Laws of Thermodynamics and the Fluctuation Dissipation Theorem (FDT). Long-range fluctuating hydrodynamics interactions between suspended particles are described by an explicit solvent model. To this purpose, the Smoothed Dissipative Particle Dynamics method is adopted, which is a GENERIC-compliant Lagrangian meshless discretization of the fluctuating Navier–Stokes equations. In dense multi-particle systems, the average inter-particle distance is typically small compared to the particle size and short-range hydrodynamics interactions play a major role. In order to bypass an explicit—computationally costly—solution for these forces, a lubrication correction is introduced based on semi-analytical expressions for spheres under Stokes flow conditions. We generalize here the lubrication formalism to Brownian conditions, where an additional thermal-lubrication contribution needs to be taken into account in a way that discretely satisfies FDT. The coupled lubrication dynamics is integrated in time using a generalized semi-implicit splitting scheme for stochastic differential equations. The model is finally validated for a single particle diffusion as well as for a Brownian multi-particle system under homogeneous shear flow. Results for the diffusional properties as well as the rheological behavior of the whole suspension are presented and discussed.

An Eulerian-Lagrangian Approach for the Numerical Simulation and Visualization of Two-Dimensional Fluidized Beds

2002 ◽  
Author(s):  
Ph. Traore´ ◽  
C. Herbreteau ◽  
R. Bouard
Keyword(s):  
Stokes Equations ◽  
Distinct Element ◽  
Fluid Phase ◽  
Lagrangian Approach ◽  
Lagrangian Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Type Method ◽  
Contact Points ◽  
Mechanical Models

This paper deals with an Eulerian-Lagrangian model for dispersed multiphase flow in which all the interactions of any kind are taking into account. The fluid phase and particles interactions are two way coupled while all the collisions between the particles or between the particles and the walls are calculated. The Navier-Stokes equations (fluid phase continuity and momentum equations including exchange from the particle to the fluid is modeled to simulate the effect of the presence of the particles in the fluid phase) are solved on a staggered Eulerian grid by a finite volume discretisation type method. The originality of the Lagrangian approach used here for the particles motion, lies in the way of managing the collisions which are calculated using simple mechanical models such as a spring, dashpot and friction slider at the contact points following the Distinct Element Method DEM [1]. In the Lagrangian stage, motion’s calculation of each discrete particle including collisions effects is generally time consuming. In the context of this paper we shall show how to optimized the contacts tracking algorithm in an efficient way to increase significantly the capability of the DEM.

STOCHASTIC DYNAMICS OF VISCOELASTIC SKEINS: CONDENSATION WAVES AND CONTINUUM LIMITS

2008 ◽  
Vol 18 (supp01) ◽  
pp. 1149-1191 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
WOLFGANG ALT
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Particle System ◽  
Force Balance ◽  
Navier Stokes ◽  
Dimensional System ◽  
Neighbor Distance ◽  
Balance Equations ◽  
Velocity Function ◽  
One Dimensional

Skeins (one-dimensional queues) of migrating birds show typical fluctuations in swarm length and frequent events of "condensation waves" starting at the leading bird and traveling backward within the moving skein, similar to queuing traffic waves in car files but more smooth. These dynamical phenomena can be fairly reproduced by stochastic ordinary differential equations for a "multi-particle" system including the individual tendency of birds to attain a preferred speed as well as mutual interaction "forces" between neighbors, induced by distance-dependent attraction or repulsion as well as adjustment of velocities. Such a one-dimensional system constitutes a so-called "stochastic viscoelastic skein." For the simple case of nearest neighbor interactions we define the density between individualsu = u(t, x) as a step function inversely proportional to the neighbor distance, and the velocity function v = v(t, x) as a standard piecewise linear interpolation between individual velocities. Then, in the limit of infinitely many birds in a skein of finite length, with mean neighbor distance δ converging to zero and after a suitable scaling, we obtain continuum mass and force balance equations that constitute generalized nonlinear compressible Navier–Stokes equations. The resulting density-dependent stress functions and viscosity coefficients are directly derived from the parameter functions in the original model. We investigate two different sources of additive noise in the force balance equations: (1) independent stochastic accelerations of each bird and (2) exogenous stochastic noise arising from pressure perturbations in the interspace between them. Proper scaling of these noise terms leads, under suitable modeling assumptions, to their maintenance in the continuum limit δ → 0, where they appear as (1) uncorrelated spatiotemporal Gaussian noise or, respectively, (2) certain spatially correlated stochastic integrals. In both cases some a priori estimates are given which support convergence to the resulting stochastic Navier–Stokes system. Natural conditions at the moving swarm boundaries (along characteristics of the hyperbolic system) appear as singularly perturbed zero-tension Neumann conditions for the velocity function v. Numerical solutions of this free boundary value problem are compared to multi-particle simulations of the original discrete system. By analyzing its linearization around the constant swarm state, we can characterize several properties of swarm dynamics. In particular, we compute approximating values for the averaged speed and length of typical condensation waves.

scholarly journals Predicting the Diameters of Droplets Produced in Turbulent Liquid-Liquid Dispersion

2021 ◽  
Author(s):  
John Thomas ◽  
Brian DeVincentis ◽  
Johannes Wutz ◽  
Francesco Ricci
Keyword(s):  
Stokes Equations ◽  
Droplet Diameter ◽  
A Priori ◽  
Droplet Size Distribution ◽  
Operating Conditions ◽  
Droplet Breakup ◽  
Turbulence Theory ◽  
Lagrangian Model ◽  
Navier Stokes ◽  
Impeller Type

The droplet size distribution in liquid-liquid dispersions is a complex convolution of impeller speed, impeller type, fluid properties, and flow conditions. In this work, we present three a priori modeling approaches for predicting the droplet diameter distributions as a function of system operating conditions. In the first approach, called the two-fluid approach, we use high-resolution solutions to the Navier-Stokes equations to directly model the flow of each phase and the corresponding droplet breakup/coalescence events. In the second approach, based on an Eulerian-Lagrangian model, we describe the dispersed fluid as individual spheres undergoing ongoing breakup and coalescence events per user-defined interaction kernels. In the third approach, called the Eulerian-Parcel model, we model a sub-set of the droplets in the Eulerian-Lagrangian model to estimate the overall behavior of the entire droplet population. We discuss output from each model within the context of predictions from first principles turbulence theory and measured data.

scholarly journals Euler–Lagrange Simulations of Bubble Cloud Dynamics Near a Wall

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Jingsen Ma ◽  
Chao-Tsung Hsiao ◽  
Georges L. Chahine
Keyword(s):  
High Pressures ◽  
Stokes Equations ◽  
Rigid Wall ◽  
Lagrangian Model ◽  
Navier Stokes ◽  
Driving Frequency ◽  
Two Phase ◽  
Mixture Density ◽  
Bubble Cloud ◽  
Spherical Bubbles

We present in this paper a two-way coupled Eulerian–Lagrangian model to study the dynamics of clouds of microbubbles subjected to pressure variations and the resulting pressures on a nearby rigid wall. The model simulates the two-phase medium as a continuum and solves the Navier–Stokes equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting singularities representing moving and oscillating spherical bubbles, following a modified Rayleigh–Plesset–Keller–Herring equation and are tracked in a Lagrangian fashion. A two-way coupling between the Euler and Lagrange components is realized through the local mixture density determined by the bubbles' volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures at different frequencies. The results show that the frequency of the driving pressure is critical in determining the overall dynamics: either a collective strongly coupled cluster behavior or nonsynchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressure. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall also affects significantly the resulting pressures. A bubble cloud collapsing very close to the wall exhibits a cascading collapse, with the bubbles farthest from the wall collapsing first and the nearest ones collapsing last, thus the energy accumulates and this results in very high pressure peaks at the wall. At farther cloud distances from the wall, the bubble cloud collapses quasi-spherically with the cloud center collapsing last.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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