On the dynamics of grafted branched polymers—a Monte Carlo simulation study

A simplified model of grafted branched polymers was designed and investigated. The model consisted of star-branched chains constructed on a simple cubic lattice. The star polymers were built of three arms of equal lengths. The chains were attached to an impenetrable flat surface with one arm’s end. The arm attached to the surface (a stem) was built of segments different from those in two remaining arms (branches). During the Monte Carlo simulation of the system, the conformation of each chain was modified according to the metropolis sampling algorithm with local changes of chain conformations. The simulations were performed for different chain lengths and the temperature of the system (solvent conditions). The structure of a polymer film formed on the grafting surfaces depended strongly on the temperature and the low temperature films consisted of two separate layers with the insoluble layer located near the grafting surface. The short-time relaxation of the branches and stems of chains was also investigated. The analysis of the dynamics of the model system shows the influence of the structure of the system on relaxation times of various parameters. Paper presented at the AERC 2005 held on April 21–23, 2005 in Grenoble, France.     

Direct 2D simulation of small gas bubble clusters: from the expansion step to the equilibrium state

A numerical strategy, based on an adaptive finite element method, is proposed for the direct two‐dimensional simulation of the expansion of small clusters of gas bubbles within a Newtonian liquid matrix. The velocity and pressure fields in the liquid are first defined through the Stokes equations and are subsequently extended to the gas bubbles. The liquid–gas coupling is imposed through the stress exerted on the liquid by gas pressure (ruled by an ideal gas law) and by surface tension. A level set method, combined with a mesh adaptation technique, is used to track liquid–gas interfaces. Many numerical simulations are presented. The single bubble case allows to compare the simulations to an analytical model. Simulations of the expansion of small clusters are then presented showing the interaction and evolution of the gas bubbles to an equilibrium state, involving topological rearrangements induced by Plateau's rule. Copyright © 2006 John Wiley & Sons, Ltd.     

Direct numerical simulation of the laminar-turbulent transition in a thick spherical layer

The results of a numerical study of the laminar-turbulent transition in unsteady isothermal three-dimensional flows of viscous incompressible fluid in a thick spherical layer between counter-rotating spherical boundaries are presented. The calculations are performed for the governing parameters corresponding to the experimental data [1, 2]. The numerical investigations include both solving the complete system of Navier-Stokes equations and analyzing the linear stability of steady-state axisymmetric flows with respect to three-dimensional disturbances. A stochastic flow regime is calculated for the first time. The limits of existence of different flow regimes and the hysteresis regions are found. The spatial flow patterns and frequency characteristics are obtained, which makes it possible to extend and refine the existing experimental data.     

Investigation on a coupled Navier–Stokes–Direct Simulation Monte Carlo method for the simulation of plume flowfield of a conical nozzle

To assess the plume effects of space thrusters, the accurate plume flowfield is indispensable. The plume flow of thrusters involves both continuum and rarefied flow regimes. Coupled Navier–Stokes–Direct Simulation Monte Carlo (NS–DSMC) method is a major approach to the simulation of continuum‐rarefied flows. An axisymmetric coupled NS–DSMC solver, possessing adaptive‐interface and two‐way coupling features, is investigated in this paper for the simulation of the nozzle and plume flows of thrusters. The state‐based coupling scheme is adopted, and the gradient local Knudsen number is used to indicate the breakdown of continuum solver. The nitrogen flows in a conical nozzle and its plume are chosen as the reference case to test the coupled solver. The threshold value of the continuum breakdown parameter is studied based on both theoretical kinetic velocity sampling and coupled numerical tests. Succeeding comparisons between coupled and full DSMC results demonstrate their conformities, meanwhile, the former saves 58.8% computational time. The pitot pressure evaluated from the coupled simulation result is compared with the experimental data proposed in literatures, revealing that the coupled method makes precise predictions on the experimental pitot pressure. Copyright © 2014 John Wiley & Sons, Ltd.     

Flow regimes of a high-viscosity polymer mass bounded by the free surface in the region of drastic expansion of a channel

Flow regimes of the polymer mass filling cylindrical variable-section molds are studied by means of the numerical solution of the problem of a nonlinear viscoplastic fluid flow with a free surface in cylindrical channels of geometrically complicated shapes. A mathematical formulation of the problem is given, and factors affecting the molding process are analyzed. Numerical experiments performed in a wide range of problem parameters make it possible not only to elucidate the specific features of the hydrodynamic behavior of the free surface of the moving polymer mass, but also to establish the existence of two flow regimes depending on the ratio of the generalized Reynolds number to the Froude number. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 81–88, January–February, 2008.     

Use of a Monte Carlo PDF method in a study of the influence of turbulent fluctuations on selectivity in a jet-stirred reactor

A model for single-phase turbulent reacting flow is presented and a solution algorithm is described. The model combines the standardk - model for the velocity field with a transport equation for the probability density function (PDF) of the thermochemical variables. In this equation terms describing spatial transport by velocity fluctuations and mixing on the smallest scales are modelled. The essential advantage of this approach is that the effect of nonlinear kinetics appears in closed form and that the influence of turbulent fluctuations on mean reaction rates is included. A stochastic algorithm for the solution of the PDF transport equation, essentially due to Pope, is described. Cylindrical symmetry is assumed. The PDF is represented by ensembles ofN representative values of the thermochemical variables in each cell of a nonuniform finite-difference grid and operations on these elements representing convection, diffusion, mixing and reaction are derived. A simplified model and solution algorithm which neglects the influence of turbulent fluctuations on mean reaction rates is also described. Both algorithms are applied to a selectivity problem in a real reactor studied earlier by Liu and Barkelew. Spatial profiles of mean species mole fractions and of relative selectivity to the target product are obtained. The profiles are clearly different in both models but at the end of the reactor the same selectivity is predicted.Presented at the Shell Conference on Computational Fluid Dynamics for Petrochemical Process Equipment, Hoenderloo, December 10–12, 1989.     

Experimental study on the direct contact condensation of the steam jet in subcooled water flow in a rectangular channel: Flow patterns and flow field

Direct contact condensation (DCC) of steam jet in subcooled water flow in a channel was experimentally studied. The main inlet parameters, including steam mass flux, water mass flux and water temperature were tested in the ranges of 200–600 kg/(m² s), 7–18 × 10³ kg/(m² s), 288–333 K, respectively. Two unstable flow patterns and two stable flow patterns were observed via visualization window by a high speed camera. The flow patterns were determined by steam mass flux, water mass flux and water temperature, and the relationship between flow patterns and flow field parameters was discussed. The results indicated that whether pressure or temperature distributions on the bottom wall of channel could represent different flow patterns. And the position of pressure peak on the bottom wall could almost represent the condensation length. The upper wall pressure distributions were mainly dependent on steam and water mass flux; and the upper wall temperature distributions were affected by the three main inlet parameters. Moreover, the bottom wall pressure and temperature distributions of different unstable flow patterns had similar characteristics while those of stable flow patterns were affected by shock and expansion waves. The underlying cause of transition between different flow patterns under different inlet parameters was reflected and discussed based on pressure distributions.     

A STUDY OF THE CATASTROPHE AND THE CAVITATION FOR A SPHERICAL CAVITY IN HOOKE’S MATERIAL WITH 1/2 POISSON’S RATIO

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A theory and a simulation capability for the growth of a solid electrolyte interphase layer at an anode particle in a Li-ion battery

A major mechanism for electrochemical aging of Li-ion batteries is the growth of a solid electrolyte interphase (SEI) layer on the surface of anode particles, which leads to capacity fade and also results in a rise in cell resistance. We have formulated a continuum theory for the growth of an SEI layer—a theory which accounts for the generation of the attendant growth stresses. The theory has been numerically implemented in a finite-element program. This simulation capability for SEI growth is coupled with our previously published chemo-mechanical simulation capability for intercalation of Li-ions in electrode particles. Using this new combined capability we have simulated the formation and growth of an SEI layer during cyclic lithiation and delithiation of an anode particle, and predicted the evolution of the growth stresses in the SEI layer. The evolution of the stress state within the SEI layer and at the SEI/anode-particle interface for spherical- and spheroidal-shaped graphite particles is studied. This knowledge of the local interfacial stresses provides a good estimate for the propensity of potential delamination of an SEI layer from an anode particle.     

Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate

The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵ are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 3–15, September–October, 2006.     

Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.