Computational Cell Size Research Articles

On the consequences of successively repeated collisions in no-time-counter collision scheme in DSMC

The current paper investigates the appropriateness and consequences of avoiding successively repeated collisions usually recommended in the Direct Simulation Monte Carlo (DSMC) solvers, which use the No Time Counter (NTC) collision technique. A sensitive test case, i.e., Fourier heat transfer problem at the early slip regime, is considered in the presence and absence of the successively repeated collisions. The effects of repeated collisions and avoiding them on different parameters such as heat flux, collision frequency, collision separation distance, accepted-to-selected collisions ratio, and probability distribution functions for the number of collisions and relative velocities of collision pairs are evaluated and discussed. The investigations are performed considering contributions of different computational parameters, i.e., cell sizes, time step, and number of particles. In addition to collision frequency and collision separation distance, which were reported previously as crucial parameters affecting the accuracy of the DSMC solution, we found that the level of repeated collisions also plays a pivotal role in the accuracy of the heat flux prediction in the Fourier problem. We show that direct avoiding of repeated collisions can lead to a distortion of collision probability distribution and consequently, to introduction of a systematic error in collision frequency and predicted heat flux. This error is negligible if one uses a large number of particles per cell, but it is of considerable importance if there are a few particles per cell.

Particle mixing rates using the two-fluid model

In this work, a new methodology is introduced to calculate the solids mixing rate in dense gas-fluidized beds using the two-fluid model. The implementation of this methodology into an existing two-fluid model code was carefully verified. The solids phase continuity equation was satisfied using our method, and the sensitivity of the computational results to the time step, computational cell size, and discretization scheme was investigated to determine the optimal simulation settings. Using these simulation settings, the degree of solids mixing was observed to rapidly (exponentially) increase with increasing operating pressure and linearly decrease with increasing bed diameter. Our novel methodology can be applied to analyze mixing processes in large lab-scale beds as an alternative to existing time-consuming simulation techniques such as computational fluid dynamics combined with the discrete element model.

A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows

LES for industrial applications with complex geometries is mostly characterised by: a) a finite volume CFD method using a non-staggered arrangement of the flow variables and second order accurate spatial and temporal discretisation schemes, b) an implicit top-hat filter, where the filter length is equal to the local computational cell size, and c) eddy-viscosity type LES models. LES based on these three main characteristics is indicated as industrial LES in this paper.It becomes increasingly clear that the numerical dissipation in CFD codes typically used in industrial applications with complex geometries may inhibit the predictive capabilities of explicit LES. Therefore, there is a need to quantify the numerical dissipation rate in such CFD codes. In this paper, we quantify the numerical dissipation rate in physical space based on an analysis of the transport equation for the mean turbulent kinetic energy. Using this method, we quantify the numerical dissipation rate in a quasi-Direct Numerical Simulation (DNS) and in under-resolved DNS of, as a basic demonstration case, fully-developed turbulent channel flow. With quasi-DNS, we indicate a DNS performed using a second order accurate finite volume method typically used in industrial applications. Furthermore, we determine and explain the trends in the performance of industrial LES for fully-developed turbulent channel flow for four different Reynolds numbers for three different LES mesh resolutions. The presented explanation of the mechanisms behind the observed trends is based on an analysis of the turbulent kinetic energy budgets.The presented quantitative analyses demonstrate that the numerical errors in the industrial LES computations of the considered turbulent channel flows result in a net numerical dissipation rate which is larger than the subgrid-scale dissipation rate.No new computational methods are presented in this paper. Instead, the main new elements in this paper are our detailed quantification method for the numerical dissipation rate, the application of this method to a quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow, and the explanation of the effects of the numerical dissipation on the observed trends in the performance of industrial LES for fully-developed turbulent channel flows.

Parametric sensitivity comparison of simulation models for flyer plate impact experiments

This article presents a study of the sensitivities of different parameters that affect the accuracy of simulating flyer plate impact experiments. Two approaches are explored: the CTH hydrodynamic and the LS-DYNA smoothed particle hydrodynamic (SPH) codes. Simulations using these two methods are compared to experimental data from a single-stage gas gun experiment in which a copper flyer plate impacted another copper target plate. The experiment was designed to cause spall in the target plate. The numerical simulations are conducted using these combined physics models: the Mie– Gruneisen equation of state, the Johnson–Cook compressive strength model, and spall rupture. Effects of artificial viscosity, spall strength, and computational cell size are studied and discussed with the objective of improving the accuracy of these simulations. The results are verified by applying the proposed simulation approach to other flyer plate experiments.

Effective field model of roughness in magnetic nano-structures

An effective field model is introduced here within the micromagnetics formulation, to study roughness in magnetic structures, by considering sub-exchange length roughness levels as a perturbation on a smooth structure. This allows the roughness contribution to be separated, which is found to give rise to an effective configurational anisotropy for both edge and surface roughness, and accurately model its effects with fine control over the roughness depth without the explicit need to refine the computational cell size to accommodate the roughness profile. The model is validated by comparisons with directly roughened structures for a series of magnetization switching and domain wall velocity simulations and found to be in excellent agreement for roughness levels up to the exchange length. The model is further applied to vortex domain wall velocity simulations with surface roughness, which is shown to significantly modify domain wall movement and result in dynamic pinning and stochastic creep effects.

An Euler–Lagrange particle approach for modeling fragments accelerated by explosive detonation

SummaryIn this paper, a method is proposed for modeling explosive‐driven fragments as spherical particles with a point‐particle approach. Lagrangian particles are coupled with a multimaterial Eulerian solver that uses a three‐dimensional finite volume framework on unstructured grids. The Euler–Lagrange method provides a straightforward and inexpensive alternative to directly resolving particle surfaces or coupling with structural dynamics solvers. The importance of the drag and inviscid unsteady particle forces is shown through investigations of particles accelerated in shock tube experiments and in condensed phase explosive detonation. Numerical experiments are conducted to study the acceleration of isolated explosive‐driven particles at various locations relative to the explosive surface. The point‐particle method predicts fragment terminal velocities that are in good agreement with simulations where particles are fully resolved, while using a computational cell size that is eight times larger. It is determined that inviscid unsteady forces are dominating for particles sitting on, or embedded in, the explosive charge. The effect of explosive confinement, provided by multiple particles, is investigated through a numerical study with a cylindrical C4 charge. Decreasing particle spacing, until particles are touching, causes a 30–50% increase in particle terminal velocity and similar increase in gas impulse. Copyright © 2015 John Wiley & Sons, Ltd.

A turbulence model for large interfaces in high Reynolds two-phase CFD

A model for two-phase (six-equation) CFD modelling of turbulence is presented, for the regions of the flow where the liquid–gas interface takes place on length scales which are much larger than the typical computational cell size. In the other regions of the flow, the liquid or gas volume fractions range from 0 to 1. Heat and mass transfer, compressibility of the fluids, are included in the system, which is used at high Reynolds numbers in large scale industrial calculations. In this context, a model based on k and ɛ transport equations in each phase was chosen. The paper describes the model, with a focus on the large interfaces, which require special treatments and transfer terms between the phases, including some approaches inspired from wall functions. The validation of the model is based on high Reynolds number experiments with turbulent quantities measurements of a liquid jet impinging a free surface and an air water stratified flow. A steam–water stratified condensing flow experiment is also used for an indirect validation in the case of heat and mass transfer.

Influence of void fraction calculation on fidelity of CFD‐DEM simulation of gas‐solid bubbling fluidized beds

The correct calculation of cell void fraction is pivotal in accurate simulation of two‐phase flows using a computational fluid dynamics‐discrete element method (CFD‐DEM) approach. Two classical approaches for void fraction calculations (i.e., particle centroid method or PCM and analytical approach) were examined, and the accuracy of these methodologies in predicting the particle‐fluid flow characteristics of bubbling fluidized beds was investigated. It was found that there is a critical cell size (3.82 particle diameters) beyond which the PCM can achieve the same numerical stability and prediction accuracy as those of the analytical approach. There is also a critical cell size (1/19.3 domain size) below which meso‐scale flow structures are resolved. Moreover, a lower limit of cell size (1.63 particle diameters) was identified to satisfy the assumptions of CFD‐DEM governing equations. A reference map for selecting the ideal computational cell size and the suitable approach for void fraction calculation was subsequently developed. © 2014 American Institute of Chemical EngineersAIChE J, 60: 2000–2018, 2014

Simulated western spruce budworm defoliation reduces torching and crowning potential: a sensitivity analysis using a physics-based fire model

The widespread, native defoliator western spruce budworm (Choristoneura occidentalis Freeman) reduces canopy fuels, which might affect the potential for surface fires to torch (ignite the crowns of individual trees) or crown (spread between tree crowns). However, the effects of defoliation on fire behaviour are poorly understood. We used a physics-based fire model to examine the effects of defoliation and three aspects of how the phenomenon is represented in the model (the spatial distribution of defoliation within tree crowns, potential branchwood drying and model resolution). Our simulations suggest that fire intensity and crowning are reduced with increasing defoliation compared with un-defoliated trees, regardless of within-crown fuel density, but torching is only reduced with decreasing crown fuel density. A greater surface fire intensity was required to ignite the crown of a defoliated compared with an un-defoliated tree of the same crown base height. The effects of defoliation were somewhat mitigated by canopy fuel heterogeneity and potential branchwood drying, but these effects, as well as computational cell size, were less pronounced than the effect of defoliation itself on fire intensity. Our study suggests that areas heavily defoliated by western spruce budworm may inhibit the spread of crown fires and promote non-lethal surface fires.

Generic unified rating for Cutthroat flumes

Computational fluid dynamics (CFD) software was used to generate water depth and discharge data for the 24 standard-size Cutthroat flumes (CTF), as well as an additional 27 intermediate sizes. The hydraulic model was validated using information from several sources, including physical model test data for 16 standard sizes and 3 intermediate sizes. Grid-size independence was also confirmed for a range of computational cell sizes, and the calibration results for 16 of the standard-size flumes were compared with previously published calibration parameters. Through the CFD simulations, a full set of calibration and validation data was generated for each of the 51 tested flume sizes, filling the gaps in the experimental data from physical models and permitting a full analysis of flume hydraulic performance. The study resulted in a “generic” (any CTF in the dimensional range of the 24 standard sizes and specified dimensional ratios according to the original design criteria) and “unified” (for both free- and submerged-flow conditions) calibrations. From these results, a single algebraic equation was developed for free and submerged flow, relating upstream water depth and submergence to discharge. The error in the CFD-predicted discharge for all flume sizes is less than 3 % of the full-scale discharge, and the equation is applicable to both standard and nonstandard sizes.

Generic Free-Flow Rating for Cutthroat Flumes

Computational fluid dynamics (CFD) software was used to generate water depth and discharge data for 51 Cutthroat flume sizes, including all 24 standard sizes published by the flume's developer and 27 intermediate sizes. The hydraulic model was validated by using data from several sources, including physical model testing for 15 standard sizes and three intermediate sizes. Grid-size independence was also confirmed for a range of computational cell sizes and the calibration results for 15 standard flume sizes were compared with previously published calibration parameters. Through the validated CFD simulations, a full set of calibration and validation data was generated for each of 51 flume sizes, filling the gaps in the experimental data and permitting a full analysis of the performance of the flume. The study resulted in a generic calibration for free-flow conditions for any Cutthroat flume in the dimensional range of the 24 standard sizes and specified dimensional ratios according to the original design criteria. The error in the predicted discharge for all flume sizes is less than 3% of the full-scale discharge. DOI: 10.1061/(ASCE)HY.1943-7900.0000732. © 2013 American Society of Civil Engineers. CE Database subject headings: Flow measurement; Flumes; Canals; Calibration; Computational fluid dynamics technique. Author keywords: Flow measurement; Flumes; Cutthroat flume; Canals; Calibration.

A new method for choosing the computational cell in stochastic reaction–diffusion systems

How to choose the computational compartment or cell size for the stochastic simulation of a reaction-diffusion system is still an open problem, and a number of criteria have been suggested. A generalized measure of the noise for finite-dimensional systems based on the largest eigenvalue of the covariance matrix of the number of molecules of all species has been suggested as a measure of the overall fluctuations in a multivariate system, and we apply it here to a discretized reaction-diffusion system. We show that for a broad class of first-order reaction networks this measure converges to the square root of the reciprocal of the smallest mean species number in a compartment at the steady state. We show that a suitably re-normalized measure stabilizes as the volume of a cell approaches zero, which leads to a criterion for the maximum volume of the compartments in a computational grid. We then derive a new criterion based on the sensitivity of the entire network, not just of the fastest step, that predicts a grid size that assures that the concentrations of all species converge to a spatially-uniform solution. This criterion applies for all orders of reactions and for reaction rate functions derived from singular perturbation or other reduction methods, and encompasses both diffusing and non-diffusing species. We show that this predicts the maximal allowable volume found in a linear problem, and we illustrate our results with an example motivated by anterior-posterior pattern formation in Drosophila, and with several other examples.

LES model of large scale hydrogen–air planar detonations: Verification by the ZND theory

The large eddy simulation (LES) model of hydrogen–air detonation at very large scales, which doesn't require Arrhenius chemistry, is presented. The progress variable equation is applied for the first time to simulate propagation of a reaction front following and coupled with a leading shock. The gradient method, based on a product of pre-shock mixture density and detonation velocity, is employed as a source term in the progress variable equation. Chemical kinetics enters the combustion model only through its influence on the detonation velocity and modelling of detailed chemistry is omitted. The LES model is verified against theoretical solution by the Zel'dovich–von Neumann–Doring (ZND) theory for a case of planar 29.05% hydrogen–air detonation in elongated 3 × 3 × 100 m calculation domain. Thermodynamically calculated values of the specific heats ratio for burned mixture γ = 1.22 and the standard heat of combustion Δ H c = 3.2 MJ/kg are applied without any adjustment often applied in other models. Numerical simulation reproduced theoretical values of von Neumann spike, Chapman–Jouguet pressure, Taylor wave and detonation propagation velocity. There are no adjustable parameters in the model. Practically no grid sensitivity for the planar detonation wave is demonstrated by the LES model. Detonation velocity and pressures are shown to be nearly independent of the computational cell size in a wide range of cell sizes 0.1–1.0 m. Impulse depends to some extent on a cell size. Three-dimensional version of the LES model is under development to simulate pressure effects and identify design solutions, including mitigating techniques, for hydrogen safety engineering. There is no intention to use this oriented on large scale applications engineering LES model to reproduce fine structure of the detonation wave.

Parasitic current generation in Combined Level Set and Volume of Fluid immiscible fluid simulations

The Continuum Surface Force technique is a popular tool used to implement surface tension forces in Eulerian based Computational Fluid Dynamics codes. Under this technique, inaccuracies present in calculating the surface tension force can manifest themselves as `parasitic' currents. We detail a new Combined Level Set and Volume of Fluid implementation of the Continuum Surface Force method. We then develop a correlation for the magnitude of parasitic currents that are generated under this new method, as a function of both the numerical and physical parameters employed in a simulation. A set of numerical experiments validate this correlation and show that, importantly, the magnitude of currents produced by the method decreases as the computational cell size reduced. References J. U. Brackbill, D. B. Kothe, and C. Zemach. A continuum method for modelling surface tension. Journal of Computational Physics, 100:335--354, 1992. Dalton J. E. Harvie, M. R. Davidson, and Murray Rudman. An analysis of parasitic current generation in volume of fluid simulations. Appl. Math Mod., 30(10):1056--1066, 2006. doi:10.1016/j.apm.2005.08.015 D. B. Kothe and R. C. Mjolsness. RIPPLE: A new model for incompressible flows with free surfaces. American Institue of Aeronautics and Astronautics, 30 (11):2694--2700, 1992. Bruno Lafaurie, Carlo Nardone, Ruben Scardovelli, Stephane Zaleski, and Gianluigi Zanetti. Modelling merging and fragmentation in multiphase flows with SURFER. Journal of Computational Physics, 113:134--147, 1994. Murray Rudman. A volume-tracking method for incompressible multifluid flows with large density variations. International Journal for Numerical Methods in Fluids, 28:357--378, 1998. Ruben Scardovelli and Stepahe Zaleski. direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics, 31:567--603, 1999. J. A. Sethian and Peter Smereka. Level set methods for fluid interfaces. Annual Review of Fluid Mechanics, 35:341--372, 2003. doi:10.1146/annurev.fluid.35.101101.161105 Mark Sussman. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. Journal of Computational Physics, 187:110--136, 2003. doi:10.1016/S0021-9991(03)00087-1 Mark Sussman and Elbridge Gerry Puckett. A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows. Journal of Computational Physics, 162:301--337, 2000. doi:10.1006/jcph.2000.6537 Mark Sussman, Peter Smereka, and Stanley Osher. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, 114:146--159, 1994. S. P. van der Pijl, A. Segal, C. Vuik, and P. Wesseling. A mass-conserving level-set method for modelling of multi-phase flows. International Journal for Numerical Methods in Fluids, 47:339--361, 2005. doi:10.1002/fld.817

Anisotropy in homogeneous dislocation nucleation by nanoindentation of single crystal Cu

This paper addresses the anisotropy in homogeneous dislocation nucleation by nanoindentation on different crystallographic surfaces in perfect single crystal Cu. The interatomic potential finite-element model is used to extend the computational cell size to micron-scale for eliminating boundary effects. Simulation results reveal that significant anisotropy exists for the critical indentation depth, the critical resolved shear stress and the critical indentation hardness. The calculated indentation moduli for the (0 0 1), (0 1 1), (1 1 1) surfaces fit the experimental data well.

Vacancy clustering and prismatic dislocation loop formation in aluminum

The formation of prismatic dislocation loops is an important factor leading to radiation damage of metals. However, the formation mechanism and the size of the smallest stable loop has remained unclear. In this Rapid Communication, we use electronic structure calculations with millions of atoms to address this problem in aluminum. Our results show that there is a cascade of larger and larger vacancy clusters with smaller and smaller energy. Further, the results show that a seven vacancy cluster on the (111) plane can collapse into a stable prismatic loop. This supports the long-standing hypothesis that vacancy clustering leads to a prismatic loop, and that these loops can be stable at extremely small sizes. Finally our results show that it is important to conduct calculations using realistic concentrations (computational cell size) to obtain physically meaningful results.

Tort solutions to the three-dimensional MOX benchmark, 3-D Extension C5G7MOX

Solutions to the OECD/NEA three-dimensional fuel assembly benchmark problem, C5G7MOX, obtained using the discrete-ordinates neutron transport code TORT are presented. The accuracy and convergence of the effective multiplication factor and maximum pin power are examined while varying the fidelity of the geometric model and the order of the angular quadrature, specifically the Square Legendre–Chebychev quadrature. The calculated value of the effective multiplication factor is shown to converge asymptotically as the order of the quadrature is increased. The behavior of that asymptotic limit of k eff with decreasing computational cell size and increasing staircase resolution of the curved rod-moderator is less converged. Moreover, rapidly increasing computational cost with geometric configuration refinement prevented us from achieving asymptotic convergence with the spatial approximation. The maximum pin power results are generally shown to asymptotically converge to within the statistical error of the reference solution for the problem slices where control rods are not present. For the zones that contain control rods, the solution does not appear to be tightly converged for the meshes and quadrature orders employed.

Relaxation times and cell size in nonzero-temperature micromagnetics

In nonzero-temperature micromagnetics the intrinsic magnetic parameters depend on the computational cell size. For large cells the experimentally measured, only temperature dependent intrinsic properties can be used. For simulations on an atomistic level the experimentally measured zero-temperature values can be applied. In between, the intrinsic magnetic properties follow scaling laws which can be derived from Metropolis Monte Carlo simulations. Equilibrium magnetization states and thermally activated switching processes of small ferromagnetic cubes were calculated. With proper scaling of the material parameters the numerical results were found to be almost independent of the computational cell size.

Cell size corrections for nonzero-temperature micromagnetics

Micromagnetic calculations at nonzero temperatures depend on the computational cell size. This paper shows that the spontaneous magnetization MS of exchange-coupled moments has to be scaled by a Bloch-like law, which is similar to the well-known temperature dependence of MS. Using this scaling law, nonatomistic Metropolis Monte Carlo and stochastic Landau–Lifshitz–Gilbert simulations are performed in an external field of 0.1T. The error of the equilibrium magnetization at a temperature of T∕TC=0.38 and a cell size of 1.5nm is then 0.9% as compared with atomistic calculations. In contrast, a cell size-independent MS leads to an overestimation of the temperature of 3.2%.

Dort solutions to the two-dimensional C5G7MOXbenchmark problem

We present a comprehensive study of the solution error for the C5G7MOXBenchmark problem using the two-dimensional transport code DORT. We set a stringent criterion that a successful solution to the benchmark exercise must satisfy, namely that at least for some of the benchmark quantities convergence to the reference solution with computational model refinement must be demonstrated. In the present exercise this amounts to examining the evolution of the DORT solution, e.g. the multiplication factor, with increasing angular quadrature order, decreasing computational cell size, and tighter representation of the curved rod-moderator interface for all circular rods in the core model. In addition we explored the effect of angular quadrature type, comparing solution accuracy for the fully symmetric and the Square Legendre-Chebychev quadratures establishing superiority of the latter. We establish the high quality of DORT's solution to this benchmark exercise by demonstrating that the multiplication factor asymptotically approaches the reference solution as stated in our self-imposed success criterion. High accuracy of the pin power distribution is also attained, however, convergence to the reference values is not realized. We conjecture that this is due to the lack of error information in the reference values. Our results also illustrate DORT's high accuracy on reasonable meshes and quadrature orders, as well as the sufficiency of a crude, square, geometric approximation of the rod-moderator interface to achieve high accuracy.