Number Of Simulation Particles Research Articles

Neutron and gamma energy spectrum of the subcritical assembly for 99Mo production (SAMOP)

Neutronic analysis has been performed on SAMOP with Monte Carlo method using MCNP6 software. This research used SAMOP design developed by PSTA BATAN. Fuel used in the form of UO2(NO3)2 with enrichment of 19.75% and a concentration of 300 g U / L. The purpose of this study was to calculate the spectrum of γ and neutron around SAMOP by varying the water level at reactor pond tank and distance measurements and yields of fissionable nuclides by burning for 6 days. The number of simulated particles as many as 100000 with 150 cycles and the elimination of the first 50 cycles. From the results of this measurement obtained the average price and number of wells at a depth of 1500 cm with a height of air in the tank of 400 cm. The gamma spectrum is distributed at an intensity with a range of 10−8 while the neutron spectrum is distributed in the range 10−11 so it can be concluded that the gamma penetrating power is higher than the neutron.

Comparison of Cohesive Models in EDEM and LIGGGHTS for Simulating Powder Compaction.

The purpose of this work was to analyse the compaction of a cohesive material using different Discrete Element Method (DEM) simulators to determine the equivalent contact models and to identify how some simulation parameters affect the compaction results (maximum force and compact appearance) and computational costs. For this purpose, three cohesion contact models were tested: linear cohesion in EDEM, and simplified Johnson-Kendall-Roberts (SJKR) and modified SJKR (SJKR2) in LIGGGHTS. The influence of the particle size distribution (PSD) on the results was also investigated. Further assessments were performed on the effect of (1) selecting different timesteps, (2) using distinct conversion tolerances to export the three-dimensional models to standard triangle language (STL) files, and (3) moving the punch with different speeds. Consequently, we determined that a timestep equal to a 10% Rayleigh timestep, a conversion tolerance of 0.01 mm, and a punch speed of 0.1 m/s is adequate for simulating the compaction process using the materials and the contact models in this work. The results showed that the maximum force was influenced by the PSD due to the rearrangement of the particles. The PSD was also related to the computational cost because of the number of simulated particles and their sizes. Finally, an equivalence was found between the linear cohesion and SJKR2 contact models.

Simulation of gamma ray deep penetration through iron based on grid weight window iteration

To improve the efficiency of gamma ray deep penetration shielding calculation, this paper analyzed the influence of gamma ray energies, shield thickness, shielding materials and number of simulated particles on the transport calculation of gamma ray deep penetration, and proposed a Monte Carlo simulation method for gamma ray deep penetration shielding by iterative calculation based on the combination of grid weight window and material density gradually approaching true density. The simulation results show that, by using the iterative calculation method based on grid weight window in MCNP program, it can be realized that gradual transition from non deep penetration shielding simulation to deep penetration shielding simulation. The method can effectively solve the problem of gamma ray deep penetration calculation, and it can make the statistical error of the transmission coefficient of gamma ray penetrating the iron shield with a thickness of 60 times the mean free path of gamma ray less than 5%, which can meet the demand of gamma ray deep penetration simulation.

Version 4.0 of code Java for 3D simulation of the CCA model

This paper presents a new version Java code for the three-dimensional simulation of Cluster–Cluster Aggregation (CCA) model to replace the previous version. Many redundant traverses of clusters-list in the program were totally avoided, so that the consumed simulation time is significantly reduced. In order to show the aggregation process in a more intuitive way, we have labeled different clusters with varied colors. Besides, a new function is added for outputting the particle’s coordinates of aggregates in file to benefit coupling our model with other models. New version program summaryProgram Title: CCA v04Program Files doi:http://dx.doi.org10.17632/zwz37tvjny.1Licensing provisions: Apache-2.0Programming language: JavaJournal reference of previous version: Computer Physics Communications 207 (2016) 547–548Does the new version supersede the previous version?: YesNature of problem: The previous program for CCA model can be optimized for yielding better operation efficiency and visualization effects. Besides, it can be extended for coupling with other models by adding some new functions.Solution method: Some redundant traverses of the clusters-list for updating an important variable were removed technically. Furthermore, displaying different clusters with distinct colors can benefit to the effectiveness of visualization. We have also introduced a new function for outputting the aggregated clusters, so that this model can be easily coupled with other models.Reasons for the new version:1. In the previous versions [1–3], the global variable of Dmax, which means the maximum diffusion coefficient of clusters, is supposed to be calculated when aggregation occurs. In fact, this variable is critical to determine whether the currently selected cluster carries out diffusion or not. In the previous version, we had to traverse the clusters-list to update Dmax, even though it may keep unchanged after a round of aggregation. But, we have explored that it is not necessary to traverse all clusters, if we compare the previous variable of Dmax with the diffusion coefficient of the new cluster, which is formed by aggregating two clusters. In the case of the new one is larger, Dmax will be updated to it; otherwise, Dmax keep unchanged. Obviously, removing redundant traverses can enhance algorithm efficiency, and the time complexity of the algorithm is closely related to the loop in it. As a result, the new version of code can greatly cut down the simulation time, in contrast to the previous codes.2. The old versions paint all particles with same color, which does not help to identify different clusters. In order to show the visualization of the 3D aggregate process in different states intuitively, we introduce labeling different clusters with different colors. Consequently, the particles belong to one cluster are painted with the same color.3. A new function is added to record intermediate or final state of clusters so that it can be used for further research when using other relevant models.Summary of revisions:1. Reduce unnecessary traverses of the clusters-list for speeding up simulation.2. Paint clusters with different colors to pursuit better visualization effects.3. Add a new function of exporting the coordinates of clusters to a text file for benefiting other models.Additional comments:To test the optimization effects offered by the new version of code, we have carried out a comparison experimentto measure the simulation time with different initial particles, by using the new and the previous version 3.0 of code. In the experiments, we set concentration C to 0.01, diffusion exponent γ to 0, sticking probability exponent σ to 1, the sticking probability P1 to 0.1, absolute temperature T to 298 K, and the side length L of cube was respectively set to 30, 40, 50, 60, 70 and 80 to yield different initial particles, as the number of particles N can be calculated by the formula N=C∗L3 [1]. To avoid the influences of hardware and software, we use Monte Carlo steps (MCS) as our simulation time [4–6]. As shown in Fig. 1, the slope coefficient caused by this new version of code is about 1.3813, it is close to line complexity, as for the previous version, it is 1.5703, larger than the new one. It is obvious the new one has a faster running speed than the previous one. More importantly, the reduction of simulation time becomes more obvious when the number of simulated particles is getting larger.The changed visualization of our program is shownin Fig. 2. We can clearly see how much clusters in simulation system, and how they distribute. And the button “save” marked red in Fig. 2 can help realize our new function by exporting the particle coordinates to a text file, which also store the related initial conditions.AcknowledgmentsThis work was partially supported by “National Natural Science Foundation of China (Nos. 41271292, 61303038)”.

Collection/aggregation algorithms in Lagrangian cloud microphysical models: rigorous evaluation in box model simulations

Abstract. Recently, several Lagrangian microphysical models have been developed which use a large number of (computational) particles to represent a cloud. In particular, the collision process leading to coalescence of cloud droplets or aggregation of ice crystals is implemented differently in various models. Three existing implementations are reviewed and extended, and their performance is evaluated by a comparison with well-established analytical and bin model solutions. In this first step of rigorous evaluation, box model simulations, with collection/aggregation being the only process considered, have been performed for the three well-known kernels of Golovin, Long and Hall. Besides numerical parameters, like the time step and the number of simulation particles (SIPs) used, the details of how the initial SIP ensemble is created from a prescribed analytically defined size distribution is crucial for the performance of the algorithms. Using a constant weight technique, as done in previous studies, greatly underestimates the quality of the algorithms. Using better initialisation techniques considerably reduces the number of required SIPs to obtain realistic results. From the box model results, recommendations for the collection/aggregation implementation in higher dimensional model setups are derived. Suitable algorithms are equally relevant to treating the warm rain process and aggregation in cirrus.

CFD-DEM simulations of a fluidized bed crystallizer

In the present study, important features of the two-phase flow in a fluidized bed crystallizer are examined by numerical computations and companion experiments. The simulations are carried out using a coupled CFD-DEM approach (CFD: Computational Fluid Dynamics; DEM: Discrete Element Method). After validating an open-source CFD-DEM software tool for this purpose, regions within the crystallizer with unfavorable hydrodynamic features and thus a negatively impacted process outcome have been identified. This was first accomplished by single-phase CFD simulations. Then, the validated CFD-DEM model delivers valuable information that is difficult or even impossible to measure experimentally with sufficient accuracy, such as the velocity and position of fluidized crystals within the crystallizer.Since the simulations are computationally challenging, a compromise between simulated process time and number of simulated particles must be found. Hence, the CFD-DEM simulations are not utilized to simulate the whole crystallization process, but to examine a short time-window in detail. Corresponding findings confirm proper fluidization of the crystals support the model reduction carried out in a parallel project.

Development of a relativistic Particle In Cell code PARTDYN for linear accelerator beam transport

A relativistic Particle In Cell (PIC) code PARTDYN is developed for the beam dynamics simulation of z-continuous and bunched beams. The code is implemented in MATLAB using its MEX functionality which allows both ease of development as well higher performance similar to a compiled language like C. The beam dynamics calculations carried out by the code are compared with analytical results and with other well developed codes like PARMELA and BEAMPATH. The effect of finite number of simulation particles on the emittance growth of intense beams has been studied. Corrections to the RF cavity field expressions were incorporated in the code so that the fields could be calculated correctly. The deviations of the beam dynamics results between PARTDYN and BEAMPATH for a cavity driven in zero-mode have been discussed. The beam dynamics studies of the Low Energy Beam Transport (LEBT) using PARTDYN have been presented.

Vibrational spectrum and entropy in simulation of melting

We present a detailed analysis of entropy reconstruction from a velocity autocorrelation function in molecular dynamics simulation for solid and liquid states. The reconstruction is based on the vibrational density of states (VDOS) and for the liquid phase is known as a two-phase thermodynamic (2PT) model. We show that adequate accuracy of VDOS is required for successful application of this technique in the solid phase. We study the convergence of VDOS and entropy on the number of particles, time step and simulation time using aluminum as an example. We also examine the influence of temperature upon VDOS. Our analysis demonstrates that systems containing less than 500 atoms of aluminum do not reproduce the phonon density of state (PhDOS) of the crystal. Nevertheless the error of entropy calculation decreases quickly with the increase of the number of particles in simulation. We note strong influence of high temperatures on VDOS and the difference between VDOS and PhDOS near melting. We show that a time step of 0.5fs or less and trajectories of more than 10,000 time steps are required to obtain good accuracy of entropy in the solid phase. We use quantum molecular dynamics and the 2PT model with a memory function representation for the gas-like component to obtain a new point on the melting curve of aluminum at a pressure of 171GPa, that agree well with previous experimental works and calculations.

Analysis of correlations and their impact on convergence rates in Monte Carlo eigenvalue simulations

This paper provides an analysis of the generation-to-generation correlations as observed when solving full core eigenvalue problems on PWR systems. Many studies have in the past looked at the impact of these correlations on reported variance and this paper extends the analysis to the observed convergence rate on the tallies, the effect of tally size and the effect of generation size. Since performing meaningful analysis on such a large problem is inherently difficult, a simple homogeneous reflective cube problem with analytical solution was developed that exhibits similar behavior to the full core PWR benchmark. The data in this problem was selected to match the dimensionality of the reactor problem and preserve the migration length travelled by neutrons. Results demonstrate that the variance will deviate significantly from the 1/N (N being the number of simulated particles) convergence rate associated with truly independent generations, but will eventually asymptote to 1/N after 1000’s of generations regardless of the numbers of neutrons per generation. This indicates that optimal run strategies should emphasize lower number of active generations with greater number of neutrons per generation to produce the most accurate tally results. This paper also describes and compares three techniques to evaluate suitable confidence intervals in the presence of correlations, one based on using history statistics, one using generation statistics and one batching generations to reduce batch-to-batch correlation.

Modelling particle number concentrations in a typical street canyon in Germany and analysis of future trends

An aerosol box model and a gas-phase chemistry box model were coupled to simulate particle number (PN) concentrations, both solid and volatile, in a typical street canyon with a high traffic volume in Germany. The simulation accounts for emission, nucleation and aerosol aging processes while dilution is parameterised by a simple two-stage process. Calculations were performed for the years 2010, 2015, 2020 and 2025, and for a vehicle fleet consisting of electric vehicles only (“electric mobility”). Projections including a high fraction of Euro-6 vehicles in the fleet suggest that PN emissions will reduce by 90% in 2025 compared to 2010. Ambient PN concentrations are, however, expected to reduce by merely 29% over the same period. Apart from contributions of urban background air, reductions in primary particles are partially offset by secondary particle formation by nucleating exhaust gases. In the “electric mobility” scenario omitting tailpipe emissions, PN concentrations are expected to reduce by 60% from 2010 to 2025. For an aerosol assumed to be mixed externally only, PN of elemental carbon (EC) was calculated to reduce by 76% from 2010 to 2025, in the “electric mobility” scenario by 87%. Overall, the contribution of solid PN emissions from gasoline vehicles to PN concentration in the street canyon is expected to be approximately 4% in 2025.

Validation of a GPU-based Monte Carlo code (gPMC) for proton radiation therapy: clinical cases study

Monte Carlo (MC) methods are recognized as the gold-standard for dose calculation, however they have not replaced analytical methods up to now due to their lengthy calculation times. GPU-based applications allow MC dose calculations to be performed on time scales comparable to conventional analytical algorithms. This study focuses on validating our GPU-based MC code for proton dose calculation (gPMC) using an experimentally validated multi-purpose MC code (TOPAS) and compare their performance for clinical patient cases. Clinical cases from five treatment sites were selected covering the full range from very homogeneous patient geometries (liver) to patients with high geometrical complexity (air cavities and density heterogeneities in head-and-neck and lung patients) and from short beam range (breast) to large beam range (prostate). Both gPMC and TOPAS were used to calculate 3D dose distributions for all patients. Comparisons were performed based on target coverage indices (mean dose, V95, D98, D50, D02) and gamma index distributions. Dosimetric indices differed less than 2% between TOPAS and gPMC dose distributions for most cases. Gamma index analysis with 1%/1 mm criterion resulted in a passing rate of more than 94% of all patient voxels receiving more than 10% of the mean target dose, for all patients except for prostate cases. Although clinically insignificant, gPMC resulted in systematic underestimation of target dose for prostate cases by 1–2% compared to TOPAS. Correspondingly the gamma index analysis with 1%/1 mm criterion failed for most beams for this site, while for 2%/1 mm criterion passing rates of more than 94.6% of all patient voxels were observed. For the same initial number of simulated particles, calculation time for a single beam for a typical head and neck patient plan decreased from 4 CPU hours per million particles (2.8–2.9 GHz Intel X5600) for TOPAS to 2.4 s per million particles (NVIDIA TESLA C2075) for gPMC. Excellent agreement was demonstrated between our fast GPU-based MC code (gPMC) and a previously extensively validated multi-purpose MC code (TOPAS) for a comprehensive set of clinical patient cases. This shows that MC dose calculations in proton therapy can be performed on time scales comparable to analytical algorithms with accuracy comparable to state-of-the-art CPU-based MC codes.

Grid dependent noise and entropy growth in anisotropic 3d particle-in-cell simulation of high intensity beams

The numerical noise inherent to particle-in-cell (PIC) simulation of 3d anisotropic high intensity bunched beams in periodic focusing is compared with the analytical model by Struckmeier [Part. Accel. 45, 229 (1994)]. The latter assumes that entropy growth can be related to Markov type stochastic processes due to temperature anisotropy and the artificial “collisions” caused by using macro-particles and calculating the space charge effect. The PIC simulations are carried out with the tracewin code widely used for high intensity beam simulation. The resulting noise can lead to growth of the six-dimensional rms emittance. The logarithm of the latter is shown to qualify as rms-based entropy. We confirm the dependence of this growth on the bunch temperature anisotropy as predicted by Struckmeier. However, we also find a grid and focusing dependent component of noise not predicted by Struckmeier. Although commonalities exist with well-established models for collision effects in PIC-simulation of extended plasmas, a distinctive feature is the presence of a periodic focusing potential, wherein the beam one-component plasma extends only over relatively few Debye lengths. Our findings are applied in particular to noise in high current linac beam simulation, where they help for optimization of the balance between the number of simulation particles and the grid resolution.6 MoreReceived 15 July 2014DOI:https://doi.org/10.1103/PhysRevSTAB.17.124201This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

A comparison of weak-turbulence and particle-in-cell simulations of weak electron-beam plasma interaction

Quasilinear theory has long been used to treat the problem of a weak electron beam interacting with plasma and generating Langmuir waves. Its extension to weak-turbulence theory treats resonant interactions of these Langmuir waves with other plasma wave modes, in particular, ion-sound waves. These are strongly damped in plasma of equal ion and electron temperatures, as sometimes seen in, for example, the solar corona and wind. Weak turbulence theory is derived in the weak damping limit, with a term describing ion-sound wave damping then added. In this paper, we use the EPOCH particle-in-cell code to numerically test weak turbulence theory for a range of electron-ion temperature ratios. We find that in the cold ion limit, the results agree well, but for increasing ion temperature the three-wave resonance becomes broadened in proportion to the ion-sound wave damping rate. Additionally, we establish lower limits on the number of simulation particles needed to accurately reproduce the electron and wave distributions in their saturated states and to reproduce their intermediate states and time evolution. These results should be taken into consideration in, for example, simulations of plasma wave generation in the solar corona of Type III solar radio bursts from the corona to the solar wind and in weak turbulence investigations of ion-acoustic lines in the ionosphere.

Accelerating population balance-Monte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing

This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.

Start-to-end simulation of x-ray radiation of a next generation light source using the real number of electrons

In this paper we report on start-to-end simulation of a next generation light source based on a high repetition rate free electron laser (FEL) driven by a CW superconducting linac. The simulation integrated the entire system in a seamless start-to-end model, including birth of photoelectrons, transport of electron beam through 600 m of the accelerator beam delivery system, and generation of coherent x-ray radiation in a two-stage self-seeding undulator beam line. The entire simulation used the real number of electrons ($\ensuremath{\sim}2$ billion electrons/bunch) to capture the details of the physical shot noise without resorting to artificial filtering to suppress numerical noise. The simulation results shed light on several issues including the importance of space-charge effects near the laser heater and the reliability of x-ray radiation power predictions when using a smaller number of simulation particles. The results show that the microbunching instability in the linac can be controlled with 15 keV uncorrelated energy spread induced by a laser heater and demonstrate that high brightness and flux 1 nm x-ray radiation ($\ensuremath{\sim}{10}^{12}\text{ }\text{ }\mathrm{photons}/\mathrm{pulse}$) with fully spatial and temporal coherence is achievable.

Coupled continuum and molecular model of flow through fibrous filter

A coupled approach combining the continuum boundary singularity method (BSM) and the molecular direct simulation Monte Carlo (DSMC) is developed and validated using Taylor-Couette flow and the flow about a single fiber confined between two parallel walls. In the proposed approach, the DSMC is applied to an annular region enclosing the fiber and the BSM is employed in the entire flow domain. The parameters used in the DSMC and the coupling procedure, such as the number of simulated particles, the cell size, and the size of the coupling zone are determined by inspecting the accuracy of pressure drop obtained for the range of Knudsen numbers between zero and unity. The developed approach is used to study flowfield of fibrous filtration flows. It is observed that in the partial-slip flow regime, Kn ⩽ 0.25, the results obtained by the proposed coupled BSM-DSMC method match the solution by BSM combined with the heuristic partial-slip boundary conditions. For transition molecular-to-continuum Knudsen numbers, 0.25 < Kn ⩽ 1, the difference in pressure drop and velocity between these two approaches is significant. This difference increases with the Knudsen number that confirms the usefulness of coupled continuum and molecular methods in numerical modeling of transition low Reynolds number flows in fibrous filters.

Particle number concentrations over Europe in 2030: the role of emissions and new particle formation

Abstract. The aerosol particle number concentration is a key parameter when estimating impacts of aerosol particles on climate and human health. We use a three-dimensional chemical transport model with detailed microphysics, PMCAMx-UF, to simulate particle number concentrations over Europe in the year 2030, by applying emission scenarios for trace gases and primary aerosols. The scenarios are based on expected changes in anthropogenic emissions of sulfur dioxide, ammonia, nitrogen oxides, and primary aerosol particles with a diameter less than 2.5 μm (PM2.5) focusing on a photochemically active period, and the implications for other seasons are discussed. For the baseline scenario, which represents a best estimate of the evolution of anthropogenic emissions in Europe, PMCAMx-UF predicts that the total particle number concentration (Ntot) will decrease by 30–70% between 2008 and 2030. The number concentration of particles larger than 100 nm (N100), a proxy for cloud condensation nuclei (CCN) concentration, is predicted to decrease by 40–70% during the same period. The predicted decrease in Ntot is mainly a result of reduced new particle formation due to the expected reduction in SO2 emissions, whereas the predicted decrease in N100 is a result of both decreasing condensational growth and reduced primary aerosol emissions. For larger emission reductions, PMCAMx-UF predicts reductions of 60–80% in both Ntot and N100 over Europe. Sensitivity tests reveal that a reduction in SO2 emissions is far more efficient than any other emission reduction investigated, in reducing Ntot. For N100, emission reductions of both SO2 and PM2.5 contribute significantly to the reduced concentration, even though SO2 plays the dominant role once more. The impact of SO2 for both new particle formation and growth over Europe may be expected to be somewhat higher during the simulated period with high photochemical activity than during times of the year with less incoming solar radiation. The predicted reductions in both Ntot and N100 between 2008 and 2030 in this study will likely reduce both the aerosol direct and indirect effects, and limit the damaging effects of aerosol particles on human health in Europe.

GPU-accelerated Monte Carlo simulation of particle coagulation based on the inverse method

Simulating particle coagulation using Monte Carlo methods is in general a challenging computational task due to its numerical complexity and the computing cost. Currently, the lowest computing costs are obtained when applying a graphic processing unit (GPU) originally developed for speeding up graphic processing in the consumer market. In this article we present an implementation of accelerating a Monte Carlo method based on the Inverse scheme for simulating particle coagulation on the GPU. The abundant data parallelism embedded within the Monte Carlo method is explained as it will allow an efficient parallelization of the MC code on the GPU. Furthermore, the computation accuracy of the MC on GPU was validated with a benchmark, a CPU-based discrete-sectional method. To evaluate the performance gains by using the GPU, the computing time on the GPU against its sequential counterpart on the CPU were compared. The measured speedups show that the GPU can accelerate the execution of the MC code by a factor 10–100, depending on the chosen particle number of simulation particles. The algorithm shows a linear dependence of computing time with the number of simulation particles, which is a remarkable result in view of the n2 dependence of the coagulation.

Computational fluid dynamics based stochastic aerosol modeling: Combination of a cell-based weighted random walk method and a constant-number Monte-Carlo method for aerosol dynamics

No method is currently available to combine stochastic, particle-based PBE modeling by means of Monte-Carlo simulation of individual particles and CFD. CFD is based on solving numerically partial differential equations, whereas Monte-Carlo simulation of the PBE bases on converting kinetic rate equations into probabilities and selecting the relevant events by means of random numbers. A joint mathematical framework is thus missing. The goal of this work is to develop a method which allows combining Monte-Carlo based PBE modeling with a CFD model. As a first step towards this goal, a Weighted Random Walk (WRW) method to simulate the particle transport due to convection and diffusion is developed. The simulation particles have no exact position as in Lagrangian particle tracking methods but belong to a CFD cell. The movement of the simulation particles in space is performed by calculation of the transition probability into the neighboring cells and the use of random numbers to simulate the particle transport into these cells. As the particle number concentration can be very different in different regions of the simulated reactor volume, we introduce here also a weighting method which allows fixing the number of simulation particles per cell. The WRW method is combined with a relatively simple constant-number MC method allowing to simulate stochastically the dynamic evolution of the particle population. Four different validative case studies of increasing complexity are performed, comparing the simulation results with those of a CFD-based moment model.

Monte Carlo Simulation for Aggregative Mixing of Nanoparticles in Two-Component Systems

Gas-to-particle synthesis under high temperature is one of the most important methods for producing multicomponent nanoparticles. The volume enlargement of particles due to aggregation accompanies the component mixing within particles in a nonreactive system. To tailor nanocomposites, it is essential to gain an insight into the dynamic evolution of compositional distributions. In this paper, the differentially weighted Monte Carlo (DWMC) method for population balance modeling is used to simulate the process of aggregative mixing. On the methodological end, a new shift action is proposed to regulate a limited number of simulation particles to be distributed as homogeneously as possible over high-dimensional and inhomogeneous joint space of multiple components, where some simulation particles in less-populated regions are split into more simulation particles in order to increase sample space for stochastic statistics and then fatigue against statistical noise, at the same time a certain number of simulation particles in densely populated regions are randomly removed from the simulation to reduce computational demands. The DWMC with the new shift action is used to simulate the aggregative mixing process of bicomponent nanoparticles with compositional-independent or -dependent Brownian coagulation kernel in the free-molecular regime. It is found that the compositional distributions satisfy self-preserving formulation as the particle size distribution in monocomponent systems; and the extent of the time evolution of the degree of mixing (the mass-normalized power density of excess component A) corresponds with that of self-preserving distributions. The compositional distributions and the degree of mixing predicted by the DWMC agree well with theoretical models, while the constant-number method (using equally weighted simulation particles) fails in the more advanced stages of aggregative mixing.