Simulation of Aerosol Dynamics: A Comparative Review of Mathematical Models

A comparative review of mathematical models of aerosol dynamics is presented. Three approaches are considered that are based on continuous, discrete (sectional), and parametrized (lognormal) representations of the aerosol size distribution. Simulations of coagulation and diffusion-limited condensation are performed with these modeling approaches for three case studies typical of clear, hazy, and urban atmospheric aerosol concentrations. The relative accuracies and computational costs of models based on these approaches are compared. The models based on a continuous size distribution provide an accurate solution for both coagulation and condensation. Sectional approaches simulate coagulation very well but require a fine size resolution to minimize numerical diffusion in the simulation of condensation. The parametrized model based on log-normal modal size distributions is computationally efficient but tends to overestimate the rate of coagulation and the peak aerosol concentration resulting from condensational growth. The results of this study provide useful information for the selection of an aerosol model, depending on the accuracy requirements and computational constraints associated with a specific application.     

Eulerian modelling of lung deposition with sectional representation of aerosol dynamics

A dynamical model of respiratory deposition is developed based on an Eulerian approach. The model simulates detailed lung deposition along all generations of the respiratory tract by solving numerically the aerosol general dynamics equation (GDE). All deposition mechanisms are described mechanistically, without using any empirical correlations. The GDE is solved in a one-dimensional form using a sectional method to describe the aerosol size distribution. To describe lung geometry the classical Weibel's morphometric model is used, employing a time-varying alveolar geometry to accommodate inhalation dynamics. A computationally efficient methodology is implemented based on a time-step splitting and subcycling approach, combined with a moving grid method for the growth process. The model is validated by comparing extensively with experimental and numerical results. The simulation results show that aerosol dynamics, in particular condensational growth, significantly influence respiratory deposition of fine hygroscopic particles. Instead, the effect of coagulation was found to be negligible. Particle deposition in terms of number, surface, or mass is addressed, which is of interest to current inhalation toxicology studies.     

Simulation of Aerosol Dynamics: A Comparative Review of Algorithms Used in Air Quality Models

A comparative review of algorithms currently used in air quality models to simulate aerosol dynamics is presented. This review addresses coagula tion, condensational growth, nucleation, and gas particle mass transfer. Two major approaches are used in air quality models to represent the particle size distribution: (1) the sectional approach in which the size distribution is discretized into sections and particle properties are assumed to be constant over particle size sections and (2) the modal approach in which the size distribution is approxi mated by several modes and particle properties are assumed to be uniform in each mode. The sectional approach is accurate for coagulation and can reproduce the major characteristics of the evolution of the particle size distribution for condensa tional growth with the moving-center and hybrid algorithms. For coagulation and condensational growth, the modal approach provides more accurate results when the standard deviations of the modes are allowed to vary than it does when they are fixed. Predictions of H₂SO₄ nucleation rates are highly sensitive to environ mental variables and simulation of relative rates of condensation on existing particles and nucleation is a preferable approach. Explicit treatment of mass transfer is recommended for cases where volatile species undergo different equilib rium reactions in different particle size ranges (e.g., in the presence of coarse salt particles). The results of this study provide useful information for use in selecting algorithms to simulate aerosol dynamics in air quality models and for improving the accuracy of existing algorithms.     

Simulation of Aerosol Coagulation and Deposition Under Multiple Flow Regimes with Arbitrary Computational Precision

In computational aerosol coagulation models, a widely used technique is the sectional treatment of the particle size distribution. This approach is used in many first- and second-generation computer codes, where the section boundaries are selected to obey a geometric constraint. While this technique improves computational efficiency, it introduces a number of limitations, including poor representation of the initial size distribution and loss of resolution in the coagulated or final distribution. A robust and versatile computer model, SEROSA, has been developed, which permits an arbitrary number of sections with arbitrary size boundaries to simulate the temporal evolution of coagulation and deposition under multiple flow-regimes and coagulation types. The code permits a large number of parameter combinations and what-if scenarios under user control. Results are benchmarked against an analytical model as well as three coagulation models using coincident section boundaries and coagulation mechanisms. The comparison shows excellent agreement in cases where other computer models are known to perform well. The test cases also included scenarios where previously published computational coagulation models lack capabilities or exhibit numerical difficulties. Computational time varies depending on the number of sections, ageing, and coagulation types from a few seconds to minutes. The software is distributed by the Radiation Safety Information Computational Center of Oak Ridge National Laboratory as Code Package PSR 573.

Copyright 2013 American Association for Aerosol Research     

FORMATION OF SULPHURIC ACID AEROSOLS AND CLOUD CONDENSATION NUCLEI: AN EXPRESSION FOR SIGNIFICANT NUCLEATION AND MODEL COMPRARISON

A new analytical expression has been derived to predict atmospheric conditions where homogeneous water–sulphuric acid nucleation will have a significant effect on aerosol and cloud condensation nuclei population. In the expression, the condensational sink due to pre-existing aerosol particles and source due to chemical production of sulphuric acid have been taken into account. The analytical expression has been derived using a sectional aerosol dynamic model including nucleation, condensation, coagulation, deposition and sulphuric acid formation in the gas phase. In the present study we have also compared the sectional model with modal and monodisperse models. All models may be used for predicting the onset of significant new particle formation. However, the computationally more efficient models—monodisperse, modal, and sectional with low number of sections—over- or underpredict particle formation in some situations.     

Experimental and computational studies of liquid aerosol evaporation

The phenomenon of liquid aerosol evaporation was investigated both experimentally and computationally in this project. A vibrating orifice aerosol generator (VOAG) was utilised to generate a monodispersed stream of liquid droplets of a desired initial size. Three types of liquids, ethanol, hexane and water, of distinct volatilities were used. The droplets were allowed to travel through air at ambient temperature and pressure. The change in diameter of the droplets as evaporation occurs was measured dynamically using a variety of experimental techniques. Global sizing velocimetry (GSV) was applied to visualize the motion and change in diameter of droplets in real time so as to select an optimal set of operating conditions under which coalescence of droplets did not occur. A phase Doppler interferometer (PDI) was used to measure the Sauter mean diameter and axial velocity of droplets at various distances from the nozzle of the VOAG. The size and velocity profiles obtained were compared with calculations carried out using computational fluid dynamics (CFD) coupled with two different theoretical liquid evaporation models. It was observed that both liquid evaporation models produced similar droplets size profiles for ethanol and water, but a significant difference in the predicted sizes was observed for hexane. In general, a good qualitative agreement between the experimental and computational results was obtained. This represents the first report of a study involving direct comparisons of dynamic measurements of the size evolution of evaporating liquid aerosols with numerical predictions obtained from CFD calculations.     

Numerical investigation on new configurations for vapor-phase aerosol reactors

Non-ideal aerosol reactors for synthesizing nano- and micro-metal-oxide powders can currently be accurately designed by means of computational fluid dynamics (CFD) models instead of an expensive trial-and-error experimental technique. According to a multi-scale approach, fluid dynamics of the reacting volume is modeled by an appropriate population balance equation (PBE) coupled to momentum, energy and chemical species conservative equations. The present work refers to the modeling of non-ideal vapor-phase aerosol reactors, in particular to the numerical investigation on the effects of feeding nozzle arrangement, where the most significant gradients and aerosol phenomena occur. The described aerosol CFD model, which a priori assumes a log-normal particle size distribution (PSD), has been validated against both an experimental and an industrial case, and therefore it has been applied to the study of new reactor configurations. Numerical results show that traditional axial-symmetric and jet-opposed nozzle arrangements can be improved adopting a tangential geometry.     

Aerosol Dynamics in Atmospheric Aromatic Photooxidation

Aerosol formation and growth in aromatic hydrocarbon / NO_x systems was studied in a series of outdoor smog chamber experiments. Analysis of the aerosol size distributions in those experiments that exhibited steady condensational growth provides estimates for the gas-phase partial pressures of the condensing species. Saturation ratios during these growth periods are estimated by comparing these partial pressures with vapor pressures obtained from an analysis of nucleation (Stern et al., 1987), and are found to be in the range of 5 to 20. Modeling of the size–distribution dynamics during the experiments is carried out using the sectional model ESMAP (Warren and Seinfeld, 1985). The full size-distribution model predicts more nucleation than an integral model (Stern et al., 1987), because the polydisperse aerosol representation leads to a lower condensation rate than that predicted for a monodisperse aerosol.     

CFD modeling of pervaporative mass transfer in the boundary layer

Modeling mass transfer in the liquid boundary layer accounting for concentration polarization in pervaporation (PV) is particularly challenging since there is no practical way of experimentally determining solute concentration at the membrane surface. We have developed a computational fluid dynamics (CFD) approach to describe not only velocity distribution but also concentration profile in the liquid boundary layer of a slit membrane channel. The satisfactoriness of the numerical methodology used in CFD for obtaining concentration profiles were verified using a classic diffusion problem with its known analytical solution. The overall mass transfer coefficients from the numerical study were also compared with those from the experiment.     

Monte Carlo Simulation of Multicomponent Aerosols Undergoing Simultaneous Coagulation and Condensation

A Monte Carlo method was developed to simulate multicomponent aerosol dynamics, specifically with simultaneous coagulation and fast condensation where the sectional method suffers from numerical diffusion. This method captures both composition and size distributions of the aerosols. In other words, the composition distribution can be obtained as a function of particle size. In this method, particles are grouped into bins according to their size, and coagulation is simulated by statistical sampling. Condensation is incorporated into the Monte Carlo method in a deterministic way. If bins with fixed boundaries are used to simulate the condensation process numerical dispersion occurs, and thus a moving bins approach was developed to eliminate numerical dispersion. The method was validated against analytical solutions, showing excellent agreement. An example of the usefulness of this model in understanding aerosol evolution is presented. The effects of the number of particles and number of bins on the accuracy of the numerical results are also discussed. It was found that with 20 bins per decade and 105particles in the control volume results with less than 5%error can be obtained. The results are further improved to within 2%error by filtering the statistical noise with a cubic spline algorithm.     

A novel algorithm for solving population balance equations: the parallel parent and daughter classes. Derivation, analysis and testing

A novel numerical method, the parallel parent and daughter classes (PPDC) technique, for solving population balance equations (PBEs) is presented in this paper. In many practical applications, the PBE of particles under investigation is coupled with the thermo-fluid dynamics of the surrounding fluid. Hence, the PBE needs to be implemented in a computational fluid dynamics (CFD) code, which leads to an additional computational load. The computational cost becomes intractable when techniques such as methods of classes (CM) or Monte Carlo method are used. Quadrature method of moments (QMOM) and direct quadrature method of moments (DQMOM) are accurate and require a relatively low additional computational cost when applied to CFD. The PPDC is shown to be as accurate as QMOM and DQMOM, and even more accurate in some cases, when the same number of classes is used. In the present work, the PPDC technique has been derived and tested. This technique can be used for solving a wide class of problems involving PBE such as polymerization, aerosol dynamics, bubble columns, etc. Numerical simulations have been carried out on aggregation processes with different kernels and on simultaneous aggregation and breakage processes. The numerical predictions are compared either with analytical solutions, when available, or with the numerical solutions obtained by methods of classes.     

A coupled CFD-Monte Carlo method for simulating complex aerosol dynamics in turbulent flows

A coupled computational fluid dynamics (CFD)-Monte Carlo method is presented to simulate complex aerosol dynamics in turbulent flows. A Lagrangian particle method-based probability density function (PDF) transport equation is formulated to solve the population balance equation (PBE) of aerosol particles. The formulated CFD-Monte Carlo method allows investigating the interaction between turbulence and aerosol dynamics and incorporating individual aerosol dynamic kernels as well as obtaining full particle size distribution (PSD). Several typical cases of aerosol dynamic processes including turbulent coagulation, nucleation and growth are studied and compared to the sectional method with excellent agreement. Coagulation in both laminar and turbulent flows is simulated and compared to demonstrate the effect of turbulence on aerosol dynamics. The effect of jet Reynolds (Re_j) number on aerosol dynamics in turbulent flows is fully investigated for each of the studied cases. The results demonstrate that Re_j number has significant impact on a single aerosol dynamic process (e.g., coagulation) and the simultaneous competitive aerosol dynamic processes in turbulent flows. This newly modified CFD-Monte Carlo/PDF method renders an efficient method for simulating complex aerosol dynamics in turbulent flows and provides a better insight into the interactions between turbulence and the full PSD of aerosol particles.

Copyright © 2017 American Association for Aerosol Research     

搅拌反应器内气液两相流的CFD研究进展

搅拌式气液反应器因其操作灵活、适用性强等优点,在过程工业中应用广泛.综述了采用计算流体力学CFD技术对搅拌反应器内气液两相流动行为的数值模拟研究.Euler-Euler双流体模型作为主要方法用于描述气液两相流动,在其基础上耦合相对简单的气泡数密度函数模型或复杂的群体平衡模型,可较为准确地预测搅拌反应器内气泡尺寸和局部气含率及其分布规律.CFD模拟结果可用以分析和评价不同搅拌桨叶、搅拌桨组合和气体分布器的气液分散性能,对气液反应器的结构优化和过程强化提供了有效手段.     

Process simulation of gas-to-particle-synthesis via population balances: Investigation of three models

The simulation of complex gas-phase reactors for the synthesis of fine particles requires the coupling of particle and fluid dynamics. A previously developed CFD-coupled simulation technique based on a monodisperse population balance model is an efficient tool but seriously restricted when the product's polydispersity is of interest. Therefore, two other sectional population balance models have been developed: an extended 1-dimensional model and a simplified 2-dimensional model. Comparing calculations were performed with all three models, and temperature, concentration and sintering time were chosen as varying parameters. Using the 2-dimensional model as a benchmark, the conformity with the 1-dimensional sectional model is excellent for all cases investigated. Hence, due to the enormous difference in computational effort and time, clear preference can be given to the simpler sectional model. With respect to the monodisperse model, quite satisfactory results are found deviating mainly because of the typical, slower coagulation behavior of monodisperse particle systems. As a CFD-coupled technique only the 1-dimensional model is considered as an alternative to the simple monodisperse model as the computational demand of the 2-dimensional model is extremely high. A simple test simulation proves that the 1-dimensional model coupled with a commercial CFD software is a generally feasible technique. However, the computational time required is tremendous and impedes the present application.     

Computational Modeling of Silicon Nanoparticle Synthesis: II. A Two-Dimensional Bivariate Model for Silicon Nanoparticle Synthesis in a Laser-Driven Reactor Including Finite-Rate Coalescence

In this work, a two-dimensional model was developed for silicon nanoparticle synthesis by silane thermal decomposition in a six-way cross laser-driven aerosol reactor. This two-dimensional model incorporates fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics, with particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, coagulation, and coalescence processes. Because of the complexity of the problem at hand, the simulation was carried out via several sub-models. First, the chemically reacting flow inside the reactor was simulated in three dimensions in full geometric detail, but with no aerosol dynamics and with highly simplified chemistry. Second, the reaction zone was simulated using an axisymmetric two-dimensional CFD model, whose boundary conditions were obtained from the first step. Last, a two-dimensional aerosol dynamics model was used to study the silicon nanoparticle formation using more complete silane decomposition chemistry, together with the temperature and velocities extracted from the reaction zone CFD simulation. A bivariate model was used to describe the evolution of particle size and morphology. The aggregates were modeled by a moment method, assuming a lognormal distribution in particle volume. This was augmented by a single balance equation for primary particles that assumed locally equal number of primary particles per aggregate and fractal dimension. The model predicted the position and size at which the primary particle size is frozen in, and showed that increasing the peak temperature was a more effective means of improving particle yield than increasing silane concentration or flowrate.     

CFD simulation and experimental validation of fluid flow and particle transport in a model of alveolated airways

Accurate modeling of air flow and aerosol transport in the alveolated airways is essential for quantitative predictions of pulmonary aerosol deposition. However, experimental validation of such modeling studies has been scarce. The objective of this study is to validate computational fluid dynamics (CFD) predictions of flow field and particle trajectory with experiments within a scaled-up model of alveolated airways. Steady flow (Re=0.13) of silicone oil was captured by particle image velocimetry (PIV), and the trajectories of 0.5 and 1.2 mm spherical iron beads (representing 0.7–14.6 μm aerosol in vivo) were obtained by particle tracking velocimetry (PTV). At 12 selected cross sections, the velocity profiles obtained by CFD matched well with those by PIV (within 1.7% on average). The CFD predicted trajectories also matched well with PTV experiments. These results showed that air flow and aerosol transport in models of human alveolated airways can be simulated by CFD techniques with reasonable accuracy.     

Targeted Lung Delivery of Nasally Administered Aerosols

Using the nasal route to deliver pharmaceutical aerosols to the lungs has a number of advantages, including coadministration during noninvasive ventilation. The objective of this study was to evaluate the growth and deposition characteristics of nasally administered aerosol throughout the conducting airways based on delivery with streamlined interfaces implementing two forms of controlled condensational growth technology. Characteristic conducting airways were considered including a nose-mouth-throat (NMT) geometry, complete upper tracheobronchial (TB) model through the third bifurcation (B3), and stochastic individual path (SIP) model to the terminal bronchioles (B15). Previously developed streamlined nasal cannula interfaces were used for the delivery of submicrometer particles using either enhanced condensational growth (ECG) or excipient enhanced growth (EEG) techniques. Computational fluid dynamics (CFD) simulations predicted aerosol transport, growth, and deposition for a control (4.7 μm) and three submicrometer condensational aerosols with budesonide as a model insoluble drug. Depositional losses with condensational aerosols in the cannula and NMT were less than 5% of the initial dose, which represents an order-of-magnitude reduction compared to the control. The condensational growth techniques increased the TB dose by a factor of 1.1–2.6×, delivered at least 70% of the dose to the alveolar region, and produced final aerosol sizes ≥2.5 μm. Compared to multiple commercial orally inhaled products, the nose-to-lung delivery approach increased dose to the biologically important lower TB region by factors as large as 35×. In conclusion, nose-to-lung delivery with streamlined nasal cannulas and condensational aerosols was highly efficient and targeted deposition to the lower TB and alveolar regions.

Copyright 2014 American Association for Aerosol Research