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     

Validation of an anisotropic model of turbulent flows containing dispersed solid particles applied to gas–solid jets

A mathematical model of turbulent flows containing dispersed solid particles is described together with its application to gas–solid jets. Flow fields are predicted by solution of the density-weighted transport equations expressing conservation of mass and momentum, with closure achieved through the k–? turbulence model and a second-moment closure. The particle phase is calculated using a Lagrangian particle tracking technique which involves solving the particle momentum equation in a form that accounts for the spatial, temporal and directional correlations of the Reynolds stresses experienced by a particle. The two phases are coupled via modification of the fluid-phase momentum equations. Predictions of the complete model are validated against available experimental data on a number of single-phase and two-phase, gas–solid jet flows with various particle loadings, and both mono- and poly-dispersed particle size distributions. Overall, predictions of the models compare favourably with the data examined, with results obtained from the anisotropic second-moment turbulence closure being superior to eddy viscosity-based predictions.     

Numerical simulation of turbulent gas–particle flow in a 90° bend: Eulerian–Eulerian approach

A numerical investigation into the physical characteristics of dilute gas–particle flows over a square-sectioned 90° bend is reported. The modified Eulerian two-fluid model is employed to predict the gas–particle flows. The computational results using both the methods are compared with the LDV results of Kliafas and Holt, wherein particles with corresponding diameter of 50 μm are simulated with a flow Reynolds number of 3.47 × 10⁵. RNG-based κ–? model is used as the turbulent closure, wherein additional transport equations are solved to account for the combined gas–particle interactions and turbulence kinetic energy of the particle phase turbulence. Moreover, using the current turbulence modelling formulation, a better understanding of the particle and the combined gas–particle turbulent interaction has been shown. The Eulerian–Eulerian model used in the current study was found to yield good agreement with the measured values.     

Numerical study of mixing of passive and reactive scalars in two-dimensional turbulent flows using orthogonal wavelet filtering

We present the application of orthogonal wavelet filtering to study mixing and chemical reaction in 2D turbulent flows. We show that the coherent vortices are responsible for the mixing dynamics. Therefore, we perform direct numerical simulation of decaying and statistically stationary homogeneous isotropic 2D turbulence. We split the flow in each time step into coherent vortices represented by few wavelet modes and containing most of the kinetic energy and an incoherent background flow. We quantify the mixing properties of both flow components and demonstrate that efficient mixing of scalars is triggered by the coherent flow, while the influence of the incoherent flow on the mixing corresponds to pure diffusion. These results hold for both passive scalars and reactive scalars with simple and multi-step kinetics.     

A second-order moment three-phase turbulence model for simulating gas-liquid-solid flows

To simulate the bubble, liquid and particle turbulence properties and their interactions in three-phase flows, a second-order moment three-phase turbulence model for gas-liquid-solid flows is proposed. The bubble, liquid and particle Reynolds stress equations, bubble-liquid and liquid-solid two-phase correlation equations are derived using the mass-weighed and time averaging and the closure models of diffusion, dissipation and pressure-strain terms similar to those used in single-phase flows. The two-phase correlation equations are closed with a two-time-scale dissipation term. The proposed model is applied to simulate gas-liquid flows and gas-liquid-solid flows in a channel. The prediction results for two-phase flows are in good agreement with the PIV measurement results. The prediction results for three-phase flows give the gas, liquid and solid velocities, volume fractions and Reynolds stresses, showing that in the case studied the turbulent fluctuation of 5 mm bubbles is stronger than that of liquid, while the turbulent fluctuation of 0.5 mm particles is weaker than that of liquid. Bubbles enhance liquid turbulence, while particles reduce liquid turbulence.     

Prediction of the ignition characteristics of flammable jets using intermittency-based turbulence models and a prescribed pdf approach

A mathematical model capable of predicting the ignition hazards presented by turbulent releases of flammable materials is presented. The model is based on solutions of the fluid flow equations, with closure of this equation set achieved using either a k–?–γ turbulence model or an intermittency-based second moment closure. Solutions are coupled to a prescribed, three-part probability density function (pdf) to allow the prediction of the bimodal scalar distributions observed in intermittent free shear flows which can have a significant influence on ignition characteristics. Integration of this pdf over the flammable range of the release material then leads to the probability of ignition at any point in the flow. Predictions of the complete model are compared with data obtained in a number of jets, with comparisons for velocity and concentration fields, intermittency, concentration pdf's and ignition probabilities demonstrating that both turbulence modelling approaches are capable of reliably predicting ignition probabilities in the jet flows examined. Overall, results derived from the second-order modelling approach are superior to k–?–γ turbulence model predictions.     

PDF modelling of turbulent non-premixed combustion with detailed chemistry

Although the significant advantage for the probability density function (PDF) methods of the exact treatment of chemical reactions in turbulent combustion problems, a detailed chemistry mechanism (e.g., the GRI mechanism) has not been implemented in the practical calculations by now due to the prohibitive computation of PDF methods. In this work, a detailed mechanism (GRI-Mech 3.0, consisting of 53 species and 325 elemental reactions) is firstly incorporated into the PDF calculation of a turbulent non-premixed jet flame (Sandia Flame D). The flow is formulated in the boundary layer form. The joint composition PDF closure level is applied and a multiple-time-scale (MTS) k-ε turbulence model is combined for the closure of turbulent transport terms. The molecular mixing process is modelled by the Euclidean minimum spanning tree (EMST) mixing model. The solutions are obtained by using the space marching algorithm for turbulence equations and node-based Monte Carlo particle method for PDF evolution equation. The chemical reaction source terms are integrated directly. Extensive comparisons between the predictions and the measurements are made, which involve radial profiles of mean and rms (root mean square), conditional mean, scatter plots of scalars and conditional PDF distribution etc. The flame structures are well represented by the present calculation, including intermediate species (e.g. CO and H₂) mass fractions, pollutant NO emission and local extinction.     

Turbulence model predictions of the radial jet — A comparison of κ-ϵ models

The (κ-?) turbulence closure model has become a widely used means of predicting turbulent fluid flows. In this paper the turbulent radial jet, the round jet and the plane jet are calculated in their similarity regions using various versions of the (κ-?) model to determine which is the most satisfactory for both plane and axisymmetric flows. The most general predictions were obtained using a model which contained additional terms to account for the effect of irrotational strains on the production of turbulence energy. Additionally, detailed mean velocity profiles and turbulence kinetic energy profiles of the radial jet are compared to the available experimental data.     

Numerical study of particle dispersion behind a sudden expansion geometry and its effect on step heights

Numerical simulations were performed for dilute gas–particle flows over two-dimensional turbulent backward-facing step geometry to examine the effects of step heights on turbulent separated flow with particles and their inherent dispersion behaviour. Eulerian two-fluid model along with RNG based k– model is used as the turbulent closure to study this mechanism. However, additional turbulence transport equations are solved to better represent the combined gas–particle turbulence interactions. Two different particle classes with different Stokes number are considered in this study in order to gain a better understanding of the particle behaviour/response to the mean flow and also their effective dispersion. This study helps to better understand the effective particulate viscosity used by two-fluid practioners in order to better capture dispersed phase distribution. The mean flow of the carrier phase along with the dispersed particulate phase is simulated and compared against the experimental data for the step height with maximum expansion ratio (ER). The main objective of this process is to streamline the code to replicate the experimental results and use it further to simulate various other step heights and their particle distribution. This is carried out by keeping the inlet velocity and the flow exit width the same throughout all the different step heights. On the general standing, it is observed that the modelled particulate viscosity works in tandem to the particle number density (PND) of the dispersed phase particles.     

Predictive simulation of nanoparticle precipitation based on the population balance equation

Nanoparticle precipitation is an interesting process to generate particles with tailored properties. In this study we investigate the impact of various process steps such as solid formation, mixing and agglomeration on the resulting particle size distribution (PSD) as representative property using barium sulfate as exemplary material. Besides the experimental investigation, process simulations were carried out by solving the full 1D population balance equation coupled to a model describing the micromixing kinetics based on a finite-element Galerkin h-p-method. This combination of population balance and micromixing model was applied successfully to predict the influence of mixing on mean sizes (good quantitative agreement between experimental data and simulation results are obtained) and gain insights into nanoparticle precipitation: The interfacial energy was identified to be a critical parameter in predicting the particle size, poor mixing results in larger particles and the impact of agglomeration was found to increase with supersaturation due to larger particle numbers. Shear-induced agglomeration was found to be controllable through the residence time in turbulent regions and the intensity of turbulence, necessary for intense mixing but undesired due to agglomeration. By this approach, however, the distribution width is underestimated which is attributed to the large spectrum of mixing histories of fluid elements on their way through the mixer. Therefore, an improved computational fluid dynamics-based approach using direct numerical simulation with a Lagrangian particle tracking strategy is applied in combination with the coupled population balance-micromixing approach. We found that the full DNS-approach, coupled to the population balance and micromixing model is capable of predicting not only the mean sizes but the full PSD in nanoparticle precipitation.     

Assessment of gel formation in colloidal dispersions during mixing in turbulent jets

Onset of gel formation upon mixing between colloidal dispersions and coagulant solutions in turbulent jets was studied using a combination of computational fluid dynamics (CFD) and population balance equation (PBE). To describe the interaction between turbulence fluctuations and particle aggregation, a micromixing model based on presumed probability density function was implemented inside the CFD code. Furthermore, effect of the solid phase on the fluid flow was modeled through an effective viscosity of the mixture evaluated from PBE. The results are presented in the parameter space of the primary particle diameter and the solid volume fraction where strong interplay between mixing and aggregation mechanisms controls the gelation phenomena and consequently also the fluid dynamics. Simulation results are in good agreement with observations from gelation experiments of concentrated nanoparticle suspensions injected into coagulant solutions. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4567–4581, 2013     

Numerical modeling of gas-particle flow using a comprehensive kinetic theory with turbulence modulation

In most fluidized beds, both solids flux and gas phase Reynolds number are high and the flow are usually turbulent. It is therefore necessary to consider both the effects of particle-particle collisions and particle phase turbulence in any mathematical model for simulating gas-particle flows. A comprehensive model is developed in the present work in which a two-equation (k-?) turbulence model is used for calculating the gas phase. In addition, a transport equation of particle phase turbulent kinetic energy is proposed and used for modeling the particle phase turbulence (k_p model). Similar to that of the single gas phase, effective viscosity of the particle phase is the sum of the laminar viscosity caused by particle-particle collisions described by kinetic theory and the turbulent viscosity caused by collections of particles described by the k_p model. The proposed model is used to predict gas-particle flows in a vertical pipe. Results obtained using this model compare well with experimental data.     

Application of the direct quadrature method of moments to polydisperse gas-solid fluidized beds

Most of today's computational fluid dynamics (CFD) calculations for gas-solid flows are carried out assuming that the solid phase is monodispersed, whereas it is well known that in many applications, it is characterized by a particle size distribution (PSD). In order to properly model the evolution of a polydisperse solid phase, the population balance equation (PBE) must be coupled to the continuity and momentum balance equations. In this work, the recently formulated direct quadrature method of moments (DQMOM) is implemented in a multi-fluid CFD code to simulate particle aggregation and breakage in a fluidized-bed (FB) reactor. DQMOM is implemented in the code by representing each node of the quadrature approximation as a distinct solid phase. Since in the multi-fluid model, each solid phase has its own momentum balance, the nodes of the DQMOM approximation are convected with their own velocities. This represents an important improvement with respect to the quadrature method of moments (QMOM) where the moments are tracked using an average solid velocity. Two different aggregation and breakage kernels are tested and the performance of the DQMOM approximation with different numbers of nodes are compared. These results show that the approach is very effective in modeling solid segregation and elutriation and in tracking the evolution of the PSD, even though it requires only a small number of scalars.     

A dual-scale turbulence model for gas-liquid bubbly flows☆

A dual-scale turbulence model is applied to simulate cocurrent upward gas–liquid bubbly flows and validated with available experimental data. In the model, liquid phase turbulence is split into shear-induced and bubble-induced turbulence. Single-phase standard k-εmodel is used to compute shear-induced turbulence and another transport equation is added to model bubble-induced turbulence. In the latter transport equation, energy loss due to interface drag is the production term, and the characteristic length of bubble-induced turbulence, simply the bubble diameter in this work, is introduced to model the dissipation term. The simulated results agree well with experimental data of the test cases and it is demonstrated that the proposed dual-scale turbulence model outperforms other models. Analysis of the predicted turbulence shows that the main part of turbulent kinetic en-ergy is the bubble-induced one while the shear-induced turbulent viscosity predominates within turbulent vis-cosity, especially at the pipe center. The underlying reason is the apparently different scales for the two kinds of turbulence production mechanisms:the shear-induced turbulence is on the scale of the whole pipe while the bubble-induced turbulence is on the scale of bubble diameter. Therefore, the model reflects the multi-scale phe-nomenon involved in gas–liquid bubbly flows.     

SCHMIDT, DAMKOHLER AND REYNOLDS NUMBER EFFECTS ON SECOND-ORDER REACTIONS IN ISOTROPIC TURBULENCE

A two-point pdf evolution equation is developed to describe second-order reactions in isotropic turbulence. The model employs the LMSE closure for molecular diffusion, and an EDQNM closure for turbulent advection. Reactions needs no modeling in a pdf format. Numerical simulation results are obtained for single-species and two-species decaying reactions for Schmidt numbers, Sc = 0.7 and 2.1; Damkohler numbers of the first kind, Da₁ =0.2, 2 and 10; Damkohler numbers of the second kind, Da₂ = 18.7, 170, 691; and Reynolds numbers, R_λ =49.2 and 200. The results are discussed in terms of the effect of these parameters on scalar Held statistical quantities such as means, variances, dissipation rates, correlations and the moments which occur in the decay equations for means and variances.     

Solution of population balance equation with pure aggregation in a fully developed turbulent pipe flow

This paper presents our preliminary effort in predicting particle size distributions in particulate processes in turbulent flow systems. The focus has been on processes of pure aggregation, occurring in a turbulent environment. A remarkably simple strategy has been used to solve the population balance equation (PBE) for spatially dependent pure aggregation with insignificant diffusive transport of particles in turbulent flow systems. The method makes use of the solution of a batch PBE through a mathematical transformation linking time to spatial variables. Furthermore, we investigate the self-similar solution of batch aggregation to show scaling behavior of particle size distributions in such flow systems using spatially dependent average particle sizes. Average particle sizes across the pipe cross section have been computed using both averaged frequencies as well as spatially varying frequencies. Comparison of the two solutions shows significant differences between them, establishing the sheer inappropriateness of the use of average aggregation frequencies in the prediction of absolute particle size distribution as done in the past.     

TURBULENCE CLOSURE MODELING OF TWO-PHASE FLOWS

A second order turbulence closure model is developed for the numerical prediction of isothermal non-reacting, two-phase turbulent shear flows. This model is based on the two-equation (k - ?) model but treats the continuous (gas) phase and (solid) particulate phase as separate interacting continua. The presence of the particles will increase the dissipation rate in the gas phase and additional terms based on the particle size and loading are added to the traditional k and ? equations. The model is tested by making predictions of the spreading rate and velocity decay in the developing region of the two-phase axisymmetric jet. The predictions agree favorably with available experimental data in this region.