A stochastic Langevin model of turbulent particle dispersion in the presence of thermophoresis

Direct numerical simulation (DNS) and experimental data have shown that inertial particles exhibit concentration peaks in isothermal turbulent boundary layers, whereas tracer-like particles remain well mixed in the domain. It is therefore expected that the interactions between turbulence and thermophoresis will be strong in particle-laden flows where walls and carrier fluid are at significantly different temperatures. To capture turbulent particle dispersion with active thermophoresis, a coupled CFD-Lagrangian continuous random walk (CRW) model is developed. The model uses 3D mean flow velocities obtained from the Fluent 6.3 CFD code, to which are added turbulent fluid velocities derived from the normalized Langevin equation which accounts for turbulence inhomogeneities. The mean thermophoretic force is included as a body force on the particle following the Talbot formulation. Validation of the model is performed against recent integral thermophoretic deposition data in long pipes as well as the TUBA TT28 test with its detailed local deposition measurements. In all cases, the agreement with the data is very good. In separate parametric studies in a hypothetical cooled channel flow, it is found that turbulence strongly enhances thermophoretic deposition of particles with dimensionless relaxation times τ⁺ of order 1 or more. On the other hand, the thermophoretic deposition of very small inertia particles (τ⁺ < 0.2) in the asymptotic region far from the injection point tends to that which characterizes stagnant flow conditions, in agreement with the DNS results of Thakurta et al.     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

This paper presents a review of authors' collective works in the field of two-phase flow modeling done in the past few decades. The paper is aimed at the construction of mathematical models for simulation of particle-laden turbulent flows. A kinetic equation was obtained for the probability density function (PDF) of the particle velocity distribution in turbulent flows. The proposed kinetic equation describes both the interaction of particles with turbulent eddies of the carrier phase and particle-particle collisions. This PDF equation is used for the derivation of different schemes describing turbulent momentum transfer in the dispersed particle phase. The turbulent characteristics of the gaseous phase are calculated on the basis of the k - turbulence model with a modulation effect of particles on the turbulence.

The constructed models have been applied to the calculation of various two-phase gas-particle turbulent flows in jets and channels as well as particle deposition in tubes and separators. For validating the theoretical and numerical results, a wide range of comparisons with experimental data from Russian and foreign sources has been done.     

A model for tracking inertial particles in a lattice Boltzmann turbulent flow simulation

A computationally inexpensive model for tracking inertial particles through a turbulent flow is presented and applied to the turbulent flow through a square duct having a friction Reynolds number of Re_τ = 300. Prior to introducing particles into the model, the flow is simulated using a lattice Boltzmann computation, which is allowed to evolve until a steady state turbulent flow is achieved. A snapshot of the flow is then stored, and the trajectories of particles are computed through the flow domain under the influence of this static probability field. Although the flow is not computationally evolving during the particle tracking simulation, the local velocity is obtained stochastically from the local probability function, thus allowing the dynamics of the turbulent flow to be resolved from the point of view of the suspended particles. Particle inertia is modeled by using a relaxation parameter based on the particle Stokes number that allows for a particle velocity history to be incorporated during each time step. Wall deposition rates and deposition patterns are obtained and exhibit a high level of agreement with previously obtained DNS computational results and experimental results for a wide range of particle inertia. These results suggest that accurate particle tracking through complex turbulent flows may be feasible given a suitable probability field, such as one obtained from a lattice Boltzmann simulation. This in turn presents a new paradigm for the rapid acquisition of particle transport statistics without the need for concurrent computations of fluid flow evolution.     

Transition from Countergradient to Gradient Scalar Transport in Developing Premixed Turbulent Flames

A simple model of turbulent scalar flux developed recently by the present authors is applied to determine the direction of the flux in a statistically planar one-dimensional premixed flame that does not affect turbulence and has self-similar mean structure. Results obtained in the case of statistically stationary turbulence indicate that transition from countergradient to gradient turbulent scalar transport may occur during flame development, as the peak mean rate of product creation moves to the trailing edge of the flame brush. In the case of decaying turbulence, the opposite transition (from gradient to countergradient transport) was simulated in line with available DNS data. In both cases, transition instant depends strongly on turbulence and mixture characteristics. In particular, countergradient transport is suppressed by an increase in the rms turbulent velocity and by a decrease in the laminar flame speed or density ratio, in line with available experimental and DNS data. The obtained results lend qualitative support to the model of turbulent scalar flux addressed in the present work.     

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.     

Lattice Boltzmann model for predicting the deposition of inertial particles transported by a turbulent flow

Deposition of inertial solid particles transported by turbulent flows is modelled in a framework of a statistical approach based on the particle velocity Probability Density Function (PDF). The particle-turbulence interaction term is closed in the kinetic equation by a model widely inspired from the famous BGK model of the kinetic theory of rarefied gases. A Gauss-Hermite Lattice Boltzmann model is used to solve the closed kinetic equation involving the turbulence effect. The Lattice Boltzmann model is used for the case of the deposition of inertial particles transported by a homogeneous isotropic turbulent flows. Even if the carrier phase is homogeneous and isotropic, the presence of the wall coupled with particle-turbulence interactions leads to inhomogeneous particle distribution and non-equilibrium particle fluctuating motion. Despite these complexities the predictions of the Lattice Boltzmann model are in very good accordance with random-walk simulations. More specifically the mean particle velocity, the r.m.s. particle velocity and the deposition rate are all well predicted by the proposed Lattice Boltzmann model.     

Modeling droplet dispersion and interphase turbulent kinetic energy transfer using a new dual-timescale Langevin model

Dispersion of spray droplets and the modulation of turbulence in the ambient gas by the dispersing droplets are two coupled phenomena that are closely linked to the evolution of global spray characteristics, such as the spreading rate of the spray and the spray cone angle. Direct numerical simulations (DNS) of turbulent gas flows laden with sub-Kolmogorov size particles, in the absence of gravity, report that dispersion statistics and turbulent kinetic energy (TKE) evolve on different timescales. Furthermore, each timescale behaves differently with Stokes number, a non-dimensional flow parameter (defined in this context as the ratio of the particle response time to the Kolmogorov timescale of turbulence) that characterizes how quickly a particle responds to turbulent fluctuations in the carrier or gas phase. A new dual-timescale Langevin model (DLM) composed of two coupled Langevin equations for the fluctuating velocities, one for each phase, is proposed. This model possesses a unique feature that the implied TKE and velocity autocorrelation in each phase evolve on different timescales. Consequently, this model has the capability of simultaneously predicting the disparate Stokes number trends in the evolution of dispersion statistics, such as velocity autocorrelations, and TKE in each phase. Predictions of dispersion statistics and TKE from the new model show good agreement with published DNS of non-evaporating and evaporating droplet-laden turbulent flow.     

Transport and deposition of colliding particles in turbulent channel flows

The purpose of this paper is twofold: (i) to present statistical models that describe particle–turbulence interactions as well as particle–particle collisions and (ii) to gain a better understanding of the effect of inter-particle collisions on transport, deposition, and preferential concentration of heavy particles in turbulent channel flows. The models presented are based on a kinetic equation for the probability density function of the particle velocity distribution in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations.     

A Band-Width Filtered Forcing Based Generation of Turbulent Inflow Data for Direct Numerical or Large Eddy Simulations and its Application to Primary Breakup of Liquid Jets

Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of spatially inhomogeneous flows strongly depend on turbulent inflow boundary conditions. Realistic coherent structures need to be prescribed to avoid the immediate damping of random velocity fluctuations. A new turbulent inflow data generation method based on an auxiliary simulation of forced turbulence in a box is presented. The new methodology combines the flexibility of the synthetic turbulence generation with the accuracy of precursor simulation methods. In contrast to most auxiliary simulations, the new approach provides full control over the turbulence properties and computational costs remain reasonable. The lack of physical information and artificiality attested with pseudo-turbulence methods is overcome since the inflow data stems from a solution of the Navier-Stokes equations. The generated velocity fluctuations are by construction divergence-free and exhibit the non-Gaussian characteristics of turbulence. The generated inflow data is applied to the simulation of multiphase primary breakup.     

Parallel large eddy simulation of turbulent flow around MIRA model using linear equal‐order finite element method

A parallel large eddy simulation code that adopts domain decomposition method has been developed for large‐scale computation of turbulent flows around an arbitrarily shaped body. For the temporal integration of the unsteady incompressible Navier–Stokes equation, fractional 4‐step splitting algorithm is adopted, and for the modelling of small eddies in turbulent flows, the Smagorinsky model is used. For the parallelization of the code, METIS and Message Passing Interface Libraries are used, respectively, to partition the computational domain and to communicate data between processors. To validate the parallel architecture and to estimate its performance, a three‐dimensional laminar driven cavity flow inside a cubical enclosure has been solved. To validate the turbulence calculation, the turbulent channel flows at Re_τ = 180 and 1050 are simulated and compared with previous results. Then, a backward facing step flow is solved and compared with a DNS result for overall code validation. Finally, the turbulent flow around MIRA model at Re = 2.6 × 10⁶ is simulated by using approximately 6.7 million nodes. Scalability curve obtained from this simulation shows that scalable results are obtained. The calculated drag coefficient agrees better with the experimental result than those previously obtained by using two‐equation turbulence models. Copyright © 2007 John Wiley & Sons, Ltd.     

基于直接数值模拟的可压缩湍流模型评估和改进

对来流Mach数2.25和6的平板边界层湍流进行了直接数值模拟, 并通过与理论、实验及他人计算结果的对比对数值结果进行了验证. 基于直接数值模拟得到的湍流数据库, 对常用的湍流模型进行了先验评估. 评估的湍流模型有k-εvarepsilon模型(包括标准k-εvarepsilon 模型、可实现的k-εvarepsilon模型及低Reynolds数k-εvarepsilon模型)、SA模型及BL模型. 结果显示, 对于Mach2.25的平板边界层, 可实现的k-εvarepsilon 模型及低Reynolds 数k-εvarepsilon模型具有较好的预测能力, 而标准k-εvarepsilon模型预测的湍流黏性系数偏高; SA模型在边界层内层预测准确度较高, 而在外层预测值偏高. 而对于Mach6的平板边界层, k-εvarepsilon模型及SA模型预测的湍流黏性系数均偏高, 尤其是标准k-εvarepsilon模型. 对于Mach6的平板边界层, BL模型低估了内-外层交界位置, 造成湍流黏性系数预测值严重偏低. 作者通过修改模型系数及内-外层交界位置对BL模型进行了修改, 修改后模型预测的湍流黏性系数与DNS给出的值吻合较好.     

Measuring turbulence energy with PIV in a backward-facing step flow

Turbulence energy is estimated in a backward-facing step flow with three-component (3C, stereo) particle image velocimetry (PIV). Estimates of turbulence energy transport equation for convection, turbulence transport, turbulence production, viscous diffusion, and viscous dissipation in addition to Reynolds stresses are computed directly from PIV data. Almost all the turbulence energy terms in the backward-facing step case can be measured with 3C PIV, except the pressure-transport term, which is obtained by difference of the other turbulence energy terms. The effect of the velocity spatial sampling resolution in derivative estimations is investigated with four two-dimensional PIV measurement sets. This sampling resolution information is used to calibrate the turbulence energies estimated by 3C PIV measurements. The focus of this study is on the separated shear layer of the backward-facing step. The measurements with 3C PIV are carried out in a turbulent water flow at Reynolds number of about 15,000, based on the step height h and the inlet streamwise maximum mean velocity U₀. The expansion ratio (ER) is 1.5. Turbulence energy budget profiles in locations x/h=4, x/h=6, and x/h=10 are compared with DNS data of a turbulent flow. The shapes of profiles agree well with each other. Different ERs between the PIV case (1.5) and the DNS case (1.2) cause higher values for the turbulence energies measured by PIV than the energies by DNS when x/h=10 is approached. PIV results also show that the turbulence energy level in these experiments is generally higher than that of the DNS data.     

可压缩均匀剪切湍流的二阶矩模拟

基于对可压缩湍流中脉动压力场和脉动速度场特征的理论分析以及ＤＮＳ结果,建立了可均匀剪切湍流中压力－变形率关联的压缩性修正模式,应用这个模式,加上Ｓａｒｋａｒ等建立的脉动体胀率项（ｄｉｌａｔａｔｉｏｎａｌ ｔｅｒｍｓ）的模式,预测可压缩均匀剪切湍流随时间的发展,所得雷诺应力各是性张量的平衡值与Ｂｌａｉｓｄｅｌｌ等的ＤＮＳ数据非常一致。这个模式准确地预测出均匀剪切湍流中压缩性导致的雷诺应力结构的“流向     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

湍流横掠固定颗粒的全尺度直接数值模拟

气固两相流模拟中,当固相尺度接近或大于Kolmogorov尺度时,普通的点源模型将不再适用,固体相的体积效应和表面效应将对流体相产生显著的影响。通过采用直接数值模拟方法,结合内嵌边界方法对湍流中不同湍流强度流体横掠大于Kolmogorov尺度的固相颗粒进行了全尺度模拟,讨论分析了在两种湍流度下方形颗粒对湍流的调制影响以及颗粒的受力情况。     

KOLMOGOROV BEHAVIOR OF NEAR-WALL TURBULENCE AND ITS APPLICATION IN TURBULENCE MODELING

The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder¹ and followers^2,3,4,5. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterised by Kolmogorov microscales. According t o this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become “Kolmogorov” eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As a n example, the concept is incorporated in the standard κ - εmodel which is then applied t o channel and boundary layer flows. Using appropriate boundary conditions (based on Kolmogorov behaviour of near-wall turbulence), there is no need for any wall-modification to the κ - ε equations (including model constants). Results compare very well with the DNS and experimental data.