Characteristics of turbulence transport for momentum and heat in particle-laden turbulent vertical channel flows

The dynamic and thermal performance of particle-laden turbulent flow is investigated via direction numerical simulation combined with the Lagrangian point-particle tracking under the condition of two-way coupling, with a focus on the contributions of particle feedback effect to momentum and heat transfer of turbulence. We take into account the effects of particles on flow drag and Nusselt number and explore the possibility of drag reduction in con-junction with heat transfer enhancement in particle-laden turbulent flows.The effects of particles on momentum and heat transfer are analyzed,and the possibility of drag reduc-tion in conjunction with heat transfer enhancement for the prototypical case of particle-laden turbulent channel flows is addressed.We present results of turbulence modification and heat transfer in turbulent particle-laden channel flow,which shows the heat transfer reduction when large inertial parti-cles with low specific heat capacity are added to the flow. However,we also found an enhancement of the heat transfer and a small reduction of the flow drag when particles with high specific heat capacity are involved.The present results show that particles,which are active agents,interact not only with the velocity field,but also the temperature field and can cause a dissimilarity in momentum and heat transport.This demonstrates that the possibility to increase heat transfer and suppress friction drag can be achieved with addition of par-ticles with different thermal properties.     

Filtered particle tracking in isotropic turbulence and stochastic modeling of subgrid-scale dispersion

A numerical study based on the Eulerian–Lagrangian formulation is performed for dispersed phase motion in a turbulent flow. The effect of spatial filtering, commonly employed in large-eddy simulations, and the role of the subgrid scale turbulence on the statistics of heavy particles, including preferential concentration, are studied through a priori analysis of DNS of particle-laden forced isotropic turbulence. In simulations where the subgrid scale kinetic energy attains 30–35% of the total we observe the impact of residual fluid motions on particles of a smaller inertia. It is shown that neglecting the influence of subgrid scale fluctuations has a significant effect on the preferential concentration of those particles. A stochastic Langevin model is proposed to reconstruct the residual (or subgrid scale) fluid velocity along particle trajectories. The computation results for a selection of particle inertia parameters are performed to appraise the model through comparisons of particle turbulent kinetic energy and the statistics of preferential concentrations.     

Direct numerical simulation of a particle-laden low Reynolds number turbulent round jet

Direct numerical simulation method is used for the investigating of particle-laden turbulent flows in a spatially evolution of low Reynolds number axisymmetric jet, and the Eulerian–Lagrangian point-particle approach is employed in the simulation. The simulation uses an explicit coupling scheme between particles and the fluid, which considers two-way coupling between the particle and the fluid. The DNS results are compared well with experimental data with equal Reynolds number (R_e = 1700). Our objects are: (i) to investigate the correlation between the particle number density and the fluctuating of fluid streamwise velocity; (ii) to examine whether the three-dimensional vortex structures in the particle-laden jet are the same as that in the free-air jet and how the particles modulate the thee-dimensional vortex structures and turbulence properties with different Stokes number particles; (iii) to discover the particle circumferential dispersion with different Stokes number particles. Our findings: (i) all the particles, regardless of their particle size, tend to preferentially accumulate in the region with large-than-mean fluid streamwise velocity; (ii) the small Stokes number particles take an important part in the modulation of three-dimensional vortex structures, but for the intermediate and larger sized particles, this modulation effect seems not so apparent; (iii) the particle circumferential dispersion is more effective for the smaller and intermediate sized particles, especially for the intermediate sized particles.     

Effect of inertial particles with different specific heat capacities on heat transfer in particle-laden turbulent flow

The effect of inertial particles with different specific heat on heat transfer in particle-laden turbulent channel flows is studied using the direct numerical simulation(DNS) and the Lagrangian particle tracking method. The simulation uses a two-way coupling model to consider the momentum and thermal interactions between the particles and turbulence. The study shows that the temperature fields display differences between the particle-laden flow with different specific heat particles and the particle-free flow,indicating that the particle specific heat is an important factor that affects the heat transfer process in a particle-laden flow. It is found that the heat transfer capacity of the particle-laden flow gradually increases with the increase of the particle specific heat. This is due to the positive contribution of the particle increase to the heat transfer. In addition,the Nusselt number of a particle-laden flow is compared with that of a particle-free flow.It is found that particles with a large specific heat strengthen heat transfer of turbulent flow, while those with small specific heat weaken heat transfer of turbulent flow.     

Direct numerical simulation of a particle-laden flow in a flat plate boundary layer

In this paper, a direct numerical simulation of particle-laden flow in a flat plate boundary layer is performed, using the Eulerian–Lagrangian point-particle approach. This is, as far as we know, the first simulation of a particle-laden spatially-developing turbulent boundary layer with two-way coupling. A local minimum of the particle number density is observed in the close vicinity of the wall. The present simulation results indicate that the inertial particles displace the quasi-streamwise vortices towards the wall, which, in turn, enhance the mean streamwise fluid velocity. As a result, the skin-friction coefficient is increased whereas the boundary layer integral thicknesses are reduced. The presence of particles augments the streamwise fluctuating velocity in the near-wall region but attenuates it in the outer layer. Nevertheless, the wall-normal and spanwise velocity fluctuations are significantly damped, and so is the Reynolds stress. In addition, the combined effect of a reduced energy production and an increased viscous dissipation leads to the attenuation of the turbulent kinetic energy.     

Spectral-based simulations of particle-laden turbulent flows

In this paper, we discuss the application of spectral-based methods to simulation of particle-laden turbulent flows. The primary focus of the article is on the past and ongoing works by the authors. The particles are tracked in Lagrangian framework, while direct numerical simulation (DNS) or large-eddy simulation (LES) is used to describe the carrier-phase flow field. Two different spectral methods are considered, namely Fourier pseudo-spectral method and Chebyshev multidomain spectral method. The pseudo-spectral method is used for the simulation of homogeneous turbulence. DNS of both incompressible and compressible flows with one- and two-way couplings are reported. For LES of particle-laden flows, two new models, developed by the authors, account for the effect of sub-grid fluctuations on the dispersed phase. The Chebyshev multidomain method is employed for the works on inhomogeneous flows. A number of canonical flows are discussed, including flow past a square cylinder, channel flow and flow over backward-facing step. Ongoing research on particle-laden LES of inhomogeneous flows is briefly reported.     

Accounting for finite-size effects in simulations of disperse particle-laden flows

A numerical formulation for Eulerian–Lagrangian simulations of particle-laden flows in complex geometries is developed. The formulation accounts for the finite-size of the dispersed phase. Similar to the commonly used point-particle formulation, the dispersed particles are treated as point-sources, and the forces acting on the particles are modeled through drag and lift correlations. In addition to the inter-phase momentum exchange, the presence of particles affects the fluid phase continuity and momentum equations through the displaced fluid volume. Three flow configurations are considered in order to study the effect of finite particle size on the overall flowfield: (a) gravitational settling, (b) fluidization by a gaseous jet, and (c) fluidization by lift in a channel. The finite-size formulation is compared to point-particle representations, which do not account for the effect of finite-size. It is shown that the fluid displaced by the particles plays an important role in predicting the correct behavior of particle motion. The results suggest that the standard point-particle approach should be modified to account for finite particle size, in simulations of particle-laden flows.     

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.     

Measurement of turbulent spectra of particle-laden flows in a horizontal channel

Frequency spectra of air turbulence of particle-laden flows were investigated by use of a laser-Doppler velocimeter to discover the eddy-length scales that are influenced by the transported particles. The influence of glass and steel particles of 100–1,000 μm diameter was measured in a horizontal channel and a horizontal pipe for the streamwise and transverse components of the velocity vector. Particles that were small compared with the integral length scale of the particle-laden flow decrease the turbulent power density of the greatest eddies in varying degrees, depending on mass loading and distance from the wall. All fractions create turbulence in their wakes, the size of which depends on loading and slip velocity. These results support the hypothesis that the particles consume energy by following the large eddies that are much greater than the particle diameters, and in so doing, turbulence is created by this energy. Received: 28 September 2000/Accepted: 9 April 2001     

Investigation of Convective Heat and Mass Transfer in Northern Reservoirs using an Eddy-Resolving Model

This paper presents a mathematical formulation of the problem of thermodynamic interaction between a reservoir with supercooled bottom and ice cover on the free surface. Turbulent flows with coherent structures was simulated using the equations of thermohydrodynamics in the Boussinesq approximation in which the average (uniform along the horizontal) and convective (large eddies) components are distinguished. Motions of subgrid scales are described using a one-parameter model for the kinetic energy of turbulence. The applicability of models of various classes for calculating vertical heat transfer in deep-water reservoirs above permafrost zones are discussed.     

Gas turbulence modulation in the pneumatic conveying of massive particles in vertical tubes

The present work is concerned with the interaction between large particles and gas phase turbulence. Gas turbulence modulation in these systems is considered to be dominated by a generation mechanism which arises due to the presence of wakes behind particles. Following a recent proposal, a closure for gas turbulence modulation accounting for the effect of wakes is employed within the context of a mathematical model for particle-laden, turbulent flows. The model accounts for particle particle and particle-wall interactions associated with larger particles based on concepts from gas kinetic theory. It is shown that due to the significant flattening of the mean gas velocity profile with the addition of particles, and the corresponding decrease in turbulent energy production, a generation mechanism must be present in order to produce gas velocity fluctuation predictions which are consistent with the experimental measurements, even in the case where the experimental results indicate a net suppression of gas phase turbulence in the presence of particles.     

Direct numerical simulation of a freely decaying turbulent interfacial flow

Whereas Large Eddy Simulation (LES) of single-phase flows is already widely used in the CFD world, even for industrial applications, LES of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is the development of subgrid scale models well suited for two-phase interfacial flows. The aim of this work is to generate a detailed data base from direct numerical simulation (DNS) of two-phase interfacial flows in order to clearly understand interactions between small turbulent scales and the interface separating the two phases. This work is a first contribution in the study of the interface/turbulence interaction in the configuration where the interface is widely deformed and where both phases are resolved by DNS. To do this, the interaction between an initially plane interface and a freely decaying homogeneous isotropic turbulence (HIT) is studied. The densities and viscosities are the same for both phases in order to focus on the effect of the surface tension coefficient. Comparisons with existing theories built on wall-bounded or free-surface turbulence are carried out. To understand energy transfers between the interfacial energy and the turbulent one, PDFs of the droplet sizes distribution are calculated. An energy budget is carried out and turbulent statistics are performed including the distance to the interface as a parameter. A spectral analysis is achieved to highlight the energy transfer between turbulent scales of different sizes. The originality of this work is the study of the interface/turbulence interactions in the case of a widely deformed interface evolving in a turbulent flow.     

Direct numerical simulation of modulation of isotropic turbulence by poly‐dispersed particles

A direct numerical simulation technique based on two‐way coupling is presented to study a particle‐laden, decaying isotropic turbulent flow. Physical characteristics of turbulence modulation because of the mono‐dispersed (i.e., particles with single Stokes number) and poly‐dispersed particles (i.e., particles with more than one Stokes number) were investigated. A scale dependent effective viscosity that summarizes the aspects of the interaction between the velocity field and particles is defined in the study. Particles of Stokes number (St) 3.2,6.4 and 12.8 were used in performing the simulations. Poly‐dispersed particles were acquired by mixing particles of two different Stokes numbers at a time. As a whole, decay of turbulence because of the poly‐dispersed particles is observed to be larger than that of the decay of turbulence because of the mono‐dispersed particles. Simulations of poly‐dispersed particle indicate nonlinear characteristics in the modification of the temporal evolution of turbulence energy and dissipation. The scale dependent effective viscosity, which correlates with the energy spectrum plot, indicates that the decay of turbulence is mostly observed at the intermediate scales of turbulence. The effective viscosity for the simulations of the poly‐dispersed particles was calculated to be higher than that of the simulations of the mono‐dispersed particles. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking

This paper addresses computational models for dilute gas-particle multiphase flow in which the three dimensional, time-dependent fluid motion is calculated in an Eulerian frame, and a large number of particles are tracked in a Lagrangian frame. Point forces are used to represent the back effect of the particles on the turbulence. The paper describes the early development of the technique, summarizes several experiments which show how dilute particle loadings can significantly alter the turbulence, and demonstrates how the point-particle method fails when the particles are comparable in scale to the small scale turbulence. High-resolution simulations and experiments which demonstrate the importance of the flow details around individual particles are described. Finally, opinions are stated on how future model development should proceed.     

Looking for Turbulence Structures: A Numerical Exploration

The purpose of this paper, dedicated to the memory of our friend Hieu Ha Minh, is to wander through the turbulence universe using deterministic computational tools based on large-eddy simulations (LES) in physical and spectral space. We first briefly recall the subgrid models used, then apply them to mixing layers, jets, separated flows (the backstep in particular, on which Hieu worked a lot) and boundary layers. The influence of compressibility will be also considered. These fine-grain LES allow us to decipher very nicely the intimate vortical structure of turbulence, and predict their statistics. Finally, we discuss of the applicability of these methods to industrial flows. This revised version was published online in August 2006 with corrections to the Cover Date.     

Lagrangian particle dispersion in turbulent flow over a wall mounted obstacle

Large-eddy simulations (LES) of particle-laden turbulent flows are presented in order to investigate the effects of particle response time on the dispersion patterns of a space developing flow with an obstruction, where solid particles are injected inside the wake of an obstacle [Vincont, J.Y., Simoens, S., Ayrault M., Wallace, J.M., 2000. Passive scalar dispersion in a turbulent boundary layer from a line source at the wall and downstream of an obstacle. J. Fluid Mech. 424, 127–167]. The numerical method is based on a fully explicit fractional step approach and finite-differences on Cartesian grids, using the immersed boundary method (IBM) to represent the existence of solid obstacles. Two different turbulence models have been tested, the classical Smagorinsky turbulence model and the filtered structure function model. The dispersed phase was modelled either by an Eulerian approach or a Lagrangian particle tracking scheme of solid particles with Stokes numbers in the range St = 0–25, assuming one-way coupling between the two phases. A very good agreement was observed between the Lagrangian and Eulerian approaches. The effect of particle size was found to significantly differentiate the dispersion pattern for the inhomogeneous flow over the obstacle. Although in homogeneous flows like particle-laden turbulent channels near-wall particle clustering increases monotonically with particle size, for the examined flow over an obstacle, preferential concentration effects were stronger only for an intermediate range of Stokes numbers.     

Modulation of homogeneous turbulence seeded with finite size bubbles or particles

The dynamics of homogeneous, isotropic turbulence seeded with finite sized particles or bubbles is investigated in a series of numerical simulations, using the force-coupling method for the particle phase and low wavenumber forcing of the flow to sustain the turbulence. Results are given on the modulation of the turbulence due to massless bubbles, neutrally buoyant particles and inertial particles of specific density 1.4 at volumetric concentrations of 6%. Buoyancy forces due to gravity are excluded to emphasize finite size and inertial effects for the bubbles or particles and their interactions with the turbulence. Besides observing the classical entrapment of bubbles and the expulsion of inertial particles by vortex structures, we analyze the Lagrangian statistics for the velocity and acceleration of the dispersed phase. The turbulent fluctuations are damped at mid-range wavenumbers by the bubbles or particles while the small-scale kinetic energy is significantly enhanced. Unexpectedly, the modulation of turbulence depends only slightly on the dispersion characteristics (bubble entrapment in vortices or inertial sweeping of the solid particles) but is closely related to the stresslet component (finite size effect) of the flow disturbances. The pivoting wavenumber characterizing the transition from damped to enhanced energy content is shown to vary with the size of the bubbles or particles. The spectrum for the energy transfer by the particle phase is examined and the possibility of representing this, at large scales, through an additional effective viscosity is discussed.     

青藏铁路冻土区环境问题对工程安全可靠性影响

当大涡模拟用于研究化学反应流动时，传统的滤波方法会导致化学反应项不封闭. 为克服这 个困难，发展了条件滤波大涡模拟方法. 在选择适当的条件变量后，条件滤波的化学反 应项可以表达为一个封闭项. 但同时也带来了新的问题：条件滤波耗散或条件滤波扩散项的 不封闭. 为解决这一问题，采用了直接数值模拟方法研究了它们在大小尺度上的统计特 性. 研究结果表明：条件滤波耗散和扩散对于大尺度的依赖主要体现在大尺度标量场中扩散 层结构的影响，同时小尺度脉动的变化几乎与条件滤波扩散无关，而它对条件滤波耗散却显 现出明显的作用. 在构造条件滤波耗散的亚格子模型时，小尺度脉动的作用不容忽视.     

Progress in subgrid-scale transport modelling for continuous hybrid non-zonal RANS/LES simulations

The partially integrated transport modelling (PITM) method can be viewed as a continuous approach for hybrid RANS/LES modelling allowing seamless coupling between the RANS and the LES regions. The subgrid turbulence quantities are thus calculated from spectral equations depending on the varying spectral cutoff location [Schiestel, R., Dejoan, A., 2005. Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theoretical and Computational Fluid Dynamics 18, 443–468; Chaouat, B., Schiestel, R., 2005. A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Physics of Fluids, 17 (6)] The PITM method can be applied to almost all statistical models to derive its hybrid LES counterpart. In the present work, the PITM version based on the transport equations for the turbulent Reynolds stresses together with the dissipation transport rate equation is now developed in a general formulation based on a new accurate energy spectrum function E(κ) valid in both large and small eddy ranges that allows to calibrate more precisely the c_sgs2 function involved in the subgrid dissipation rate _sgs transport equation. The model is also proposed here in an extended form which remains valid in low Reynolds number turbulent flows. This is achieved by considering a characteristic turbulence length-scale based on the total turbulent energy and the total dissipation rate taking into account the subgrid and resolved parts of the dissipation rate. These improvements allow to consider a large range of flows including various free flows as well as bounded flows. The present model is first tested on the decay of homogeneous isotropic turbulence by referring to the well known experiment of Comte-Bellot and Corrsin. Then, initial perturbed spectra E(κ) with a peak or a defect of energy are considered for analysing the model capabilities in strong non-equilibrium flow situations. The second test case is the classical fully turbulent channel flow that allows to assess the performance of the model in non-homogeneous flows characterised by important anisotropy effects. Different simulations are performed on coarse and refined meshes for checking the grid independence of solutions as well as the consistency of the subgrid-scale model when the filter width is changed. A special attention is devoted to the sharing out of the energy between the subgrid-scales and the resolved scales. Both the mean velocity and the turbulent stress computations are compared with data from direct numerical simulations.