Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.     

On Two-dimensional Predictions of Turbulent Cross-flow Induced Vibration: Forces on a Cylinder and Wake Interaction

In this paper a typical fluid-structure interaction scenario is investigated for a turbulent flow past a circular cylinder at a relatively low subcritical Reynolds number. Numerous experimental and numerical studies have been undertaken for a baseline Reynolds number of 4,000 involving a stationary cylinder to study in detail the near wake mean flow and turbulence characteristics. These studies conclusively show that the turbulent wake displays significant coherent periodic structures of large eddies that could be adequately and profitably resolved by “low order modelling” of turbulence. In this study, an unsteady numerical framework is employed for the simulations, incorporating an Arbitrary Lagrangian–Eulerian (ALE) method for the associated grid deformation to simulate the coupled motion of the circular cylinder with a single degree of freedom in the initial zone in a typical cylinder-flow response map or what is called “initial regime”. Particular attention is paid towards resolving the large scales of the fluid motion and the inherent coupling of the cylinder’s motion towards the associated evolution of the time averaged flow field. The flow-induced vibration effects regarding the kinetic energy exchange between the mean flow and the coherent periodic scales are investigated further. The predictions discussed and analyzed in detail in the paper display reasonable agreement with the chosen benchmark tests of the stationary cylinder and suggest that the conclusions outlined regarding the coupled flow-cylinder system potentially provides a valuable contribution to the state of the art.     

充分发展圆管湍流的实验研究

采用粒子数字图像测速（digital particle image velocimetry,DPIV)和定量流动显示技术（quantitative flow visualization,QFA)对充分发展的圆管湍流进行了研究。测量结果和直接数值模拟（direct numerical simulation,DNS)结果进行了比较，结果表明作者开发的DPIV技术取得了满意的精度。在此基础上对圆管湍流的动力学机理进行了研究，分析了上抛和下扫在湍流生成中的贡献以及流动显示结构内的脉动速度分布，测量结果显示在圆管湍流的近壁区存在横向强脉冲现象和流动显示所能观察到的结构为上抛占主导地位的结构。     

Large-Eddy Simulation of Lean Premixed Turbulent Flames of Three Different Combustion Configurations using a Novel Reaction Closure

This large eddy simulation (LES) study is applied to three different premixed turbulent flames under lean conditions at atmospheric pressure. The hierarchy of complexity of these flames in ascending order are a simple Bunsen-like burner, a sudden-expansion dump combustor, and a typical swirl-stabilized gas turbine burner–combustor. The purpose of this paper is to examine numerically whether the chosen combination of the Smagorinsky turbulence model for sgs fluxes and a novel turbulent premixed reaction closure is applicable over all the three combustion configurations with varied degree of flow and turbulence. A quality assessment method for the LES calculations is applied. The cold flow data obtained with the Smagorinsky closure on the dump combustor are in close proximity with the experiments. It moderately predicts the vortex breakdown and bubble shape, which control the flame position on the double-cone burner. Here, the jet break-up at the root of the burner is premature and differs with the experiments by as much as half the burner exit diameter, attributing the discrepancy to poor grid resolution. With the first two combustion configurations, the applied subgrid reaction model is in good correspondence with the experiments. For the third case, a complex swirl-stabilized burner–combustor configuration, although the flow field inside the burner is only modestly numerically explored, the level of flame stabilization at the junction of the burner–combustor has been rather well captured. Furthermore, the critical flame drift from the combustor into the burner was possible to capture in the LES context (which was not possible with the RANS plus k–ɛ model), however, requiring tuning of a prefactor in the reaction closure.     

Dispersion modeling by kinematic simulation: Cloud dispersion model

A new technique has been developed to compute mean and fluctuating concentrations in complex turbulent flows (tidal current near a coast and deep ocean). An initial distribution of material is discretized into any small clouds which are advected by a combination of the mean flow and large scale turbulence. The turbulence can be simulated either by kinematic simulation (KS) or direct numerical simulation. The clouds also diffuse relative to their centroids; the statistics for this are obtained from a separate calculation of the growth of individual clouds in small scale turbulence, generated by KS. The ensemble of discrete clouds is periodically re-discretized, to limit the size of the small clouds and prevent overlapping. The model is illustrated with simulations of dispersion in uniform flow, and the results are compared with analytic, steady state solutions. The aim of this study is to understand how pollutants disperses in a turbulent flow through a numerical simulation of fluid particle motion in a random flow field generated by Fourier modes. Although this homogeneous turbulent is rather a “simple” flow, it represents a building block toward understanding pollutant dispersion in more complex flow. The results presented here are preliminary in nature, but we expect that similar qualitative results should be observed in a genuine turbulent flow.     

The effect of particles on fluid turbulence in a turbulent boundary layer over a cylinder

The turbulent fluid and particle interaction in the turbulent boundary layer for cross flow over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30μm–60μm and 80μm–150μm) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross flow over a cylinder. The project supported by the National Natural Science Foundation of China     

Numerical and experimental investigation on droplet dynamics and dispersion of a jet engine injector

In the case of turbine combustors operating with liquid fuel the combustion process is governed by the liquid fuel atomization and its dispersion in the combustion chamber. By highly unsteady flow field conditions the transient interaction between the liquid and the gaseous phase is of interest, because it results in a temporal variation of air–fuel ratio which leads to a fluctuating temperature distribution. The objective of this research was the investigation of transient flow field phenomena (e.g. large coherent structures) on droplet dynamics and dispersion of an isothermal flow (of inert water droplets) as a necessary first step towards a full analysis of spray combustion in real-life devices. The advanced injector system for lean jet engine combustors PERM (Partial Evaporated Rapid Mixing) was applied, generating a dilute polydispersed spray in a swirled flow field. Experiments were performed using Phase Doppler Anemometry (PDA) and a patternator to determine the droplet polydispersity, concentration maps, and velocity profiles in the flow. An important finding is the effect of large-scale coherent structures due mainly to the precessing of the vortex core (PVC) of the swirling air jet on the particle dispersion patterns. The experimental results then serve as reference data to assess the accuracy of the Eulerian–Lagrangian computations using a Large Eddy Simulation (LES), a Unsteady Reynolds-Average Navier–Stokes Simulation (URANS) and two simplified (steady-state) simulations. There, a simplified droplet injection model was used and the required boundary conditions of injected droplet sizes were obtained from measurements. Important transient effects of deterministic droplet separation observed during experiments, could be perfectly replicated with this injection model. It is convincingly shown, through extensive computations, that the resolution of instantaneous vortical structures is indeed crucial; hence the LES, or a reasonably-well resolved URANS are preferred over the steady-state solutions with additional, stochastic-type, turbulent dispersion models.     

Education of coherent structures in a numerically simulated plane wake

Coherent structures (CS) are educed using a conditional sampling technique involving alignment of vorticity patches of largest size and strength; hence we educe dominant CS. A numerically simulated spatially evolving wake of a thick flat plate is used as the database, and the inflow condition for the simulated wake includes random velocity perturbations which emulate turbulent conditions at a plate exit in the laboratory. In addition to previously educed properties such as coherent vorticity and production, and incoherent Reynolds stress and turbulence intensity, other measures such as coherent pressure and passive scalar distributions are also studied. In spite of the geometry difference, the near-wake dynamics of the plate seem quite similar to that of a cylinder. For example, turbulence is mostly produced by vortex stretching of the ribs at the saddle and then advected to the structure center, where it accumulates, and is balanced by incoherent dissipation. The distribution of coherent passive scalar indicates that mixing occurs in the saddle regions and that the mixed fluid is advected into the structure center.     

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     

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.     

Coherent Vortex Simulation (CVS), A Semi-Deterministic Turbulence Model Using Wavelets

In the spirit of Ha Minh's semi-deterministic model, we propose a new method for computing fully-developed turbulent flows, called Coherent Vortex Simulation (CVS). It is based on the observation that turbulent flows contain both an organized part, the coherent vortices, and a random part, the incoherent background flow. The separation into coherent and incoherent contributions is done using the wavelet coefficients of the vorticity field and the Biot–Savart kernel to reconstruct the coherent and incoherent velocity fields. The evolution of the coherent part is computed using a wavelet basis, adapted at each time step to resolve the regions of strong gradients, while the incoherent part is discarded during the flow evolution, which models turbulent dissipation. The CVS method is similar to LES, but it uses nonlinear multiscale band-pass filters, which depend on the instantaneous flow realization, while LES uses linear low-pass filters, which do not adapt to the flow evolution. As example, we apply the CVS method to compute a time developing two-dimensional mixing layer and a wavelet forced two-dimensional homogeneous isotropic flow. We also demonstrate how walls or obstacles can be taken into account using penalization and compute a two-dimensional flow past an array of cylinders. Finally, we perform the same segmentation into coherent and incoherent components in a three-dimensional homogeneous isotropic turbulent flow. We show that the coherent components correspond to vortex tubes, which exhibit non-Gaussian statistics and long-range correlation, with the same k ^−5/3power-law energy spectrum as the total flow. In contrast, the incoherent components correspond to an homogeneous random background flow which does not contain organized structures and presents an energy equipartition together with a Gaussian PDF of velocity. This justifies their elimination during the CVS computation to model turbulent dissipation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels

Eccentric annular pipe flows represent an ideal model for investigating inhomogeneous turbulent shear flows, where conditions of turbulence production and transport vary significantly within the cross-section. Moreover recent works have proven that in geometries characterized by the presence of a narrow gap, large-scale coherent structures are present. The eccentric annular channel represents, in the opinion of the present authors, the prototype of these geometries. The aim of the present work is to verify the capability of a numerical methodology to fully reproduce the main features of the flow field in this geometry, to verify and characterize the presence of large-scale coherent structures, to examine their behavior at different Reynolds numbers and eccentricities and to analyze the anisotropy associated to these structures. The numerical approach is based upon LES, boundary fitted coordinates and a fractional step algorithm. A dynamic Sub Grid Scale (SGS) model suited for this numerical environment has been implemented and tested. An additional interest of this work is therefore in the approach employed itself, considering it as a step into the development of an effective LES methodology for flows in complex channel geometries. Agreement with previous experimental and DNS results has been found good overall for the streamwise velocity, shear stress and the rms of the velocity components. The instantaneous flow field presented large-scale coherent structures in the streamwise direction at low Reynolds numbers, while these are absent or less dominant at higher Reynolds and low eccentricity. After Reynolds averaging is performed over a long integration time the existence of secondary flows in the cross session is proven. Their shape is found to be constant over the Reynolds range surveyed, and dependent on the geometric parameters. The effect of secondary flows on anisotropy is studied over an extensive Reynolds range through invariant analysis. Additional insight on the mechanics of turbulence in this geometry is obtained.     

Novel Implementation and Assessment of a Digital Filter Based Approach for the Generation of LES Inlet Conditions

A novel implementation of a digital filter based inlet condition generator for Large Eddy Simulation (LES) is presented. The effect of using spatially varying turbulence scales as inputs is investigated; it is found that this has impact on both accuracy and affordability, and has prompted the algorithm implementation changes described in the paper. LES of a channel flow with a periodically repeating constriction was used as a test case. The accuracy of the present simulation using a streamwise periodic boundary condition (PBC) was first established by comparison with a previously published highly resolved LES study. Post-processed statistics from the PBC simulation were then input into a Digital Filter Generator (DFG) algorithm. Three time series were created using the DFG for subsequent use as LES inlet conditions. In the first, as well as inputting the spatially varying first and second moments of the velocity field over the inlet plane from the PBC simulation, the turbulence scales input into the DFG were chosen to be spatially uniform with values specified by an area weighted average across the channel inlet height. In the second and third time-series, the turbulence scales were allowed to change in the wall normal direction, their variation again being deduced from the PBC simulation. These various time series were then used as inlet boundary conditions for LES prediction of the same flow case. Analysis of the results and comparison to the PBC predictions showed that the use of spatially varying turbulence scales increased the accuracy of the simulation in some important areas. However, the cost of generating unsteady inlet conditions using the DFG approach increased significantly with the use of spatially varying turbulence scales. Consequently, a new technique applied as part of the DFG approach is described (used as an ‘on the fly’ method), which significantly reduces the cost of generating LES inlet conditions, even when spatially non-uniform turbulent scales are used.     

Measurement of laminar,transitional and turbulent pipe flow using Stereoscopic-PIV

Stereoscopic particle image velocimetry (SPIV) is applied to measure the instantaneous three component velocity field of pipe flow over the full circular cross-section of the pipe. The light sheet is oriented perpendicular to the main flow direction, and therefore the flow structures are advected through the measurement plane by the mean flow. Applying Taylor’s hypothesis, the 3D flow field is reconstructed from the sequence of recorded vector fields. The large out-of-plane motion in this configuration puts a strong constraint on the recorded particle displacements, which limits the measurement accuracy. The light sheet thickness becomes an important parameter that determines the balance between the spatial resolution and signal to noise ratio. It is further demonstrated that so-called registration errors, which result from a small misalignment between the laser light sheet and the calibration target, easily become the predominant error in SPIV measurements. Measurements in laminar and turbulent pipe flow are compared to well established direct numerical simulations, and the accuracy of the instantaneous velocity vectors is found to be better than 1% of the mean axial velocity. This is sufficient to resolve the secondary flow patterns in transitional pipe flow, which are an order of magnitude smaller than the mean flow.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

Heavy particle dispersion from a point source in turbulent pipe flow

Dispersion of heavy particles from a point source in high-Reynolds pipe flow was studied using large-eddy simulation, LES. A stochastic Langevin type Lagrangian model developed by Berrouk et al. was used to account for heavy particle transport by the sub-grid scale motion. In both the LES and in an experiment by Arnason, the larger particles dispersed more than the small ones. The change in diffusivity with particle size is interpreted in terms of the effect of inertia and cross-trajectory effects and qualitatively compared with the analysis of heavy particle dispersion in isotropic turbulence by Wang and Stock. Particle inertia has a much larger influence on the dispersion than the crossing-trajectories effects.     

Turbulent flow simulation of liquid jet emanating from pressure-swirl atomizer

The performances of three linear eddy viscosity models (LEVM) and one algebraic Reynolds stress model (ARSM) for the simulation of turbulent flow inside and outside pressure-swirl atomizer are evaluated by comparing the interface position with available experimental data and by comparing the turbulence intensity profiles at the atomizer exit. It is found that the turbulence models investigated exhibit zonal behaviors, i.e. none of the models investigated performs well throughout the entire flow field. The turbulence intensity has a significant influence on the global characteristics of the flow field. The turbulence models with better predictions of the turbulence intensity, such as Gatski-Speziale’s ARSM model, can yield better predictions of the global characteristics of the flow field, e.g. the reattachment lengths for the backward-facing step flow and the sudden expansion pipe flow, or the discharge coefficient, film thickness and the liquid sheet outer surface position for the atomizer flows. The standard k–ε model predicts stronger turbulence intensity as compared to the other models and therefore yields smaller film thickness and larger liquid sheet outer surface position. In average, the ARSM model gives both quantitatively and qualitatively better results as compared to the standard k–ε model and the low Reynolds number models.     

Hysteresis phenomenon in turbulent convection

Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of 10⁷–10⁸). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant (A=2–2.23). We found that the change of the sign of the degree of the anisotropy of turbulence was accompanied by the change of the flow pattern. The developed theory of coherent structures in turbulent convection (Phys Rev E 66:1–15, 2002, Boundary-Layer Meteorol, 2005) is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. The redistribution of the turbulent heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection.     

Decomposition of Mixing Layer Turbulence into Coherent Structures and Background Fluctuations

The eduction of coherent structures from cross-wire rake data in a fully turbulent incompressible mixing layer confirms the feasibility of a decomposition of a turbulent flow field, first suggested by Farge, as non-periodic non-equilibrium coherent structures interacting with a ‘thermalized’ broad-band turbulence. A simple wavelet coefficient decimation algorithm and orthogonalization yields non-periodic dominant flow structures and a background field that has a Gaussian distribution of velocities at the centerline. The coherent structures are classified in terms of their topology. The non-coherent background field has flat energy spectra and normal distribution of velocity components. Most background field statistics depend only weakly on the type of structure on which they are superposed. It may be possible to adapt existing subgrid scale models to this decomposition. This revised version was published online in July 2006 with corrections to the Cover Date.