Two-phase micro- and macro-time scales in particle-laden turbulent channel flows

The micro-and macro-time scales in two-phaseturbulent channel flows are investigated using the direct numerical simulation and the Lagrangian particle trajectorymethods for the fluid-and the particle-phases,respectively.Lagrangian and Eulerian time scales of both phases are calculated using velocity correlation functions.Due to flowanisotropy,micro-time scales are not the same with the theoretical estimations in large Reynolds number(isotropic) turbulence.Lagrangian macro-time scales of particle-phaseand of fluid-phase seen by particles are both dependent onparticle Stokes number.The fluid-phase Lagrangian integral time scales increase with distance from the wall,longerthan those time scales seen by particles.The Eulerian integral macro-time scales increase in near-wall regions but decrease in out-layer regions.The moving Eulerian time scalesare also investigated and compared with Lagrangian integraltime scales,and in good agreement with previous measurements and numerical predictions.For the fluid particles themicro Eulerian time scales are longer than the Lagrangianones in the near wall regions,while away from the walls themicro Lagrangian time scales are longer.The Lagrangianintegral time scales are longer than the Eulerian ones.Theresults are useful for further understanding two-phase flowphysics and especially for constructing accurate predictionmodels of inertial particle dispersion.     

Direct numerical simulation of turbulent flow with evaporating droplets at high temperature

Direct numerical simulation (DNS) is used to investigate turbulent flows with evaporating fuel droplets. For the solution of the carrier gas fluid, the Eulerian method is employed, while for fuel droplets, the Lagrangian method is used. The two-way coupling interactions between the carrier fluid and the fuel droplets are described by the mass, momentum and energy transfers. Direct numerical simulation is performed by a compressible code, named S3D. In this paper, the effects of evaporating and non-evaporating droplets on isotropic turbulent flows are investigated. From the simulations it is found that for the case without evaporation, the inclusion of small droplets suppresses the turbulence, while evaporation usually enhances turbulence at later times for higher mass-loading ratios.     

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.     

Possibilities and Limitations of Computer Simulations of Industrial Turbulent Dispersed Multiphase Flows

We give an overview on the usage of computer simulations in industrial turbulent dispersed multiphase flows. We present a few examples of industrial flows: bubble columns and bubbly pipe flows, stirred tanks, cyclones, and a fluid catalytic cracking unit. The fluid catalytic cracking unit is used to illustrate the complexity of the physical phenomena involved, and the possibilities and limitations of the different approaches used: Eulerian–Lagrangian (particle-tracking) and Eulerian–Eulerian (two-fluid). In the first approach, the continuous phase is solved using either RANS simulations (Reynolds-Averaged Navier–Stokes simulations) or DNS/LES (Direct Numerical Simulations/Large-Eddy Simulations), and the individual particles are tracked. In the second approach, the dispersed phase is averaged, leading to two sets equations, which are quite similar to the RANS equations of single-phase flows. The Eulerian–Eulerian approach is the most commonly used in industrial applications, however, it requires a significant amount of modelling. Eulerian–Lagrangian RANS can be simpler to use; in particular in situations involving complex boundary conditions, polydisperse flows and agglomeration/breakup. The key issue for the success of the simulations is to have good models for the complex physics involved. A major weakness is the lack of good models for: the turbulence modification promoted by the particles, the inter-particle interactions, and the near-wall effects. Eulerian–Lagrangian DNS/LES can play an important role as a research tool, in order to get a better physical understanding, and to improve the models used in the RANS simulations (either Eulerian–Eulerian or Eulerian–Lagrangian).     

A hybrid Lagrangian–Eulerian particle‐level set method for numerical simulations of two‐fluid turbulent flows

A coupled Lagrangian interface‐tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two‐fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle‐based Lagrangian re‐initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface‐moving’ problems and two‐fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle‐level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle‐level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable‐density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of unsteady gas–liquid flows in a rectangular tank: Comparison of Euler–Eulerian and Euler–Lagrangian simulations

We study the dynamics of gas–liquid flows experimentally and computationally in a rectangular bubble column where the gas source is introduced at the corner. The flow in this reactor is complex and inherently unsteady in nature. The two-dimensional liquid phase velocity field is calculated by an Eulerian approach solving the unsteady Reynolds Averaged Navier Stokes equations. The conservation equations are closed using a two parameter turbulence model. The two-way coupling was accounted for by adding source terms in the conservation equations of the continuous phase to take into account the interaction with the dispersed phase. Bubble tracking is achieved through a Lagrangian approach. Here the equations of motion are solved taking into account the drag, pressure, buoyancy and gravity forces. The time-averaged flows along with the variables which characterize turbulence are analyzed for a wide range of gas flow-rates using Euler–Lagrangian simulations. These simulation predictions are validated with Euler–Eulerian simulations where the gas-phase distribution is captured as a void fraction and PIV experiments. The motion of bubbles induces turbulence in the flow. The applicability of two parameter models for turbulence like the standard k–ε model on time-averaged flow properties is addressed. From the results of the time averaged velocity field, turbulence intensity, turbulent viscosity and gas hold-up profiles, it is concluded that the Euler–Lagrangian model is applicable at lower gas flow-rates. The Euler–Eulerian approach was found to be valid at lower as well as higher gas flow-rates.     

Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach

A Lagrangian continuous random walk (CRW) model is developed to predict turbulent particle dispersion in arbitrary wall-bounded flows with prevailing anisotropic, inhomogeneous turbulence. The particle tracking model uses 3D mean flow data obtained from the Fluent CFD code, as well as Eulerian statistics of instantaneous quantities computed from DNS databases. The turbulent fluid velocities at the current time step are related to those of the previous time step through a Markov chain based on the normalized Langevin equation which takes into account turbulence inhomogeneities. The model includes a drift velocity correction that considerably reduces unphysical features common in random walk models. It is shown that the model satisfies the well-mixed criterion such that tracer particles retain approximately uniform concentrations when introduced uniformly in the domain, while their deposition velocity is vanishingly small, as it should be. To handle arbitrary geometries, it is assumed that the velocity rms values in the boundary layer can locally be approximated by the DNS data of fully developed channel flows. Benchmarks of the model are performed against particle deposition data in turbulent pipe flows, 90° bends, as well as more complex 3D flows inside a mouth-throat geometry. Good agreement with the data is obtained across the range of particle inertia.     

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.     

A Lagrangian–Eulerian model of particle dispersion in a turbulent plane mixing layer

A Lagrangian–Eulerian model for the dispersion of solid particles in a two‐dimensional, incompressible, turbulent flow is reported and validated. Prediction of the continuous phase is done by solving an Eulerian model using a control‐volume finite element method (CVFEM). A Lagrangian model is also applied, using a Runge–Kutta method to obtain the particle trajectories. The effect of fluid turbulence upon particle dispersion is taken into consideration through a simple stochastic approach. Validation tests are performed by comparing predictions for both phases in a particle‐laden, plane mixing layer airflow with corresponding measurements formerly reported by other authors. Even though some limitations are detected in the calculation of particle dispersion, on the whole the validation results are rather successful. Copyright © 2002 John Wiley & Sons, Ltd.     

The motion of fibres in turbulent flow, stochastic simulation of isotropic homogeneous turbulence

The state of fibres suspended in a turbulent fluid is described in terms of a probability distribution function of fibre orientation and position throughout the suspending fluid. The evolution of the fibre's probability distribution function is governed by a convection–dispersion equation, where the randomizing effect of the turbulence is modelled by rotational and translational dispersion coefficients. To estimate these coefficients a numerical simulation of fibres moving in a turbulent fluid was developed. The trajectory of an ensemble of inertialess, rigid, thin, free-draining fibres was calculated through a stochastic model of homogeneous, isotropic turbulence. The results of the simulation were compared with analytical estimates and were found to provide reasonable agreement over a wide range of fibre length. However, the simulation showed that the Lagrangian integral time scale for rotation was significantly smaller than for translation and the ratio of rotational to translational Lagrangian time scales was smaller than the ratio of Eulerian time scales. The simulation also showed that the Lagrangian velocity correlation increased as fibre length increased and that the temporal correlations approached the analytical estimates of the Eulerian correlations in the limit of long fibres.     

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.     

Particle and droplet deposition in turbulent swirled pipe flow

In this work we study deposition of particles and droplets in non-rotating swirled turbulent pipe flow. We aim at verifying whether the capability of swirl to enhance particle separation from the core flow and the capability of turbulence to efficiently trap particles at the wall can co-exist to optimize collection efficiency in axial separators. We perform an Eulerian–Lagrangian study based on Direct Numerical Simulation (DNS) of turbulence, considering the effect of different swirl intensities on turbulence structures and on particle transfer at varying particle inertia. We show that, for suitably-chosen flow parameters, swirl may be superimposed to the base flow without disrupting near-wall turbulent structures and their regeneration mechanisms. We also quantify collection efficiency demonstrating for the first time that an optimal synergy between swirl and wall turbulence can be identified to promote separation of particles and droplets.     

Evaluation of erosion in a two‐way coupled fluid–particle system

In this study, the effects of flow turbulence intensity, temperature, particle sizes and impinging velocity on erosion by particle impact are demonstrated numerically. Underlying turbulent flow on an Eulerian frame is described by the compressible Reynolds averaged Navier–Stokes equations with a RNG k–ε turbulence model. The particle trajectories and particle–wall interactions are evaluated by a Eulerian–Lagrangian approach in a two‐way coupling system. An erosion model considering material weight removal from surfaces is used to predict erosive wear. Computational validation against measured data is demonstrated satisfactorily. The analysis of erosion shows that the prevention of erosion is enhanced by increasing the effects of flow temperature and turbulence intensity and reducing particle inertial momentum. Copyright © 2001 John Wiley & Sons, Ltd.     

Acoustic Lagrangian velocity measurement in a turbulent air jet

Measuring Lagrangian velocities in a turbulent flow is of a great interest for turbulence modeling. We report measurements made in an axisymmetric turbulent air jet at Reynolds number R _λ ≃ 320, using acoustical Doppler scattering. Helium-filled soap bubbles are used as Lagrangian tracers. We describe an experimental setup which allows the simultaneous measurement of the full three-component Lagrangian velocity and the longitudinal Eulerian one. Lagrangian velocity probability density functions (PDF) are found Gaussian, close to Eulerian ones. Velocity correlations are analysed as well as the statistical dependence between components.     

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.     

Accounting for Polydispersion in the Eulerian Large Eddy Simulation of the Two-Phase Flow in an Aeronautical-type Burner

A major issue for the simulation of two-phase flows in engines concerns the modeling of the liquid disperse phase, either in the Lagrangian or the Eulerian approach. In the perspective of massively parallel computing, the Eulerian approach seems to be more suitable, as it uses the same algorithms as the gaseous phase solver. However taking into account the whole physics of a turbulent spray, especially in terms of polydispersity, requires an additional modeling effort. The Mesoscopic Eulerian Formalism (MEF) [13] accounts for the effect of turbulence on the disperse phase, and was extended to the Large Eddy Simulation framework [41], but is limited to monodisperse flows. In [38], the influence of polydispersity on resolved and unresolved turbulent motions of the disperse phase was highlighted, and a first model was proposed, based on size-conditioned statistics. Starting from this idea, a coupling between the MEF and the Multifluid Approach (MA) [30] is proposed. The MA decomposes the Eulerian phase into several fluid classes called sections, and corresponding to size intervals. Each section uses then size-conditioned closures. The original idea of this work is to use the MEF closures independently in each section, taking into account the mean droplet size of this section. This new approach, called Multifluid Mesoscopic Eulerian Formalism (MMEF), is then able to capture polydispersion with associated size-conditioned turbulent dynamics. First, the importance of polydispersity and the ability of MMEF to capture it are highlighted with a 0D evaporation case and a 2D vortex case, showing its impact on dynamics in both size and physical spaces. Then, the MMEF is applied to the MERCATO configuration of ONERA [18]. Results are compared to monodisperse Eulerian, Lagrangian and experimental results.     

Space-time correlations in turbulent flow: A review

This paper reviews some of the principal uses, over almost seven decades, of correlations, in both Eulerian and Lagrangian frames of reference, of properties of turbulent flows at variable spatial locations and variable time instants. Commonly called space—time correlations, they have been fundamental to theories and models of turbulence as well as for the analyses of experimental and direct numerical simulation turbulence data.