Corrélations de vitesse lagrangienne et échelle intégrale temporelle en simulation des grandes échellesLagrangian velocity correlations and timescales by a large-eddy simulation

Velocity correlations and Lagrangian timescales are studied numerically by means of a direct numerical simulation (DNS) and a large-eddy simulation (LES) coupled with a subgrid Lagrangian stochastic model, in the case of a homogeneous and isotropic turbulence. A Langevin model is used to determine the subgrid component of the velocity of fluid particles. Numerical results of Lagrangian velocity correlations and timescales are presented. These quantities play an important role in turbulent mixing and scalar dispersion. To cite this article: G. Wei et al., C. R. Mecanique 334 (2006).     

Influence of gravity and lift on particle velocity statistics and transfer rates in turbulent vertical channel flow

The present study reports detailed statistics for velocity and transfer rates of heavy particles dispersed in turbulent boundary layers. Statistics have been extracted from a homogeneous source of data covering a large target parameter space and are used here to analyze the effects of gravity and lift on particle dispersion and deposition in a systematic way. Datasets were obtained performing Direct Numerical Simulation (DNS) of particle-laden turbulent upward/downward flow in a vertical channel. Six values for the particle timescale (the particle Stokes number, St) ranging three orders of magnitude were considered to analyze the deposition process as the controlling mechanism was shifting from turbulent diffusion to inertia-moderated crossing trajectories. For the particle timescales examined, gravity and lift do not influence the qualitative behavior of particles even though velocity profiles and deposition coefficients are modified in a non-monotonic fashion, reaching an optimum for St ? 15. Physical mechanisms for the different behavior are discussed. Raw data and statistics obtained from the present DNS are made available at http://cfd.cineca.it (mirror site: http://158.110.32.35/download/database) and can be used to test simple models and closure equations for multiphase RANS and Large Eddy simulations.     

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.     

Numerical Study and Lagrangian Modelling of Turbulent Heat Transport

A stochastic Lagrangian model for both fluid velocities and temperature fluctuations is evaluated from Direct Numerical Simulation of heat transport in homogeneous isotropic turbulence submitted to a linear mean temperature gradient. The first stage lies on the study of the Lagrangian fluid turbulence statistics (Lagrangian correlations functions) computed from predictions of DNS. They are crucial for the analysis and the modelling of the fluid turbulent properties along discrete particle trajectories. In the second stage, a velocity-scalar Lagrangian stochastic model is proposed and evaluated from the DNS data. The coefficients of the drift and diffusion terms of the model are determined by only Lagrangian timescales, temperature variance and turbulent flux. The shapes of correlation functions present a good agreement between DNS results and stochastic modelling approach.     

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.     

Effect of Particle Clusters on Carrier Flow Turbulence: A Direct Numerical Simulation Study

Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas-phase turbulence, and to guide model development. The DNS approach is based on a discrete-time, direct-forcing immersed boundary method (IBM) that imposes no-slip and no-penetration boundary conditions on each particle’s surface. Results are reported for mean flow Reynolds number Re _p ?=?50 and the ratio of the particle diameter d _p to Kolmogorov scale is 5.5. The DNS confirm experimental observations that the clustered configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than the uniform configurations, and this increase is found to arise from a lower dissipation rate in the clustered particle configuration. The simulations also reveal that the particle-fluid interaction results in significantly anisotropic fluid-phase turbulence, the source of which is traced to the anisotropic nature of the interphase TKE transfer and dissipation tensors. This study indicates that when particles are larger than the Kolmogorov scale (d _p ?>?η), modeling the fluid-phase TKE alone may not be adequate to capture the underlying physics in multiphase turbulence because the Reynolds stress is anisotropic. It also shows that multiphase turbulence models should consider the effect of particle clustering in the dissipation model.     

Agglomeration of inertial particles in a random rotating symmetric straining flow

This paper is concerned with the development and validation of a simple Lagrangian model for particle agglomeration in a turbulent flow involving the collision of particles in a sequence of correlated straining and vortical structures which simulate the Kolmogorov small scales of motion of the turbulence responsible for particle pair dispersion and collision. In this particular study we consider the collision rate of monodisperse spherical particles in a symmetric (pure) straining flow which is randomly rotated to create an isotropic flow. The model is similar to the classical model of Saffman and Turner (S&T) (1956) for the collision (agglomeration) of tracer particles suspended in a turbulent flow. However unlike S&T, the straining flow is not frozen in time persisting only for timescales ∼Kolmogorov timescale. Furthermore, we consider the collision of inertial particles as well as tracer particles, and study their behavior not only at the collision boundary but also in its vicinity. In the simulation, particles are injected continuously at the boundaries of the straining flow, the size of the straining region being typical of the Kolmogorov length scale η_K of the turbulence. For steady state conditions, we calculate the flux of particles colliding with a test particle at the centre of the straining flow and consider its dependence on the inertia of the colliding particles (characterized by the particle Stokes number, St). The model replicates the segregation and accumulation observed in DNS and in particular the maximum segregation for St ∼ 1 (where St is the ratio of the particle response time to the Kolmogorov timescale). We also calculate the contributions of the various turbulent forces in the momentum balance equation for satellite particles and show for instance that for small Stokes number, there is a balance between turbulent diffusion and turbophoresis (gradient of kinetic stresses) which in turn is responsible for the build-up of concentration at the collision boundary. As found in previous studies, for the case of inertialess tracer particles, the collision rate turns out to be significantly smaller than the S&T prediction due to a lowering of the concentration at the collision boundary compared to the fully mixed value. The increase in collision rate for St ∼ 0.5 is shown to be a combination of particle segregation (build-up of concentration near the collision boundary) and the decorrelation of the relative velocity between the local fluid and a colliding particle. The difference from the S&T value for the agglomeration kernel is shown to be a consequence of the choice of perfectly absorbing boundary conditions at collision and the influence of the time scale of the turbulence (eddy lifetime). We draw the analogy between turbulent agglomeration and particle deposition in a fully developed turbulent boundary layer.     

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.     

Direct Numerical Simulation of Statistically Stationary One- and Two-Phase Turbulent Combustion: A Turbulent Injection Procedure

A new turbulent injection procedure dedicated to fully compressible direct numerical simulation (DNS) or large eddy simulation (LES) solvers is proposed. To avoid the appearance of spurious acoustic waves, this method is based on an accurate tracking of the turbulent structures crossing the boundary at the inlet of the domain. A finite difference DNS solver has been coupled with a spectral simulation in which a statistically stationary homogeneous turbulence evolves to provide fluctuating boundary conditions.A new turbulence forcing method, dedicated to spectral solvers, has been developed as well to control the major properties of the injected flow (turbulent kinetic energy, dissipation rate and integral length scale). One-dimensional Navier–Stokes characteristic boundary conditions extended to non-stationary flows are coupled with the injection procedure to evaluate is potential in four various configurations: spatially decaying turbulence, dispersion of vaporizing sprays, propagation of one- and two-phase V-shape turbulent flames.     

Modeling Turbulent Droplet Motion in Vaporizing Sprays

The present article is concerned with the influence of turbulent gas-velocity fluctuations on both droplet dispersion and droplet-gas slip velocity in the context of spray simulation. The role of turbulence in generating slip and thus enhancing interphase heat and mass transfer has so far received little attention and is investigated in this work. A model for turbulent gas-velocity fluctuations along droplet trajectories is presented and is first tuned to reproduce elementary dispersion phenomena. It is then shown to give good results for more general dispersion problems as well as for slip velocities. As a fundamental source of information and for the purpose of model validation and comparison, direct numerical simulation (DNS) of droplet motion in homogeneous isotropic steady turbulence (HIST) is used. Dispersion of “injected” droplets (i.e. droplets under the influence of drift due to high injection velocity) as well as slip velocities for linear and nonlinear droplet drag are studied, and reasonable agreement is found with the model. The distributions of the slip velocity are found to be very similar for linear and highly nonlinear drag law. The present model is also used to investigate the influence of turbulence on droplet penetration. Comparison is made with an eddy-interaction model (the KIVA-2 model), which reveals various weaknesses of this model, in particular the underprediction of average slip velocity. The influence of slip due to turbulence on vaporization is shown for a fuel spray injected into a premix gas-turbine combustor. The classical eddy-interaction model is seen to underestimate the rate of vaporization due to the underprediction of slip. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling of Liquid Fuel Injection, Evaporation and Mixing in a Gas Turbine Burner Using Large Eddy Simulations

The interaction of turbulence, temperature fluctuation, liquid fuel transport, mixing and evaporation is studied by using Large Eddy Simulations (LES). To assess the accuracy of the different components of the methods we consider first isothermal, single phase flow in a straight duct. The results using different numerical methods incorporating dynamic Sub-Grid-Scale (SGS) models are compared with DNS and experimental data. The effects of the interactions among turbulence, temperature fluctuation, spray transport, evaporation and mixing of the gaseous fuel are studied by using different assumptions on the temperature field. It has been found that there are strong non-linear interactions among temperature-fluctuation, evaporation and turbulent mixing which require additional modeling if not full LES is used. The developed models and methods have been applied to a gas turbine burner into which liquid fuel is injected. The dispersion of the droplets in the burner is described. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stochastic modeling of particle diffusion in a turbulent boundary layer

Several Continuous Random Walk (CRW) models were constructed to predict turbulent particle diffusion based on Eulerian statistics that can be obtained with Reynolds-Averaged Navier Stokes (RANS) solutions. The test conditions included a wide range of particle inertias (Stokes numbers) with a near-wall injection (y⁺ = 4) in a turbulent boundary layer that is strongly anisotropic and inhomogeneous. To assess the performance of the models, the CRW results were compared to particle diffusion statistics gathered from a Direct Numerical Simulation (DNS). In particular, comparisons were made with transverse concentration profiles, root-mean-square of particle trajectory coordinates, and mean transverse particle velocity away from the wall.The results showed that accurate simulation required a modified (non-dimensionalized) Markov chain to handle the large gradients in turbulence near the wall as shown by simulations with fluid-tracer particles. For finite-inertia particles, an incremental drift correction for the Markov chain developed herein to account for Stokes number effects was critical to avoiding non-physical particle collection in low-turbulence regions. In both cases, inclusion of anisotropy in the turbulence model was found to be important, but the influence of off-diagonal terms was found to be weak. The results were generally good, especially for long-time and large inertia particles.     

Large eddy simulation of droplet dispersion for inhomogeneous turbulent wall flow

A large eddy simulation (LES) coupled with a Lagrangian stochastic model has been applied to the study of droplet dispersion in a turbulent boundary layer. Droplets are tracked in a Lagrangian way. The velocity of the fluid particle along the droplet trajectory is considered to have a large-scale part and a small-scale part given by a modified three-dimensional Langevin model using the filtered subgrid scale (SGS) statistics. An appropriate Lagrangian correlation timescale is considered in order to include the influences of gravity and inertia. Two-way coupling is also taken into account. The inter-droplet collision has been introduced as the main mechanism of secondary breakup. A stochastic model for breakup has been generalized for coalescence simulation, thereby two phenomena, coalescence and breakup are simulated in the framework of a single stochastic model. The parameters of this model, selectively for coalescence and for breakup, are computed dynamically by relating them to the local resolved properties of the dispersed phase compared to the main fluid. The model is validated by comparison with an agglomeration model and with experimental results on secondary breakup. The LES coupled with Lagrangian particle tracking and the model for droplet coalescence and breakup is applied to the study of the atmospheric dispersion of wet cooling tower plumes. The simulations are done for different droplet size distributions and volume fractions. We focused on the influence of these parameters on mean concentration, concentration variance and mass flux profiles.     

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.     

A PDF propagation approach to model turbulent dispersion in swirling flows

A computationally efficient approach that solves for the spatial covariance matrix along the dense particle ensemble-averaged trajectory has been successfully applied to describe turbulent dispersion in swirling flows. The procedure to solve for the spatial covariance matrix is based on turbulence isotropy assumption, and it is analogous to Taylor's approach for turbulent dispersion. Unlike stochastic dispersion models, this approach does not involve computing a large number of individual particle trajectories in order to adequately represent the particle phase; a few representative particle ensembles are sufficient to describe turbulent dispersion. The particle Lagrangian properties required in this method are based on a previous study (Shirolkar and McQuay, 1998). The fluid phase information available from practical turbulence models is sufficient to estimate the time and length scales in the model. In this study, two different turbulence models are used to solve for the fluid phase – the standard k–ε model, and a multiple-time-scale (MTS) model. The models developed here are evaluated with the experiments of Sommerfeld and Qiu (1991). A direct comparison between the dispersion model developed in this study and a stochastic dispersion model based on the eddy lifetime concept is also provided. Estimates for the Reynolds stresses required in the stochastic model are obtained from a set of second-order algebraic relations. The results presented in the study demonstrate the computational efficiency of the present dispersion modeling approach. The results also show that the MTS model provides improved single-phase results in comparison to the k–ε model. The particle statistics, which are computed based on the fundamentals of the present approach, compare favorably with the experimental data. Furthermore, these statistics closely compare to those obtained using a stochastic dispersion model. Finally, the results indicate that the particle predictions are relatively unaffected by whether the Reynolds stresses are based on algebraic relations or on the turbulence isotropy assumption.     

Measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging

We present the first measurements of relative velocity statistics of inertial particles in a homogeneous isotropic turbulent flow with three-dimensional holographic particle image velocimetry (holographic PIV). From the measurements we are able to obtain the radial relative velocity probability density function (PDF) conditioned on the interparticle separation distance, for distances on the order of the Kolmogorov length scale. Together with measurements of the three-dimensional radial distribution function (RDF) in our turbulence chamber, these statistics, in principle, can be used to determine interparticle collision rates via the formula derived by Sundaram and Collins (1997). In addition, we show temporal development of the RDF, which reveals the existence of an extended quasi-steady-state regime in our facility. Over this regime the measured two-particle statistics are compared to direct numerical simulations (DNS) with encouraging qualitative agreement. Statistics at the same Reynolds number but different Stokes numbers demonstrate the ability of the experiment to correctly capture the trends associated with particles of different inertia. Our results further indicate that even at moderate Stokes numbers turbulence may enhance collision rates significantly. Such experimental investigations may prove valuable in validating, guiding and refining numerical models of particle dynamics in turbulent flows.     

Simulating turbulent Dean flow in Cartesian coordinates

A simplified approach to simulate turbulent flows in curved channels is proposed. A set of governing equations of motion in Cartesian coordinates is derived from the full Navier–Stokes equations in cylindrical coordinates. Terms to first order in the dimensionless curvature parameter are retained, whereas higher‐order terms are neglected. The curvature terms are implemented in a conventional Navier–Stokes code using Cartesian coordinates. Direct numerical simulations (DNS) of turbulent flow in weakly curved channels are performed. The pronounced asymmetries in the mean flow and the turbulence statistics observed in earlier DNS studies are faithfully reproduced by the present simplified Navier–Stokes model. It is particularly rewarding that also distinct pairs of counter‐rotating streamwise‐oriented vortices are embedded in the simulated flow field. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical simulation of expansion/compression effect on shock induced turbulent flow

The interaction of homogeneous and isotropic turbulence with a shock wave is observed by solving the Reynolds-averaged Navier–Stokes equations with the k–? turbulence model. All turbulent fluctuations are measured at the period of expansion in the turbulent field and during compression by the reflected shock on turbulent field, and it is observed that the longitudinal turbulent velocity fluctuation is enhanced more at the period of expansion due to incident shock wave movement far from the turbulent field. The amplification of the turbulent kinetic energy (TKE) level in the shock/turbulence interaction depends on the shock wave strength and the longitudinal velocity difference across the shock wave. On decreasing the longitudinal velocity difference across the shock, the turbulent kinetic energy (TKE) level is less amplified. The TKE level is amplified by the factor of 1.5–1.8 in the shock/turbulence interaction where the dissipation rate of TKE decreases in all cases of shock/turbulence interaction. After the shock/turbulence interaction, the turbulent dissipative-length scale is amplified slightly and the amplification of the length scales decreases when increasing the shock strength. To cite this article: M.A. Jinnah, K. Takayama, C. R. Mecanique 333 (2005).     

Accurate analysis of multicomponent fuel spray evaporation in turbulent flow

The aim of this paper is to perform an accurate analysis of the evaporation of single component and binary mixture fuels sprays in a hot weakly turbulent pipe flow by means of experimental measurement and numerical simulation. This gives a deeper insight into the relationship between fuel composition and spray evaporation. The turbulence intensity in the test section is equal to 10%, and the integral length scale is three orders of magnitude larger than the droplet size while the turbulence microscale (Kolmogorov scales) is of same order as the droplet diameter. The spray produced by means of a calibrated droplet generator was injected in a gas flow electrically preheated. N-nonane, isopropanol, and their mixtures were used in the tests. The generalized scattering imaging technique was applied to simultaneously determine size, velocity, and spatial location of the droplets carried by the turbulent flow in the quartz tube. The spray evaporation was computed using a Lagrangian particle solver coupled to a gas-phase solver. Computations of spray mean diameter and droplet size distributions at different locations along the pipe compare very favorably with the measurement results. This combined research tool enabled further investigation concerning the influencing parameters upon the evaporation process such as the turbulence, droplet internal mixing, and liquid-phase thermophysical properties.