Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion

Modeling turbulent two-phase flows using Large-Eddy Simulation

Turbulent two-phase flows occur in a wide range of industrial processes, which strongly encourages the development of numerical methods for such flows. This work focuses on the physical phenomena of dispersion and preferential concentration of solid particles in a gas flow. The main purpose is to extend to Large-Eddy Simulation (LES), the Eulerian mesoscopic formalism introduced by Février et al. (2005) and first implemented by Kaufmann et al. (2006) to perfom Direct Numerical Simulation (DNS). When extending the Eulerian mesoscopic approach to LES, two main issues arise. First, as far as modeling is concerned, two different kinds of unclosed terms appear in the transport equations for the dispersed phase, which is very specific to this approach. Those terms are due either to ensemble averaging introduced by the mesoscopic approach, or by LES spatial filtering. Several closure models are proposed and tested a priori by Moreau (2006) who performs Discrete Particle Simulation (DPS) of particle-laden Homogeneous Isotropic decaying Turbulence (HIT). A posteriori validating these models is then required, which is the aim of the present work. Second, it is delicate to handle numerically the set of transport equations for the dispersed phase. Indeed, there are no physical diffusive terms in the transport equations and strong gradients difficult to represent on the grid must be accounted for. Consequently, first in this work, a new numerical method is proposed. The numerical scheme TTGC (Colin & Rudgyard, 2000) that is known to be few dispersive and few dissipative, is adapted to the dispersed phase and combined with a stabilising numerical method. Then, comparing Direct Numerical Simulation (DNS) of particle-laden decaying HIT flows performed with the Eulerian mesoscopic approach and the Lagrangian one shows the robustness and the accuracy of the numerical method proposed. Finally, the LES Eulerian mesoscopic modeling is validated a posteriori in two different complex geometries. For both, a detailed bank of experimental data are available. The first configuration consists of a particle-laden turbulent jet (Hishida et al., 1987). It requires to develop specific inlet Boundary Conditions (BC) for the dispersed phase. The second configuration is a particle-laden bluff body (Borée et al., 2001) where Eulerian mesoscopic and Lagrangian approaches can be evaluated. Comparing LES using the Eulerian mesoscopic approach with the experiments, and even with the DPS for the second geometry, shows that this new approach is able to accurately capture the dynamics of such particle-laden turbulent flows

FEDSM2008-55143 EULER-EULER LARGE-EDDY SIMULATION APPROACH FOR NON ISOTHERMAL PARTICLE-LADEN TURBULENT JET

ABSTRACT This paper presents an Euler-Euler Large-Eddy Simulation (LES) approach for the numerical modeling of non isothermal dispersed turbulent two-phase flows. The proposed approach is presented and validated by a priori tests from an EulerLagrange database, provided using discrete particle simulation (DPS) of the particle phase coupled with direct numerical simulation (DNS) of the turbulent carrier flow, in a non isothermal particle-laden temporal jet configuration. A statistical approach, the Mesoscopic Eulerian Formalism (MEF) [Février et al., J. Fluid Mech., 2005, vol. 533, pp. 1-46], is used to write local and instantaneous Eulerian equations for the dispersed phase and then, by spatial averaging, to derive the LES equations governing the filtered variables. In this work, the MEF approach is extended to scalar variables transported by the particles in order to develop LES for reactive turbulent dispersed two-phase flows with mass and heat turbulent transport. This approach leads to separate the instantaneous particle temperature distribution in a Mesoscopic Eulerian field, shared by all the particles, and a Random Uncorrelated distribution which may be characterized in terms of Eulerian fields of particle moments such as the uncorrelated temperature variance. In this paper, the DPS-DNS numerical database is presented, LES Eulerian equations for the dispersed phase are derived in the frame of the Mesoscopic approach and models for the unresolved subgrid and random uncorrelated terms are proposed and a priori tested using the DPS-DNS database

Large-eddy simulation of a particle-laden turbulent channel flow

Large-eddy simulations of a vertical turbulent channel flow with 420,000 solid particles are performed in order to get insight into fundamental aspects of a riser flow The question is addressed whether collisions between particles are important for the ow statistics. The turbulent channel ow corresponds to a particle volume fraction of 0.013 and a mass load ratio of 18, values that are relatively high compared to recent literature on large-eddy simulation of two-phase ows. In order to simulate this ow, we present a formulation of the equations for compressible ow in a porous medium including particle forces. These equations are solved with LES using a Taylor approximation of the dynamic subgrid-model. The results show that due to particle-uid interactions the boundary layer becomes thinner, leading to a higher skin-friction coefcient. Important effects of the particle collisions are also observed, on the mean uid prole, but even more o on particle properties. The collisions cause a less uniform particle concentration\ud and considerably atten the mean solids velocity prole

A new statistical model for subgrid dispersion in large eddy simulations of particle-laden flows

This article is published under a CC BY licence. The Version of Record is available online at: http.//dx.doi.org/10.1088/1742-6596/745/3/032115Dispersed multiphase turbulent flows are present in many industrial and commercial applications like internal combustion engines, turbofans, dispersion of contaminants, steam turbines, etc. Therefore, there is a clear interest in the development of models and numerical tools capable of performing detailed and reliable simulations about these kind of flows. Large Eddy Simulations offer good accuracy and reliable results together with reasonable computational requirements, making it a really interesting method to develop numerical tools for particle-laden turbulent flows. Nonetheless, in multiphase dispersed flows additional difficulties arises in LES, since the effect of the unresolved scales of the continuous phase over the dispersed phase is lost due to the filtering procedure. In order to solve this issue a model able to reconstruct the subgrid velocity seen by the particles is required. In this work a new model for the reconstruction of the subgrid scale effects over the dispersed phase is presented and assessed. This innovative methodology is based in the reconstruction of statistics via Probability Density Functions (PDFs).Peer ReviewedPostprint (published version

An algebraic-closure-based momentmethod for unsteady Eulerian modeling of non-isothermal particle-laden turbulent flows in very dilute regime and high Stokes number

An algebraic-closure-based moment method (ACBMM) is developed for unsteady Eulerian particle simulations coupled with direct numerical simulations (DNS) of non-isothermal fluid turbulent flows, in very dilute regime and for large Stokes numbers. It is based on a conditional statistical approach which provides a local instantaneous characterization of the dynamic of the dispersed phase accounting for the effect of crossing between particle trajectories which occurs for large Stokes numbers

On the Eulerian Large Eddy Simulation of disperse phase flows: an asymptotic preserving scheme for small Stokes number flows

In the present work, the Eulerian Large Eddy Simulation of dilute disperse phase flows is investigated. By highlighting the main advantages and drawbacks of the available approaches in the literature, a choice is made in terms of modelling: a Fokker-Planck-like filtered kinetic equation proposed by Zaichik et al. 2009 and a Kinetic-Based Moment Method (KBMM) based on a Gaussian closure for the NDF proposed by Vie et al. 2014. The resulting Euler-like system of equations is able to reproduce the dynamics of particles for small to moderate Stokes number flows, given a LES model for the gaseous phase, and is representative of the generic difficulties of such models. Indeed, it encounters strong constraints in terms of numerics in the small Stokes number limit, which can lead to a degeneracy of the accuracy of standard numerical methods. These constraints are: 1/as the resulting sound speed is inversely proportional to the Stokes number, it is highly CFL-constraining, and 2/the system tends to an advection-diffusion limit equation on the number density that has to be properly approximated by the designed scheme used for the whole range of Stokes numbers. Then, the present work proposes a numerical scheme that is able to handle both. Relying on the ideas introduced in a different context by Chalons et al. 2013: a Lagrange-Projection, a relaxation formulation and a HLLC scheme with source terms, we extend the approach to a singular flux as well as properly handle the energy equation. The final scheme is proven to be Asymptotic-Preserving on 1D cases comparing to either converged or analytical solutions and can easily be extended to multidimensional configurations, thus setting the path for realistic applications

Detailed characteristics of drop-laden mixing layers: Large eddy simulation predictions compared to direct numerical simulation

Results are compared from direct numerical simulation (DNS) and large eddy simulation (LES) of a temporal mixing layer laden with evaporating drops to assess the ability of LES to reproduce detailed characteristics of DNS. The LES used computational drops, each of which represented eight physical drops, and a reduced flow field resolution using a grid spacing four times larger than that of the DNS. The LES also used models for the filtered source terms, which express the coupling of the drops with the flow, and for the unresolved subgrid-scale (SGS) fluxes of species mass, momentum, and enthalpy. The LESs were conducted using one of three different SGS-flux models: dynamic-coefficient gradient (GRD), dynamic-coefficient Smagorinsky (SMD), and constant-coefficient scale similarity (SSC). The comparison of the LES with the filtered-and-coarsened (FC) DNS considered detailed aspects of the flow that are of interest in ignition or full combustion. All LESs captured the largest-scale vortex, the global amount of vapor emanating from the drops, and the overall size distribution of the drops. All LESs tended to underpredict the global amount of irreversible entropy production (dissipation). The SMD model was found unable to capture either the global or local vorticity variation and had minimal small-scale activity in dynamic and thermodynamic variables compared to the FC-DNS. The SMD model was also deficient in predicting the spatial distribution of drops and of the dissipation. In contrast, the GRD and SSC models did mimic the small-scale activity of the FC-DNS and the spatial distribution of drops and of the dissipation. Therefore, the GRD and SSC models are recommended, while the SMD model seems inappropriate for combustion or other problems where the local activity must be predicted