A note on the consistency of Hybrid Eulerian/Lagrangian approach to multiphase flows

The aim of the present paper is to introduce and to discuss inconsistencies errors that may arise when Eulerian and Lagrangian models are coupled for the simulations of turbulent poly-dispersed two-phase flows. In these hydrid models, two turbulence models are in fact implicitely used at the same time and it is essential to check that they are consistent, in spite of their apparent different formulations. This issue appears in particular in the case of very-small particles, or tracer-limit particles, and it is shown that coupling inconsistent turbulence models (Eulerian and Lagrangian) can result in non-physical results, notably for second-order fluid velocity moments. This problem is illustrated by some computations for fluid particles in a turbulent channel flow using several coupling strategies.Comment: 14 pages, 3 figure

The FDF or LES/PDF method for turbulent two-phase flows

In this paper, a new formalism for the filtered density function (FDF) approach is developed for the treatment of turbulent polydispersed two-phase flows in LES simulations. Contrary to the FDF used for turbulent reactive single-phase flows, the present formalislm is based on Lagrangian quantities and, in particular, on the Lagrangian filtered mass density function (LFMDF) as the central concept. This framework allows modeling and simulation of particle flows for LES to be set in a rigorous context and various links with other approaches to be made. In particular, the relation between LES for particle simulations of single-phase flows and Smoothed Particle Hydrodynamics (SPH) is put forward. Then, the discussion and derivation of possible subgrid stochastic models used for Lagrangian models in two-phase flows can set in a clear probabilistic equivalence with the corresponding LFMDF.Comment: 11 pages, proceedings of the 13 europena turbulence conference, submitted to JPC

Langevin PDF simulation of particle deposition in a turbulent pipe flow

The paper deals with the description of particle deposition on walls from a turbulent flow over a large range of particle diameter, using a Langevin PDF model. The first aim of the work is to test how the present Langevin model is able to describe this phenomenon and to outline the physical as- pects which play a major role in particle deposition. The general features and characteristics of the present stochastic model are first recalled. Then, results obtained with the standard form of the model are presented along with an analysis which has been carried out to check the sensitivity of the predictions on different mean fluid quantities. These results show that the physical repre- sentation of the near-wall physics has to be improved and that, in particular, one possible route is to introduce specific features related to the near-wall coherent structures. In the following, we propose a simple phenomenological model that introduces some of the effects due to the presence of turbulent coherent structures on particles in a thin layer close to the wall. The results obtained with this phenomenological model are in good agreement with experimental evidence and this suggests to pursue in that direction, towards the development of more general and rigorous stochastic models that provide a link between a geometrical description of turbulent flow and a statistical one.Comment: 40 pages, 8 figure

A two-dimensional relaxation scheme for the hybrid modelling of two-phase flows

International audienceRecently, a new relaxation scheme for hybrid modelling of two-phase flows has been proposed. This one allows to obtain stable unsteady approximations for a system of partial differential equations containing non-smooth data. This paper is concerned with a two-dimensional extension of the present method, in which two alternative relaxation schemes are compared. A partial analysis of continuous stability is given

PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow,

The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001 ]. Consequently, the present work is mainly focused on complementary aspects, that are often overlooked and that require particular attention. In particular, the following points are analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the PDF formalism. The important-physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation (SDE) written in continuous time (Langevin equations) for the velocity of the fluid seen. The interests and limitations of Langevin equations, compared to the single-phase case, are reviewed. From the numerical point of view, the model corresponds to an hybrid Eulerian/Lagrangian approach where the fluid and particle phases are simulated by different methods. Important aspects of the Monte Carlo particle/mesh numerical method are emphasised. Finally, the complete model is validated and its performance is assessed by simulating a bluff-body case with an important recirculation zone and in which two-way coupling is noticeable.Comment: 23 pages, 10 figure

A relaxation scheme for hybrid modelling of gas-particle flows

International audienceThis paper aims at proposing a relaxation scheme that allows to obtain stable approximations for a system of partial differential equations which governs the evolution of the void fraction and the mean velocity in the particle phase of two-phase flows. This system involves the divergence of a particle kinetic tensor, which is provided by a Lagrangian code and whose components are not smooth. The simulation algorithm is based on the combined use of upwinding and relaxation techniques. The main properties of the method are given, together with the Finite Volume Godunov scheme and this approach is compared to an analogous one that was developed earlier. Some measured rates of convergence in L 1-norm are provided, for a particular choice of the kinetic tensor. To complete the picture, we present some numerical results obtained when non-smooth external data are provided to the system

A time-step-robust algorithm to compute particle trajectories in 3-D unstructured meshes for Lagrangian stochastic methods

The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields used in the time integration by splitting, for each particle, the time step into sub-steps such that each of these sub-steps corresponds to particle cell residence times. This reduces the spatial discretization error. Given the stochastic nature of the models, a key aspect is to derive estimations of the residence times that do not anticipate the future of the Wiener process. To that effect, the new algorithm relies on a virtual particle, attached to each stochastic one, whose mean conditional behavior provides free-of-statistical-bias predictions of residence times. After consistency checks, this new algorithm is validated on two representative test cases: particle dispersion in a statistically uniform flow and particle dynamics in a non-uniform flow