Jean-Pierre Minier

The pdf approach to turbulent polydispersed two-phase flows

Abstract The purpose of this paper is to develop a probabilistic approach to turbulent polydispersed two-phase flows. The two-phase flows considered are composed of a continuous phase, which is a turbulent fluid, and a dispersed phase, which represents an ensemble of discrete particles (solid particles, droplets or bubbles). Gathering the difficulties of turbulent flows and of particle motion, the challenge is to work out a general modelling approach that meets three requirements: to treat accurately the physically relevant phenomena, to provide enough information to address issues of complex physics (combustion, polydispersed particle flows, …) and to remain tractable for general non-homogeneous flows. The present probabilistic approach models the statistical dynamics of the system and consists in simulating the joint probability density function (pdf) of a number of fluid and discrete particle properties. A new point is that both the fluid and the particles are included in the pdf description. The derivation of the joint pdf model for the fluid and for the discrete particles is worked out in several steps. The mathematical properties of stochastic processes are first recalled. The various hierarchies of pdf descriptions are detailed and the physical principles that are used in the construction of the models are explained. The Lagrangian one-particle probabilistic description is developed first for the fluid alone, then for the discrete particles and finally for the joint fluid and particle turbulent systems. In the case of the probabilistic description for the fluid alone or for the discrete particles alone, numerical computations are presented and discussed to illustrate how the method works in practice and the kind of information that can be extracted from it. Comments on the current modelling state and propositions for future investigations which try to link the present work with other ideas in physics are made at the end of the paper.

On the Lagrangian turbulent dispersion models based on the Langevin equation

Abstract A Lagrangian approach is used to describe turbulent two-phase particulate flows. Special attention focuses on a currently used model based on the Langevin equation with instantaneous relative velocity of fluid and particles. A detailed analysis of the model is performed and its drawbacks are discussed. Afterwards, a novel model for particle dispersion in homogeneous turbulence is proposed. It is built on physical arguments quite different from those underlying the previous model: rather than instantaneous relative velocities, averaged characteristics of the motion of solid–fluid particle pairs are considered. The new model accounts for both inertia and external force effects. It is validated by comparison with existing experimental data on particle dispersion in grid turbulence and with large-eddy simulations of homogeneous turbulence.

Towards a description of particulate fouling: from single particle deposition to clogging.

Particulate fouling generally arises from the continuous deposition of colloidal particles on initially clean surfaces, a process which can even lead to a complete blockage of the fluid cross-section. In the present paper, the initial stages of the fouling process (which include single-particle deposition and reentrainment) are first addressed and current modelling state-of-the-art for particle-turbulence and particle-wall interactions is presented. Then, attention is specifically focused on the later stages (which include multilayer formation, clogging and blockage). A detailed review of experimental works brings out the essential mechanisms occurring during these later stages: as for the initial stages, it is found that clogging results from the competition between particle-fluid, particle-surface and particle-particle interactions. Numerical models that have been proposed to reproduce the later stages of fouling are then assessed and a new Lagrangian stochastic approach to clogging in industrial cases is detailed. These models further confirm that, depending on hydrodynamical conditions (the flow velocity), fluid characteristics (such as the ionic strength) as well as particle and substrate properties (such as zeta potentials), particle deposition can lead to the formation of either a single monolayer or multilayers. The present paper outlines also future numerical developments and experimental works that are needed to complete our understanding of the later stages of the fouling process.

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, Phys. Rep. 352, 1 (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 analyzed: the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of two-way coupling, the theoretical and numerical evaluations of particle averages and the fulfillment of the particle mass-continuity constraint. The theoretical model is developed within the probability density function (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 written in continuous time (Langevin equation...

Analysis of the incompressibility constraint in the smoothed particle hydrodynamics method

SUMMARY Smoothed Particle Hydrodynamics (SPH) is a particle-based, fully Lagrangian method for fluid-flow simulations. In this work, fundamental concepts of the method are first briefly recalled. Then, we present a thorough comparison of two different incompressibility treatments in SPH: the weakly compressible approach, where a suitably chosen equation of state is used, and the truly incompressible method (in two basic variants), where the velocity field projection onto a divergence-free space is performed. A noteworthy aspect of the study is that in each incompressibility treatment, the same boundary conditions are used (and further developed) that allows a direct comparison to be made. Two-dimensional and three-dimensional validation cases are studied. Problems associated with the numerical setup are discussed, and an optimal choice of the computational parameters is proposed and verified. The efficiency issues of the incompressibility treatments are considered, and the speed-up features are highlighted. The results show that the present state-of-the-art truly incompressible methods (based on a velocity correction) suffer from density accumulation errors. To address this issue, an algorithm, based on a correction for both particle velocities and positions, is presented. The usefulness of this density correction is examined and demonstrated. Copyright

A stochastic model of coherent structures for particle deposition in turbulent flows

In this paper, we propose a new stochastic Lagrangian model that is used to compute particle deposition rate in turbulent flows. This one dimensional boundary-layer model of the velocity of the flow seen by a particle explicitly simulates the interaction of particles with the near-wall coherent phenomena governing the wall-normal transport of particles (the so-called sweep and ejections events). For this purpose, a Markovian jump process, driving other stochastic processes, is introduced to model the coherent events. This method is believed to be one of the first attempts to include relevant geometrical features of the near-wall region in a statistical Lagrangian description. The model is first validated by comparing results obtained in the fluid-particle limit to available statistics of the boundary layer and by ensuring that the well-mixed condition is satisfied. Then, the deposition velocity is computed, and good agreement with experimental data is obtained. Furthermore, the two deposition regimes (“free flight” and “diffusional”) recently identified by direct numerical simulations are qualitatively retrieved.

Numerical Study on the Deposition Rate of Hematite Particle on Polypropylene Walls: Role of Surface Roughness

In this paper, we investigate the deposition of nanosized and microsized particles on rough surfaces under electrostatic repulsive conditions in an aqueous suspension. This issue arises in the general context of modeling particle deposition which, in the present work, is addressed as a two-step process: first particles are transported by the motions of the flow toward surfaces and, second, in the immediate vicinity of the walls, the forces between the incoming particles and the walls are determined using the classical DLVO theory. The interest of this approach is to take into account both hydrodynamical and physicochemical effects within a single model. Satisfactory results have been obtained in attractive conditions but some discrepancies have been revealed in the case of repulsive conditions, in line with other studies which have noted differences between predictions based on the DLVO theory and experimental measurements for similar repulsive conditions. Consequently, the aim of the present work is to focus on this particular range and, more specifically, to assess the influence of surface roughness on the DLVO potential energy. For this purpose, we introduce a new simplified model of surface roughness where spherical protruding asperities are placed randomly on a smooth plate. On the basis of this geometrical description, approximate DLVO expressions are used and numerical calculations are performed. We first highlight the existence of a critical asperity size which brings about the highest reduction of the DLVO interaction energy. Then, the influence of the surface covered by the asperities is investigated as well as retardation effects which can play a role in the reduction of the interaction energy. Finally, by considering the random distribution of the energy barrier of the DLVO potential due to the random geometrical configurations, the overall effect of surface roughness is demonstrated with one application of the complete deposition model in an industrial test case. These new numerical results show that nonzero deposition rates are now obtained even in repulsive conditions, which confirms that surface roughness is a relevant aspect to introduce in general approaches to deposition.

Probability density function computation of turbulent flows with a new near-wall model

The modeling and computation of near-wall turbulent flows is addressed with the probability density function (PDF) method for velocity and the turbulent frequency. Near-wall extensions are considered in detail and a new model for viscous transport is proposed. A method of elliptic relaxation for a blending function is applied to model the pressure–strain term. A numerical integration scheme is developed to deal with the near-wall singularity of coefficients that appears in the discrete formulation. The PDF equation is solved by a Monte Carlo method and the whole approach appears as a self-contained Lagrangian simulation using stochastic particles. For the sake of a numerical example, the fully developed channel flow case is computed; results are compared with the available direct numerical simulation data.

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 aspects 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 representation 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, toward the development of more general and rigorous stochastic models that provide a link between a geometrical description of turbulent flow and a statistical one.

WALL-BOUNDARY CONDITIONS IN PROBABILITY DENSITY FUNCTION METHODS AND APPLICATION TO A TURBULENT CHANNEL FLOW

An application of a probability density function (PDF), or Lagrangian stochastic, approach to the case of high-Reynolds number wall-bounded turbulent flows is presented. The model simulates the instantaneous velocity and dissipation rate attached to a large number of particles and the wall-boundary conditions are formulated directly in terms of the particle properties. The present conditions aim at reproducing statistical results of the logarithmic region and are therefore in the spirit of wall functions. A new derivation of these boundary conditions and a discussion of the resulting behavior for different mean variables, such as the Reynolds stress components, is proposed. Thus, the present paper complements the work of Dreeben and Pope [Phys. Fluids 9, 2692 (1997)] who proposed similar wall-boundary particle conditions. Numerical implementation of these conditions in a standalone two-dimensional PDF code and a pressure-correction algorithm are detailed. Moments up to the fourth order are presented for a...