Micro/Meso simulations of a fluidized bed with heat transfer

Particulate flows encountered in fluidized beds are frequently used in industrial applications (refining, energy, chemicals/petrochemicals, pharmaceutics). The wide range of spatial scales and interactions between the phases in such systems yields a complex flow often coupled with mass and/or heat transfer. These transfer have been widely investigated in the past in an experimental and numerical manners for dilute (1, 2) and dense suspensions (3, 4). Multi-scale modeling is a numerical approach developed to understand these phenomena from the particle scale (microscale) to process unit (macroscale). An intermediate scale (mesoscale) ranging from 104 to 108 particles is also introduced. Fluid phase is resolved using an Eulerian description while particles may be followed in a Lagrangian or an Eulerian manner. Meso/macroscale require closure laws for momentum, heat/mass transfer that can be derived either from experiments or microscale Particle-Resolved simulations (PRS). In this work, numerical simulations of gas-solid fluidization with heat transfer are performed at the microscale (DLM/FD) and the mesoscale (Euler/Lagrange) with our massively parallel code PeliGRIFF (5). A soft-sphere model combined with a Discrete Element Method (DEM) to track particles trajectory and contacts is used at both scales and interphase drag/heat transfer closure laws derived from our own PRS are used at the mesoscale. We select a system that comprises a few thousands of particles and extract statistically averaged local and global heat transfer. We carry out a direct comparison of the predictions obtained at both scales and suggest how the mesoscale modeling might be improved to provide more accurate solutions. REFERENCES W.E. Ranz and W.R. Marshall. Evaporation from drops, Part I and I. Chemical Engineering Science, 48:141-146;173-180, 1952. Z.G. Feng and E.E. Michaelides. Heat transfer in particulate flows with Direct Numerical Simulation (DNS). International Journal of Heat and Mass Transfer, 52:777-786, 2009. D.J. Gunn. Transfer of heat or mass to particles in fixed and fluidized beds, International Journal of Heat and Mass Transfer, 21:467-476,1978. N.G. Deen and E.A.J.F. Peters, J.T. Padding and J.A.M. Kuipers. Review of direct numerical simulation of fluid-particle mass, momentum and heat transfer in dense gas-solid flows, Chemical Engineering Science, 116:710-724, 2014. A. Wachs, A. Hammouti, G. Vinay, and M. Rahmani. Accuracy of finite Volume/Staggered grid Distributed Lagrange Multipliers/Fictitious Domain simulations of particulate Flows. Computers & Fluids 115, 154–172, 2015

Coupling the fictitious domain and sharp interface methods for the simulation of convective mass transfer around reactive particles: towards a reactive Sherwood number correlation for dilute systems

We suggest a reactive Sherwood number model for convective mass transfer around reactive particles in a dilute regime. The model is constructed with a simple external-internal coupling and is validated with Particle-Resolved Simulation (PRS). The PRS of reactive particle-fluid systems requires numerical methods able to handle efficiently sharp gradients of concentration and potential discontinuities of gradient concentrations at the fluid-particle interface. To simulate mass transfer from reactive catalyst beads immersed in a fluid flow, we coupled the Sharp Interface Method (SIM) to a Distributed Lagrange Multiplier/Fictious Domain (DLM/FD) two-phase flow solver. We evaluate the accuracy of our numerical method by comparison to analytic solutions and to generic test cases fully resolved by boundary fitted simulations. A previous theoretical model that couples the internal diffusion-reaction problem with the external advection-diffusion mass transfer in the fluid phase is extended to the configuration of three aligned spherical particles representative of a dilute particle-laden flow. Predictions of surface concentration, mass transfer coefficient and chemical effectiveness factor of catalyst particles are validated by DLM-FD/SIM simulations. We show that the model captures properly the effect of an internal first order chemical reaction on the overall respective reactive Sherwood number of each sphere depending on their relative positions. The proposed correlation for the reactive Sherwood number is based on an existing non-reactive Sherwood number correlation. The model can be later used in Euler/Lagrange or Euler/ Euler modelling of dilute reactive particle-laden flows

Direct numerical simulation of reactive flow through a fixed bed of catalyst particles

Many catalytic refining and petrochemical processes involve two-phase reactive systems in which the continuous phase is a fluid and the porous phase consists of rigid particles randomly stacked. Improving both the design and the operating conditions of these processes represents a major scientific and industrial challenge in a context of sustainable development. Thus, it is above all important to better understand all the intricate couplings at stake in these flows: hydrodynamic, chemical and thermal contributions. The objective of our work is to build up a multi-scale modelling approach of reactive particulate flows and at first to focus on the development of a microscopic-scale including heat and mass transfers and chemical reactions for the prediction of reactive flows through a dense or dilute fixed bed of catalyst particles. Please download the full abstract below

DNS of dispersed multiphase flows with heat transfer and rarefaction effects

We propose a method for DNS of particle motion in non-isothermal systems. The method uses a shared set of momentum and energy balance equations for the carrier- and the dispersed phases. Measures are taken to ensure that non-deformable entities (solid particles) behave like rigid bodies. Moreover, deformable entities (e.g. bubbles) as well as rarefaction effects can be accommodated. The predictions of the method agree well with the available data for isothermal solid particles motion in the presence of walls and other particles, natural convection around a stationary particle, solid particles motion accompanied with heat transfer effects and isothermal solid particles motion under rarefied conditions. The method is used to investigate the simultaneous effects of heat transfer and rarefaction on the motion of a solid catalyst particle in an enclosure, the interaction of a solid particle and a microbubble in a flotation cell and a case with more than 1000 particles

Particle-resolved numerical simulations of the gas–solid heat transfer in arrays of random motionless particles

Particle-resolved direct numerical simulations of non-isothermal gas–solid flows have been performed and analyzed from microscopic to macroscopic scales. The numerical configuration consists in an assembly of random motionless spherical particles exchanging heat with the surrounding moving fluid throughout the solid surface. Numerical simulations have been carried out using a Lagrangian VOF approach based on fictitious domain framework and penalty methods. The entire numerical approach (numerical solution and post-processing) has first been validated on a single particle through academic test cases of heat transfer by pure diffusion and by forced convection for which analytical solution or empirical correlations are available from the literature. Then, it has been used for simulating gas–solid heat exchanges in dense regimes, fully resolving fluid velocity and temperature evolving within random arrays of fixed particles. Three Reynolds numbers and four solid volume fractions, for unity Prandtl number, have been investigated. Two Nusselt numbers based, respectively, on the fluid temperature and on the bulk (cup-mixing) temperature have been computed and analyzed. Numerical results revealed differences between the two Nusselt numbers for a selected operating point. This outcome shows the inadequacy of the Nusselt number based on the bulk temperature to accurately reproduce the heat transfer rate when an Eulerian–Eulerian approach is used. Finally, a connection between the ratio of the two Nusselt numbers and the fluctuating fluid velocity–temperature correlation in the mean flow direction is pointed out. Based on such a Nusselt number ratio, a model is proposed for it

Towards an analysis of shear suspension flows using radial basis functions

In this paper, radial basis functions are utilised for numerical prediction of the bulk properties of particulate suspensions under simple shear conditions. The suspending fluid is Newtonian and the suspended particles are rigid. Results obtained are compared well with those based on finite elements in the literature

A Review on Contact and Collision Methods for Multi-body Hydrodynamic problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.Comment: 37 pages, 12 Figure