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

Modelling and Simulation of Turbulent Gas-Solid Flows applied to Fluidization

Modelling of gas-solid suspensions has been studied with emphasis on suitable closure laws. A study of characteristic time scales and energy dissipation mechanisms is made for the case of a simple shear flow. Applications of the modelling are presented in the form of simulation and validation of experiments in fluidized beds.<p /> The Eulerian formulation applied to isothermal gas-solid flows is given in the form of continuity and momentum equations of both phases. Closure laws are discussed for the stress tensors in both phases and for the interfacial momentum transfer. A summary and a critical assessment of published work on simulations of fluid dynamics in circulating and non-circulating fluidized beds are presented.<p /> A study of the equation of motion of a single sphere in a fluid shows that drag, gravity and transverse forces are the important mechanisms in gas-solid flows. Transverse forces are discussed in detail. Results from the Lagrangian formulation are used to derive an expression for the interfacial momentum transfer.<p /> Closure laws for the drift velocity, the fluid-particle velocity correlation tensor and the second order velocity moments in both phases are studied, and it is shown under which assumptions the models can be derived. The second order velocity moment in the discrete phase is modelled with the kinetic theory of granular flow. Models for the drift velocity and for the fluid-particle velocity correlation tensor are presented, first based on algebraic models and secondly, based on transport equations with a fluid-particle joint probability density function. Two-way coupling is discussed, and a two-equation model is introduced for modelling the gas phase turbulence. Boundary conditions are formulated. A discussion on the usefulness of the models is given as well as an application to fluidization and especially to circulating fluidized bed combustors.<p /> A mesh refinement study and a validation of two-fluid model closures has been carried out for a stationary bubbling fluidized bed application. To handle the long simulation times required to obtain acceptable statistical values, a parallel version of the two-fluid model solver, GEMINI-2D, was developed, based on a domain decomposition method for distributed memory computers. A number of problems related to the parallelization are investigated. The Eulerian two-phase solver GEMINI-2D is presented in its original version and the extension to turbulent gas-solid flows is also given.<p /> Estimates of the characteristic time scales (particle relaxation time, eddy-particle interaction time, inter-particle collision time), and of the energy dissipation mechanisms are performed together with a turbulent kinetic energy budget, for a simple equilibrium shear flow. The influence of several parameters (integral length scale, density ratio, mean velocity gradient, particle diameter and mean volume fraction) is investigated for Geldart group A and B particles.<p /> A three-dimensional simulation of a circulating fluidized bed is presented and numerical results are compared to local time-averaged measurements (vertical pressure profile and vertical and horizontal concentration profiles)