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

Doktorsavhandling, 1998

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. 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. 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. 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. 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. 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. 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).