Discrete particle simulation of two-dimensional fluidized bed

Detailed knowledge of solids circulation, bubble motion, and frequencies of porosity oscillations is needed for a better understanding of tube erosion in fluidized bed combustors. A predictive two-phase flow model was derived starting with the Boltzman equation for velocity distribution of particles. The model is a generalization of the Navier-Stokes equations of the type proposed by R. Jackson, except that the solids viscosities and stresses are computed by simultaneously solving a fluctuating energy equation for the particulate phase. The model predictions agree with time-averaged and instantaneous porosities measured in two-dimensional fluidized beds. Observed flow patterns and bubbles were also predicted.

A bubbling fluidization model using kinetic theory of granular flow

Discrete particle simulation of particulate systems: Theoretical developments

This report describes the MFIX (Multiphase Flow with Interphase exchanges) computer model. MFIX is a general-purpose hydrodynamic model that describes chemical reactions and heat transfer in dense or dilute fluid-solids flows, flows typically occurring in energy conversion and chemical processing reactors. MFIX calculations give detailed information on pressure, temperature, composition, and velocity distributions in the reactors. With such information, the engineer can visualize the conditions in the reactor, conduct parametric studies and what-if experiments, and, thereby, assist in the design process. The MFIX model, developed at the Morgantown Energy Technology Center (METC), has the following capabilities: mass and momentum balance equations for gas and multiple solids phases; a gas phase and two solids phase energy equations; an arbitrary number of species balance equations for each of the phases; granular stress equations based on kinetic theory and frictional flow theory; a user-defined chemistry subroutine; three-dimensional Cartesian or cylindrical coordinate systems; nonuniform mesh size; impermeable and semi-permeable internal surfaces; user-friendly input data file; multiple, single-precision, binary, direct-access, output files that minimize disk storage and accelerate data retrieval; and extensive error reporting. This report, which is Volume 1 of the code documentation, describes the hydrodynamic theory used in the model: the conservation equations,more » constitutive relations, and the initial and boundary conditions. The literature on the hydrodynamic theory is briefly surveyed, and the bases for the different parts of the model are highlighted.« less

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MFIX documentation theory guide

Numerical flow simulation utilising a full multiphase model is impractical for a suspension possessing wide distributions in the particle size or density. Various approximations are usually made to simplify the computational task. In the simplest approach, the suspension is represented by a homogeneous single-phase system and the influence of the particles is taken into account in the values of the physical properties. This study concentrates on the derivation and closing of the model equations. The validity of the mixture model is also carefully analysed. Starting from the continuity and momentum equations written for each phase in a multiphase system, the field equations for the mixture are derived. The mixture equations largely resemble those for a single-phase flow but are represented in terms of the mixture density and velocity. The volume fraction for each dispersed phase is solved from a phase continuity equation. Various approaches applied in closing the mixture model equations are reviewed. An algebraic equation is derived for the velocity of a dispersed phase relative to the continuous phase. Simplifications made in calculating the relative velocity restrict the applicability of the mixture model to cases in which the particles reach the terminal velocity in a short time period compared to the characteristic time scale of the flow of the mixture. (75 refs.)

On the mixture model for multiphase flow

Erosion in bubbling fluidized-bed combustors is a serious issue that may affect their reliability and economics. Available evidence suggests that the key to understanding this erosion is detailed knowledge of the coupled and complex phenomena of solids circulation and bubble motion. A thin transparent “two-dimensional” rectangular fluidized bed with an obstacle served as a rough model for a fluidized-bed combustor. This model was studied experimentally and computationally using two hydrodynamic equation sets. The computed hydrodynamic results agree reasonably well with experimental data. Bubble frequencies and sizes compare well with those obtained from analyzing a high-speed motion picture frame-by-frame. Time-averaged porosities computed from both models agree with time-averaged porosity distributions measured with a gamma-ray densitometer. The principal diferences between the data and the computations in this paper are due to asymmetries present in the experiment and to the simplified solids rheology used in the hydrodynamic models.

Porosity distributions in a fluidized bed with an immersed obstacle

Multiphase hemodynamic simulation of pulsatile flow in a coronary artery

A multiphase computational fluid dynamics (CFD) model was applied to a commonly used industrial experiment known as the collapsing fluidized-bed experiment. The experiment involves several hydrodynamic regimes including the bed expansion, bubbling, sedimentation, and consolidation of the fluidized bed. The CFD model is capable of predicting all four of these regimes. The three Geldart Groups, C, A, and B were simulated in a bubbling and subsequently collapsing fluidized bed. Results show that hydrodynamic Models A and B, the use of the modified Ergun equation or the MFIX code drag models, and solids rheology have limited impact on the bubbling- and collapsing-bed simulations. The major finding of this study is that the solids modulus, G, is the controlling parameter during the consolidation regime. The simulated bubble sizes and bed collapse rates for all three Geldart groups were found to be within reported experimental error. The computed high turbulent intensity of Geldart Group A particles also agrees with data in the literature measured using an acoustic shot noise probe. It is also demonstrated that the traditional interpretation of the collapsing bed as consisting of separate bubble escape and sedimentation regimes is incorrect and that, in fact, they occur simultaneously.

CFD Simulations of bubbling/collapsing fluidized beds for three Geldart Groups

State-of-the-art review of erosion modeling in fluid/solids systems

Hemodynamic data on the roles of physiologically critical blood particulates are needed to better understand cardiovascular diseases. The blood flow patterns and particulate buildup were numerically simulated using the multiphase non-Newtonian theory of dense suspension hemodynamics in a realistic right coronary artery (RCA) having various cross sections. The local hemodynamic factors, such as wall shear stress (WSS), red blood cell (RBC) buildup, viscosity, and velocity, varied with the spatially nonuniform vessel structures and temporal cardiac cycles. The model generally predicted higher RBC buildup on the inside radius of curvature. A low WSS region was found in the high RBC buildup region, in particular, on the area of maximum curvature of a realistic human RCA. The complex recirculation patterns, the oscillatory flow with flow reversal, and vessel geometry resulted in RBC buildup due to the prolonged particulate residence time, specifically, at the end of the diastole cycle. The increase of the initial plasma viscosity caused the lower WSS. These predictions have significant implications for understanding the local hemodynamic phenomena that may contribute to the earliest stage of atherosclerosis, as clinically observed on the inside curvatures and torsion of coronary arteries.

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Robert W. Lyczkowski

Papers

Porosity distributions in a fluidized bed with an immersed obstacle

Multiphase hemodynamic simulation of pulsatile flow in a coronary artery

CFD Simulations of bubbling/collapsing fluidized beds for three Geldart Groups

State-of-the-art review of erosion modeling in fluid/solids systems

Hemodynamic computation using multiphase flow dynamics in a right coronary artery.