Multi-dimensional transient mathematical simulator of blast furnace process based on multi-fluid and kinetic theories

The ironmaking blast furnace is regarded as one of the biggest and most complex industrial reactors, because it includes various materials like gas, lump granular materials, liquids and powders and more than 30 major reactions and phase changes in a single reaction vessel. The mathematical simulator of this process developed in this study used the multi-fluid treatment as its framework, since the motions of these materials were governed by different flow mechanisms. The rates of the interactions among the phases and the chemical reactions were evaluated based on kinetic theories. The model successfully reproduced the fields of velocity, temperature and reaction in the furnace and its validity was confirmed. The simulator was also applied to a novel operation, namely the top gas recycling combined with the carbon-composite iron-ore charging and the waste plastics injection, and the advantages in furnace efficiency and environmental load were quantitatively indicated.     

A multi-fluid nonrandom lattice fluid model: General derivation and application to pure fluids

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems is presented. The multi-fluid nonrandom lattice fluid (MF-NLF) model with the local composition concept was capable of describing properties for complex systems. However, the MF-NLF model has strong temperature dependence of energy parameters and segment numbers of pure systems; thus empirical correlations as functions of temperature were represented for reliable and convenient use in engineering practices. The MF-NLF model without temperature dependence of pure parameters could not predict thermodynamic properties accurately. It was found that the present model with three parameters describes quantitatively the vapor pressure and the saturated density for the pure fluid.     

Computational fluid dynamics and electrostatic modeling of polymerization fluidized-bed reactors

Electrostatics plays an important role in gas-solid polymerization fluidized-bed reactors. Agglomeration of polymer particles can occur due to either electrostatic and/or thermal effects, and can lead to reactor operability problems if not properly mitigated. In this work a first-principles electrostatic model is developed and coupled with a multi-fluid computational fluid dynamic (CFD) model to understand the effect of electrostatics on the bulk polymer, polymer fines, and catalyst particles. The multi-phase CFD model for gas-solid flow is based on the kinetic theory of granular flows and the frictional theory. The electrostatic model is developed based on a fixed, size-dependent charge for each type of particle (catalyst, polymer fines and polymer). The combined CFD model is first verified using simple test cases and then applied to a pilot-plant-scale polymerization fluidized-bed reactor. The multi-phase CFD model is applied to reproduce qualitative trends in particle segregation and entrainment due to electrostatic charges observed in experiments.     

Multi-fluid simulation of turbulent bubbly pipe flows

Radial distributions of void fraction α_G, bubble aspect ratio E, phasic velocities V_G and V_L and turbulent kinetic energy k in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The experimental results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liquid in the near wall region. Drag coefficient C_D of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on C_D is estimated by the correlation proposed by Legendre and Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by Lopez de Bertodano et al. (1994) and by Hosokawa and Tomiyama (2004a) give good predictions for turbulence modification caused by bubbles.     

Direct numerical simulation of complex multi-fluid flows using a combined front tracking and immersed boundary method

In this paper a simulation model is presented for the Direct Numerical Simulation (DNS) of complex multi-fluid flows in which simultaneously (moving) deformable (drops or bubbles) and non-deformable (moving) elements (particles) are present, possibly with the additional presence of free surfaces. Our model combines a Front Tracking (FT) model developed by van Sint Annaland et al. (2008. Numerical simulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47-70.) and an Immersed Boundary (IB) model developed by van der Hoef et al. (2008. Numerical simulation of dense gas-solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47-70.) The FT part circumvents the explicit computation of the interface curvature. The IB part incorporates both particle-fluid and particle-particle interaction via a direct forcing method and a hard sphere Discrete Particle (DP) approach. In our model a fixed (Eulerian) grid is utilised to solve the Navier-Stokes equations for the entire computational domain. The no-slip condition at the surface of the moving particles is enforced via a momentum source term that only acts in the vicinity of the particle surface. For the enforcement of the no-slip condition Lagrangian force points are used, which are distributed evenly over the surface of the particle. Dissipative particle-particle and/or particle-wall collisions are accounted via a hard sphere DP approach using a three-parameter particle-particle interaction model accounting for normal and tangential restitution and tangential friction. The capabilities of the hybrid FT-IB model are demonstrated with a number of examples in which complex topological changes in the interface are encountered.     

Tuning a multi-fluid model for gas lift simulations in wells

A multi-fluid formulation based on the k–? turbulence closure is used for modeling bubbly flow in vertical pipes. Each bubble-size group is considered as a separate dispersed phase. The current k–? based multi-fluid models suffer from the problem of large overprediction of void fraction peak and lead to satisfactory results in limited ranges. In this study, first, we establish a model for gas lift simulations in wells. For this purpose, we propose new modified lift and wall force coefficients by tuning the model with many experimental databases. As shown here, the tuned multi-fluid model is able to predict flows in all the three bubbly flow subregimes, namely the wall-peak, core-peak, and transition subregimes, with reasonable accuracy. The predictions by the tuned model are compared with other numerical simulations, as well. Finally, the tuned model is used to simulate gas-lift problems in oil wells and the performance of eight empirical and semi-empirical correlations for predicting pressure drop is investigated, carefully. It is observed that, there is a correlation (i.e. Guet, S., Ooms, G., Oliemans, R.V.A., Mudde, R.F., 2004. Bubble size effect on low liquid input drift-flux parameters. Chem. Eng. Sci. 59, 3315–3329) which predicts gravitational pressure drop in very good agreement with the tuned multi-fluid model in all ranges of bubble diameters, including the wall-peak and core-peak regimes.     

PDRF: A general dispersion relation solver for magnetized multi-fluid plasma

A general dispersion-relation solver that numerically evaluates the full propagation properties of all the waves in fluid plasmas is presented. The effects of anisotropic pressure, external magnetic fields and beams, relativistic dynamics, as well as local plasma inhomogeneity are included.     

A multi-fluid nonrandom lattice fluid model: Mixtures

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems and its consistent method for phase equilibrium calculation were presented in the previous paper. In this work, the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state and it was applied to vapor-liquid equilibrium. We consistently tested the present model on 17 phase equilibrium data sets of vapor-liquid equilibria and compared it with the MF-NLF model and the SAFT model. The present model (3 pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the MF-NLF model (6 adjustable pure parameters and one binary interaction parameter) and the SAFT model (3 pure parameters and one binary interaction parameter).     

Advanced physics calculations using a multi-fluid plasma model

The multi-fluid plasma model is derived from moments of the Boltzmann equation and typically has two fluids representing electron and ion species. Large mass differences between electrons and ions introduce disparate temporal and spatial scales and require a numerical algorithm with sufficient accuracy to capture the multiple scales. Source terms of the multi-fluid plasma model couple the fluids to themselves (interspecies interactions) and to the electromagnetic fields. The numerical algorithm must treat the inherent stiffness introduced by the multiple physical effects of the model and tightly couple the source terms of the governing equations. A discontinuous Galerkin method is implemented for the spatial representation. Time integration is investigated using explicit, implicit, semi-implicit methods. Semi-implicit treatment is accomplished using a physics-based splitting. The algorithm is applied to study drift turbulence in field reversed configuration plasmas to illustrate the physical accuracy of the model. The algorithm is also applied to plasma sheath formation which demonstrates Langmuir wave propagation.     

CFD simulation of coal-water slurry flowing in horizontal pipelines

An Eulerian multiphase approach based on kinetic theory of granular flow was used to simulate flow of coal-water slurries (CWS) in horizontal pipelines. The RNG k-ɛ turbulent model was incorporated in the governing equation to model turbulent two-phase flow with strong particle-particle interactions. In this model, the coal particles with bimodal distribution were considered as two solid-phase components, and the moment exchange between solid and liquid as well as that between solid and solid were accounted for. The model was firstly validated with pressure gradient and concentration profile data from the open literature, and then validated with pressure gradient data of the authors’ experiments. The effects of influx velocity, total influx concentration and grain composition were numerically investigated, and the results have displayed some important slurry flow characteristics, such as constituent particle concentration distribution and velocity distribution as well as pressure gradients, which are very difficult to display in the experiments. The results suggest that both gravity difference between large and small particles and strong particle-particle interaction had significant effects on concentration distribution as well as velocity distribution. This work was presented at the 7 ^th Korea-China Workshop on Clean Energy Technology held at Taiyuan, China, July 25–28, 2008.