Compresibilidad y cambios térmicos en el comportamiento ondulatorio de la fluidización rápida
Fast fluidization of a two-phase gas-solid flow was modeled by a set of space-time averaged equations. The space-time average is defined and the conservation and balance equations of mass, momentum, energy and entropy with space-time averaging were obtained. These equations were systematically obtai...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | México |
| Institución: | Universidad Autónoma Metropolitana |
| Repositorio: | Repositorio Institucional de la UAM Iztapalapa |
| Idioma: | español |
| OAI Identifier: | oai:bindani.izt.uam.mx:kh04dp84d |
| Acceso en línea: | https://doi.org/10.24275/uami.kh04dp84d |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/LEM/Termodinámica info:eu-repo/classification/LEM/Chemical engineering info:eu-repo/classification/LEM/Fluidización rápida info:eu-repo/classification/LEM/Ingeniería química info:eu-repo/classification/LEM/Thermodynamics info:eu-repo/classification/LEM/Fluidization info:eu-repo/classification/LEM/Multiphase flow -- Mathematical models info:eu-repo/classification/LEM/Flujo multifásico -- Modelos matemáticos info:eu-repo/classification/cti/7 |
| Sumario: | Fast fluidization of a two-phase gas-solid flow was modeled by a set of space-time averaged equations. The space-time average is defined and the conservation and balance equations of mass, momentum, energy and entropy with space-time averaging were obtained. These equations were systematically obtained from the corresponding local-instantaneous equations. Space-time averaging contains volume averaging and time averaging as asymptotic cases. The conditions under which this occurs is demonstrated and discussed. The entropy balance is studied and when the second law of thermodynamics is applied, constraints on the source terms resulting from averaging were found which require closure. These restrictions provide a criterion to deduce positive definite quadratic forms that satisfy the second law of thermodynamics. The space-time averaging approach allows obtaining a state equation in which first or higher order corrections on state variables deviations are incorporated. This is a substantial difference between the space-time averaging of multiphase systems and the extended kinetic theory approach to granular media of Gidaspow (1994). Nevertheless, in this first study this correction is not considered and the ideal gas state equation was used to represent the gas phase compressibility, whereas the solid phase was assumed incompressible. The incompressibility hypothesis in fluidized beds models is evaluated by comparing the incompressible and compressible 1-D models. All compressible terms appear multiplied by the squared sound propagation speed, s. In both proposed models, the incompressible part was retrieved in the limit s . Liu’s (1982) linear stability analysis was extended to estimate the compressibility contribution. A criterion based on the propagation speeds and the wave number was developed. This method was applied to two physical systems whose solid properties differ widely: FCC cata catalyst-water vapor and CFB sand-air. Two third-order propagation speeds were identified with pressure wave propagation. All the fourth-order model eigenvalues coincide with the fourth-order propagation speeds. It was shown that the effect of the fluid compressibility is as important as the effect of the solid compressibility modulus. The second-order wave is incomplete, since there is only one wave operator acting in a space derivative. It is shown that when wall friction is considered, a propagation mode associated to the wall is included. This completes the second-order wave, passing from parabolic to hyperbolic. The wall dynamics is separated from the tube core thus resulting in a generalized Liu’s criterion. In addition, it is shown how the wall enhances the stability region based on the wave number criterion. A non-isothermal model was developed which closure is in agreement with the second law of thermodynamics assuming that the interfacial effects overcome the volumetric ones. In this model we separate the terms associated to both considered effects: compressibility and thermicity. All thermal-associated terms appear multiplied by the volumetric expansion coefficient, V . The isothermal model is retrieved by the limit, 0 V . It was continued with FCC and CFB systems, but with its non-isothermal extension at the level of the coefficients finding how thermal effects module the isothermal coefficients. It was demonstrated that the void fraction, pressure and gas temperature are governed by the same fifth order wave operator, since the solid temperature is governed by the fifth wave operator acting in a first order wave of the solid particles temperature. Finally, the adiabatic wall effect is incorporated and it was shown how this model is the most general and allows studying an eight cases set. These cases are given by the combination of the effects: incompressibility, compressibility, thermal effects and tube wall. The methodology designed in this work allows studying the impact of each effect over the dynamic and the stability, as well as in the modeling strategies. |
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