Heat transfer in fluidized beds with immersed surface: Effect of geometric parameters of surface
Graphical abstract
Introduction
Fluidized beds are versatile equipment characterized by high rates of heat and mass transfer, which allow numerous uses in the chemical industry. The applications of fluidized beds encompass a vast range of physical and chemical processes, including fluid catalytic cracking [1], [2], coating [3], drying [4], synthesis reactions [5], combustion [6], and gasification [7], [8]. Despite the several uses of fluidized beds, engineers and researchers still encounter challenges in their modeling and scale up. These difficulties prove that the complex phenomena occurring inside fluidized beds are still not completely understood.
Often, the addition or removal of heat in a fluidized bed is required, especially when the process includes chemical reactions. Therefore, it is extremely important to understand how this phenomenon is affected by several of its parameters. Over the years, researchers have been conducting experiments to clarify this question. They identified the solids suspension density as the factor that most influences the heat transfer coefficient [9], [10], [11], [12], [13]. One of the main advantages of the fluidized bed is the high rates of heat transfer between the bed and the immersed surface. Thus, the study of this phenomenon is an important field of research that needs to be further elucidated. Stefanova et al. [14] measured the heat transfer coefficient between the bed and a heated tube and found that this parameter was larger in the turbulent regime. Abid et al. [15] studied the influence of the angle of a heated tube inside a fluidized bed in the heat transfer, verifying changes caused by the hydrodynamic behavior close to the tube. Sundaresan and Kolar [9] analyzed the effects of the size and axial position of the heat transfer surface. Di Natale et al. [16] empirically tested different heated surface geometries and verified that the heat transfer coefficient can vary up to 40% depending on the geometry.
In recent years, computational advances have given rise to computational fluid dynamics (CFD), an important tool that has been widely used by researchers to gain an understanding of the hydrodynamics and heat transfer in fluidized beds. Two different approaches are regularly employed in studies of fluidized beds. The Lagrangean approach is a discrete method based on molecular dynamics. The Eulerian approach considers both gas and particulate phases as an interpenetrating continuum [17]. The first approach requires a large computational effort and is not viable for industrial cases. Thus, the Eulerian approach is most commonly used for the simulation of fluidized beds, and even though it does not provide the same level of detail as the Lagrangean approach, it has been producing satisfactory results. When using the Eulerian approach, it is a common practice to use the kinetic theory of granular flows to describe the rheology of the particulate phase.
The kinetic theory of granular flows (KTGF) assumes that the behavior of the particulate phase is similar to that of gases, by drawing analogy with the kinetic theory of gases [18], [19]. The KTGF was used along with the Eulerian approach in various heat transfer studies in a fluidized bed. Schmidt and Renz [20] used the KTGF to predict the heat transfer coefficients of a fluidized bed with an immersed tube. Behjat et al. [21] simulated a polymerization reactor and verified an increase in the temperature at the top of the bed due to the exothermic reaction. Armstrong et al. [22] conducted a parametric study for various restitution coefficients, particle diameter sizes and inlet velocities in a fluidized bed. Chang et al. [23] investigated the heat transfer between particles of different classes in a bubbling bed. They concluded that this heat transfer mechanism is much smaller than the heat transfer between gas and particles. Armstrong et al. [24] showed that the addition of immersed tubes in a fluidized bed leads to changes in the hydrodynamics of the bed and consequently in the heat transfer phenomenon. Although a large number of parameters have already been studied, the role of the immersed surface geometry in the heat transfer phenomenon is still not complete elucidated.
This study aims to show how the heat transfer coefficient is influenced by the geometric shape of the immersed heat transfer surface. For this, the Eulerian approach was used along with the KTGF. The influence of different drag models, specularity coefficients and turbulence modeling in the heat transfer coefficient is shown. Results for the heat transfer coefficient for ten distinct surface geometries are presented.
Section snippets
Mathematical modeling
The Eulerian multiphase model for granular flows was used in FLUENT 14.0 to describe the behavior and interactions of the granular and gas phases in a fluidized bed. This model solves the two phases individually using the conservation equations shown in Table 1. Both phases are present in all control volumes of the grid so that the sum of the volume fraction of both phases is equal to unity. The conservation of momentum for different phases is coupled through the drag force term . Most
Results
Initially a simplified geometry, containing only Cylinder 1 as the immersed heated surface was created for preliminary studies. Several drag models and specularity coefficients were tested using this geometry. After defining the best drag model and specularity coefficient, a polyethylene rod was included in the geometry, as shown in Fig. 2. In this step, a turbulence model was also included. This setup was used to conduct all surface geometry tests. The validation was obtained by comparing the
Discussion
The first part of this work consisted of a parametric study whose objective was to determine the best setup for future simulations. This was done by testing different parameters and comparing the results obtained computationally with the experimental results of Di Natale et al. [16]. The experimental work of Di Natale [16] does not present data of pressure drop and volume fraction distribution, therefore the validation of the drag model was done by comparing the computational and experimental
Conclusion
The results obtained with the Eulerian-granular model showed the efficiency of CFD techniques in describing fluidized beds. The studies conducted for different heat transfer geometries proved the close relationship between the bed hydrodynamics and the heat transfer phenomenon. An increase in the cylinder diameter produced deformities in the bubble passing the surface, increasing solids velocity, decreasing the solids fraction in that area and consequently reducing the heat transfer
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2019, International Journal of Heat and Mass TransferCitation Excerpt :To introduce the interphase momentum exchange, the drag function proposed by Gidaspow et al. [60] is used. For the earlier CFD works published in the literarture for bubbling fluidized beds, it was shown that the Gidaspow drag function is most appropriate drag model, therefore, this model is used in the present simulations [55,61,62]. The momentum balance equations for the gas and solid phases are given as: