(543f) Modeling of Sub-Grid Heterogeneity of Gas-Solid Suspension in Bubbling Fluidized Beds

Due to increasing computer power the numerical simulation of fluidized and moving beds has become feasible. However, while kinetic theory based CFD (Computational Fluid Dynamics) has become a valuable design tool for modeling pilot plant scale gas-solid fluidized bed reactors, a fully resolved simulation of industrial scale reactor is still nearly unfeasible. Many sub-grid drag modifications have, therefore, been put forth by academic researchers to account for the effect of small unresolved scales on the resolved meso-scales in this case. However, all these models significantly differ in terms of their dependencies on the void fraction and on the particle slip velocity. In a first step, we, therefore, thoroughly implemented the sub-grid drag models of (i) EMMS¹, (ii) Kuipers², (iii) Sundaresan³ and (iv) Simonin⁴ and compared them to (v) our relation^5,6(CD-Lab model) and to (vi) the homogenous drag law of Wen and Yu in case of a three dimensional bubbling fluidized bed. The results are verified by a fine grid reference simulation. It is shown that

1. Applying the homogenous drag law of Wen and Yu, which ignores unresolved sub-grid structures, fails to predict the hydrodynamics of the bubbling fluidized bed using coarse meshes.
2. Applying each of the discussed sub-grid drag modifications reveals the bed expansion adequately.
3. The bubble size is estimated suitably by the investigated sub-grid drag closures.
4. However, the bubble rise velocity is significantly overestimated by these closures, which indicates the requirement of sub-grid stress modifications for the frictional regime.
5. Compared to the fine grid simulation the computational demand is reduced by approximately two orders of magnitude using the coarse grid for equal time step sizes. Coarse meshes, however, allow larger time steps that additionally improves the computational efficiency by approximately one order of magnitude in our study.

Since it appears that the sub-grid stress contribution is strongly connected to the predicted bubble rise velocity, we study the contribution of the sub-grid heterogeneities to the effective particle stresses in a second step. In this study, we derive closures for the unresolved parts of the drag and the solids stresses starting from the filtered two-fluid model equations. In the kinetic-collisional regime these are based on the assumption that the heterogeneity inside fluidized beds is triggered by the formation of local clusters. In contrast, in the frictional regime sub-grid stresses (SGS) arise from strain-rate and solids phase fluctuations of sub-grid shear layers mainly. These sub-grid correlations are then applied again to the three dimensional bubbling fluidized bed of fine glass particles. This study reveals that

1. The contribution from the sub-grid stresses has minor impact on the hydrodynamics of the fluidized bed. Especially, bed expansion, solids phase distribution, gas flow, particle mass flux and bubble sizes are insensitive to the magnitude of the particle stresses.
2. However, without consideration for the contribution from the sub-grid stresses the effective particle stresses are underestimated significantly by the coarse grid simulations. It is shown that the bubble rise velocity is, therefore, overestimated considerably in this case.
3. Applying the presented sub-grid modifications yields fairly good agreement of the stresses and the solids phase velocity fluctuations with the fully resolved simulation and, therefore, the correct rise velocity of bubbles and slugs. Hence, a sub-grid stress modification for the frictional stresses is indispensable to estimate the bubble rise velocity in bubbling fluidized beds precisely.

To conclude, this study demonstrates that the presented sub-grid drag modifications apply well to the coarse grid simulation of a bubbling fluidized bed of fine particles. Nevertheless, the sub-grid contribution to the frictional stresses has to be taken into account to compute the bubble rise velocity correctly.

Finally, several tasks remain. For example, the models should also be validated at large scale fluidized beds (O(10)m). Thus, the general validity of the models must be further studied. These will be discussed in future publications.

References:

1. Lu, B, Wang, W & Li, J. Searching for a mesh-independent sub-grid model for CFD simulation of gas-solid riser flows. Chemical Engineering Science 64, 3437–3447 (2009).
2. Wang, J, Van der Hoef, MA & Kuipers, JAM. Coarse grid simulation of bed expansion characteristics of industrial-scale gas-solid bubbling fluidized beds. Chemical Engineering Science 65, 2125–2131 (2010).
3. Igci, Y & Sundaresan, S. Constitutive Models for Filtered Two-Fluid Models of Fluidized Gas-Particle Flows. Industrial & Engineering Chemistry Research 50, 13190–13201 (2011).
4. Parmentier, J-F, Simonin, O & Delsart, O. A functional subgrid drift velocity model for filtered drag prediction in dense fluidized bed. AIChE Journal 58, 1084–1098 (2012).
5. Schneiderbauer, S, Schellander, D & Pirker, S. A filtered frictional-kinetic model for gas-solid fluidized and moving beds. Proceedings of the 9th International Conference on CFD in the Minerals and Process Industries 7 (2012).
6. Schneiderbauer, S, Puttinger, S & Pirker, S. Comparative analysis of sub-grid drag modifications for dense gas - particle flows in bubbling fluidized beds. AIChEJ (accepted for publication) (2013).