(395g) Micro-Scale CFD Modeling of Packed-Beds

A. Problem Definition: The intricate structure of packed beds directly affects heat, mass, and momentum transport across multiple length scales. On a reactor scale, bed geometry strongly influences overall pressure drop, residence time distribution, and dispersion of species. On the interstitial and particle scale, thin film flow, interphase mass transfer, local eddy formation, etc. are also strongly influenced. Recently, there has been work investigating near particle single phase flow using a unit cell approach (Gunjal et al., 2005) and small clusters (less than 20) of pseudo-random particles (Dixon et al., 2006). However, much more work could be done to extend to larger (hundreds) domains of randomly packed non-spherical particles. It is the goal of this project to extend models to larger domains and to improve the fundamental understanding of the effect of bed geometry on transport phenomena on the interstitial and particle scale.

B. Research Objectives

The overall objective of this project is to elucidate the phenomena of heat, mass, and momentum transport on the length scale of the catalyst particle. Developing knowledge in this area will improve the fundamental understanding of the effect of bed geometry on the transport phenomena seen in packed beds. In order to achieve this objective, several milestones need to be reached:

Domain Generation: A computational domain representing a packed bed of catalyst particles must be created that is both random and industrially relevant/realistic. Randomly packed catalyst particles will be arranged via a Monte Carlo type simulation. The particles present will be realistic (cylinders, trilobes, and quadlobes) and have a distribution of lengths and radii similar to particles seen industrially.

Model Development: An interstitial-scale model that captures the phenomena of heat, mass, and momentum transport common to non-isothermal reacting flow through interstitial spaces in a catalytic packed bed will be created. Specifically, single and multiphase flows will be simulated using computational fluid dynamics as a research tool to resolve local transport phenomena. Single phase flows will be modeled with a steady-state solver as an initial investigation.

Integration of Advanced Computing Technology: Graphics processing units (GPUs) will be used to increase computational capability through integration into the open source C++ library OpenFOAM. Specifically, task specific sparse matrix solvers (preconditioned conjugate gradient or BiCGStab) using a GPU programming language (CUDA) will be developed. The OpenFOAM library will be used for all other tasks not related to the solving of sparse matrices (discretization, boundary conditions, mesh manipulation, matrix assembly, etc.). This has not been previously achieved and integrated into a standard CFD library, and represents a new feature in the current OpenFOAM library.

C. Results and Discussion

Milestones 1 (Domain Generation): A packing algorithm has been developed to pack both cylinders and more complex cylinder based particles (trilobes and quadlobes). The algorithm is able to generate computational meshes of packed particles on the order of hundreds to less than three thousand particles with bulk bed porosities less than seventy percent. An example of a generated domain is shown in figure 1. Also, radial porosity distributions of packed cylinders show similar results with previous experimental work by Roblee et al. are shown in figure 2 (Roblee et al., 1958).

Figure 1 shows a packed domain of 1000 packed cylindrical particles. The particle location and orientation are known exactly so that a computational mesh can be easily generated in a CAD or meshing software such as GAMBIT (www.ansys.com). Once a mesh is generated, a CFD simulation can be run on the domain. To date, simulations on much smaller domains have been completed. Simulations on larger domains will be accomplished in the next few months with the use of integration of advanced computing technology, outlined later in this section. From figure 2, it is seen that the packed domain of particles shows the most porosity in the near wall region. This is consistent with result seen in literature (Roblee et al., 1958). The trend shows similarity with a slight difference in the realm of oscillation around 0.6, with error bars less than the size of the points on the plot. This value shows a higher local porosity, representing a more loosely packed domain of particles that is still within a realistic range of bed porosity. This particular example has a bulk porosity of around 0.63. Meshes from loosely packed domains may be courser (fewer mesh points and smaller matrices) and therefore will require less computational power than their tightly packed counterparts. These results are currently being prepared for publication.

Milestones 2 (Model Development): Currently, a model based on the OpenFOAM C++ library has been completed. This CFD model is capable of modeling steady-state laminar and turbulent flow for isothermal flows. Minor changes can be made to include energy transport within the system including transport within the solid catalyst particles. This is achieved through a conjugate heat transfer model utilizing a coupled matrix based approach. In this approach, the linear system describing heat transport in the fluid and solid are solved in the same matrix rather than sequential solving of separate regions (fluid and solid) with a matching of mesh values near the region interfaces. Because the meshes tend to be very large, milestone 3 is integral in the success of integrating this type of model with the complex packed bed geometry.

Milestones 3 (Integration of Advanced Computing Technology): Currently, sparse linear solvers based on CUDA have been developed in house using a CUDA-based BLAS library called CUBLAS. These solvers include conjugate gradient solvers for symmetric linear systems (pressure term of Navier-Stokes Equations) and a bi-conjugate gradient solver for asymmetric linear systems (velocity variable). Both of these are preconditioned solvers, using simple preconditioners. The integration of these CUBLAS codes into OpenFOAM has been accomplished on a preliminary basis at this time. The goal of this integration is to increase the speed of the simulations by shifting to a new computational paradigm from a central processing unit (CPU) to a graphics processing unit (GPU). More information on GPU computing can be found at (www.nvidia.com) and search for the keyword ?CUDA?.

D. References

A. Dixon, M. Nijemeisland, and H. Stitt. ?Packed Tubular Reactor Modeling and Catalyst design using CFD?. Advances in Chemical Engineering, 2006, vol 1, 307.

Prashant Gunjal, Vivek V. Ranade, and Raghunath V. Chaudri, ?Computational Study of a Single-Phase Flow in Packed Bed of Spheres?. AICHE Journal 2005, 51(2), 365.

L. H. S. Roblee, R. M. Baird, J. W. Tierney. ?Radial porosity variations in packed beds?. AICHE Journal, 1958, vol 4, 460.