267365 Filtered Drag Models for Euler-Lagrange Simulations of Gas-Solid Flow

Tuesday, October 30, 2012: 1:10 PM
Conference C (Omni )
Stefan Radl, Institute for Process and Particle Engineering, Graz University of Technology, Graz, Austria and Sankaran Sundaresan, Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ

It is well known that fluidized gas-particle mixtures manifest meso-scale structures such as clusters and bubbles. Resolving small meso-scale structures in device-scale simulations is too expensive and this has led to the development of filtered Euler-Euler (EE) two-fluid models and related constitutive models [1,2]. In this contribution, we ask how the constitutive models for, say, fluid-particle interaction force, should be filtered in Euler-Lagrange (EL) simulations (using the averaged equations for the gas phase and Discrete Element Method for the particle phase – sometimes referred to as the CFD-DEM approach).

To address this question, we performed CFD-DEM simulations of O(106) particles that freely sediment in a periodic box, and recorded statistics of the domain-averaged slip velocity, as well as of numerous spatially-averaged (i.e., filtered) quantities. Variations in the microscopic drag law, grid resolution, domain size, and mapping schemes show that our results are robust with respect to these settings.

We define two sets of filtered slip velocities and corresponding drag laws: First, we filter only the fluid velocity and define a filtered slip velocity as the difference between a filtered fluid velocity and the instantaneous particle velocity. The corresponding “fluid-only” filtered drag model is relevant for simulations where particles (or groups of particles) are tracked and coarse fluid grid cells have to be used (e.g., MP-PIC [3], or other parcel-based approaches [4]). Second, we define the filtered slip velocity based on the filtered fluid velocity and an average particle velocity in the filter region. The corresponding “particle-and-fluid” filtered drag model is relevant for coarse-grid EE simulations. Finally, we discuss the differences between the two classes of filtered drag laws, and provide closed expressions for their inclusion in parcel- and EE-based coarse-grid simulations. Variations in the particle size and density were used to extract the correct reference length scale that makes our filtered model applicable to gas-particle systems with sufficiently low particle Reynolds numbers.

Dimensionless filtered drag coefficient for various filter sizes and volume fractions (symbols: data from EL simulations; black lines: model prediction)

References

[1]      Y. Igci and S. Sundaresan, Constitutive Models for Filtered Two-Fluid Models of Fluidized Gas-Particle Flows. Ind. Eng. Chem. Res. 50 (2011) 13190-13201.

[2]      J.-F. Parmentier, O. Simonin, and O. Delsart, A functional subgrid drift velocity model for filtered drag prediction in dense fluidized bed. AIChE J. 58 (2012) 1084-1098.

[3]      D.M. Snider, An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows. J. Comput. Phys. 170 (2001) 523-549.

[4]      N.A. Patankar and D.D. Joseph, Modeling and numerical simulation of particulate flows by the Eulerian-Lagrangian approach. Int. J. Multiphase Flow 27 (2001) 1659-1684.

 


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