(139h) Advances in Voidage Reconstruction Schemes for the Simulation of Dense Gas-Particle Flows

Euler-Lagrange (EL) models of dense fluid-particle suspensions are often treated as the “gold standard” for simulating flow in these suspensions. When using so-called particle-unresolved (PU) EL models, one relies on (i) tracking every particle and (ii) using spatially-averaged transport equations to describe fluid flow. In the context of such PU-EL models of dense particulate systems it is necessary to accurately reconstruct the local voidage at the particle position. This is since the voidage is of central importance for estimating exchange coefficients, e.g., for the drag force or the rate of interphase heat transfer. Preliminary work showed that standard approaches to reconstruct the voidage at the particle position often lead to results that are highly grid sensitive. This is the case even though we use advanced smoothing, mapping and interpolation schemes.¹ Especially systems involving polydisperse granular materials in which the particle volume fraction can surpass 0.8, i.e., an extremely stiff particle-fluid coupling is present, are problematic.

Similar as Li et al.² we start our study with a naïve analysis of the total force acting on a fixed bed of particles bound by regions void of particles. In these situations fluid flow is aligned with the voidage gradient. As expected, upon coarsening we find that the grid both force and heat transfer rates are significantly underpredicted. Thus, a positive drag correction is required for these systems due to the latent underprediction of voidage gradients when using a finite grid size. Surprisingly, this underprediction is more extreme for PU-EL-based simulations compared to predictions by an Euler-Euler approach. Consequently, we work towards an improved voidage reconstruction algorithm for PU-EL that compensates this underprediction, both for systems with finite and infinitely large voidage gradients. In order to generalize our ideas, we combine the idea of an angle-dependent correction to the drag coefficient² with the newly proposed voidage reconstruction scheme. By considering the closure for the modified drag coefficient proposed by Radl and Sundaresan,³ we then benchmark the combined approach for a variety of systems including fixed and fluidized beds.

Finally we put our developments into perspective by a comparison with the recent study of Li et al.² (which considered Euler-Euler models), as well as the progressive analysis provided by Schneiderbauer.⁴ While the latter study already laid the foundation for a positive drag correction, it relied on an oversimplified picture for the correlation of voidage and gas-phase velocity fluctuations. The study of Li et al.² relied on pre-tabulated correction factors, which lacks of generality and is valid for Euler-Euler-based simulations only. We conclude our study by documenting key advantages of our advanced voidage reconstruction algorithm, which appears to most significantly improve predictions when studying polydisperse fluid-particle suspensions.

References

1. Radl, S., Gonzalez, B., Goniva, C. & Pirker, S. State of the Art in Mapping Schemes for Dilute and Dense Euler-Lagrange Simulations. 10th Int. Conf. CFD Oil Gas, Metall. Process Ind. 1–9 (2014).

2. Li, T., Wang, L., Rogers, W., Zhou, G. & Ge, W. An Approach for Drag Correction Based on the Local Heterogeneity for Gas–Solid Flows. AIChE J. 63, 1203–1212 (2017).

3. Radl, S. & Sundaresan, S. A drag model for filtered Euler-Lagrange simulations of clustered gas-particle suspensions. Chem. Eng. Sci. 117, 416–425 (2014).

4. Schneiderbauer, S. A Spatially-Averaged Two-Fluid Model for Dense Large-Scale Gas-Solid Flows. AIChE J. in press, 1–19 (2017).