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Title: An Investigation into Solution Verification for CFD-DEM

Abstract

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of an experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6 th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flowmore » problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.« less

Authors:
 [1];  [2]
  1. National Energy Technology Lab. (NETL), AECOM, Morgantown, WV (United States)
  2. National Energy Technology Lab. (NETL), Morgantown, WV (United States)
Publication Date:
Research Org.:
National Energy Technology Lab. (NETL), Morgantown, WV (United States); AECOM, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE Office of Fossil Energy (FE)
OSTI Identifier:
1427020
Report Number(s):
NETL-PUB-21504; NETL-TRS-X-2017
DOE Contract Number:  
FE0004000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; solution verification; CFD-DEM; MFIX; MFIX-DEM

Citation Formats

Fullmer, William D., and Musser, Jordan. An Investigation into Solution Verification for CFD-DEM. United States: N. p., 2017. Web. doi:10.2172/1427020.
Fullmer, William D., & Musser, Jordan. An Investigation into Solution Verification for CFD-DEM. United States. https://doi.org/10.2172/1427020
Fullmer, William D., and Musser, Jordan. Sun . "An Investigation into Solution Verification for CFD-DEM". United States. https://doi.org/10.2172/1427020. https://www.osti.gov/servlets/purl/1427020.
@article{osti_1427020,
title = {An Investigation into Solution Verification for CFD-DEM},
author = {Fullmer, William D. and Musser, Jordan},
abstractNote = {This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of an experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.},
doi = {10.2172/1427020},
url = {https://www.osti.gov/biblio/1427020}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {10}
}