Abstract
A particle packing algorithm for simulating realistic packed beds of spheres with size distribution is described. The algorithm used the Monte Carlo method combined with the simulated annealing minimisation algorithm to solve the packed bed simulations. The objective function which was minimised was a combination of two functions, one describing the deviation from the target mean coordination number of the spheres in each size interval and the other the average fraction of overlapping volume of the spheres per contact. In this way a realistic bed structure was maintained while at the same time controlling the coordination number of the spheres. The algorithm used an experimentally validated model to predict the mean coordination number of the spheres in each size interval.
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Abbreviations
- D N :
-
neighbouring distance (m)
- E :
-
simulated annealing energy (–)
- k :
-
simulated annealing Boltzmann constant (–)
- m :
-
number of spheres (–)
- P :
-
Boltzmann probability (–)
- R :
-
particle radius (m)
- T :
-
simulated annealing temperature (–)
- T ∞ :
-
simulated annealing stop temperature (–)
- T o :
-
simulated annealing start temperature (–)
- t solve :
-
time taken for packing to solve (min)
- T solve :
-
simulated annealing temperature at which the algorithm solved (–)
- x, y, z :
-
coordinates of particle centroid (m)
- β :
-
parameter for weighing objective function (–)
- δ :
-
magnitude of sphere relocation parameter (–)
- ΔE CN :
-
change in coordination number objective function (–)
- ΔE OV :
-
change in overlap volume objective function (–)
- ϵ:
-
porosity (–)
- γ :
-
neighbour parameter (–)
- ζ :
-
random number between 0 and 1 (–)
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Acknowledgments
This work is part of the E.E.T. (Economy, Ecology and Technology) project (http://www.vg2.nl) supported by the Dutch government. The financial support from the E.E.T. program is gratefully acknowledged.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Georgalli, G.A., Reuter, M.A. A particle packing algorithm for packed beds with size distribution. Granular Matter 10, 257–262 (2008). https://doi.org/10.1007/s10035-008-0097-z
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DOI: https://doi.org/10.1007/s10035-008-0097-z