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Transport in Porous Media

, Volume 120, Issue 1, pp 207–225 | Cite as

Influence of Resolution of Rasterized Geometries on Porosity and Specific Surface Area Exemplified for Model Geometries of Porous Media

  • Tobias Heidig
  • Thomas Zeiser
  • Hannsjörg Freund
Article

Abstract

Rasterized representations of geometrical structures are commonplace in science and engineering. They are used in analysis and design of complex geometrical structures; however, the introduced errors for volume and surface estimation are often not considered in detail. To provide insight and information on these effects, in this study model geometries of porous media (simple cubic, body-centered cubic, face-centered cubic) are used to investigate the influence of resolution (voxels per length) on volume and surface approximation. The numerically obtained results are compared with analytical solutions for porosity and specific surface area. Small deviations from the real volume are found for the rasterized geometry at reasonable resolution. For the estimated surface area, in contrast, when using marching cubes considerable deviations from the analytically calculated surface area are found even at relatively fine resolutions. These findings are especially important for the use of rasterized voxel data as input for engineering correlations to estimate characteristic physical transport properties such as pressure drop or effective heat transport.

Keywords

Voxel Raster data Porosity Specific surface area Additive manufacturing 

List of Symbols

A

Area [\(\hbox {L}^{2}\)]

h

Overlap [%]

L

Length [L]

R

Radius including overlap [L]

S

Surface area [L\(^{2}\)]

V

Volume [L\(^{3}\)]

\(\epsilon \)

Porosity [-]

Subscripts

real

Analytically calculated real value of ideal model structure

num

Numerically calculated approximation

sp

Sphere

sp,sp

Sphere–sphere (intersection)

cap

Spherical cap

tot

Total

V

Volumetric

1

Case for \(R-h=1.0\)

Abbreviations

bcc

Body-centered cubic

fcc

Face-centered cubic

sc

Simple cubic

line

Neighboring spheres share two coordinates

plane

Neighboring spheres share one coordinate

space

Neighboring spheres share no coordinate

Notes

Acknowledgements

The authors gratefully acknowledge the funding of the German Research Foundation (DFG), which, within the framework of its “Excellence Initiative”, supports the Cluster of Excellence “Engineering of Advanced Materials” at the Friedrich-Alexander-Universität Erlangen-Nürnberg (www.eam.fau.de).

Supplementary material

11242_2017_916_MOESM1_ESM.pdf (975 kb)
Supplementary material 1 (pdf 974 KB)

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Lehrstuhl für Chemische Reaktionstechnik, Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Regionales Rechenzentrum Erlangen, Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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