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PathFinder (C) Wojciech Sobieski - a program destined for analysis the spatial structure of granular beds, or its parts, of a cylindrical or cubical shape (Fig. 1). The program is available free of charge with source code and can be used on Windows or Unix/Linux. The program needs additional software to work: gfortran compiler (for compiling source code), the Gnuplot environment (for basic visualization and analysis of the calculations) and ParaView (for the visualization and analysis of results). These programs are also available free of charge under the GPL license for both Windows and Unix/Linux.

Path Tracking Method (PTM) (C) Wojciech Sobieski - iterative method of determination of the length of pore channel in the chosen space direction, which consists in analyzing the local structure of the pore space based on vector geometry.

In the case of Pathfinder code, the length of pore channel is determined between two parallel planes based on the sum of the unitary lengths, calculated based on so-called tetrahedral structures (Fig. 2), which establish the basis for the calculation algorithm. Tetrahedral structures are created based on the data on the location and diameter of each particle in the bed. The data for calculations are obtained from DEM simulation or from the analysis of a set of tomography scans. Details concerning method are available in the User's Guide.

Wojciech Sobieski developed PTM for granular beds in 2009 during an internship at the University of Manitoba in Winnipeg (see the official confirmation). The inspiration to start work on a method was observation, resulting from the author's extensive experience in programming, that DEM simulation results can be used to analyze the internal structure of porous media, in particular for the calculation of various geometrical parameters, including tortuosity. In 2009, the first working version of the program was created; the process of its creation was described in the Research Report 1/2009 (in Polish or in English) This report later became the basis for several articles in peer-reviewed journals.

Licence: The conditions for using each of elements of the PathFinder project are as follows:

• The software is free of charge and can be used for any purpose by institutions and individuals.
• In case of publishing any material, for creation of which contributed the elements of the PathFinder project, in particular scientific articles, their authors are required to cite suitable articles from publication lists placed on the project website.
• In case of redistribution of the software, no part of the installation package can be removed, in particular the terms of the license.
• Copyright holders of each component of the project are indicated in the headers of the source code or in the documentation.
• The authors of the project are not responsible for any damage or losses resulting from the use of software and the use of the information contained therein. The authors also assure that they have made every effort to make the project error-free and containing reliable information.

Download:	Description:
	PathFinder IV.3 – source code with examples
	pathGUI 1.2.2 – source code
	PathFinder IV.3 – Users Guide v. IV.3
	Path Tracking Method - short presentation

Features of PathFinder program:

• calculation of bed height (with a correction of its upper surface)
• calculation of bed volume
• calculation of pore volume of the bed
• calculation of porosity
• calculation of total outer surface of bed particles
• calculation of the specific surface area as defined by Kozeny and Carman
• determination of default starting coordinates for the so-called nine-point method
• calculation of path length (a path that fluid will travel between particles, moving in flow direction - the Z-axis), in the five characteristic locations of bed
• calculation of path length using smoothing algorithm (for fluid can not change the direction of movement suddenly), in five characteristic locations of bed
• calculation of number of points and sections of path
• calculation of angles between successive segments of path and average angle
• computing total area and wet area for each triangle
• computing total perimeter, wet perimeter and friction perimeter for each triangle
• calculation of tortuosity
• calculation of tortuosity using the Yu-Li formula
• calculation of the linear term of Kozeny-Carman equation (with a model constant equal to 1)
• calculation of the linear and nonlinear terms of Ergun equation
• calculation of the deviation (distance) of path points from the plumb-line
• visualization of the deviation (distance) of path points from the plumb-line
• visualization of the spatial step changes in path points on Z directions
• visualization of the tortuosity distribution in characteristic bed points

Installation package contains also User's Guide as well as a few supporting tools:

• pathGUI - graphical interface (currently for Windows only)
• program converting PFC3D output files to PathFinder input files
• program converting YADE output files to PathFinder input files
• program calculating values of Kozeny-Carman equation for air flow
• program calculating values of Ergun equation for air flow
• program for sensitivity analysis of Kozeny-Carman and Ergun models

References:

• Sobieski W., Lipiński S.: The influence of particle size distribution on parameters characterizing the spatial structure of porous beds. GRANULAR MATTER, Vol. 21:14 (2019), 15 p. DOI: https://doi.org/10.1007/s10035-019-0866-x
• Sobieski W., Matyka M., Gołembiewski J., Lipiński S.: The Path Tracking Method as an alternative for tortuosity determination in granular beds. GRANULAR MATTER, Vol. 20:72 (2018), 14 p. DOI: https://doi.org/10.1007/s10035-018-0842-x
• Sobieski W., Lipiński S., Dudda W., Trykozko A., Marek M., Wiącek J., Matyka M., Gołembiewski J.: Granular porous media (in Polish). Department of Mechanics and Machine Design, Olsztyn 2016. ISBN 978-83-60493-04-5.
• Dudda W., Sobieski W.: Modification of the PathFinder algorithm for calculating granular beds with various particle size distributions. TECHNICAL SCIENCES, Vol. 17, No 2 (2014), pp. 135-148. ISSN 1505-4675.
• Sobieski W., Lipiński S.: PathFinder User's Guide. University of Warmia and Mazury in Olsztyn (Poland), 2013.
• Sobieski W., Zhang Q., Liu, C.: Predicting tortuosity for airflow through porous beds consisting of randomly packed spherical particles. TRANSPORT IN POROUS MEDIA, Vol. 93, No. 3 (2012), pp. 431-451.
• Liu, C. Zhang Q., Chen Y.: Discrete element simulations of vibration characteristics of bulk grain in storage bins. Transactions of the ASABE, Vol. 53, No. 5 (2010), pp. 1653-1659.
• Sobieski W.: Calculating tortuosity in a porous bed composed of spherical particles with known size and distribution in space. Research Report 1/2009.
• Sobieski W.: GNU Fortran with data visualization elements (in Polish). University of Warmia and Mazury, Olsztyn 2008, 403 pages.
• Liu, C., Zhang Q., Chen Y.: PFC3D simulations of lateral pressures in model bins. Paper No 083340 (2008). American Society of Agricultural and Biological Engineers, St. Joseph, MI. 13 pp.
• Liu, C., Zhang Q., Chen Y.: PFC3D simulations of vibration characteristics of bulk solids in storage bins. Paper No 083339 (2008), American Society of Agricultural and Biological Engineers, St. Joseph, MI. 14 pp.