Predicting Tortuosity for Airflow Through Porous Beds Consisting of Randomly Packed Spherical Particles

Abstract

This article presents a numerical method for determining tortuosity in porous beds consisting of randomly packed spherical particles. The calculation of tortuosity is carried out in two steps. In the first step, the spacial arrangement of particles in the porous bed is determined by using the discrete element method (DEM). Specifically, a commercially available discrete element package (PFC 3D ) was used to simulate the spacial structure of the porous bed. In the second step, a numerical algorithm was developed to construct the microscopic (pore scale) flow paths within the simulated spacial structure of the porous bed to calculate the lowest geometric tortuosity (LGT), which was defined as the ratio of the shortest flow path to the total bed depth. The numerical algorithm treats a porous bed as a series of four-particle tetrahedron units. When air enters a tetrahedron unit through one face (the base triangle), it is assumed to leave from another face triangle whose centroid is the highest of the four face triangles associated with the tetrahedron, and this face triangle will then be used as the base triangle for the next tetrahedron. This process is repeated to establish a series of tetrahedrons from the bottom to the top surface of the porous bed. The shortest flow path is then constructed geometrically by connecting the centroids of base triangles of consecutive tetrahedrons. The tortuosity values calculated by the proposed numerical method compared favourably with the values obtained from a CT image published in the literature for a bed of grain (peas). The proposed model predicted a tortuosity of 1.15, while the tortuosity estimated from the CT image was 1.14.

The use of Path Tracking Method for determining the tortuosity field in a porous bed

“…-The Standard Method seems to be sufficient if only the average value of the tortuosity is needed. This conclusion is in agreement with the earlier investigations, described in the paper [32]. -It can be assumed that the relative error between average values obtained with the use of the SM and the RGM increases if the number of particles grows.…”

“…If such a structure is defined, the analysis of the local spatial arrangement of the particles is than possible. The description of the PTM may be found in the following papers [27,32,33,36,37] and that is why it is not described in detail in the hereby article. The algorithm for calculating path length L g p may be summarized as follows ( in which the next sphere (P4) surrounding the path should be located; -Move the Ideal Location closer to the triangle plane (due to the fact, that particles forming the triangle basis may be separated from one another and in such case the fourth particle is located closer to the triangle plane); -Find the particle nearest to the Ideal Location-this is the Real Location (RL) of the 4th particle forming tetrahedron in the space; -Remove the lowest sphere from tetrahedron 1-4 to obtain the base triangle for the next tetrahedron; -Calculate the local length of the path inside the current tetrahedron (a local path is the line connecting centroids of base triangles of two neighbouring tetrahedrons); -Continue the calculations, until reaching the top surface of the bed.…”

“…To reach the article aim the so-called Path Tracking Method (PTM), developed by the author in the year 2009 and recently improved, is applied here. In the report [27] and paper [32], the mathematical basis of the PTM were shown as well as the first experimental verification of this approach. In the work [33], a mathematical modification of the PTM was described.…”

Changes in Pore Structures of Porous Beds When Subjected to Vertical Vibration

“…However, flowing air cannot make sharp turns. Therefore, a procedure proposed by Sobieski W. et al (2012) was used to replace each sharp turn angle with an arc (Fig. 3). …”

“…et al, 2008;Yiotis A.G. et al, 2010) and 3D models (Balhoff M.T. et al, 2007;Sobieski W. et al, 2012;Thompson K.E., 2002;Thompson K.E. and Fogler H.S., 1997) have been developed to describe pore structures of porous media.…”