Pore scale evaluation of thermal conduction anisotropy in granular porous media using Lattice Boltzmann method

Abstract

Purpose Thermal conduction anisotropy, which is defined by the dependency of thermal conductivity on direction, is an important parameter in many engineering and research studies such as the design of nuclear waste depositional sites. In this context, the authors aim to investigate the effect of grain shape in thermal conduction anisotropy using pore scale modeling that utilizes real shapes of grains, pores and throats to characterize petrophysical properties of a porous medium. Design/methodology/approach The authors generalize the swelling circle approach to generate porous media composed of randomly arranged but regularly oriented elliptical grains at various grain ratios and porosities. Unlike previous studies that use fitting parameters to capture the effect of grain–grain thermal contact resistance, the authors apply roughness to grains’ surface. The authors utilize Lattice Boltzmann method to solve steady state heat conduction through medium. Findings Based on the results, when the temperature field is not parallel to either major or minor axes of grains, the overall heat flux vector makes a “deviation angle” with the temperature field. Deviation angle increases by augmenting the ratio of thermal conductivities of solid to fluid and the aspect ratios of grains. In addition, the authors show that porosity and surface roughness can considerably change the anisotropic properties of a porous medium whose grains are elliptical in shape. Originality/value The authors developed an algorithm for generation of non-circular-based porous medium with a novel approach to include grain surface roughness. In previous studies, the effect of grain contacts has been simulated using fitting parameters, whereas in this work, the authors impose the roughness based on the its fractal geometry.

Effect of deformation on the thermal conductivity of granular porous media with rough grain surface

“…The algorithm is referred to as the swelling circles algorithm, which is based on the gradual evolution of the grains in a porous medium as explained by Fyrillas and Pozrikidis [2001] and Askari et al [2016]. The algorithm is referred to as the swelling circles algorithm, which is based on the gradual evolution of the grains in a porous medium as explained by Fyrillas and Pozrikidis [2001] and Askari et al [2016].…”

“…We developed a computer simulator to construct 2-D porous media for a given grain-size distribution. The algorithm is referred to as the swelling circles algorithm, which is based on the gradual evolution of the grains in a porous medium as explained by Fyrillas and Pozrikidis [2001] and Askari et al [2016]. To construct the model granular medium, we need to define (i) a frame containing the grains, (ii) the number of the grains, and (iii) the grain-size distribution.…”

“…Fyrillas and Pozrikidis [2001] developed an analytical model for periodic rough surfaces with small amplitudes, while Laraqi and Bairi [2002] developed a similar model in which the contact area was composed of numerous circles of various radii that were randomly distributed over the contacting surfaces. There have also been several studies of conduction in dry soil and other types of granular media [Yun and Santamarina, 2008;Wang et al, 2013;Tsory et al, 2013;Askari et al, 2015Askari et al, , 2016. There have also been several studies of conduction in dry soil and other types of granular media [Yun and Santamarina, 2008;Wang et al, 2013;Tsory et al, 2013;Askari et al, 2015Askari et al, , 2016.…”

“…Wang et al [2013] investigated the effect of grain size on the effective thermal conductivity of granular porous media. Choo et al [2013] evaluated the anisotropy that is induced in conduction through dry granular media when they are subject to external stress, while Askari et al [2016] assessed the effect of grain shape on the anisotropy.…”

“…Several other such analytical models for conductions in porous media with rough surfaces exist [Zhang et al, 2004;Lee et al, 2008;Wang and Zhao, 2010;Belghazi et al, 2010]. There have also been several studies of conduction in dry soil and other types of granular media [Yun and Santamarina, 2008;Wang et al, 2013;Tsory et al, 2013;Askari et al, 2015Askari et al, , 2016. For example, Askari et al [2015] discussed the possibility of including the effect of surface roughness in the numerical simulation of conduction in the Utah oil sand data.…”