# Direct numerical simulations of moisture transport in porous media by a multi-component/phase-change lattice Boltzmann method

## Significance

Transport phenomena in porous media and their related applications in various fields have been extensively studied. Early theoretical studies mainly focused on investigating convective heat transfer in single-phase flow of water in fluid saturated porous media based on ad hoc mathematical formulation, which consisted of the classical continuity and energy equations plus the empirical Darcy’s law as the momentum equation. With the growing need for effective numerical simulation tools for studying two phase flow and heat transport in porous media with applications to geothermal energy and fuel cells, more rigorous mathematical formulation based on a volumetric average of conservation equations of heat, mass and energy on a representative volume has been reported.

The moisture transport in porous media is a more complex phenomenon due to the co-existence of the liquid and gaseous mixture, which is a multi-component multiphase flow and transport problem. In early days, the problem was simplified as diffusion of species. Subsequently, macroscopic models involving the derivation of volume-averaged equations and using Darcy’s law for each fluid phase as the momentum equation have been developed and widely used in the numerical study of multi-component/multiphase flows. However, the unavailability of correlation equations for physical parameters such as thermal conductivity and relative permeability in unsaturated porous media limit the application of this macroscopic approach. Other difficulties of this macroscopic approach are to take into consideration of contact angle (wettability) effects and to trace interfaces of phases numerically. The latter requires sophisticated numerical techniques.

Recently, the lattice Boltzmann (LB) method has been identified as a promising mesoscale method for simulating phase changes phenomena due to its advantage that contact angle effects can be taken into consideration easily, and it does not require tracking deforming interfaces. Due to these advantages, single-component/two-phase LB models have been used extensively for simulation of many condensations and boiling problems in recent years. The single component phase-change LB model has recently been extended to a multi-component phase-change LB model for studying droplet evaporation by Guo and Cheng.

Most recently, Baradaran Kazemian (PhD candidate), Qing Guo (PhD candidate) and led by Professor Ping Cheng from Shanghai Jiao Tong University used the newly developed multi-component phase-change LB scheme to study heat and mass transport simultaneously in the following two problems: (i). unsaturated porous media enclosure with differentially heated vertical walls, and (ii) the capillary rise of a liquid in porous hydrophilic beds initially filled with vapor/air mixture. The effects of homogeneity, contact angle, evaporation and directionality were also examined. This novel LB scheme does not require correlation equations for physical properties of the random porous media as input data.

For the first heat and mass transfer simulation problem, the authors showed that the mass transfer and transient heat occurred when the temperature on one of the vertical walls began to decrease. Accordingly, the fluid adjacent to the cold wall became denser to form a convective flow down the wall. The condensed humidity at the bottom of the cold wall released latent heat. Although the condensation effects caused temperature distribution and a drop in the relative humidity, the system attained a steady-state with new humidity and temperature distribution upon completion of condensation. For the second problem of capillary rise, the liquid rose to its final height due to capillary pressure, surface evaporation and gravity. The pressure and density of the various components were higher near the solid walls but decreased with an increase in height. Additionally, a decrease in the particle contact angle increased the steady-state liquid level. A faster and higher-level liquid rise was achieved in either heterogeneous or directional packed beds than in homogenous packed beds. The role of surface evaporation was instrumental in achieving the capillary rise in the packed hydrophilic bed. This work is currently published in the International Journal of Heat and Mass Transfer.

In summary, the research team used the newly developed multiphase-multicomponent LB method to simulate simultaneous heat and mass transfer process within packed beds with random structures. This is the first attempt to perform a direct numerical investigation of the moisture transport in an unsaturated random porous medium using a multi-component phase-change LB scheme without using any correlation equations for physical properties as input data, i.e., a direct numerical simulation. In a statement to Advances in Engineering, Professor Ping Cheng believes that the approach used in this paper has a wide range of applications for simulating moisture transport processes in random porous media without using correlation equations for physical properties of the random porous media filled with moist air as input data. The results of this study will have important applications in improving the design of evaporative cooling systems.

Ping Cheng received his B.S. degree from Oklahoma State University, M.S. degree in Mechanical Engineering from MIT, and Ph.D. degree in Aeronautics and Astronautics from Stanford University. He is a Chair Professor Emeritus in School of Mechanical Engineering at Shanghai Jiaotong University. Professor Cheng is an internationally renowned specialist in heat transfer. He has done seminal research work in porous-media heat transfer, radiative gas dynamics, and microscale boiling/condensation heat transfer. He has published over 320 SCI journal papers, and was listed as one of the world’s highly cited researchers by Thomson Reuters in 2014. Professor Cheng has received four top international honors, including 2006 ASME/AICHE Max Jakob Memorial Award, 1996 ASME Heat Transfer Memorial Award, 2003 AIAA Thermophysics Award, and 2006 ASME Heat Transfer Division Classic Paper Award. Professor Cheng is an elected member of Chinese Academy of Sciences, and a Fellow in both ASME and AIAA. He served as Editors for Int. J. Heat Mass Transfer and Int. Comm. Heat Mass Transfer for a period of 18 years from 2003 to 2021, and is a member of editorial board of 12 international heat transfer journals. He was the Chair of the 16th International Heat Transfer Conference, which was held in Beijing in 2018.

Behzad Baradaran Kazemian received his B.S. degree from Birjand University and his Master’s degree from Sharif University of Technology (Iran). He is a Ph.D. candidate at Shanghai Jiao Tong University, and his thesis supervisor is Professor Ping Cheng. His research interests are in the area of multi-phase flows, porous media, and boiling heat transfer.

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Qing Guo received her B.S. degree from Xi’an Jiaotong University. She is a Ph.D. candidate at Shanghai Jiao Tong University, and her thesis supervisor is Professor Ping Cheng. Her research interests are in the area of phase change in moist air, nucleation and ice growth during freezing.

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Reference

Kazemian, B., Guo, Q., & Cheng, P. (2021). Direct numerical simulations of moisture transport in porous media by a multi-component/phase-change lattice Boltzmann methodInternational Journal of Heat and Mass Transfer, 176, 121264.