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Achieving the Inside–Outside Coupling During Network Simulation of Isothermal Drying of a Porous Medium in a Turbulent Flow

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Abstract

The problem of isothermal (slow) drying of a porous medium in the form of a square bluff body resting on a flat surface while being exposed to turbulent air flow is investigated in this paper. The porous medium is represented by a pore-network model consisting of a network of volume-less nodes connected to each other via narrow throats. As the air flows past the water-saturated network, the water evaporates in the network and the evaporated water vapors diffuse through the air inside the network to advect away in the outside domain. In the history of such simulations coupling the ‘outside–inside’ processes during drying, this paper investigates, for the first time, the effect of turbulent flow on drying of a porous medium after coupling the outside-the-network flow and transport with the inside-the-network drying and liquid redistribution. Also, a commercial software package is used for the first time to obtain the outside flow. The water redistribution inside the network is predicted by the invasion-percolation algorithm after assuming the dominance of capillary forces over viscous and gravity forces. The outside velocity field is first obtained using the \(k\hbox {-}\varepsilon \) model in ANSYS Fluent package. Then, the velocity field is used in a finite-volume-based code in order to solve for mass transfer outside the network using the regular convective-diffusive species transport equation. The drying mechanism and vapor transport inside the pore network is coupled with the outside mass-transfer simulation by considering a flux-balancing condition at the top surface of the network. After achieving grid independence and demonstrating the suitability of the no-slip boundary condition for the network top, the effects of the outside-flow Reynolds number and different turbulent flow models on several global drying parameters such as evaporation or drying rate, cumulative drying time, and top-surface saturation were studied. The resistance to vapor transport within the network was observed to dominate the enhanced vapor transport outside the network through the use of turbulent flow. Though the effect of variations in the network throat-size distribution upon saturation distribution within the network was found to be significant, its effect on the drying rate evolution was minimal. The concentration boundary layer thickness, which is employed to set the mass-transfer boundary condition in pore-network simulations and has been hitherto taken as constant in the literature, was found to change not only with position on the network top, but was also found to decline with time due to the drying of the network top.

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Notes

  1. Though the top of the network is porous, (Shaeri et al. 2013) found that due to very low velocities inside the network, the assumption of the no-slip boundary condition on top of the network for the determination of outside velocity field is quite accurate.

  2. The smallness of the throat diameter may raise a question about the applicability of the continuum models for simulating transport of phases through the network. If we choose the mean throat diameter as the characteristic width of the channels, the typical Knudsen number (Kn) for the throat will only be 0.00076 during the invasion of the throat by the air. And if it is full of water, Kn is even smaller. Note that the continuum hypothesis is applicable for \(Kn<< 1\) (Gad-el-Hak 1999–2006).

  3. Note that for extremely fine grids, it is possible that the distance between two neighboring nodes may become less than the mean free path of air molecules.

  4. Also known as the interface saturation or the top-plane saturation, this quantity is defined as the percentage of the combined volume of all top-plane throats occupied by the liquid.

  5. The reason for the jaggedness of the profile is that the vapor concentration is only checked at discrete grid points. For every line normal to the network top plane at a certain x, the concentration is monitored at all the grid points on that line. At the first grid point from the bottom where the concentration reaches below 1 % of the saturation concentration, the distance of that grid point to the network top plane is recorded as CBLT for that x. This method leads to steplike increases and decreases in the profile.

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Beyhaghi, S., Xu, Z. & Pillai, K.M. Achieving the Inside–Outside Coupling During Network Simulation of Isothermal Drying of a Porous Medium in a Turbulent Flow. Transp Porous Med 114, 823–842 (2016). https://doi.org/10.1007/s11242-016-0746-3

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