A Fourier Series Solution for Transient Three‐Dimensional Thermohaline Convection in Porous Enclosures

Abstract

Thermohaline convection (THC) in porous media is frequently investigated using the problem of porous enclosure. Most of the existing modeling-based studies are limited to 2-D simulations, because 2-D assumption is widely used to deal with computational requirement of 3-D numerical solutions. Analytical solutions serve as an alternative to deal with computational requirement of numerical solutions. Existing analytical solutions of THC are mostly limited to 2-D and also under steady-state regime. In this work, we develop a meshless 3-D semianalytical solution for the problem of THC in a porous box under crossed thermal and solute gradients, for both steady state and transient regimes. The semianalytical solution is developed using the Fourier series (FS) method applied to the vector potential form of the governing equations. The extension to transient solutions represents an important technical feature of this work, as the applications of the FS method to density-driven problems have been limited to steady-state conditions. The FS solution is validated against a finite element solution obtained using COMSOL Multiphysics. Numerical experiments show the worthiness of the developed FS solution as a benchmark because it clearly allows making distinction between different numerical techniques. The effects of governing parameters on three-dimensional THC have not been investigated previously. We perform a detailed parameter sensitivity analysis to address this gap. A vortex convective flow is observed and the orientation and intensity of the flow is sensitive to the gravity number. The increase in the temperature gradient reduces the salinity flux.

Effect of temperature on convective-reactive transport of CO2 in geological formations

“…This method leads to high accuracy solutions as it reduces numerical diffusion and unphysical oscillations (Miller et al, 2013). The dispersion-diffusion operators for mass and heat transfer are discretized using the MPFA method (Younes et al, 2013) Advantages of this combination of FE formulations have been discussed in (Fahs et al, 2016;Shao et al, 2018;Tabrizinejadas et al, 2020). The equations of flow, mass transfer and energy balance, under variable density, are solved sequentially.…”

“…Thus, Dirichlet boundary conditions of temperature and concentration on the vertical walls of the domain and assuming that there is no heat and mass fluxes across the horizontal walls. This case is inspired from (Tabrizinejadas et al, 2020).In order to avoid potential numerical oscillations in the FE solution, the comparison between TRACES and COMSOL is made for a test case with a smooth distribution of concentration and temperature (low convective flow regime and relatively slow reaction rate).…”

“…In the previous sections, Nusselt and Sherwood number are used to discuss the accuracy of the newly developed numerical model. As common in the literature (Tabrizinejadas et al, 2020), these numbers are used to provide quantitative comparison between different models. In this section, as the main goal is understanding the effect of temperature on convective processes of CO2 we used more relevant outputs, as follows:…”

Salinity and Temperature Variations near the Freshwater-Saltwater Interface in Coastal Aquifers Induced by Ocean Tides and Changes in Recharge

“…A fully saturated porous media was assumed with changes in the boundary conditions to replicate tidal oscillations to simplify the system. The model represented the effect of fluid density variations, which are caused by temperature and solute concentration variations [59,60]. In a similar manner, fluid viscosity was considered using an equation of state that relates viscosity to concentration and temperature [56].…”