On the Solution of Coupled Heat and Moisture Transport in Porous Material

Abstract

Comparisons of experimental observation of heat and moisture transfer through porous building materials with numerical results have been presented in numerous studies reported in literature. However, some discrepancies have been observed, highlighting underestimation of sorption process and overestimation of desorption process. Some studies intend to explain the discrepancies by analysing the importance of hysteresis effects as well as carrying out sensitivity analyses on the input parameters as convective transfer coefficients. This article intends to investigate the accuracy and efficiency of the coupled solution by adding advective transfer of both heat and moisture in the physical model. In addition, the efficient Scharfetter and Gummel numerical scheme is proposed to solve the system of advection-diffusion equations, which has the advantages of being wellbalanced and asymptotically preserving. Moreover, the scheme is particularly efficient in terms of accuracy and reduction of computational time when using large spatial discretisation parameters. Several linear and non-linear cases are studied to validate the method and highlight its specific features. At the end, an experimental benchmark from the literature is considered. The numerical results are compared to the experimental data for a pure diffusive model and also for the proposed model. The latter presents better agreement with the experimental data. The influence of the hysteresis effects on the moisture capacity is also studied, by adding a third differential equation.

An efficient numerical model for the simulation of coupled heat, air, and moisture transfer in porous media

“…As one may notice, the stability conditions of the latter equation is nonlinear with respect to Δ x . For large space discretisation Δ x , and we obtain . Thus, it is one order less restrictive than standard approach and the so‐called COURANT‐FRIEDRICHS‐LEWY (CFL) conditions .…”

“…Then, for the heat and mass advection‐diffusion Equations and , the SCHARFETTER‐GUMMEL numerical scheme is used. Preliminary studies showed the efficiency of the approach to extend the stability conditions and the accuracy of the solution. As a last step of the proposed methodology, the time discretisation of these two equations, an innovative two‐step RUNGE‐KUTTA approach is used of the time discretisation of these two advection‐diffusion equations, enabling to extend further the stability region of the numerical scheme .…”

“…Similar approach can be applied to the boundary conditions at x = 1 and for the field v. Furthermore, It can be extended to any type (NEUMANN or DIRICHLET) of boundary condition along the directions given above. Interested readers are invited to consult 24 for more details.…”

“…For large space discretisation Δx, tanh ( a kl,j Δx 2k kl,j ) = (1) and we obtain Δt ≤ CΔx. 24 Thus, it is one order less restrictive than standard approach and the so-called COURANT-FRIEDRICHS-LEWY (CFL) conditions Δt ≤ CΔx 2 . Using, the SCHARFETTER-GUMMEL scheme, the spatial discretisation does not need to be extremely refined.…”

Critical assessment of a new mathematical model for hysteresis effects on heat and mass transfer in porous building material

“…Various works in the literature highlight these results. In [3][4][5], it was demonstrated that the simulation of material moisture buffering capacity is inaccurate without hysteresis effects. In [6], the absence of hysteresis in the model yield in the prediction of erroneous indoor air comfort.…”