Advanced Reduced-Order Models for Moisture Diffusion in Porous Media

Abstract

It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are promising approaches to bring a solution to this issue since they do not degrade the physical model and provide a significant reduction of computational cost. Therefore, this article explores in details the capabilities of two model-reduction techniques -the Spectral Reduced-Order Model (Spectral-ROM) and the Proper Generalised Decomposition (PGD) -to numerically solve moisture diffusive transfer through porous materials. Both approaches are applied to three different problems to provide clear examples of the construction and use of these reduced-order models. The methodology of both approaches is explained extensively so that the article can be used as a numerical benchmark by anyone interested in building a reduced-order model for diffusion problems in porous materials. Linear and non-linear unsteady behaviors of unidimensional moisture diffusion are investigated. The last case focuses on solving a parametric problem in which the solution depends on space, time and the diffusivity properties. Results have highlighted that both methods provide accurate solutions and enable to reduce significantly the order of the model around ten times lower than the large original model. It also allows an efficient computation of the physical phenomena with an error lower than 10 −2 when compared to a reference solution.

Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

“…With spectral methods [20], the PGD method is one of the unique methods that allows to create a complete parametric model without knowing a priori the solution of the problem.…”

Machine Learning-Based Soft Sensors for the Estimation of Laundry Moisture Content in Household Dryer Appliances

“…As a matter of fact, in several cases, the advection moisture transfer phenomenon should also be considered in the context of porous media. Moisture advection is the transport of water vapor by the air and is included as an additional term in the equation of the process (4) (details are not reported here, the reader can see [28,29] as recent references). Berger et al [28] show the inclusion of an advective term in the model and results in the context of moisture transfer in porous building elements, whereas Gasparin et al [29] discuss numerically efficient methods for moisture diffusion, with a reduced computational effort.…”

“…Moisture advection is the transport of water vapor by the air and is included as an additional term in the equation of the process (4) (details are not reported here, the reader can see [28,29] as recent references). Berger et al [28] show the inclusion of an advective term in the model and results in the context of moisture transfer in porous building elements, whereas Gasparin et al [29] discuss numerically efficient methods for moisture diffusion, with a reduced computational effort. Azeem et al [30] focused recently on a review on the liquid moisture transport behavior of fabric, stating that transportation of liquid water in the fabric cannot be defined at only one condition, but a range of conditions that should be measured regarding the ability to transport liquid moisture.…”

A spectral method for solving heat and moisture transfer through consolidated porous media

“…In recent works, researchers have implemented spectral methods for solving heat and moisture transfer in food engineering and on fluid flow . Recently, Gasparin et al, have studied the moisture transfer in porous building materials considering layered domains, and in the other work of Gasparin et al, they have compared the spectral method to others ROMs, applied to parametric problems of the building physics field.…”

“…Therefore, the scope of this work is to continue the investigations presented in [20] and [18], extending it to the coupled heat and mass transfer. Here, the Spectral method is used to compute one-dimensional heat and moisture diffusion transfer in porous materials, which is validated against experimental data from the literature.…”