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Current hygrothermal behaviour prediction models neglect the hysteresis phenomenon. This leads to a discrepancy between numerical and experimental results, and a miscalculation of buildings' durability. In this paper, a new mathematical model of hysteresis is proposed and implemented in a hygrothermal model to reduce this discrepancy. The model is based on a symmetry property between sorption curves and uses also a homotopic transformation relative to a parameter s ∈ [ 0 , 1 ]. The advantage of this model lies in its ease of use and implementation since it could be applied with the knowledge of only one main sorption curve by considering s = 0 , in other words, we only use the axisymmetric property here. In the case where the other main sorption curve is known, we use this curve to incorporate the homotopy property in order to calibrate the parameter s.The full version of the proposed model is called Axisymmetric + Homotopic. Furthermore, it was compared not only with the experimental sorption curves of different types of materials but also with a model that is well known in the literature (CARMELIET's model). This comparison shows that the Axisymmetric + Homotopic model reliably predicts hysteresis loops of various types of materials even with the knowledge of only one of the main sorption curves. However, the full version of Axisymmetric + Homotopic model is more reliable and covers a large range of materials. The proposed model was incorporated into the mass transfer model. The simulation results strongly match the experimental ones. [ABSTRACT FROM AUTHOR]

The design of numerical tools to model the behavior of building materials is a challenging task. The crucial point is to save computational costs and maintain the high accuracy of predictions. There are two main limitations on the time scale choice, which places an obstacle to solving the above issues. The first one is the numerical restriction. A number of research studies are dedicated to overcome this limitation and it is shown that it can be relaxed with innovative numerical schemes. The second one is the physical restriction. It is imposed by the properties of a material, the phenomena itself, and the corresponding boundary conditions. This study is focused on the study of a methodology that enables to overcome the physical restriction on the time grid; a so‐called average reduced model is suggested. It is based on smoothing the time‐dependent boundary conditions. Besides this, the approximate solution is decomposed into average and fluctuating components. The primer is obtained by integrating the equations over time, whereas the latter is a user‐defined EM. The methodology is investigated for both heat diffusion and coupled heat and mass transfer. It is demonstrated that the signal core of the boundary conditions is preserved and the physical restriction can be relaxed. The model proved to be reliable, accurate, and efficient also in comparison with the experimental data of 2 years. The implementation of the scarce time‐step of 1h is justified. It is shown, that by maintaining the tolerable error, it is possible to cut computational effort up to almost four times in comparison with the complete model with the same time grid. [ABSTRACT FROM AUTHOR]

The sorption curve is an essential feature for the modelling of heat and mass transfer in porous building materials. Several models have been proposed in the literature to represent the amount of moisture content in the material according to the water activity (or capillary pressure) level. These models are based on analytical expressions and few parameters that need to be estimated by inverse analysis. This article investigates the reliability of eight models through the accuracy of the estimated parameters. For this, experimental data for a wood fibre material are generated with special attention to the stop criterion to capture long time kinetic constants. Among five sets of measurements, the best estimate is computed. The reliability of the models is then discussed. After proving the theoretical identifiability of the unknown parameters for each model, the primary identifiability is analysed. It evaluates whether the parameters influence on the model output is sufficient to proceed the parameter estimation with accuracy. For this, a continuous derivative-based approach is adopted. Seven models have a low primary identifiability for at least one parameter. Indeed, when estimating the unknown parameters using the experimental observations, the parameters with low primary identifiability exhibit large uncertainties. Finally, an Approximation Bayesian Computation algorithm is used to simultaneously select the best model and estimate the parameters that best represent the experimental data. The GAB and Fredlund-Xing models, together with a proposed model in this work, were the best ones selected by this algorithm. [ABSTRACT FROM AUTHOR]

• D-optimum criterion is applied to select an optimal experiment duration. • Identifiability of parameters is demonstrated. • Thermal conductivity is estimated over the reduced measurement plan. • Parameter estimation problem is solved with hybrid optimization method. • Reliability of the model for one year experiment is achieved. The in situ estimation of the thermal properties of existing building wall materials is a computationally expensive procedure. Its cost is highly proportional to the duration of measurements. To decrease the computational cost a methodology using a D-optimum criterion to select an optimal experiment duration is proposed. This criterion allows to accurately estimate the thermal properties of the wall using a reduced measurement plan. The methodology is applied to estimate the thermal conductivity of the three-layer wall of a historical building in France. Three different experiment sequences (one, three and seven days) and three spatial distributions of the thermal conductivity are investigated. Then using the optimal duration of observations the thermal conductivity is estimated using the hybrid optimization method. Results show a significant reduction of computational time; and reliable simulation of physical phenomena using the estimated values. [ABSTRACT FROM AUTHOR]

The reliability of mathematical models for heat and mass transfer in building porous material is of capital importance. A reliable model permits to carry predictions of the physical phenomenon with sufficient confidence in the results. Among the physical phenomena, the hysteresis effects on moisture sorption and moisture capacity need to be integrated in the mathematical model of transfer. This article proposes to explore the use of an smooth Bang–Bang model to simulate the hysteresis effects coupled with heat and mass transfer in porous material. This model adds two supplementary differential equations to the two classical ones for heat and mass transfer. The solution of these equations ensures smooth transitions between the main sorption and desorption curves. Two parameters are required to control the speed of transition through the intermediary curves. After the mathematical description of the model, an efficient numerical model is proposed to compute the fields with accuracy and reduced computational efforts. It is based on the Du Fort–Frankel scheme for the heat and mass balance equations. For the hysteresis numerical model, an innovative implicit–explicit approach is proposed. Then, the predictions of the numerical model are compared with experimental observations from literature for two case studies. The first one corresponds to a slow cycle of adsorption and desorption while the second is based on a fast cycling case with alternative increase and decrease of moisture content. The comparisons highlight a very satisfactory agreement between the numerical predictions and the observations. In the last Section, the reliability and efficiency of the proposed model is investigated for long term simulation cases. The importance of considering hysteresis effects in the reliability of the predictions are enhanced by comparison with classical approaches from literature. • Building numerical model for heat and mass transfer with hysteresis effects. • Use of Bang–Bang model for modeling hysteresis on moisture sorption and capacity. • Comparison of the model reliability with two experimental benchmark from literature. • Saved computational effort and satisfactory agreement with experimental observations. [ABSTRACT FROM AUTHOR]