Dynamic state-space model and performance analysis for solar active walls embedded phase change material

Highlights

• An adaptive dynamic state space model is proposed to model innovative PCM-based active solar system.

• The passive part of the model is validated by attended experimental setup.

• A finite difference-based numerical scheme is proposed to resolve the state space model.

• The thermal performances of the system are then evaluated by dynamic simulation.

Abstract

Building-based active envelopes play an important role to reduce active heating supplies. Several techniques are developed to enhance the energy performances of active building envelopes; meanwhile, numerous numerical and mathematical models are also developed to conduct the performance analysis of these techniques. In this paper, we propose a state-space model for solar active wall-based Phase Change Materials (PCM). The advantage of this method remains in its simplicity to provide details of internal nodes and input/output parameters. The low-cost calculation is a supplementary advantage versus a heavy numerical method. The proposed numerical model is applied for a multi-layer wall with PCM Wallboards (PCMW) embedded between indoor and outdoor environments. The results show the ability of the state-space model to estimate the thermal behavior of the system, as well as the thermal characteristics of embedding PCM in the internal face of the wall. It significantly contributes to stabilize the indoor temperature and to ensure the thermal comfort.

Introduction

The International Energy Agency (IEA) reported that buildings are the largest energy-consuming sector in the world and they account for over one-third of the total final energy consumption and are equally an essential source of carbon dioxide [1]. However, reducing the energy consumption in our buildings while guaranteeing thermal comfort constitutes a challenge today.

The phase change materials (PCMs) are substances that can release and absorb latent heat simultaneously during phase change process. They are largely used in energy storage systems [2], [3], [4], [5] as in building integration technics. Two building-integrated PCM options are found in the literature, the first one is passive solution [6], [7], [8], [9], [10], [11] which consists to store natural heat gains and restitute it in the needing time. The benefit of passive option is to reduce the PCM volume in a composite wall by increasing the microencapsulated PCM mass fraction, as well as to improve the energy efficiency compared to conventional building materials [12] and [13]. Cui et al. [14] found with using a developed structural–functional integrated energy storage concrete with innovative microencapsulated PCM that the indoor room temperature is 3%–6% lower than that of normal concrete panels. Some tests and thermal performance evaluations of two identical rooms constructed by incorporating PCM-based paraffin on the roofs and walls [15] concluded that rooms without PCM consume more energy than rooms integrated with PCM under the conditions of an outdoor temperature of 40–44 °C, to stabilize the indoor thermal comfort at 24 °C. Hu et al. [16] reviewed the application of the Trombe wall system in a building that allows accumulating solar heat and provides the heat inside the building for its space heating. Lei et al. [17] emphasized the effect of lowering the energy gains through PCMs incorporated in building envelopes in tropical areas throughout the whole year, while other regions have a seasonal impact on the PCMs. Madessa [18] reviewed the application of PCMs in a building located in a northern cold climate and highlighted the effect of a PCM on savings in terms of energy gains and costs eventually in peak periods. Marin et al. [19] studied the performance of PCM integration for different climates by using relocatable lightweight buildings integrated with PCM. Yao et al. introduce a novel technic to fabricate preferment PCM made up with paraffin and expended perlite, and they show high energy reducing performance in building application [8]. From these previous works, it can be conclude that the PCM integration by passive way play an important role in building envelope such as in roofs and walls, but the limitation of this way manifested in winter, when the outside temperature is low, then the natural heat source cannot accomplish the PCM thermal cycle.

The second type can substitute the passive integration in winter which is qualified as active PCM integration that use active heat supply to improve the heat amount to the PCM in winter. Active wall techniques constitute one of improved possibilities for enhancing the thermal performance of building envelopes. Navarro et al. [20] reviewed different energy-saving and storage strategies for passive and active systems and promoted that the building core activation of PCMs is the demonstrated to an interesting technology for new constructions. Hasan et al. [21] investigated the impact of integrated solar photovoltaic cells with active PCM latent heat storage system which results the increase of the PV efficiency by 7.2% at peak and 5.5% on daily average. Kong et al. [10] developed a novel experimental hybrid system of active composite PCM and solar thermal for clean heating supply in winter that can reduce energy consumption in building by 44.16%. Li et al. [22] innovated further this system with integrating parabolic through collector (PTC) as solar thermal source, and they reached an optimal set of system parameters for 0.024 m² of collector area, hot water flow of 2.8 kg/s, initial melting temperature of 27 °C, and 20 mm of the optimal PCM thickness. In other works, Li et al. [23] proposed multi-layer roof system integrated with 30 mm thicknesses of PCM and actively ventilated to fulfill the energy needing inside the building. The found results show high performances in temperature reduction and enhancement in time delay of peak temperature achievement. The active PCM technics integrated building envelopes has been also innovatively designed and optimized by Qiao et al. [11] by developing active solar heating wall with PCM. They found that the optimal designs that guaranty the indoor thermal comfort is that which the PCM wallboard is too close to inner surface with 3 cm thickness’s and 9 water pipes capillaries and for 30° heating temperature.

Despite these experimental works, it is still essential to develop a robust mathematical and numerical model to accurately and quickly predict the thermal behavior of a building to achieve several goals, such as thermal control vs. ambient and load fluctuations, an optimization design, and thermodynamic analysis. The works of Yu et al. [24] indicated good agreement of a state-space thermal model of an active flat plate solar thermal collector integrated into a building wall with experimental work. Elarga et al. [25] proposed a simplified model for a mechanically ventilated double skin façade for dynamic simulations and validated the results with another detailed simulation model. The advantage of their method is to obtain an accurate simplified model for designers to guide them, making the right decision without an extensive scientific background. However, the percentage differences between their model and the validated cases are still higher in summer, when the solar gains become more important. Oliviti et al. [26] developed an accurate model in a steady periodic state for external walls by the harmonic method. Their study considered the external air temperature, the apparent sky temperature and solar irradiation as loads. Ogunsola et al. [27] used simplified equations for a differential system for a real-time thermal load simulation. They achieved satisfactory results compared to heavy mathematical models. Kharbouch et al. [6] developed a numerical model based on the finite difference method for PCMW. Sassine et al. [28] proposed a practical in situ methodology based on a mathematical model for the thermal characterization of existing walls with reasonable accuracy. Nevertheless, the method remains unsophisticated from an experimental point of view since it does not require any imposition of particular boundary conditions. Kibria et al. [29] studied numerically the effect of managing high-temperature influences on the PV module and PCM system integrated into buildings in transient mode.

In this paper, through embedding PCM Wallboards (PCMW) in internal faces as well as integrating active solar collectors in the external face, we can improve the energy efficiency and allow stabilizing temperature shapes in the indoor climate, ensuring more indoor thermal comfort. The research work suggests a developed mathematical transient model for innovative “multi-component” system. The original idea may resolve the problem with the so called state-space method, as well as, to provide an opening on the development of flexible and simple mathematical models for building integrated solar thermal systems. Even more, the dynamic state-space model knows as prospect framework to manage and control the systems behavior.