Uncertainty and global sensitivity analysis on thermal performances of pipe-embedded building envelope in the heating season

Highlights

• Uncertainty and sensitivity analysis framework for pipe-embedded walls is proposed.

• The variables’ ranking is obtained by two different sensitivity analysis methods.

• Four key variables are identified, and the pipe spacing affects heat accumulation.

• The climate zone no longer dominates the thermal radiation of the interior surface.

• Pipe location has a slight influence on heat transfer indicators of wall surfaces.

Abstract

Pipe-embedded building envelope, which is of particular interest to architects and engineers due to its excellent performances and invisibility characteristic, has been regarded as a potential technology for future buildings. Understanding the impacts of multiple uncertainties associated with design, construction, and operational control on its thermal performances is critical to the development of this burgeoning active insulation technology. Aiming at this goal, an in-depth uncertainty analysis (UA) and global sensitivity analysis (GSA) study was numerically conducted to investigate the influence mechanism of 12 different variables on 5 performance indicators in winter conditions. The UA results indicated that a dual-effect, i.e., better indoor thermal comfort and “zero” or even “negative” thermal load of the exterior walls, could be achieved only when relevant variables were properly selected. Due to the increase in the quantities and types of input variables, as well as the internal heat transfer process became more complicated, the importance rankings of variables obtained by two different GSA methods became different. Therefore, the treed Gaussian process method was proven to be more effective in identifying the uncertain variables. The GSA results stated that heat-source temperature, indoor set-point, charging duration, and thermal conductivity of pipe-embedded layer were the four most significant variables. For heat-source temperature and indoor set-point, there always existed an obvious mutual restriction relationship between them among all indicators except exterior surface heating loss. Meanwhile, the suggested value of the charging duration was no less than 6 h, and the optimal range of the thermal conductivity of pipe-embedded layer given by GSA was 0.5–2.75 W/m·℃. Under the blocking effect of the thermal barrier, the uncertainty of the climate zone on interior surface heating load was greatly reduced, and the climate zone was no longer a key variable affecting the cumulative subcooling duration. Besides, it was proved that the pipe spacing had a great influence on the heat accumulation inside the pipe-embedded layer, pipe location had a slight influence on interior surface heating load and exterior surface heating loss, and the pipe diameter did not influence thermal performances. From the perspective of energy density, the optimal range of the pipe spacing was 100–250 mm. Overall, this study highlighted the positive effect of the pipe-embedded system on the development of new-built and existing buildings towards zero-carbon targets, and also provided useful guidance for its further applications and investigations.

Introduction

The building sector is one of the three largest non-renewable energy consumers worldwide, which approximately takes up 32% of global energy consumption [1]. In China, the proportion of building energy consumption in national energy consumption is expected to grow by another decade to 2030 [2]. These affirm the urgency of implementing stringent energy requirements for both the new-built and existing buildings. Recently, the demanding plans and policies concerning the passive house in European Union [3], zero energy buildings (ZEBs) in the United States [4] and nearly-zero energy buildings (NZEBs) in China [5], etc., have been challenging both the engineering and research community to develop new high-efficient systems and construction techniques for building energy conservation and renewable energy utilization.

As a physical dividing interface between the indoor and outdoor environment, the building envelope is one of the main bottlenecks to design and construct NZEBs or even ZEBs [6]. Currently, it is of great significance to improve the thermal insulation performance for building energy conservation in the context of carbon neutrality. According to differences in technical principles, the current thermal insulation technologies can be divided into two categories [6], [7], [8], i.e., passive method and active method. Among them, the passive method takes the thermal resistance (R-value) as the control parameter, which can be further divided into the static type and dynamic type. Meanwhile, the active method is a burgeoning technology that utilizes low-grade or renewable energy to realize building thermal insulation [8]. Unlike the passive method, the active method regards the temperature difference which forms the building thermal load as its control parameter. For passive static thermal insulation (PSTI), it is the most common way to reduce building energy consumption and improve the built environment by installing insulation layers with constant R-value on either side or in the middle of the wall. Here, “static” mainly refers to the insulation material that can maintain its thermo-physical parameters, especially the R-value, in its life cycle. With decades of continuous development, the current PSTI has obtained good thermal performance [9], [10]. However, there still exist some other issues caused by PSTI that may limit its future applications. Firstly, a thick PSTI layer will take up lots of building space, and the potential fire-safety issues that existed in PSTI still lie ahead [9]. Although new PSTI techniques with higher R-value have progressively emerged [11], their durability and reliability still need to be verified by long-term tests. Besides, a stable R-value also affects the full use of night cooling in transition and cooling seasons, and this may result in an extra increase in energy consumption [12]. For passive dynamic thermal insulation (PDTI), it can dynamically adjust its R-value through physical or chemical methods according to the boundary conditions, thus achieving the purpose of minimizing building energy consumption [8]. Thibault et al. [13] briefly summarized the existing dynamic insulation concepts in their studies. However, the role of dynamic insulation is still limited to adjust the thermal performance of the enclosure structure within a fixed R-value range, and their durability and reliability also lack the supports from real applications.

Therefore, there is an urgent need for new cost-effective alternatives to the above approaches. A promising method is to consider building components as multifunctional elements which are expected to perform several functions simultaneously, such as energy and structural aspects [14], [15]. Pipe-embedded building envelopes, as a typical representative of this kind of technology, are of particular interest to architects and engineers due to its excellent performances and invisibility characteristic [16], [17], [18]. This technique is evolved from the concept of the thermo-activated building system (TABS) which supplies energy not into the internal air but the external walls [19]. Existing nomenclatures include: thermal barrier (TB) [20], [21], pipe-embedded building envelope (transparent or opaque) [22], [23], [24], and south-north pipe-embedded closed-water-loop system [25]. By injecting low-grade energy into the exterior envelopes and thereafter creating an invisible thermal barrier zone, the pipe-embedded layer could achieve the technical effect of blocking the direct heat transfer between the indoor and outdoor environment.

Krzaczek and Kowalczuk [20] presented the concept of TB with approximately constant temperature throughout the year by embedding the U-pipes into the external walls and controlling the flow rate and water temperature. Results showed that TB could reduce heating and cooling demands at least three times as compared to the reference wall, and it is also capable of decreasing the total annual heating and ventilation demand of a passive house almost to zero. Meggers et al. [26] developed an active low exergy geothermal insulation system, which directly utilized geothermal heat to reduce heat losses. The steady-state analysis stated that a 6 cm thick active insulation system had equivalent performance to 11 cm of PSTI at an outside design temperature of −10 °C. Kisilewicz et al. [27] presented the preliminary results of research performed in an experimental residential building equipped with an innovative ground-coupled wall heat exchanger in Hungary. In the analyzed periods, the building heat loss could be reduced by an average of 63% compared with standard insulation, while the minimum reduction in the cold period was higher than 50% and the maximum temporary reduction was even 81%. Yu et al. [21], [28] applied the capillary tube network in the pipe-embedded wall to increase the contact area and further relax the constraints on water temperature. Results showed that the heat transfer process inside the pipe-embedded layer dominated its energy performance, and the influence of water temperature and pipe location should be considered in its practical application. As part of active building environmental design, Jobli et al. [29] proposed a similar novel pipe-embedded system with capillary tubes embedded in phase change material. To solve the installation suitability issues of the pipe-embedded system in existing buildings, a novel precast insulation panel with pipes arranged in its milled channels was proposed by Simko et al. [30]. Results indicated that the wall system had the potential to significantly reduce heat loss when it was directly attached to the facades and used as TB. Except for the shallow soils which could provide both natural and artificial heat sources [6], [9], the low-grade energy could also come from the cooling tower, air-source heat pump (ASHP), solar collector, etc. For example, the ASHP and cooling tower were separately used to produce low-grade hot and cold water in the different seasons by Shen and Li [9], [31]. Results obtained under heating season conditions indicated that 84% of the heat transfer on the interior surface could be eliminated, whereas the heat dissipation on the exterior surface was increased by only 18% in Beijing. Meanwhile, the water temperature had a significant impact on the performance of the system, and the technical economy was relatively better when room temperature water was applied. Considering that the solar radiation falling on the south facade could not be effectively utilized, a novel closed wall-loop system is proposed by Ibrahim et al. [25], [32] to capture this wasted energy available during non-cloudy winter days and transfer it to the north facade through water pipes embedded in an external coating. Variables such as flow rate, outside convective heat transfer coefficient, indoor set-point temperature and solar absorptivity were also parametrically studied. In addition to the above research on the applications and their performances, Xu et al. [24], [33], [34] investigated two different heat transfer models for thermal performance prediction, including the semi-dynamic simplified model and dynamic simplified model. Recently, Yan et al. [33], [34] proposed a PCM-embedded wall coupled with a nocturnal sky radiator for active heat defense with the outer dynamic thermal environment. Comparing with a common wall, the average interior surface temperature of this composite wall was reduced by 1.6 ℃, and the reduction of the cooling demand and energy-saving ratio was 37.8%-57.8% and 15.7%-24.1% respectively. Lydon et al. [14] applied the pipe-embedded system in the lightweight curved roof structure of a net-energy building to satisfy the environmental control demand, and the optimization method of thermal design of this system was further also investigated to improve its lifecycle energy performance [15].

The above researches highlight the great potential of the pipe-embedded walls in building load reduction and cooling/heating energy supplement. However, the following research gaps still exist, which bring great challenges to architects and engineers. Firstly, the thermal interactions between the embedded pipe and the pipe-embedded layer will inevitably have impacts on processes of heat injection, heat storage and heat release, resulting in a series of new problems related to thermodynamics and architectural design. Currently, there are few studies focused on the uncertainties of thermal performances, identification of key influencing factors and the corresponding interaction mechanism. Regarding the 12 input variables in 3 types listed in Table 1, the variables involved in the existing parametric researches are summarized. It can be observed that the number of the variables involved in these researches is relatively small, and the research possessed the largest number of variables only involves four variables [18]. Except for variables like pipe spacing (PS), pipe location (PL), heat-source temperature (HT) and climate zone (CZ), other variables are not paid enough attention, e.g., orientation (OT), indoor set-point (IS), thermal conductivity of pipe-embedded layer (Mtc), charging duration (CD) and solar radiation absorptance (RA), or even not involved at all, e.g., pipe diameter (PD), specific heat of pipe-embedded layer (Msc) and thermal conductivity of embedded pipe (Ptc). This research gap can be attributed to the fact that the local sensitivity analysis (LSA) method is adopted in these studies [9], [17], [18], [19]. Although the LSA method requires less calculation, it is widely considered not suitable for the parametric research of complex non-linear problems [38]. Secondly, the research object in the relevant literature usually focuses on a single brick wall [9], [19] or concrete wall [14], [39], and there is a lack of parametric research on the thermal performances of the pipe-embedded pipe wall constructed by lightweight or other types of materials. Therefore, the conclusions obtained in these studies are also limited to a large extent. Thirdly, the previous researches are more concerned with the dynamic heat transfer characteristics and energy-saving performances. The corresponding evaluation indicators are embodied in the interior surface heat load and exterior surface heat loss [17], [18]. Therefore, a comprehensive evaluation study on the thermal performances of the pipe-embedded wall with more different types of indicators, such as the improvement of the thermal radiation of interior surface and the indicators reflecting the heat injection, heat storage and heat release ability, is still missing.

The pipe-embedded building envelopes can significantly improve the building thermal performances, but the uncertainties always run through its design, construction and operating process. To eliminate the above research gaps, the UA and GSA on thermal performances of the pipe-embedded wall are conducted in this paper. Section 2 introduces the 3D transient heat transfer model of the pipe-embedded wall verified by open experimental data in the literature. Section 3 details the procedures and methodologies of UA and GSA investigation which including pre-processing (i.e., uncertainty characterization), uncertainty model execution (i.e., uncertainty propagation and output) and post-processing (i.e., uncertainty and sensitivity analysis). Section 4 firstly presents and discusses the UA and GSA results regarding the 5 performance indicators in 3 types for the pipe-embedded wall and 3 performance indicators in 2 types for the reference wall. On this basis, Section 4 further makes a comparative analysis of the ranking results of variables obtained by the SRC and TGP method, and the key influencing variables and its influencing mechanism are identified. Finally, concluding remarks are summarized in Section 5. Results of UA and GSA can provide valuable theoretical guidance and data support for the optimal design and practical application of the pipe-embedded wall.