Article 正式发布 Versions 1 Vol 28 (6) : 1129-1140 2019
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Assessment of Building External Wall Thermal Performance Based on Temperature Deviation Impact Factor under Discontinuous Radiant Heating;非连续辐射供暖条件下基于温度偏离影响因子的建筑外墙热工性能评价
: 2019 - 11 - 05
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Abstract & Keywords
Abstract: As the variation and timely meeting thermal environment requirement of indoor air temperature has a close relationship with the thermal performance of building external wall under discontinuous radiant heating condition, one appropriate assessment method or index for assessing the building external wall thermal performance is very necessary. In order to reasonably evaluate the thermal performance of external wall under discontinuous radiant heating condition and build the direct connections and interactions among the indoor air temperature, external wall inner surface temperature and outdoor air temperature, the first and second impact factors of temperature deviation were established, based on one mathematical model of room heat transfer. For one experimental room and four types of external walls under discontinuous radiant heating condition, both the influence of the external wall inner surface temperature deviation on the indoor air temperature and that of the outdoor air temperature deviation on the external wall inner surface temperature were determined effectively with the first and second impact factors of temperature deviation. In addition, favourable performance for the self-insulation and inner insulation walls were found, due to their superiority in effectively and timely improving the indoor thermal environment under discontinuous radiant heating condition. 在非连续辐射供暖条件下,室内空气温度的变化与及时响应热环境要求程度问题都与建筑外墙热工性能有密切关系,因此需要一种合理评价建筑外墙热工性能的方法或指标。为了合理评价在非连续辐射供暖条件下建筑外墙的热工性能以及建立室内空气温度、外墙内表面温度、室外空气温度之间的直接联系和相互影响作用,本研究基于房间传热数学模型提出了温度偏离第一和第二影响因子。其次,针对实验房间以及非连续辐射供暖条件下的四种外墙构造形式,采用温度偏离第一和第二影响因子研究分析确定了外墙内表面温度偏离对室内空气温度的影响以及室外空气温度偏离对外墙内表面温度的影响。此外,研究发现自保温和内保温在非连续辐射供暖条件下具有很好的性能,这归因于其能够对室内热环境的有效及时改善。
Keywords: temperature deviation impact factor, building external wall, thermal performance, discontinuous radiant heating
1. Introduction
The advantages of great indoor thermal comfort and energy savings are the primary reasons why floor radiant heating has become such a popular heat supply mode [1–3]. In southern China, although building energy saving is very necessary [4–5], room heating demand in winter is one increasingly important issue, as a result of outdoor climatic impact and people’s concerning about indoor comfort. As to avoid the rapid growth of energy consumption and improve indoor thermal environment in winter, discontinuous radiant heating has widespread application in this region. The discontinuous radiant heating is used to meet the need of heating when someone is inside room and has thermal comfort requirement, but stop heating when no one is in the room. Namely, the discontinuous radiant heating can meet the heating demand of part time and part space under reasonable control strategy. At present, the floor radiant heating system is a universal form of discontinuous radiant heating in southern China. For the whole process of discontinuous radiant heating, effective and timely guarantee of indoor thermal environment depends on the features of floor radiant heating system, the control system, the thermal insulation performance of the external walls and outdoor climate.
The performance of floor radiant heating is one basic factor impacting the indoor thermal environment under discontinuous radiant heating, which is affected by multiple parameters. Sattari et al. [6] studied the effects of design parameters on the performance of typical radiant floor heating system using the finite element method; transient conduction, convection and radiation heat transfer mechanisms were considered. Fontana [7] examined the thermal performance of floor radiant heating system on a scale model and evaluated the effect of furniture. Zhang et al. [8] presented a simplified calculation of the heating capacity of radiant heating floor, the uniformity of the surface temperature distribution and the lowest temperature at the surface, found that the thickness and heat conductivity of each layer had important influences on the performance of radiant floor and the influence of the water pipes should not be ignored. Zhang et al. [9] analysed the operating characteristics of one lightweight radiant floor heating (LRFH) system and investigated a heat transfer model for the evaluation of LRFH. They determined the heat-transfer capability, temperature field distribution and thermal comfort of the LRFH system by using the model. The above research results indicate that there is a complex heat transfer process in floor radiant heating system. The process includes internal heat transfer and surface heat exchange. Accordingly, the thermal boundary condition derived from the radiant heating floor should be reasonably determined in the heat transfer model of building room. In addition, regarding the advantage of radiant heating, Milorad Bojić et al. [10] investigated the energy, environmental and economic performances of the floor, wall, ceiling and floor-ceiling heating and found that the floor-ceiling heating had the best performances, including the lowest energy and exergy consumption, the lowest exergy destruction, the lowest carbon dioxide emissions (compound, direct, and avoidable), the lowest operation costs, and the use of a boiler of the lowest power. Zheng et al. [11] found the non-heating surface temperature had a significant impact on the heat output of the radiant floor. Koca and Çetin [12] found when the wall was integrated to the ceiling, total and radiant heat transfer coefficients decreased in both ceiling and wall, convective heat transfer coefficient also decreased in wall but increased in ceiling cases. Wang et al. [13] built a dynamic heat transfer model based on thermal-electrical analogy to compare convective and radiative heating systems for intermittent heating. Kuznetsov et al. [14] revealed the mean convective Nusselt number at the bottom solid-fluid interface was slightly altered in the cavity with the local radiant heater when varying the governing parameters. In addition, Jia et al. [15] found it is possible to use the air temperature for controlling the radiant systems in lieu of the operative temperature, as a result of reducing both first cost and maintenance costs. It can be seen from above research results that the performance of radiant heating may change with multiple factors.
For another thing, the thermal performance of building external wall is one important factor impacting the achievement of floor radiant heating property, especially under discontinuous operation. At present, according to the form and structure of thermal insulation, there are four types of external wall thermal insulation applied in building room, as shown in Fig. 1. Moreover, according to actual function of each layer, external wall structure and constitution can be divided into three layers, namely, the coating layer, insulating layer and structural layer, although they may be multi-layered. The self-insulating layer has functions of both thermal insulation and structural force bearing. The structural layer is only used for structural force bearing. Their thermal performance index can be adjusted by choosing reasonable materials for each layer and meet requirements of the local situations. As to obtain the differences of diverse external wall thermal performance, the heat transfer models and assessment methods are necessary. Diasty [16] developed a finite difference model that had advantages in describing the thermal performance of multi-layered wall panels. Saleh [17] studied and evaluated three different arrangements of building insulation with different thicknesses, considering their thermal performance and impact on indoor temperature in a hot-dry climate context. The utilization of thermal insulation showed a significant improvement when the thermal insulation was located on the outer side of the building envelope. Kossecka et al. [18] analysed the effect of mass and insulation location on the heating and cooling loads for six characteristic wall configurations and discussed the correlations between the structural and dynamic thermal characteristics of walls. According to the energy analysis of a one-story residential building with various external wall configurations for six different US climate conditions, the best thermal performance was obtained when massive material layers were located at the inner side and directly exposed to the interior space. Praditsmanont et al. [19] found that the Main Hall's lightweight and highly insulated building envelope outperformed other commonly used heavyweight envelopes in preventing building energy gain in the hot-humid climate of Thailand. Peng et al. [20] developed a new harmonic method, the thermoelectricity analogy method (TEAM), to compute the periodic heat transfer in external building envelopes (EBEs). Comparisons showed that this method was highly accurate and efficient. Aste et al. [21] assessed the parameters enhancing or damping the role of thermal inertia and provided a variety of results. Several external wall systems with the same thermal transmittance but different dynamic properties were investigated to calculate the associated achievable energy savings. Tosun et al. [22] proposed a new approach for determining the thermal insulation layer using the artificial neural network (ANN) technique. Their research results showed that the ANN model can be used as a reliable modelling method. Alterman et al. [23] developed a novel concept for characterizing the dynamic thermal response of walling systems and assisting in the evaluation of thermal performance of walling systems and possible housing. Kaynakli [24] provided optimization procedures and economic analysis methods for insulation thickness, implemented a practical application and investigated the effective parameters to achieve the optimum value. Giancola et al. [25] found the ventilated facade could play an important role in reducing the heating and cooling thermal loads as long as the outdoor temperatures were not extreme in warm climates with high levels of solar radiation. Moreover, Giancol and Soutullo et al. [26–27] evaluated the improvement of indoor environment by upgrading the thermal characteristics of building envelope in a social housing. They found the refurbishment of building envelope was always convenient for better indoor microclimate and thus energy savings. Mirsadeghi et al. [28] discussed the uncertainty related to the use of external convective heat transfer coefficient models by means of a case study. Zhang et al. [29] developed a method of determining the ideal thermal conductivity of an external wall with constant volumetric specific heat based on the concept of ideal passive energy-efficient buildings. After the optimization of external wall used in a passive room of Beijing, the integrated discomfort degree was reduced by 64.3%, compared with that of the traditional external wall. Stazi et al. [30] verified the dynamic performance of three kinds of envelopes characterized by different traditional wall constructions adopted in temperate climates and determined the impact of different retrofit solutions on the buildings. The results indicated that the behaviour of three kinds of envelopes differed greatly because they interacted in different ways according to changes in the climate. Sanchez et al. [31] focuses on the analysis of open joint ventilated facades with both vertical and horizontal apertures. The mean velocity and the turbulence quantities were enhanced by buoyancy. It had also been observed that the instabilities in the flow increased with the Ra numbers. As confirmed by the above studies, the influence level of the insulation location on the thermal performance of building external wall strongly depends on their exposure conditions to the thermal environment.
It can be seen from existing studies that, as to certain floor radiant heating system and outdoor climate condition, the performance behaviour of building external wall has a close relationship with effective and timely improvement and realization of indoor thermal environment, especially for discontinuous radiant heating. Namely, reasonable assessment of thermal performance of building external wall is very necessary under discontinuous radiant heating condition. However, basic parameters, such as heat transfer coefficient, heat storage coefficient and so on, can’t directly reflect the perfor- mance behaviour of building external wall under discontinuous radiant heating condition and outdoor climate impact. In addition, direct heat exchange is occurring between external wall inner surface and indoor air. Moreover, the inner surface temperature for specific external wall is depending on outdoor and indoor air temperature. Therefore, the direct connections and interactions among the indoor air temperature, external wall inner surface temperature, and outdoor air temperature should be established to reveal the mechanism of coupled heat transfer occurring among


 
Fig. 1 Four kinds of external wall used in building room
them. For the aforementioned research purpose, this present study involves a proposed method, namely, the first and second impact factors of temperature deviation based on a mathematical model of room heat transfer, which establishes the direct connections of these three kinds of temperature and is used to evaluate the thermal performance of external wall of one experimental room and four types of external walls under discontinuous radiant heating condition.
2. Impact Factor of Temperature Deviation
2.1   Mathematical model of room heat transfer
For the temperature boundaries of the inner surfaces of the room walls, except for the external wall, the room thermal process can be regarded as coupled heat transfer between the indoor air and the external wall, as shown in Fig. 2. The mass, momentum, turbulence and energy conservation of the indoor air, energy conservation of the external wall and coupled heat transfer between the indoor air and the external wall are taken into account. Moreover, the impact of thermal buoyancy induced by the floor radiant heating may be described by the Boussinesq model. In addition, the turbulence of indoor air and heat transfer through the wall boundary layer are described by the renormalization group (RNG) k-ε model and the standard wall function [32].
Therefore, the corresponding mathematic model depicting the room thermal process is expressed as the following equation:
(1)
where ϕ is the common variable, e.g., temperature or velocity; ρ is the air or wall material density; U is the indoor air velocity; Γ is the diffusion coefficient; S is the source term; and t is time. The expressions of the variables, diffusion coefficients and source terms for
indoor air and external wall are given in Table 1. In Table 1, ui represents the air velocity component at the direction i; Ta , Tw1 , Tw2 and Tw3 are the temperatures of the indoor air, layer 1, layer 2 and layer 3, respectively; μ and μt are the molecular and turbulent viscosities, respectively; α is the turbulent Prandtl number; λ expresses the thermal conductivity; p is the pressure of indoor air; ρ0 is the (constant) density of indoor air; β is the thermal expansion coefficient; Ta0 is the operating temperature; g is the gravitational acceleration; Gk is the generation of turbulence kinetic energy. In addition, the αk and αε are equal to 1.39; Cε1 and Cε2 are 1.42 and 1.68, respectively.
For the interface between the indoor air and the external wall (x=L), the flux of coupled heat transfer is conserved:
(2)


 
Fig. 2 The room thermal process under radiant heating
Table 1 Expressions of ϕ, Γϕ and Sϕ
 
EquationsS
AirMass conservation100
Momentum conservationuiμ +μt
Energy conservationTa(μ+μt )/αT0
Turbulent energyk(μ+μt )/αkGk
Dissipation rate of turbulent energyε(μ+μt )/αε
Layer 1Energy conservationTw1λ10
Layer 2Energy conservationTw2λ20
Layer 3Energy conservationTw3λ30
For the interface between two layer materials, the heat flux is also conserved:
(3)
For the outer surface of the external wall, x=0:
(4)
For the top and bottom surfaces of the external wall, y=0 and y=H:
(5)
(6)
For the usual initial condition that there is a non-uniform temperature distribution in the indoor air and each layer of the external wall, the initial condition is presented as the following equations:
(7)
(8)
Here, λw,in and λw,out are the thermal conductivities at the inner surface and outer surface of external wall, respectively; Tw,in and Tw,out express the temperature at the inner surface and outer surface of external wall, respectively; hin and hout are the inside and outside convective heat transfer coefficients, respectively; Ta,in and Ta,out denote the indoor air and outdoor air temperature, respectively; σ is the Stefan-Boltzmann constant; ω is the surface emissivity; As,i represents the area of the other inner surfaces except the external wall; and X is the radiation shape factor.
2.2   Calculation method
Regarding the building room with floor radiant heating, one common requirement is that its indoor air temperature reaches 18°C. According to the thermal equilibrium between the indoor air and inner surfaces of the room walls, the following relationship exists for the indoor air temperature at 18°C:
(9)
where Afloor and Aw,in are the areas of the floor and the external wall, respectively; Tf denotes the surface temperature of the floor; is the required inner surface temperature of the external wall under the condition of the floor, and the other inner surfaces are at a definite temperature.
Another thermal equilibrium relationship can be established for the inner surface of the external wall with the required inner surface temperature:
(10)
Here, expresses the required outdoor air temperature to achieve ; δj is the thickness of the j layer material; and λj is the thermal conductivity of the j layer material.
However, while the floor and other inner surfaces temperature maintain their original definite temperature and the inner surface temperature of external wall (Tw,in ) deviates from its required value (), namely, temperature deviation , the indoor air temperature (Ta,in ) may deviate from its required value of 18°C, as shown in Fig. 3. It’s worth pointing out that the south wall is chosen as the external wall in Fig. 3, which just represents one possible form. When other direction walls serve as external walls, the calculation method is also applicative.


 
Fig. 3 The interaction between temperature deviations (TD) of external wall inner surface and indoor air
To evaluate the influence of on the deviation of indoor air temperature (Ta,in ), the first impact factor of temperature deviation is proposed and defined as the following:
(11)
Alternatively, when the indoor air temperature remains at 18°C and the floor and other inner surfaces temperature maintain their original definite temperature, the temperature deviation emerges because the outdoor air temperature (Ta,out ) deviates from its required value (), as illustrated in Fig. 3. Therefore, the second impact factor of temperature deviation is given to assess the influence of on the deviation of the external wall inner surface temperature.
(12)
In fact, the first and second impact factors of temperature deviation (TD) provide a new method for evaluating the thermal performance of a building external wall under discontinuous radiant heating, i.e., the dynamic thermal response of the external wall. Moreover, the direct connections and interactions among the indoor air temperature, external wall inner surface temperature, and outdoor air temperature can be obtained from these two proposed impact factors.
3. Application of the New Method in One Experimental Room


 
Fig. 4 The experimental room with floor capillary radiant heating system
Table 2 Physical properties of each layer materials for the south wall of experimental room [33]
 
Thermal insulation system
(from outside to inside)
Thickness/
mm
Density/
kg·m-3
Specific heat/
J·kg-1·K-1
Thermal conductivity/
W·m-1·K-1
Self insulationδ120160010500.63
δ2200130018710.38
δ320160010500.63


 
Fig. 5 The experiment results of outdoor air temperature and related surfaces temperature


 
Fig. 6 Geometric model and meshes used for the numerical simulation (1,018,500 nodes): (a) view of the geometric model and (b) view of the total mesh


 
Fig. 7 Variations of indoor air and south wall inner surface temperature and impact factors of temperature deviation with time
4. Thermal Performance of Diverse Building External Wall
Table 3 Physical properties of each layer materials for different thermal insulation forms [24]
 
Heat transfer coefficient (K) of 1.0 W·m-2·K-1
Thermal insulation system
(from outside to inside)
Thickness/
mm
Density/
kg·m-3
Specific heat/
J·kg-1·K-1
Thermal conductivity/
W·m-1·K-1
External insulationδ12713551022.00.730
δ215302475.20.024
δ319819001064.51.100
Cavity insulationδ11102100920.01.254
δ220255346.40.030
δ31102100920.01.254
Inner insulationδ121214001062.30.573
δ218182414.80.042
δ3105001050.00.230
Self insulationδ12512001050.00.360
δ21907001782.10.270
δ32512001050.00.360
Heat transfer coefficient (K) of 1.5 W·m-2·K-1
External insulationδ12713551022.01.310
δ215302475.20.039
δ319819001064.51.914
Cavity insulationδ11102100920.01.517
δ220255346.40.055
δ31102100920.01.517
Inner insulationδ121214001062.31.230
δ218182414.80.059
δ3105001050.00.320
Self insulationδ12512001050.00.578
δ21907001782.10.450
δ32512001050.00.578


 
Fig. 8 Variations of south wall inner surface temperature with time for four kinds of external wall


 
Fig. 9 Variations of indoor air temperature with time for four kinds of external wall


 
Fig. 10 Variations of first impact factor of temperature deviation with time for four kinds of external wall


 
Fig. 11 Variations of second impact factor of temperature deviation with time for four kinds of external wall
5. Conclusions
This study proposed the first and second impact factors of temperature deviation, combined with a mathematical model of room heat transfer, which gave the direct connections and interactions among the indoor air temperature, external wall inner surface temperature, and outdoor air temperature. Moreover, one meaningful method for assessing the thermal performance of building external wall was provided under discontinuous radiant heating condition. Based on the application of the first and second impact factors of temperature deviation in one experimental room and diverse building external walls, the influence may be clearly revealed, including both the influence of the external wall inner surface temperature deviation on the indoor air temperature and that of the outdoor air temperature deviation on the external wall inner surface temperature. Furthermore, in the case of discontinuous radiant heating, both the self-insulation wall and inner insulation wall exhibited great performance for effectively and timely improving the indoor thermal environment. This present research provides one innovative method for choosing the reasonable structure and constitution of external wall in building room with discontinuous radiant heating.
Acknowledgements
The authors gratefully acknowledge the financial support from the Huimin Project of Chengdu Science and Technology Grant No. 2015-HM01-00548-SF and the National Nature Science Foundation of China under Grant No. 51308361 and Science and Technology Plan Project in Sichuan province Grant No. 2014GZ0133.
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Article and author information
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YANG Jie1
WANG Jun1*
wangjunhvac@163.com
XIONG Feng1
LIANG Hao2
LI Yunzhang1
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Published: Nov. 5, 2019 (Versions1
References
Journal of Thermal Science