A semi-dynamic model of active pipe-embedded building envelope for thermal performance evaluation

International Journal of Thermal Sciences 88 (2015) 170e179

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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts

A semi-dynamic model of active pipe-embedded building envelope for thermal performance evaluation Qiuyuan Zhu a, b, Xinhua Xu a, c, *, Jiajia Gao a, Fu Xiao c a

Department of Building Environment & Energy Engineering, Huazhong University of Science & Technology, Wuhan, China Wuhan 2nd Ship Design and Research Institute, Wuhan, China c Department of Building Services Engineering, The Hong Kong Polytechnic University Kowloon, Hong Kong, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 December 2013 Received in revised form 22 September 2014 Accepted 23 September 2014 Available online

Active pipe-embedded building envelope is a new kind of pipe-embedded building external wall/roofs. Usually, pipes are embedded in the wall slab or roof slab to allow water circulating in these pipes for heat transfer. Low-grade energy sources can be used for this structure since the enlarged heat transfer surface between the slab mass and water in the pipe allowing for substantial heat flow for relatively small temperature difference. This structure may reduce building cooling/heating load and improve indoor thermal comfort by intercepting the heat/coolth from the ambient air to indoor space. This paper presents a semi-dynamic model of this structure for thermal performance evaluation for system design or indoor environment control etc. This semi-dynamic model is a coupled model. The first part is a simplified dynamic RC model (i.e., resistance and capacitance model). The heat transfer along the width of this structure can be predicted easily by the RC model. The second part is a classical NTU model for evaluating the heat transfer along the pipe and total heat transfer on both surfaces of this structure. A CFD model is developed to act as a virtual experimental test rig to simulate the thermal characteristics of this structure. The simulated results are used to validate this semi-dynamic model and its performance prediction. © 2014 Elsevier Masson SAS. All rights reserved.

Keywords: Active pipe-embedded building envelope Low temperature difference heat transfer RC model NTU model Performance evaluation

1. Introduction It is a common concern that energy is in short supply and the building energy consumption is increasing in the world. In China, building energy consumption is also increasing every year, and consumes about 30% of the yearly end energy use [2]. Air conditioning energy consumption is the main part of the building energy consumption. The energy consumption of air conditioning (usually using the high grade energy) is used to remove the cooling/heating load for keeping the required indoor environment. Reducing the heat transfer through building envelope is one of the means to reduce the cooling/heating load. Conventional means are to change the construction material, increase the thickness of the external wall, use phase change materials (PCM), or directly install insulation on the opaque building envelope, etc.

* Corresponding author. Department of Building Environment & Energy Engineering, Huazhong University of Science & Technology, Wuhan, China. Tel.: þ86 27 8779 2165x403; fax: þ86 27 8779 2101. E-mail address: [email protected] (X. Xu). http://dx.doi.org/10.1016/j.ijthermalsci.2014.09.014 1290-0729/© 2014 Elsevier Masson SAS. All rights reserved.

Active pipe-embedded building envelope is a new building envelope structure. It is an external wall or roof with embedded pipes and can utilize circulating water in the pipe to remove heat/coolth inside the structure directly [22,26]. Active pipe-embedded building envelope has the similar advantages with pipe-embedded floors or ceilings for radiant heating or cooling, which may significantly enlarge heat transfer surface between the structure mass and the water in the pipe for allowing substantial heat flows even for relatively small temperature difference between the mass and water [3,4,19]. One of the big advantages is that it can use renewable energy sources to trap heat or coolth from outdoor to indoor space through the pipe water to reduce indoor cooling load or heating load. These low-grade energy sources may be groundwater, the cooling water produced by cooling towers, and geothermal energy produced by the ground-coupled heat exchanger system, etc. [11,12,23]. From this point, active pipe-embedded building envelope is different from the pipe-embedded floor and pipeembedded ceiling (usually called as thermally activated building systems). Active pipe-embedded building envelope has been used for many actual building envelopes in the world. An air-conditioned office with a cool roof system located within an industrial

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building in Rome is analyzed by Pisello et al. [13]. The results show that this system can reduce cooling loads and improve cooling system efficiency. The efficient cooling and heating of an office building with the active pipe-embedded building envelope (called thermally-active building system in the paper) in UK is presented by Babiak [5]. IDOM Madrid headquarter building uses a thermal activated structure (TABS) as the main part of the HVAC system [15]. The comfort evaluation and the annual energy consumption of this system were also presented. Song et al. [16] considered an active pipe-embedded building envelope to be an energy-efficient HVAC system to reduce and shift the peak load of an HVAC system in a campus building in South Korea, and the optimized operation strategy is also presented. Although active pipe-embedded building envelope has been used for many actual building envelopes in the world, the heat transfer model is barely mentioned, while the heat transfer model is very important to analyze the heat transfer thermal performance [7,25]. As the active pipe-embedded building envelope with the embedded pipe, the structure is complicated. The heat transfer model of this structure is difficult developed. The heat transfer models of the pipe-embedded structure (such as pipe-embedded structure for snow melting system, pipeembedded floors, and pipe-embedded ceiling etc.) for thermal performance prediction have been presented by many researchers. The pipe-embedded structure for snow melting system is the earliest application of the pipe-embedded structure, Schnurr and Rogers [17] proposed a two-dimensional steady-state heat transfer model of this structure, and finite difference method is employed to solve the temperature distribution for optimizing system design. The pipe-embedded structure for floors or ceilings began in 1980s. The earliest two-dimensional steady model of pipe-embedded structure as ceiling for hot water heating is proposed by Zhang and Pate [27]. Subsequently, the accompanying experiments were conducted to validate the accuracy of this model [28,29]. In the 1990s, a steady-state fin model for predicting the heat transfer performance of the pipe-embedded structure as floor/ceiling is presented by Kilkis et al. [8]. Subsequently Kilkis et al. [9] used a finite element package to validate the accuracy of this model. In addition, some simplified models of this structure also have been presented. A simplified steady-state model of the active pipeembedded structure for air-conditioning was presented by Koschenz and Dorer [10]. This simplified steady-state model is in fact a pure resistant model. This model was used for the design of an active pipe-embedded structure for a new exhibition building in Zurich, and can be used for simple hand calculation for rough system configuration. In 2005, a dynamic simplified RC-network model for pipe-embedded structure was proposed by hannesson [20]. Dynamic simplified RC model (i.e., resistance and Jo

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capacitance model) is the best candidate for thermal performance prediction since the dynamic thermal process in the structure can be predicted accurately by this model. This kind model also can be solved easily for convenient integration with energy simulation software. Active pipe-embedded building envelope is similar to floors/ ceiling in term of structure. However, the heat transfer of the active pipe-embedded building envelopes is affected additionally and significantly by the outdoor environment. Zhu et al. [26,30] presented the frequency-domain finite difference (FDFD) model of the active pipe-embedded building envelope for frequency response analysis of the active embedded-pipe building envelope under various disturbances. FDFD model can predict the frequency characteristics directly and quickly. However, this model is still a numerical model and hard to be integrated with conventional energy simulation software. Subsequently, Zhu et al. [31,32] proposed a dynamic simplified thermal model (RC model) of this structure. RC model can predict the frequency characteristics and can be integrated with conventional energy simulation software. However, the heat transfer along the pipe is not considered in this model. This paper presents a semi-dynamic thermal model of active pipe-embedded building envelope including two parts. The first part is the simplified dynamic RC model, which is used to calculate the heat transfer along the width of this structure. The second part is a classical NTU model for calculating the heat transfer along the pipe and total heat transfer on both surfaces of this structure. Both parts are coupled together to determine the average temperature of the building envelope mass and the outlet water temperature of the active structure etc. A CFD model is developed to act as a virtual experimental test rig to simulate the thermal characteristics of this structure for validating the semi-dynamic model and for performance evaluation. The accuracy of the semi-dynamic model with different water flow and the accuracy of the semi-dynamic model of different active pipe-embedded building envelopes are also presented and analyzed. 2. Overview of the semi-dynamic simplified model An active pipe-embedded building envelope can be coupled with low-grade energy sources to offer reductions in energy consumption, peak electrical demand and energy costs without lowering the desired level of comfort conditions [31]. A dynamic model of the active pipe-embedded building envelope is of important to be integrated in conventional energy simulation tools to evaluate the energy and environment performance when this structure is integrated in a building system and coupled with lowgrade energy sources. Fig. 1 shows the overview for developing a semi-dynamic simplified model. To develop this semi-dynamic

Fig. 1. Overview of the semi-dynamic simplified model.

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simplified model of this structure, RC model and the NTU model are needed to be developed and should be coupled together by the node temperatures and water temperature (detail given in Section 3.3). To identify the parameters of the simplified RC model, Genetic Algorithm (i.e., GA) is used for allowing the frequency responses of the simplified RC model to match the theoretical frequency responses by FDFD model. The process mainly involves four steps as described below. Step 1 Development of the theoretical model of the active pipeembedded building envelope in frequency domain, and the numerical solution of the frequency characteristics of the theoretical model under various disturbances (details given in Section 3.1). Step 2 Development of the dynamic simplified model (i.e., RC model) of the active pipe-embedded building envelope along the width of this structure, deduction of its frequency characteristics (details given in Section 3.1), and parameter identification of the RC model. Step 3 Development of the NTU model of the active pipeembedded building envelope, and deduction of heat transfer along the pipe and total heat transfer on both surfaces of this structure (details given in Section 3.2). Step 4 Development of the semi-dynamic simplified model by coupling the RC model and the NTU model through the node temperatures and water temperature (details given Section 3.3).

3. Semi-dynamic simplified model development To develop the heat transfer model of active pipe-embedded building envelope, the analysis object should be specified first. Fig. 2 shows the typical schematic of the cross section of the active pipe-embedded building envelope. This cross section is normal to the pipe direction. This structure includes two construction layers (usually brick, concrete, stucco etc. are used) and one embeddedpipe layer (usually concrete and plaster are used) for embedding pipes. In this study, the typical section abcd (which is the typical cross section of this structure) is used for prototype model. The pipe

is embedded in the middle of the embedded-pipe layer. The pipe material should be economic, reasonable, durable, and allow heat to pass through efficiently. Polybutylene tube with the diameter of 20 mm is used in this study, and the thickness of pipe is neglected for investigating the thermal performance of the active pipeembedded building envelope conveniently since the heat transfer resistance of the pipe is small and neglected. The heat transfer resistance of the pipe width is very small when compared with the resistance of the concrete. The model development of FDFD and CFD models is more convenient when the thickness of pipe is neglected. In practical applications, the embedded-pipe building envelope may have different pipe spacing such as 100 mm, 150 mm, 200 mm, 250 mm and 300 mm etc. In this study, the pipe spacing is taken as 200 mm. 3.1. RC model development Dynamic simplified RC (i.e., resistance and capacitance) models are the best candidates for modeling building structure since it can simulate the dynamic thermal process in the structure, and this kind model can be solved easily for convenient integration with energy simulation software [21,24]. Although various configurations of R and C may be used for this simplified model, reasonable accuracy with less order is preferable. Usually, two-order model may well represent the dynamic characteristics of opaque building envelopes [24,33]. Fig. 3 shows the schematic of the dynamic simplified RC model of the active-embedded building envelope typical section abcd. In this model, Tout is the temperature of the external wall surface. Tin is the temperature of the internal wall surface. Tw is the temperature of the fluid. T1 and T2 is the node temperature of the dynamic simplified model. 5R2C model for this pipe-embedded building structure is developed. For the parameter determination of the simplified RC model, Frequency-Domain-Finite-Difference (FDFD) model (i.e., theoretical model) is used to calculate the theoretical frequency characteristic of this structure for reference since Frequency thermal characteristics may represent exactly the dynamical thermal behaviors of this structure under various disturbances. GA estimator is used to identify these parameters of the simplified model for allowing the frequency responses of the simplified RC model to match the theoretical frequency responses by using FDFD method. The details of the model development and validation can be found in Refs.[26,31]. 3.2. NTU model and parameter determination In this section, the classical effectiveness-number of transfer units (ε-NTU or NTU) model of active pipe-embedded building envelope is developed to evaluate the heat transfer along the pipe and total heat transfer on both surfaces of this structure. NTU method is a well-known method for solving heat transfer problems for

Fig. 2. Schematic of the cross section of the active pipe-embedded building envelope.

Fig. 3. Schematic of the dynamic simplified RC model of the active pipe-embedded building envelope.

Q. Zhu et al. / International Journal of Thermal Sciences 88 (2015) 170e179

sensible heat exchangers. In heat exchanger analysis, if the fluid outlet temperatures are not available, NTU or effectiveness method is used. To define the effectiveness of a heat exchanger, the maximum possible heat transfer is needed to be found that can be hypothetically achieved in a counter-flow heat exchanger of infinite length. The minimal thermal capacity flow rate fluid should be defined since the smaller thermal capacity flow rate is to include maximum feasible heat transfer among the working fluids during calculation. If one of the fluid's state is changed (condensation or evaporation), the thermal capacity flow rate is assumed as infinity. The other fluid is the minimal thermal capacity flow rate fluid. Therefore, the NTU method can be used to calculate the minimal thermal capacity flow rate fluid outlet temperatures. NTU model was ever used to predict the heat exchange along the ventilated slab between the slab cores and the ventilation air of the ventilated slab thermal storage system by Ren and Wright [14]. In this study, the NTU model for the active pipe-embedded building envelope is similar to that for the ventilated slab by Ren and Wright [14]. For the NTU model of this structure, some simplifications are assumed. The heat exchange between the circular water and the structure mass is assumed as the heat exchange between the two sides of the heat exchanger. One side of this structure is the water, and the other side is the concrete side. For the concrete side, the thermal capacity flow rate is much larger than that of the water. Therefore, for this structure, the temperature of the concrete side changes very small even if the water temperature significantly. It can be seen as a phase change process with large heat flux exchange and very small temperature change. It is similar to the condensation and evaporation of the fluid from the heat transfer point. The schematic of the cross section of the typical section abcd in Fig. 2 of the active pipe-embedded building envelope along the pipe is shown as Fig. 4. This cross section is along the pipe and the width of this structure. NTU method is used for predicting the heat transfer performance along the pipe direction of this structure. In Fig. 4, an analysis object is selected. Equation (1) shows the heat transfer balance equations of the analysis object. Then, Equation (1) can be transferred to the integral equation easily as showed as Equation (2). Equation (3) is the boundary conditions. Equation (2) can be transferred to a general linear equation as Equation (4) when the boundary conditions is used, and the value of the overall heat transfer coefficient (i.e., K) is constant, and the average temperature of structure mass (i.e., Tm) is constant since it assumes phase change occurs on the solid mass of this structure (i.e. condensation or evaporation occurs). Meanwhile, the water in the embedded pipe is the minimal thermal capacity flow rate fluid. The number of transfer units (i.e., NTU) is determined by the Equation (5). Then the outlet water temperature and the average water temperature along the pipe are showed as Equations (6) and (7) respectively.

173

dQ ¼ cw $mw $dTw ðDlÞ ¼ K$dS$ðTw ðlÞ  Tm ðlÞÞ ZTw2 Tw1



dTw ðDlÞ ¼ Tw ðlÞ  Tm ðlÞ

ZS 0

(1)

K$dS cw $mw

l ¼ 0; SðlÞ ¼ 0; Tm ðlÞ ¼ Tm l ¼ L; SðlÞ ¼ S; Tm ðlÞ ¼ Tm

ln

Tm  Tw2 KS ¼ ; Tm  Tw1 cw mw

NTU ¼

S ¼ p$D$L

KS cw mw

(2)

(3)

(4)

(5)

Tw2 ¼ Tm þ ðTw1  Tm Þ$eNTU

(6)

1  eNTU Tw ¼ Tm þ ðTw1  Tm Þ$ NTU

(7)

where: dQ is incremental of the heat flux of the analysis object, cw is the specific heat of the water, mw is the mass flow rate of the water, dTw(Dl) is the temperature incremental of the analysis object, Dl is incremental of the length along the pipe, K is the overall heat transfer coefficient, dS is the incremental area of the pipe, D is the diameter of the pipe, Tm(l) is the temperature of the structure mass at particular position, Tw(l) is the temperature of the water at the corresponding position, Tm is the average temperature of the structure mass, Tw is the average water temperature of the fluid, Tw1 is the inlet water temperature, Tw2 is the outlet water temperature, L is the total length of the pipe, NTU is the number of transfer units. Tm is the average temperature of the structure mass. It represents the average temperature over the width of the structure at a time. It is a virtual temperature and an intermediate variable used in NTU model. It can be calculated by Equation (8) by taking the arithmetic mean value of the node temperature, average water temperature, external wall surface temperature and internal wall surface temperature while the temperature is calculated by the RC model, and the value of temperatures are changed as the change of the time. The heat flux of the node of Tw can be considered as the heat flux taken away by the water as Equation (9) by the RC model. Then the overall heat transfer coefficient is calculated as Equation (10) by the RC model since the value of K is difficult to be obtained by the NTU method.

Tm ¼ ðTout þ Tin þ Tw þ T1 þ T2 Þ=5

(8)

Qw ¼ ðT1  Tw Þ=R3 þ ðT2  Tw Þ=R4

(9)

K ¼ Qw =ðTm  Tw Þ

(10)

where: Qw is the heat flux taken away by the water, K is the overall heat transfer coefficient, Tm is the average temperature of the structure mass, Tout is the temperature of the external wall surface. Tin is the temperature of the internal wall surface. 3.3. Numerical solution of the semi-dynamic model Fig. 4. Schematic of the cross section of the active pipe-embedded building envelope along the pipe.

RC model is a good model for predicting the heat transfer performance. However, it only can be used to analyze the heat transfer

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performance along the width direction. The heat transfer along the length direction of the pipe is neglected. NTU model is a good way to predict the heat transfer performance along the pipe direction. However, the NTU model is a steady model, and NTU is difficult to be defined without knowing the solid mass temperature. The semidynamic model is a coupled model of the dynamic RC model and the steady NTU model. The model development shows that the average water temperature is related to the average temperature of structure mass (i.e., Tm) and NTU as Equation (7). When the water temperature (i.e., average temperature), and the temperature of the external wall surface (i.e., Tout), and the temperature of the internal wall surface (i.e., Tin) are known, the heat transfer along the width of this structure can be calculated easily by the RC model, the node temperatures can be solved. The average temperature of the structure mass is related to the temperature of the external wall surface (i.e., Tout), the temperature of the internal wall surface (i.e., Tin), the average temperature of the water (i.e., Tw), and the node temperature (i.e., T1 and T2) as Equation (8). The value of the overall heat transfer coefficient (K) is related to heat flux taken away by the water (i.e., Qw), the average temperature of structure mass (i.e., Tm), and the average temperature of the water (i.e., Tw) as Equation (10). When the average temperature of structure mass and the NTU are known, the heat along the pipe and total heat transfer on the surface of this structure can also be calculated easily by the NTU model. Both models (i.e., RC model and NTU model) can be coupled together (called semi-dynamic model) by the link of Tm, T1, and T2 etc. The procedure for solving the semi-dynamic model is showed as Fig. 5, and described as follows. First, the value of the temperature of the external wall surface (i.e., Tout), the value of temperature of the internal wall surface (i.e., Tin) are the given boundaries, the value of these two temperature are detailed given in Fig. 7 of Chapter 5. And the initial value of the average water temperature (i.e, Tw,o) is selected. Then the value of the average temperature of structure mass (i.e., Tm,i), the value of the heat flux taken away by the water (i.e., Qw,i), and the value of the overall heat transfer coefficient (Ki) can be calculated by the RC model and Equations (8)e(10). In the next step, the value of the NTU can be got by Equation (5). Future, a new value of the average water temperature (Tw,i) can be calculated by NTU model and Equation (7). In the

Fig. 5. Procedure of the solution of the semi-dynamic model.

Fig. 6. Schematic diagram of the virtual experiment rig.

meantime, a residual error is set as ε (105 is used in this study). If the absolute difference between the Tw,i and Tw,o is less than ε, the iteration should stop. Otherwise, next iteration should start, and the iteration process continues until the absolute difference between the value of the Tw,i in the present step and the value of the Tw,i1 in the previous step is less than ε. When the iteration stops, the output is the final value of the Tw,i. And the thermal performance of this structure can be calculated easily. For this numerical calculation, a FORTRAN code is developed. 4. Test facilities Actual experiments are preferable for validating the accuracy of a simulation model or a numerical solution. However, actual experiments are usually expensive and time-consuming. Virtual experiment rigs are often used to produce system thermal performance for model validation of simplified models. CFD is a detailed numerical model, and is usually used for solving and analyzing problems that involve fluid flows. However, it is also can be used to predict the heat transfer performance of solid and calculate the heat transfer inside the solid, liquid, and the simultaneous heat transfer between them. Many researchers [6,18] used CFD technology to establish numerical simulation model for analyzing the unsteady heat transfer of the ground-coupled heat exchanger of a heat pump system or others. In this paper, CFD method is used to develop a virtual experiment model of pipeembedded building envelopes acting as a virtual experiment rig for validating the semi-dynamic model. Fig. 6 shows the CFD model of this structure as the virtual experiment rig. The length and the height of the active pipeembedded building envelope are set as 3000 mm and 2000 mm respectively, the total length of the embedded pipe between inlet and outlet is about 30 m the width is changed with structure configuration. The pipe is embedded in the plaster layer between two bricks or in the concrete etc. in series.

Fig. 7. The external and internal wall surface temperature profiles of a typical summer day in Wuhan.

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Table 1 Details of the 240 brick wall. Description

Brick Plaster

Thickness and thermal properties L (mm)

l (W m1 K1)

r (kg m3)

Cp (J kg1 K1)

R (m2 K W1)

120 40

0.81 0.87

1800 1700

1050 1050

0.148 0.046

To develop the CFD model of this structure, a dynamic CFD model is more accurate and needed to be established since the external wall surface temperature and internal wall temperature are changed in one day in the actual environment. Although CFD packages are available in the market, conventional CFD software cannot deal with periodical boundary conditions automatically [6]. Periodical boundary conditions are used just for producing periodical output for reference for comparison. A CFD interface program was developed to import the periodical dynamic temperature boundary conditions as the input of the CFD model in this paper. In the dynamic CFD model of this structure, the boundary conditions of the external wall surface and internal wall surface are set as the first boundary conditions with given temperature profiles of the external wall surface and internal wall surface. Of course, time terms of the energy, momentum and mass conservation equations of CFD model have to be considered for producing dynamic results. The material properties of this structure, such as density and specific heat are used as parameters of the CFD model. Combination of the thermal capacity and time term may take the thermal inertia into account. The boundary condition of the water inlet is set as the velocity inlet, and the inlet water temperature is constant. The outlet water temperature and the heat flux taken away by the water can be calculated easily. In this simulation, one cycle is 24 h, and the periodical condition repeats on this model continuously until the heat transfer reaches a periodically steady state. The judge criterion is that the outlet water temperature and the heat flux taken away by the water in the present day are the same as the previous day. Usually, five cycles may reach periodically steady state. 5. Validation tests and test results In this paper, the validation of the first part of the semi-dynamic simplified model, i.e., the 5R2C model, is not duplicated here for space saving since it is presented detailed in Ref. [31]. In the overview of the semi-dynamic simplified model as shown in Fig. 1, the heat transfer performance of this structure by the semidynamic model and CFD model in the time domain are used to validate the semi-dynamic model. To validate the accuracy of the semi-dynamic model of this structure, the outlet water temperature and the heat flux taken away by the water predicted by these two models (i.e., CFD model and semi-dynamic model) are used as thermal performances for comparison. Many kinds of active pipeembedded building envelopes are tested for validation. However, only three typical pipe-embedded building envelopes (i.e., a medium-weighted wall, a light-weighted wall, a heavy-weighted wall) are presented. 5.1. Case study I A brick wall with two bricks of 120 mm in thickness in series is widely used in buildings as external wall in China. In this study, this wall is used as active pipe-embedded building envelope. A plaster layer of 40 mm is added between these two bricks for embedding pipes. The detailed properties of the wall in SI unit are given in Table 1. The identified parameters of the RC model by using the method by Ref. [31] are shown in Table 2.

This case study is used to validate the accuracy of the semidynamic model of the brick wall as shown in Table 1 with different velocity of the inlet water. The semi-dynamic model is the coupled model of the RC model and the NTU model. The validation of the simplified RC model of this structure is described in reference [31]. For the NTU model, the NTU value is important since it affects the accuracy of this model when the boundary conditions are specified. Equation (5) shows that the NTU value is determined by the overall heat transfer coefficient (K), the area of the pipe (S), the specific heat of the water (cw), and the mass flow rate of the water (mw). The value of the cw is constant. The value of S is determined since the area of the active pipe-embedded building envelope, the pipe spacing and the diameter of the embedded-pipe is specified. The value of K is determined based on the above variables in the numerical solution of the semi-dynamic model (details given in Section 3.3). Therefore, the mass flow rate of the water (mw) is the important parameter to affect the thermal performance of this model. In following figures, the velocity is used instead of the water mass flow rate for more intuition. To obtain the thermal performance of the active pipe-embedded building envelope, the boundary conditions of the CFD model and semi-dynamic model should be specified in advance. In this study, the typical external and internal wall surface temperature profiles in a sunny day of the hot-summer region of Wuhan as shown in Fig. 7 are acted as the boundary conditions of these two models (CFD model and the semi-dynamic model). The inlet water temperature is 20  C, and the velocity of the inlet water is from 0.5 m/s to 0.7 m/s for allowing turbulent flow. The accuracy of the semidynamic model with different velocities of the inlet water are also presented and analyzed. Fig. 8(a) presents the outlet water temperature profiles predicted by the CFD steady model, CFD dynamic model and the semidynamic model respectively. For the CFD steady model, the single point external wall temperature and internal wall temperature are imposed on this CFD model. After many iterations, the output reaches steady state (i.e., the output does not change). Fig. 8(a) shows that when the external wall and internal wall temperature changed slowly, the outlet water temperature calculated by the semi-dynamic model agrees well with that predicted by the CFD dynamic model from 0 o'clock to 13 o'clock. When the temperature changes quickly from 14 o'clock to 23 o'clock, the outlet water temperature predicted by the semi-dynamic model still agrees with that predicted by the CFD dynamic model although marginal deviation may be observed. Fig. 8(b) shows the heat flux taken away by the water predicted by the CFD steady model, CFD dynamic model and the semi-dynamic model respectively. Similarly phenomenon is observed when the external wall surface and internal wall surface temperature change significantly. The total heat transfer taken away by the water is 7.03 MJ/m2 and 7.12 MJ/m2 predicted by the CFD model and the semi-dynamic model respectively. The relative error is about 1.2%. Fig. 8(a) and (b) also shows that the outlet water temperature and the heat flux taken away by the water predicted by the CFD steady model. The results show obvious deviation is observed between the outputs predicted by the dynamic CFD model and the steady CFD model. This is because the calculation result by the CFD steady model has nothing to do

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Table 2 Identified parameters of the simplified 5R2C model of the active pipe-embedded building envelope. Model

RC model

Parameters of resistance, R (m2 K W1), and capacitance, C (J m2 K1) R1

R2

R3

R4

R5

C1

C2

R*

C*

0.010

0.085

0.032

0.032

0.010

130,342

130,342

0.056

2,606,084

R*, C* are the calculated total resistance and capacitance based on the identified parameters.

with time, and the calculation result only is affected by the discrete boundary. However, the external wall and internal wall temperature are continuous in fact. Therefore, CFD steady model cannot present the real situation and is not accuracy. In this paper, the CFD model represents the CFD dynamic model thereafter for conciseness. Figs. 9 and 10 presents the thermal performance of the active pipe-embedded building envelope predicted by the CFD model and the semi-dynamic model when the velocity of the inlet water is 0.6 m/s and 0.7 m/s respectively. Figs. 8 and 9 also show that the predicted thermal performance (i.e., outlet water temperature and the heat flux taken away by water) exist a little deviation from 14 o'clock to 23 o'clock between these two models when the external wall and internal wall temperature change significantly, However, the semi-dynamic model can predict the thermal performance of this structure well as the CFD model in general. Based on the comparison of the thermal performance (i.e., the outlet water temperature and the heat flux taken away by water) of the active pipe-embedded building envelope with different velocity of the inlet water, it can be concluded that the thermal performance

predicted by using semi-dynamic model agrees well with that by using CFD model. It demonstrates that semi-dynamic model is good for thermal performance prediction of active pipe-embedded building envelopes. Both the CFD model and the semi-dynamic model can predict the outlet water temperature and thermal performance of this structure accurately. Figs. 8(b), 9(b) and 10(b) also show that the impact of velocity on heat flux is not obvious. Figs. 8(a), 9(a) and 10(a) show that the outlet temperature of the fluid with peak water temperature difference of about 1  C, and the average difference of about 0.5  C throughout the day. This is because the external wall surface temperature is much high from 12 o'clock to 19 o'clock as shown in Fig. 7, and the inertia of this structure is very obvious. The heat transfer is very large due to big temperature difference during this period. Similar phenomena occur in Figs. 8(b)e10(b). However, for the same common configured desktop computer with Inter core i7-3770 of 8 core processor, frequency of 3.4 GHz, and memory of 16G, the semi-dynamic model takes about 10 min

Fig. 8. Thermal performance of this structure predicted by the CFD model and the semi-dynamic model (water velocity 0.5 m/s).

Fig. 9. Thermal performance of this structure predicted by the CFD model and the semi-dynamic model (water velocity 0.6 m/s).

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177

Table 3 Details of the light weighted wall. Description

Thickness and thermal properties L (mm)

l (W m1 r (kg m3) Cp (J kg1 R (m2 K K1)

Stucco Light density concrete Plaster

20 100 20

0.692 0.571 0.727

1858 609 1602

K1)

W1)

840 840 840

0.029 0.175 0.028

Table 4 Identified parameters of the simplified 5R2C model of the light-weighted active pipe-embedded building envelope. Model

Parameters of resistance, R (m2 K W1), and capacitance, C (J m2 K1) R1

RC

R2

R3

R4

R5

C1

C2

R*

C*

0.022 0.217 0.261 0.134 0.061 44,343 51,150 0.223 95,493 model

R*, C* are the calculated total resistance and capacitance based on the identified parameters.

evaluated by imposing dynamic boundary conditions on the models as shown in Fig. 7. The inlet water temperature is 20  C, and the inlet water velocity is 0.5 m/s for allowing turbulent flow. The outlet water temperature and the heat flux taken away by the water are also used for comparison. The thermal performance of the light-weighted wall predicted by the CFD model and the semi-dynamic model are presented as Fig. 11. The results show that the semi-dynamic model can predict

Fig. 10. Thermal performance of this structure predicted by the CFD model and the semi-dynamic model (water velocity 0.7 m/s).

for calculation while the CFD model needs 20 h for doing it. In addition, the semi-dynamic model (coupled RC model and NTU model) can be solved very easily and can be integrated with conventional building simulation package for building performance evaluation. Therefore, the semi-dynamic model is good and quick for thermal performance analysis of active pipe-embedded building envelopes. It is mentioned here that in this manuscript, the value of the temperature of the external wall surface (i.e., Tout) and the internal wall surface (i.e., Tin) are given as boundary condition. When the external wall and internal wall temperature are given, an external thermal resistance (reciprocal of the external convection coefficient) and an internal thermal resistance (reciprocal of the internal convection coefficient) are needed to be connected in series with R1 and R5 of the RC model as shown in Fig. 3 respectively. 5.2. Case study II The brick wall is a typical medium-weighted wall. In this section, a typical light-weighted is used for embedding pipes as pipeembedded building envelopes for validating the accuracy of the semi-dynamic model. A light-weighted wall is selected from the ASHRAE Handbook [1]. Pipes are embedded in the concrete layer. The detailed properties of these two walls in SI unit are given in Table 3. The identified parameters of the RC model by using the method by Ref. [31] are shown in Table 4. Similarly, the dynamic thermal performance of the semidynamic model and the CFD model of these two walls are

Fig. 11. Thermal performance predicted by the CFD model and the semi-dynamic model of the light-weighted wall.

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Q. Zhu et al. / International Journal of Thermal Sciences 88 (2015) 170e179

Table 5 Details of the heavy weighted wall. Description

Thickness and thermal properties

l (W m1

r (kg m3)

Cp (J kg1 K1)

R (m2 K W1)

100 200

1.333 1.731

2002 2243

920 840

0.075 0.116

20

0.727

1602

840

0.028

L (mm)

K1) Face brick Height density concrete Plaster

the thermal performance of different active pipe-embedded building envelopes as well as CFD model although a little deviation may observed in high frequency region (i.e., temperature changes quickly). The relative error of the total heat transfer taken away by the water for the light-weighted wall is about 5.2%. The semi-dynamic models of pipe-embedded light-weighted wall also consume much less computation time than the CFD models do.

5.3. Case study III A heavy weighted wall is also selected from ASHRAE Handbook of Fundamentals [1] for embedding pipes to develop the semidynamic model and performance evaluation. It is a typical heavy weight wall, and mainly composed of face brick, high density concrete and plaster etc. The details of properties in SI unit are shown in Table 5. The identified parameters of the RC model by using the method by Ref. [31] are shown in Table 6. This case study is also used to validate the accuracy of the semidynamic model. The boundary conditions on the models are the same as the pipe-embedded light-weighted wall. For the paper saving, only the inlet water temperature is 20  C, and the inlet water velocity is 0.5 m/s is presented and analyzed. Fig. 12(a) and (b) shows the outlet water temperature and the heat flux taken away by the water by using the semi-dynamic model and CFD model respectively. It shows that the outlet water temperature and the heat flux taken away predicted by the semidynamic model still agrees with that predicted by the CFD model although marginal deviation may be observed. The relative error of the total heat transfer taken away by the water for the heavyweighted wall is 2.3%. The semi-dynamic models still consume much less computation time.

6. Conclusion This paper presents a semi-dynamic model of active pipeembedded building envelopes for thermal performance evaluation. This semi-dynamic model is a coupled model with two parts. The first part is a simplified dynamic RC model (i.e., resistance and capacitance model), and the second part is a classical NTU model. The classical NTU model is a model to predict the heat transfer along the pipe and total heat transfer on both surfaces of this structure. CFD model is developed as a virtual experiment rig for producing the thermal performance of the active pipe-embedded building envelopes for the validation of the semi-dynamic model.

Fig. 12. Thermal performance predicted by the CFD model and the semi-dynamic model of the heavy-weighted wall.

For the validation of the semi-dynamic model, the thermal performances of three typical various-weighted walls with different inlet water velocities are predicted by the semi-dynamic model and CFD model. All the validation results demonstrate that the thermal performance of the active pipe-embedded building envelopes can be predicted accurately by the semi-dynamic model taking the predicted thermal performance by CFD model as reference. These results further show that the thermal performance predicted by the semi-dynamic model almost overlaps with that by the CFD model when external wall and internal wall surface temperature changed slowly. When the temperature changes quickly, the outlet water temperature as well as the heat flux predicted by the semi-dynamic model still agrees with that predicted by the CFD model although marginal deviation may be observed. The average relative error of the total heat transfer taken away by the water is about 5% by the CFD model and the semi-dynamic model. The semi-dynamic model has better computation performance than CFD model. For the same common configured desktop computer, the semi-dynamic model takes about 10 min for calculation while the CFD model needs many hours for doing it. At the meantime, the semi-dynamic model can be solved very easily and

Table 6 Identified parameters of the simplified 5R2C model of the heavy-weighted active pipe-embedded building envelope. Model

RC model

Parameters of resistance, R (m2 K W1), and capacitance, C (J m2 K1) R1

R2

R3

R4

R5

C1

C2

R*

C*

0.082

0.163

0.107

0.089

0.042

308,408

235,168

0.213

543,576

R*, C* are the calculated total resistance and capacitance based on the identified parameters.

Q. Zhu et al. / International Journal of Thermal Sciences 88 (2015) 170e179

can be integrated with conventional building simulation package for building performance evaluation. Acknowledgments This work presented in this paper is financially supported by a grant (No. 51178201) of Natural Science Foundation of China and supported by the research fund of “Program for New Century Excellent Talents in University” (No. 2011CDB292) as well as a grant (No. 20120142110078). Nomenclature C cw dQ dS D dTw(Dl) K L NTU Qw R T1 T2 Tin Tm(l) Tm Tout Tw Tw1 Tw2 Tw (l)

capacitance of the dynamic simplified RC model (J/(m2 K) specific heat of the water (J kg1 K1) incremental of the heat flux of the analysis object (W) incremental area of the pipe (m2) diameter of the pipe (m) temperature incremental of the analysis object ( C) overall heat transfer coefficient total length of the pipe (m) number of transfer units heat flux taken away by the water (W) resistance of the dynamic simplified RC model (m2 K/W) node temperature of the dynamic simplified RC model ( C) node temperature of the dynamic simplified RC model ( C) temperature of the internal wall surface ( C) temperature of the structure mass at particular position ( C) average temperature of the structure mass ( C) temperature of the external wall surface ( C) average water temperature ( C) inlet water temperature ( C) outlet water temperature ( C) temperature of the water at the corresponding position ( C)

Greek symbols frequency (rad s1) incremental of the length along the pipe

u Dl

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