Study on the heat transfer model and the application of the underground pipe system

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1 Study on the heat transfer model and the application of the underground pipe system Xiang ZHOU 1, Yingxin ZHU 1, Chunhai XIA 1 1 Tsinghua University, Beijing, P.R.China Corresponding zhuyx@tsinghua.edu.cn SUMMARY The underground pipe system (UPS) cools the intake outdoor air through the underground pipe before supplying it to the indoor space, so that the cooling load of the air-conditioning system of the building can be obviously reduced. In this paper, a quasi-three-dimensional heat transfer model was developed, which was made up with a two-dimensional unsteady heat transfer model of earth and a one-dimensional fluid model of air. The total heat transfer process was considered when the condensation happened on the pipe wall during the calculation. Moreover the model was validated by the comparison between simulated result and measured data of a built project applied UPS. By means of this model, the earth-to-air heat exchanging process was simulated and the effect of the pipe parameters, such as the length,depth of burial and ventilation velocity of underground pipe system, on the cooling/heating capability was analyzed. The simulated result was also used to direct the design, operation and management of the UPS. INTRODUCTION Underground Pipe System (UPS) utilizes the energy accumulating in the soil to cool or heat outdoor air, and then supplies it into rooms. The system can ameliorate indoor environment and save energy. Moreover its air-conditioning efficiency is limited by outdoor climate, structure of underground pipe, operating schema, etc. Therefore the mathematic model which can be used to simulate the earth-air heat exchange process accurately is a very important tool for engineering design. In most studies of the earth-air heat transfer models, the models can be separated into two kinds: one is steady models; the other is unsteady model. A steady model based on the assumption of constant heat flux and half-infinite object heat transfer was simple and fit for engineering design [1]. Another steady model utilized the empirical equation which was regressed by the measurement data [2]. The unsteady model includes regression model, finite difference model and finite element model. Some researchers introduced the finite difference model to solve the 3-dimension unsteady sensible heat transfer process, and analyzed the influencing factors of operating effect [3][4]. Furthermore, a 3-dimension finite-element model, which can judge whether moisture will condense on the wall of UPS, was developed to depose the simulation of total heat transfer process while the air went through the underground pipe [5]. In this field great progress has been made, however the present models still don t satisfy the requirements. The steady models mentioned above can t predict the temperature variation during the operation of UPS. The 3-demintional models required a lot of computations, so it was hard to accomplish annual simulation of UPS due to the complex computations. There is

2 still dearth of accuracy, general and swift computation model to direct the design of UPS projects. In this paper, a quasi-three-dimensional heat transfer model was developed, which was made up with a two-dimensional unsteady heat transfer model of earth and a one-dimensional fluid model of air. By means of this model, the effect of the pipe parameters, such as the length, depth of burial and ventilation velocity of underground pipe system, on the cooling/heating capability was analyzed. The simulated result can also be used to help the designers to determine the structure and the operation scheme of the UPS. METHODS 2.1 Numerical simulation model The heat & mass exchanging process can be predicted by a quasi-three-dimensional model, which assumes that heat transfer of soil along the direction of pipe can be ignored. For the z basic calculate surface in Figure 1, energy balance equation of soil and air are respectively presented as: 2 2 t t t soil a( soil soil ) 2 2 (1) x y and iair, z V air G ( iair, z 1 iair, z ) dq (2) where t soil is temperature of soil( C), τ is time(s), a is thermal diffusivity(m 2 /s), V is volume of air for a basic grid(m 3 ), i air,z is air enthalpy of computational unit in Z coordinate axis(kj/kg), ρ air is density of air(kg/m 3 ), G is fresh air volume(m 3 /s), and dq is heat transfer quantity between air and earth(w). Figure 1. Grid division for numerical simulation Figure 2. Cross-section of the UPS Because latent heat exchange may exist between air and earth, dq can be calculated by Eq.(3) for only sensible heat exchange or by Eq.(4) for total heat exchange. J dq hf ( t t ) j 1 J j 1 Z, j b, Z, j k, Z hf ( t i 2500 d ) Z, j b, Z, j k, Z k, Z (3)

3 J ' dq h FZ, j ib, Z, j ik, Z j 1 ( ) (4) where j is No.j earth-to-air heat transfer surface, h is convective heat transfer coefficient (w/(m 2. C)), h is convective mass transfer coefficient (kg/(m 2.s)), F Z,j is area of earth-to-air heat transfer surface of computational unit Z (m 2 ), t b,z,j is surface temperature of the pipe of No,j surface, t k,z is air temperature in the pipe of computational unit Z, i k,z is saturated enthalpy corresponding to temperature of pipe wall(kj/kg), d k,z is absolute humidity of air (kg/kg). Finite difference method is applied to solve the problem, and temperature and humidity of air extracted from the UPS can be achieved. 2.2 Experimental Measurement of a UPS To validate the availability of numerical calculation model, the airflow velocity, inlet and outlet air temperature and humidity of a UPS was measured. The experimental result would be compared with the simulation result. The Building applied UPS system is in Beijing. The shape of cross-section of the UPS is shown in Figure.2. Table.1 reveals the main parameters of the system. The experiment time was from Jul.15th, 2002 to Aug.18th, The system operated from 7:00am to 19:00pm everyday. Table 1. Parameters of an UPS in a college in Beijing Mean annual Length Diameter Material of pipe wall Burial depth temperature of soil surface 250m 1.4m Steel concrete 3m 13.1 C 2.3 Effect of factors of UPS Based the heat transfer model, the effect of different parameters, such as length, burial depth, airflow velocity and operating mode of UPS, on air-conditioning performance was investigated. The outdoor air temperature and humidify data from Jul.7th, 2002 to Jul.9th, 2002 were selected as computational conditions (Figure.3). The cross-section size of pipe is 1m 1m. In the system, only one pipe was buried under the ground. RESULTS 3.1 Measurement result of UPS Figure 3. Weather parameters from July 7th to 9th in Beijing

4 The airflow velocity and temperature in the outlet of the UPS was measured. When the system was running, the wind speed maintained at about 3 m/s (Figure.4). Figure.5 shows the comparison between the measured outlet temperature and the simulated temperature; the outdoor temperature is also presented in the figure. From Jul. 17th to Jul. 29th, the measured data accorded with the simulated data on the whole. The average temperature which was measured in the outlet was 20.3 C; and the computed temperature was 20.6 C, which was 0.3 C higher than the measured data. Figure 4. Measured air velocity Figure 5. Measured and simulated air temperature 3.2 Influence of UPS parameters on the operating effects Length of UPS As the calculated examples, the depth of burial of pipe was 3.5m; the air velocity was 3m/s, the length was 50m, 100m, 200m and 300m respectively. The outlet air temperature, desiccation and cooling capacity are shown in Figure.6. When the length increased, the outlet temperature decreased; and the desiccant and cooling capacity rose. The amplitude of temperature fell after the outdoor air went through the system. The outdoor air can be cooled down below 26 C by a 50m long pipe, and below 22 C by a 300m long pipe (Figure.6a). For example, the maximal desiccant capacity of a 300m long pipe was 2~3g/kg (Figure.6b); its maximal cooling capacity reached 30~40kw (Figure.6c); and its average daily cooling duty was 340kWh (Figure.6d). a. Outlet air temperature of UPS b. Desiccant capacity of UPS

5 c. Cooling capacity of UPS d. Average daily cooling duty of UPS Figure 6. Influence of different length of UPS Burial depth of UPS In the simulation, the length of pipe was 200m; airflow velocity in the pipe was 3.5m/s; burial depth was 2.5m, 3.5m, 4.5m, 5.5m respectively. Figure.7 shows the variation of outlet air temperature, desiccant capacity and average daily cooling duty of the UPS. a. Outlet air temperature of UPS b. Desiccant capacity of UPS c. Average daily cooling duty of UPS Figure 7. Influence of different depth of UPS Airflow velocity of UPS The simulated UPS was 200m long, 3.5m deep from the ground. The airflow velocity in the pipe was 1m/s, 3m/s, 5m/s and 7m/s respectively. The lower the velocity was, the lower the outlet air temperature was (Figure.8-a), the higher the desiccant capacity was (Figure.8-b), and the smaller the average daily cooling duty was (Figure.8-c). When the wind speed was 1m/s, the outlet air temperature was in the range of 18~21 C. And the maximal desiccant capacity can reach 4g/kg Operating mode of UPS In this case, the length of pipe was 200m; the burial depth was 3.5m; the airflow velocity was 3m/s. The system was operated in the two different modes: One was running continuously, the other was only operated at 8:00~18:00 daily. The outlet air temperature and cooling capacity are shown in Figure.9.

6 a. Outlet air temperature of UPS b. Desiccant capacity of UPS c. Average daily cooling duty of UPS Figure 8. Influence of different air velocity DISCUSSION a.outlet air temperature of UPS b. Cooling capacity of UPS Figure 9. Influence of different working mode In this study, a heat transfer model was developed to predict the operating effects of UPS. The influence of UPS parameters on outlet air temperature, desiccant and cooling capacities and average daily cooling duty was investigated. 4.1 Length of UPS The simulated data indicated that the underground pipe system (UPS) can dehumidify outdoor air in summer, if the system is long enough. When moisture is removed from air, the heat transfer capability between air and pipe wall is enhanced. In this paper, while the length of UPS was greater than 100m, the air intake can be cooled below its dew-point temperature; and then heat transfer process was stronger due to desiccant capacity of the pipe. The average daily cooling duty increased by 12kWh as the length of pipe was lengthened by 10m. Beside these, while the length was less than 100m, the system had less dehumidification capability and less cooling effect than longer system; an increment of 10kWh in the average daily cooling duty associated with a 10m increase in length.

7 4.2 Burial depth of UPS As a result of our simulation, when the burial depth was 1.5m, the UPS had little dehumidification capability; the moisture content of air change little while it went through the pipe. When the burial depth increased to 2.5m, the desiccant and cooling capacity rose significantly. However the cooling capability increased slowly as the burial depth was deeper than 3.5m. As the deeper the burial depth was, the more expensive the project cost was; it is likely that the optimum burial depth of UPS was 3~4m. 4.3 Airflow velocity of UPS The average daily cooling duty increased as the airflow velocity increased, because the coefficient of heat transfer of pipe was positively proportional to the velocity 0.8-power. The increment of velocity led to the growth of the cooling capacity. Moreover while the velocity increased, the outlet air temperature rose; and the desiccant capacity decreased. It is because heat exchange increased slower than the flow rate of air, as the velocity increased the unit mass heat transfer of the air decreased; the air temperature in the pipe increased. So the latent heat exchange part is shortened, and the unit mass desiccant capacity decreased. Accordingly, if the airflow velocity is low in UPS, the system has lower cooling capacity and application effect. In contrast if the velocity is too high, the outlet air temperature and humidity is excessively high; thus the supplied air has little air-conditioning effect. For the UPS with specific length, there should be an optimal range of the airflow velocity in which the system operate effectively and economically. This optimal velocity would rise when the length of the pipe increase. 4.4 Operating mode of UPS When the UPS ran in the intermittent mode, the outlet air temperature was 1 C lower than that in the continuous mode. Because the quantity of heat absorbed by the pipe wall in the daytime can be transfer to the deep soil when the system stopped operating at night, the temperature of the wall was lower. Thus the cooling capacity of system rose by 40 percent in the intermittent mode relative to that in the continuous mode. Therefore the rationalized design can improve the cooling capacity of the system effectively. This paper only used the pipes with some specific size as the calculated examples to obtain the results. If the pipe parameters are changed, the quantitative results should be varied. But the qualitative conclusions presented in the paper are still available. CONCLUSIONS Based on the experimental investigations and numerical simulations presented in this paper, the following conclusions may be made: a) The quasi-three-dimensional heat transfer model was developed to predict the heat and mass transfer process between air and soil. It was verified by experimental measurement and can be used to direct the design, operation and management of the UPS. b) The cooling capacity and the length of UPS were positively related. The increment of cooling capacity of longer pipe was greater than that of short pipe, when the length

8 increase by the same distance. c) The deeper the burial depth was, the higher the cooling capacity was. However the cooling capability increased slowly as the burial depth was deeper than 3.5m. It appeared that the optimum burial depth of UPS was 3~4m. d) While the airflow velocity rose, the quality of heat exchange increased; the outlet air temperature and humidity went up also. A UPS with specific length should have an optimal velocity at which the cooling effect and economical efficiency can be performed. The optimal velocity was positively related with the length of system. e) In the intermittent operating mode, the cooling capacity was increased by 40% than that in the continuous operating mode. In the development of the paper we considered that the comprehensive analysis of the factors investigated hereinbefore should be presented to discover the interrelationship among these factors. To study the economical efficiency of UPS is also among our future research goals. ACKNOWLEDGEMENT This work was supported by the Project Fund of National Eleven Five-Year Scientific and Technical Support Plans(NO 2006BAJ02A06 & NO 2006BAJ02A02). The authors also acknowledge the support of Ling Song of Miami University and Hongsheng Yang of China Aeronautical Project & Design Institute for their assistance in the experiments and measurements. REFERENCES 1. Mu, L, (1982). Calculation and application of underground pipe system. Beijing: Architecture Industry Publishing Company. 2. Mihalakakou, G., Santamouris, M., and Asimakopoulos, D., (1995). Parametric prediction of the buried pipes cooling potential for passive cooling applications, Solar Energy, 55(3), Waquer, R., Beisel, S., Spieler, A., and Vajen, K., (2000). Measurement modeling and simulation of an earth-to-air heat exchanger, 4th ISES Europe Solar Congress, Kopenhagen, Dänemark 4. Song, L., (2003). Simulation study on passive ventilation for cooling, Master thesis, Beijing, Tsinghua University. 5. Feng, Y., Chen, Q., (1994). Study on thermal process of buried tube beneath the earth surface to improve the indoor thermal environment, Acta Energiae Solaris Sinica, 15(4),