Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 110 (2017) 365 – 370
1st International Conference on Energy and Power, ICEP2016, 14-16 December 2016, RMIT University, Melbourne, Australia
Numerical modeling of a simplified ground heat exchanger coupled with sandbox Wenxin Lia,b,c,*, Jingliang Donga,b,c, Yong Wanga,b, Jiyuan Tuc b
a College of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400045, China Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment, Chongqing University, Chongqing 400045, China c School of Engineering, RMIT University, Melbourne 3000, Australia
Abstract The ground heat exchanger (GHE) system is an energy-efficient application employing the geothermal energy in residential and commercial buildings. Compared with field tests or laboratory measurements, computational fluid dynamics and heat transfer offers a cost-effective approach to give accurate prediction on thermal performance assessment of the GHE system. In this study, the effects of different boundary configurations were numerically investigated based on a referred laboratory GHE experiment. First, both recorded input water temperature profile and the given heat load were used as heat input for numerical simulations, and all facets of the ground domain were set as adiabatic condition. Through comparing the numerically predicted output water temperature profile with the experimental recorded one, the first approach using the recorded input water temperature profile as heat input gave a close prediction with the experimental data, while the numerical results based on the second approach using the given heat load showed a considerable discrepancy compared with experimental data. This comparison discrepancy can be attributed to the adiabatic assumption for the ground domain facets through heat balance analysis, and can be addressed by introducing a dynamic thermal boundary configuration for side- and end-walls. This study demonstrated the significance of boundary conditions consideration and provided a solution by utilizing dynamic thermal boundary treatments compared with the adiabatic assumption. The numerical modeling methods can contribute towards improved GHE numerical simulations based on finite ground domains. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2017 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review underresponsibility responsibility of the organizing committee 1st International Conference Energy Peer-review under of the organizing committee of the of 1stthe International Conference on Energyonand Power.and Power. Keywords: Ground Heat Exchanger; Boundary Condition; CFD; Heat Loss; Temperature Distribution.
* Corresponding author. Tel.: +61-3-9925-6191; fax: +61-3-9925-6108. E-mail address:
[email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 1st International Conference on Energy and Power. doi:10.1016/j.egypro.2017.03.154
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1. Introduction As an energy-efficient application using renewable energy, ground-coupled heat pump (GCHP) system has been widely used for building air conditioning purpose all over the world [1]. The ground heat exchanger (GHE) is the main component distinguishing GSHP systems from conventional air conditioning systems with higher efficiency and lower running costs. Thus it is of great significance to accurately model the thermal behavior of GHEs, especially the outlet temperature of the GHEs which determines the performance of the whole system. Field tests or laboratory measurements are commonly adopted approaches to assess the thermal performance of the GHE system [2]. However, the testing process requires extensive studies that demand prolonged time and expensive resources. Heat transfer models of GHEs including analytical, numerical and hybrid models are able to give thermal performance predictions [3, 4]. Analytical models are easy programmed and widely applied [3] due to no special requirement for calculation, which involve line source model [5], cylindrical source models [6], the finite line source models [7]. Combining the advantages of analytical and numerical models, hybrid models are first presented by Eskilson [8] using non-dimensional temperature response factors, and then developed in recent years [9, 10]. However, due to the ignorance of grout, U-pipe and fluid thermal capacities, both analytical and hybrid models fail to provide entire time scale prediction, especially in the first several hours. Numerical models such as computational fluid dynamics (CFD) models provide an alternative and more accurate approach on thermal performance prediction, which also can elaborate mechanism and complexity of the GHE heat transfer [11]. As boundary conditions are vital to the simulation accuracy, they should be carefully determined especially the one where heat inputted to the GHE. Most numerical models impose a heat flux on the pipe [12, 13], and some adopt inlet water temperature as the boundary condition [14, 15], while few researchers focus on the simulation difference brought by different boundary conditions. Although both analytical and numerical models are well developed to model the transient temperature performance of the GHEs, few of them take boundary conditions into detailed consideration. In this study, a numerical GHE heat transfer model based on a laboratory sandbox was developed to investigate the effects of different boundary configurations for ground domain. A dynamic thermal boundary modeling approach was proposed to overcome the limitation of adiabatic assumption, and the improved thermal boundary treatment can contribute towards improved GHE numerical simulations based on finite numerical domains. 2. Methods Data from a GHE coupled with laboratory sandbox reported by Beier [16] is used to validate the numerical accuracy and obtain a better understanding of heat transfer process of GHEs. The sandbox is a large wooden box filled with homogeneous wet sand, which consists of an aluminum pipe (severed as the borehole wall), a 18.3m U-pipe both centered along the length of the wooden box and bentonite-based grout filled as backfilling material (Fig.1(a)). Detailed parameters of this experiment are listed in Table.1. A 52h thermal response test with constant heat input experiment conducted in this sandbox is used in this study, and the data set consists of temperature responses per min at the inlet and outlet of the U-pipe, and soil temperatures recorded by 20 thermistors at different radial and vertical positions within the sandbox. The CFD model of this study is based on governing equations of fluid flow and transport principles for incompressible turbulent flow in terms of mass, momentum and energy conservation equations, equations for turbulent kinetic energy and turbulent dissipations rate are solved with standard k-ε closure scheme. All governing equations are solved by using the commercial CFD code ANASYS Fluent (ANSYS, NH, USA). To simplify the calculation, only a half of the actual space domain was taken into calculation due to the symmetrical geometry feature. Besides symmetry is allocated to the symmetry-axis side, boundary conditions of other sides are set as adiabatic. The solid properties are assumed homogeneous for each material, and the initial temperatures in these domains are identical to the undisturbed ground temperature. The thermal resistance formed in the pipe interface can be taken into account by treated as thin-wall thermal resistance in FLUENT. The fluid temperatures at inlet (Tin(t)) and outlet (Tout(t)) of the tube are joined by: Tin (t ) Tout (t ) 'T (t ) (1)
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where 'T (t )
Q U wcwVw
(2)
where Q is the heat load extracted or rejected to the ground; ρw, cw and Vw are the density, heat capacity and volumetric flow rate of water. Table 1. Detail parameters for the sandbox experiment [16-18] Parameter Length of the sandbox (L1) Width of the the sandbox (L2) Depth of the sandbox (H) Inner diameter of borehole (Db) Length of the borehole (Hb) Length of the U-tube (Hp) Outer diameter of the U-tube(Dpo) Inner diameter of the U-tube (Dp) Distance between centers of pipe (d) Thermal conductivity of soil (ks) Thermal conductivity of grout (kg) Thermal conductivity of pipe (kp) Volumetric heat capacity of soil (Cs) Volumetric heat capacity of grout (Cg) Volumetric heat capacity of pipe (Cp) Average fluid volumetric flow rate (m) Undisturbed ground temperature (T0)
Value 1.826 m 1.8 m 18.32m 0.126 m 18.32 m 18 m 0.0668 m 0.05466 m 0.053 m 2.82 W/mK 0.73 W/mK 0.39 W/mK 3.2×106 J/(K m3) 3.8×106 J/(K m3) 1,848,352 J/(K m3) 1.97×10-4 m3/s 22 oC
In this study, with sufficient available data, two kinds of boundary conditions - recorded inlet water temperature (Tin) and heat load (Q) can be imposed as inlet boundary condition. The former one gives the outlet temperature predictions calculated by numerical heat transfer; the latter one is more frequently used as the heat load can be obtained in advance [13, 19, 20]: with a given initial inlet water temperature, the outlet one can be calculated by imposing heat load in every time step by integrating Eq.(1) and Eq.(2). User defined file (UDF) is used to input transient inlet temperature in each time step. Transient simulation with a time step of 30s [13] is performed for transient heat transfer purpose. The dimension of the computational domain is meshed with combined uniform and non-uniform grid. Prior to performing CFD simulations, grid independent study has been conducted with different numbers of grids, and mesh with elements numbers of 471,098 is used for further simulation in this study.
(a)
(b)
Fig.1. (a) Schematic diagram and (b) heat balance analysis of the GHE.
It should be noticed that in reality the heat exchange may occur at the walls of the sandbox or through external pipes. Though the sandbox is surrounded by a wooden box with 22oC air circulated outside the box in order to minimize the heat loss [16], heat loss still occurs between the sandbox walls and the surrounding air. Therefore, a heat balance analysis should be conducted as showed in Fig.1 (b). According to energy conservation of the water, pipe,
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grout and the soil, thermal boundary conditions should follow to this principle: the majority of the heat carried by the fluid (Qin) is stored in the soil, pipe and grout (Qsink), and minority is transferred as heat loss (Qloss). (3) Qin Qsink Qloss In this case, the heat loss occurs on every surface of the sandbox, and it can be calculated by subtraction of the inputted heat load in two boundary conditions. For simplification, only heat loss in soil domain is taken into consideration, and it can be divided into two parts: through end-walls (Qend) and side-walls (Qside). (4) Qloss Qend Qside Moreover, it takes a period of time for heat to transfer from the tube to the side-walls, thus this part of heat loss should not be considered at the beginning stage, and critical time (tc) [21] is employed to indicate the time when farfield surfaces start to release heat loss. Therefore, the whole operation time can be divided into two stages: When t ≤ tc, the heat loss are only transferred through the two end-walls of the sandbox, and the side-walls can still be set as adiabatic with no heat transferred through them; when t > tc, both the end- and side-walls have the heat loss. 3. Results and Discussion To validate the numerical prediction accuracy, the numerically predicted outlet water temperature was compared with recorded data, and results are shown in Figure 2 (a). The prediction using inlet water temperature shows a good agreement with experimental outlet water temperature during the entire experimental period, with an average relative error of 0.38%. Fig.2 (b) and (c) gives the prediction results of soil temperature at two time points: t=10h and t=50h, which shows that most of the simulation results matched well with the results recorded by 20 thermocouples. All the soil temperatures increase with the time and decrease in the radial direction from borehole wall to side-walls. As more heat load is stored near the borehole where temperature deviation will have a large impact, special attention should be paid to the soil temperature near the pipe. The soil temperature prediction at the borehole wall showed a good match except the deepest position (No.15), while only one point was validated when a transient quasi-3D line source model is used [22]. A Large gap between point No.15 and the other three shows that No.15 may attribute to the measurement error. Overall, the reasonably good agreements demonstrate that the proposed numerical model with recorded inlet water temperature used as boundary conditions can be used for validation.
(a)
(b)
(c)
Fig. 2. Comparison for of (a) outlet water temperature profiles and soil temperature profiles at various differences from borehole wall after (b) 10 h and (c) 50 h between experiment results (points) and simulation results (solid lines) with boundary condition of inlet fluid temperature.
However, compared with the former approach using recorded inlet water temperature, the predicted outlet water temperature calculated with the given heat load imposed shows a considerable discrepancy compared with experimental data (Fig.3), where the discrepancy becomes evident and stable in the late stage with a relative error of 4.75%, around 1.8oC at the end of the operation. Such large discrepancy can also be found in other validations using heat load as boundary conditions, Li and Lai noticed an absolute differences of 2–3oC with all relative errors smaller than 10% when validating the proposed composite-medium line-source model [19]. Couples of factors can affect the thermal behaviors of the GHE coupled with sandbox, as well as the experiment reliability. In the experiment, five water lines were installed along the length on the bottom of the sandbox and the sandbox was saturated with the water flow seeped upward and laterally through the sand, which made it impossible
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to achieve a complete uniform saturation in the sand. However, with limited given information, the soil domain was assumed to be uniform with the ignorance of water advection in the numerical model, and it also can explain a less evident deviation of prediction temperatures in the depth direction. Moreover, non-uniform initial temperatures (with a variation range of 0.7 oC) can be observed in the soil domain, while a uniform soil temperature distribution (22oC) was initialized when simulation, and such simplification makes the prediction values but not the tendency deviated from the measured one. Additionally, as wet sand was used in this experiment, it should be noticed that the thermal properties of the sand changes with the temperature variation [23], thus assumed constant thermal properties could be another error source induces numerical results discrepancy.
Fig. 3. Comparison for outlet water temperature profiles between experiment and simulation results.
Li and Lai [13, 19] also concluded three reasons accounting for their errors produced with heat load used as boundary condition: heat input rate, uncertainties from thermal conductivities and heat capacities of the sand and grouting material, and the first one was considered to be the main reason. Apart from the uncertainty of the heat input, heat loss should be the main reason contributing to the discrepancy in the prediction of outlet water temperature. Ideally, the heat load carried in water should be completely transferred to the sand via the GHE, while due to some inevitable factors like incomplete insulation and outer edge effect, some heat may diffuse into air through connecting pipes and outer wall of the sandbox. As majority of the heat loss have been taken into account previously, a good match appeared when recorded inlet water temperature was used as boundary condition; while the one with heat load seems to be an ideal condition. Such heat loss can be minor at the beginning, and it then accumulates to have a stable influence only after 1.5h. Thus a large discrepancy appears at the outlet water temperature comparison can be attributed to the adiabatic assumption for the ground domain facets, and it can be minimized by a proper thermal boundary treatment. Based on the energy balance analysis (Fig.1 (b)), the Qloss can be calculated by subtracting Eq.(3) of two boundary conditions. It should be noticed that the ground heat storages (Qsink) are different when two kinds of the thermal boundary conditions employed because of different soil temperatures. Actually, tc are different in every facets because the temperatures and heat transfer rate changes when the water flows, but it is difficult and needless to calculate an accurate tc to change the adiabatic boundary condition for the side-walls. Therefore, based on the calculated heat loss distribution and specific time, a dynamic boundary treatment of soil domain is proposed to offset the heat loss when heat load is used as the inlet thermal boundary conditions. 4. Conclusions The effects of different thermal boundary configurations used in numerical models of a GHE is investigated. Based on a laboratory sandbox, a 3D numerical model is built and validated by the experimental data [16]. The conclusions yielded from this study are summarized as follows: 1) This three-dimensional CFD model with recorded inlet water temperature inputted can give accurate predictions on the temperatures of both fluid and soil, and such method can be used for validation. 2) Various predictions of outlet water temperature profile are obtained when employing different heat input. Compared with a good match appeared when recorded inlet water temperature is used as boundary condition,
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a large discrepancy shows when inputting heat load. Thus thermal boundary conditions of the fluid inlet should be carefully taken into consideration when selection. 3) Such discrepancy is attributed to the heat loss through facets of the sandbox, then a dynamic thermal boundary treatment for side- and end-walls is proposed based on the heat balance analysis, and it can offset the heat loss and overcome the limitation of adiabatic assumption. Despite some limitations of this study, such as the assumption of uniform heat loss distribution in every surface, the new findings presented in this study can improve the understanding and modeling of heat transfer process in GHE. This research can contribute to a more sophisticated numerical modeling approach to overcome the limitations of adiabatic assumption and finite numerical domain with the consideration of heat loss. Acknowledgements The financial supports of the National Nature Science Foundation of China (Project ID 51576023), the Fundamental Research Funds for the Central Universities (Project ID: 106112016CDJCR211221) are gratefully acknowledged. Wenxin Li also especially thanks for the scholarship provided by China Scholarship Council (CSC Student ID: 201506050034). References [1] Mustafa Omer A. Ground-source heat pumps systems and applications. Renew Sust Energ Rev 2008;12:344-71. [2] Soni SK, Pandey M, Bartaria VN. Ground coupled heat exchangers: A review and applications. Renew Sust Energ Rev 2015;47:83-92. [3] Li M, Lai ACK. Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): A perspective of time and space scales. Appl Energ 2015;151:178-91. [4] Yang H, Cui P, Fang Z. Vertical-borehole ground-coupled heat pumps: A review of models and systems. Appl Energ 2010;87:16-27. [5] Ingersioll L, Zobel OJ, Ingersoll AC. Heat Conduction: With Engineering Geological And Other Applications. 3rd ed. London: Ingersoll; 1955. [6] Carslaw HS, Jaeger JC. Conduction of heat in solids. 2nd ed. Oxford: Clarendon Press; 1959. [7] Zeng HY, Diao NR, Fang ZH. A finite line-source model for boreholes in geothermal heat exchangers. Heat Tran Asian Res 2002;31:558-67. [8] Eskilson P. Thermal Analysis of Heat Extraction Boreholes. Sweden: Lund University Press; 1987. [9] Li M, Lai ACK. New temperature response functions (G functions) for pile and borehole ground heat exchangers based on composite-medium line-source theory. Energy 2012;38:255-63. [10] Ma W, Li M, Li P, Lai ACK. New quasi-3D model for heat transfer in U-shaped GHEs (ground heat exchangers): Effective overall thermal resistance. Energy 2015;90:578-87. [11] Carotenuto A, Ciccolella M, Massarotti N, Mauro A. Models for thermo-fluid dynamic phenomena in low enthalpy geothermal energy systems: A review. Renew Sust Energ Rev 2016;60:330-55. [12] Florides GA, Christodoulides P, Pouloupatis P. Single and double U-tube ground heat exchangers in multiple-layer substrates. Appl Energ 2013;102:364-73. [13] Yang Y, Li M. Short-time performance of composite-medium line-source model for predicting responses of ground heat exchangers with single U-shaped tube. Int J Therm Sci 2014;82:130-7. [14] Zheng T, Shao H, Schelenz S, Hein P, Vienken T, Pang Z, et al. Efficiency and economic analysis of utilizing latent heat from groundwater freezing in the context of borehole heat exchanger coupled ground source heat pump systems. Appl Therm Eng 2016;105:314-26. [15] Li Z, Zheng M. Development of a numerical model for the simulation of vertical U-tube ground heat exchangers. Appl Therm Eng 2009;29:920-4. [16] Beier RA, Smith MD, Spitler JD. Reference data sets for vertical borehole ground heat exchanger models and thermal response test analysis. Geothermics 2011;40:79-85. [17] Beier RA. Transient heat transfer in a U-tube borehole heat exchanger. Appl Therm Eng 2014;62:256-66. [18] Pasquier P, Marcotte D. Joint use of quasi-3D response model and spectral method to simulate borehole heat exchanger. Geothermics 2014;51:281-99. [19] Li M, Lai ACK. Analytical model for short-time responses of ground heat exchangers with U-shaped tubes: Model development and validation. Appl Energ 2013;104:510-6. [20] Qian H, Wang Y. Modeling the interactions between the performance of ground source heat pumps and soil temperature variations. Energy Sustain Dev 2014;23:115-21. [21] Wang J, Long E, Qin W. Numerical simulation of ground heat exchangers based on dynamic thermal boundary conditions in solid zone. Appl Therm Eng 2013;59:106-15. [22] Zhang L, Zhang Q, Huang G. A transient quasi-3D entire time scale line source model for the fluid and ground temperature prediction of vertical ground heat exchangers (GHEs). Appl Energ 2016;170:65-75. [23] Farouki O. Thermal properties of soils. Germany: Trans Tech Publications; 1986.
