## THERMAL SCIENCE

International Scientific Journal

### STUDY ON THE SIMPLIFIED MODEL OF VERTICAL DOUBLE U-PIPE GROUND HEAT EXCHANGER

**ABSTRACT**

A simplified semi-analytical model of vertical double U-pipe ground heat exchanger was established. The validity of the established model is examined by contrasting the figured outcomes with experiment data, emulation results of 3-D numerical model and calculation results of infinite line-source model for different inlet boundary conditions and configurations. After one hour, the semi-analytical model’s relative error is less than 0.32% under the boundary condition of given inlet fluid temperature. Under the boundary condition of given total heat input rate, the semi-analytical model’s relative error after ten hours is less than 0.11%, while the infinite line-source model’s relative error is less than 0.60%. The semi-analytical model is in good agreement with experiment and numerical model, and has higher calculation accuracy than infinite line-source model.

**KEYWORDS**

PAPER SUBMITTED: 2022-09-22

PAPER REVISED: 2022-12-15

PAPER ACCEPTED: 2022-12-22

PUBLISHED ONLINE: 2023-03-11

**THERMAL SCIENCE** YEAR

**2023**, VOLUME

**27**, ISSUE

**Issue 5**, PAGES [4035 - 4048]

- Li, W. X., et al., Experimental and Numerical Studies on the Thermal Performance of Ground Heat Exchangers in a Layered Subsurface with Groundwater, Renewable Energy, 147 (2020), Mar., pp. 620-629
- Cenejac, A. R., et al., Covering of Heating Load of Object by Using Ground Heat as a Renewable Energy Source, Thermal Science, 16 (2012), July, pp. S225-S235
- Zhang, Y., Qi, Y. F., The 3-D Numerical Simulation of Heat Transfer for The Vertical U-Type Berried Pipe of the Ground Source Heat Pump, Advanced Materials Research, 827 (2013), Oct., pp. 203-208
- Chen, J. H., et al., Simulation and Experimental Analysis of Optimal Buried Depth of The Vertical U-Tube Ground Heat Exchanger for a Ground-Coupled Heat Pump System, Renewable Energy, 73 (2015), Jan., pp. 46-54
- Liu, Y., et al., Vertical U-Shaped Heat Exchangers for Construction Engineering New Promises and Future Challenges, Thermal Science, 25 (2021), 3B, pp. 2253-2261
- You, S., et al., Operation Mode and Heat Performance of Energy Drilled Piles, Thermal Science, 25 (2021), 6B, pp. 4553-4560
- Raymond, J., et al., Extending Thermal Response Test Assessments with Inverse Numerical Modelling of Temperature Profiles Measured in Ground Heat Exchangers, Renewable Energy, 99 (2016), Dec., pp. 614-621
- Sun, Z. C., et al., Research on Heat Transfer Characteristics and Borehole Field Lay-Out of Ground Heat Exchangers to Alleviate Thermal Accumulation with Groundwater Advection, Thermal Science, 25 (2021), 4A, pp. 2781-2794
- Kayaci, N., Demir, H., Numerical modelling of transient soil temperature distribution for horizontal Ground Heat Exchanger of Ground Source Heat Pump, Geothermics, 73 (2018), Jan., pp. 33-47
- Gan, G. H., A numerical Methodology for Comprehensive Assessment of the Dynamic Thermal Performance of Horizontal Ground Heat Exchangers, Thermal Science and Engineering Progress, 11 (2019), Apr., pp. 365-379
- Habibi, M., et al., A Numerical Study on Utilizing Horizontal Flat-Panel Ground Heat Exchangers in Ground-Coupled Heat Pumps, Renewable Energy, 147 (2020), Sep., pp. 996-1010
- Zeng, H. Y., et al., Heat Transfer Analysis of Boreholes in Vertical Ground Heat Exchangers, International Journal of Heat Transfer, 46 (2003), Apr., pp. 4467-4481
- Conti, P., et al., Revised Heat Transfer Modelling of Double-U Vertical Ground-Coupled Heat Exchangers, Applied Thermal Engineering, 106 (2016), Aug., pp. 1257-1267
- Zarrella, A., et al., Short Time Step Analysis of Vertical Ground-Coupled Heat Exchangers: The Approach of CaRM, Renewable Energy, 36 (2011), Sep., pp. 2357-2367
- Luo, Y, Q., Xu, G. Z., Dynamic Thermal Analysis of Vertical Double-U Type Ground Heat Exchanger (in Chinese), Journal of Huazhong University of Science and Technology (Nature Science Edition), 49 (2021), Jan., pp. 122-127
- Magraner, T., et al., Thermal Response Test Analysis for U-Pipe Vertical Borehole Heat Exchangers Under Groundwater Flow Conditions, Renewable Energy, 165 (2021), Nov., pp. 391-404
- Zeng, H. Y., et al., A Finite Line-Source Model for Boreholes in Geothermal Heat Exchangers, Heat Transfer - Asian Research, 31 (2002), 7, pp. 558-567
- Babak, D. B., Kukrer, E., A New 1-D Analytical Model for Investigating the Long Term Heat Transfer Rate of a Borehole Ground Heat Exchanger by Green's Function Method, Renewable Energy, 108 (2017), Aug., pp. 615-621
- Erol, S., Francois, B., Multilayer Analytical Model for Vertical Ground Heat Exchanger with Groundwater Flow, Geothermics, 71 (2018), Sep., pp. 294-305
- Nian, Y. L., Cheng, W. L., Analytical g-Function for Vertical Geothermal Boreholes with Effect of Borehole Heat Capacity, Applied Thermal Engineering, 140 (2018), May., pp. 733-744
- Pan, A. Q., et al., A Novel Analytical Multilayer Cylindrical Heat Source Model for Vertical Ground Heat Exchangers Installed in Layered Ground, Energy, 200 (2020), 117545
- Li, M., Lai, A. C. K., New Temperature Response Functions (G Functions) for Pile and Borehole Ground Heat Exchangers Based on Composite-Medium Line-Source Theory, Energy, 38 (2012), Feb., pp. 255-263
- Li, M., Lai, A. C. K., Analytical Model for Short-Time Responses of Ground Heat Exchangers with U-Shaped Tubes: Model Development And Validation, Applied Energy, 104 (2013), Apr., pp. 510-516
- Li, M., Yang, Y., Short-Time Performance of Composite-Medium Line-Source Model for Predicting Responses of Ground Heat Exchangers With Single U-Shaped Tube, International Journal of Thermal Science, 82 (2014), Aug., pp. 130-137
- Li, M., et al., Full-Scale Temperature Response Function (G-Function) for Heat Transfer by Borehole Ground Heat Exchangers (Ghes) From Sub-Hour To Decades, Applied Energy, 136 (2014), Dec., pp. 197-205
- Wang, C. L., et al., A Simplified Semi-Numerical Model to Simulate a U-Pipe Ground Heat Exchanger, Numerical Heat Transfer - Part A: Applications, 77 (2020), Jan., pp. 482-496
- Wei, J. H., et al., A New Analytical Model for Short-Time Response of Vertical Ground Heat Exchangers Using Equivalent Diameter Method, Energy and Buildings, 119 (2016), Mar., pp. 13-19
- Su, H., et al., Fast Simulation of a Vertical U-Tube Ground Heat Exchanger by Using A 1-D Transient Numerical Model, Numerical Heat Transfer - Part A: Applications, 60 (2011), Aug., pp. 328-346
- Diao, N. R., et al., Improvement in Modelling Of Heat Transfer In Vertical Ground Heat Exchangers, HVAC and R Research, 10 (2004), Feb., pp. 459-470
- Ma, Z. D., et al., Numerical Simulation on Heat Transfer Inside and Outside of Vertical Buried Pipes Based on Two-Model Order Reduction Methods, Numerical Heat Transfer - Part A: Applications, 79 (2021), Jan., pp. 631-655
- Liao, Q., et al., Effective Borehole Thermal Resistance of A Single U-Tube Ground Heat Exchanger, Numerical Heat Transfer, Part A: Applications, 62 (2012), Apr., pp. 197-210
- Lee, C. K., Lam, H. N., Computer Simulation of Borehole Ground Heat Exchangers for Geothermal Heat Pump Systems, Renewable Energy, 33 (2008), Aug., pp. 1286-1296
- Liu, Z. Y., et al., Multilayer Quasi-3-D Model for the Heat Transfer Inside the Borehole Wall of a Vertical Ground Heat Exchanger, Geothermics, 83 (2020), 101711
- Al-Khoury, R., Bonnier, P. G., Efficient Finite Element Formulation for Geothermal Heating Systems - Part II: Transient, International Journal For Numerical Methods in Engineering, 67 (2006), Jan., pp. 725-745
- Al-Khoury, R., et al., Efficient Numerical Modelling of Borehole Heat Exchangers, Computers and Geosciences, 36 (2010), Dec., pp. 1301-1315
- Marcotte, B., Bernier, M., Experimental Validation of a TRC Model for a Double U-Tube Borehole with Two Independent Circuits, Applied Thermal Engineering, 162 (2019), 114229
- Spitler, J. D., Gehlin, S. E. A., Thermal Response Testing for Ground Source Heat Pump System - An Historical Review, Renewable and Sustainable Energy Reviews, 50 (2015), May, pp. 1125-1137
- Li, W. X., et al., Numerical Modelling of Thermal Response of a Ground Heat Exchanger with Single U-Shaped Tube, Science and Technology for the Built Environment, 25 (2018), Nov., pp. 525-533
- Beier, R. A., Transient Heat Transfer in A U-Tube Borehole Heat Exchanger, Applied Thermal Engineering, 62 (2014), July, pp. 256-266
- Lamarche, L., Beauchamp, B., New Solutions for the Short-Time Analysis of Geothermal Vertical Boreholes, International Journal of Heat and Mass Transfer, 50 (2017), Nov., pp. 1408-1419
- Chen, J. H., A Study on Layered Heat Transfer Model of Vertical Double U-Tube Ground Heat Exchangers (in Chinese), M. Sc. thesis, Chongqing University, Chongqing, China, 2015