Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps

Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the re...
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Autor*in:	Ting Wei [verfasserIn] Yuezan Tao [verfasserIn] Yameng Zhang [verfasserIn] Honglei Ren [verfasserIn] Fei Lin [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	ground-coupled heat pump hole spacing heat penetration distance viscous Burgers’ equation

Übergeordnetes Werk:	In: Processes - MDPI AG, 2013, 11(2023), 227, p 227
Übergeordnetes Werk:	volume:11 ; year:2023 ; number:227, p 227

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/pr11010227

Katalog-ID:	DOAJ081715323

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520			\|a Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system.
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allfields	10.3390/pr11010227 doi (DE-627)DOAJ081715323 (DE-599)DOAJ34cbce8f3e9b4a8fb3f1160861e5880d DE-627 ger DE-627 rakwb eng TP1-1185 QD1-999 Ting Wei verfasserin aut Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system. ground-coupled heat pump hole spacing heat penetration distance viscous Burgers’ equation Chemical technology Chemistry Yuezan Tao verfasserin aut Yameng Zhang verfasserin aut Honglei Ren verfasserin aut Fei Lin verfasserin aut In Processes MDPI AG, 2013 11(2023), 227, p 227 (DE-627)750371439 (DE-600)2720994-5 22279717 nnns volume:11 year:2023 number:227, p 227 https://doi.org/10.3390/pr11010227 kostenfrei https://doaj.org/article/34cbce8f3e9b4a8fb3f1160861e5880d kostenfrei https://www.mdpi.com/2227-9717/11/1/227 kostenfrei https://doaj.org/toc/2227-9717 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 227, p 227
spelling	10.3390/pr11010227 doi (DE-627)DOAJ081715323 (DE-599)DOAJ34cbce8f3e9b4a8fb3f1160861e5880d DE-627 ger DE-627 rakwb eng TP1-1185 QD1-999 Ting Wei verfasserin aut Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system. ground-coupled heat pump hole spacing heat penetration distance viscous Burgers’ equation Chemical technology Chemistry Yuezan Tao verfasserin aut Yameng Zhang verfasserin aut Honglei Ren verfasserin aut Fei Lin verfasserin aut In Processes MDPI AG, 2013 11(2023), 227, p 227 (DE-627)750371439 (DE-600)2720994-5 22279717 nnns volume:11 year:2023 number:227, p 227 https://doi.org/10.3390/pr11010227 kostenfrei https://doaj.org/article/34cbce8f3e9b4a8fb3f1160861e5880d kostenfrei https://www.mdpi.com/2227-9717/11/1/227 kostenfrei https://doaj.org/toc/2227-9717 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 227, p 227
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allfieldsGer	10.3390/pr11010227 doi (DE-627)DOAJ081715323 (DE-599)DOAJ34cbce8f3e9b4a8fb3f1160861e5880d DE-627 ger DE-627 rakwb eng TP1-1185 QD1-999 Ting Wei verfasserin aut Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system. ground-coupled heat pump hole spacing heat penetration distance viscous Burgers’ equation Chemical technology Chemistry Yuezan Tao verfasserin aut Yameng Zhang verfasserin aut Honglei Ren verfasserin aut Fei Lin verfasserin aut In Processes MDPI AG, 2013 11(2023), 227, p 227 (DE-627)750371439 (DE-600)2720994-5 22279717 nnns volume:11 year:2023 number:227, p 227 https://doi.org/10.3390/pr11010227 kostenfrei https://doaj.org/article/34cbce8f3e9b4a8fb3f1160861e5880d kostenfrei https://www.mdpi.com/2227-9717/11/1/227 kostenfrei https://doaj.org/toc/2227-9717 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 227, p 227
allfieldsSound	10.3390/pr11010227 doi (DE-627)DOAJ081715323 (DE-599)DOAJ34cbce8f3e9b4a8fb3f1160861e5880d DE-627 ger DE-627 rakwb eng TP1-1185 QD1-999 Ting Wei verfasserin aut Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system. ground-coupled heat pump hole spacing heat penetration distance viscous Burgers’ equation Chemical technology Chemistry Yuezan Tao verfasserin aut Yameng Zhang verfasserin aut Honglei Ren verfasserin aut Fei Lin verfasserin aut In Processes MDPI AG, 2013 11(2023), 227, p 227 (DE-627)750371439 (DE-600)2720994-5 22279717 nnns volume:11 year:2023 number:227, p 227 https://doi.org/10.3390/pr11010227 kostenfrei https://doaj.org/article/34cbce8f3e9b4a8fb3f1160861e5880d kostenfrei https://www.mdpi.com/2227-9717/11/1/227 kostenfrei https://doaj.org/toc/2227-9717 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 227, p 227
language	English
source	In Processes 11(2023), 227, p 227 volume:11 year:2023 number:227, p 227
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authorswithroles_txt_mv	Ting Wei @@aut@@ Yuezan Tao @@aut@@ Yameng Zhang @@aut@@ Honglei Ren @@aut@@ Fei Lin @@aut@@
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Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. 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callnumber-first	T - Technology
author	Ting Wei
spellingShingle	Ting Wei misc TP1-1185 misc QD1-999 misc ground-coupled heat pump misc hole spacing misc heat penetration distance misc viscous Burgers’ equation misc Chemical technology misc Chemistry Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps
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topic_title	TP1-1185 QD1-999 Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps ground-coupled heat pump hole spacing heat penetration distance viscous Burgers’ equation
topic	misc TP1-1185 misc QD1-999 misc ground-coupled heat pump misc hole spacing misc heat penetration distance misc viscous Burgers’ equation misc Chemical technology misc Chemistry
topic_unstemmed	misc TP1-1185 misc QD1-999 misc ground-coupled heat pump misc hole spacing misc heat penetration distance misc viscous Burgers’ equation misc Chemical technology misc Chemistry
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title	Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps
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title_full	Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps
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title_sort	application of the heat penetration distance in the design of the hole spacing of ground-coupled heat pumps
callnumber	TP1-1185
title_auth	Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps
abstract	Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system.
abstractGer	Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system.
abstract_unstemmed	Due to issues such as heat accumulation, the site area, and project investment, the reasonable determination of the hole spacing for heat exchangers has become one of the key design points of the ground-coupled heat pump system. Based on the definition of heat penetration in heat transfer and the research method of the inverse problem, a direct algorithm of the heat penetration distance in the aquifer was proposed using the analytical solution to the mathematical model for one-dimensional heat convection–conduction problems. Taking a vertical ground-coupled heat pump project in Hefei, Anhui Province, China, as an example, a three-dimensional hydro-thermal coupling numerical simulation model was established, and the influence radius during the refrigeration and heating periods under the action of a single borehole heat exchanger was determined. Comparing the heat penetration distance with the influence radius, the results show that the relative errors of the results obtained by the two methods are less than 10%, which verifies the rationality and effectiveness of the calculated penetration distance in the aquifer. At the end of the cooling or heating period, the heat penetration distance in the aquifer is calculated to be 7.59 m. Therefore, the proposed method is straightforward and efficient, which can provide a convenient approach to determining the reasonable hole spacing of the heat pump system.
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title_short	Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps
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Application of the Heat Penetration Distance in the Design of the Hole Spacing of Ground-Coupled Heat Pumps

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