{"title":"用于模拟 U 型管孔热交换器的传导模型与包括沿流能量平衡在内的模型之间的比较","authors":"","doi":"10.1016/j.applthermaleng.2024.124311","DOIUrl":null,"url":null,"abstract":"<div><p>Most ground-coupled heat pumps exchange heat with the ground by means of a borehole-heat-exchanger (BHE) field. The time evolution of the fluid temperature at the outlet of the BHE field, employed for the design of the heat pump, is often determined starting from that of the mean temperature of the surface between the BHEs and the ground, evaluated by means of a dimensionless function called <em>g-function</em>. In order to obtain an accurate thermal response to peak loads, this method must be coupled with a short-term simulation tool. Simulation models that yield accurately the time evolution of either the outlet fluid temperature or the mean fluid temperature both in the short and in the long term are also available. The simplest of these models, called here conduction models, represent the fluid by a solid that receives or generates heat. Models that include the energy balance for the flow along the pipes, called here complete models, have also been proposed. Complete models are the most accurate, but can hardly be applied for long-term simulations. In this paper, the results of finite-element simulations of U-tube BHES performed by conduction models are compared with those obtained by complete models, implemented through the COMSOL Pipe Flow Module. It is shown that there is an excellent agreement between the models in the short term, while complete models yield slightly higher values of the mean fluid temperature in the medium and long term. It is also shown that one can obtain by a conduction model the same time evolution of the mean fluid temperature that would be yielded by a complete model, replacing the real 2D BHE thermal resistance, <em>R<sub>b</sub></em><sub>2D</sub>, with a virtual one, equal to the asymptotic value of the 3D thermal resistance yielded by the complete model, <em>R<sub>bPF</sub></em>. For BHEs with length 100 m, diameter 152 mm, grout thermal conductivity 1.6 W/(m K), ground thermal conductivity 1.8 W/(m K) and flow rate 14 L per minute, the ratio <em>R<sub>bPF</sub></em>/<em>R<sub>b</sub></em><sub>2D</sub> is, for instance, 1.032 for a single U-tube BHE with shank spacing <em>s</em> = 94 mm, and 1.090 for a double U-tube BHE with <em>s</em> = 85 mm. Dimensionless correlations yielding the value of <em>R<sub>bPF</sub></em>/<em>R<sub>b</sub></em><sub>2D</sub> for any U-tube BHE will be provided in a future paper.</p></div>","PeriodicalId":8201,"journal":{"name":"Applied Thermal Engineering","volume":null,"pages":null},"PeriodicalIF":6.1000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1359431124019793/pdfft?md5=f0641e332766d8c496f83b13f658e1d6&pid=1-s2.0-S1359431124019793-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Comparison between conduction models and models including the energy balance along the flow, for the simulation of U-tube borehole heat exchangers\",\"authors\":\"\",\"doi\":\"10.1016/j.applthermaleng.2024.124311\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Most ground-coupled heat pumps exchange heat with the ground by means of a borehole-heat-exchanger (BHE) field. The time evolution of the fluid temperature at the outlet of the BHE field, employed for the design of the heat pump, is often determined starting from that of the mean temperature of the surface between the BHEs and the ground, evaluated by means of a dimensionless function called <em>g-function</em>. In order to obtain an accurate thermal response to peak loads, this method must be coupled with a short-term simulation tool. Simulation models that yield accurately the time evolution of either the outlet fluid temperature or the mean fluid temperature both in the short and in the long term are also available. The simplest of these models, called here conduction models, represent the fluid by a solid that receives or generates heat. Models that include the energy balance for the flow along the pipes, called here complete models, have also been proposed. Complete models are the most accurate, but can hardly be applied for long-term simulations. In this paper, the results of finite-element simulations of U-tube BHES performed by conduction models are compared with those obtained by complete models, implemented through the COMSOL Pipe Flow Module. It is shown that there is an excellent agreement between the models in the short term, while complete models yield slightly higher values of the mean fluid temperature in the medium and long term. It is also shown that one can obtain by a conduction model the same time evolution of the mean fluid temperature that would be yielded by a complete model, replacing the real 2D BHE thermal resistance, <em>R<sub>b</sub></em><sub>2D</sub>, with a virtual one, equal to the asymptotic value of the 3D thermal resistance yielded by the complete model, <em>R<sub>bPF</sub></em>. For BHEs with length 100 m, diameter 152 mm, grout thermal conductivity 1.6 W/(m K), ground thermal conductivity 1.8 W/(m K) and flow rate 14 L per minute, the ratio <em>R<sub>bPF</sub></em>/<em>R<sub>b</sub></em><sub>2D</sub> is, for instance, 1.032 for a single U-tube BHE with shank spacing <em>s</em> = 94 mm, and 1.090 for a double U-tube BHE with <em>s</em> = 85 mm. Dimensionless correlations yielding the value of <em>R<sub>bPF</sub></em>/<em>R<sub>b</sub></em><sub>2D</sub> for any U-tube BHE will be provided in a future paper.</p></div>\",\"PeriodicalId\":8201,\"journal\":{\"name\":\"Applied Thermal Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.1000,\"publicationDate\":\"2024-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S1359431124019793/pdfft?md5=f0641e332766d8c496f83b13f658e1d6&pid=1-s2.0-S1359431124019793-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Thermal Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1359431124019793\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENERGY & FUELS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Thermal Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1359431124019793","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENERGY & FUELS","Score":null,"Total":0}
引用次数: 0
摘要
大多数地面耦合热泵通过钻孔换热器(BHE)与地面进行热交换。热泵设计所采用的 BHE 场出口处流体温度的时间变化通常是从 BHE 与地面之间表面的平均温度开始确定的,通过一种称为 g 函数的无量纲函数进行评估。为了获得对峰值负荷的准确热响应,这种方法必须与短期模拟工具相结合。目前也有一些模拟模型可以精确地计算出短期和长期的出口流体温度或平均流体温度的时间变化。这些模型中最简单的称为传导模型,用接收或产生热量的固体来表示流体。还提出了包括沿管道流动的能量平衡的模型,这里称为完整模型。完整模型最为精确,但很难用于长期模拟。本文比较了通过传导模型和通过 COMSOL 管道流模块实现的完整模型对 U 型管 BHES 进行有限元模拟的结果。结果表明,两种模型在短期内非常一致,而在中长期内,完整模型得出的平均流体温度值略高于传导模型。研究还表明,通过传导模型可以获得与完整模型相同的平均流体温度的时间演化,只需用一个虚拟热阻 Rb2D 代替实际的二维 BHE 热阻 Rb2D,该虚拟热阻等于完整模型得出的三维热阻 RbPF 的渐近值。对于长度为 100 米、直径为 152 毫米、灌浆热导率为 1.6 W/(m K)、地面热导率为 1.8 W/(m K)、流速为每分钟 14 升的 BHE,例如,对于柄间距 s = 94 毫米的单 U 型管 BHE,RbPF/Rb2D 之比为 1.032;对于 s = 85 毫米的双 U 型管 BHE,RbPF/Rb2D 之比为 1.090。我们将在今后的论文中提供得出任何 U 型管 BHE 的 RbPF/Rb2D 值的无量纲相关性。
Comparison between conduction models and models including the energy balance along the flow, for the simulation of U-tube borehole heat exchangers
Most ground-coupled heat pumps exchange heat with the ground by means of a borehole-heat-exchanger (BHE) field. The time evolution of the fluid temperature at the outlet of the BHE field, employed for the design of the heat pump, is often determined starting from that of the mean temperature of the surface between the BHEs and the ground, evaluated by means of a dimensionless function called g-function. In order to obtain an accurate thermal response to peak loads, this method must be coupled with a short-term simulation tool. Simulation models that yield accurately the time evolution of either the outlet fluid temperature or the mean fluid temperature both in the short and in the long term are also available. The simplest of these models, called here conduction models, represent the fluid by a solid that receives or generates heat. Models that include the energy balance for the flow along the pipes, called here complete models, have also been proposed. Complete models are the most accurate, but can hardly be applied for long-term simulations. In this paper, the results of finite-element simulations of U-tube BHES performed by conduction models are compared with those obtained by complete models, implemented through the COMSOL Pipe Flow Module. It is shown that there is an excellent agreement between the models in the short term, while complete models yield slightly higher values of the mean fluid temperature in the medium and long term. It is also shown that one can obtain by a conduction model the same time evolution of the mean fluid temperature that would be yielded by a complete model, replacing the real 2D BHE thermal resistance, Rb2D, with a virtual one, equal to the asymptotic value of the 3D thermal resistance yielded by the complete model, RbPF. For BHEs with length 100 m, diameter 152 mm, grout thermal conductivity 1.6 W/(m K), ground thermal conductivity 1.8 W/(m K) and flow rate 14 L per minute, the ratio RbPF/Rb2D is, for instance, 1.032 for a single U-tube BHE with shank spacing s = 94 mm, and 1.090 for a double U-tube BHE with s = 85 mm. Dimensionless correlations yielding the value of RbPF/Rb2D for any U-tube BHE will be provided in a future paper.
期刊介绍:
Applied Thermal Engineering disseminates novel research related to the design, development and demonstration of components, devices, equipment, technologies and systems involving thermal processes for the production, storage, utilization and conservation of energy, with a focus on engineering application.
The journal publishes high-quality and high-impact Original Research Articles, Review Articles, Short Communications and Letters to the Editor on cutting-edge innovations in research, and recent advances or issues of interest to the thermal engineering community.