地埋管熱交換之理論分析與運用

Abstract

本研究主要目的是探討地埋管熱交換器(BHE：Borehole Heat Exchangers)之理論分析與運用，地埋管熱交換器一般是以U型鑽孔熱交換器(UBHE)為主要探討標的，本研究亦以U型鑽孔熱交換器為主要研究對象。首先在理論分析部份包含：UBHE熱傳分析模式之確定、UBHE溫度分佈與出口溫度之計算、使用映像法(mapping)以及形狀因子法(shape factor)計算UBHE之熱阻、UBHE無因次熱傳分析等四大部份。在運用部份包含加裝隔熱版之效應以及八支管型UBHE之運用等。本研究亦採用實際之實驗數據以為模擬預估之基本數據以驗證本研究之正確性，進而探討各相關變數對出口溫度之影響，以得知BHE之一般設計準則，並且找出熱回流效應之影響變數，以期在設計BHE時能有最佳之熱傳效率。 地埋管熱交換器之熱傳分析可分為兩個部份，即鑽孔內部及鑽孔外部，鑽孔外部是使用有限長線熱源理論，來計算穩定狀態與非穩態時鑽孔壁面之溫度，而鑽孔內部是用準三維之熱傳理論，計算地埋管熱交換器中U型管內流體之溫度分佈。結果顯示使用映像法計算熱阻，再代入準三維之熱傳理論，所計算出之出口溫度，在散熱狀況時，比使用Hellstorm G. 的熱阻計算方法有1.33%之準確度提昇，且在單一U型管熱交換器之測試數據中，此模式計算之結果準確度在3.1%以內。 對於U型鑽孔熱交換器中加裝隔熱板之效應，結果顯示在鑽孔正中央處裝一隔板，對於有嚴重熱回流之情況，有降低出口溫度之功效，但對熱回流較不嚴重之情況反而會使出口溫度上昇降低了熱傳效率。會有熱回流之狀況為，兩支管間距(2D)較小以及鑽井深度(H)較深，且Q(流率)較小時之狀況，因此增加兩支管間距會比加裝隔熱板較有效率。 本研究也進一步的探討八支管型BHE之熱傳效率，經由理論分析顯示，在相同之總流率下，八支管型BHE比單一U型BHE，能量效率提升了23.5%(低總流率)至44.7％(高總流率)，而總熱傳率則提升了23.63% (低總流率)至42.18%(高總流率)，故此八支管型BHE為一良好之熱傳效率提升之新方法；相同的在設計八支管型BHE時應避免熱回流之效應發生，在鑽井深度較深且流率較小，若再加上D值較小時，則熱回流之效應就會更明顯，此時選用絕熱之中央上昇支管則會有顯著的提昇熱傳效率之效果。 本研究之貢獻主要包含下列各項： 1.找出簡單又正確之UBHE溫度分佈及出口溫度之預估模式。 2.用Matlab編輯一簡單之預估程式，可縮短預估時間。 3.提供mapping 及shape factor 熱阻之計算法。 4.提供設計UBHE之一般基本準則，以及影響熱回流效應之相關變數。 5.提供UBHE無因次之熱傳分析。 6.發展新型UBHE，即八支管型BHE，提高UBHE之熱傳效能。

The aim of this study is to explore the theoretical analysis and application of Borehole Heat Exchangers (BHE). The U-shaped Borehole Heat Exchangers (UBHE) is usually used for the main subject of research of BHE. There, this study also uses the UBHE as its main research subject. The four major parts of the theoretical analysis are: determination of UBHE heat transfer analysis model, calculation of temperature distribution and outlet temperature of UBHE, using the mapping method and the shape factor method to calculate thermal resistance of UBHE, dimensionless UBHE heat transfer analysis. In this study, the applications of UBHE include installation of adiabatic plate and design of eight-branch-pipes UBHE. In addition, this research paper also compares the results with practical experimental data for verification, and further discusses the influences from related variables on outlet temperature of UBHE, so that can understand the general design criteria of UBHE. Moreover, this study investigated the influence variables of heat backflow for the optimal heat transfer performance of UBHE. In this study, the heat transfer analysis includes measurements of both outside and inside of the borehole. Outside the borehole, the finite line-source theory is applied to calculate wall temperature of the borehole in the steady and unsteady state. Inside the borehole, the quasi-three-dimensional theory is applied to evaluate temperature distribution of the working fluid. The research results show that mapping method were more accurate than Hellstorm G. method in the case of heat dissipation. Furthermore, compare calculated results with four cases of experimental data, and the accuracy range is within 3.1% for single UBHE. The study proposes a new thermal resistances calculation method to solve the heat transfer of UBHE. In this study, the effect of adiabatic plate in the middle of borehole was also considered. The major purpose of adiabatic plate was to prevent heat backflow which would cause raised of outlet temperature of UBHE and decrease the heat dissipation rate. The heat backflow would occur when the distance between two branch pipes (2D) was shorter and the depth of well (H) was deeper, and when the flow rate (Q) of working fluid was lower. For the condition of serious heat backflow, adiabatic plate can be added in the middle of borehole to increase the heat transfer rate. However, if the heat backflow is not so much, the adiabatic plate will block the heat transfer from one to the other side of borehole and result in temperature raise in outlet of UBHE. Hence, the increasing of D value is more efficient to raise the heat transfer of UBHE than using the adiabatic plate. This study takes one step further to investigate heat transfer of 8-branch-pipes BHE. Our theoretical analysis showed that, the energy efficiency of 8-branch-pipes BHE raised from 23.5% (low total flow rate) to 44.7 % (high total flow rate) when comparing with the single U-tube in the same total flow rate; and the total heat transfer rate of 8-branch-pipes BHE raised from 23.63 % (low total flow rate) to 42.18% (high total flow rate). Hence the 8-branch-pipes BHE proved to be a good design for increasing heat transfer rate of UBHE. Similarly, for the design of 8-branch-pipes BHE, it should try to avoid the occurrence of heat backflow. When the depth of well is deeper, the distance of downward branch pipe and central upward branch pipe is smaller, and the flow rate is lower, the effect of heat backflow will become more obvious. In this condition, the use of central upward branch pipe coated with adiabatic material will increase the heat transfer rate.