基于混合解換熱模型的地源熱泵系統井群熱干擾特性

第32卷第10期農業(yè)工程學(xué)報VolL.32 No.10194 2016年5月Transactions of the Chinese Society of Agricultural EngineeringMay 2016基于混合解換熱模型的地源熱泵系統井群熱干擾特性王俊清,袁艷平※,曹曉玲,秦萍(西南交通大學(xué)機械工程學(xué)院,成都610031)摘要:為建立井群換熱快速求解模型并研究其熱干擾特性 ,提出了一種基于解析數值計算的混合解模型，以16井群為研究對象,通過(guò)試驗和數值模擬的方法研究了井群熱干擾特性。研究結果表明:隨著(zhù)換熱的進(jìn)行井群中各井間產(chǎn)生熱干擾并逐漸增強,同-運行時(shí)刻中井受熱干擾程度最大、邊井次之、角井則最小;由于井間熱千擾的影響，角井換熱能力最大、井壁溫度最低,邊井換熱能力和井壁溫度居中,中井換熱能力最小、井壁溫度最高,則運行90 d時(shí)角井換熱量比邊井大6.5%，邊井換熱量比中井大7.1%;角井對井群換熱量的貢獻率隨換熱時(shí)間延長(cháng)逐漸增加,中井對井群換熱量的貢獻率則逐漸減少,而邊井對井群換熱量的貢獻率基本不變。關(guān)鍵詞:熱泵系統;井群;傳熱;熱干擾特性doi: 1.11975/jissn. 1002- 6819.2016.10.027中圖分類(lèi)號:TK523文獻標志碼:A文章編號: 1002- -6819(2016)-10-0194-07王俊清，袁艷平，曹曉玲,秦萍.基于混合解換熱模型的地源熱泵系統井群熱干擾特性[J] 農業(yè)工程學(xué)報, 2016, 32(10):194- 200. doi: 11975/jissn.1002- 6819.2016.10.027 ht:/wwwtsac.or，.Wang Junqing, Yuan Yanping, Cao Xiaoling, Qin Ping. Thermal interference characteristics of wells in ground source heat pumpsystem based on analytical and numerical calculation of mixed solution{J]. Transactions of the Chinese Society of AgriculturalEngineering (Transactions of the CSAE), 2016, 32(10): 194- -200. (in Chinese with English abstract) doi: 10.1 1975/jissn.1002-6819.2016.10.027 htp://www .tcsae.org材料的熱影響及管井間的熱干擾。高青等6對G函數進(jìn)行0引言簡(jiǎn)化,提出了簡(jiǎn)化柱熱源模型,該方法可準確計算出井孔淺層地熱能的利用對建筑節能、構建綠色建筑具有周?chē)寥赖膶嵯禂?。方肇洪等P提出了豎直埋管換熱器重要意義。在淺層地熱能利用中地源熱泵是其中的重要鉆孔內傳熱過(guò)程的準三維模型，給出鉆孔內熱阻解析表達技術(shù),該項技術(shù)的研究核心和應用基礎是地下埋管換熱，式，求得有限長(cháng)線(xiàn)熱源在半無(wú)限大介質(zhì)中的瞬態(tài)溫度響應而建立地埋管傳熱模型是進(jìn)行地下埋管換熱研究的前提解析解;并在考慮有地下水滲流時(shí),導出了無(wú)限大介質(zhì)中無(wú)與基礎。目前國內外學(xué)者對地埋管傳熱模型已進(jìn)行了大限長(cháng)線(xiàn)熱源溫度響應的解析解。楊衛波等利用能量平衡及量研究，就現有地下埋管傳熱計算方法可分為簡(jiǎn)化解析變熱流圓柱源理論建立了二區域U型埋管傳熱模型，該模解和離散化數值計算",其傳熱計算模型各具特點(diǎn),簡(jiǎn)化型可直接求解出熱泵進(jìn)液溫度，亦可與熱泵機組模型耦合解析解模型計算簡(jiǎn)便、快捷;離散化數值計算模型善于計進(jìn)行地源熱泵系統動(dòng)態(tài)模擬及相應能耗分析和優(yōu)化設計。算復雜傳熱問(wèn)題。目前在解析解方面，最主要的理論是在數值解方面,Lei9對U形埋管換熱器兩支管分別建1948年Ingersoll等12提出的Kelvin 線(xiàn)熱源理論以及1954立二維柱坐標系,假定傳熱僅發(fā)生在徑向,采用有限差分年Ingersoll等B給出的圓柱源理論。Hart 等H在Kelvin線(xiàn)法求解該模型的偏微分方程，未考慮地表面各因素及多源理論的基礎上,建立了線(xiàn)熱源到周?chē)寥离S時(shí)間變化的鉆孔之間熱干擾的影響。唐志偉等利用有限體積法對單溫度分布傳熱模型，該模型未考慮熱泵機組間歇運行工U埋管換熱器的溫度場(chǎng)及流場(chǎng)進(jìn)行了數值模擬，軸向上建況管內對流換熱熱阻、灌漿材料的熱影響。Kavanaugh等[9立兩支管一-維對流換熱模型,深度方向上,每隔一定間距以Ingersoll等改進(jìn)的柱熱源理論為基礎,建立了埋管周?chē)钠矫鎯扰汉锨蠼夤軆攘黧w與土壤間的傳熱,實(shí)現2個(gè)區土壤隨時(shí)間變化的溫度分布傳熱模型，但其未考慮灌漿域間傳熱的耦合,構建了準三維傳熱模型。王勇等叫"建立了地源熱泵豎直地埋管換熱器的三維傳熱溫度場(chǎng)數學(xué)模收稿日期:2015-11-21修訂日期:2016-03-28型,提出了層換熱理論,將換熱器及其周?chē)膸r土分為3基金項目:建筑環(huán)境與能源高效利用四川省青年科技創(chuàng )新研究團隊項目個(gè)換熱層一飽和換熱層、換熱層、未換熱層。(2015TD0015)作者簡(jiǎn)介:王俊清，男,河南駐馬店人,主要從事空調節能技術(shù)研究。成此外，亦有學(xué)者將解析解與數值計算法結合使用以都西南交通大學(xué)機械工程學(xué)院,610031。獲得簡(jiǎn)單快速的求解。Ekslison 等12采用解析法與數值法Email: yourongxinan@163.com混合求解埋管周?chē)寥罍囟确植?對于單鉆孔采用有限長(cháng)※通信作者:袁艷平,男,湖北洪湖人,教授,博士生導師,主要從事建筑線(xiàn)熱源數值法;對多鉆孔區域溫度響應采用單鉆孔溫度能源存儲、轉換與高效利用,地下空間熱濕環(huán)境模擬與控制等方面的研響應疊加計算,從而確定任意時(shí)間的鉆孔壁溫。Hellstrom究。成都西南交通大學(xué)機械 工程學(xué)院,6100310Email: ypyuan@home.swjtu.edu.cn等13研究了多個(gè)鉆孔密集模型布置的儲熱模型,對局部問(wèn)第10期王俊清等:基于混合解換熱模型的地源熱泵系統井群熱干擾特性195題采用一維(徑向)有限差分法,對全局問(wèn)題采用二維(徑邊界。向一軸向)有限差分法,當達到穩定熱流時(shí)采用解析法疊對鉆孔外土壤計算區域進(jìn)行二維網(wǎng)格離散，在控制加它們，但該模型并不適用于地源熱泵系統長(cháng)期運行計容積內對控制方程( 1 )進(jìn)行空間和時(shí)間積分,組建差分方算分析。陸志等14提出數值計算與有限長(cháng)線(xiàn)熱源綜合模程組,結合邊界條件和初始條件對方程組進(jìn)行求解,得到型,以替代半徑將計算區域分為兩部分,半徑以?xún)韧寥赖你@孔外土壤區域溫度分布,亦可知各鉆孔壁溫To溫度通過(guò)數值迭代法計算得出，半徑以外土壤溫度通過(guò)井群鉆孔外土壤計算區域如圖1,q1 為單位井深換熱有限長(cháng)線(xiàn)熱源模型計算得到，數值計算區域的外邊界溫量(由鉆孔內傳熱模型計算),賦值給井壁邊界。度由有限長(cháng)線(xiàn)熱源法計算給出，有限長(cháng)線(xiàn)熱源法中單位長(cháng)度的熱流密度通過(guò)計算管內流體與管壁對流換熱的熱流量得出。在課題組前期,袁艷平等15-8提出以鉆孔壁為遠邊界。Infinite邊界將計算區域分為鉆孔內和鉆孔外2個(gè)部分，鉆孔以鉆孔壁Boreholewallboundary內部分,基于能量平衡建立穩態(tài)解析解傳熱模型,對于鉆孔外土壤區域，采用非穩態(tài)有限體積法進(jìn)行傳熱計算,兩q區域通過(guò)鉆孔壁溫或熱流量耦合，建立了快速求解的地埋管傳熱模型;并以此為基礎對單井在連續運行和間歇運行下的換熱特性進(jìn)行了研究。k:從文獻綜述情況來(lái)看,地埋管傳熱模型大都針對單井,但在實(shí)際工程中地埋管都是以群井形式出現，目前對于群注:q1為單位井深換熱量。井換熱量的計算,大致分為兩種思路:-是計算單井的換熱Note: qi is the heat exchange of unit well depth.量,直接乘以鉆孔數得到。這種方法計算簡(jiǎn)單,但井群中因圖1井群鉆孔外計算區域鉆孔間距有限，各井間會(huì )出現相互熱干擾,其基本換熱特性Fig.1 Borehole external calculation area of wells與單井有明顯不同,故需要考慮井間傳熱相互影響。二是直.2 鉆孔內傳熱模型接采用解析解或數值模擬進(jìn)行計算，數值解功能強大善于對鉆孔內傳熱進(jìn)行以下簡(jiǎn)化:計算復雜傳熱問(wèn)題，能有效把握地埋管動(dòng)態(tài)換熱特性,但其1 )忽略埋管與回填材料及回填材料與孔洞壁間的接傳熱空間區域大幾何配置復雜,計算時(shí)間過(guò)長(cháng)。觸熱阻;本文在保證求解準確性的基礎上加快求解速度,建2)忽略埋管內介質(zhì)軸向導熱和U型地埋管底部彎管立井群混合解傳熱模型,其基本思路為:以鉆孔壁為界將的影響;井群換熱空間區域分為鉆孔內(包含多個(gè)鉆孔)和鉆孔外3)管內流體流速均勻-致,任意截面內流體溫度均勻2個(gè)區域;各鉆孔內傳熱通過(guò)穩態(tài)解析解計算，獲取各鉆恒定,只沿井深方向變化;孔換熱量,并將其作為對應鉆孔壁的邊界條件,采用數值4)回填土、管內流體的熱特性參數恒定;方法計算孔外土壤溫度動(dòng)態(tài)響應。在此基礎上對井群熱5)忽略熱濕遷移的影響,認為回填士中的傳熱為純導干擾特性進(jìn)行研究，得到了井群中不同位置地埋管換熱熱問(wèn)題。規律,為地源熱泵系統地埋管設計提供參考。井群中每個(gè)鉆孔內傳熱情況完全-樣,故在此僅對其中一個(gè)鉆孔為對象分析其傳熱情況，鉆孔內微元體傳1井群傳 熱模型熱示意如圖2所示。1.1鉆孔外土壤區 域傳熱模型鉆孔壁Borehole wall壁溫Well temperature對鉆孔外土壤區域傳熱進(jìn)行以下簡(jiǎn)化:).....。01)假設土壤熱物性參數及初始地溫均勻一致,且物性進(jìn)水管換熱出水管換熱量不隨時(shí)間變化;Heat transfrofHea transfer ofwaterutletpipe2)忽略滲流及熱濕遷移,認為土壤中的傳熱為均勻純whter inft pipe,導熱問(wèn)題;。...... i 0四(Ta2)3)認為傳熱過(guò)程僅發(fā)生在水平方向。進(jìn)水溫度出水溫度基于以上簡(jiǎn)化,土壤區域傳熱控制方程為啊IiMet waterOutlet watertemperuturetempefaturepe)=0(k0)+影(k工)+So(1)兩管間換熱量Heat tansfer between two tubes式中p為土壤密度,kg/m';c為土壤定壓比熱,J/(kg.9C);k為土壤導熱系數,W/(m*C);T為土壤溫度,C;S為源項，圖2鉆孔內微元體傳熱示意圖求解中進(jìn)行線(xiàn)性化處理，分解為常數項及隨時(shí)間和溫度Fig.2 Borehole micro body heat transfer diagram變化項?；谝陨虾?jiǎn)化，考慮地埋管內流體溫度沿程變化及初始條件:7(x,y,z )=T。(其中To為初始地溫)。兩支管間熱干擾影響,參照圖2對于埋管深度z處的微元邊界條件:各鉆孔壁為變熱流邊界,遠邊界為絕熱體dz,可根據能量平衡得控制方程組:196農業(yè)工程學(xué)報( ht:/://w tcsae.org )2016年MdT(s)=q+q= (7T-T](z)+ R[Tx(z)-T;(z)]2單井傳 熱模型試驗驗證dz(2)1_ ydT6(z)dTaz2=qrqn=+Tr-T(x)-a-1[2()-7T()]判定井群傳熱模型預測結果是否符合實(shí)際情況,是定解條件:T:(O)=Tm;Tj(H)=T2(H)(其中H為鉆孔深度)。進(jìn)行井群換熱模擬計算的前提。由井群傳熱模型建立過(guò)程可知，井群傳熱模型的數學(xué)描述與單井傳熱模型僅在式中M為循環(huán)流體的熱容量,M=c;m(其中C。為流體邊界條件方面有差別，因此只要確保單井傳熱模型的正的定壓比熱容;m為U型管內循環(huán)流體的質(zhì)量流量)，確，即可證明井群傳熱模型預測結果的準確性。故本節建J/(s.C);T(z)、Tp(z)為z處U型管進(jìn)/出口流體溫度,C;立單鉆孔地埋管換熱系統夏季工況試驗臺，驗證單井換91.92分別為u型地埋管兩支管與鉆孔壁間的單位管長(cháng)換熱模型。試驗中鉆孔直徑為0.1 m,鉆孔深度為1.2 m,U型熱量,q口為U型地埋管兩支管間單位管長(cháng)換熱量,W/m;埋管采用內徑0.014 m的銅管,兩支管間距為0.06m。試T。為鉆孔壁溫度,C;R、R胎與R臺分別為兩支管內流體與孔驗系統原理圖如圖4所示。壁及鄰近兩支管內流體間的等效傳熱熱阻(其中Ri=R{)，流量計保溫管恒溫水箱C/w ;R^、R$的計算參見(jiàn)文獻[1]。FlowmetergnsulatinConstanttemperature令e;(z)=T-T(z),8(z)=T-Tp(z),a=( 1/Ri+1IR )/M，FrT100熱電阻Hot rsistangewater tankb=( 1/RA )/M,則式(2)可化簡(jiǎn)為:填充土壤Soil公調節閥水泵Pupd6__RepulaNing wea =b0-abr一數據采集僅上H(3)Data acquisition istupent∪型銅管d=a0_bO)U-copper土壤溫度測點(diǎn)....對方程組(3)進(jìn)行Laplace變換,采用求解常微分方tubeTemperature PIDmeasuring控制但程組的方法進(jìn)行求解可得pointontrol。(4)圖4試驗系統原理圖Fig4 Schematic diagram of experimental system6(z)=Cre" +Cze式中Ci.C2為待定常數,可結合定解條件求取。任何試驗均存在系統誤差，為了保證試驗結果的可確定C,C2后,進(jìn)而可求得地埋管出口溫度及單位井靠性,試驗系統誤差不能過(guò)大，否則會(huì )對試驗結果產(chǎn)生較深換熱量:Tu=T,- 06(0)。(5)大影響。本試驗的系統誤差主要來(lái)源于儀器測量精度;試(6)驗使用四線(xiàn)式P100熱電阻測量埋管進(jìn)出口水溫，其精q=M(Tm-T)/H。度≤0.15 C;使用T型熱電偶測定土壤層溫度,其精度≤式中q為單位井深換熱量, Wm;H為鉆孔深度,m。0.5c;使用小型橢圓齒輪流量計測量進(jìn)水流量,其測量該井群地埋管傳熱模型中兩區域的求解計算通過(guò)鉆精度≤19%;使用Hot Disk2500測量土壤導熱系數,其測量孔壁溫度進(jìn)行耦合鏈接，首先由初始壁溫通過(guò)孔內模型精度≤3%。由以上可知,本試驗系統誤差較小，可以保證計算換熱量，將換熱量作為熱邊界條件計算孔外土壤傳試驗結果的可信度。熱,然后再提取下一-時(shí)間壁溫計算換熱量,之后往復循環(huán)本試驗方案為:埋管內流體處于紊流狀態(tài)下,換熱直至滿(mǎn)足所設條件;通過(guò)FLUENT軟件平臺利用用戶(hù)接系統維持恒定進(jìn)水流量及進(jìn)水溫度連續運行7h,每間口(UDF )求解計算的具體流程如圖3所示。隔1 min采集1次各測點(diǎn)溫度數據。土壤初始溫度Soil itial temperature T。本試驗過(guò)程測得 土壤熱物性參數及系統運行參數見(jiàn)(4o時(shí)刻l moment)表1。鉆孔內傳熱模型計算表1試驗參數Cllatinaav位井深換熱量)1 boreholeTable 1 Test parametersw(Heat transfer per unit depth of wells)項目Projet參數Value項目Project鉆孔外土壤傳熱模型計算土壤密度Soil density/土層初溫外土壤del utside borehole1322| Soil initial temperature/C18.9Clculation of (乳外工壤溫度場(chǎng)usdeboreh(kg*"m)(Outside the hole soil temperaure feld)土壤比熱Specific heat of1016系統流量0.105 53soi/J*kg'.K-)System flow/(m"'h")d時(shí)間各井壁平均溫度d time average temperature of each土壤導熱系數Conductivity0.79進(jìn)水溫度48.6emperborehole wall Toof si/W*m'.K-) _t≤L_通過(guò)公式(7)和(8)計算可 獲得U型地埋管進(jìn)出口溫IN差和單位孔深換熱量。(結束End(7q=cmOT/H。圖3井群傳熱模型計算流程式中AT為地埋管進(jìn)出水溫差,C;Tm為U型地埋管進(jìn)口Fig.3 Calculation poss of wells heat transfer model第10期王俊清等:基于混合解換熱模型的地源熱泵系統井群熱干擾特性197溫度,C;Tu為U型地埋管出口溫度,C;qi為單位井深換鉆孔中心距離200 mm,測點(diǎn)3距鉆孔中心距離300 mm,熱量,W/m;c為流體比熱,kJ/(kg* C);m為流體質(zhì)量流量，則測點(diǎn)溫度試驗數據與模擬值對比分析結果如圖6。kg/s;H為鉆孔深度,m。通過(guò)對比試驗可知，模擬預測值與試驗數據變化趨通過(guò)計算獲得埋管單位井深換熱量,試驗數據與模勢一致，在系統啟動(dòng)初期換熱量相對誤差較大為5%~型預測值對比分析結果如圖5。埋管內流體平均溫度沿鉆12%，運行穩定后相對誤差在5%以?xún)?3個(gè)測點(diǎn)對應地溫孔方向變化很小，熱量在土壤層主要沿徑向擴散,垂直方的相對誤差在3.5%以?xún)?表明模型預測結果是可信的,其向測點(diǎn)溫度相差很小,在此取土壤中層3個(gè)溫度測點(diǎn)溫度存在誤差主要原因有:一、試驗系統及過(guò)程存在誤差,二、進(jìn)行對比驗證,測點(diǎn)1距鉆孔中心距離100 mm,測點(diǎn)2距數學(xué)模型簡(jiǎn)化所致。170160-150+ - -試驗值Experimental value模擬值Simulation value130送縣110-書(shū)三100-90-70-60-5010015020025030035040045050 10150200250300350 400 450時(shí)間Time/mina.換熱量試驗值與模擬值b.相對誤差a. Experimental and simulated values of heat exchangeb. Fractional error日5 換熱量驗證分析Fig.5 Validation analysis of heat exchange28[27牛3井群熱 干擾特性分析。23.1井群鉆孔數目的確定昌22考慮到工程應用中井群布置形式和埋管數量都是以工程復24實(shí)際來(lái)確定,無(wú)統-形式,在此本文僅對方形井群進(jìn)行研究,[ 23|并以16和25井群為對象加以分析,以確定井群的鉆孔數目。雅21↑圖7分別是16和25井群位置分布圖,兩井群中井間距均為4m。對2個(gè)井群換熱進(jìn)行模擬計算,所用幾何參數、物性參數和初始條件均相同。本文在井群模擬計算中所用參數均如表2和表3所示。測點(diǎn)1-模擬值 Measuring point I Simulation value測點(diǎn)1-試驗值Measuring point I-Experimental value測點(diǎn)2-模擬值Measuring point 2-Simulation value●中井t測點(diǎn)2-試驗值Measuring point 2-Experimental valueCenter well←測點(diǎn)3-模擬值Measuring point 3-Simulation value◆測點(diǎn)3-試驗值Measuring point 3-Experimental value,邊井a(chǎn).地溫試驗值與模擬值Edge wella. Experimental and simulated values of soil temperature土壤SoilComer well45a. 16井群a 16 wells group+測點(diǎn)1 Measuring point 1數-一測點(diǎn)2 Measuring point2◎中井+測點(diǎn)3 Measuring point 3, 10醫1)邊井16171819200角井.0 50 100 150 200250 300 350 400450Corner wellb. 相對誤差b.25 井群b. 25 wells group圖6地溫驗證分析日7 井群分布圖Fig.6 Validation analysis of soil temperatureFig.7 Map of wells group198農業(yè)工程學(xué)報tp://www.tcsae.org )2016年表2埋管換熱器幾何參數兩井群中各井的換熱量計算結果如圖8所示。由圖Table 2 Geometrical parameters of heat exchanger7a和8a可以看出,16井群中#1、#4、#13、#16換熱規律埋管內徑埋管外徑管腳間距鉆孔直徑埋管深度- 致，處于井群頂角處，與其直接相鄰的有2口井;#2、InternalOutside Distance between Borehole Depth of burieddiameter/m diameter/mtwo legs/mdiameter/mpipe/m#3、#5、#8、#9、#12、#14、#15換熱規律一致， 處于井群邊0.0260.0320.0350.1260沿處，與其直接相鄰的有3口井;#6、#7、#10、#11換熱規表3模擬計算參數律- -致,處于井群中部，與其直接相鄰的有4口井,從圖Table 3 Simulation calculation of parameters7b和8b可看出,25井群和16井群各井的換熱情況相項目Project參數Value項目Projet同;同時(shí)從圖8還可看出,換熱進(jìn)行至90d時(shí),兩井群中管壁導熱系數Heat三類(lèi)井平均單位井深換熱量幾乎沒(méi)有差別。故可知,方形土壤密度Soil densityl2000conductivity of U-tube/0.42(kg"*m)對稱(chēng)布置的16和25井群中均存在僅和位置有關(guān)的三類(lèi)流體導熱Thermal井,其每類(lèi)井中各井換熱規律完全一致, 依據三類(lèi)井所在土壤比熱Speife heatoo-ga 1500conductivity eoffcient of 0.64井群中的位置，在此把三類(lèi)井分別命名為“中井”、“邊f(xié)uid(W+(m-K))井”、“角井”。土壤導熱系數回填土導熱系數ThermalConductivity of soil/2.2conductivity coefficient of2.4綜上分析知，方形井群中鉆孔數量對各井換熱情(W*m'+K-)backfill soil(W 'm"K")況無(wú)影響，各井的換熱僅與井群中的位置有關(guān)。因16進(jìn)水流速Water flow).8進(jìn)水溫度Water inlettemperature/9C井群具有較好的對稱(chēng)性,在建模時(shí)只需建立1/4的井群:流體密度Fluid土壤初始溫度Soil nitial空間區域,便于應用計算,本文選取16井群物理模型92density/(kg'm)temperature/C進(jìn)行模擬計算分析。16井群中三類(lèi)井位置示意圖如圖流體比熱Fluid heat4 174流體運動(dòng)黏度Kinematic0.659x10*7a所示。capacity(]*kg'K*)viscosity of fluid/(m2.s+)52r22# 16#1#548-3# 20#846-214# 22#3#94455.6#23#6#, 12。42r 10# 24#40-14#員色38-15#sEe7# 14#36-347#8#17#-0#12#19#3社28L102030405060708090102030405060708090運行時(shí)間Time/da. 16井群中各井換熱量b. 25井群中各井換熱量a. Heat exchange of wells in 16 wells groupb. Heat exchange of wells in 25 wells group圖8兩類(lèi)井群中各 井單位井深換熱量變化情況Fig.8 Heat exchange for unit depth of wells in two kinds of wells group3.2井群熱干擾系數定義類(lèi)井換熱量逐漸遞減，-段時(shí)間后三類(lèi)井換熱量出現差圖8a為同樣條件下單井與井群中三類(lèi)井單位井深換值,從大到小順序依次為角井、邊井中井,至90d時(shí),井熱量隨運行時(shí)間的變化。從圖中可看出,換熱進(jìn)行-段時(shí)群中的中井、邊井、角井換熱量相對于單井分別減少間后，井群中三類(lèi)井換熱量出現差值且均小于單井換熱23.4%617.9%.11.3%6，而中井和邊井換熱量相對于角井分量,表明隨著(zhù)換熱進(jìn)行井群各井間會(huì )產(chǎn)生熱干擾,在此將別減少13.6% .6.5%，原因是隨換熱進(jìn)行各井間產(chǎn)生熱干單井換熱量作為標準,引人井群熱干擾系數(k;),以反應擾,中井、邊井、角井所受熱干擾的程度依次減小。井群中各井受熱干擾強度大小。圖8b為單井及井群中三類(lèi)井平均壁溫隨運行時(shí)間的井群熱干擾系數(k)是指井群中各井單位井深換熱變化情況。從圖中可以發(fā)現,隨著(zhù)換熱的進(jìn)行各井平均壁量與未有熱干擾的單井單位井深換熱量之比。溫不斷升高,-段時(shí)間后出現差值,壁溫從高到低依次為設井群中角井、邊井及中井的逐時(shí)單位井深換熱量中井、邊井、角井,至90d時(shí),井群中的中井邊井、角井的分別為g;.q6.q,未有熱干擾的單井單位井深換熱量為qo,平均壁溫相對于單井分別升高了4.2% 3.1%、2.1%,而中井和邊井平均璧溫相對于角井分別升高了2.1%、1.0%,其原則井群中三類(lèi)井的熱干擾系數為k;=9i ;ks=9;k.=L。(3)因亦是井群各井間產(chǎn)生熱干擾，相同時(shí)間內中井附近土壤累積的換熱量最多、邊井次之角井則最少，且中井位于由上述定義可知,herhovke越小則表明井群中各類(lèi)井井群中部換熱量不容易擴散,邊井、角井位于周邊換熱量受到熱干擾的強度越大。易于擴散。3.3計算結果及分析圖9c為三類(lèi)井各自換熱量占井群換熱量的百分比隨通過(guò)圖8a進(jìn)-一步分析可知，隨著(zhù)換熱進(jìn)行井群中三運行時(shí)間的變化情況， 其中以X表示三類(lèi)井的換熱量百第10期王俊清等:基于混合解換熱模型的地源熱泵系統井群熱干擾特性199分比。從圖中可知,邊井x,不隨運行時(shí)間變化為- -定值，井 群換熱量的貢獻率不變?yōu)槎ㄖ?，而角井對井群換熱量這是因物理計算模型的特殊性所致;運行初期中井X.=角的貢獻率逐漸增加，中井對井群換熱量的貢獻率逐漸減井x;=0.25,之后隨換熱進(jìn)行x。逐漸減小,X;逐漸增大,至少,兩者差值逐漸增大，原因是運行一段時(shí)間后井間產(chǎn)生90d時(shí)X.=0.233,X;=0.267,兩者增減幅度均為1.7%, 其換熱干擾，中井受熱干擾程度較大,角井受熱干擾程度較熱量百分比相差3.4%,這表明隨換熱時(shí)間的延長(cháng),邊井對小,相同時(shí)間內中井換熱量的減小值要大于角井。60+單井Single well美冒會(huì )55。角井Cormer well :一邊井Edge well一角井Comer well蛋點(diǎn)50-+中井Center well油星0.40年-中井Center well中井Center well80.29邊井Edge well善0.273525.00.25十角井Comer well圣30包0.210102030405060708090102030405060708090運行時(shí)間Timelda井深換熱量b.井壁溫度e.換熱量百分比a. Heat exchange for unit well depthb. Bore temperaturecC. Percentage of heat exchange圖9井群熱干擾特性Fig.9 Thermal interference characteristics of well group圖10為三類(lèi)井的熱干擾系數隨運行時(shí)間的變化情3)角井對井群換熱量的貢獻率隨運行時(shí)間增加逐漸兄。從圖中可看出,在運行初期k;=kz=k.=1 ,之后隨換熱進(jìn)增加，中井對井群換熱量的貢獻率隨運行時(shí)間增加逐漸行ki;kovk.均逐漸減小,k。減小速度最快,ko減小速度次減少,至90d時(shí)兩者換熱量百分比相差3.4%,而邊井對井之,h減小速度則最慢;運行至90d時(shí)ke降至0.766,k6降群換熱量貢獻率為定值。至0.829 ,k;降至0.886，表明三類(lèi)井的熱干擾強度隨系統4)井群中三類(lèi)井所受熱干擾強度隨換熱進(jìn)行逐漸增運行時(shí)間延長(cháng)逐漸增加，同- -運行時(shí)刻中井受熱干擾的加,相同運行時(shí)刻中井受熱干擾影響最大、邊井次之角井程度大于邊井，邊井大于角井。最小。.[參考文獻]0.94 t0.92 t1] 曲云霞.地源熱泵系統模型與仿真[D].西安:西安建筑科技0.90-大學(xué)，2004.0.88-Qu Yunxia. Modeling and Simulation for Ground Source Heat器號0:845Pumps System[D]. Xi an: Xi' an University of Architecture andTechnology, 2004.(in Chinese with English abstract)0.78 t[2] Ingersoll L R, Plass H J Theory of the ground pipe heat sourcefor the heat pump[J]. Heating, Piping & air Conditioning, 1948,074 [20: 119-122.72[3] Ingersoll L R, Zoeble 0 J, Ingersoll A C. 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Geothermics, 2015, 54:115- 121.and linear heat source integrated modelof vertical embedded[19] 李人憲.有限體積法基礎[M].北京:國防工業(yè)出版社, 2008.Thermal interference characteristics of wells in ground source heat pumpsystem based on analytical and numerical calculation of mixed solutionWang Junqing, Yuan Yanping*, Cao Xiaoling, Qin Ping(The College of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China)Abstract: In practical engineering, buried pipe is the form of well group. At present, there are two ways to calculate theheat transfer in a group of wells. One is to calculate the heat transfer of a single well, which is then directly multiplied bythe number of holes to get the heat transfer of well group, without consideration of the thermal interference between wells.The other is the direct use of analytical solution or numerical simulation. The numerical solution of the powerful is good atcalculating complex heat transfer problems, and can effectively grasp the dynamic heat transfer characteristics of buriedpipe. The heat transfer space is large and the geometry configuration is complex, 80 the computation time is too long. Inorder to establish a heat transfer model of well group that can be quickly solved and used for thermal disturbancecharacteristics, the mixed solution heat transfer model based on analytical and numerical calculation is presented. Thebasic idea is to divide the space of the well group into the space inside borehole(including multiple drilling holes) andoutside borehole taking the borehole wall as the boundary. Both steady-state analytical method and transient numerical heattransfer method are used to analyze the heat transfer characteristics inside and outside borehole respectively, and the 2regions are coupled by the borehole wall temperature. After the establishment of summer conditions of single drill pipe heatexchanger test-bed, and the verification of single well heat transfer model, the FLUENT software in combination with theheat transfer model of well group is used to further study the wells at 3 kinds of special postions in the square well group(middle well, edge well and corner well), and the typical well group of physical model is determined and the thermalinterference coffcient of the well group is defined. Finally, the thermal interference characteristics of the typical wellgroup are studied mainly under the condition of continuous operation in summer. The research results show that with thedevelopment of heat exchanger of well group, the heat interference between wells in well group is generated and graduallyincreases, and at the same time the degree of heat interference for the middle of well is the largest, followed by the edge ofwell and the corner of well; due to the influence of heat interference, the heat transfer capability of the corner of well is thebiggest and its borehole wall temperature is the lowest, the heat exchange ability and borehole wall temperature of the edgeof well are in the middle, and the heat transfer capability of the middle of well is the minimum and its borehole walltemperature is the highest. After running for 90 d, the heat exchange of the corner of well is 6.5% more than the edge ofwell, and the heat exchange of the edge of well is 7.1% more than the middle of well; the contribution rate of heat exchangeof the corner of well to the well group is gradually increased with the running time, that of the middle of well is graduallyreduced with the running time, while that of the edge of well is basically unchanged.Keywords: heat pump systems; well; heat transfer; heat interference characteristics