第32卷第10期農(nóng)業(yè)工程學(xué)報(bào)Vol 321942016年5月Tanstietecinesesoietgiounalngmei基于混合解換熱模型的地源熱泵系統(tǒng)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(jī)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(shù)值計(jì)算的混合解模型,以16井群為研究對(duì)象,通過試驗(yàn)和數(shù)值模擬的方法研究了井群熱干擾特性。研究結(jié)果表明:隨著換熱的進(jìn)行井群中各井間產(chǎn)生熱干擾并逐漸增強(qiáng),同一運(yùn)行時(shí)刻中井受熱干擾程度最大、邊井次之、角井則最小;由于井間熱干擾的影響,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(yùn)行90d時(shí)角井換熱量比邊井大65%,邊井換熱量比中井大7.1%;角井對(duì)井群換熱量的貢獻(xiàn)率隨換熱時(shí)間延長(zhǎng)逐漸增加,中井對(duì)井群換熱量的貢獻(xiàn)率則逐漸減少,而邊井對(duì)井群換熱量的貢獻(xiàn)率基本不變。關(guān)鍵詞:熱泵系統(tǒng);井群;傳熱;熱干擾特性doi:10.11975/isn.1002-68192016.10.027中圖分類號(hào):TK523文獻(xiàn)標(biāo)志碼:A文章編號(hào):1002-6819(2016)-10-019407王俊清,袁艷平,曹曉玲,秦萍基亍混合解換熱模型的地源熱泵系統(tǒng)井群熱干擾特性J,農(nóng)業(yè)工程學(xué)報(bào),2016,32(10):194-200.doi:10.1975/jisn.1002-68192016.10.027htp/www.csae.orgWang Junqing, Yuan Y anping, Cao Xiaoling, Qin Ping. Thermal interference characteristics of wells in ground source heatsystem based on analytical and numerical calculation of mixed solution [J]. Transactions of the Chinese Society of agricuEngineering (Transactions of the CSAE), 2016, 32(10): 194-200(in Chinese with English abstract) doi: 10. 11975/).issn 100268192016.10027htp:/www.tcs0引言材料的熱影響及管井間的熱干擾。高青等對(duì)G函數(shù)進(jìn)行簡(jiǎn)化,提出了簡(jiǎn)化柱熱源模型,該方法可準(zhǔn)確計(jì)算出井孔淺層地?zé)崮艿睦脤?duì)建筑節(jié)能、構(gòu)建綠色建筑具有周圍土壤的導(dǎo)熱系數(shù)。方肇洪等提出了豎直埋管換熱器重要意義。在淺層地?zé)崮芾弥械卦礋岜檬瞧渲械闹匾@孔內(nèi)傳熱過程的準(zhǔn)三維模型,給出鉆孔內(nèi)熱阻解析表達(dá)技術(shù),該項(xiàng)技術(shù)的研究核心和應(yīng)用基礎(chǔ)是地下埋管換熱,式,求得有限長(zhǎng)線熱源在半無限大介質(zhì)中的瞬態(tài)溫度響應(yīng)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(dǎo)出了無限大介質(zhì)中無與基礎(chǔ)。目前國(guó)內(nèi)外學(xué)者對(duì)地埋管傳熱模型已進(jìn)行了大限長(zhǎng)線熱源溫度響應(yīng)的解析解。楊衛(wèi)波等明用能量平衡及量研究,就現(xiàn)有地下埋管傳熱計(jì)算方法可分為簡(jiǎn)化解析變熱流圓柱源理論建立了二區(qū)域U型埋管傳熱模型,該模解和離散化數(shù)值計(jì)算叫,其傳熱計(jì)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(jī)組模型耦合解析解模型計(jì)算簡(jiǎn)便、快捷;離散化數(shù)值計(jì)算模型善于計(jì)進(jìn)行地源熱泵系統(tǒng)動(dòng)態(tài)模擬及相應(yīng)能耗分析和優(yōu)化設(shè)計(jì)。算復(fù)雜傳熱問題。目前在解析解方面,最主要的理論是在數(shù)值解方面,Le門對(duì)U形埋管換熱器兩支管分別建1948年 ingersoll等提出的 Kelvin線熱源理論以及1954立二維柱坐標(biāo)系假定傳熱僅發(fā)生在徑向,采用有限差分年 Ingersoll等給出的圓柱源理論。Hant等在 Kelvin線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(chǔ)上,建立了線熱源到周圍土壤隨時(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(duì)單溫度分布傳熱模型,該模型未考慮熱泵機(jī)組間歇運(yùn)行工U埋管換熱器的溫度場(chǎng)及流場(chǎng)進(jìn)行了數(shù)值模擬,軸向上建況管內(nèi)對(duì)流換熱熱阻灌漿材料的熱影響。 Kavanaugh等立兩支管一維對(duì)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(chǔ)建立了埋管周圍的平面內(nèi)藕合求解管內(nèi)流體與土壤間的傳熱,實(shí)現(xiàn)2個(gè)區(qū)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(gòu)建了準(zhǔn)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(shù)學(xué)模型,提出了層換熱理論,將換熱器及其周圍的巖土分為3基金項(xiàng)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(tuán)隊(duì)項(xiàng)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(diào)節(jié)能技術(shù)研究。成此外,亦有學(xué)者將解析解與數(shù)值計(jì)算法結(jié)合使用以都西南交通大學(xué)機(jī)械工程學(xué)院,610031。獲得簡(jiǎn)單快速中國(guó)煤化工解析法與數(shù)值法Email:yourongxinan@163.com混合求解埋管單鉆孔采用有限長(zhǎng)通信作者;艷平男湖北洪湖人,教授博士生導(dǎo)師主要從事建筑線熱源數(shù)值以,見JCNMH間熱濕采用單鉆孔溫度究。成都西南交通大學(xué)機(jī)械工程學(xué)院,61003響應(yīng)疊加計(jì)算,從而確定任意時(shí)間的鉆孔壁溫。 HellstromEmail: ypyuan@home. swjtu.edu.en等研究了多個(gè)鉆孔密集模型布置的儲(chǔ)熱模型,對(duì)局部問第10期王俊清等:基于混合解換熱模型的地源熱泵系統(tǒng)井群熱干擾特性題采用一維(徑向)有限差分法,對(duì)全局問題采用二維(徑邊界向一軸向)有限差分法,當(dāng)達(dá)到穩(wěn)定熱流時(shí)采用解析法疊對(duì)鉆孔外土壤計(jì)算區(qū)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(tǒng)長(zhǎng)期運(yùn)行計(jì)容積內(nèi)對(duì)控制方程(1)進(jìn)行空間和時(shí)間積分,組建差分方算分析。陸志等叫提出數(shù)值計(jì)算與有限長(zhǎng)線熱源綜合模程組結(jié)合邊界條件和初始條件對(duì)方程組進(jìn)行求解,得到型,以替代半徑將計(jì)算區(qū)域分為兩部分,半徑以內(nèi)土壤的鉆孔外土壤區(qū)域溫度分布,亦可知各鉆孔壁溫T。溫度通過數(shù)值迭代法計(jì)算得出,半徑以外土壤溫度通過井群鉆孔外土壤計(jì)算區(qū)域如圖1,q為單位井深換熱有限長(zhǎng)線熱源模型計(jì)算得到,數(shù)值計(jì)算區(qū)域的外邊界溫量(由鉆孔內(nèi)傳熱模型計(jì)算),賦值給井壁邊界。度由有限長(zhǎng)線熱源法計(jì)算給出,有限長(zhǎng)線熱源法中單位長(zhǎng)度的熱流密度通過計(jì)算管內(nèi)流體與管壁對(duì)流換熱的熱流量得出。在課題組前期,袁艷平等提出以鉆孔壁為:±纏sn遠(yuǎn)邊界邊界將計(jì)算區(qū)域分為鉆孔內(nèi)和鉆孔外2個(gè)部分,鉆孔以Infinite內(nèi)部分,基于能量平衡建立穩(wěn)態(tài)解析解傳熱模型,對(duì)于鉆孔外土壤區(qū)域,采用非穩(wěn)態(tài)有限體積法進(jìn)行傳熱計(jì)算,兩區(qū)域通過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(chǔ)對(duì)單井在連續(xù)運(yùn)行和間歇運(yùn)行下的換熱特性進(jìn)行了研究。從文獻(xiàn)綜述情況來看,地埋管傳熱模型大都針對(duì)單井,但在實(shí)際工程中地埋管都是以群井形式出現(xiàn),目前對(duì)于群注:q為單位井深換熱量井換熱量的計(jì)算,大致分為兩種思路:是計(jì)算單井的換熱Note: qu is the heat exchange of unit well depth量,直接乘以鉆孔數(shù)得到。這種方法計(jì)算簡(jiǎn)單,但井群中因圖1井群鉆孔外計(jì)算區(qū)域鉆孔間距有限,各井間會(huì)出現(xiàn)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12鉆孔內(nèi)傳熱模型接采用解析解或數(shù)值模擬進(jìn)行計(jì)算,數(shù)值解功能強(qiáng)大善于對(duì)鉆孔內(nèi)傳熱進(jìn)行以下簡(jiǎn)化計(jì)算復(fù)雜傳熱問題,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(qū)域大、幾何配置復(fù)雜,計(jì)算時(shí)間過長(zhǎng)。觸熱阻本文在保證求解準(zhǔn)確性的基礎(chǔ)上加快求解速度,建2)忽略埋管內(nèi)介質(zhì)軸向?qū)岷蚒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(qū)域分為鉆孔內(nèi)(包含多個(gè)鉆孔)和鉆孔外3)管內(nèi)流體流速均勻一致,任意截面內(nèi)流體溫度均勻2個(gè)區(qū)域;各鉆孔內(nèi)傳熱通過穩(wěn)態(tài)解析解計(jì)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(duì)應(yīng)鉆孔壁的邊界條件,采用數(shù)值4)回填土、管內(nèi)流體的熱特性參數(shù)恒定;方法計(jì)算孔外土壤溫度動(dòng)態(tài)響應(yīng)。在此基礎(chǔ)上對(duì)井群熱5)忽略熱濕遷移的影響,認(rèn)為回填土中的傳熱為純導(dǎo)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題。規(guī)律,為地源熱泵系統(tǒng)地埋管設(shè)計(jì)提供參考。井群中每個(gè)鉆孔內(nèi)傳熱情況完全一樣,故在此僅對(duì)1井群傳熱模型其中一個(gè)鉆孔為對(duì)象分析其傳熱情況,鉆孔內(nèi)微元體傳熱示意如圖2所示。1.1鉆孔外土壤區(qū)域傳熱模型鉆孔壁 Borehole wall對(duì)鉆孔外土壤區(qū)域傳熱進(jìn)行以下簡(jiǎn)化:壁溫 Well temperature1)假設(shè)土壤熱物性參數(shù)及初始地溫均勻一致,且物性牛水管換熱量水管換熱量不隨時(shí)間變化qz Heat transfer of2)忽略滲流及熱濕遷移,認(rèn)為土壤中的傳熱為均勻純導(dǎo)熱問題;3)認(rèn)為傳熱過程僅發(fā)生在水平方向。進(jìn)水溫度出水溫基于以上簡(jiǎn)化,土壤區(qū)域傳熱控制方程為InNet waterOutlet wat ax"ax /dady兩管間換熱量式中ρ為土壤密度,kg/m3;c為土壤定壓比熱,J/(kg:℃);kHeat transfer between two tubes為土壤導(dǎo)熱系數(shù),W(m℃);T為土壤溫度,℃;S為源項(xiàng)圖2鉆孔內(nèi)微元體傳熱示意圖求解中進(jìn)行線性化處理,分解為常數(shù)項(xiàng)及隨時(shí)間和溫度EV凵中國(guó)煤化工 r diagram變化項(xiàng)?；谝陨下凜NMHG溫度沿程變化及初始條件:T(x,y,z)=76(其中T為初始地溫)。兩支管間熱干擾影響,參照?qǐng)D2對(duì)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(yuǎn)邊界為絕熱體d,可根據(jù)能量平衡得控制方程組啊農(nóng)業(yè)工程學(xué)報(bào)(htp:/www.tcsae.org)2016年dT(z)d2+=R(7-T(2)+Ra[Tx)-T(2dr,(z)M在0-T)(2)2單井傳熱模型試驗(yàn)驗(yàn)證判定井群傳熱模型預(yù)測(cè)結(jié)果是否符合實(shí)際情況,是進(jìn)行井群換熱模擬計(jì)算的前提。由井群傳熱模型建立過定解條件:7n(0)=7h;Tn(H)=TA(H)(其中H為鉆孔深度)。式中M為循環(huán)流體的熱容量,M=cmn(其中c為流體程可知,井群傳熱模型的數(shù)學(xué)描述與單井傳熱模型僅在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(nèi)循環(huán)流體的質(zhì)量流量),確,即可證明井群傳熱模型預(yù)測(cè)結(jié)果的準(zhǔn)確性。故本節(jié)建J(s:℃);Tn(z)、Tn(z)為z處U型管進(jìn)/出口流體溫度,℃;立單鉆孔地埋管換熱系統(tǒng)夏季工況試驗(yàn)臺(tái),驗(yàn)證單井換g、g2分別為U型地埋管兩支管與鉆孔壁間的單位管長(zhǎng)換熱模型。試驗(yàn)中鉆孔直徑為01m,鉆孔深度為12m,U型熱量,qn為U型地埋管兩支管間單位管長(zhǎng)換熱量,Wm;埋管采用內(nèi)徑0014m的銅管,兩支管間距為0m。試T為鉆孔壁溫度,℃;R、R與R分別為兩支管內(nèi)流體與孔驗(yàn)系統(tǒng)原理圖如圖4所示。壁及鄰近兩支管內(nèi)流體間的等效傳熱熱阻(其中R=R),℃/W;R、R的計(jì)算參見文獻(xiàn)[流量計(jì)保溫管恒溫水箱lown令1(z)=T-Tn(z),B(z)=T-Tn(z),a=(1/R+1/R合M,hT100熱電阻 Hot resistaneb=(1/R點(diǎn)M,則式(2)可化簡(jiǎn)為:填充土壤Soil周節(jié)閥水泵Pumpg(3)數(shù)據(jù)采集儀de,U型銅管Data acquisition instrument壤對(duì)方程組(3)進(jìn)行 Laplace變換,采用求解常微分方Temperature PID程組的方法進(jìn)行求解可得控制柜ContreJa()c:gYab2、+C2b圖4試驗(yàn)系統(tǒng)原理62(z)=C1eVa-b)z -(Va-3)Fig 4 Schematic diagram of experimental system式中C1,C2為待定常數(shù),可結(jié)合定解條件求取。任何試驗(yàn)均存在系統(tǒng)誤差,為了保證試驗(yàn)結(jié)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(yàn)系統(tǒng)誤差不能過大否則會(huì)對(duì)試驗(yàn)結(jié)果產(chǎn)生較深換熱量:Tm=Th-62(0)。(5)大影響。本試驗(yàn)的系統(tǒng)誤差主要來源于儀器測(cè)量精度;試qi=M(T-T)/H.(6)驗(yàn)使用四線式P100熱電阻測(cè)量埋管進(jìn)出口水溫,其精度≤015℃;使用T型熱電偶測(cè)定土壤層溫度,其精度≤式中q為單位井深換熱量W為鉆孔深度,四05℃;使用小型橢圓齒輪流量計(jì)測(cè)量進(jìn)水流量其測(cè)量孔壁溫度進(jìn)行耦合鏈接,首先由初始壁溫通過孔內(nèi)模型精度≤1%;使用 Hot disk2500測(cè)量土壤導(dǎo)熱系數(shù),其測(cè)量精度≤3%。由以上可知,本試驗(yàn)系統(tǒng)誤差較小,可以保證計(jì)算換熱量,將換熱量作為熱邊界條件計(jì)算孔外土壤傳試驗(yàn)結(jié)果的可信度。熱,然后再提取下一時(shí)間壁溫計(jì)算換熱量,之后往復(fù)循環(huán)本試驗(yàn)方案為:埋管內(nèi)流體處于紊流狀態(tài)下,換熱直至滿足所設(shè)條件;通過 FLUENT軟件平臺(tái)利用用戶接系統(tǒng)維持恒定進(jìn)水流量及進(jìn)水溫度連續(xù)運(yùn)行7h,每間口(UDF)求解計(jì)算的具體流程如圖3所示。隔1min采集1次各測(cè)點(diǎn)溫度數(shù)據(jù)土壤初始溫度 Soil initial temperature To(o時(shí)刻 to moment)本試驗(yàn)過程測(cè)得土壤熱物性參數(shù)及系統(tǒng)運(yùn)行參數(shù)見鉆孔內(nèi)傳熱模型計(jì)算Calculation各并單位井探熱 borehole表1試驗(yàn)參數(shù)(Heat transfer per unit depth of wells)Table 1 Test parameters參數(shù)vlue孔外士壤傳熱模型計(jì)算項(xiàng)目 Project項(xiàng)目 Project參數(shù) Valuecatuianon t乎王壤溫度咒le borehole土壤密度 Soil density土層初溫Soil initial temperature/C土壤比熱 Specific heat of系統(tǒng)流量1016d時(shí)間各井壁平均溫度soi/U·kg…K)ystem flow/(mh)0.105 53dt time average temperature of each土壤導(dǎo)熱系數(shù) Conductivity019| Water inlet temperature/(486進(jìn)水溫度通過公式(中國(guó)煤化工地埋管進(jìn)出口溫差和單位孔深結(jié)束EndCNMHG(7)圖3井群傳熱模型計(jì)算流程q=cm△TH(8)ig. 3 Calculation process of wells heat transfer model式中△T為地埋管進(jìn)出水溫差,℃;Tm為U型地埋管進(jìn)口第10期王俊清等:基于混合解換熱模型的地源熱泵系統(tǒng)井群熱干擾特性197溫度,℃;T為U型地埋管出口溫度,℃;q為單位井深換鉆孔中心距離200mm,測(cè)點(diǎn)3距鉆孔中心距離300mm,熱量,W/m;c為流體比熱,kJ/kg:℃);m為流體質(zhì)量流量,則測(cè)點(diǎn)溫度試驗(yàn)數(shù)據(jù)與模擬值對(duì)比分析結(jié)果如圖6。kgs;H為鉆孔深度,mo通過對(duì)比試驗(yàn)可知,模擬預(yù)測(cè)值與試驗(yàn)數(shù)據(jù)變化趨通過計(jì)算獲得埋管單位井深換熱量,試驗(yàn)數(shù)據(jù)與模勢(shì)一致,在系統(tǒng)啟動(dòng)初期換熱量相對(duì)誤差較大為5%型預(yù)測(cè)值對(duì)比分析結(jié)果如圖5。埋管內(nèi)流體平均溫度沿鉆12%,運(yùn)行穩(wěn)定后相對(duì)誤差在5%以內(nèi),3個(gè)測(cè)點(diǎn)對(duì)應(yīng)地溫孔方向變化很小,熱量在土壤層主要沿徑向擴(kuò)散垂直方的相對(duì)誤差在35%以內(nèi);表明模型預(yù)測(cè)結(jié)果是可信的,其向測(cè)點(diǎn)溫度相差很小,在此取土壤中層3個(gè)溫度測(cè)點(diǎn)溫度存在誤差主要原因有:一、試驗(yàn)系統(tǒng)及過程存在誤差,二、進(jìn)行對(duì)比驗(yàn)證,測(cè)點(diǎn)1距鉆孔中心距離100mm,測(cè)點(diǎn)2距數(shù)學(xué)模型簡(jiǎn)化所致。50試驗(yàn)值 Experimental value模擬值 Simulation value107005010015020025030035040045050100150200250300350400450時(shí)間Time/min時(shí)間Time/mina.換熱量試驗(yàn)值與模擬值b.相對(duì)誤差perimental and simulated values of heat exchangeb. Fractional error圖5換熱量驗(yàn)證分析Fig5 Validation analysis of heat exchange8763井群熱干擾特性分析31井群鉆孔數(shù)目的確定E25考慮到工程應(yīng)用中井群布置形式和埋管數(shù)量都是以工程實(shí)際來確定,無統(tǒng)一形式,在此本文僅對(duì)方形井群進(jìn)行研究,并以16和25井群為對(duì)象加以分析,以確定井群的鉆孔數(shù)目圖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(duì)2個(gè)井群換熱進(jìn)行模擬計(jì)算,所用幾何參050100150200250300350400450數(shù)、物性參數(shù)和初始條件均相同。本文在井群模擬計(jì)算中時(shí)間Tme/min所用參數(shù)均如表2和表3所示。測(cè)點(diǎn)1-模擬值 Measuring point 1-Simulation value測(cè)點(diǎn)1-試驗(yàn)值 Measuring point1- Experimental value4測(cè)點(diǎn)2-模擬值 Measuring point2 Simulation value●中井測(cè)點(diǎn)2-試驗(yàn)值 Measuring point2- Experimental value78Center well測(cè)點(diǎn)3-模擬值 Measuring point3 Simulation value測(cè)點(diǎn)3-試驗(yàn)值 Measuring point3- Experimental value91011●邊井a(chǎn).地溫試驗(yàn)值與模擬值a Experimental and simulated values of soil temperatureO角井土壤SoilCormer wella.16井群a. 16 wells group測(cè)點(diǎn)1 Measuring point測(cè)點(diǎn)2 Measuring point25測(cè)點(diǎn)3 Measuring point3|●中井Center well●邊井1617181920Edge wellO角井50100150200250300350400450時(shí)間 Time/min中國(guó)煤化工erweb.相對(duì)誤差CNMHGb. Fractional errorb 25 wells group圖6地溫驗(yàn)證分析圖7井群分布圖Fig 6 Validation analysis of soil temperatureFig 7 Map of wells grou農(nóng)業(yè)工程學(xué)報(bào)(htp:/www.tcae.org)2016年表2埋管換熱器幾何參數(shù)兩井群中各井的換熱量計(jì)算結(jié)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(guī)律埋管內(nèi)徑埋管外徑管腳間距鉆孔直徑埋管深度Internal Outside Distance between Borehole Depth of buried致,處于井群頂角處,與其直接相鄰的有2口井;#2、diameter/m#3、#5、#8、擬#12、#14、#15換熱規(guī)律一致,處于井群邊003200350.12沿處,與其直接相鄰的有3口井;#6、#7、#10、#11換熱規(guī)表3模擬計(jì)算參數(shù)律一致,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(xiàng)目 Project參數(shù)vlu項(xiàng)目pet參數(shù)Ve同;同時(shí)從圖8還可看出,換熱進(jìn)行至90d時(shí),兩井群中土壤密度 Soil density/2000管壁導(dǎo)熱系數(shù)Heat三類井平均單位井深換熱量幾乎沒有差別。故可知,方形conductivity of U-tube/對(duì)稱布置的16和25井群中均存在僅和位置有關(guān)的三類井,其每類井中各井換熱規(guī)律完全一致,依據(jù)三類井所在土壤比熱 Specific流體導(dǎo)熱 Thermalof soill(J·kg“K)1500conductivity coefficient of 0. 64fuid(W·(mK))井群中的位置,在此把三類井分別命名為“中井”“邊土壤導(dǎo)熱系回填土導(dǎo)熱系數(shù) Thermal井”、“角井”綜上分析知,方形井群中鉆孔數(shù)量對(duì)各井換熱情backfill soil(W·m2k)進(jìn)水流速 Water now進(jìn)水溫度 Water inlet況無影響,各井的換熱僅與井群中的位置有關(guān)。因160.8井群具有較好的對(duì)稱性,在建模時(shí)只需建立14的井群體密度Fuid土壤初始溫度 Soil initial空間區(qū)域,便于應(yīng)用計(jì)算,本文選取16井群物理模型進(jìn)行模擬計(jì)算分析。16井群中三類井位置示意圖如圖流體比熱 Fluid heat4174流體運(yùn)動(dòng)黏度 Kinematic0659×107a所示。s2082#4#22#6#23#10#24#斜乏315#15#8642087#14#8#17#9#18#3013#2030405060運(yùn)行時(shí)間 Timed運(yùn)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8兩類井群中各井單位井深換熱量變化情況Fig8 Heat exchange for unit depth of wells in two kinds of wells group3.2井群熱干擾系數(shù)定義類井換熱量逐漸遞減,一段時(shí)間后三類井換熱量出現(xiàn)差圖8a為同樣條件下單井與井群中三類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(yùn)行時(shí)間的變化。從圖中可看出,換熱進(jìn)行一段時(shí)群中的中井、邊井、角井換熱量相對(duì)于單井分別減少間后,井群中三類井換熱量出現(xiàn)差值且均小于單井換熱234%、17.1%、11.3%,而中井和邊井換熱量相對(duì)于角井分量,表明隨著換熱進(jìn)行井群各井間會(huì)產(chǎn)生熱干擾,在此將別減少13.6%65%,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(biāo)準(zhǔn),引入井群熱干擾系數(shù)(k),以反應(yīng)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(qiáng)度大小圖8b為單井及井群中三類井平均壁溫隨運(yùn)行時(shí)間的井群熱干擾系數(shù)(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(xiàn),隨著換熱的進(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,一段時(shí)間后出現(xiàn)差值,壁溫從高到低依次為設(shè)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q、q5q,未有熱干擾的單井單位井深換熱量為qo平均壁溫相對(duì)于單井分別升高了42%31%、2.%,而中井則井群中三類井的熱干擾系數(shù)為和邊井平均壁溫相對(duì)于角井分別升高了21%、10%,其原k=9;=;k:=9。因亦是井群各井間產(chǎn)生熱干擾,相同時(shí)間內(nèi)中井附近土壤累積的換熱廠YH中國(guó)煤化工最少,且中井位于由上述定義可知,k、k、k越小則表明井群中各類井井群中部換熱CNMHG位于周邊換熱量受到熱干擾的強(qiáng)度越大。易于擴(kuò)散。33計(jì)算結(jié)果及分析圖9c為三類井各自換熱量占井群換熱量的百分比隨通過圖8a進(jìn)一步分析可知,隨著換熱進(jìn)行井群中三運(yùn)行時(shí)間的變化情況,其中以X表示三類井的換熱量百第10期王俊凊等:基于混合解換熱模型的地源熱泵系統(tǒng)井群熱干擾特性199分比。從圖中可知,邊井X不隨運(yùn)行時(shí)間變化為一定值,井群換熱量的貢獻(xiàn)率不變?yōu)槎ㄖ?而角井對(duì)井群換熱量這是因物理計(jì)算模型的特殊性所致;運(yùn)行初期中井X=角的貢獻(xiàn)率逐漸增加,中井對(duì)井群換熱量的貢獻(xiàn)率逐漸減井x=025,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(yùn)行一段時(shí)間后井間產(chǎn)生90d時(shí)κ=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349,這表明隨換熱時(shí)間的延長(zhǎng),邊井對(duì)小,相同時(shí)間內(nèi)中井換熱量的減小值要大于角井。單井 Single well28.5050角井 Corner well→邊井 Edge well一邊井 Edge well坐275一中井 Center well耗坦045角井 Corner well中井 Center well量265中井 Center well30.29→邊井 Edge well0.27單井 Single well0.25→角井 Corner wel0102030405060700102030運(yùn)行時(shí)間 Time/d運(yùn)行時(shí)間 Time/d運(yùn)行時(shí)間 Time/da.井深換熱b.井壁溫度c換熱量百分比a Heat exchange for unit well depthc. Percentage of heat exchange圖9井群熱干擾特性Fig9 Thermal interference characteristics of well group圖10為三類井的熱干擾系數(shù)隨運(yùn)行時(shí)間的變化情3)角井對(duì)井群換熱量的貢獻(xiàn)率隨運(yùn)行時(shí)間增加逐漸況。從圖中可看出,在運(yùn)行初期k=kk,=l,之后隨換熱進(jìn)增加,中井對(duì)井群換熱量的貢獻(xiàn)率隨運(yùn)行時(shí)間增加逐漸行k、k、k均逐漸減小,k.減小速度最快,k減小速度次減少,至90d時(shí)兩者換熱量百分比相差34%,而邊井對(duì)井之,減小速度則最慢;運(yùn)行至90d時(shí)k降至0.766k降群換熱量貢獻(xiàn)率為定值。至0.8209,k降至0.88,表明三類井的熱干擾強(qiáng)度隨系統(tǒng)4)井群中三類井所受熱干擾強(qiáng)度隨換熱進(jìn)行逐漸增運(yùn)行時(shí)間延長(zhǎng)逐漸增加,同一運(yùn)行時(shí)刻中井受熱干擾的加,相同運(yùn)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(xiàn)][]曲云霞地源熱泵系統(tǒng)模型與仿真[D.西安:西安建筑科技大學(xué),2004.Qu Yunxia. Modeling and Simulation for Ground Source HeatPumps System[D]. Xi'an: Xi'an University of Architecture andTechnology, 2004.(in Chinese with English abstract)[2 Ingersoll L R, Plass H J. Theory of the ground pipe heat source0.74for the heat pump[J]. Heating, Piping air Conditioning, 19480.7220:119-122010203040506070[3]Ingersoll L R, Zoeble O J, Ingersoll A C. Heat Conduction with行時(shí)間 TimedEngineering, Geological and Other Application [M]. New York注:k、k6、k為角井、邊井、中井的熱干擾系數(shù)。McGraw-Hill. 1954.Note: k, ku, k, is thermal interference coefficient of corner well, edge well and [4] Hart D P, Couvillion R. Earth Coupled Heat Transfer[M]Publication of the National Water Well association. 1986.圖10三類井的熱干擾系數(shù)隨運(yùn)行時(shí)間的變化[5 Deerman J D, Kavanaugh S P. Simulation of vertieal U-tubegorund coupled heat pump systems using the cylindrical heatFig 10 Thermal interference coefficient for three kinds of wellssource solution[J]. ASHRAE Transactions, 1991, 97(1): 287-295along with change of running time6]高青,余傳輝.地下土壤導(dǎo)熱系數(shù)簡(jiǎn)化柱熱源模型確定方法小太陽能學(xué)報(bào),2007,2812):1402-1406Gao Qing, Yu Chuanhui. The simplified cylindrical source4結(jié)論model for determining the thermal conductivity[J]. Acta Energiae Solaris Sinica, 2007, 28(12): 1402-1406 (inChinese with English abstract)1)提出了能準(zhǔn)確快速求解的解析一數(shù)值混合計(jì)算的方肇洪,刁乃仁地?zé)釗Q熱器的傳熱分析建筑熱能通風(fēng)井群傳熱模型,并利用試驗(yàn)驗(yàn)證了其準(zhǔn)確性?？照{(diào),2004,23(1):11-202)隨著換熱的進(jìn)行,井群中各井換熱能力逐漸降低Fang Zhaohong, Diao Nairen. Heat transfer analysis of ground井換熱量和井壁平均溫度出現(xiàn)差值換熱量從大到小順序④D:02021各井平均壁溫逐漸升高,因井間熱干擾的影響,井群中各1-20.in依次為角井、邊井、中井,井壁平均溫度從高到底的順序依工程熱V中國(guó)煤化工模型及其實(shí)驗(yàn)驗(yàn)證次為中井、邊井、角井,至90d時(shí)中井、邊井、角井的換熱量CN MH Geat transfer model of相對(duì)于單井分別減少23.4%、17.1%、11.3%,而中井、邊井、U-tube ground heat exchanger and its experiment validation[J]Journal of Engineering Thermophysics, 2008, 29(5): 857-860.(in角井的平均壁溫相對(duì)于單井分別高了42%、3.1%、21%。Chinese with English abstract)200農(nóng)業(yè)工程學(xué)報(bào)(htt/www.tcae.org)2016年[91 Lei TK. Development of a computational model for a groundipe for ground source heat pump[J. Journal of Shanghai Jiaotongcoupled heat exchanger!J). 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Heat transferofVentilating and Air Conditioning, 2007, 37(9): 35-39.( in Chineseground heat exchanger for GSHP (3): Transient heat transferwith English abstract)characteristic of U-type ground heat exchanger with variable[12] EskilsonP, Claesson]. Simulation model for thermally interactingheat flow boundary[]. Heating Ventilating and Air Conditioning,heat extraction bore holes[J]. Numerical Heat Transfer, 1988, 132009, 39(12): 10-15(in Chinese with English abstract)2:149-165[17 Yuan Yanping, Cao Xiaoling, Sun Liangliang, et al. Ground[13] Hellstrom G, Sanner B, Klugescheid M, et al. Experiences withource heat pump system: A review of simulation in China[Jthe borehole heat exchanger software EED [C]/MegastockRenewable and Sustainable Energy Reviews, 2012, 16(9)sapporo, Japan, 1997.681468224陸志連之偉,劉薇巍等地源熱泵豎直埋管數(shù)值線源綜合18] Cao Xiaoling, Yuan Yanping, Sun Liangliang, et al. Restoration模型[J上海交通大學(xué)學(xué)報(bào),2008,42(3):409414performance of vertical ground heat exchanger with variousLu Zhi. Lian Zhiwei. Liou Weiwei, et al. Numerical simulationtermittent ratios[]. Geothermics, 2015, 54: 115-121and linear heat source integrated modelof vertical embedded[19李人憲.有限體積法基礎(chǔ)M北京國(guó)防工業(yè)出版社,2008Thermal interference characteristics of wells in ground source heat pumpsystem based on analytical and numerical calculation of mixed solutionWang Junqing, Yuan Yanping Cao Xiaoling, Qin Pir(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 atalculating 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, so 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 disturbanceharacteristics, 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 positions 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 coefficient 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 comer 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中國(guó)煤化工 than the edge ofwell, and the heat exchange of the edge of well is 7. 1%more than the middle ofCNMHGof heat exchangeof the cormer 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 unchangedKeywords: heat pump systems; well; heat transfer; heat interference characteristics