毛秀麗,陳星錕,溫國慶,袁一凡,任 巖,熊 妍
混流式水輪機多工況運行轉(zhuǎn)輪特性
毛秀麗1,2,陳星錕1,溫國慶1,袁一凡1,任 巖3,熊 妍4
(1. 西北農(nóng)林科技大學(xué)水利與建筑工程學(xué)院,楊凌 712100;2.西北農(nóng)林科技大學(xué)旱區(qū)農(nóng)業(yè)水土工程教育部重點實驗室,楊凌 712100;3. 華北水利水電大學(xué)能源與動力工程學(xué)院,鄭州 450046;4. 華電福新周寧抽水蓄能有限公司,寧德 352000)
為提高水輪機運行性能,該研究首先采用SST-湍流模型探討混流式水輪機多工況運行轉(zhuǎn)輪內(nèi)流特性,并基于流固耦合方法研究0.35Q,Q(Q為設(shè)計工況),1.09Q工況下的結(jié)構(gòu)場特性。量化分析三維流場速度、壓力、渦流黏度、轉(zhuǎn)輪等效應(yīng)力與變形特征等參量,結(jié)果表明最大等效應(yīng)力和最大變形量均隨負荷增加而增大,且各工況下最大等效應(yīng)力均出現(xiàn)在轉(zhuǎn)輪葉片出水邊靠近上冠處,最大變形量均產(chǎn)生在葉片出口邊中間區(qū)域。0.35Q、1.09Q工況運行時水流在轉(zhuǎn)輪進口的撞擊產(chǎn)生軸向渦是渦流黏度、等效應(yīng)力、變形量增加的主要原因,Q工況最大等效應(yīng)力大于0.35Q工況,而小于1.09Q工況。葉片與上冠連接處應(yīng)力集中,且因連接位置約束性較強,其結(jié)構(gòu)變形量較小。上冠處強約束使得葉片中心位置產(chǎn)生的變形量最大,進一步采用理論分析與數(shù)值模擬相結(jié)合的方法探討不同材料轉(zhuǎn)輪性能,研究表明Q345材料轉(zhuǎn)輪的濕模態(tài)頻率下降率最高,最大下降率為24.5%。Q345的濕模態(tài)頻率下降率大于ZG00Cr13Ni5Mo,因此使用Q345材料時應(yīng)充分考慮流體阻尼效應(yīng)。各材料轉(zhuǎn)輪臨界轉(zhuǎn)速均遠高于水輪機工作轉(zhuǎn)速,不會引發(fā)共振,Q345和1Cr18Ni9Ti的轉(zhuǎn)輪抗變形能力最強,但Q345轉(zhuǎn)輪質(zhì)量相對1Cr18Ni9Ti轉(zhuǎn)輪較輕,Q345更適用于制造轉(zhuǎn)輪。不同材料轉(zhuǎn)輪的等效應(yīng)力、變形量等靜力學(xué)特性分布規(guī)律相同,且轉(zhuǎn)輪具有相同的模態(tài)振型,故相關(guān)研究成果可推廣至其他常用材料,為水輪機設(shè)計及運行提供一定的參考與指導(dǎo)。
混流式水輪機;轉(zhuǎn)輪;流場特性;等效應(yīng)力;變形量
全球能源格局正在向追求清潔可再生能源深度轉(zhuǎn)變,中國提出“雙碳”目標助力清潔能源發(fā)展。水力發(fā)電在滿足日益增長的國民生產(chǎn)電力需求的同時,逐步從承擔基荷角色向調(diào)荷方向運行,從而為諸如風能、太陽能等新能源的發(fā)展保駕護航[1]。
水輪機是水力發(fā)電的“靈魂”所在,當下其正朝著大容量、高水頭、高轉(zhuǎn)速的方向發(fā)展,水輪機運行性能直接關(guān)系到電站能否安全、穩(wěn)定、高效地運行[2]。國內(nèi)外學(xué)者研究表明外激勵頻率(1)與水輪機固有頻率(0)相近時極易引發(fā)的共振現(xiàn)象,以及紊亂流場產(chǎn)生的局部應(yīng)力集中現(xiàn)象等均是加速水輪機結(jié)構(gòu)破壞的重要原因[3-4]。尤其在非設(shè)計工況下運行的轉(zhuǎn)輪葉片由于長期承受過大交變載荷,極易出現(xiàn)疲勞裂紋甚至葉片斷裂等事故[5]。水輪機研究主要包含以下幾個方面,1)工況研究:揭示典型穩(wěn)態(tài)、瞬態(tài)工況內(nèi)流演變機理,從內(nèi)流角度尋找優(yōu)良結(jié)構(gòu)與合適的運行條件,湍流模型改進提升數(shù)值模擬求解精度等[6-8]。2)內(nèi)外特性研究:基于計算流體動力學(xué)探討內(nèi)流演變規(guī)律[9-10],基于流固耦合方法研究關(guān)鍵部件力學(xué)特性等[11-13],然而,針對水輪機內(nèi)外協(xié)同特性研究甚少。
理論分析與數(shù)值模擬相結(jié)合的研究方法得到廣泛應(yīng)用,國內(nèi)外學(xué)者的大量研究工作驗證了數(shù)值模擬技術(shù)的可靠性[14-15]。一方面計算流體動力學(xué)(CFD,Computational fluid dynamics)能夠準確地求解水輪機三維內(nèi)流演變過程[16-18],另一方面流固耦合方法能夠準確地預(yù)測轉(zhuǎn)輪裂紋位置,獲得結(jié)構(gòu)振動、應(yīng)力與變形等信息[19]。
轉(zhuǎn)輪作為水輪機的核心部件,現(xiàn)有公開資料鮮見對其多工況運行時流場與結(jié)構(gòu)場的耦合特性進行研究,并且未見轉(zhuǎn)輪材料性能多角度分析。因此,本文以某電站混流式水輪機為研究對象,采用理論分析與數(shù)值模擬相結(jié)合的研究方法,開展多工況運行條件下混流式水輪機轉(zhuǎn)輪特性研究,根據(jù)多工況下三維流場特性,重點解析轉(zhuǎn)輪內(nèi)流渦旋演變過程,并基于內(nèi)流荷載從結(jié)構(gòu)振動、材料、應(yīng)力應(yīng)變特性、變形量等多角度開展研究。此外,側(cè)重于不同材料的轉(zhuǎn)輪模態(tài)特性,重點解析轉(zhuǎn)輪力學(xué)性能。以期在豐富相關(guān)理論的同時,研究結(jié)果能夠從一定程度上指導(dǎo)電站實際運行,進一步助力于電站運行穩(wěn)定性與供電質(zhì)量的提高。
采用SST-湍流模型求解混流式水輪機三維流場,該模型對旋轉(zhuǎn)機械復(fù)雜流動有較高的求解精度,而且能夠準確地捕捉內(nèi)流場湍流運動,從而被廣泛應(yīng)用于水力機械研究。SST-的湍動能及比耗散率輸運方程分別為[20]
式中為湍動能,J/kg;為比耗散率,s-1;為密度,kg/m3;μ為速度矢量,m/s;為層流黏度,N·s/m2;μ為湍流動力黏度,N·s/m2;β、、σ、σ、σ均為方程閉合系數(shù),其中β=0.09,=0.075,σ=0.5,σ=0.856;σ=0.5;為混合平滑系數(shù);P為湍動生成項。
結(jié)構(gòu)分析采用單向流固耦合方法,將各工況下流場載荷加載至轉(zhuǎn)輪結(jié)構(gòu)場,以量性解析結(jié)構(gòu)變形、應(yīng)力等參量。單向流固耦合的矩陣方程如式(3)[21],模態(tài)分析采用結(jié)構(gòu)力學(xué)方程,如式(4)[22]。
如圖1所示為某電站混流式水輪機試驗臺布置,對應(yīng)的原型機水頭377 m,額定出力110 MW,轉(zhuǎn)輪直徑出口1.779m。,表1給出了0.35Q、Q、1.09Q3個典型工況參數(shù)。
1.壓力水箱 2.閥門 3.電磁流量計 4.發(fā)電機 5.水輪機
表1 三種典型工況參數(shù)
圖2為該水輪機三維模型及其局部放大網(wǎng)格,模型與原型比例為1:5.1。流體域包含1個蝸殼、14個固定導(dǎo)葉、28個活動導(dǎo)葉、帶長短葉片各15個的轉(zhuǎn)輪,以及1個彎肘形尾水管。蝸殼進口采用質(zhì)量流量(mass flow rate),尾水管出口設(shè)置靜壓(static pressure)。固體壁面采用無滑移邊界條件(no-slip),近壁面采用Scalable壁面函數(shù),不同流域交界面采用GGI(general graphics interface)連接,相鄰動靜流域設(shè)置凍結(jié)轉(zhuǎn)子交界面,數(shù)值模擬計算所有殘差精度為10-6。
1.蝸殼 2.固定導(dǎo)葉 3.活動導(dǎo)葉 4.轉(zhuǎn)輪 5.尾水管
對混流式水輪機進行結(jié)構(gòu)化網(wǎng)格劃分,為避免網(wǎng)格數(shù)對數(shù)值計算結(jié)果的影響,采用了576萬、700萬、870萬、960萬、1 100萬5套網(wǎng)格方案,以水輪機效率為評價指標進行網(wǎng)格無關(guān)性驗證。如圖3所示,當計算域網(wǎng)格數(shù)≥960萬時,效率趨近于穩(wěn)定。綜合考慮計算精度與耗算量,后續(xù)研究水輪機模型的網(wǎng)格數(shù)取約為960萬的方案。
結(jié)構(gòu)場轉(zhuǎn)輪網(wǎng)格如圖4所示(網(wǎng)格數(shù)188.8萬),其邊界條件包含:1)轉(zhuǎn)輪上冠通過螺栓與主軸相連接,約束模態(tài)設(shè)置主軸表面為固定約束,以限制轉(zhuǎn)輪在、、3個方向上的位移。2)轉(zhuǎn)輪運行時受到重力和離心力的雙重作用,因而對轉(zhuǎn)輪整體分別施加重力、離心力約束條件。3)濕模態(tài)轉(zhuǎn)輪葉片表面受到水壓力作用,需將流場水壓力通過流固耦合交界面共享至結(jié)構(gòu)場葉片表面,并設(shè)置主軸為固定約束。
圖3 網(wǎng)格無關(guān)性驗證
圖4 轉(zhuǎn)輪固體域模型
轉(zhuǎn)輪靜力學(xué)計算邊界條件:0.35Q、Q、1.09Q3種工況下流場壓力作為載荷邊界條件施加到轉(zhuǎn)輪葉片,并設(shè)置主軸表面為固定約束。為探討轉(zhuǎn)輪材料對結(jié)構(gòu)性能的影響,取ZG00Cr13Ni5Mo,ZG0Cr13Ni4Mo,Q345,Q235,0Cr18Ni9,1Cr18Ni9Ti這6類常用型水輪機制造材料,材料參數(shù)如下表2[23]。
表2 轉(zhuǎn)輪材料參數(shù)
CARL等[24]對該混流式水輪機模型在上述3個研究工況進行了試驗,其試驗結(jié)果與本文數(shù)值模擬結(jié)果對比如表3,從壓力、扭矩和效率三方面對比說明了數(shù)值模擬研究的可靠性。Q、1.09Q工況結(jié)果相近,0.35Q工況存在差別,主要原因一方面存在比尺效應(yīng);第二方面數(shù)值模擬計算低估了損失,尤其在嚴重偏離設(shè)計工況更為明顯;第三方面數(shù)值模擬難以捕捉尾水管錐體中發(fā)生的旋渦破裂。
表3 三種工況下試驗與數(shù)值模擬結(jié)果對比
注:p為進口壓強;為進出口壓強差;為扭矩;為效率。
Note: pis the pressure of inlet;is the difference of pressure between inlet and outlet;is the torque;is the efficiency.
轉(zhuǎn)輪內(nèi)流部分以速度場及渦流黏度分布為代表對內(nèi)流態(tài)進行分析,以研究混流式水輪機轉(zhuǎn)輪內(nèi)流特性。渦流黏度計算式為
其中
為研究轉(zhuǎn)輪振動特性,對轉(zhuǎn)輪進行干濕模態(tài)分析,對比干濕模態(tài)下固有頻率特性,并進行動靜干涉頻率計算,模態(tài)頻率下降率為
式中為模態(tài)頻率下降率,%;0為干模態(tài)頻率,Hz;wet為濕模態(tài)頻率,Hz。
流激振動激勵頻率為
式中f為轉(zhuǎn)輪轉(zhuǎn)頻,Hz;為活動導(dǎo)葉或轉(zhuǎn)輪葉片數(shù)。
如圖5所示,流道漸縮結(jié)構(gòu)使水流速度從進口至出口逐漸增大,旋轉(zhuǎn)離心力進一步作用導(dǎo)致流速在轉(zhuǎn)輪出口側(cè)靠近下環(huán)處高于靠近上冠區(qū)域,符合做功原理。設(shè)計工況轉(zhuǎn)輪流態(tài)良好(圖5b),葉片進口邊無撞擊損失,流動順暢,葉間無脫流(渦流黏度接近0,圖6b),轉(zhuǎn)輪內(nèi)水流均勻?qū)ΨQ分布且緊貼葉片,水力損失小。
0.35Q工況水流相對速度方向角大于葉片進口角,水流與葉片產(chǎn)生撞擊,致使葉間流道出現(xiàn)顯著的流動分離(圖5a)。進口撞擊回旋流存在撞擊損失,且回旋流進一步發(fā)展至葉間流道軸向渦。水流撞擊渦與葉間較小流量空腔渦雙重作用使得葉間流道形成管狀渦,該工況下渦流黏度最大值為1.18 Pa·s,是Q工況的3.93倍。渦旋向下游擴散至葉片出口邊時,各葉間流道渦相互匯聚,最終在轉(zhuǎn)輪出口區(qū)域連成片狀(圖6)。由于渦占據(jù)葉間流道大部分區(qū)域,阻礙了水流順利通過使得轉(zhuǎn)輪內(nèi)流紊亂,降低了有效流量,并且在轉(zhuǎn)輪與導(dǎo)葉的無葉區(qū)形成帶有周向速度的水環(huán)。無葉區(qū)水環(huán)除了自身振蕩頻率外,亦受到動靜干涉作用,極易引起0.35Q工況結(jié)構(gòu)部件振動。
1.09Q工況(圖5c)流態(tài)與Q相似,但因水流方向角小于葉片進口角,產(chǎn)生負沖角,轉(zhuǎn)輪進口輕微撞擊引起少量渦旋,該處渦流黏度為0.67 Pa·s,為工況的2.23倍,該渦旋是引起1.09Q工況效率下降的主要原因(表 3),此處局部渦流現(xiàn)象并未進一步發(fā)展。
圖5 不同工況下轉(zhuǎn)輪內(nèi)速度流線
水力激振頻率與轉(zhuǎn)輪0相近極易引發(fā)共振,是造成結(jié)構(gòu)破壞的重要原因,分別從干模態(tài)和濕模態(tài)對多工況運行轉(zhuǎn)輪進行分析。理論上,轉(zhuǎn)輪應(yīng)具有無窮多個模態(tài)數(shù)量,然而高頻模態(tài)振幅小,低頻模態(tài)振幅大且危害嚴重,因此實際工程中考慮的結(jié)構(gòu)振動主要由前6階模態(tài)振型疊加而成[25]。
表4為不同材料轉(zhuǎn)輪干模態(tài)前6階頻率,各材料對應(yīng)階次頻率差距均小于10%。隨著模態(tài)階數(shù)增加,約束模態(tài)頻率逐漸增大,且前2階、4階與5階模態(tài)均為重模態(tài),即0相同時產(chǎn)生不同的振型。以材料ZG00Cr13Ni5Mo轉(zhuǎn)輪為例分析約束模態(tài)(圖7)。轉(zhuǎn)輪因其軸對稱性,各組重模態(tài)振型的振動形式相似,但其振型角度分別相差90°(1階與2階)和45°(4階與5階)。
前2階振型皆繞軸旋轉(zhuǎn)且位移量呈對稱性分布,同視角下相鄰兩階重模態(tài)(1階與2階、3階與4階)振型旋轉(zhuǎn)中心線方向不同。第3階振型是均勻徑向變形,變形量沿徑向增大,是繞軸旋轉(zhuǎn)的主模態(tài)。4、5階振型均是彎曲型模態(tài),不同之處在于中心線角度不同,變形量呈現(xiàn)X狀對稱分布。第6階振型表現(xiàn)為軸向平動,變形量由轉(zhuǎn)輪中心沿徑向增大,最大位移量在進水側(cè)上冠、下環(huán)最外邊緣處,是沿軸的平動主模態(tài)。
圖6 不同工況下轉(zhuǎn)輪內(nèi)渦流黏度
表4 不同材料轉(zhuǎn)輪固有頻率
轉(zhuǎn)輪前6階固有頻率對比如表5所示,轉(zhuǎn)輪受水流阻尼效應(yīng)影響,因此濕模態(tài)轉(zhuǎn)輪各階頻率比干模態(tài)小。前3階干、濕模態(tài)頻率相近,值約為0.8%,4、5階值均超過20%。值得注意的是Q345材料轉(zhuǎn)輪在4、5階模態(tài)的值高于其他材料,第6階模態(tài)值低于其他材料轉(zhuǎn)輪。
圖7 約束模態(tài)前6階振型
注:wet為濕模態(tài)固有頻率,Hz;為模態(tài)頻率下降率,%
Note:wetis the natural frequency of wet modal, Hz;is the modal frequency drop rate, %.
轉(zhuǎn)輪過速將加劇其運行不穩(wěn)定性,外在表現(xiàn)為振動、噪聲,甚至出現(xiàn)故障事故等。各材料轉(zhuǎn)輪臨界轉(zhuǎn)速見表6,反向渦動(backward whirl,BW)使得臨界轉(zhuǎn)速變小。正向渦動(forward whirl,F(xiàn)W)使得臨界轉(zhuǎn)速變大,臨界轉(zhuǎn)速一般取決于正向渦動。
不同材料轉(zhuǎn)輪FW臨界轉(zhuǎn)速值均遠高于水輪機的工作轉(zhuǎn)速(max=406.2 r/min),因此不會產(chǎn)生共振。其中ZG00Cr13Ni5Mo材料轉(zhuǎn)輪臨界轉(zhuǎn)速最低,相較于Q235A、Q345和1Cr18Ni9Ti材料低約2.8%。
轉(zhuǎn)輪結(jié)構(gòu)受到外激勵頻率1影響中,重點考慮導(dǎo)葉尾流渦街頻率與轉(zhuǎn)輪葉片旋轉(zhuǎn)頻率,由式(9)計算得到3種工況下導(dǎo)葉激勵頻率分別為189.56、156.52、172.48 Hz,轉(zhuǎn)輪激勵頻率分別為203.1、167.7、184.8Hz。
對比各材料轉(zhuǎn)輪外激勵頻率0與固有頻率1可得:各工況下轉(zhuǎn)輪與導(dǎo)葉間無葉區(qū)水流壓力脈動主頻均為28f,該壓力脈動引起轉(zhuǎn)輪振動是節(jié)徑為2的激勵型(主頻30f)。此外,各工況下不同材料轉(zhuǎn)輪葉片與導(dǎo)葉產(chǎn)生的1均遠小于0,1max(203.1Hz)<<0min(690.85Hz),因此不會誘發(fā)共振。
ZG00Cr13Ni5Mo、Q235A、Q345、1Cr18Ni9Ti轉(zhuǎn)輪質(zhì)量相同(136.38kg),大于ZG00Cr13Ni4Mo(134.30 kg),小于0Cr18Ni9(137.77kg)的質(zhì)量,ZG00Cr13Ni4Mo質(zhì)量最小,可用于輕量化設(shè)計,以提高轉(zhuǎn)輪速動性,對于頻繁啟停機的機組較為適用。不同材料轉(zhuǎn)輪(最大變形量max)及(最大等效應(yīng)力max)對比見表7,ZG00Cr13Ni4Mo轉(zhuǎn)輪max最小,但max較大,其max僅次于ZG00Cr13Ni5Mo和0Cr18Ni9,ZG00Cr13Ni4Mo的max比Q345和1Cr18Ni9Ti轉(zhuǎn)輪均高約3%。Q345和1Cr18Ni9Ti轉(zhuǎn)輪max最小,抗變形能力較強,二者max略大于ZG00Cr13Ni5Mo。0Cr18Ni9的max最大,其比ZG00Cr13Ni4Mo高約1%,且0Cr18Ni9的max比Q345和1Cr18Ni9Ti均高約5%。ZG00Cr13Ni5Mo的max最大,比Q345和1Cr18Ni9Ti均高約6%,且max僅次于0Cr18Ni9。ZG00Cr13Ni5Mo和ZG00Cr13Ni4Mo安全系數(shù)(安全系數(shù)=極限應(yīng)力/許用應(yīng)力)最高,約為1Cr18Ni9Ti的2.7倍,6種材料的安全系數(shù)均超過40。
表6 轉(zhuǎn)子系統(tǒng)前3階臨界轉(zhuǎn)速
結(jié)合表7與圖8可得轉(zhuǎn)輪等效應(yīng)力在各工況下分布規(guī)律相似,max均位于葉片出口邊靠近下環(huán)側(cè),且等效應(yīng)力值自上冠至下環(huán)先遞減后遞增,葉片中心線附近等效應(yīng)力值最小。水流受重力及離心力的雙重作用,因此各工況下葉片靠近下環(huán)處等效應(yīng)力值均高于靠近上冠側(cè)區(qū)域。此外轉(zhuǎn)輪各處等效應(yīng)力均小于各材料的屈服強度,且各工況下安全系數(shù)均大于40,以第四強度理論[27]為準則可知6種材料轉(zhuǎn)輪結(jié)構(gòu)強度均是穩(wěn)定可靠的。
圖8中轉(zhuǎn)輪max隨著負荷增加而增加,但高等效應(yīng)力區(qū)域在非設(shè)計工況面積比設(shè)計工況大,主要體現(xiàn)在靠近下環(huán)位置。綜合分析流場(圖5、圖6)與結(jié)構(gòu)場(圖 8、圖9),非設(shè)計工況高等效應(yīng)力區(qū)域面積增加的主要原因是轉(zhuǎn)輪內(nèi)流失穩(wěn),出現(xiàn)葉間渦、脫流等現(xiàn)象作用導(dǎo)致。具體來講,0.35Q工況葉片進口區(qū)域存在大量軸向渦,渦流黏度高達1.18 Pa·s(圖5、圖6),該位置對應(yīng)圖8的Max標記處,此處軸向渦引發(fā)交變載荷進一步擴大高等效應(yīng)力區(qū)域范圍。相對地,圖5Q工況良好流態(tài)對應(yīng)圖8Q較小面積高等效應(yīng)力區(qū)。此外,轉(zhuǎn)輪葉片進、出口邊與上冠、下環(huán)連接處產(chǎn)生局部應(yīng)力集中現(xiàn)象,在非設(shè)計工況更為突出,其中出口邊與下環(huán)連接處最為嚴重(圖8矩形框)。
表7 不同材料的轉(zhuǎn)輪最大變形量dmax及最大等效應(yīng)力Smax
圖8 不同工況下轉(zhuǎn)輪等效應(yīng)力
圖9 不同工況下轉(zhuǎn)輪變形
轉(zhuǎn)輪變形量與等效應(yīng)力特性相似(圖8、圖9),max隨流量增大而增大,各工況下max均出現(xiàn)在葉片出口邊的中心位置。從結(jié)構(gòu)角度,max位置雖靠近上冠、下環(huán)與葉片的連接處,但該區(qū)域因約束性強,因此變形量較小。然而由于杠桿效應(yīng),約束點較小的變形量在距離約束點最遠的位置將引起極大的變形量,因而轉(zhuǎn)輪最大變形量發(fā)生在葉片出口邊中心處。受高等效應(yīng)力區(qū)影響,0.35Q工況下轉(zhuǎn)輪整體變形量最大,因此小流量工況是水輪機應(yīng)避免長期運行的工況區(qū)。
本文基于流場與結(jié)構(gòu)場對混流式水輪機轉(zhuǎn)輪多工況運行特性展開研究,采用SST-湍流模型求解內(nèi)流場,流固耦合方法用于研究不同材料轉(zhuǎn)輪結(jié)構(gòu)特性。主要結(jié)論如下:
1)非設(shè)計工況轉(zhuǎn)輪進口水流相對速度方向角與葉片進口角之間存在偏差,使得水流撞擊葉片進口進一步引發(fā)軸向渦,0.35Q與1.09Q工況渦流黏度最大值分別約為設(shè)計工況Q的3.93倍與2.23倍。
2)約束模態(tài)下轉(zhuǎn)輪前兩階以及4、5階振型均為重模態(tài),第3階振型為徑向變形,第6階振型為軸向平動。不同材料轉(zhuǎn)輪前3階干、濕模態(tài)頻率相近,模態(tài)頻率下降率均在0.8%左右,4、5階相差較大,超過了20%。
3)轉(zhuǎn)輪最大等效應(yīng)力、最大變形量均隨流量增加而增大,且分別出現(xiàn)在葉片出口邊靠近上冠側(cè)與葉片出口邊的中心位置。各材料轉(zhuǎn)輪應(yīng)力均在許用范圍,ZG00Cr13Ni4Mo轉(zhuǎn)輪質(zhì)量最小適合輕量化設(shè)計,Q345和1Cr18Ni9Ti轉(zhuǎn)輪抗變形能力較強,是長期在非設(shè)計工況運行機組的較優(yōu)選擇。
[1] 于倩倩. 關(guān)于“十三五”中期我國水電發(fā)展的幾點思考[J]. 水力發(fā)電,2019,45(11):112-116. YU Qianqian. Studies on the mid-term evaluation of the hydropower development in China during the 13th Five-Year Plan[J]. Water Power, 2019, 45(11): 112-116. (in Chinese with English abstract)
[2] ZHANG L J, YIN G J, WANG S, et al. Study on FSI analysis method of a large hydropower house and its vortex-induced vibration regularities[J]. Advances in Civil Engineering, 2020:7596080.
[3] XIN Lu, LI Qifei, LI Henggui, et al. Analysis of runner dynamics of reversible hydraulic turbine by alternating fluid–solid action[J]. Frontiers in Energy Research, 2022, 10: 943339.
[4] PRAVEEN S, MARIMUTHU S, MANIVANNAN S, et al. Effect of cavitation with vibration on the powerhouse structure of bulb turbines installed in hydropower stations[J]. Advances in Materials Science and Engineering, 2022, 1: 1-7.
[5] FANG Y J, YUAN S Q, LI J W, et al. Evaluation of the hydraulic resonance in turbine mode of a medium-head pump-turbine[J]. Journal of Vibration Engineering & Technologies, 2017, 5: 451-468.
[6] SKRIPKIN S, ZUO Z G, MIKHAIL T, et al. Oscillation of cavitating vortices in draft tubes of a simplified model turbine and a model pump–turbine[J]. Energies, 2022, 15: 2965.
[7] WANG L K, LU J L, LIAO W L, et al. Numerical analysis of the hydraulic force of a pump turbine under partial load conditions in turbine mode.[J]. IOP Conf. Series: Earth and Environmental Science, 2019(240): 72041.
[8] 孫龍剛,郭鵬程,鄭小波, 等. 混流式水輪機葉道空化渦誘發(fā)高振幅壓力脈動特性[J]. 農(nóng)業(yè)工程學(xué)報,2021,37(21):62-70. SUN Longgang, GUO Pengcheng, ZHENG Xiaobo, et al. Characteristics of high-amplitude pressure fluctuation induced by inter-blade cavitation vortex in Francis turbine[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(21): 62-70. (in Chinese with English abstract)
[9] 吳子娟,梁武科,董瑋,等. 轉(zhuǎn)輪下環(huán)間隙對混流式水輪機內(nèi)部流動特性的影響[J]. 農(nóng)業(yè)工程學(xué)報,2020,36(2):23-29, 337. WU Zijuan, LIANG Wuke, DONG Wei, et al. Influence of seal clearance of runner on internal fluid field in Francis turbine[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2020, 36(2): 23-29, 337. (in Chinese with English abstract)
[10] 郭俊勛,周大慶,陳會向,王胤淞. 導(dǎo)葉波動對抽蓄機組低水頭空載穩(wěn)定影響分析[J]. 中國電機工程學(xué)報,2022,42(15):5587-5595. GUO Junxun, ZHOU Daqing, CHEN Huixiang, et al. Influence analysis of guide vane fluctuation rate on pump storage units under no-load condition of low head[J], Proceedings of the CSEE, 2022, 42(15): 5587-5595. (in Chinese with English abstract)
[11] 趙亞萍,黨夢帆,馮建軍, 等. 自由液面及水體重力對貫流式水輪機葉片應(yīng)力應(yīng)變的影響[J]. 農(nóng)業(yè)工程學(xué)報,2022,38(6):52-60. ZHAO Yaping, DANG Mengfan, FENG Jianjun, et al. Effects of free surface and water gravity on the stress-strain of tubular turbine blades[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2022, 38(6): 52-60. (in Chinese with English abstract)
[12] 朱國俊,李康,馮建軍,等. 空化對軸流式水輪機尾水管壓力脈動和轉(zhuǎn)輪振動的影響[J]. 農(nóng)業(yè)工程學(xué)報,2021,37(11):40-49. ZHU Guojun, LI Kang, FENG Jianjun, et al. Effects of cavitation on pressure fluctuation of draft tube and runner vibration in a Kaplan turbine[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(11): 40-49. (in Chinese with English abstract)
[13] 劉德民,鄧祥平,趙永智,等. 大型混流式模型機組動應(yīng)力及壓力脈動測試研究[J]. 機械工程學(xué)報,2019,55(19):9-18. LIU Demin, DENG Xiangping, ZHAO Yongzhi, et al. Dynamic stress and pressure fluctuation test on model unit of huge Francis turbine[J]. Journal of Mechanical Engineering, 2019, 55(19): 9-18. (in Chinese with English abstract)
[14] MAO Xiuli, GIORGIO P, CHEN D, et al. Flow induced noise characterization of pump turbine in continuous and intermittent load rejection processes[J]. Renewable Energy, 2019, 139: 1029-1039.
[15] LABORDERIE J, DUCHAINE F, GICQUEL L, et al. Numerical analysis of a high-order unstructured overset grid method for compressible LES of turbomachinery[J]. Journal of Computational Physics, 2018, 363: 371-398.
[16] 毛秀麗,孫奧冉,GIORGIO Pavesi,等. 水泵水輪機甩負荷過程流動誘導(dǎo)噪聲數(shù)值模擬[J]. 農(nóng)業(yè)工程學(xué)報,2018,34(20):52-58. MAO Xiuli, SUN Aoran, GIORGIO Pavesi, et al. Simulation of flow induced noise in process of pump-turbine load rejection[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(20): 52-58. (in Chinese with English abstract)
[17] DENG W, XU L, LI Z, et al. Stability analysis of vaneless space in high-head pump-turbine under turbine mode: Computational fluid dynamics simulation and particle imaging velocimetry measurement[J]. Machines, 2022, 10(143): 1-20.
[18] 張飛,王憲平. 抽水蓄能機組甩負荷試驗時尾水錐管壓力[J]. 農(nóng)業(yè)工程學(xué)報,2020,36(20):93-101. ZHANG Fei, WANG Xianping. Draft cone tube pressure of pumped-storage power unit in load rejection test[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2020, 36(20): 93-101. (in Chinese with English abstract)
[19] ZHU D, TAO R, XIAO R, et al. Solving the runner blade crack problem for a Francis hydro-turbine operating under condition-complexity[J]. Renewable Energy, 2020(149): 298-320.
[20] MAO X, LIU Z, LI T, et al. A brief review of numerical solving methods for internal fluid of pumped storage unit[J/OL]. International Journal of Energy Research, 2020, DOI: 10.1002/er.5474.
[21] 何玲艷. 水泵水輪機轉(zhuǎn)輪動力特性研究與共振預(yù)測[D]. 北京:中國農(nóng)業(yè)大學(xué),2019. HE Lingyan. Dynamic Behavior Analysis and Resonance Prediction of Pump-turbine Runner[D]. Beijing: China Agricultural University, 2019. (in Chinese with English abstract)
[22] 楊景云,王文韞,戴巨川. 基于攝動模態(tài)分析的風電葉片動力學(xué)特性研究[J/OL]. 太陽能學(xué)報,2022. https://doi.org/10.19912/j.0254-0096.tynxb.2022-1045 YANG Jingyun, WANG Wentao, DAI Juchuan. Research on dynamic characteristics of wind power blades based on perturbation mode analysis[J]. Acta Energiae Solaris Sinica, 2022. https://doi.org/10.19912/j.0254-0096.tynxb.2022-1045. (in Chinese with English abstract)
[23] 溫秉權(quán),王賓,路學(xué)成.金屬材料手冊[M].北京:電子工業(yè)出版社,2013.
[24] CARL B, KAVEH A, MICHEL J C, et al Preliminary measurements of the radial velocity in the Francis-99 draft tube cone[J]. Journal of Physics: Conference Series, 2015(579): 012014.
[25] 孫嵩松,萬茂松,徐曉美,等. 不同強度理論在曲軸疲勞研究中的對比應(yīng)用[J]. 中國機械工程,2019,30(23):2784-2789. SUN Songsong, WAN Maosong, XU Xiaomei, et al. Comparable application of different strength criterions in crankshaft fatigue researches[J]. China Mechanical Engineering, 2019, 30(23): 2784-2789. (in Chinese with English abstract)
Runner characteristics of Francis turbine under multiple conditions
MAO Xiuli1,2, CHEN Xingkun1, WEN Guoqing1, YUAN Yifan1, REN Yan3, XIONG Yan4
(1.,,712100,; 2.,,712100,; 3.,,450046,; 4.,352000,)
Hydropower plant can be expected gradually undertake the task of peak shaving and frequency modulation in the power grid, in order to reduce the impact from the renewable energy, such as the solar, and wind energy. In the switch operating conditions of hydraulic turbines, it is a high demand to fully meet the grid requirements during power generation. Consequently, the turbine can be required to work at the off-design conditions, particularly with the high operation stability. This study aims to explore the flow and structure characteristics of Francis turbine under different conditions (0.35Q,Q, and 1.09Q). The turbulence model of SSTwas used to solve the internal fluid, whereas the method of fluid-solid coupling was adopted in the structure field. There was the deviation between the relative velocity direction angle of flow and the inlet angle of blade at the off-design points, where the maximum eddy viscosity at 0.35Qand 1.09Qwere 3.97 and 2.23 times ofQ,respectively. Some parameters were analyzed quantitatively, including the velocity, pressure, eddy viscosity, equivalent stress, and deformation extent. The results show that bothmaxandmaxincreased with the increasement of load. The large values ofmaxappeared at the outlet edge of blade, which was close to the upper crown, whereas themaxappeared in the middle region of blade outlet edge, under all three conditions. The axial vortex generated by the impact flow at the runner inlet was the main reason for the increment of eddy viscosity, equivalent stress, and deformation extent under off-design conditions, wherein themaxatQis larger than that of 0.35Qand smaller than 1.09Q, respectively. Stress concentration occurred at the connection area between the blades and the crown, due to the strong constraint at the connection position, where deformation extent was small. However, themaxappeared at the center position of blades that caused by the strong constraint of upper crown, In addition, the combination of theoretical analysis and numerical simulation was applied to investigate the runner performance, with the different manufacturing materials. The results illustrated that the frequency of Q345 runner at the wet modal shared the highest decrease rate. Among them, the maximum decreasing ratio was 24.5%, which frequency drop rate is bigger than that of ZG00Cr13Ni5Mo. Thus, the fluid damping effect should be fully considered, when using Q345, but Q345 was lighter form the aspect of weight. The critical speed of each material runner was much higher than the working speed of turbine. There was no resonance during this time. The critical speed of ZG00Cr13Ni5Mo runner was the lowest. The runner presented the strongest ability of deformation resistance, when it was made of Q345 and 1Cr18Ni9Ti materials. Therefore, the Q345 was more suitable for the runner manufacture. Moreover, there were the similar developments of static characteristics on the equivalent stress and deformation extent for runners with different materials. Furthermore, all runners with different materials showed the similar vibration modes. Hence, each material can be extended to the other common materials.This finding can provide some reference and guidance for the design and operation of hydraulic turbine.
Francis turbine; runner; flow field characteristics; equivalent stress; deformation extent
2022-12-30
2023-03-20
國家自然科學(xué)基金資助項目(51909222);陜西省引進國內(nèi)博士專項(F2020221009);企業(yè)橫向項目(K4050422547)。
毛秀麗,博士,副教授,研究方向為水力機械及系統(tǒng)、抽水蓄能與新能源技術(shù)。Email:maoxl@nwafu.edu.cn
10.11975/j.issn.1002-6819.202212194
TK730
A
1002-6819(2023)-08-0095-08
毛秀麗,陳星錕,溫國慶,等. 混流式水輪機多工況運行轉(zhuǎn)輪特性[J]. 農(nóng)業(yè)工程學(xué)報,2023,39(8):95-102. doi:10.11975/j.issn.1002-6819.202212194 http://www.tcsae.org
MAO Xiuli, CHEN Xingkun, WEN Guoqing, et al. Runner characteristics of Francis turbine under multiple conditions[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2023, 39(8): 95-102. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.202212194 http://www.tcsae.org