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        混流式水輪機(jī)多工況運(yùn)行轉(zhuǎn)輪特性

        2023-07-28 02:32:16毛秀麗陳星錕溫國(guó)慶袁一凡
        關(guān)鍵詞:混流式轉(zhuǎn)輪水輪機(jī)

        毛秀麗,陳星錕,溫國(guó)慶,袁一凡,任 巖,熊 妍

        混流式水輪機(jī)多工況運(yùn)行轉(zhuǎn)輪特性

        毛秀麗1,2,陳星錕1,溫國(guó)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(diǎn)實(shí)驗(yàn)室,楊凌 712100;3. 華北水利水電大學(xué)能源與動(dòng)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(jī)運(yùn)行性能,該研究首先采用SST-湍流模型探討混流式水輪機(jī)多工況運(yùn)行轉(zhuǎn)輪內(nèi)流特性,并基于流固耦合方法研究0.35Q,QQ為設(shè)計(jì)工況),1.09Q工況下的結(jié)構(gòu)場(chǎng)特性。量化分析三維流場(chǎng)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(fù)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(yùn)行時(shí)水流在轉(zhuǎn)輪進(jìn)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(qiáng),其結(jié)構(gòu)變形量較小。上冠處強(qiáng)約束使得葉片中心位置產(chǎn)生的變形量最大,進(jìn)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(shí)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(yuǎn)高于水輪機(jī)工作轉(zhuǎn)速,不會(huì)引發(fā)共振,Q345和1Cr18Ni9Ti的轉(zhuǎn)輪抗變形能力最強(qiáng),但Q345轉(zhuǎn)輪質(zhì)量相對(duì)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(jī)設(shè)計(jì)及運(yùn)行提供一定的參考與指導(dǎo)。

        混流式水輪機(jī);轉(zhuǎn)輪;流場(chǎng)特性;等效應(yīng)力;變形量

        0 引 言

        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(guó)提出“雙碳”目標(biāo)助力清潔能源發(fā)展。水力發(fā)電在滿足日益增長(zhǎng)的國(guó)民生產(chǎn)電力需求的同時(shí),逐步從承擔(dān)基荷角色向調(diào)荷方向運(yùn)行,從而為諸如風(fēng)能、太陽(yáng)能等新能源的發(fā)展保駕護(hù)航[1]。

        水輪機(jī)是水力發(fā)電的“靈魂”所在,當(dāng)下其正朝著大容量、高水頭、高轉(zhuǎn)速的方向發(fā)展,水輪機(jī)運(yùn)行性能直接關(guān)系到電站能否安全、穩(wěn)定、高效地運(yùn)行[2]。國(guó)內(nèi)外學(xué)者研究表明外激勵(lì)頻率(1)與水輪機(jī)固有頻率(0)相近時(shí)極易引發(fā)的共振現(xiàn)象,以及紊亂流場(chǎng)產(chǎn)生的局部應(yīng)力集中現(xiàn)象等均是加速水輪機(jī)結(jié)構(gòu)破壞的重要原因[3-4]。尤其在非設(shè)計(jì)工況下運(yùn)行的轉(zhuǎn)輪葉片由于長(zhǎng)期承受過(guò)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(jī)研究主要包含以下幾個(gè)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(jī)理,從內(nèi)流角度尋找優(yōu)良結(jié)構(gòu)與合適的運(yùn)行條件,湍流模型改進(jìn)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(jì)算流體動(dòng)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(duì)水輪機(jī)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(guó)內(nèi)外學(xué)者的大量研究工作驗(yàn)證了數(shù)值模擬技術(shù)的可靠性[14-15]。一方面計(jì)算流體動(dòng)力學(xué)(CFD,Computational fluid dynamics)能夠準(zhǔn)確地求解水輪機(jī)三維內(nèi)流演變過(guò)程[16-18],另一方面流固耦合方法能夠準(zhǔn)確地預(yù)測(cè)轉(zhuǎn)輪裂紋位置,獲得結(jié)構(gòu)振動(dòng)、應(yīng)力與變形等信息[19]。

        轉(zhuǎn)輪作為水輪機(jī)的核心部件,現(xiàn)有公開資料鮮見對(duì)其多工況運(yùn)行時(shí)流場(chǎng)與結(jié)構(gòu)場(chǎng)的耦合特性進(jìn)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(jī)為研究對(duì)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(yùn)行條件下混流式水輪機(jī)轉(zhuǎn)輪特性研究,根據(jù)多工況下三維流場(chǎng)特性,重點(diǎn)解析轉(zhuǎn)輪內(nèi)流渦旋演變過(guò)程,并基于內(nèi)流荷載從結(jié)構(gòu)振動(dòng)、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(diǎn)解析轉(zhuǎn)輪力學(xué)性能。以期在豐富相關(guān)理論的同時(shí),研究結(jié)果能夠從一定程度上指導(dǎo)電站實(shí)際運(yùn)行,進(jìn)一步助力于電站運(yùn)行穩(wěn)定性與供電質(zhì)量的提高。

        1 計(jì)算方法

        1.1 數(shù)學(xué)模型

        采用SST-湍流模型求解混流式水輪機(jī)三維流場(chǎng),該模型對(duì)旋轉(zhuǎn)機(jī)械復(fù)雜流動(dòng)有較高的求解精度,而且能夠準(zhǔn)確地捕捉內(nèi)流場(chǎng)湍流運(yùn)動(dòng),從而被廣泛應(yīng)用于水力機(jī)械研究。SST-的湍動(dòng)能及比耗散率輸運(yùn)方程分別為[20]

        式中為湍動(dòng)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(dòng)力黏度,N·s/m2;β、、σ、σσ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(dòng)生成項(xiàng)。

        結(jié)構(gòu)分析采用單向流固耦合方法,將各工況下流場(chǎng)載荷加載至轉(zhuǎn)輪結(jié)構(gòu)場(chǎng),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]。

        2 數(shù)值模型及邊界條件

        2.1 模型工作參數(shù)及性能

        如圖1所示為某電站混流式水輪機(jī)試驗(yàn)臺(tái)布置,對(duì)應(yīng)的原型機(jī)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(gè)典型工況參數(shù)。

        1.壓力水箱 2.閥門 3.電磁流量計(jì) 4.發(fā)電機(jī) 5.水輪機(jī)

        表1 三種典型工況參數(shù)

        2.2 流體計(jì)算域模型建立及邊界條件設(shè)置

        圖2為該水輪機(jī)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(gè)蝸殼、14個(gè)固定導(dǎo)葉、28個(gè)活動(dòng)導(dǎo)葉、帶長(zhǎng)短葉片各15個(gè)的轉(zhuǎn)輪,以及1個(gè)彎肘形尾水管。蝸殼進(jìn)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(wú)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(dòng)靜流域設(shè)置凍結(jié)轉(zhuǎn)子交界面,數(shù)值模擬計(jì)算所有殘差精度為10-6。

        1.蝸殼 2.固定導(dǎo)葉 3.活動(dòng)導(dǎo)葉 4.轉(zhuǎn)輪 5.尾水管

        對(duì)混流式水輪機(jī)進(jìn)行結(jié)構(gòu)化網(wǎng)格劃分,為避免網(wǎng)格數(shù)對(duì)數(shù)值計(jì)算結(jié)果的影響,采用了576萬(wàn)、700萬(wàn)、870萬(wàn)、960萬(wàn)、1 100萬(wàn)5套網(wǎng)格方案,以水輪機(jī)效率為評(píng)價(jià)指標(biāo)進(jìn)行網(wǎng)格無(wú)關(guān)性驗(yàn)證。如圖3所示,當(dāng)計(jì)算域網(wǎng)格數(shù)≥960萬(wàn)時(shí),效率趨近于穩(wěn)定。綜合考慮計(jì)算精度與耗算量,后續(xù)研究水輪機(jī)模型的網(wǎng)格數(shù)取約為960萬(wàn)的方案。

        2.3 固體計(jì)算域模型及邊界條件設(shè)置

        結(jié)構(gòu)場(chǎng)轉(zhuǎn)輪網(wǎng)格如圖4所示(網(wǎng)格數(shù)188.8萬(wàn)),其邊界條件包含:1)轉(zhuǎn)輪上冠通過(guò)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(gè)方向上的位移。2)轉(zhuǎn)輪運(yùn)行時(shí)受到重力和離心力的雙重作用,因而對(duì)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(chǎng)水壓力通過(guò)流固耦合交界面共享至結(jié)構(gòu)場(chǎng)葉片表面,并設(shè)置主軸為固定約束。

        圖3 網(wǎng)格無(wú)關(guān)性驗(yàn)證

        圖4 轉(zhuǎn)輪固體域模型

        轉(zhuǎn)輪靜力學(xué)計(jì)算邊界條件:0.35Q、Q、1.09Q3種工況下流場(chǎng)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(duì)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(jī)制造材料,材料參數(shù)如下表2[23]。

        表2 轉(zhuǎn)輪材料參數(shù)

        2.4 工況設(shè)置及模型驗(yàn)證

        CARL等[24]對(duì)該混流式水輪機(jī)模型在上述3個(gè)研究工況進(jìn)行了試驗(yàn),其試驗(yàn)結(jié)果與本文數(shù)值模擬結(jié)果對(duì)比如表3,從壓力、扭矩和效率三方面對(duì)比說(shuō)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(jì)算低估了損失,尤其在嚴(yán)重偏離設(shè)計(jì)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(yàn)與數(shù)值模擬結(jié)果對(duì)比

        注:p為進(jìn)口壓強(qiáng);為進(jìn)出口壓強(qiáng)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.

        2.5 轉(zhuǎn)輪分析

        轉(zhuǎn)輪內(nèi)流部分以速度場(chǎng)及渦流黏度分布為代表對(duì)內(nèi)流態(tài)進(jìn)行分析,以研究混流式水輪機(jī)轉(zhuǎn)輪內(nèi)流特性。渦流黏度計(jì)算式為

        其中

        為研究轉(zhuǎn)輪振動(dòng)特性,對(duì)轉(zhuǎn)輪進(jìn)行干濕模態(tài)分析,對(duì)比干濕模態(tài)下固有頻率特性,并進(jìn)行動(dòng)靜干涉頻率計(jì)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(dòng)激勵(lì)頻率為

        式中f為轉(zhuǎn)輪轉(zhuǎn)頻,Hz;為活動(dòng)導(dǎo)葉或轉(zhuǎn)輪葉片數(shù)。

        3 結(jié)果與分析

        3.1 轉(zhuǎn)輪內(nèi)流場(chǎng)分析

        如圖5所示,流道漸縮結(jié)構(gòu)使水流速度從進(jìn)口至出口逐漸增大,旋轉(zhuǎn)離心力進(jìn)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(jì)工況轉(zhuǎn)輪流態(tài)良好(圖5b),葉片進(jìn)口邊無(wú)撞擊損失,流動(dòng)順暢,葉間無(wú)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(duì)速度方向角大于葉片進(jìn)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(dòng)分離(圖5a)。進(jìn)口撞擊回旋流存在撞擊損失,且回旋流進(jìn)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(kuò)散至葉片出口邊時(shí),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(guò)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(wú)葉區(qū)形成帶有周向速度的水環(huán)。無(wú)葉區(qū)水環(huán)除了自身振蕩頻率外,亦受到動(dòng)靜干涉作用,極易引起0.35Q工況結(jié)構(gòu)部件振動(dòng)。

        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(jìn)口角,產(chǎn)生負(fù)沖角,轉(zhuǎn)輪進(jìn)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(jìn)一步發(fā)展。

        圖5 不同工況下轉(zhuǎn)輪內(nèi)速度流線

        3.2 轉(zhuǎn)輪模態(tài)分析

        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(duì)多工況運(yùn)行轉(zhuǎn)輪進(jìn)行分析。理論上,轉(zhuǎn)輪應(yīng)具有無(wú)窮多個(gè)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(yán)重,因此實(shí)際工程中考慮的結(jié)構(gòu)振動(dòng)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(duì)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(shí)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(duì)稱性,各組重模態(tài)振型的振動(dòng)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(duì)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(duì)稱分布。第6階振型表現(xiàn)為軸向平動(dòng),變形量由轉(zhuǎn)輪中心沿徑向增大,最大位移量在進(jìn)水側(cè)上冠、下環(huán)最外邊緣處,是沿軸的平動(dòng)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(duì)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(guò)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, %.

        3.3 轉(zhuǎn)輪臨界轉(zhuǎn)速與流激振動(dòng)頻率分析

        轉(zhuǎn)輪過(guò)速將加劇其運(yùn)行不穩(wěn)定性,外在表現(xiàn)為振動(dòng)、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(dòng)(backward whirl,BW)使得臨界轉(zhuǎn)速變小。正向渦動(dòng)(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(dòng)。

        不同材料轉(zhuǎn)輪FW臨界轉(zhuǎn)速值均遠(yuǎn)高于水輪機(jī)的工作轉(zhuǎn)速(max=406.2 r/min),因此不會(huì)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(lì)頻率1影響中,重點(diǎn)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(jì)算得到3種工況下導(dǎo)葉激勵(lì)頻率分別為189.56、156.52、172.48 Hz,轉(zhuǎn)輪激勵(lì)頻率分別為203.1、167.7、184.8Hz。

        對(duì)比各材料轉(zhuǎn)輪外激勵(lì)頻率0與固有頻率1可得:各工況下轉(zhuǎn)輪與導(dǎo)葉間無(wú)葉區(qū)水流壓力脈動(dòng)主頻均為28f,該壓力脈動(dòng)引起轉(zhuǎn)輪振動(dòng)是節(jié)徑為2的激勵(lì)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(yuǎn)小于0,1max(203.1Hz)<<0min(690.85Hz),因此不會(huì)誘發(fā)共振。

        3.4 轉(zhuǎn)輪結(jié)構(gòu)靜力學(xué)分析

        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(jì),以提高轉(zhuǎn)輪速動(dòng)性,對(duì)于頻繁啟停機(jī)的機(jī)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(duì)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(qiáng),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(guò)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(qiáng)度,且各工況下安全系數(shù)均大于40,以第四強(qiáng)度理論[27]為準(zhǔn)則可知6種材料轉(zhuǎn)輪結(jié)構(gòu)強(qiáng)度均是穩(wěn)定可靠的。

        圖8中轉(zhuǎn)輪max隨著負(fù)荷增加而增加,但高等效應(yīng)力區(qū)域在非設(shè)計(jì)工況面積比設(shè)計(jì)工況大,主要體現(xiàn)在靠近下環(huán)位置。綜合分析流場(chǎng)(圖5、圖6)與結(jié)構(gòu)場(chǎng)(圖 8、圖9),非設(shè)計(jì)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(lái)講,0.35Q工況葉片進(jìn)口區(qū)域存在大量軸向渦,渦流黏度高達(dá)1.18 Pa·s(圖5、圖6),該位置對(duì)應(yīng)圖8的Max標(biāo)記處,此處軸向渦引發(fā)交變載荷進(jìn)一步擴(kuò)大高等效應(yīng)力區(qū)域范圍。相對(duì)地,圖5Q工況良好流態(tài)對(duì)應(yīng)圖8Q較小面積高等效應(yīng)力區(qū)。此外,轉(zhuǎn)輪葉片進(jìn)、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(jì)工況更為突出,其中出口邊與下環(huán)連接處最為嚴(yán)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(qiáng),因此變形量較小。然而由于杠桿效應(yīng),約束點(diǎn)較小的變形量在距離約束點(diǎn)最遠(yuǎn)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(jī)應(yīng)避免長(zhǎng)期運(yùn)行的工況區(qū)。

        4 結(jié) 論

        本文基于流場(chǎng)與結(jié)構(gòu)場(chǎng)對(duì)混流式水輪機(jī)轉(zhuǎn)輪多工況運(yùn)行特性展開研究,采用SST-湍流模型求解內(nèi)流場(chǎng),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(jì)工況轉(zhuǎn)輪進(jìn)口水流相對(duì)速度方向角與葉片進(jìn)口角之間存在偏差,使得水流撞擊葉片進(jìn)口進(jìn)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(jì)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(dòng)。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(guò)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(jì),Q345和1Cr18Ni9Ti轉(zhuǎn)輪抗變形能力較強(qiáng),是長(zhǎng)期在非設(shè)計(jì)工況運(yùn)行機(jī)組的較優(yōu)選擇。

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        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(guó)家自然科學(xué)基金資助項(xiàng)目(51909222);陜西省引進(jìn)國(guó)內(nèi)博士專項(xiàng)(F2020221009);企業(yè)橫向項(xiàng)目(K4050422547)。

        毛秀麗,博士,副教授,研究方向?yàn)樗C(jī)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(guó)慶,等. 混流式水輪機(jī)多工況運(yùn)行轉(zhuǎn)輪特性[J]. 農(nóng)業(yè)工程學(xué)報(bào),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

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