李猛, 郭勇, 馬駿, 高進(jìn), 徐自力

(1.西安交通大學(xué)機(jī)械結(jié)構(gòu)強(qiáng)度與振動(dòng)國(guó)家重點(diǎn)實(shí)驗(yàn)室, 710049, 西安; 2.上海航天精密機(jī)械研究所, 210699, 上海; 3.東方汽輪機(jī)有限公司, 618000, 四川德陽(yáng))

應(yīng)用遺傳算法的汽輪機(jī)轉(zhuǎn)子啟動(dòng)優(yōu)化

李猛1,2, 郭勇3, 馬駿3, 高進(jìn)3, 徐自力1

(1.西安交通大學(xué)機(jī)械結(jié)構(gòu)強(qiáng)度與振動(dòng)國(guó)家重點(diǎn)實(shí)驗(yàn)室, 710049, 西安; 2.上海航天精密機(jī)械研究所, 210699, 上海; 3.東方汽輪機(jī)有限公司, 618000, 四川德陽(yáng))

為了對(duì)汽輪機(jī)啟動(dòng)過(guò)程進(jìn)行優(yōu)化,發(fā)展了一種轉(zhuǎn)子熱應(yīng)力半解析遞推計(jì)算模型。該模型考慮蒸汽換熱系數(shù)的變化,將啟動(dòng)過(guò)程分解為多個(gè)換熱系數(shù)不變的升溫過(guò)程,各升溫過(guò)程的換熱系數(shù)值取為該升溫過(guò)程開(kāi)始時(shí)刻的換熱系數(shù)。同時(shí),將每個(gè)升溫過(guò)程結(jié)束時(shí)刻轉(zhuǎn)子的溫度場(chǎng)擬合為只含偶數(shù)次冪的4次多項(xiàng)式,并將擬合的溫度場(chǎng)作為下個(gè)升溫過(guò)程的初始溫度場(chǎng),通過(guò)拉普拉斯變換法,計(jì)算出下個(gè)升溫過(guò)程的瞬態(tài)溫度場(chǎng)。利用半解析遞推模型構(gòu)造轉(zhuǎn)子啟動(dòng)優(yōu)化的目標(biāo)函數(shù),采用遺傳算法對(duì)660 MW機(jī)組的冷態(tài)啟動(dòng)曲線進(jìn)行了優(yōu)化,優(yōu)化后轉(zhuǎn)子的最大熱應(yīng)力減小了19.4%,且啟動(dòng)時(shí)間減小了4.9%。為驗(yàn)證該半解析遞推模型的計(jì)算精度和效率,分別采用有限元模型和半解析遞推模型計(jì)算了660 MW機(jī)組轉(zhuǎn)子冷態(tài)啟動(dòng)過(guò)程中的瞬態(tài)溫度場(chǎng)、應(yīng)力場(chǎng),計(jì)算結(jié)果表明:兩種模型計(jì)算的轉(zhuǎn)子關(guān)鍵部位熱應(yīng)力變化趨勢(shì)相同,最大熱應(yīng)力相差0.11%,而遞推模型計(jì)算的時(shí)間約為有限元模型計(jì)算時(shí)間的2.8%。

轉(zhuǎn)子;熱應(yīng)力;啟動(dòng)優(yōu)化;遺傳算法

轉(zhuǎn)子啟動(dòng)曲線優(yōu)化的關(guān)鍵是轉(zhuǎn)子熱應(yīng)力的確定。轉(zhuǎn)子熱應(yīng)力計(jì)算常用有限元法[1-5],該方法計(jì)算精度高,但計(jì)算時(shí)間長(zhǎng),且無(wú)法直接得到轉(zhuǎn)子熱應(yīng)力與蒸汽參數(shù)之間的函數(shù)關(guān)系。對(duì)于最優(yōu)化問(wèn)題模型,需要得到目標(biāo)函數(shù),因此有限元法不宜用于啟動(dòng)優(yōu)化中轉(zhuǎn)子熱應(yīng)力計(jì)算。轉(zhuǎn)子熱應(yīng)力計(jì)算的另一種方法為解析法,解析法一般忽略啟動(dòng)過(guò)程中換熱系數(shù)隨時(shí)間的變化,將換熱系數(shù)作為常數(shù),通過(guò)積分變換、分離變量等方式計(jì)算出轉(zhuǎn)子熱應(yīng)力場(chǎng)[6-10]。然而,在轉(zhuǎn)子啟動(dòng)過(guò)程中,換熱系數(shù)變化范圍很大,特別是在啟動(dòng)初期,換熱系數(shù)變化對(duì)轉(zhuǎn)子熱應(yīng)力有很大的影響。為提高解析法的計(jì)算精度,文獻(xiàn)[11]考慮換熱系數(shù)的變化,提出了一種轉(zhuǎn)子熱應(yīng)力解析遞推算法,但是該遞推算法計(jì)算公式復(fù)雜,計(jì)算當(dāng)前時(shí)間步下熱應(yīng)場(chǎng)時(shí)需考慮歷史熱載荷對(duì)當(dāng)前熱載荷的影響,在時(shí)間步較多時(shí),計(jì)算量很大。由于上述轉(zhuǎn)子熱應(yīng)力計(jì)算方法各自的優(yōu)缺點(diǎn),以往轉(zhuǎn)子啟動(dòng)優(yōu)化的研究多采用經(jīng)驗(yàn)或試算的方式,即先分析原啟動(dòng)曲線下轉(zhuǎn)子熱應(yīng)力變化歷程,然后針對(duì)原啟動(dòng)曲線中不合理的部分進(jìn)行調(diào)整,得到更合理的啟動(dòng)曲線[12-15]。這種優(yōu)化方式簡(jiǎn)單有效,但優(yōu)化后的啟動(dòng)曲線通常不是最優(yōu)的結(jié)果。

針對(duì)轉(zhuǎn)子熱應(yīng)力解析計(jì)算方法存在的問(wèn)題,本文提出了一種轉(zhuǎn)子熱應(yīng)力半解析遞推計(jì)算模型。該計(jì)算模型考慮換熱系數(shù)的變化,且計(jì)算量小,適合于轉(zhuǎn)子啟動(dòng)優(yōu)化中的熱應(yīng)力計(jì)算。將該遞推模型應(yīng)用于轉(zhuǎn)子啟動(dòng)優(yōu)化中的熱應(yīng)力計(jì)算,采用遺傳算法對(duì)某660 MW機(jī)組冷態(tài)啟動(dòng)曲線進(jìn)行了優(yōu)化。

1 轉(zhuǎn)子熱應(yīng)力半解析遞推計(jì)算模型

1.1 轉(zhuǎn)子溫度場(chǎng)遞推計(jì)算過(guò)程

將轉(zhuǎn)子視為無(wú)限長(zhǎng)圓柱,轉(zhuǎn)子初始溫度均勻,轉(zhuǎn)子材料參數(shù)不隨溫度變化。

考慮蒸汽對(duì)轉(zhuǎn)子表面的換熱系數(shù)隨時(shí)間變化時(shí),將啟動(dòng)過(guò)程分解為多個(gè)換熱系數(shù)不變的升溫過(guò)程,各個(gè)升溫過(guò)程的換熱系數(shù)取為該升溫過(guò)程開(kāi)始時(shí)刻的換熱系數(shù),則轉(zhuǎn)子的瞬態(tài)溫度場(chǎng)為下列方程的解

(1)

式中:T為轉(zhuǎn)子溫度;t為時(shí)間;r為轉(zhuǎn)子徑向坐標(biāo);R為轉(zhuǎn)子外徑;a為轉(zhuǎn)子導(dǎo)溫系數(shù);λ為轉(zhuǎn)子導(dǎo)熱系數(shù);αi為ti時(shí)刻換熱系數(shù);TS,i為ti時(shí)刻蒸汽溫度;ηi為ti時(shí)刻蒸汽溫升率。

采用遞推方法求解各個(gè)升溫過(guò)程的瞬態(tài)溫度場(chǎng),假設(shè)ti時(shí)刻的溫度場(chǎng)已求解得到,可以證明,在初始溫度場(chǎng)為常數(shù)情況下,轉(zhuǎn)子瞬態(tài)溫度場(chǎng)中只含r的偶數(shù)次冪,因此用只含偶數(shù)次冪的4次多項(xiàng)式擬合ti時(shí)刻的溫度場(chǎng),t>ti后的瞬態(tài)溫度場(chǎng)為如下方程的解

(2)

對(duì)式(2)進(jìn)行拉普拉斯變換,可得

(3)

(4)

(5)

式中:U*為非齊次貝塞爾方程(3)的任一特解;J0(x)為0階貝塞爾函數(shù)。由級(jí)數(shù)展開(kāi)法,可得

(6)

將式(6)代入式(4),可得

(7)

由拉普拉斯逆變換和留數(shù)定理,可得

(8)

(9)

Cn=

(10)

由式(8)可通過(guò)遞推的方法依次得到各個(gè)升溫過(guò)程中轉(zhuǎn)子瞬態(tài)溫度場(chǎng)。式(8)的級(jí)數(shù)展開(kāi)形式只含有r的偶數(shù)次冪,且r的高次冪對(duì)應(yīng)的系數(shù)比低次冪對(duì)應(yīng)的系數(shù)要小,當(dāng)t*→∞時(shí)T中只含有r2項(xiàng)和常數(shù)項(xiàng),在各升溫過(guò)程的時(shí)長(zhǎng)選取合適的情況下,用只含r的偶數(shù)次冪項(xiàng)的四次多項(xiàng)式擬合各升溫結(jié)束時(shí)刻的溫度場(chǎng)能達(dá)到很好的擬合效果。

轉(zhuǎn)子瞬態(tài)溫度場(chǎng)得到后,可由文獻(xiàn)[16]中的公式計(jì)算轉(zhuǎn)子外表面的熱應(yīng)力

(11)

1.2 算例驗(yàn)證

為驗(yàn)證本文所提溫度場(chǎng)遞推公式,采用半解析遞推公式計(jì)算某660 MW機(jī)組轉(zhuǎn)子關(guān)鍵部位冷態(tài)啟動(dòng)過(guò)程中的溫度場(chǎng)和熱應(yīng)力,并與有限元計(jì)算結(jié)果進(jìn)行對(duì)比,轉(zhuǎn)子溫度場(chǎng)半解析遞推計(jì)算模型與有限元模型的計(jì)算流程、轉(zhuǎn)子二維剖面如圖1、2所示。

(a)溫度場(chǎng)半解析遞推計(jì)算流程

(b)溫度場(chǎng)有限元計(jì)算流程圖1 溫度場(chǎng)半解析遞推計(jì)算與有限元計(jì)算流程

圖2 轉(zhuǎn)子二維剖面圖

當(dāng)采用遞推公式計(jì)算轉(zhuǎn)子關(guān)鍵部位溫度場(chǎng)時(shí),不考慮轉(zhuǎn)子關(guān)鍵部位的倒圓角對(duì)溫度場(chǎng)的影響,忽略轉(zhuǎn)子軸向熱流的影響,將轉(zhuǎn)子視為無(wú)限長(zhǎng)圓柱。轉(zhuǎn)子的導(dǎo)熱系數(shù)、密度和比熱容分別為26 W/(m·K)、7 800 kg/m3、523.7 J/(kg·K),轉(zhuǎn)子關(guān)鍵部位外徑為0.315 m,關(guān)鍵部位蒸汽參數(shù)變化曲線如圖3所示,啟動(dòng)過(guò)程中轉(zhuǎn)子關(guān)鍵部位表面蒸汽平均溫升率為0.71 ℃/min。

(a)蒸汽溫度

(b)換熱系數(shù)圖3 轉(zhuǎn)子關(guān)鍵部位蒸汽參數(shù)變化曲線

(a)軸心溫度

(b)表面金屬溫度及表面蒸汽溫度圖4 兩種模型計(jì)算的轉(zhuǎn)子關(guān)鍵部位溫度變化曲線

有限元與半解析遞推模型計(jì)算的轉(zhuǎn)子關(guān)鍵部位表面與軸心溫度對(duì)比如圖4所示。由圖4可知:沖轉(zhuǎn)時(shí)刻關(guān)鍵部位蒸汽溫度比轉(zhuǎn)子金屬溫度高約150 ℃,在熱沖擊下轉(zhuǎn)子表面金屬溫度迅速增加,轉(zhuǎn)子表面金屬與蒸汽的溫差不斷減小,在約200 min時(shí)表面金屬與蒸汽溫差變?yōu)? ℃,而軸心溫度在沖轉(zhuǎn)后約20 min才開(kāi)始逐漸上升。兩種模型計(jì)算的溫度場(chǎng)對(duì)比可看出:兩種模型計(jì)算的轉(zhuǎn)子表面溫度、軸心溫度最大相對(duì)偏差分別為4.0%、4.2%,兩種模型計(jì)算的轉(zhuǎn)子表面溫度、軸心溫度平均相對(duì)偏差分別為0.42%、2.4%,半解析遞推模型計(jì)算轉(zhuǎn)子表面溫度時(shí)精度相對(duì)較高,半解析遞推模型計(jì)算軸心溫度時(shí)精度相對(duì)較低。這是因?yàn)檗D(zhuǎn)子表面與蒸汽對(duì)流換熱,轉(zhuǎn)子表面金屬溫度受軸向熱流的影響很小。

兩種模型下轉(zhuǎn)子關(guān)鍵部位的Mises應(yīng)力計(jì)算結(jié)果曲線如圖5所示。由圖5可知,轉(zhuǎn)子最大熱應(yīng)力出現(xiàn)時(shí)刻在約50 min,最大熱應(yīng)力約為360 MPa,熱應(yīng)力達(dá)到峰值后一直下降。這是因?yàn)闆_轉(zhuǎn)時(shí)刻轉(zhuǎn)子受到的熱沖擊太大,啟動(dòng)后期蒸汽溫升率相對(duì)較低導(dǎo)致,因此機(jī)組冷態(tài)啟動(dòng)曲線需要進(jìn)行優(yōu)化以減小啟動(dòng)初期轉(zhuǎn)子受到的熱載荷,同時(shí)增加啟動(dòng)后期轉(zhuǎn)子溫升率以減小啟動(dòng)時(shí)間。在約400 min時(shí),可看到,轉(zhuǎn)子關(guān)鍵部位熱應(yīng)力曲線有明顯轉(zhuǎn)折,這是因?yàn)樵摃r(shí)刻轉(zhuǎn)子表面蒸汽溫度變化曲線出現(xiàn)轉(zhuǎn)折,而轉(zhuǎn)子表面金屬溫度與蒸汽溫度變化基本一致,轉(zhuǎn)子表面熱應(yīng)力與轉(zhuǎn)子表面金屬溫度和轉(zhuǎn)子體積平均溫度之差成正比,由于熱傳導(dǎo)需要時(shí)間,轉(zhuǎn)子體積平均溫度在蒸汽溫度轉(zhuǎn)折之后繼續(xù)上升一段時(shí)間才會(huì)逐漸保持不變。

兩種模型下轉(zhuǎn)子關(guān)鍵部位熱應(yīng)力變化趨勢(shì)相同,兩種模型計(jì)算的最大熱應(yīng)力相對(duì)偏差為0.11%。啟動(dòng)約400 min后,兩種模型計(jì)算的熱應(yīng)力相對(duì)偏差變大,這與啟動(dòng)后期軸向熱流變大有關(guān),但400 min后主蒸汽溫度已達(dá)到額定值,轉(zhuǎn)子最大熱應(yīng)力一般都在蒸汽升溫階段。總體而言,采用該遞推模型計(jì)算轉(zhuǎn)子最大熱應(yīng)力滿足精度要求,而該遞推模型計(jì)算所需時(shí)間約為有限元模型計(jì)算時(shí)間的2.8%,適用于轉(zhuǎn)子啟動(dòng)優(yōu)化中轉(zhuǎn)子熱應(yīng)力的計(jì)算。

圖5 轉(zhuǎn)子關(guān)鍵部位Mises應(yīng)力計(jì)算結(jié)果對(duì)比

2 基于遺傳算法的轉(zhuǎn)子啟動(dòng)優(yōu)化

2.1 優(yōu)化對(duì)象與目標(biāo)

優(yōu)化對(duì)象為汽輪機(jī)轉(zhuǎn)子,為減小轉(zhuǎn)子在冷態(tài)啟動(dòng)過(guò)程中最大熱應(yīng)力以及縮短啟動(dòng)時(shí)間,采用遺傳算法對(duì)轉(zhuǎn)子的冷態(tài)啟動(dòng)曲線進(jìn)行優(yōu)化。原冷態(tài)啟動(dòng)曲線如圖6所示,將轉(zhuǎn)子啟動(dòng)過(guò)程分為3個(gè)階段,每個(gè)階段的溫升率、時(shí)長(zhǎng)以及沖轉(zhuǎn)時(shí)刻主蒸汽溫度確定后即可確定啟動(dòng)過(guò)程中的蒸汽溫度變化曲線及啟動(dòng)時(shí)間,在優(yōu)化過(guò)程中,選取參數(shù)作為設(shè)計(jì)變量,參數(shù)為

(12)

式中:TS,0為沖轉(zhuǎn)時(shí)刻主蒸汽溫度;t1為第1階段結(jié)束時(shí)刻(中速暖機(jī)時(shí)刻);t2為第2階段結(jié)束時(shí)刻(并網(wǎng)時(shí)刻);η1為第1階段溫升率;η2為第2階段溫升率;η3為第3階段溫升率。

圖6 冷態(tài)啟動(dòng)主蒸汽溫度和壓力變化曲線

有限元方法計(jì)算的原冷態(tài)啟動(dòng)轉(zhuǎn)子瞬態(tài)溫度場(chǎng)和應(yīng)力場(chǎng)結(jié)果表明:轉(zhuǎn)子啟動(dòng)過(guò)程中最大應(yīng)力部位在圖2所示的關(guān)鍵部位。為減小優(yōu)化計(jì)算時(shí)間,將轉(zhuǎn)子簡(jiǎn)化為無(wú)限長(zhǎng)圓柱,由本文推導(dǎo)的熱應(yīng)力遞推公式計(jì)算關(guān)鍵部位表面的熱應(yīng)力。以同時(shí)減小啟動(dòng)時(shí)間和啟動(dòng)過(guò)程中的最大應(yīng)力為優(yōu)化目標(biāo),建立目標(biāo)函數(shù)

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式中:σmax為啟動(dòng)過(guò)程中的最大熱應(yīng)力;σmax,0為原啟動(dòng)過(guò)程中的最大熱應(yīng)力;tend為啟動(dòng)時(shí)間;tend,0為原啟動(dòng)時(shí)間;c1、c2為加權(quán)系數(shù),c1、c2的和為1,c1越大,優(yōu)化更側(cè)重于減小啟動(dòng)中的最大應(yīng)力,c2越大,優(yōu)化更側(cè)重于減小啟動(dòng)時(shí)間,在對(duì)660 MW機(jī)組進(jìn)行啟動(dòng)優(yōu)化時(shí),認(rèn)為減小啟動(dòng)時(shí)間和應(yīng)力具有同樣意義,優(yōu)化計(jì)算時(shí)c1、c2都取為0.5。

2.2 優(yōu)化原理與思路

遺傳算法借鑒生物進(jìn)化理論,將要解決的問(wèn)題模擬成一個(gè)生物進(jìn)化的過(guò)程,通過(guò)復(fù)制、交叉、突變等操作產(chǎn)生下一代的解,并逐步淘汰掉適應(yīng)度低的解,增加適應(yīng)度高的解,這樣進(jìn)化N代后就很有可能會(huì)進(jìn)化出適應(yīng)度很高的個(gè)體。

利用遺傳算法對(duì)轉(zhuǎn)子啟動(dòng)進(jìn)行優(yōu)化時(shí),每一代個(gè)體數(shù)量為40,最大遺傳代數(shù)為20,采用二進(jìn)制方式編碼,優(yōu)化進(jìn)行到20代后停機(jī)并輸出最優(yōu)解,遺傳算法優(yōu)化流程如圖7所示。

圖7 遺傳算法優(yōu)化流程

2.3 優(yōu)化結(jié)果與對(duì)比

優(yōu)化過(guò)程中每一代種群適應(yīng)度均值變化如圖8所示,可知種群適應(yīng)度均值隨進(jìn)化代數(shù)增加而減小,進(jìn)化到16代時(shí)開(kāi)始收斂,最終優(yōu)化解為

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圖8 種群適應(yīng)度均值變化曲線

優(yōu)化前、后主蒸汽溫升曲線對(duì)比如圖9所示,可知優(yōu)化后,沖轉(zhuǎn)時(shí)刻主蒸汽溫度降低了約25 ℃,并網(wǎng)前主蒸汽平均溫升率降低,減小了啟動(dòng)前期轉(zhuǎn)子受到的熱載荷,并網(wǎng)后溫升率升高,且并網(wǎng)時(shí)間提前,縮短了啟動(dòng)時(shí)間。

圖9 優(yōu)化前、后主蒸汽溫度曲線

采用有限元法計(jì)算優(yōu)化后轉(zhuǎn)子瞬態(tài)熱應(yīng)力,優(yōu)化前、后轉(zhuǎn)子關(guān)鍵部位熱應(yīng)力變化曲線對(duì)比如圖10所示,由圖10可知,優(yōu)化后轉(zhuǎn)子最大熱應(yīng)力減小,優(yōu)化后轉(zhuǎn)子熱應(yīng)力在時(shí)間域上分布更均勻,優(yōu)化前、后轉(zhuǎn)子最大熱應(yīng)力發(fā)生時(shí)刻相同,都在沖轉(zhuǎn)后約50 min。

圖10 優(yōu)化前、后關(guān)鍵部位熱應(yīng)力變化曲線

優(yōu)化前、后轉(zhuǎn)子最大熱應(yīng)力分別為362 MPa、291.6 MPa,優(yōu)化前、后的啟動(dòng)時(shí)間分別為450 min、428 min,優(yōu)化后最大熱應(yīng)力和啟動(dòng)時(shí)間較優(yōu)化前減小了19.4%、4.9%,優(yōu)化效果非常明顯。

3 結(jié) 論

針對(duì)轉(zhuǎn)子啟動(dòng)優(yōu)化中熱應(yīng)力的計(jì)算,本文發(fā)展了一種轉(zhuǎn)子熱應(yīng)力半解析遞推計(jì)算模型。采用該遞推模型,計(jì)算了某660 MW機(jī)組轉(zhuǎn)子冷態(tài)啟動(dòng)過(guò)程中的溫度場(chǎng)和熱應(yīng)力場(chǎng),并與有限元法計(jì)算的結(jié)果進(jìn)行對(duì)比,結(jié)果表明,兩種模型計(jì)算結(jié)果差別不大,說(shuō)明該半解析遞推計(jì)算模型精度滿足要求,且計(jì)算時(shí)間僅為有限元法的2.8%。利用熱應(yīng)力半解析遞推計(jì)算方法,建立轉(zhuǎn)子啟動(dòng)優(yōu)化的數(shù)學(xué)模型,并采用遺傳算法對(duì)轉(zhuǎn)子的冷態(tài)啟動(dòng)進(jìn)行了優(yōu)化,優(yōu)化后轉(zhuǎn)子熱應(yīng)力在時(shí)域上分布更加均勻,轉(zhuǎn)子最大熱應(yīng)力減小了19.4%,且啟動(dòng)時(shí)間減小了4.9%,優(yōu)化效果非常明顯。

[1] 鄔文睿, 王煒哲, 蔣普寧, 等. 660 MW超超臨界汽輪機(jī)高壓轉(zhuǎn)子的高溫蠕變強(qiáng)度分析 [J]. 動(dòng)力工程學(xué)報(bào), 2009, 29(2): 99-103.

WU Wenrui, WANG Weizhe, JIANG Puning, et al. Strength analysis of high-temperature creep for a 660 MW ultra-supercritical steam turbine high-pressure rotor [J]. Journal of Power Engineering, 2009, 29(2): 99-103.

[2] 張超, 徐自力, 劉石, 等. 采用熱固雙向耦合模型的轉(zhuǎn)子熱應(yīng)力計(jì)算方法研究 [J]. 西安交通大學(xué)學(xué)報(bào), 2014, 48(4): 68-72.

ZHANG Chao, XU Zili, LIU Shi, et al. Steam turbine rotor thermal stress calculation with thermo-structural coupled model [J]. Journal of Xi’an Jiaotong University, 2014, 48(4): 68-72.

[3] 徐自力, 王凱, 方宇, 等. 汽輪機(jī)起動(dòng)過(guò)程溫升分配對(duì)轉(zhuǎn)子熱應(yīng)力的影響 [J]. 機(jī)械工程學(xué)報(bào), 2013, 49(12): 136-141.

XU Zili, WANG Kai, FANG Yu, et al. Effect of temperature rising distribution on thermal stress of rotor during steam turbine start-up [J]. Journal of Mechanical Engineering, 2013, 49(12): 136-141.

[4] JING Jianping, MENG Guang, SUN Yi, et al. A continuum damage mechanics model on creep rupture life assessment of a steam turbine rotor [J]. Journal of Engineering for Gas Turbines & Power, 2006, 128(1): 173-177.

[5] GONG Mingxiang, DI Guo, WANG Zhaoxi, et al. Transient analysis of LP rotor from NPP 900 MW turbine [J]. Procedia Engineering, 2012, 27: 1575-1581.

[6] 黃仙, 倪維斗. 汽輪機(jī)轉(zhuǎn)子熱應(yīng)力的“復(fù)頻法”建模研究 [J]. 動(dòng)力工程, 1995, 15(6): 6-11.

HUANG Xian, NI Weidou. Thermal stress of steam turbine rotor based on complex frequency method [J]. Journal of Power Engineering, 1995, 15(6): 6-11.

[7] 呂智強(qiáng), 韓萬(wàn)金. 采用熱流法計(jì)算汽輪機(jī)轉(zhuǎn)子表面熱應(yīng)力 [J]. 動(dòng)力工程學(xué)報(bào), 2005, 25(6): 765-769.

Lü Zhiqiang, HAN Wanjin. Calculation of thermal stress on steam turbine rotor surfaces by the heat flux method [J]. Journal of Power Engineering, 2005, 25(6): 765-769.

[8] 張恒良, 謝誕梅, 熊揚(yáng)恒, 等. 600 MW汽輪機(jī)轉(zhuǎn)子高精度熱應(yīng)力在線監(jiān)測(cè)模型研制 [J]. 中國(guó)電機(jī)工程學(xué)報(bào), 2006, 26(1): 21-25.

ZHANG Hengliang, XIE Danmei, XIONG Yangheng, et al. The research and development of high-quality thermal-stress online monitoring model for 600 MW turbine rotors [J]. Proceedings of the Chinese Society for Electrical Engineering, 2006, 26(1): 21-25.

[9] ANTONIO C P, LUS S R, JESS N G, et al. Integration of thermal stress and lifetime supervision system of steam turbine rotors [C]∥ASME Turbo Expo 2008: Power for Land, Sea, and Air. New York, USA: ASME, 2008: 1035-1044.

[10] SONG G, KIM B, CHANG S. Fatigue life evaluation for turbine rotor using green’s function [J]. Procedia Engineering, 2011, 10: 2298-2303.

[11] 支小牧, 寇可新, 曹向欣, 等. 汽輪機(jī)轉(zhuǎn)子熱應(yīng)力在線監(jiān)測(cè)、壽命管理及優(yōu)化啟動(dòng)的研究 [J]. 動(dòng)力工程學(xué)報(bào), 2000, 20(1): 543-548.

ZHI Xiaomu, KOU Kexin, CAO Xiangxin, et al. Steam turbine rotor thermal stress online supervision, life management and optimal start-up study [J]. Journal of Power Engineering, 2000, 20(1): 543-548.

[12] NAKAI A, NAKAMOTO M, KAKEHI A, et al. Turbine start-up algorithm based on prediction of rotor thermal stress [C]∥Proceedings of the SICE Conference. Piscataway, NJ, USA: IEEE, 1995: 1561-1564.

[13] 牛國(guó)平, 沈月芬. 國(guó)產(chǎn)200 MW調(diào)峰機(jī)組啟動(dòng)曲線的優(yōu)化 [J]. 中國(guó)電力, 1996(3): 8-11.

NIU Guoping, SHEN Yuefen. Optimization of starting curve of domestic 200 MW peak shaving unit [J]. Electric Power, 1996(3): 8-11.

[14] 任浩仁, 盛德仁, 任容, 等. 600 MW機(jī)組中壓缸啟動(dòng)過(guò)程的優(yōu)化研究 [J]. 動(dòng)力工程學(xué)報(bào), 2002, 22(5): 1954-1958.

REN Haoren, SHENG Deren, REN Rong, et al.

Research on optimization of intermediate pressure cylinder start process for 600 mw unit [J]. Journal of Power Engineering, 2002, 22(5): 1954-1958.

[15] 丁陽(yáng)俊, 盛德仁, 陳堅(jiān)紅, 等. 某電廠聯(lián)合循環(huán)汽輪機(jī)啟動(dòng)過(guò)程優(yōu)化 [J]. 中國(guó)電機(jī)工程學(xué)報(bào), 2013, 33(2): 9-15.

DING Yangjun, SHENG Deren, CHEN Jianhong, et al. Optimization of start-up process in combined cycle steam turbine of a power plant [J]. Proceedings of the Chinese Society for Electrical Engineering, 2013, 33(2): 9-15.

[16] 竹內(nèi)洋一郎. 熱應(yīng)力 [M]. 郭廷瑋, 李安定, 譯. 北京: 科學(xué)出版社, 1977: 105-109.

RotorStart-UpOptimizationofSteamTurbineBasedonGeneticAlgorithm

LI Meng, GUO Yong, MA Jun, GAO Jin, XU Zili

(1. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China; 2. Shanghai Aerospace Precision Machinery Research Institute, Shanghai 210699, China; 3. Dong Fang Turbine Co. Ltd., Deyang, Sichuan 618000, China)

To optimize the start-up process of steam turbine, a semi-analytical recursive calculation model of rotor temperature field is developed. Considering the change of heat transfer coefficient with time, the start-up process is divided into multiple heating processes with constant heat transfer coefficient in the algorithm. The value of heat transfer coefficient of each heating process is taken as the initial value of heat transfer coefficient at the beginning of the process. The temperature field at the end of each process is fitted as 4th-order polynomial, and the 4th-order polynomial will be the initial temperature field of the next temperature rising process. Then, the transient temperature field of the next temperature rising process is calculated through the Laplace transform method. To verify the accuracy and efficiency of the semi-analytical recursive model, finite element method and recursive model are used to calculate the temperature field and stress field of the rotor during cold start of a 660 MW turbine unit. The calculation results show that the trend of the thermal stress calculated by two models is the same. The thermal stress calculated by two models differs by 0.11%, and the computation time of the recursive model is about 2.8% of the finite element model. An objective function of rotor start-up optimization is constructed by the semi-analytical recursive model, and the genetic algorithm is used to optimize the rotor cold start-up of a 660 MW unit. After optimization, the maximum thermal stress of the rotor is reduced by 19.4% and the starting time is reduced by 4.9%.

rotor; thermal stress; start-up optimization; genetic algorithm

2017-06-05。 作者簡(jiǎn)介: 李猛(1991—),男,碩士生;徐自力(通信作者),男,教授,博士生導(dǎo)師。 基金項(xiàng)目: 國(guó)家自然科學(xué)基金資助項(xiàng)目(51675406)。

時(shí)間: 2017-11-06

網(wǎng)絡(luò)出版地址: http:∥kns.cnki.net/kcms/detail/61.1069.T.20171106.1409.006.html

10.7652/xjtuxb201801009

TK263

A

0253-987X(2018)01-0054-07

(編輯 趙煒)