石麗建¹湯方平¹劉超¹謝榮盛¹謝傳流¹孫丹丹²

1　揚(yáng)州大學(xué)水利與能源動(dòng)力工程學(xué)院　江蘇　揚(yáng)州　225100；

2　徐州市水利建筑設(shè)計(jì)研究院　江蘇　徐州　221000

摘要：為了提高軸流泵非設(shè)計(jì)工況的運(yùn)行效率，拓寬軸流泵高效區(qū)范圍，對(duì)軸流泵進(jìn)行多工況優(yōu)化設(shè)計(jì)。結(jié)合軸流泵段的模型試驗(yàn)，采用數(shù)值模擬手段和數(shù)值優(yōu)化技術(shù)，改變?nèi)~輪的幾何設(shè)計(jì)參數(shù)。對(duì)軸流泵葉片進(jìn)行參數(shù)化建模，再對(duì)軸流泵葉輪結(jié)果進(jìn)行泵段數(shù)值模擬。最后以軸流泵段3個(gè)流量工況點(diǎn)的加權(quán)平均效率最高，揚(yáng)程為約束條件，改變軸流泵葉輪的設(shè)計(jì)參數(shù)，對(duì)軸流泵段進(jìn)行多工況優(yōu)化設(shè)計(jì)。研究結(jié)果表明：優(yōu)化后軸流泵段效率曲線較初始泵段明顯變寬，其中小流量工況點(diǎn)效率提高約2.6％，設(shè)計(jì)工況點(diǎn)效率提高約0.5％，大流量工況點(diǎn)效率提高最多，約7.4％，而對(duì)于揚(yáng)程變化范圍較小，各工況點(diǎn)揚(yáng)程均能滿足運(yùn)行要求，大大降低了運(yùn)行成本，縮短了優(yōu)化設(shè)計(jì)的周期。同時(shí)采用CFD計(jì)算的學(xué)科分析方式，結(jié)合試驗(yàn)研究的手段取代人工憑經(jīng)驗(yàn)的優(yōu)化方式，證實(shí)了軸流泵段多工況優(yōu)化設(shè)計(jì)的可靠性、高效性。該研究將為泵站的高效運(yùn)行和軸流泵的多工況優(yōu)化設(shè)計(jì)提供參考。

關(guān)鍵詞：泵；優(yōu)化；計(jì)算機(jī)仿真；軸流泵段；多工況；試驗(yàn)分析

Optimization design and effect analysis of multi-operation conditions

Of axial-flow pump device

Shi Lijian¹, Tang Fangping¹ , Liu Chao¹, Xie Rongsheng¹, Xie Chuanliu¹, Sun Dandan²

1. School of Hydraulic Energy and Power Engineering, Yangzhou University, Yangzhou 225100, China；2. Institute of Water Conservancy Works Design of Xuzhou, Xuzhou 221000, China

Abstract: The flow units of pump device will produce a bad flow regime when the axial-flow pump runs under off-designcondition. The paper uses the numerical simulation and numerical optimization techniques, changes the geometric designparameters of axial-flow impeller, and carries out the optimization design of multi-operation conditions of axial-flow pumpdevice. The optimization design based on pump device experiment analysis aims to improve the efficiency of operation underoff-design conditions, broaden the scope of the efficiency of pump device, and reduce the operating cost of pump station.Firstly, this paper performs the parametric modeling of axial-flow impeller, and uses fewer design parameters to control theshape of pump blades by FORTRAN. According to the design condition to design an axial-flow impeller with high efficiency,and design the guide vane based on the design condition and the impeller. Use the impeller, the guide vane, and the standardinlet and outlet pipe to calculate the hydraulic performance of axial-flow pump device. Then do the experiment of the pumpdevice to verify the accuracy and reliability of the numerical simulation of the pump device. Lastly, this paper carries out theoptimization design of multi-operation conditions of axial-flow pump device. The design flow is 360 L/s, the small flow is 300 L/s and the large flow is 420 L/s, and the 3 flow conditions is chosen as the multi-operation conditions. Change the designparameters of axial-flow impeller, select the weighted average efficiency of pump device as the optimization object and the head of each condition as the constraint, and carry out the optimization design of multi-operation conditions of axial-flow pump device. For each design parameter, every change corresponds to a complete numerical simulation of pump device. Lastbut not least, this article does the internal flow field analysis of pump before and after optimization. The analysis mainlyincludes the streamline comparison of the different flow conditions for the outlet pipe, and the pressure comparison of thedifferent flow conditions in the outlet of the impeller; besides, the NPSH(net positive suction head) is compared before and after optimization. The optimization results show that the optimized high efficiency range of axial-flow pump device iswidened obviously compared to the initial pump device. The efficiency of small flow condition is increased by about 2.6％, theefficiency of design flow condition is increased by about 0.5％, and the efficiency of large flow condition is increased by about7.4％, which is the most. As to the head of the axial-flow pump device, it is little changed, and can also meet the operationrequirement. The optimized pump device can greatly reduce the operation cost of pump station, and the optimization designmethod of multi-operation conditions of axial-flow pump device can greatly shorten the design cycle. From the comparison ofstreamline and pressure before and after optimization, it can be seen that the optimized streamline is smoother and the pressuredistribution is more reasonable. And the NPSH is similar, and does not become worse. This paper adopts the computationalfluid dynamics (CFD) simulation as the subject analysis method, which is combined with experimental study and replacesartificial way of optimization design based on experience, and proves the reliability and efficiency of the optimization design of multi-operation conditions of axial-flow pump device.

Keywords:pumps；optimization；computer simulation；axial-flow pump device；multi-operation conditions；experimentanalysis

0 引言

軸流泵葉輪葉片設(shè)計(jì)質(zhì)量高低很大程度上決定著水泵的性能。目前軸流泵葉片設(shè)計(jì)通常采用升力法、圓弧法和奇點(diǎn)分布法等。隨著計(jì)算機(jī)技術(shù)的快速發(fā)展，基于CFD的優(yōu)化設(shè)計(jì)方法得到快速發(fā)展，根據(jù)軸流泵的數(shù)值計(jì)算結(jié)果，調(diào)整軸流泵葉片的幾何參數(shù)，使得泵內(nèi)流態(tài)較好，以避免漩渦、回流和二次流等不穩(wěn)定的流動(dòng)出現(xiàn)^`1-2`。目前，國(guó)內(nèi)外對(duì)軸流泵葉輪優(yōu)化設(shè)計(jì)基本都是對(duì)軸流泵設(shè)計(jì)工況性能進(jìn)行單目標(biāo)或多目標(biāo)優(yōu)化設(shè)計(jì)，并沒有進(jìn)行多工況的水力性能優(yōu)化設(shè)計(jì)^`3-9`。江蘇大學(xué)^`10-11`對(duì)離心泵的多工況優(yōu)化設(shè)計(jì)進(jìn)行了研究，研究出了具有良好的外特性、速度場(chǎng)、壓力場(chǎng)等分布更為合理的葉輪。另外，國(guó)內(nèi)其他一些學(xué)者在風(fēng)力機(jī)葉片、汽輪機(jī)和水輪機(jī)葉片上也進(jìn)行了多工況優(yōu)化設(shè)計(jì)研究^`12-14`。然而，根據(jù)工程實(shí)際可以發(fā)現(xiàn)，大型泵站工程軸流泵運(yùn)行揚(yáng)程是根據(jù)一年四季站下站上水位要求確定的，并不是一直處于設(shè)計(jì)工況條件下運(yùn)行，相反大部分時(shí)間處于非設(shè)計(jì)工況運(yùn)行，運(yùn)行費(fèi)用大大增加。在設(shè)計(jì)軸流泵時(shí)，不僅應(yīng)考慮設(shè)計(jì)工況下的高效率，同時(shí)也應(yīng)滿足在非設(shè)計(jì)工況下使用時(shí)的可靠性。故對(duì)軸流泵葉片進(jìn)行多工況優(yōu)化設(shè)計(jì)，提高非設(shè)計(jì)工況的運(yùn)行效率，拓寬高效區(qū)范圍，降低運(yùn)行成本顯得尤為重要。

設(shè)計(jì)工況時(shí)液體通過(guò)軸流泵段各通流部件的流動(dòng)，可以認(rèn)為處于最佳狀況，近似于理想流動(dòng)。但是偏離設(shè)計(jì)工況時(shí)，由于真實(shí)液體的黏滯性，在泵內(nèi)將產(chǎn)生漩渦、回流、失速和脫流等，而且這些不良流態(tài)會(huì)逐漸增大。改變軸流泵葉輪幾何設(shè)計(jì)參數(shù)，減小非設(shè)計(jì)工況泵段內(nèi)的不良流動(dòng)，提高非設(shè)計(jì)工況的效率，同時(shí)使得設(shè)計(jì)工況點(diǎn)的效率保持較高是本文的主要研究?jī)?nèi)容。本文結(jié)合某軸流泵段的模型試驗(yàn)，采用數(shù)值模擬手段和數(shù)值優(yōu)化技術(shù)，適當(dāng)?shù)倪x取葉輪的幾何參數(shù)，對(duì)軸流泵模型進(jìn)行多工況優(yōu)化設(shè)計(jì)，提高多個(gè)工況點(diǎn)泵段的效率，拓寬軸流泵高效區(qū)范圍，為軸流泵多工況優(yōu)化設(shè)計(jì)提供參考。

1 軸流泵葉輪的參數(shù)化建模

一般在葉輪設(shè)計(jì)時(shí)，將葉片沿徑向均分成11個(gè)翼型斷面。本文通過(guò)FORTRAN編寫的程序，輸入軸流式葉輪基本設(shè)計(jì)參數(shù)，生成11個(gè)斷面的三維翼型坐標(biāo)值。將坐標(biāo)值文件導(dǎo)入Turbo-Grid中，對(duì)軸流泵進(jìn)行建模并劃分網(wǎng)格。對(duì)葉輪性能影響比較大的主要有葉片數(shù)、輪轂比、葉柵稠密度和翼型安放角。本文保證葉片數(shù)、翼型、拱度等設(shè)計(jì)參數(shù)相同，通過(guò)改變各斷面葉柵稠密度和翼型安放角，進(jìn)而改變軸流泵葉片形狀，研究小流量工況、設(shè)計(jì)工況和大流量工況3種工況下泵段的水力性能，從而達(dá)到拓寬高效區(qū)范圍，降低運(yùn)行成本的目的。

1.1 葉柵稠密度

葉柵稠密度是軸流泵葉輪設(shè)計(jì)重要的幾何參數(shù)^`15-18`，它直接影響泵的效率，也是決定水泵汽蝕性能的重要參數(shù)。葉柵稠密度是根據(jù)在葉柵中能量損失最小以及具有較好汽蝕性能的條件確定。葉柵稠密度減小，水泵葉片總面積減小，葉片工作面和背面的壓差增加，汽蝕性能變差。但是葉片總面積減小，相應(yīng)的減小了水力摩擦損失，葉片效率可以提高。

在軸流泵葉輪設(shè)計(jì)時(shí)，通常有11個(gè)翼型斷面就需要葉片沿展向11個(gè)斷面的葉柵稠密度數(shù)據(jù)，而這11個(gè)斷面的葉柵稠密度數(shù)據(jù)采用從輪轂到輪緣近似的葉片等強(qiáng)度分布規(guī)律。因此，只需要確定葉尖葉柵稠密度和葉根葉柵稠密度倍數(shù)。通過(guò)FORTRAN編程，根據(jù)葉尖葉柵稠密度和葉根葉柵稠密度倍數(shù)生成11個(gè)斷面的葉柵稠密度。將11個(gè)設(shè)計(jì)變量減少為2個(gè)，提高葉片優(yōu)化設(shè)計(jì)的效率。即通過(guò)改變?nèi)~尖葉柵稠密度a₁和葉根葉柵稠密度倍數(shù)a₂實(shí)現(xiàn)軸流泵葉片幾何形狀的改變。

1.2 翼型安放角

葉片的翼型安放角對(duì)軸流泵水力性能同樣具有重要影響。軸流泵葉片外緣翼型很薄，近乎平直，葉片沖角很小，做功能力不強(qiáng)。而輪轂側(cè)翼型較厚，拱度大，且沖角大，導(dǎo)致葉片扭曲嚴(yán)重。因此，在優(yōu)化設(shè)計(jì)時(shí)應(yīng)適當(dāng)減小輪轂處翼型安放角，降低輪轂側(cè)的軸面速度與圓周分速度，同時(shí)適當(dāng)增大外緣翼型安放角，增大外緣葉片沖角，提高葉片做功能力。這樣不僅可以減小葉片扭曲，改善翼型工作條件，而且可以提高效率、擴(kuò)大高效區(qū)范圍。

初始設(shè)計(jì)葉輪采用基于CFD數(shù)值計(jì)算的設(shè)計(jì)方法。利用數(shù)值計(jì)算軟件CFX針對(duì)設(shè)計(jì)工況軸流泵葉輪內(nèi)部流場(chǎng)進(jìn)行全三維的紊流數(shù)值模擬。對(duì)計(jì)算結(jié)果進(jìn)行分析比較，兼顧效率和汽蝕性能要求，得到最終的初始設(shè)計(jì)方案。通過(guò)對(duì)這11個(gè)斷面翼型安放角數(shù)據(jù)的分析發(fā)現(xiàn)，用二次多項(xiàng)式對(duì)這11個(gè)翼型安放角進(jìn)行擬合，得到的標(biāo)準(zhǔn)差為0.999，誤差較小，得到翼型安放角與沿葉片展向各斷面相對(duì)半徑關(guān)系曲線如下：

β_m=90.504-129.964r+57.26r²。　?。?）

式中β_m為翼型安放角，(°)；r為各斷面相對(duì)半徑值。

對(duì)于每一種輪轂比，采用的翼型均為NACA16翼型，各翼型相對(duì)半徑值是確定的，可以通過(guò)FORTRAN編寫程序改變二次多項(xiàng)式的3個(gè)系數(shù)值，進(jìn)而改變各斷面翼型安放角的值。將二次多項(xiàng)式3個(gè)系數(shù)a₃（a₃=90.504）、a₄（a₄=129.964）和a₅（a₅=57.26）作為優(yōu)化的設(shè)計(jì)變量。

在進(jìn)行優(yōu)化設(shè)計(jì)時(shí)，只需改變以上5個(gè)變量的值即可改變軸流泵葉片的扭曲形狀，進(jìn)而改變軸流泵段的水力性能，提高優(yōu)化的效率，縮短設(shè)計(jì)的周期。

2 泵段的數(shù)值模擬

本文對(duì)整個(gè)泵段計(jì)算域進(jìn)行定常數(shù)值模擬。采用有限體積法對(duì)N-S控制方程在空間域上進(jìn)行離散。求解精度設(shè)置為高階求解格式。最大迭代步數(shù)設(shè)為1000步，迭代收斂精度設(shè)為10^-5。

2.1 計(jì)算模型的建立

軸流泵段包括：帶導(dǎo)水錐的進(jìn)水直管段，軸流泵葉輪、導(dǎo)葉體和標(biāo)準(zhǔn)60°出水彎管段。其中為了建模及網(wǎng)格劃分的方便，導(dǎo)水錐與直管段一體，導(dǎo)水錐設(shè)置成靜止壁面對(duì)輪轂區(qū)流態(tài)基本無(wú)影響。本文軸流泵葉輪名義比轉(zhuǎn)速n_s=800，其設(shè)計(jì)流量Q₀=360L/s，設(shè)計(jì)揚(yáng)程H=6.0m，轉(zhuǎn)速n=1450r/min，葉頂單邊間隙為0.2mm。后置導(dǎo)葉體為針對(duì)該葉輪的設(shè)計(jì)工況而針對(duì)設(shè)計(jì)的，導(dǎo)葉體的擴(kuò)散角為6°，導(dǎo)葉葉片數(shù)7片，葉輪葉片數(shù)4片。進(jìn)水直管段和出水彎管段采用Proe建模，葉輪和導(dǎo)葉體根據(jù)其三維坐標(biāo)數(shù)據(jù)點(diǎn)，采用Turbo-Grid建模。軸流泵段三維數(shù)值計(jì)算模型如圖1所示。

圖1　泵段數(shù)值計(jì)算模型

Fig.1　Pump device numerical calculation model

2.2 網(wǎng)格劃分

本文對(duì)進(jìn)水直管和出水彎管采用ICEM軟件進(jìn)行結(jié)構(gòu)網(wǎng)格劃分，網(wǎng)格質(zhì)量在0.4以上，質(zhì)量較好，符合計(jì)算要求。軸流泵葉輪和導(dǎo)葉在Turbo-Grid中建模并進(jìn)行結(jié)構(gòu)網(wǎng)格劃分，經(jīng)檢驗(yàn)，葉輪和導(dǎo)葉體網(wǎng)格質(zhì)量較好，同時(shí)滿足正交性要求。本文在網(wǎng)格無(wú)關(guān)性分析時(shí)，不斷改變網(wǎng)格數(shù)量并對(duì)泵段進(jìn)行外特性計(jì)算，發(fā)現(xiàn)當(dāng)網(wǎng)格增加到一定數(shù)量時(shí)，泵段效率值趨于穩(wěn)定不再隨著網(wǎng)格數(shù)量的增加而增加。在滿足網(wǎng)格無(wú)關(guān)性要求時(shí)，取泵段葉輪網(wǎng)格數(shù)330 928，導(dǎo)葉網(wǎng)格數(shù)在365 274，整個(gè)計(jì)算域網(wǎng)格數(shù)為1215 277。葉頂間隙網(wǎng)格邊界層7層，滿足計(jì)算要求。葉輪和導(dǎo)葉網(wǎng)格如圖2所示。

圖2　葉輪和導(dǎo)葉網(wǎng)格圖

Fig.2　Impeller and guide vane grid chart

2.3 邊界條件

軸流泵計(jì)算域進(jìn)口為進(jìn)水管的進(jìn)口，進(jìn)口邊界條件為總壓進(jìn)口條件，總壓設(shè)置為一個(gè)標(biāo)準(zhǔn)大氣壓。軸流泵計(jì)算域出口為出水彎管的出口，出口邊界為質(zhì)量流量出口，葉輪為旋轉(zhuǎn)域，其中葉輪輪緣壁面邊界設(shè)置為相對(duì)于葉輪反向同速旋轉(zhuǎn)，其余計(jì)算域均為靜止域。葉輪轉(zhuǎn)速1450 r/min。其余固體壁面邊界條件均采用固壁表面滿足黏性流體的無(wú)滑移條件，近壁區(qū)域采用標(biāo)準(zhǔn)壁面邊界條件。導(dǎo)水錐出口與葉輪進(jìn)口、葉輪出口與導(dǎo)葉進(jìn)口的動(dòng)靜交界面采用速度平均的Stage模型，靜交界面采用None交界面類型。

3 試驗(yàn)驗(yàn)證

針對(duì)該軸流泵設(shè)計(jì)方案，采用標(biāo)準(zhǔn)k-ε模型，選取了8個(gè)工況點(diǎn)進(jìn)行了軸流泵段的數(shù)值計(jì)算。根據(jù)參考文獻(xiàn)`3`計(jì)算處理，該軸流泵段在流量360L/s時(shí)，效率最高，符合設(shè)計(jì)要求。

將葉輪、導(dǎo)葉及進(jìn)出水管道加工出來(lái)在高精密試驗(yàn)大廳進(jìn)行泵段外特性試驗(yàn)驗(yàn)證。試驗(yàn)條件包括進(jìn)出水管道長(zhǎng)度、測(cè)壓管位置等與數(shù)值模擬時(shí)嚴(yán)格一致，以保證試驗(yàn)結(jié)果的可比性，試驗(yàn)泵段及葉輪如圖3所示。具體的試驗(yàn)步驟及試驗(yàn)方法見參考文獻(xiàn)`19`。

圖3　泵段模型試驗(yàn)圖

Fig.3　Pump model test

將軸流泵段預(yù)測(cè)的能量性能曲線與物理模型試驗(yàn)結(jié)果進(jìn)行對(duì)比，如圖4所示。

圖4　試驗(yàn)結(jié)果與數(shù)模結(jié)果對(duì)比圖

Fig.4　Comparasion of simulation results and experiment results

由圖4可知，數(shù)值模擬的預(yù)測(cè)性能曲線與試驗(yàn)曲線的變化趨勢(shì)一致，曲線吻合度較好，各點(diǎn)誤差均在3％以內(nèi)，表明軸流泵段數(shù)值計(jì)算的準(zhǔn)確性和可靠性。

4 軸流泵段的多工況優(yōu)化設(shè)計(jì)

通過(guò)CFX數(shù)值分析軟件及Isight^`20-24`數(shù)值優(yōu)化軟件對(duì)軸流泵段進(jìn)行多工況優(yōu)化設(shè)計(jì)。根據(jù)紐曼提出的葉片泵Q-H性能曲線分區(qū)原則^`1`，本文工況選擇分別選為設(shè)計(jì)工況Q₀=36L/s，小流量工況Q₁=300L/s和大流量工況Q₂=420L/s。設(shè)計(jì)工況效率最高也是工程應(yīng)用中最為重要的運(yùn)行工況，而小流量工況和大流量工況分別選擇約為設(shè)計(jì)工況的0.8倍和1.2倍。

4.1　優(yōu)化模型的建立

優(yōu)化的目的是在軸流泵葉輪設(shè)計(jì)變量的優(yōu)化范圍內(nèi)，在約束條件下，尋找設(shè)計(jì)參數(shù)的最優(yōu)值，使得軸流泵段3個(gè)工況點(diǎn)的效率最優(yōu)。本文根據(jù)上述計(jì)算結(jié)果對(duì)軸流泵段多工況優(yōu)化問(wèn)題定義為：3個(gè)流量工況下，揚(yáng)程小范圍的變化，不斷的改變?cè)O(shè)計(jì)變量的值，使得3個(gè)流量工況點(diǎn)的效率都達(dá)到最優(yōu)值，以拓寬軸流泵段的高效區(qū)范圍。本文以上述軸流泵段為初始方案，對(duì)應(yīng)的葉輪的初始設(shè)計(jì)變量為：a₁=0.9885，a₂=1.2897，a₃=90.504，a₄=?129.96，a₅=57.26，優(yōu)化模型如下。

目標(biāo)函數(shù)

max η(x)=w₁η₁(x)+W₀η₀(x)+W₂η₂(x)。 （2）

設(shè)計(jì)變量范圍 (3)

0.85≤a₁≤1.15

1.05≤a₂≤1.45

88.504≤a₃≤92.504

-133.96≤a₄≤-125.96

49.26≤a₅≤65.26

約束條件 （4）

7.4≤H₁≤8.0

6.0≤H₀≤6.2

2.6≤H₂≤3.2

設(shè)計(jì)變量x=`a<sub>l</sub>，a<sub>2</sub>，a<sub>3</sub>，a<sub>4</sub>，a<sub>5</sub>`^T。

式中η₁、η₀和η₂分別是小流量工況、設(shè)計(jì)工況和大流量工況的效率；W₁、W₀和W₂分別為對(duì)應(yīng)的權(quán)重值；a₁、a₂、a₃、a₄和a₅分別為葉輪的初始設(shè)計(jì)變量；H₁、H₀和H₂分別為各工況點(diǎn)的揚(yáng)程，m。目標(biāo)函數(shù)采用歸一化方法的加權(quán)平均法，將多目標(biāo)優(yōu)化問(wèn)題轉(zhuǎn)化為單目標(biāo)優(yōu)化問(wèn)題。權(quán)重值根據(jù)工程經(jīng)驗(yàn)及運(yùn)行要求確定^`10`。本文為了研究方便，取W₁=0.3、W₀=0.4和W₂=0.3。為了保證優(yōu)化設(shè)計(jì)之后軸流泵葉輪的設(shè)計(jì)點(diǎn)不變，比轉(zhuǎn)速保持一致，故設(shè)計(jì)工況點(diǎn)揚(yáng)程變化范圍盡可能小，其他2個(gè)工況點(diǎn)揚(yáng)程變化范圍可稍大。設(shè)計(jì)變量范圍選擇參照文獻(xiàn)`25`。

4.2優(yōu)化算法的選取

針對(duì)有約束的、非線性、多目標(biāo)并且解不唯一的軸流泵段多工況水力性能優(yōu)化設(shè)計(jì)問(wèn)題，文章選用梯度優(yōu)化算法的序列二次規(guī)劃法（sequential quadratic programming，SQP）。該方法能夠直接處理等式和不等式約束，是目前公認(rèn)的優(yōu)秀的非線性問(wèn)題求解算法之一。具有很好的全局收斂和局部超線性收斂特性，迭代次數(shù)少，收斂速度快，具有很強(qiáng)的邊界收索能力，對(duì)于本文設(shè)計(jì)變量少，約束條件不多的優(yōu)化設(shè)計(jì)問(wèn)題尤其適用。本文序列二次規(guī)劃法的目標(biāo)函數(shù)迭代最大步數(shù)設(shè)為400步，收斂精度為1.0×10^-6。

4.3優(yōu)化流程

Isight是一款基于參數(shù)的多學(xué)科設(shè)計(jì)優(yōu)化軟件，可以集成仿真優(yōu)化軟件，實(shí)現(xiàn)一套完整的自動(dòng)優(yōu)化設(shè)計(jì)計(jì)算框架。本文根據(jù)軸流泵段葉輪優(yōu)化設(shè)計(jì)的思路，采用數(shù)值模擬軟件CFX進(jìn)行泵段水力性能外特性分析。根據(jù)設(shè)計(jì)參數(shù)，通過(guò)fortran語(yǔ)言編寫的程序生成葉輪葉片三維坐標(biāo)值，然后根據(jù)葉片坐標(biāo)在Turbo-grid中進(jìn)行葉輪建模并劃分網(wǎng)格，每一組設(shè)計(jì)變量將產(chǎn)生一個(gè)新的軸流泵葉輪網(wǎng)格文件，導(dǎo)葉網(wǎng)格和進(jìn)出管網(wǎng)格分別通過(guò)Turbo-grid和ICEM劃分，然后將各部分網(wǎng)格導(dǎo)入CFX中進(jìn)行前處理并對(duì)泵段3個(gè)工況點(diǎn)進(jìn)行數(shù)值計(jì)算。每一次迭代過(guò)程都是上述一套完整的計(jì)算處理流程，其中迭代過(guò)程中導(dǎo)葉以及進(jìn)出口網(wǎng)格保持不變。

4.4優(yōu)化結(jié)果分析

不斷改變軸流泵葉輪的設(shè)計(jì)變量，在揚(yáng)程約束范圍內(nèi)，使得軸流泵段3個(gè)工況點(diǎn)的總效率最高。在工作站經(jīng)過(guò)一個(gè)月左右時(shí)間的不斷迭代計(jì)算，得到了泵段葉輪的最終設(shè)計(jì)方案。優(yōu)化過(guò)程設(shè)計(jì)變量變化范圍小，軸流泵葉輪模型形狀變化不大，保證了本文自動(dòng)優(yōu)化的可執(zhí)行性。每一次迭代優(yōu)化都采用數(shù)值模擬分析的學(xué)科分析方式，保證了優(yōu)化結(jié)果的精度。根據(jù)最終設(shè)計(jì)變量值對(duì)軸流泵段三個(gè)工況點(diǎn)進(jìn)行了最終方案數(shù)值模擬計(jì)算，計(jì)算結(jié)果與該方案優(yōu)化結(jié)果保持一致，說(shuō)明了優(yōu)化結(jié)果是可靠的，優(yōu)化效果是可信的、準(zhǔn)確的。優(yōu)化結(jié)果與初始結(jié)果對(duì)比如表1所示。

表1　泵段數(shù)值優(yōu)化結(jié)果

Table1　Pump device numerical optimization results

根據(jù)表1結(jié)果可知，葉尖葉柵稠密度減小，外緣翼型長(zhǎng)度減小，葉根葉柵稠密度增加，減小了內(nèi)外翼型的長(zhǎng)度差，均衡葉片出口揚(yáng)程，減小了徑向流動(dòng)，提高了葉輪的水力性能；同時(shí)根據(jù)翼型安放角擬合系數(shù)的變化可以發(fā)現(xiàn)，輪緣側(cè)翼型安放角增大，輪轂側(cè)翼型安放角有所減小，減小了葉輪葉片形狀的扭曲，改善了翼型的工作條件，這與軸流泵葉輪優(yōu)化設(shè)計(jì)的思路一致。優(yōu)化結(jié)果表明，設(shè)計(jì)工況點(diǎn)效率有所提高，但增加幅度不明顯，大流量工況點(diǎn)效率和小流量工況效率提高較為明顯，其中大流量工況點(diǎn)效率提高了7.4％，小流量工況點(diǎn)效率提高了2.6％，優(yōu)化效果明顯，設(shè)計(jì)工況點(diǎn)效率提高約0.5％。將優(yōu)化后各工況點(diǎn)泵段水力性能計(jì)算值與優(yōu)化前計(jì)算值、試驗(yàn)值進(jìn)行對(duì)比分析，如圖5所示

圖5　優(yōu)化前后泵段性能曲線

Fig.5　Pump device curves before and after optimization

根據(jù)圖5優(yōu)化前后泵段性能曲線圖可知，優(yōu)化后軸流泵段小流量工況和設(shè)計(jì)工況揚(yáng)程稍有降低，但是效率有所提高；大流量工況揚(yáng)程有所升高，效率也有所提高。優(yōu)化后效率曲線較試驗(yàn)曲線整體抬高，高效區(qū)范圍變寬，提高了泵站運(yùn)行穩(wěn)定性，降低了泵站運(yùn)行成本，泵段優(yōu)化效果十分明顯。

將優(yōu)化前后導(dǎo)葉和出水彎管流線圖做對(duì)比，如圖6所示。優(yōu)化前后葉輪出口壓力云圖對(duì)比如圖7所示。

圖6　各工況流線對(duì)比圖

Fig.6　Streamline comparison of different flow condition

圖7　各工況葉輪出口壓力對(duì)比圖

Fig.7　Pressure comparison of different flow conditions

由圖6可知,優(yōu)化后流線較優(yōu)化前更為平順，特別是小流量工況在優(yōu)化前導(dǎo)葉內(nèi)流線紊亂，導(dǎo)葉背面出現(xiàn)脫流現(xiàn)象，優(yōu)化后流線較好,無(wú)明顯脫流。如圖7可知，優(yōu)化前從輪轂到輪緣壓差較大，在小流量輪轂處和大流量輪緣處，壓力梯度較大，產(chǎn)生明顯回流。優(yōu)化后壓力分布更為合理，優(yōu)化效果較好?優(yōu)化前后水泵的汽蝕性能通過(guò)下列公式進(jìn)行預(yù)測(cè)

式中NPSHre為必需汽蝕余量，m；Pmin為葉片背面的最小壓強(qiáng)值，Pa；P₀為進(jìn)水流道進(jìn)口總壓，Pa；ρ為水的密度，kg/m³；g為重力加速度，m/s²?

葉片背面最小壓強(qiáng)的參考?jí)毫c(diǎn)，從輪轂開始取出葉展方向85％的翼型斷面,并距葉片進(jìn)口10％～20％左右葉片寬度吸力面最小壓強(qiáng)值計(jì)算必需汽蝕余量?設(shè)計(jì)工況下優(yōu)化前后該區(qū)域最小壓力值分別為45 757.2?39 870.3 Pa。根據(jù)式(5)計(jì)算得到優(yōu)化前后必需汽蝕余量分別為5.7?6.26m。必需汽蝕余量有所增加,但是增加幅度不大，能夠滿足工程應(yīng)用要求?

5 結(jié)論

1)提出了一套完整的基于數(shù)值分析和數(shù)值優(yōu)化技術(shù)的軸流泵段多工況優(yōu)化設(shè)計(jì)的方法?

2)采用CFD計(jì)算的學(xué)科分析方式,結(jié)合試驗(yàn)研究的手段取代人工憑經(jīng)驗(yàn)的優(yōu)化方式,提高了優(yōu)化結(jié)果的可信度,同時(shí)也證實(shí)了軸流泵段多工況優(yōu)化設(shè)計(jì)的可靠性?高效性?

3)軸流泵段在0.8倍的設(shè)計(jì)工況點(diǎn)效率提高約2.6％，設(shè)計(jì)工況點(diǎn)效率提高約0.5％，1.2倍設(shè)計(jì)工況點(diǎn)效率提高最多,約7.4％。而對(duì)于揚(yáng)程變化范圍較小，各工況點(diǎn)揚(yáng)程均能滿足運(yùn)行要求，大大降低了運(yùn)行成本,縮短了優(yōu)化設(shè)計(jì)的周期?優(yōu)化后軸流泵段高效區(qū)明顯變寬,大大的降低了泵站運(yùn)行成本，同時(shí)汽蝕性能變化不大，優(yōu)化效果十分明顯?

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基金項(xiàng)目：國(guó)家自然科學(xué)基金項(xiàng)目(51376155)；十二五農(nóng)村領(lǐng)域科技計(jì)劃項(xiàng)目(2012BAD08B03-2)；江蘇高校優(yōu)勢(shì)學(xué)科建設(shè)工程資助項(xiàng)目(PAPD)；江蘇省科研創(chuàng)新計(jì)劃項(xiàng)目(KYLX15_1365)

作者簡(jiǎn)介：石麗建，男，江蘇如皋人，博十生。主要研究方向?yàn)榱黧w功能曲INI的多學(xué)科優(yōu)化設(shè)計(jì)。揚(yáng)州揚(yáng)州大學(xué)水利與能源動(dòng)力工程學(xué)院，2251000。Email：[email protected]

通信作者：湯方平，男，浙江金華人，博十生導(dǎo)師，教授，研究方向?yàn)榱?span>體機(jī)械設(shè)計(jì)、復(fù)雜工程系統(tǒng)科學(xué)優(yōu)化設(shè)計(jì)、泵站自動(dòng)化等。揚(yáng)州 揚(yáng)州大學(xué)水利與能源動(dòng)力工程學(xué)院，2251000。Email:[email protected]

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