趙偉國，韓向東，李仁年，鄭英杰，潘緒偉

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沙粒粒徑與含沙量對離心泵空化特性的影響

趙偉國，韓向東，李仁年，鄭英杰，潘緒偉

（1. 蘭州理工大學能源與動力工程學院，蘭州 730050； 2. 甘肅省流體機械及系統(tǒng)重點實驗室，蘭州 730050）

為了研究沙粒粒徑與含沙量對離心泵空化特性的影響，對含沙條件下與清水介質(zhì)下離心泵內(nèi)部空化流場進行數(shù)值計算。所采用沙粒粒徑分別為0.005、0.010、0.015 mm，含沙量分別為0.5%、1.0%、1.5%。通過對清水介質(zhì)外特性與平頭圓柱空化流動進行數(shù)值計算并與試驗結果相對比，驗證算法的可靠性。計算結果表明：含沙量為1.0%時，隨粒徑逐漸增大，沙粒對空化的影響表現(xiàn)為先促進、后抑制；沙粒粒徑為0.010 mm時，隨含沙量不斷增多，沙粒對空化的影響表現(xiàn)為先促進、后抑制。高壓條件下，清水介質(zhì)中無空化泡產(chǎn)生，含沙水流中均有少量空化泡產(chǎn)生?？栈浞职l(fā)展時，與清水介質(zhì)相比，含沙水中空化泡分布表現(xiàn)為先增大、后接近、再變小。在沙粒磨蝕與空蝕的共同作用下，含沙水流條件下的揚程均低于清水介質(zhì)下的揚程，且分別隨粒徑、含沙量的增加，逐漸減小。

離心泵；計算機仿真；模型；空化；沙粒粒徑；含沙量

0 引 言

空化是液體內(nèi)部由于局部壓力降低而發(fā)生的汽化和液化現(xiàn)象，其本質(zhì)是相變[1]。空化是復雜的多相流動，其發(fā)生和發(fā)展能誘發(fā)振動和噪聲，使離心泵運行不穩(wěn)定，嚴重影響整個系統(tǒng)的正常運行[2-6]；同時空化泡的潰滅對離心泵部件表面材料會形成巨大破壞[7-8]，導致其性能急劇下降?？栈漠a(chǎn)生與壓力分布、流速等多種因素[9]相關，同時亦受介質(zhì)因素[10]的影響。自然界的河流或多或少的含有懸浮泥沙與固體顆粒，以黃河干流為例，年平均輸沙量達16.4億t，多年平均含沙量為37.5 kg/m3[11]。運行在含沙水流中的離心泵,除遭受磨蝕破壞作用，由于沙粒的影響，其空化特性與清水介質(zhì)下的空化特性相比，存在明顯不同。

對含沙水流空化，許多學者都進行了研究。常近時等[12-15]通過試驗得到實測水樣中，隨含沙量的增加，初生空化壓力和臨界空化壓力均近似呈線性增加。Huang Si等[16-20]通過試驗研究了固體顆粒含沙量、粒徑、硬度等因素對空蝕破壞程度的影響。Poulain等[21-22]建立了空化泡與球形顆粒之間的相互作用模式。Madadnia等[23-24]研究表明：含沙水流條件下，空蝕與磨蝕的聯(lián)合破壞作用均高于空蝕或磨蝕的單獨作用。Bostjan等[25]通過水洞研究了不同固體顆粒含沙量對水翼空化發(fā)展的影響并得到相應工況下水動力與扭矩的變化特性。Zhao Weiguo[26]通過改變沙粒粒徑與含沙量，研究了沙粒對噴嘴空化影響的規(guī)律。查閱相關文獻可知，考慮粒徑與含沙量對離心泵空化特性影響的研究并不多見。

本文基于數(shù)值方法，采用Mixture模型、RNG-湍流模型和-空化模型，對不同粒徑與含沙量下的沙粒對離心泵空化特性的影響進行研究。依據(jù)黃河蘭州段沙粒中值粒徑分布特點，粒徑分別取為0.005、0.010、0.015 mm；含沙量分別取0.5%、1.0%、1.5%。

1 數(shù)值算法

1.1 控制方程

含沙水空化流動中，沙粒作擬流體處理，混合相連續(xù)性方程、動量方程、體積分數(shù)輸運方程如下所示。

式中u、u（，為1，2，3）為混合相速度，m/s；m為混合相密度，kg/m3，m=ll+ss+vv其中l(wèi)為液相密度，kg/m3，v為汽相密度，kg/m3，s為沙粒相密度，kg/m3，l為液相體積分數(shù)，v為汽相體積分數(shù)，s為沙粒相體積分數(shù)。m為混合相黏度，kg/m·s，m=ll+vv+ss，其中l(wèi)為液相黏度，kg/m·s，v為汽相黏度，kg/m·s，s為沙粒相黏度，kg/m·s；x、x（，為1，2，3）為笛卡爾坐標系坐標；為當?shù)貕毫?，Pa；為時間，s；+為蒸發(fā)源項；-為凝結源項。

1.2 湍流模型

采用RNG-湍流模型[27]對方程進行封閉，此模型充分考慮了旋轉效應，有效提高了旋轉流動的計算精度。其方程為

式中為湍動能，m2/s2；為湍流耗散率，m2/s3；t為湍動黏度，kg/m·s；k為由于平均速度梯度引起的湍動能產(chǎn)生項；1ε、2ε為經(jīng)驗常數(shù)；α，α分別為湍動能和耗散率的有效普朗特數(shù)的倒數(shù)，其值均為1.39；C為經(jīng)驗常數(shù)，值為0.09。

考慮空化泡的可壓縮性，通過修正RNG-湍流模型[28-29]，降低空化區(qū)域湍流黏度。修正公式為

式中為常數(shù)，當取不同的值時，密度變化函數(shù)如圖1所示。本文中，取值為10。

1.3 空化模型

基于-方程的均相流空化模型常用于空化流動的數(shù)值計算。含沙水流條件下，方程（3）中的源項+和-采用-空化模型[30-31]。此空化模型中不存在經(jīng)驗系數(shù)，系完全推導而來，是一種較為理想的空化模型。

式中b為空化泡半徑，m；v為飽和蒸汽壓，Pa。

2 流場數(shù)值求解

2.1 幾何模型與網(wǎng)格劃分

以設計參數(shù)為流量d=250 m3/h, 揚程d=50 m，轉速=1 480 r/min的單級單吸離心泵為研究對象。其幾何參數(shù)為：葉片數(shù)=6，葉輪外徑2=420 mm，包角=120°，蝸殼基圓直徑3=445 mm。采用Pro/E進行三維建模，整個離心泵模型由葉輪、蝸殼、進水管路、出水管路四部分組成；通過ANSYS-ICEM軟件，采用適應性較強的四面體非結構化網(wǎng)格離散計算域，如圖2所示。為了對網(wǎng)格無關性進行驗證，采用5種不同數(shù)目的網(wǎng)格，通過Fluent15.0計算清水介質(zhì)額定工況下離心泵的流場，計算結果如表1所示。

表1 網(wǎng)格無關性驗證

由表1可知，隨網(wǎng)格數(shù)增加，所得揚程相對誤差控制在0.13%以內(nèi)，說明所采用的網(wǎng)格達到收斂要求，故在后續(xù)含沙水空化流動計算中采用中等數(shù)量網(wǎng)格的方案3。

2.2 物性參數(shù)與邊界條件

液相密度l=998.2 kg/m3，黏度l=0.001 kg/m·s，沙粒相密度s=2 650 kg/m3，黏度s=1.72×10-5kg/m·s；汽相密度v0.025 58 kg/m3，黏度v=1.26×10-6kg/m·s；汽化壓力v=3 540 Pa；空化泡半徑b=1.0×10-5m，空化泡數(shù)密度b=1.0×1013。溫度為300 K。

邊界條件設置為速度進口與壓力出口，與常規(guī)的壓力進口與速度出口設置相比，兩者數(shù)值計算結果與試驗結果差別均較小，以噴嘴空化條件下的流量系數(shù)d[32]為例進行說明。2種不同邊界條件下的數(shù)值計算結果分別為0.632與0.635，文獻[32]所提供試驗值為0.620，三者相比，差別較小。近壁面采用標準壁面函數(shù)處理。通過SIMPLEC算法求解壓力速度耦合方程組，壓力項、動量項、湍動能與湍流耗散率項均采用二階迎風格式，殘差設定為1.0×10-4。

式中d為流量系數(shù)；為質(zhì)量流量，kg/s；為橫截面積，m2；1、2分別為噴嘴進、出口壓力，Pa。

3 算法驗證

3.1 離心泵外特性驗證

圖3為離心泵性能試驗臺。試驗臺由模型泵、進水管路、出水管路、壓力表、流量計、閥門等組成。模型泵由上海凱泉泵業(yè)集團有限公司提供，型號為KQL250/400-110/4。壓力表由上海自動化儀表制造廠制造，型號為XU12087105型壓力表，精確度等級為2.5。流量計由天津儀表流量有限公司制造，型號為DN300型流量計，精度等級為1.0級。閥門由天津百利二通機械有限公司制造，型號為ZA2.T型閥門。基于上述三維離心泵模型，計算不同工況下清水介質(zhì)的揚程與效率，如圖4所示。對比表明，計算結果與試驗結果吻合良好，揚程相對誤差最大值為6.00%，效率相對誤差最大值為5.14%，驗證了算法的可靠性。同時，揚程與效率的數(shù)值計算結果均高于試驗結果，原因為數(shù)值模擬過程中，采用的是未考慮口環(huán)間隙泄漏損失的非全流場。

a. 流量-揚程性能曲線

a．Head-flow rate characteristic curve

3.2 空化流動驗證

通過計算平頭圓柱空化流動且繪制相應的壓力分布曲線，并與試驗結果相對比[33]，以此驗證模型及算法的合理性。圓柱直徑=5 mm，長度=5，計算域高度和寬度均為10，計算域及網(wǎng)格如圖5a所示。計算域采用速度進口與壓力出口，壓力由空化數(shù)確定。圓柱表面為無滑移邊界，上下邊界為滑移邊界。基于圓柱直徑的雷諾數(shù)為1.36×105，空化數(shù)為0.5。如圖5b所示為圓柱表面時均壓力系數(shù)分布圖，相對誤差為1.1%，計算結果與試驗結果吻合良好，進一步驗證了空化流動算法的可靠性。

a. 平頭圓柱計算域及網(wǎng)格

a. Computational domain and grids of flat-nosed cylinder

b. 平頭圓柱表面時均壓力系數(shù)分布

b. Distribution of time-averaged pressure coefficient of flat-nosed cylinder

注：圖5b中，雷諾數(shù)為1.36×105，空化數(shù)為0.5；為圓柱表面距圓柱頭部距離；為圓柱直徑。

Note: In Fig.5b, Reynolds number is 1.36×105and cavitation number is 0.5；is distance between surface with head of flat-nosed cylinder;is diameter of flat-nosed cylinder

圖5 平頭圓柱空化流動模型及結果

Fig.5 Model and results of cavitation flow of flat-nosed cylinder

4 計算結果及分析

4.1 沙粒粒徑對離心泵空化特性的影響

通過調(diào)研得到黃河蘭州段流經(jīng)工農(nóng)坪泵站的中值粒徑為0.010 mm，因而以0.010 mm為基準，分別再選擇2個粒徑，為0.005與0.015 mm。以粒徑分別為0.005、0.010、0.015 mm，含沙量為1.0%的沙粒為研究對象，計算了不同粒徑下的含沙水空化流動。通過與清水介質(zhì)下的相比較，研究粒徑對離心泵空化特性的影響，圖6為清水介質(zhì)，含沙量為1.0%、不同粒徑下的含沙水空化性能曲線。

出口壓力為6.0×105Pa時，清水介質(zhì)中無空化泡產(chǎn)生，如圖7a所示；而不同粒徑的含沙水流中，葉片背面靠近進口邊處均有少量空化泡產(chǎn)生，如圖7b、7c、7d所示的葉輪進口深色區(qū)域。同時由圖7b、7c、7d可得，沙粒所攜帶的空化核子對空化泡形成具有顯著影響，但由于出口壓力過高，粒徑的不同對空化泡產(chǎn)生的影響并不明顯。

a.清水介質(zhì)a. Pure waterb. 沙粒粒徑為0.005 mmb. Silt mean diameter is 0.005 mm c. 沙粒粒徑為0.010 mmc. Silt mean diameter is 0.010 mmd. 沙粒粒徑為0.015 mmd. Silt mean diameter is 0.015 mm

離心泵揚程下降3.0%時所對應的空化余量為一臨界空化余量，以NPSHc表示。清水介質(zhì)下，NPSHc為3.721 4 m；粒徑為0.005 mm時，NPSHc為4.952 m，表明沙粒促進了空化的提前發(fā)生。粒徑為0.010 mm時，NPSHc為3.747 9 m，與清水介質(zhì)下的值近似相等，相對差值為0.63%，表明粒徑為0.010 mm的沙粒對空化初生的影響并不明顯。粒徑為0.015 mm時，NPSHc為3.638 m，小于清水條件，表明沙粒抑制了空化的提前發(fā)生。

進一步降低出口壓力至5.29×105Pa時, 空化充分發(fā)展。清水介質(zhì)以及粒徑為0.005、0.010、0.015 mm的含沙水流所對應的空化余量分別為3.436、3.541、3.438 、3.337 m，表明隨粒徑的增加，沙粒對空化的影響表現(xiàn)為先促進、后抑制，這與臨界空化時的結果相一致，空化泡分布如圖8所示。清水介質(zhì)下?lián)P程為50.26 m，含沙水流下隨粒徑增加，揚程分別為49.97、49.94、48.69 m，由于沙粒的磨蝕與空蝕的共同作用，使得含沙條件下?lián)P程均低于清水介質(zhì)下的揚程，且隨粒徑增大揚程逐漸降低。

綜上分析可知，粒徑為0.005 mm，含沙量為1.0%的沙粒促進空化的發(fā)展，主要原因為：沙粒誘導產(chǎn)生更多的空化核子，從而形成更多的空化泡[34]；沙粒作為一種不被潤濕的固體顆粒，具有比清水介質(zhì)破裂更大的拉應力[35]；同時沙粒在虛擬質(zhì)量力[36]的作用下，使得混合相具有較高的動能，從而局部壓力降低，有效促進空化的發(fā)展。清水介質(zhì)中，最低壓力為?1.323×105Pa，粒徑為0.005 mm，含沙量為1.0%的含沙水流中，最低壓力為?1.33×105Pa，說明沙粒在虛擬質(zhì)量力作用下，局部壓力得到降低。粒徑為0.005 mm，含沙量為1.0%的沙粒對流場結構破壞較清水介質(zhì)下嚴重，如圖9a、9b所示，從而加劇能量損失，致使壓力降低，促進空化發(fā)展。

a.清水介質(zhì)a. Pure waterb. 沙粒粒徑為0.005 mmb. Silt mean diameter is 0.005 mm c. 沙粒粒徑為0.010 mmc. Silt mean diameter is 0.010 mmd. 沙粒粒徑為0.015 mmd. Silt mean diameter is 0.015 mm

粒徑為0.015 mm，含沙量為1.0%的沙粒抑制空化的發(fā)展，主要原因為：一方面隨粒徑的增加，粘滯性的抑制作用強于沙粒的促進作用，另一方面，粒徑為0.015 mm，含沙量為1.0%的沙粒對流場結構的破壞較粒徑為0.005 mm，含沙量為1.0%的沙粒與清水介質(zhì)下的小，如圖9c所示，從而使得壓力變大，高于清水介質(zhì)，一定程度上抑制了空化的發(fā)展。

4.2 含沙量對離心泵空化特性的影響

以粒徑為0.010 mm，含沙量分別為0.5%、1.0%、1.5%的沙粒為研究對象，計算不同含沙量下的空化流動并與清水介質(zhì)進行比較，研究含沙量變化對離心泵空化特性的影響。圖10為清水介質(zhì)，粒徑為0.010 mm、不同含沙量下的含沙水空化流動性能曲線。

出口壓力為6.0×105Pa時，清水介質(zhì)中無空化泡形成，如圖11a所示；含沙量分別為0.5%、1.0%、1.5%時，葉片背面進口邊處均出現(xiàn)少量空化泡，如圖11b、11c、 11d所示，表明沙粒的存在促進了空化泡的產(chǎn)生，同時，含沙量的不同對空化泡的分布影響較小。

a.清水介質(zhì)a. Pure waterb.含沙量為0.5%b. Silt concentration is 0.5% c. 含沙量為1.0%c. Silt concentration is 1.0%d. 含沙量為1.5%d. Silt concentration is 1.5%

清水介質(zhì)中NPSHc為3.721 4 m，含沙量為0.5%時，NPSHc為4.780 1 m，表明沙粒促進空化的提前發(fā)生。含沙量為1.0%時，NPSHc為3.747 9 m，與清水介質(zhì)相比，兩者相對誤差為0.55%，表明沙粒對空化初生的影響較小。含沙量為1.5%時，NPSHc為3.490 6 m，表明沙粒抑制空化的發(fā)展。

空化在出口壓力為5.29×105Pa時得到充分發(fā)展，清水介質(zhì)、含沙量分別為0.5%、1.0%、1.5%的含沙水流所對應空化余量分別為3.436、3.841、3.438、2.960 4 m，表明：隨含沙量的增加，沙粒對空化發(fā)展的影響表現(xiàn)為先促進，后抑制?？栈莘植既鐖D12所示，含沙水流中，空化泡分布與清水介質(zhì)下的相比較，表現(xiàn)為先變大、再接近、后變小。清水介質(zhì)下?lián)P程為50.26 m，含沙水流下隨含沙量增加，揚程分別為50.04、49.94、40.61 m，表明，由于沙粒的磨蝕作用、沙粒摩擦對能量的消耗、沙粒對流場結構破壞[37]以及空蝕的破壞，使得含沙條件下空化充分發(fā)展時的揚程均低于清水介質(zhì)，且隨含沙量的增加，揚程逐漸變小。

a.清水介質(zhì)a. Pure waterb. 含沙量為0.5%b. Silt concentration is 0.5% c. 含沙量為1.0%c. Silt concentration is 1.0%d. 含沙量，1.5%d. Silt concentration is 1.5%

綜上分析可得，粒徑為0.010 mm，含沙量為0.5%的沙粒促進空化發(fā)展，主要原因為，沙粒對空化核子、拉應力與虛擬質(zhì)量力的影響與粒徑為0.005 mm的沙粒的促進作用相類似。同時沙粒與清水密度差的影響，當水流減速運動時，由于沙粒慣性的影響，沙粒速度高于清水介質(zhì)速度，兩者間的速度差，使得沙粒某處壓力降低，使得該點處流場壓力降低，進而促進空化的發(fā)展[38-39]。清水介質(zhì)中，最低壓力為?1.323×105Pa，粒徑為0.010 mm，含沙量為0.5%的含沙水流中，最低壓力為?1.342×105Pa，表明壓力在上述因素作用下，得到有效降低。另一方面，粒徑為0.010 mm，含沙量為0.5%的沙粒對流場結構破壞較清水介質(zhì)下嚴重，如圖13a、13b所示，從而加劇能量損失，致使壓力降低，促進空化發(fā)展。

粒徑為0.010 mm，含沙量為1.5%的沙粒抑制空化發(fā)展，主要原因為，含沙量為1.5%時，沙粒粘滯性起主導作用，即此時抑制作用強于空化核子、拉應力與虛擬質(zhì)量力等的促進作用，因而此時沙粒抑制空化發(fā)展。粒徑為0.010 mm，含沙量為1.5%的沙粒對流場結構的破壞較清水介質(zhì)下的小，如圖13a、13c所示，使得壓力變大，高于清水介質(zhì)，一定程度上抑制空化發(fā)展。

5 結 論

為了研究沙粒對離心泵空化特性的影響，本文通過計算不同粒徑、含沙量下的含沙水空化流動，得到如下結論：

1）出口壓力為6.0×105Pa，清水介質(zhì)中未出現(xiàn)空化泡；含沙條件下，均有少量空化泡出現(xiàn)；表明沙粒的存在對空泡的形成具有明顯的影響。

2）出口壓力為含6.0×105Pa，沙量為1.0%時，清水介質(zhì)中臨界空化余量值為3.721 4 m，沙粒粒徑分別為0.005、0.010、0.015 mm時，臨界空化余量分別為4.952、3.747 9、3.638 m，表明沙粒粒徑對空化的影響呈現(xiàn)為先促進、后抑制的變化趨勢。

3）出口壓力為含6.0×105Pa，粒徑為0.010 mm時，清水介質(zhì)中臨界空化余量值為3.721 4 m，含沙量分別為0.5%、1.0%、1.5%時，臨界空化余量值分別為4.780 1、3.747 9、3.490 6 m，表明含沙量對空化的影響呈現(xiàn)為先促進、后抑制的變化趨勢。

4）出口壓力為5.29×105Pa，空化充分發(fā)展時，同一含沙量、不同沙粒粒徑與同一粒徑、不同含沙量下，空化泡分布均呈現(xiàn)為先增大、再接近、后減小的變化趨勢，表明此2種情況下，沙粒對空化的影響均為先促進、后抑制。

[1] 潘森森，彭曉星. 空化機理[M]. 北京：國防工業(yè)出版社，2013：5－7.

Pan Sensen, Peng Xiaoxing. Physical Mechanism of Cavitation[M]. Beijing: National Defense Industry Press, 2013: 5－7. (in Chinese with English abstract)

[2] 王勇，劉厚林，袁壽其，等.離心泵非設計工況空化振動噪聲的試驗測試[J]. 農(nóng)業(yè)工程學報，2012,28(2)：35－38.

Wang Yong, Liu Houlin, Yuan Shouqi, et al. Experimental test on cavitation vibration and noise of centrifugal pump under off-design conditions[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2012, 28(2): 35－38. (in Chinese with English abstract)

[3] 王松林，譚磊，王玉川. 離心泵瞬態(tài)空化流動及壓力脈動特性[J]. 振動與沖擊，2013，32(22)：168－173.

Wang Songlin, Tan Lei, Wang Yuchuan. Characteristics of transient cavitation flow and pressure fluctuation for a centrifugal pump[J]. Journal of Vibration and Shock, 2013, 32(22): 168－173. (in Chinese with English abstract)

[4] Wei Yingsan, Shen Yang, Jin Shuanbao. Scattering effect of submarine hull on propeller non-cavitation noise[J]. Journal of Sound and Vibration, 2016(370): 319－335.

[5] 司喬瑞，袁壽其，李曉俊，等. 空化條件下離心泵泵腔內(nèi)不穩(wěn)定流動數(shù)值分析[J]. 農(nóng)業(yè)機械學報，2014，45(5)：84－90.

Si Qiaorui, Yuan Shouqi, Li Xiaojun, et al. Numerical simulation of unsteady cavitation flow in the casing of a centrifugal pump[J]. Transactions of the Chinese Society for Agricultural Machinery, 2014, 45(5): 84－90. (in Chinese with English abstract)

[6] 盧加興，袁壽其，任旭東，等. 離心泵小流量工況不穩(wěn)定性空化特性研究[J]. 農(nóng)業(yè)機械學報，2015，46(8)：54－58.

Lu Jiaxing, Yuan Shouqi, Ren Xudong, et al. Investigation of instabilities of cavitation at low flow rate of centrifugal pump[J]. Transactions of the Chinese Society for Agricultural Machinery, 2015, 46(8): 54－58. (in Chinese with English abstract)

[7] Liu Houlin, Liu Dongxi, Wang Yong, Experimental investigation and numerical analysis of unsteady sheet cavitating flow in a centrifugal pump[J]. Journal of Hydrodynamics, 2013, 25(3): 370－378.

[8] 黎慧青. 離心泵汽蝕磨損失效分析對策措施研究[D]. 廣州：華南理工大學，2011.

Li Huiqing. Studies of Cavitation and Fretting Wear of Centrifugal Pump and Counter Measures[D]. Guangzhou: South China University of Technology, 2011. (in Chinese with English abstract)

[9] 李根生，沈曉明，施立德，等. 空化和空蝕機理及其影響因素[J]. 石油大學學報，1997，21(1)：97－102.

Li Gensheng, Shen Xiaoming, Shi Lide, et al. Review of studies on cavitation and cavitation erosion[J]. Journal of the University of Petroleum, 1997, 21(1): 97－102. (in Chinese with English abstract)

[10] Zhang Yuning, Qian Zhongdong, Ji Bin. A review of microscopic interactions between cavitation bubbles and particles in silt-laden flow[J]. Renewable and Sustainable Energy Reviews, 2016, 56: 303－318.

[11] 吳玉林，唐學林，劉樹紅，等. 水力機械空化和固液兩相流體動力學[M]. 北京：中國水利水電出版社，2007.

[12] 常近時. 水質(zhì)狀況對泵裝置空化性能的重要影響[J]. 排灌機械，2008，26(2)：23－27.

Chang Jinshi. Important effect of state of water quality on cavitation pressure performance of pump device[J]. Drainage and Irrigation Machinery, 2008, 26(2): 23－27. (in Chinese with English abstract)

[13] 王磊，常近時. 考慮水質(zhì)狀況的空化流計算理論[J]. 農(nóng)業(yè)機械學報，2010，41(3)：62－66.

Wang Lei, Chang Jinshi. Computational theory of cavitating flows with consideration of influence of water quality[J]. Transactions of the Chinese Society for Agricultural Machinery, 2010, 41(3): 62－66. (in Chinese with English abstract)

[14] 常近時. 工質(zhì)為渾水時水泵與水輪機的空化與空蝕[J]. 排灌機械工程學報，2010，28(2)：93－97.

Chang Jinshi. Cavitation and cavitation erosion of pump and turbine with silt-laden water as working medium[J]. Journal of Drainage and Irrigation Machinery Engineering. 2010, 28(2): 93－97. (in Chinese with English abstract)

[15] 王磊，朱茹莎，常近時. 青銅峽與八盤峽水電站水中泥沙含量對空化壓力的影響[J]. 水力發(fā)電學報，2008，27(4)：45－47.

Wang Lei, Zhu Rusha, Chang Jinshi. Effect of sand concentration in water on cavitation pressure in Qingtongxia and Bapanxia hydropower stations[J]. Journal of Hydroelectric and Engineering, 2008, 27(4): 45－47. (in Chinese with English abstract)

[16] Huang Si, Ihara A, Watanabe H. Effects of solid particle properties on cavitation erosion in solid-water mixtures[J]. Journal of Fluids Engineering, 1996, 118: 749－755.

[17] Dunstan P J, Li S C. Cavitation enhancement of silt erosion: Numerical studies[J]. Wear, 2010, 268: 946－954.

[18] 鐵占續(xù)，黃建德. 含沙水汽蝕對離心泵損傷的試驗研究[J].化工設備與管道，2000，37(3)：42－44.

Tie Zhanxu, Huang Jiande. Damage test and research of sand and water cavitation for centrifugal pumps[J]. Process Equipments & Piping, 2000, 37(3): 42－44. (in Chinese with English abstract)

[19] 黃建德，張奎亭，陳漣. 含砂水對離心泵葉輪磨損的實驗研究[J]. 工程熱物理學報，1999，20(4)：448－452.

Huang Jiande, Zhang Kuiting, Chen Lian. Experimental studies on the damage of centrifugal impeller due to the sand mixed in water[J]. Journal of Engineering Thermophysics, 1999, 20(4): 448－452. (in Chinese with English abstract)

[20] Chen Haosheng, Liu Shihan, Wang Jiadao. Study on effect of microparticle’s size on cavitation erosion in solid-liquid system[J]. Journal of Applied Physics, 2007, 101(10): 1－5.

[21] Poulain S, Guenoun G, Gart S. Particle motion induced by bubble cavitation[J]. Physical Review Letters, 2015, 114(21): 1－5.

[22] Mizushimaa Y, Nagamia Y, Nakamuraa Y. Interaction between acoustic cavitation bubbles and dispersed particles in a kHz-order-ultrasound-irradiated water[J]. Chemical Engineering Science, 2013, 93: 395－400.

[23] Madadnia J, Owen I. Accelerated surface erosion by cavitating particulate-laden flows[J]. Wear, 1993, 165(1): 113－116.

[24] Madadnia J, Owen I. Erosion in conical diffusers in particulate-laden cavitating flows[J]. International Journal of Multiphase Flow, 1995, 21(6): 1253－1257.

[25] Gregorc B, Hribersek M, Predin A. The analysis of the impact of particles on cavitation flow development[J]. Journal of Fluids Engineering, 2011, 133(11): 4－11.

[26] Zhao Weiguo, Han Xiangdong, Liu Ming, et al. Numerical simulation of effects of sand grains and volume fractions on mass transferring from the water-liquid to the water-vapor[C]// The 7thInternational Conference on Pumps

and Fans. Hangzhou, China, 2015.

[27] 朱紅鈞，林元華，謝龍漢. Fluent 12 流體分析及工程仿真[M]. 北京：清華大學出版社，2011：88－91.

[28] Coutier-Delgosha O, Reboud J L, Delannoy Y. Numerical simulation of the unsteady behaviour of cavitating ?ow[J]. Int. J. Numer Meth Fluids, 2003, 42: 527－548.

[29] Coutier-Delgosha O, Stutz B, Vabre A, et al. Analysis of cavitating flow structure by experimental and numerical investigations[J]. J. Fluid Mech., 2007, 578: 171－222.

[30] Schnerr G H, Sauer J. Physical and numerical modeling of unsteady cavitation dynamics[C]//Proceedings of the 4th International Conference on Multiphase Flow, New Orleans, La, USA, 2001.

[31] Schnerr G H, Sezal I H, Schmidt S J. Numerical investigation of three-dimensional cloud cavitation with special emphasis on collapse induced shock dynamics[J]. Physics of Fluids, 2008, 20(4): 3－11.

[32] Nurick W H. Orifice cavitation and its effect on spray mixing[J]. Journal of Fluids Engineering, 1976, 98(4): 681－687.

[33] Rouse H, McNown J S. Cavitation and Pressure Distribution, Head Forms at Zero Angle of Yaw[M]. Iowa: State University of Iowa, 1948: 12－39.

[34] 朱茹莎. 含沙河流水電站水輪機吸出高度的合理確定[D]. 北京：中國農(nóng)業(yè)大學，2008.

Zhu Rusha. Rational Determination of Draft Head of the Turbine in the Silt-Laden Hydropower Station[D]. Beijing: China Agricultural University, 2008. (in Chinese with English abstract)

[35] 黃繼湯. 空化與空蝕的原理及應用[M]. 北京：清華大學出版社，1991：7－8.

[36] 袁亞雄，張小兵. 高溫高壓多相流體動力學基礎[M]. 哈爾濱：哈爾濱工業(yè)大學出版社，2004：71－74.

[37] 黃思杰，邵春雷. 輸送多組分介質(zhì)的離心泵內(nèi)部固液兩相流特性[J]. 農(nóng)業(yè)工程學報，2016，32(20)：77－84.

Huang Sijie, Shao Chunlei. Solid-liquid two-phase flow characteristics in centrifugal pump with multi-component medium[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2016, 32(20): 77－84. (in Chinese with English abstract)

[38] 王智勇. 基于FLUENT軟件的水力空化數(shù)值模擬[D]. 大連：大連理工大學，2006.

Wang Zhiyong. Numerical Simulation of Hydrodynamic Cavitation Based on FLUENT[D]. Dalian: Dalian University of Technology, 2006. (in Chinese with English abstract)

[39] 程則久，段生孝，黨云平，等. 含沙河流水輪機安裝高程的選定試驗研究[J]. 水力發(fā)電，1996(10)：34－37.

Chen Zejiu, Duan Shengxiao, Dang Yunping, et al. Test and study on setting height of water turbine in silt-laden water[J]. Journal of Hydroelectric Engineering, 1996(10): 34－37. (in Chinese with English abstract)

Effects of silt diameter and silt concentration on cavitation flow in centrifugal pump

Zhao Weiguo, Han Xiangdong, Li Rennian, Zheng Yingjie, Pan Xuwei

(1.,,730050,; 2.,730050,)

To study the effects of sand particles on the cavitation flow in the centrifugal pump, the method of computational fluid dynamics (CFD) was employed to study the internal cavitation flow field of the centrifugal pump in the pure water and sand water respectively. Based on Fluent 15.0, Mixture model, RNG-(renormalization group) turbulence model and Schnerr-Sauercavitation model were used to research the cavitation flow. For the cavitation flow in the sand water, sand mean diameters selected were 0.005, 0.010 and 0.015 mm and sand concentrations were 0.5%, 1.0% and 1.5% respectively. Unstructured grids constructed by ANSYS-ICEM(Integrated Computer Engineering and Manufacturing), were applied to disperse the computational domain. Accuracy of numerical calculation was improved by grids independence check and the total number used was 2 817 398. Numerical results of pure water performance of the centrifugal pump and cavitation flow around the flat-nosed cylinder were compared with the experimental results to verify the reasonableness of the algorithm used in the simulations. Numerical results revealed that the algorithm designed was appropriate to simulate cavitation flow. To lower the turbulent viscosity in cavitation region, RNG-turbulence model was modified. Cavitation performance curves were built, the vapor had the volume fraction of 0.1 in different cavitation periods, and the effect of sand particles on the cavitation flow was investigated. To study the effect of sand mean diameter, sand concentration was 1.0% and sand mean diameter was increased from 0.005 to 0.015 mm gradually. When the outlet pressure was 6.0×105Pa, cavitation did not occur in the pure water of the centrifugal pump and vapor did not exist in the pure water. In the sand water, a few cavitation bubbles appeared. For the critical net positive suction head (NPSHc) which was the NPSH when the head was reduced by 3.0%. In the pure water, it was 3.721 4 m and in the sand water with sand mean diameter of 0.005, 0.010 and 0.015 mm, it was 4.952, 3.747 9 and 3.638 m respectively, and when cavitation developed fully, theNPSH was 3.436, 3.541, 3.438 and 3.337 m respectively for the pure water and the sand water with 3 different sand mean diameters, indicating that the effects of sand particles on the cavitation flow were accelerative at first, and then inhibited. When sand mean diameter was 0.010 mm, in the critical cavitation stage and cavitation full development stage, NPSH in the pure water and sand water had inconspicuous difference. Compared with cavitation occurring in the pure water, when sand mean diameter was 0.010 mm, sand particles had little effect on the development of cavitation in the sand water. To study the effect of sand concentration, sand mean diameter was 0.010 mm and sand concentration increased from 0.5% to 1.5% gradually. Under outlet pressure of 6.0×105Pa, cavitation did not occur in the pure water of the centrifugal pump and vapor did not appear in the pure water too. And a few cavitation bubbles existed in the sand water, stating clearly that sand particles had a close relation with the formation of cavitation bubbles. In the critical cavitation period, NPSHc was 3.721 4, 4.780 1, 3.747 9 and 3.490 6 m respectively for the pure water and the sand water with 3 different sand concentrations of 0.5%, 1.0% and 1.5%, and in the cavitation full development period, NPSHwas 3.436, 3.841, 3.438 and 2.960 4 m separately, explaining that effects of sand concentration on the cavitation flow were accelerative at first, and then inhibited too. When sand concentration was 1.0%, in the critical cavitation period and cavitation full development period, NPSH in the pure water and sand water had little difference, illustrating that compared with cavitation occurring in the pure water, sand particles had little effect on the development of cavitation under the 1.0% sand concentration. When sand particles promoted the development of cavitation, volume of vapor with volume fraction of 0.1 in sand water was larger than that in the pure water. During sand particles inhibiting the development of cavitation, the volume was smaller than that in the pure water. For sand particles had little effect on the evolution of cavitation, the distribution was similar. During cavitation fully evolving, interaction of abrasion and cavitation erosion made the head in sand water less than that in the pure water. With sand concentration being invariant, when sand mean diameter increased and with sand mean diameter being constant, when volume fraction increased gradually, head in sand water decreased continuously. Number of cavitation nuclei, virtual mass force, slip velocity, and so on had a close connection with sand particles promoting the development of cavitation. Viscosity, abrasion effect, and so on had a close relationship with sand particles inhibiting the evolution of cavitation.

centrifugal pumps; computer simulation; models; cavitation; silt mean diameter; silt concentration

10.11975/j.issn.1002-6819.2017.04.017

TH311

A

1002-6819(2017)-04-0117-08

2016-06-08

2017-02-07

國家自然科學基金項目資助（51269011）；甘肅省高等學?；究蒲袠I(yè)務費。

趙偉國，男，山東東營人，博士，副教授，主要從事流體機械空化與空蝕機理研究。蘭州 蘭州理工大學能源與動力工程學院，730050。 Email：zhaowg@zju.edu.cn

趙偉國，韓向東，李仁年，鄭英杰，潘緒偉. 沙粒粒徑與含沙量對離心泵空化特性的影響[J]. 農(nóng)業(yè)工程學報，2017，33(4)：117－124. doi：10.11975/j.issn.1002-6819.2017.04.017 http://www.tcsae.org

Zhao Weiguo, Han Xiangdong, Li Rennian, Zheng Yingjie, Pan Xuwei. Effects of silt diameter and silt concentration on cavitation flow in centrifugal pump[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(4): 117－124. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2017.04.017 http://www.tcsae.org