正態(tài)曲面丁壩三維水流數(shù)值模擬

孫志林,於剛節(jié),許　丹,馬國(guó)淇

(浙江大學(xué) 港口海岸及近海工程研究所,浙江 杭州 310058)

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正態(tài)曲面丁壩三維水流數(shù)值模擬

孫志林,於剛節(jié),許丹,馬國(guó)淇

(浙江大學(xué) 港口海岸及近海工程研究所,浙江 杭州 310058)

摘要:針對(duì)丁壩周圍流動(dòng)呈強(qiáng)三維紊流特征,相應(yīng)壩頭局部床面不可避免地產(chǎn)生沖刷坑,嚴(yán)重時(shí)導(dǎo)致丁壩水毀的問(wèn)題,提出正態(tài)曲面形式的新型丁壩結(jié)構(gòu),可以優(yōu)化丁壩周圍水流結(jié)構(gòu),減小壩頭局部沖刷.基于三維數(shù)值模擬研究新型丁壩的水動(dòng)力特性.結(jié)果表明,與梯形丁壩相比,正態(tài)曲面丁壩可以起到平順?biāo)?、減少劇烈紊動(dòng)和增大過(guò)流面積的作用,避免流線過(guò)度彎曲和集中,減小丁壩周圍的渦量強(qiáng)度,在一定程度上減弱壩頭水動(dòng)力.壩頭曲面能夠削弱壩頭下潛流的沖刷作用,降低壩頭局部沖刷深度,利于丁壩穩(wěn)定.

關(guān)鍵詞：正態(tài)曲面；丁壩；三維水流

丁壩是航道整治與維護(hù)工程中廣泛應(yīng)用的一種水工建筑物,可以起到束窄水流,沖深河槽的作用,同時(shí)能夠減弱岸邊流速,保護(hù)河岸免受沖刷[1].丁壩會(huì)改變流向,迫使水流繞過(guò)壩頭,局部地改變了流動(dòng)形態(tài).同時(shí),丁壩使河道流線集中,自壩頭至壩后產(chǎn)生分離渦,呈強(qiáng)三維紊流特征,在繞流和馬蹄渦作用下壩頭床面形成局部沖刷坑,易誘發(fā)丁壩水毀.

人們采取各種措施,如合理設(shè)置丁壩壩長(zhǎng)、壩高、間距、挑角等[2-8],以最大限度地防護(hù)河岸和改善通航條件.有些學(xué)者在壩體結(jié)構(gòu)形式方面開(kāi)展了研究,試圖平順壩頭水流,減少局部沖刷.Uijttewaal[9]提出上半部分為常規(guī)丁壩,下半部分為透水樁壩的組合式丁壩；周銀軍等[10]研究樁式透水丁壩水流及沖淤特性,發(fā)現(xiàn)透水丁壩在自身防護(hù)和保護(hù)范圍兩方面均優(yōu)于普通不透水丁壩；丁晶晶提出臺(tái)階式的新型丁壩結(jié)構(gòu),對(duì)該結(jié)構(gòu)的水動(dòng)力特性及防沖效應(yīng)進(jìn)行研究[11],臺(tái)階式壩頭能夠逐級(jí)分散集中繞流,將大流速和大渦量強(qiáng)度區(qū)外移,利于丁壩穩(wěn)定；鄧年生[12]結(jié)合天然水流的自然特性,提出一種空間流線型的丁壩結(jié)構(gòu),節(jié)省了工程費(fèi)用,整治效果也更好.

對(duì)于以防護(hù)河岸為主要目的的丁壩,其發(fā)生水毀后,容易導(dǎo)致河岸受水流沖蝕淘刷.為了保證河岸防護(hù)效果,并減少壩頭局部沖刷,本文提出新型的丁壩結(jié)構(gòu)形式,即正態(tài)曲面丁壩,并通過(guò)數(shù)值模擬的方法,研究新型丁壩附近的水動(dòng)力特性.

1數(shù)學(xué)模型

1.1控制方程

對(duì)于丁壩周圍強(qiáng)三維紊流運(yùn)動(dòng),宜采用雷諾平均的連續(xù)性方程和動(dòng)量守恒方程：

(1)

(2)

式中：t為時(shí)間,xi(i=1,2,3)為坐標(biāo)軸x、y、z方向上的坐標(biāo)分量,ui(i=1,2,3)為xi軸向上的速度分量,p為壓力,ρ和μ為流體的密度和動(dòng)力黏性系數(shù).式(2)中右手第3項(xiàng)為紊動(dòng)應(yīng)力梯度,需要紊流模型加以封閉,本文采用RNGk-ε二方程紊流模型,形式如下：

(3)

(4)

1.2自由水面處理

采用VOF法處理自由水面的基本思想如下：在網(wǎng)格單元中定義水的體積比函數(shù)F∈[0,1][14],F=0說(shuō)明該單元全為氣體,F=1表示單元充滿水體,當(dāng)0

(5)

αw的梯度可以確定自由水面的法線方向,計(jì)算出αw后,可以確定各網(wǎng)格中自由水面的近似位置.

VOF的k-ε模型與單相的k-ε模型在形式上完全一致,只是在密度ρ和黏性系數(shù)μ的表達(dá)式上有細(xì)微不同.兩者都是通過(guò)單元的體積分?jǐn)?shù)作加權(quán)平均后給出,即兩個(gè)值都是體積分?jǐn)?shù)的函數(shù)而不是單相流模型中的常數(shù),具體形式如下：

ρ=αwρw+(1-αw)ρa(bǔ),

(6)

μ=αwμw+(1-αw)μa.

(7)

式中：ρw與ρa(bǔ)分別為水和空氣的密度,μw與μa分別為水和空氣的黏性系數(shù).

2模型驗(yàn)證

采用Tmoinaga和Chiba的實(shí)驗(yàn)數(shù)據(jù)[15]進(jìn)行驗(yàn)證,試驗(yàn)水槽及丁壩示意圖如圖1所示.設(shè)x軸為沿水流方向,y軸為橫斷面方向,z軸為沿水深方向.水槽長(zhǎng)度為8 m,寬0.3 m,丁壩位于x=4 m的位置,長(zhǎng)0.15 m,寬0.03 m,高0.05 m.體積流量為3.6×10-3m3/s,水深約為0.09 m.

圖1　丁壩模型示意圖Fig.1　Sketch of spur dike model

驗(yàn)證模型選取了從x=3 m到x=6 m的水槽區(qū)域,并在模型上方增加了空氣區(qū)域,計(jì)算域尺寸為3 m×0.3 m×0.18 m,網(wǎng)格數(shù)為150×16×22,時(shí)間步長(zhǎng)為0.02 s,在丁壩附近及近壁面處對(duì)網(wǎng)格進(jìn)行加密.

分別取x=4.0 m,z=0.07 m；x=4.1 m,z=0.01 m；x=4.05 m,z=0.02 m；x=4.05 m,z=0.07 m處的4條驗(yàn)證線為dir.1、dir.2、dir.3、dir.4,流速分布的計(jì)算結(jié)果與實(shí)測(cè)數(shù)據(jù)比較見(jiàn)圖2、3.圖中,v為速度，vm為時(shí)均流速.

圖2　dir.1&2流速對(duì)比Fig.2　Comparison of flume and model results at dir.1&2

圖3　dir.3&4流速對(duì)比Fig.3　Comparison of flume and model results at dir.3&4

由流速對(duì)比圖可以看出,數(shù)值模擬結(jié)果與實(shí)驗(yàn)數(shù)據(jù)在數(shù)值和斷面分布上都比較吻合,模擬效果良好,說(shuō)明該模型是可靠的,可以用于新型丁壩附近的流場(chǎng)計(jì)算與分析.

3新型丁壩附近水動(dòng)力特性

圖4　丁壩計(jì)算模型及網(wǎng)格示意圖Fig.4　Sketch and grid of spur dike models

3.1流速分布

圖5、6給出兩種丁壩周圍的近底流速分布.可見(jiàn),梯形丁壩和正態(tài)曲面丁壩附近均存在集中繞流現(xiàn)象,相比之下,正態(tài)曲面丁壩壩頭繞流較弱,大流速區(qū)域(v>0.14 m/s)的面積減小了約75%.這是由于新型丁壩采用流線型的正態(tài)曲面設(shè)計(jì),不但增大了過(guò)流面積,同時(shí)使水流相對(duì)平順的通過(guò)壩體,避免了梯形丁壩壩頭處水流突然聚集的現(xiàn)象.

圖5　梯形丁壩近底面流速分布Fig.5　Velocity of trapezoid spur dike

圖6　新型丁壩近底面流速分布Fig.6　Velocity of new spur dike

3.2壩頭下潛流

兩種丁壩周圍下潛流的分布如圖7、8所示.圖中,虛線表示壩面范圍.由圖7、8可見(jiàn),正態(tài)曲面丁壩迎流面將壩前來(lái)流上挑越過(guò)丁壩,壩前出現(xiàn)較大面積的上升流,壩后下潛流的大流速區(qū)主要集中在壩面上,因而不會(huì)對(duì)壩頭產(chǎn)生直接沖刷.梯形丁壩的下潛流大流速區(qū)延伸較長(zhǎng),繞過(guò)壩頭至后方直沖床面,容易產(chǎn)生顯著的局部沖刷.從丁壩中心斷面流速矢量圖(見(jiàn)圖9)可以看出,正態(tài)曲面丁壩由于前端與床面相切,下潛流角度較梯形丁壩要緩得多,這避免了壩頭水流直接沖擊床面,起到減少局部沖刷的作用.

圖7　梯形丁壩近底面下潛流速分布Fig.7　Down-flow velocity of trapezoid spur dike

圖8　新型丁壩近底面下潛流速分布Fig.8　Down-flow velocity of new spur dike

圖9　兩種丁壩中心的斷面流速矢量Fig.9　Flow velocity vectors along spur dikes cross sections

3.3壩頭渦量強(qiáng)度

壩頭的漩渦對(duì)沖刷坑的形成有重要作用,漩渦的強(qiáng)弱可以用渦量強(qiáng)度Ω來(lái)反映.計(jì)算給出兩種丁壩壩面及附近床面的渦量分布.如圖10、11所示,正態(tài)曲面丁壩壩頭附近的渦量強(qiáng)度大幅減小,強(qiáng)渦量的范圍相應(yīng)減小,其中最大渦量強(qiáng)度減小了將近40%,效果十分明顯.這主要是由于壩面的流線型設(shè)計(jì),使壩頭集中繞流減弱,流速梯度相應(yīng)減小,從而削弱了壩頭漩渦產(chǎn)生的條件.

圖10　梯形丁壩壩頭渦量強(qiáng)度Fig.10　Vorticity of trapezoid spur dike

圖11　新型丁壩壩頭渦量強(qiáng)度Fig.11　Vorticity of new spur dike

4結(jié)語(yǔ)

本文首次提出新型的正態(tài)曲面丁壩結(jié)構(gòu),旨在保證河岸防護(hù)效果的前提下,優(yōu)化丁壩附近水流結(jié)構(gòu)、減少壩頭局部沖刷.基于三維數(shù)值模擬分析新型丁壩周圍的水動(dòng)力特性.結(jié)果表明,流線型的正態(tài)曲面可以平順壩面水流、減少劇烈紊動(dòng)并增大過(guò)流面積,使水流平緩地流過(guò)壩體,從而減弱了集中繞流,壩頭附近的大流速區(qū)面積和渦量強(qiáng)度相應(yīng)大幅減小.尤其是流線型壩面可以避免下潛流直沖床面,大大降低沖刷作用,致使最大局部沖刷深度明顯減小.該新型曲面丁壩對(duì)河岸防護(hù)和河口治理具有重要的應(yīng)用價(jià)值.

本文初步研究了正態(tài)曲面丁壩周圍的水動(dòng)力特性,為之后的工作奠定了基礎(chǔ).正態(tài)曲面丁壩壩面由雙變量正態(tài)曲面函數(shù)決定,在具體形態(tài)上可變可調(diào),所以有必要在后續(xù)研究中針對(duì)實(shí)際的河道情況對(duì)不同條件、不同形式下的壩體進(jìn)行計(jì)算,并對(duì)曲面形式進(jìn)行分析優(yōu)化,同時(shí)輔以相應(yīng)的物理模型實(shí)驗(yàn),使該研究結(jié)果能夠具有更好的普適性,從而很好地應(yīng)用于工程實(shí)際.

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收稿日期：2015-07-17.浙江大學(xué)學(xué)報(bào)(工學(xué)版)網(wǎng)址： www.journals.zju.edu.cn/eng

基金項(xiàng)目：教育部博士點(diǎn)基金資助項(xiàng)目(20120101110108)；國(guó)家自然科學(xué)基金資助項(xiàng)目(40776007).

作者簡(jiǎn)介：孫志林(1956-)，男，教授，從事水沙動(dòng)力學(xué)與河口海岸數(shù)值模擬研究.ORCID:0000-0002-6446-3472.E-mail: oceansun@zju.edu.cn 通信聯(lián)系人：許丹，女，助理研究員. ORCID:0000-0002-0999-0253.E-mail: darrenxu@zju.edu.cn

DOI:10.3785/j.issn.1008-973X.2016.07.004

中圖分類號(hào)：TV 863

文獻(xiàn)標(biāo)志碼：A

文章編號(hào)：1008-973X(2016)07-1247-05

Three-dimensional numerical simulation of flow around spur dike with bivariate normal surface

SUN Zhi-lin, YU Gang-jie, XU Dan, MA Guo-qi

(InstituteofPort,CoastalandOffshoreEngineering,ZhejiangUniversity,Hangzhou310058,China)

Abstract:The flow around a spur dike has strong three-dimensional turbulent characteristics, which leads to the development of a local scour around the groyne inevitably and may cause damage of the whole works. The damage of spur dike leads some problems. The river-bank will be washed by jet flow easily when it’s without the spur’s protection, which may influence channel stability. A new spur dike with bivariate normal surface was proposed to optimize the flow structure and reduce the local scour at the groyne head in order to avoid the problems. A series of numerical simulations were conducted in order to study the hydrodynamic characteristics of the new structure. The simulation results show that the bivariate normal surface can smooth the flow, reduce severe turbulence and enlarge the flow area, which make streamline not to gather together suddenly. The intensity of vorticity and flow dynamics around the groyne head were reduced. The curved surface can weaken the down-flow, which reduces the local scour and benefits the stability of spur dike．

Key words:bivariate normal surface; spur dike; three-dimensional hydrodynamic