仿自然魚道中卵石墻對池室水力特性改善效果

李廣寧，孫雙科※，柳海濤，張 超，趙桂俠，鄭鐵剛

仿自然魚道中卵石墻對池室水力特性改善效果

李廣寧1，孫雙科1※，柳海濤1，張 超1，趙桂俠2，鄭鐵剛1

（1. 中國水利水電科學(xué)研究院流域水循環(huán)模擬與調(diào)控國家重點(diǎn)實(shí)驗(yàn)室，北京 100038；2. 天津大學(xué)水利工程仿真與安全國家重點(diǎn)實(shí)驗(yàn)室，天津 300072）

仿自然魚道是重要的魚道布置方式之一，其特點(diǎn)是利用當(dāng)?shù)睾哟膊牧蠘?gòu)建透水性卵石隔墻，以便更好地模擬出天然河流流態(tài)。為了定量分析透水性卵石墻對魚道水力特性的改善效果，該文針對采用卵石隔墻與不透水隔墻的魚道水力特性進(jìn)行對比研究。結(jié)果表明：采用卵石墻的仿自然魚道，池室內(nèi)流態(tài)豐富，過魚口處流速分布差異明顯，表底流速差達(dá)到0.43～0.61 m/s為多種魚類上溯提供了可能。池室內(nèi)主流區(qū)分布較寬，紊動能較大達(dá)0.06～0.12 m2/s2，同時回流區(qū)減弱，有利于魚類找到主流，實(shí)現(xiàn)上溯。卵石隔墻的不足之處是魚道耗水流量相對較大達(dá)2.86 m3/s，在工程設(shè)計(jì)中需要綜合考慮卵石墻透水特性與耗水流量之間的平衡關(guān)系，找到適宜的布置方案。該研究可為仿自然魚道的水力設(shè)計(jì)提供參考。

魚道；流速；流量；紊動能；耗水流量；數(shù)值模擬

李廣寧，孫雙科，柳海濤，張 超，趙桂俠，鄭鐵剛. 仿自然魚道中卵石墻對池室水力特性改善效果[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2017，33(15)：184－189. doi：10.11975/j.issn.1002-6819.2017.15.024 http://www.tcsae.org

Li Guangning, Sun Shuangke, Liu Haitao, Zhang Chao, Zhao Guixia, Zheng Tiegang. Improving effect of hydraulic characteristics of nature-like fishway with pools and cobblestone weirs[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(15): 184－189. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2017.15.024 http://www.tcsae.org

0 引 言

魚道是幫助魚類克服障礙物（如各種壩、堰、水閘）實(shí)現(xiàn)洄游上溯的設(shè)施[1]。魚道分為技術(shù)型魚道和仿自然魚道，傳統(tǒng)的技術(shù)型魚道（如丹尼爾式魚道、豎縫式魚道等）的結(jié)構(gòu)與流態(tài)相對單一，一般僅適合特定過魚對象[2-6]，而在實(shí)際工程中，同一條河流中需要保護(hù)的魚類種類往往是多樣的，且魚類體型相差懸殊、生活習(xí)性和克流能力均不相同[7-9]。與傳統(tǒng)技術(shù)型魚道相比，仿自然魚道構(gòu)建的水流流態(tài)更接近于魚類熟悉的天然狀態(tài)，對魚類往往具有更廣的適用性和更高的過魚效率[10-11]。

仿自然魚道常采用水池-淺灘型式[12]，其特點(diǎn)是采用梯級低堰將魚道分隔成一系列的淺灘和深池，淺灘處水深較淺，流速較大，而深池內(nèi)水流緩慢。池室型仿自然魚道[13]是由這種魚道發(fā)展而來，其特點(diǎn)是采用隔墻將魚道分隔成多級水池，墻體通常為卵石墻（數(shù)塊卵石堆疊而成的下寬上窄的墻體），卵石間縫這種分隔方式建造的魚道，不但能夠就地取材，利用漂石與天然河道床沙質(zhì)，其水流還兼具水池式魚道與技術(shù)型魚道的雙重特性。

目前，國外針對仿自然魚道的水力特性已開展了一些研究[14-15]，國內(nèi)的相關(guān)研究尚處于起步階段[16]。相比而言，國外學(xué)者比較重視研究各種塊體障礙物對水流結(jié)構(gòu)的影響，如Acharya等[17]針對球狀障礙物、圓柱體和方柱體對水流結(jié)構(gòu)的影響進(jìn)行了模型試驗(yàn)，提出為了達(dá)到相似水流條件（弗洛德數(shù)Fr），球體的排列應(yīng)該比方柱體的排列略微緊密一些，但是球體障礙物尾流區(qū)水面連接更加平順。加拿大Alberta大學(xué)的Bretón等[18]研究了蠻石斜坡型魚道中，蠻石間的流速與紊動強(qiáng)度等水力學(xué)參數(shù)，認(rèn)為蠻石布置間距應(yīng)該足夠小，以遏制水流的加速，蠻石后尾流區(qū)的紊動能在一定的范圍內(nèi)變化（0.05～0.25 m2/s2）。Baki等[19-20]通過試驗(yàn)研究也得出了類似結(jié)論。Lacey等除了進(jìn)行蠻石周圍的紊流結(jié)構(gòu)的試驗(yàn)研究[21]，還實(shí)測了自然河流中典型蠻石周邊的水流流場及紊動能等水力參數(shù)，發(fā)現(xiàn)在天然河道中蠻石后的尾流區(qū)內(nèi)往往會形成較強(qiáng)烈的紊動[22]。在數(shù)值模擬方面，Tran等[23]利用淺水方程對蠻石斜坡型魚道的水流特性進(jìn)行了模擬，并進(jìn)行了試驗(yàn)驗(yàn)證。何雨艨等[24]采用三維湍流模型對不同工況的蠻石斜坡型魚道進(jìn)行了數(shù)值模擬與試驗(yàn)驗(yàn)證，認(rèn)為蠻石坎對縫排列比錯縫排列具有更加合理的魚道水力學(xué)特性。

本文采用Flow-3D軟件，分別針對池室型仿自然魚道內(nèi)，采用卵石墻與不透水墻2種型式進(jìn)行三維數(shù)值模擬，對兩者的流態(tài)、流速、紊動能以及過流流量進(jìn)行對比分析，以明晰兩者水力特征的區(qū)別，為工程實(shí)際應(yīng)用提供參考。

1 數(shù)學(xué)模型及驗(yàn)證

1.1 基本方程及求解方法

數(shù)值模擬采用standard k-ε湍流模型[25]，該模型基本方程包括水流連續(xù)方程、動量方程、紊動能及其耗散率方程。

連續(xù)方程：

動量方程：

紊動能k方程：

紊動能耗散率ε方程：

式中t為時間，s；u、v、w 為x、y、z方向的時均速度分量為坐標(biāo)分量，m/s；ρ為密度，kg/m3；μ、μt分別為黏性系數(shù)和紊動黏性系數(shù)，m2/s；p為時均壓強(qiáng)，Pa；k為紊動能，m2/s2；ε為紊動能耗散率，m2/s3；Gk為紊動能產(chǎn)生項(xiàng)，各項(xiàng)紊流常數(shù)取值為Cμ=0.09，σε=1.3，σk=1.0，C1ε=1.44，C2ε=1.92。

液體自由表面采用VOF方法進(jìn)行計(jì)算[26]，通過計(jì)算水和氣的體積分?jǐn)?shù)來表征物體的形態(tài)，aa表示氣體的體積分?jǐn)?shù)，aw表示水的體積分?jǐn)?shù)，其控制方程

模型求解采用有限體積法，二階迎風(fēng)格式，壓力-速度耦合采用壓力校正法，離散方程的求解采用GMRES法，時間差分采用全隱格式。

1.2 水體中障礙物的計(jì)算方法

計(jì)算模型中對于魚道內(nèi)具有一定透水性的卵石隔墻，采用FAVOR（fractional area/volume ratios）方法[27]進(jìn)行定義。其原理是利用控制體積（網(wǎng)格）的6個面定義出可以有通量通過的局部面積與可自由通過體積的比率，若無可以讓流體通過的面積則交界面不會有對流的通量，即FAVOR技術(shù)提供每個控制體積對于流體與障礙物交界面積的決定方法，網(wǎng)格與物體幾何形狀相互獨(dú)立。盡管模型復(fù)雜，利用FAVOR技術(shù)也可以精確的表示其經(jīng)過網(wǎng)格計(jì)算后的外觀。引入VF=開放體積/單元體積，為網(wǎng)格可通過的通量比率，即通量體積比（fractional volume ratio），AF=開放面積/單元邊面積，為各面可通過的通量比率，即通量面積比(fractional area ratio)，網(wǎng)格內(nèi)包含的灰色部分不會有通量通過，定義為障礙物，其余部分通量可通過，如圖1所示，即以網(wǎng)格數(shù)目尺寸來表現(xiàn)原有體型的外觀，并判斷目前網(wǎng)格密度能否精確反應(yīng)模型外觀，避免因網(wǎng)格密度不足造成結(jié)果不精確。

圖1 FAVOR技術(shù)障礙物定義示意圖Fig.1 Schematic diagram of obstacle in FAVOR technology

1.3 模型體型及邊界條件

本文以某擬建魚道工程為基礎(chǔ)開展研究，該魚道工程主要過魚對象為短須裂腹魚，體長0.25～0.36 m，持續(xù)泳速0.59～1.17 m/s，突進(jìn)泳速1.17～2.50 m/s。

魚道數(shù)值模型的模擬范圍包括水平段和池室段2個部分，水平段長15 m，池室段長40 m，池室段內(nèi)共模擬5級魚池。魚道橫斷面為梯形，底寬5 m，頂寬12.5 m，邊坡系數(shù)1.5，底坡1%。過魚口位于河槽左側(cè)，寬度1.0 m，隔墻采用交錯布置型式，開口處出流方向與主槽呈45o夾角。研究中針對池室隔墻為卵石墻和不透水墻2種型式，分別建立數(shù)學(xué)模型。其中，透水卵石墻的卵石粒徑為15～30 cm (當(dāng)?shù)伫Z卵石粒徑范圍)，共堆疊3層，底部大，頂端小，呈金字塔狀，依靠自重保持結(jié)構(gòu)穩(wěn)定，總高1.8 m，底厚1.5 m，間距6.5 m；不透水墻體型是將卵石墻替換為的矩形隔墻，其高度、厚度和位置均保持不變。上述布置體型見圖2a與2b。

計(jì)算模型采用嵌套加密的矩形網(wǎng)格，卵石墻附近網(wǎng)格尺寸0.05 m，其余部位網(wǎng)格尺寸0.1～0.5 m，網(wǎng)格總數(shù)約176萬。計(jì)算網(wǎng)格劃分情況如圖2c所示。

計(jì)算過程中，模型入口和出口邊界均設(shè)置為固定水深1.4 m；卵石墻與固壁均采用無滑移條件；卵石表面糙率取值，nl=0.015；魚道邊壁及池底糙率參照魚道實(shí)際情況進(jìn)行取值，np=0.03；卵石墻的孔隙率約12%，為縱剖面孔隙所占過流面積的比例。

圖2 具有不同隔水墻的魚道模型及其網(wǎng)格劃分Fig.2 Fishways with different weir types and computational mesh

1.4 模型驗(yàn)證

卵石墻仿自然魚道模型按重力相似準(zhǔn)則設(shè)計(jì)，模型比尺λL=5，其結(jié)構(gòu)布置形式與數(shù)值計(jì)算體型一致。仿自然魚道原型底部糙率為0.03，由糙率比尺=λ1/6=1.308可知，模型基礎(chǔ)糙率應(yīng)為n=0.023。模型試驗(yàn)中，魚道基礎(chǔ)底面采用混凝土抹面，糙率為n=0.014，因此需要通過加糙試驗(yàn)，達(dá)到目標(biāo)糙率。

由明渠均勻流公式可知，明渠糙率n可以表達(dá)為式中，A為體型明渠過水面積，m2；Q為流量，m3/s；R為水力半徑，m；J為渠底坡降，%。根據(jù)模型橫斷面尺寸，可知過水面積A=h(b+mh)=h(1+1.5h)；對應(yīng)濕周；對應(yīng)的水力半徑為。由此可知，只要知道上游來流量Q和均勻流水深h，即可求解渠道糙率值n。試驗(yàn)中采用了正方形梅花加糙方法，顆粒直徑2.5 cm，顆粒之間間距20 cm，測得模型糙率在0.022～0.023之間，滿足試驗(yàn)精度要求。

試驗(yàn)中通過調(diào)節(jié)進(jìn)口來流流量及出口尾門的開度，確保魚道上下游水深均為1.4 m。試驗(yàn)測點(diǎn)布置如圖3a所示，其中V1～V6為速度測點(diǎn)，位于各級池室過魚口處，A1～E2均為水面線測點(diǎn)，位于隔墻上下游滯水區(qū)。圖3b與3c為流速和水面線的試驗(yàn)與計(jì)算結(jié)果對比，流速誤差小于0.1 m/s，水面線誤差小于0.05 m，表明兩者吻合良好。

圖3 測點(diǎn)布置、流速、水面線計(jì)算值和試驗(yàn)值Fig.3 Arrangement of measuring points and comparison of simulation and test velocity values and water surface elevation

2 結(jié)果與分析

2.1 流態(tài)和流速

根據(jù)魚道設(shè)計(jì)基本原則，魚道池室內(nèi)最大流速一般出現(xiàn)在過魚口附近，其大小決定了魚類是否能夠成功通過該水池，其值以不超過魚類的突進(jìn)流速為宜[28-29]。過魚口處的流速分布在垂向上應(yīng)存在一定差異，可為不同游泳能力的魚類的提供上溯通道。主流區(qū)分布范圍不宜過于集中，兩側(cè)不宜形成大范圍的回流區(qū)，以便于休息區(qū)的魚類能夠迅速找到主流，繼續(xù)上溯，池室內(nèi)休息區(qū)的水流具有豐富的流態(tài)，以接近自然河流形態(tài)為宜[11]，可為魚類提供休息、覓食場所與上溯通道。上述流場特性的影響因素較多，如隔墻類型，底坡變化，運(yùn)行水深等等。

圖4a和4b為卵石墻池室內(nèi)表層與底層流場計(jì)算結(jié)果。分析表明，其主流流速呈現(xiàn)“表層小，底層大”的分布規(guī)律。卵石墻開口處流速分布具有“表層小，底層大，兩側(cè)小，中間大”的特征，如流速測點(diǎn)V3的表底流速在1.33～1.94 m/s，差值為0.61 m/s，測點(diǎn)V4的表底流速在1.43～1.86 m/s，差值為0.43 m/s。流速量值垂向分布范圍較寬，且介于魚類突進(jìn)泳速1.17～2.5 m/s范圍內(nèi)，滿足目標(biāo)魚類上溯需求。主流兩側(cè)未出現(xiàn)大范圍回流區(qū)，有利于魚類重新感應(yīng)主流，繼續(xù)上溯。

圖4c和4d為不透水墻池室內(nèi)表層與底層流場計(jì)算結(jié)果，相比而言，其流態(tài)分布更接近于技術(shù)型魚道。首先，池室開口處流速分布上下基本一致。如流速測點(diǎn)V3的表底流速在1.56～1.64 m/s，差值為0.08 m/s，測點(diǎn)V4的表底流速在1.63～1.69 m/s，差值為0.06 m/s。流速分布較為單一。其次，主流區(qū)較為集中，休息區(qū)內(nèi)分別形成了兩個回流區(qū)，主流區(qū)與回流區(qū)之間存在流速接近于0的流速帶，不利于魚類發(fā)現(xiàn)主流，實(shí)現(xiàn)上溯。

圖4 兩種體型第3級水池（池3）流速分布Fig.4 Velocity distributions of third stage pool (Pool 3) in two schemes

2.2 紊動能

水流紊動能（turbulence kinetic energy, TKE）是反映水流紊動強(qiáng)度的指標(biāo)，魚道中水流保持適當(dāng)?shù)奈蓜訌?qiáng)度，一方面有利于魚類感應(yīng)主流位置，同時也有利于增加水體含氧量，維持水質(zhì)指標(biāo)[30-31]。圖5為卵石隔墻與不透水條件下，池室內(nèi)表層與底層水體紊動能分布。計(jì)算結(jié)果分析表明，采用不透水墻的仿自然魚道，池室內(nèi)主流區(qū)紊動能僅為0.01～0.06 m2/s2；采用卵石墻的仿自然魚道，受卵石不規(guī)則外形和縫隙間水流的沖擊影響，池室內(nèi)主流區(qū)紊動能可達(dá)0.06～0.12 m2/s2，便于魚類感應(yīng)到主流位置，實(shí)現(xiàn)上溯。卵石墻體型下，水體紊動能高于不透水墻池室體型，其原因主要是水體受到卵石不規(guī)則外形的干擾，以及卵石縫隙間水流的沖擊所致。池室內(nèi)表層水體紊動能高于底層，如卵石墻體型的表層紊動能最大值為0.12 m2/s2，底層最大值為0.06 m2/s2。究其原因在于，魚道池室間存在水面落差，水流跌落對水體表面沖擊所致。總體而言，采用卵石墻的魚道體型，池室內(nèi)紊動能較不透水墻魚道體型有所增加。

圖5 兩種體型第3級水池紊動能分布Fig.5 Turbulent kinetic energy distributions of third stage pool in two schemes

2.3 過流流量

表1為兩種魚道體型各個池室的水位變化與耗水流量。在魚道內(nèi)水位保持相同（對應(yīng)各級池室內(nèi)的水深約1.4 m）的條件下，不透水墻魚道體型的耗水流量為Q=1.39 m3/s，而卵石墻魚道體型的耗水流量為Q=2.86 m3/s，增大了一倍左右。究其原因在于，隔墻內(nèi)的縫隙增加了魚道整體的過流面積，在相同運(yùn)行水深下，卵石墻魚道體型較不透水隔墻魚道需要消耗更多的水量。

表1 兩種體型各個池室水位及耗水流量Table 1 Pool water level and consumption flow in two schemes

3 結(jié) 論

本文采用Flow-3D建立了不同隔墻類型的魚道三維數(shù)學(xué)模型，結(jié)合物理模型試驗(yàn)驗(yàn)證，針對卵石墻仿自然魚道和不透水隔墻魚道中的水力特性進(jìn)行了對比分析，研究表明：

1）本文建立的三維數(shù)學(xué)模型可以較好地描述透水性卵石墻對魚道內(nèi)流場的影響，數(shù)學(xué)模型計(jì)算結(jié)果與物理模型試驗(yàn)結(jié)果吻合良好，為仿自然魚道的研究提供了可靠的手段。

2）采用不透水隔墻的魚道，池室開口處流速分布較為單一，表底流速差僅為0.06～0.08 m/s；而采用卵石墻的仿自然魚道，過魚口處流速分布表現(xiàn)出“表層小，底層大，兩側(cè)小，中間大”的特征，且流速分布垂向差異明顯，表底流速差達(dá)到0.43～0.61 m/s，為多種魚類上溯提供了可能。

3）采用不透水隔墻的魚道，各池室內(nèi)主流較為集中，兩側(cè)形成較大的回流區(qū)，兩者之間存在一個低流速帶，不利于魚類回到主流，繼續(xù)上溯；采用卵石墻后，水體受到卵石縫隙間水流的沖擊，流態(tài)豐富，回流區(qū)減弱，有利于魚類重新找到主流，實(shí)現(xiàn)上溯。

4）采用不透水墻的仿自然魚道，池室內(nèi)主流區(qū)紊動能僅為0.01～0.06 m2/s2；采用卵石墻的仿自然魚道，受卵石不規(guī)則外形和縫隙間水流的沖擊影響，池室內(nèi)主流區(qū)紊動能可達(dá)0.06～0.12 m2/s2，便于魚類感應(yīng)到主流位置，實(shí)現(xiàn)上溯。

5）采用透水性卵石墻后，魚道耗水流量較之不透水墻體型，增大1倍左右。建議在實(shí)際工程設(shè)計(jì)中，通過改變卵石墻透水特性，尋求水流流態(tài)與耗水流量之間的平衡，制定適宜的布置方案。

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Improving effect of hydraulic characteristics of nature-like fishway with pools and cobblestone weirs

Li Guangning1, Sun Shuangke1※, Liu Haitao1, Zhang Chao1, Zhao Guixia2, Zheng Tiegang1
(1. State Key Laboratory of Simulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China; 2. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China)

The nature-like fish way is one of the most promising layouts of fish pass structures, its remarkable characteristics are that the individual cobblestone weirs from local river bed substrates are adopted in the fishway construction to imitate as closely as possible the flow pattern of Natural River. Therefore it has higher running efficiency for fish migration than traditional technical fishways. In order to identify the differences of the hydraulic characteristics between the nature-like fishway and the traditional fishway, we conducted comparative studies. The three-dimensional mathematical models of the fishways with cobblestone weirs and water proof weirs were developed respectively. The cobblestone weirs had porosity about 12%. It was defined as the ratio of pervious area to total area of the vertical section along with the longitudinal direction. Each mathematical cobblestone feature was defined as obstacles with special shapes as the natural one. The gaps between the cobblestones allowed water to pass through existing calculation elements. A hydraulic model of the fishway with cobblestone weirs was designed based on the law of gravity similarity at a scale of 1:5. The fishway structure of the model test was consistent with the mathematical model. The water depth and velocity at typical measurement points were recorded. The results were used to verify the numerical model. In the scenario that the fish way upstream and downstream water depth was 1.4 m, the hydraulic characteristics in the fish ways, such as flow pattern, flow velocity, turbulence kinetic energy, and flow rate were compared. The results showed that the currents coming from the cobblestone gaps improved the flow dynamics conditions in the pools. The velocity distributions of the gaps in the staggered weirs appeared as the velocities of the surface were smaller than the bottom; the velocities of the sides were smaller than that of the middle. Obviously, using permeable weir fishway, the abundance of velocity distribution for fish was quite obvious, and the velocity distribution of impervious weir fishway was close to uniform. Turbulence in the mainstream can attract fish back to migration, the turbulence kinetic energy (TKE) was considered as a potential index to assess the suitability of the fishway structure. The turbulent intensity preferred by fish may depend on their swimming capabilities. In the fishways with cobblestone weirs, the TKE had greatly increased; the TKE on the surface was higher than that near the bottom. As the water surface of each of the pool was kept at the same level, the water consumption flow is very different between the impervious weir and cobblestone weir fishway. The consumption flow of the impervious weir fishway was Q=1.39 m3/s, while the consumption flow of the cobblestone weir fishway was Q=2.86 m3/s, which was increased to about twice. Thus, the nature-like fishways with cobblestone weirs needed more water flow in operating. The flow pattern of the nature-like fishway was rich and varied, and it was closer to the natural river; environment. As such it provided abundant hydrodynamic conditions for different types of migration fish. The effecting factors on the hydraulic characteristics of the nature-like fishway were analyzed, such as partition type, bottom slope, and different operation depth and so on. In general, the simulation technique of nature-like fishway was still at the exploratory stage, and the study should be further developed with a consideration with special life habits of migratory fish. The approach used in this paper can provide reference for the hydraulic design and optimization of nature-like fishway.

fishways; flow velocity; flow rate; turbulence kinetic energy; consumption flow; numerical simulation

10.11975/j.issn.1002-6819.2017.15.024

TV61

A

1002-6819(2017)-15-0184-06

2017-02-09

2017-07-05

國家自然科學(xué)基金項(xiàng)目（51679261），國家自然科學(xué)青年基金項(xiàng)目（51709278）

李廣寧，男，河北邢臺人，工程師，博士，主要從事水力學(xué)研究工作。北京 中國水利水電科學(xué)研究院，100038。Email：94174061@qq.com

※通信作者：孫雙科，男，河南南陽人，教授，博士，博士生導(dǎo)師，主要從事水力學(xué)研究工作。北京 中國水利水電科學(xué)研究院，100038。

Email：sunshuangke@126.com