水流通過高滲透性多孔介質結構物水理特性之研究

行政院國家科學委員會補助專題研究計畫

行政院國家科學委員會補助專題研究計畫

行政院國家科學委員會補助專題研究計畫

行政院國家科學委員會補助專題研究計畫

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水流通過高滲透性多孔介質結構物水利特性之研究

Hydraulic Characteristics of Flow over a Highly Permeable

Porous Structure

計畫類別：■ 個別型計畫 □ 整合型計畫

計畫編號：NSC －96－2221－E－006－076

執行期間：96 年 08 月 01 日 至 97 年 07 月 31 日

計畫主持人：呂珍謀

共同主持人：賴泉基

計畫參與人員：黃偉哲

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執行單位：國立成功大學水利及海洋工程研學系

中 華 民 國 97 年 07 月 31 日

中文摘要

本研究透過渠道試驗探討低水位時透水與非透水性結構物之流場特性。試驗過程中， 利用聲波都卜勒流速儀（ADV）量測透水性結構物（孔隙率γ =0.349與γ =0.475）及非透 水性結構物（孔隙率γ =0）附近之流場，利用測得之流場資料分析平均速度、紊流強度及 紊流動能於不同孔隙率結構物附近之差異。多孔介質結構物具可透水的特性，造成結構物 與水體交界面處有滑動速度存在，使得水體與多孔介質結構物交界處的流速梯度較非透水 性結構物小，且多孔介質結構物上方的水流為由結構物外部流進結構物內。在紊流強度的 分佈上，多孔介質結構物頂部與後方之紊流強度比非透水結構物小；大孔隙率結構物上方 與後方之紊流強度略大於小孔隙率結構物。多孔介質結構物下游因穿越流的流出使得結構 物頂部後方紊流動能有顯著降低的趨勢，顯示多孔介質結構物可減低結構物頂部與後方水 流造成的紊動，進而減低水流對結構物的沖刷破壞。 關鍵字:透水性結構物、紊流強度、滑動速度

Abstract

An experimental investigation is carried out in the open channel for the measurement of the flow field of the flow over permeable structures in low water level. Detailed measurements of the time-averaged velocity components, turbulent intensity and turbulence kinetic energy of permeable and solid structures are taken by the acoustic doppler velocimeter（ADV）. The characteristic feature of porous medium is permeable. The vertical distributions of time-averaged velocities above permeable structures are more uniform than solid structure due to the slip velocity at the fluid/porous interface, and the flow above permeable structure penetrated into structure. The turbulence intensities above structure with large porosity are slightly greater than small porosity structure, and the permeable structures have smaller turbulence intensity and turbulence kinetic energy than solid structure around the structures due to the bleed flow through the downstream edge of permeable structure. The results show that the porous medium reduces the turbulence intensity effectively, and then reduce the local scour.

Keywords: permeable structure, slip velocity, turbulence intensity

一、前言

以往河溪整治工程主要著重於防洪安全與耐久性，故傳統混凝土工法廣泛的應用於河 川堤防與水工構造物，因混凝土結構物不具透水性而阻斷了河川中泥砂的輸運與水中生物 縱向遷徙的能力，因而造成河川自然生態的破壞。近年來，隨著國人生活品質的提升，對 自然資源保育及生態環境需求日漸重視，因此現階段的河溪整治工程除防洪安全考量外， 同時亦須考慮河溪原有的自然形態及生態系統。將生態維護與復育的概念融入工程設計之 中，在河川治理的同時可兼具安全有效的防洪功能又能保有河川自然生態環境，也因此兼

顧防洪安全及維護生態的自然生態工法已廣泛地應用於目前的河溪整治工程中。與傳統混 凝土工法所使用的材料相比，生態工法其材料特點為材料具「多孔性」，多孔介質結構物能 提供水體中溶解性有機顆粒、無機離子與氣體的交換，除了可增加河川水質的自淨作用之 外，結構物中的孔隙亦可作為水中動植物棲息之空間。因此，多孔介質結構物乃成為河溪 整治工程中生態工法所廣泛使用之材料，故於工程設計之初透過試驗研究瞭解透水結構物 與非透水結構物附近流場的差異，除可用於預估工程的效果亦可作為結構安全設計之依據。

二、文獻探討

Larichkin et al. (2003) 利用數值與試驗方式，探討水流通過矩形非透水結構物對邊界層 結構之影響，指出結構物後方迴流區的長度會隨著結構物高度的減小而增長。Gao et al. (2005) 針對不同冪次律流速分佈通過矩形結構物進行數值模擬，結果顯示結構物頂部接觸 區長_{度(attachment length)隨著冪次律的指數增大而增長。在透水結構物方面，陳(2001)、黃} (2002)與董(2003)對水流通過透水式橋墩保護工進行試驗探討，試驗結果顯示在保護工頂部 之流速分佈不符合一般明渠流的對數律分佈，且通過橋墩內部之滲流量隨上游水位之增加 而增大。Michioku et al. (2005)透過理論及試驗研究礫石堰在非浸沒情況下內部滲流量，指 出礫石堰內部滲流量為堰上下游水位比、孔隙率、堰長、粒徑及渠道坡度之函數。呂（2005） 及 Chan 等人（2006）對水流通過透水與非透水結構物之流場進行試驗研究，依據不同的水 理條件與透水結構物的幾何型態，將水流通過透水結構物之流況，依水位高至低的變化將 其流況概分為四種：(a)浸沒第一型(submerge flow type I )；(b)浸沒第二型(submerge flow type II)；(c)過渡型(transient flow)與(d)內部滲流型(subsurface flow)，並於試驗室試驗水槽中佈置 自製透水性結構物模組進行浸沒第一型之流場量測試驗，研究結果顯示透水結構物上方的 流速分佈因多孔介質結構物表面有滑動速度存在，造成水體與多孔介質結構物交界面附近 平均流速較非透水性結構物大且結構物頂部的流速分佈亦較均勻。在結構物後方迴流區內 流場之特性上因穿越流從多孔介質結構物下游面流出，結構物後方流場因受穿越流推擠之 影響造成迴流區往下游延長，使得透水結構物後方的迴流區長度較非透水性結構物之迴流 區長。試驗結果顯示透水結構物迴流區長度約為非透水結構物的 1.45 倍，且流場整體的紊 流強度與紊流動能隨孔隙率增加而逐漸減弱。上述之研究僅針對高水位之浸沒第一型流況 做分析探討，其它三種流況仍尚未進行試驗研究，其中更以浸沒第二型流況為一般河川中 最常發生之流況，故本研究將針對浸沒第二型之流況進行渠道試驗，探討多孔介質結構物 於浸沒第二型流況下附近流場之特性，以供河川生態工法中透水性結構物保護工設計之依 據。

三、研究方法

3.1

試驗設備與佈置

本研究之試驗係於國立成功大學水利及海洋工程學系生態水力研究室河工試驗場循環 水槽中進行。該水槽長 15m，寬 0.6m，高 0.6m 為可變坡度之玻璃水槽，入口處設有蜂巢 狀整流裝置可減低水流液面的波動以加速水流達到完全發展流況。水槽下游設有尾水蓄水 箱與電動馬達做為試驗水槽之流量循環系統，頭水箱入口處設有塑膠閥門用以調節渠道內 之流量，渠道內的試驗流量乃利用設置於尾水蓄水箱中之三角銳緣堰量測，玻璃水槽末端 設置一下射式尾水閘門用於控制水槽之水位、福祿數等初始條件。 透水結構物模型則利用直徑 2.5cm 與 1.5cm 之玻璃珠，以規則排列方式分別組合成 2 個尺寸皆為長 15cm，寬 60cm，高 7.5cm 具不同孔隙率的矩型透水結構物模型，圖 1 為以 直徑 2.5cm 所組成之透水結構物模型。透水結構物之孔隙率經排水體積法量測之結果分別 為 0.475 與 0.349；對照組使用之不透水結構物則以壓克力製成，其尺寸與透水結構物相同。 結構物模型設置於距水槽進水口 8m 處，結構物前方之流速分佈經檢測後呈完全發展之對 數律流速分佈，顯示此處之水流已達完全發展。 流速量測採用挪威 NORTEK 公司生產之三維側視型(3-D side-looking)聲波都卜勒流速 儀(acoustic Doppler velocimeter, ADV)，可同時量測 x 軸、y 軸與 z 軸之瞬時點流速，測點位 置位 於 發 射 器 前 方 5cm 處， 資料擷 取頻 率為 25Hz ，流 速量 測範圍介 於±3cm/sec ～ ±250cm/sec，精確度為量測值的±0.5%±1mm/s。試驗水位則利用針尺進行量測，試驗進行 時將針尺與流速儀架設於渠道上方可三維移動之台車上，台車移動距離解析度為 0.025cm， 沿試驗渠道中心軸量測不同斷面之水位與流速分佈，試驗水槽之設置與座標系統如圖 2 所 示。

3.2

試驗條件與方法

本研究針對多孔介質結構物於浸沒第二型流況時之流場特性進行試驗研究，試驗中加 入不透水結構物之試驗組作為與透水結構物試驗結果之比較。試驗進行時水槽之坡度固定 為 1/300，並調整入口流量與尾水閘門高度使水流通過結構物之流況為浸沒第二型，分別量 測水流通過三種不同孔隙率結構物(γ=0.475，0.349，0)之流速分佈處。利用聲波都卜勒流速 儀量測各試驗斷面中心垂線流速分佈，由流況分佈之情形作為選擇量測斷面之依據，在接 近結構物前方、頂部與後方流況變化較大處將量測斷面加密，共 15 個量測斷面，不同垂線 之流速測點有 10～25 個。 因紊流為隨機不規則的運動故若要以雷諾平均的方式來研究紊流的結構，每個測點則 須要有足夠長的量測時間使測得之流速擾動量不為時間的函數，其所測得之流速方為穩定 且一致的資料，本試驗每個測點量測延時為 300sec 該點流速的總取樣數為 7500 所測得之 流速已為穩定之資料。本研究以不同流量進行渠道試驗各組試驗條件如表 1 所示。各測點 相關之紊流特性乃依據雷諾平均法則之定義，由每個測點所得之時序列流速資料依下列公 式計算獲得： u U U = + (1) w W W = + (2)

2 u Tu = (3) 2 w Tw = (4)

(

2 2 2

)

2 1 w v u k = + + (5) 其中： U 、W = 分別為x 方向與 w 方向瞬時速度 U、W = 分別為 x 方向與 w 方向平均速度 u、v、w = 分別為 x、y 與 w 方向擾動速度 Tu 、 Tw = 分別為x 方向與 w 方向紊流強度 k = 紊流動能 試驗資料分析時，長度與速度分別以結構物高度H_p(=7.5cm)與入口流速U₀(=35.26cm/sec) 來進行無因次化，紊流動能則以 2 0 U 進行無因次化。

四、結果與討論

本文之研究目的在探討水流通過孔隙率結構物於浸沒第二型流況時紊流流場之變 化。利用 ADV 流速儀量測不同孔隙率結構物附近之流速資料分析流場之紊流特性，試驗中 並加入固體結構物之試驗作為比較，探討透水與非透水結構物於浸沒第二型流況下之流速 分佈與紊流特性。

4.1 平均流速

平均流速為流場中重要的水理參數之ㄧ，可用來描述流場中流體運動的趨勢，故流場 中的許多物理現象可藉由觀察平均流速分佈來了解其生成的機制，以下將對不同孔隙率結 構物前方、頂部與後方其縱向與垂向平均流速做一分析比較。

4.1.1 結構物前方平均流速分佈

水流通過透水與非透水結構物於浸沒第二型之流況如圖 3 所示，圖 4-(A)，(B)，(C)， (D)，(E)，(F)分別為各試驗組所測得水流通過不同孔隙率結構物其無因次 x 方向平均流速 分 佈 圖 。 本 研 究 定 義 結 構 物 前 方 區 域 為 ：-8≤x H_P ≤0 ， 不 同 孔 隙 率 結 構 物 前 方 -2 H x 8 - ≤ _P ≤ 區域內各斷面 x 方向平均流速之分佈無明顯的差異，此區之流速分佈與明渠 流速之對數律分佈一致，為紊流完全發展區；在結構物前方x H_P >-1之流速逐漸偏離對數 律分佈顯示此區水流已開始受到結構物之影響，其流速分佈受渠道斷面束縮效應之影響使 得此區在y H_P <1範圍內 x 方向之平均流速有開始減小之情況產生，而在y H_P >1區域之 流速則有增大之趨勢以滿足斷面流量連續之特性，使得在x H_P >-1區域之流速偏離對數型 態分佈。由於多孔介質結構物允許流體由其內部通過，故多孔介質結構物於渠道中所造成

之斷面束縮效應較不透水結構物為小，使得透水性結構物前方流速分佈變化之趨勢較非透 水性結構物平緩。 圖 5-(A)，(B)，(C)，(D)，(E)，(F)分別為水流通過不同孔隙率結構物其無因次 w 方向 平均流速分圖，在結構物前方x H_P =-1處，因此區水流開始受斷面束縮效應之影響，在高 度y H_P =1附近 w 方向之平均流速明顯開始增大，顯示此區之水流呈現向上流動的趨勢且 w 方向之平均流速隨結構物孔隙率的減小而增大，且多孔介質結構物與非透水結構物其 w 方向平均流速的最大值皆發生在y H_P =1處。

4.1.2 結構物頂部平均流速分佈

圖 6 與圖 7 分別為 A、B、C 與 D、E、F 各試驗組結構物頂部 x 方向之平均流速分佈， 試驗結果顯示於浸沒第二型流況下結構物頂部之流速皆隨著水深而增加﹔在透水結構物頂 部與水體交界處(y H_P =1)之水流有滑動速度(slip velocity)存在，使透水結構物頂部之流速 分佈較非透水結構物均勻，且結構物頂部 x 方向平均流速隨著結構物孔隙率之減小而遞增。 圖 8 與圖 9 分別為 A、B、C 與 D、E、F 各試驗組結構物頂部 w 方向之平均流速分佈。 在0<x H_P <0.5區域之斷面，水體與結構物交界面之水流為向上流動且流速分佈隨水深的 增加而遞增。當斷面位置在x H_P ≥0.5之區域時，結構物交界面處 w 方向之平均流速則轉 變為負值，顯示透水結構物頂部的部分水流在此區為由結構物外部往結構物內部流動，且 此區 w 方向之平均流速隨著距離往下游而增大。此一流速分佈顯示當水流通過透水性結構 物於浸沒第二型之流況下，其結構物上方的流量將隨著往下游距離之增加而減少。

4.1.3 結構物下游平均流速分佈

圖 10-(a)、(b)分別為 A、B、C 與 D、E、F 各試驗組結構物下游 x 方向之平均流速分 佈，因透水結構物允許水流自結構物內部通過，故於結構物下游近底床處存在一股由結構 物內部流出之穿越流，使結構物下游處近底床附近之流速分佈皆為正值，且穿越流之強度 隨結構物孔隙率的增加而遞增；與透水結構物相比，非透水結構物下游之流速分佈則呈現 完全不同之趨勢，非透水結構物下游在高度y H_P <0.25區域內之流速呈現負值，顯示非透 水結構物下游有迴流區存在。 圖 12 與圖 13 分別為 A、B、C 與 D、E、F 各試驗組於不同孔隙率結構物下游 w 方向 之平均流速分佈。因為自透水結構物內部流出之穿越流可於近底床處形成水墊效應，因而 可削減結構物下游自由跌水 w 方向之水流強度，且結構物下游處穿越流之強度隨著結構物 孔隙率之增加而遞增，故 w 方向之流速隨著結構物孔隙率的減小而遞增。因此，透水結構 物可減低結構物下游 w 方向之流速進而減低自由跌水對結構物下游底床之沖刷。

4.2 紊流強度

紊流的流動過程中，紊流的能量乃透過不同週期與不同旋轉方向的漩渦來進行交換， 而使流場速度出現紊動的現象。紊流強度代表流場中流體紊動的程度，以下將以試驗測的 之結果討論結構物附近紊流強度分佈之情況。

4.2.1 結構物前端紊流強度分佈

圖 14-(A)、(B)、(C)、(D)、(E)、(F)分別為各試驗組結構物附近 x 方向無因次紊流強度 之分佈情況。試驗結果顯示 x 方向的紊流強度於結構物前方x H_P =-1處開始增大，因此處 水流已開始受結構物之影響使得水流的紊動開始增大。因透水性結構物對渠道造成之斷面

束縮效應較小，故其對結構物附近流況之改變亦較非透水性結構物小，所以透水性結構物 前端之紊流強度小於非透水性結構物，試驗結果顯示結構物前端之紊流強度隨著結構物孔 隙率之減小而有增加之趨勢。 圖 15-(A)、(B)、(C)、(D)、(E)、(F)分別為不同孔隙率結構物附近 w 方向無因次紊流 強度分佈圖。其 w 方向紊流強度分佈之趨勢與 x 方向一致，即 w 方向的紊流強度在結構物 前方-1≤x H_P ≤0的區域明顯開始增大，而紊流強度增大之趨勢則與結構物之孔隙率成反 比。

4.2.2 結構物頂部紊流強度分佈

圖 16 為不同孔隙率結構物頂部 x 方向之紊流強度分佈。比較透水與非透水結構物上方 x 方向的紊流強度可發現，整體平均來說透水性結構物上方的紊流強度小於非透水性結構 物，且其紊流強度最大值皆發生在y H_P =1附近；同時比較不同孔隙率結構物上方 x 方向 的紊流強度可知，大孔隙率結構物上方的紊流強度略大於小孔隙率結構物。 圖 17 為不同孔隙率結構物頂部 w 方向之紊流強度分佈，比較結構物上方 w 方向的紊 流強度可發現，紊流強度皆隨著水深的增加而增大其最大值皆發生在結構物交界面處 （y H_P =1），且非透水結構物上方的紊流強度大於透水性結構物，此一結果顯示透水性結 構物與水體交界處 w 方向之水流可有效降低結構物交界面處的紊流強度。

4.2.3 結構物下游紊流強度分佈

水流於浸沒第二型流況下結構物下游區域因自由跌水之影響使得結構物下游處的紊流 強度明顯急遽增加並呈現強烈的非等向性（anisotropic）特徵。圖 18-(a)、(b)分別為試驗組 A、B、C 與 D、E、F 之縱向紊流強度分佈圖，比較透水與非透水結構物後方之紊流強度可 發現透水結構物後方區域之紊流強度小於非透水性結構物，在高度y H_P <0.5區域紊流強 度之分佈由底床處隨著距底床距離之增加而增大，在y H_P =0.5附近縱向紊流強度達到最 大，隨後於高度y H_P >0.5區域之紊流強度則隨著距底床距離之增加而減小。此乃因為自 透水結構物後方流出之穿越流可將結構物頂部自由跌水之水流往下游推送，使得透水性結 構物下游整體之紊流強度低於非透水性結構物。

圖 19-(a)、(b)分別為試驗組 A、B、C 與 D、E、F 之垂向紊流強度分佈圖，在垂向紊 流強度的分佈上，試驗結果顯示其分佈趨勢與縱向紊流強度一致，透水性結構物之垂向紊 流強度小於非透水性結構物且其垂向紊流強度最大值亦發生於y H_P =0.5附近。由於透水 性結構物下游近底床處之穿越流可減低自由跌水向下水流之紊流強度，因而減弱結構物末 端水流因自由跌水所造成的強烈紊動，此一結果顯示多孔介質結構物可有效降低結構物後 方縱向與垂向的紊流強度，進而降低結構物後方自由跌水對底床之沖刷。

4.3 紊流動能

紊流動能為紊流流場中渦流運動的平均動能，為描述流場中紊流特性常用的指標，以 下將以試驗測的之結果討論結構物附近紊流強度分佈之情況。

4.3.1 結構物前端紊流動能分佈

圖 20 與圖 21 分別為 A、B、C 與 D、E、F 各試驗組結構物附近無因次紊流動能分佈 圖，在結構物前端﹕-8≤x H_P ≤-1透水與非透水結構物於各斷面在紊流動能的分佈上並無 明顯差異，其紊流動能皆趨近於零。紊流動能在x H_P >-0.5之斷面開始增大，由試驗結果

可知紊流動能由結構物前端開始急遽增大且不同孔隙率結構物其紊流動能最大值皆發生在 1 H y _P = 附近，顯示水體與結構物交界處渦流運動強烈。比較透水與非透水結構物頂部紊 流動能分佈之情況，顯示透水結構物頂部紊流動能集中的位置有向下游移動之現象，觀察 結構物附近之紊流動能發現透水結構物流場整體的紊流動能較非透水結構物小，此乃因透 水結構物允許水流自其內部通過使得結構物對渠道造成的斷面束縮效應較小，因而水流通 過結構物時所產生的分離流較非透水結構物小，亦同時降低水體與結構物交界面附近之紊 流動能。不透水結構物下游因有迴流區存在使得該區之紊流動能大於透水結構物，試驗結 果顯示透水結構物可降低水體/結構物交界面及結構物下游處之紊流動能，進而降低因渦流 運動劇烈對結構物所造成之破壞。

五、結論

目前國內對生態工法的理論分析與施工技術之研究尚屬起步階段，對於多孔介質結構 物之水理特性多著重於定性上之討論而較缺乏定量上的分析研究。本研究旨在探討水流通 過透水與非透水性結構物於浸沒第二型流況下結構物附近流場之變化，針對三種不同孔隙 率（孔隙率分別為 0、0.349、0.475）的結構物進行渠道試驗，比較分析流場的平均速度、 紊流強度以及紊流動能，得到下列主要結論： 1. 透水性結構物表面有滑動速度存在，使得透水結構物頂部之流速分佈較非透水結構物均 勻，且結構物頂部之平均流速有隨結構物孔隙率之增加而遞減之趨勢。 2. 水體與透水性結構物交界處的流速分佈顯示，部份水流會經由交界面往結構物內部流動 且結構物頂部之垂向流速會沿水流方向往下游有遞增之趨勢，故結構物頂部之流量會沿 水流方向往下游遞減。 3. 透水性結構物下游有自結構物內部流出之穿越流存在，於結構物下游近底床處形成水墊 效應而減低結構物下游自由跌水對底床及結構物的沖刷。 4. 水流通過透水結構物所形成之分離流較固體結構物小，使得結構物頂部縱向及垂向之紊 流強度皆較固體結構物小，此外在結構物下游流場分佈方面透水性結構物下游並無迴流 區存在。 5. 由透水與非透水性結構物頂部紊流動能分佈型態可知，透水性結構物紊流動能集中的位 置有向下游移動之趨勢。 6. 透水性結構物可有效降低流場整體之紊流動能，特別在結構物頂部與下游區域紊流動能 降低的效果更為顯著，此一效應可對結構物下游底床提供保護進而降低水流對結構物基 礎的沖刷破壞。

六、計畫成果自評

1. 研究內容與原計畫相符程度 本研究透探討低水位時透水與非透水性結構物之流場特性，成果與計畫內容完全相符。 2. 研究成果的學術或應用價值 本研究成果的應用價值在於流場特性可提供供河川生態工法中透水性結構物保護工設 計之依據。學術價值在於完整的探究透水性結構物對紊流流場特性之影響。 3. 是否適合在學術期刊發表或申請專利 已發表於SCI 國際學刊兩篇、國際研討會一篇與國內研討會一篇，包括：

Leu, J. M., Chan, H. C., and Chu, M. S. (2008). “Comparison of turbulent flow over solid and porous structures mounted on the bottom of a rectangular channel”, Flow

Measurement and Instrumentation, In press. doi:10.1016/j.flowmeasinst.2008.05.001.
Leu, J. M., Chan, H. C., Tu, Lih-Fu, Jia, Yafei, and Wang, Sam S.Y. (2008). “Velocity distribution of non-Darcy Flow in Porous medium”, Journal of Mechanics, Accepted.
Huang, W. C., Leu, J. M., and Chan, H. C. “Hydraulic Characteristics of Flow over a Highly Permeable Porous Structure”, World Environmental & Water Resources

Congress 2008. May 12~May 16, Honolulu, Hawaii, On CD-ROM.

呂珍謀、賈亞非、詹勳全、黃偉哲，「生態工法水動力模式之開發研究」，2007 台灣環境資源永續發展研討會，國立中央大學，中壢市，第6-86-6-93 頁，(2007.12)。 (本文獲研討會優良論文獎本文獲研討會優良論文獎本文獲研討會優良論文獎本文獲研討會優良論文獎) 4. 主要發現或其他有關價值 本研究除利用所流測得到之流速時序列資料進行紊流時間平均特性探究，主要貢獻於多 孔結構物滑動速度與穿越流之特性分析，未來可針對流速時序列資料之頻譜分析，探討 紊流瞬時特性，擴充研究之學術價值。

參 考 文 獻

1. Beavers, G. S. and Joesph, D. D. (1967). “Boundary conditions at a naturally permeable wall.” J. Fluid Mech., 30, 197–207.

2. Choi, C. Y. and Waller, P. M. (1997). “Momentum transport mechanism for water flow over porous media.” J. Env. Engrg., 123(8), 792-799.

3. Kuwahara, F., Kameyama, Y., Yamashita, S. and Nakayama, A. (1998). “Numerical modeling of turbulent flow in porous media using a spatially periodic array.” J. Porous Media, 1, 47–55.

4. Masuoka, T. and Takatsu, Y.(1996). “Turbulence model for flow through porous media.” Int. J. Heat Mass Transf., 39, pp. 2803–2809.

5. Mendoza, C. and Zhou, D. (1992). “Effect of porous bed on turbulent stream flow above bed.” J. of Hydraul. Engrg., 118(9), 1222-1240.

6. Prinos, P., Sofialidis, D. and Keramaris, E. (2003). “Turbulent flow over and within a porous bed.” J. of Hydraul. Engrg., 129(9), 720-733.

7. Vafai, K. and Kim, S. J. (1989). “Forced convection in a channel filled with a porous medium: An exact solution.” ASME J. Heat Transfer, 111, 1103–1106.

8. Vafai, K. and Thiyagaraja, R. (1987). “Analysis of flow and heat transfer at the interface region of a porous medium.” Int. J. Heat Mass Transfer, 30, 1391–1405.

9. Venkataraman, P. and Rama Mohan Rao, P. (1998). “Darcian, Transitional, and Turbulent Flow through Porous Media.” J. Hydraul. Engrg. 124(8), 840–846.

10. Wang, H. and Takle, E. S. (1995). “Boundary-layer flow and turbulence near porous obstacles.” Boundary-Layer Meteorology, 74, 73–88.

11. Xingwei Chen and Yee-Meng Chiew, M. ASCE (2004). “Velocity Distribution of Turbulent Open-Channel Flow with Bed Suction.” J. Hydr. Engrg., 130(2), 140-148.

水利，第五十三卷，第四期， 2005。 13. 陳建文，2000，「水流通過橋下保護工之流速分佈探討」，國立成功大學水利及海洋工 程學系碩士論文。 14. 黃偉哲，2001，「水流通過透水式橋墩保護工之流況分析」，國立成功大學水利及海洋 工程學系碩士論文。 15. 詹勳全、呂珍謀、賴泉基、李明靜，「紊流通過多孔介質二維水理模式之建立」，台灣 水利，第五十五卷，第一期， 2007。 16. 董志昌，2002，「水流通過橋墩保護工之流況比較分析」，國立成功大學水利及海洋工 程學系碩士論文。

圖 1 透水結構物(γ=0.475，D=25mm) 圖 2 水槽佈置與結構物尺寸及座標示意圖 表 1 各組之試驗條件 試驗組 試驗組 試驗組 試驗組 孔隙率孔隙率孔隙率孔隙率 入口流速入口流速 入口流速入口流速 (cm/s) 福祿數福祿數福祿數福祿數 雷諾數雷諾數雷諾數雷諾數 流量 流量 流量 流量 (cms) A 0.475 37.47 0.3 59953 0.035 B 0.349 37.45 0.29 61418 0.035 C 0 37.45 0.29 61418 0.035 D 0.475 30.64 0.26 43815 0.027 E 0.349 30.01 0.25 44670 0.026 F 0 27.23 0.22 43568 0.026 15cm 7 .5 cm 800cm 685cm 多孔介質 結購物 A D V w x 頭水箱 整流裝置

(a) (b) 圖 3 浸沒第二型流況:(a)透水性結構物,(b)非透水性結構物 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 1 2 3 U/U0 x/Hp y /H p (A) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 U/U0 x/Hp y /H p (B)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 U/U0 x/Hp y /H p (C) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 1 2 3U/U0 X/HP (D) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3U/U0 X/HP (E) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 1 2 3 4U/U0 X/HP (F) 圖 4 各試驗組縱向平均流速分佈圖

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 W/U0 x/Hp y /H p (A) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 W/U0 x/Hp y /H p (B) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 W/U0 x/Hp y /H p (C) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2W/U0 X/HP y /HP (D)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 1 2W/U0 X/HP y /HP (E) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 W/U0 X/HP y /HP (F) 圖 5 各試驗組垂向平均流速分佈圖 0 1 2 3 0 1 2 3 y /H p U/U0 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 x/H=0.33 x/H=0.67 x/H=1.00 x/H=1.33 _x/H=1.67 0 349 . 0 475 . 0 = = = γ γ γ 圖 6 試驗組 A、B、C 結構物頂部縱向流速分佈

0 1 2 3 0 1 2 3 y /H p U/U0 x/Hp=0 0 1 2 3 0 1 2 3 x/Hp=0.5 x/Hp=1.0 0 1 2 3 x/Hp=1.5 0 1 2 3 x/Hp=2.0 0 349 . 0 475 . 0 = = = γ γ γ 圖 7 試驗組 D、E、F 結構物頂部縱向流速分佈 -1 0 1 y /H p W/U0 0 1 2 3 -1 0 1 -1 0 1 -1 0 1 -1 0 1 x/H=0.33 x/H=0.67 x/H=1.00 x/H=1.33 x/H=1.67 0 349 . 0 475 . 0 = = = γ γ γ 圖 8 試驗組 A、B、C 結構物頂部垂向流速分佈 -1 -0 .5 0 0.5 1 y /H p W/U0 0 1 2 3 x/Hp=0 -1 -0.5 0 0.5 1 x/Hp=0.5 -1 -0.5 0 0.5 1 x/Hp=1.0 -1 -0.5 0 0.5 1 x/Hp=1.5 -1 -0.5 0 0.5 1 x/Hp=2.0 0 349 . 0 475 . 0 = = = γ γ γ 圖 9 試驗組 D、E、F 結構物頂部垂向流速分佈

(a) (b) 圖 10 各試驗組結構物下游縱向流速分佈 (a) (b) 圖 12 各試驗組結構物下游垂向流速分佈 -2 0 2 4 0 1 2 3 0 349 . 0 475 . 0 = = = γ γ γ y /H P U/U0 -2 0 2 4 0 1 2 3 0 349 . 0 475 . 0 = = = γ γ γ y/ HP U/U0 -2 -1 0 1 0 1 2 3 0 349 . 0 475 . 0 = = = γ γ γ y/ HP W/U0 -3 -2 -1 0 1 0 1 2 3 0 349 . 0 475 . 0 = = = γ γ γ y/ HP W/U0

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 0.5 Tu/U0 x/Hp y /H p (A) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 0.5 Tu/U0 x/Hp y /H p (B) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 Tu/U0 0 0.5 x/Hp y /H p (C) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 0.5Tu/U0 X/HP y /HP (D)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 0.5 1Tu/U0 X/HP y /H P (E) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 0.5 1 Tu/U0 X/HP y /H P (F) 圖 14 各試驗組縱向紊流強度分佈圖 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 0.5 1 Tw/U0 x/Hp y /H p (A) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 0 0.5 1 Tw/U0 x/Hp y /H p (B)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 3 Tw/U0 0 0.5 1 x/Hp y /H p (C) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2Tw/U0 X/HP y /HP (D) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2Tw/U0 X/HP y /H P (E) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 Tw/U0 X/HP 0 1 2 y /H P (F) 圖 15 各試驗組垂向紊流強度分佈圖

0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 x/H=0.33 x/H=0.67 x/H=1.00 x/H=1.33 x/H=1.67 0 349 . 0 475 . 0 = = = γ γ γ 0 0.5 1 y /H p Tu/U0 0 1 2 3 x/H=0 圖 16 試驗組 A、B、C 結構物頂部縱向紊流強度分佈 0 0.5 1 y /H p Tu/U0 0 1 2 3 x/Hp=0 0 0.5 1 x/Hp=0.5 0 0.5 1 x/Hp=1.0 0 0.5 1 x/Hp=1.5 0 0.5 1 x/Hp=2.0 圖 17 試驗組 D、E、F 結構物頂部垂向紊流強度分佈 (a) (b) 圖 18 各試驗組結構物下游之縱向紊流強度分佈 0 0.5 1 1.5 0 1 2 3 0 349 . 0 475 . 0 = = = γ γ γ y /H P Tu/U0 0 0.5 1 1.5 0 1 2 3 y /H P Tu/U0 0 349 . 0 475 . 0 = = = γ γ γ

(a) (b) 圖 19 各試驗組結構物下游之垂向紊流強度分佈 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 0.5 1 U K/ 2₀ x/Hp y /H p 0 349 . 0 475 . 0 = = = γ γ γ 圖 20 試驗組 A、B、C 之紊流動能分佈 圖 21 試驗組 D、E、F 之紊流動能分佈 0 1 2 3 0 1 2 3 0 349 . 0 475 . 0 = = = γ γ γ y /H P Tw/U0 0 1 2 3 4 0 1 2 3 0 349 . 0 475 . 0 = = = γ γ γ y /H P Tw/HP -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 y /HP X/HP 0 349 . 0 475 . 0 = = = γ γ γ 0 0.5 1 U K/ 2₀

出席國際會議心得報告

摘

摘

摘

摘

要

要

要

要

本次出席之國際會議名稱為「WORLD ENVIRONMENTAL & WATER

RESOURCES CONGRESS 2008」

；會議地點為位於美國夏威夷，會議時間為

2008 年 5 月 12 至 16 日，共計 5 日。發表之論文名稱為「Hydraulic

Characteristics of Flow over a Highly Permeable Porous Structure」

，論文作者

為水利及海洋工程學系呂珍謀副教授及黃偉哲博士候選人，出席進行論文簡報

者為黃偉哲同學。發表之論文旨在經由渠道實驗的方式探討低水位時透水與非

透水性結構物附近流場與紊流特性。本研究利用聲波都普勒流速儀量測透水結

性構物及非透水性結構物附近流場，依測得之流場資料分析流場的平均速度、

紊流強度及紊流動能。研究結果顯示，多孔介質結構物具可透水的特性，造成

結構物與水體交界面處有滑動速度存在，使透水性結構物上方之流速分佈較非

透水結構物均勻。在紊流強度的分佈上，大孔隙率透水結構物上方與後方之紊

流強度略大於小孔隙率透水結構物；透水性結構物上方與後方之紊流強度又比

非透水結構物小，顯示多孔介質結構物可減低結構物上方與後方水流造成的紊

動，進而減低水流對結構物的沖刷破壞。

Abstract

The congress that I attend is 「WORLD ENVIRONMENTAL & WATER

RESOURCES CONGRESS 2008」. The place of the congress is at HAWAI’I, and

the time is MAY 12-16, 2008. The publish paper is 「Hydraulic Characteristics of

Flow over a Highly Permeable Porous Structure」, the authors of the paper are

Jan-Mou Leu and Wei-Che Huang et al., and the speaker of the paper is Wei-Che

Huang. The aim of this paper is to investigate the velocity fields and turbulence

characteristics of the flow over permeable structures by channel experiment in low

water level. Detailed measurements of the time-averaged velocity components,

turbulence intensity components of permeable and solid structures are taken by the

acoustic doppler velocimeter（ADV）. The characteristic feature of porous medium

is permeable, and the vertical distributions of time-averaged velocities above

permeable structures are more uniform than solid structure due to the slip velocity

at the fluid/porous interface. The turbulence intensity above structure with large

porosity are slightly greater than small porosity structure, and the permeable

structures have smaller turbulence intensity than solid structure around the

structures. The results show that the porous medium reduces the turbulence

intensity, and then reduce the scour to structures.

I. Process

The World Environmental & Water Resources Congress is being held in

Honolulu, Hawaii on May 12-16, 2008. The congress received approximately 1,100

abstracts. About 740 of these were selected for podium presentations and another

200 are to be presented as posters. The subjects of the congress contain: urban

watershed management, groundwater hydrology quality and management,

environmental engineering and public health, hydraulics, international issues, river

and watershed restoration, surface water hydrology etc. During the congress,

numbers of Short Courses are also being presented. The Short Courses are designed

for both public and private professionals engaged in water resources and hydraulic

research workers.

My report was selected for podium presentation, and was arranged in the subject

of hydraulics: Computational Hydraulics and Hydrodynamics on May 15, 2008. I

reported my paper to the participant and took part in the discussion with the

scholars from Mississippi University. During the ice breaker reception I had a talk

with Glendon T. Stevens. He is a engineer of U.S. Army Corps, he was doing

groundwater flow research with numerical model.

During the congress I also attend several discourses and technical sessions, the

titles and brief introduction as below:

1. Gas Transfer Inside a Deep Airlift Reactor: The focus of the study is the

effects of changing the geometry and operating conditions of a full scale airlift

reactor operating in the bubbly flow regime on the liquid film coefficient.

2. Integrated Surface Water and Groundwater Modeling to Study Water

Level Fluctuations of Isolated Lakes in Florida: This paper discusses the

results of an integrated hydrologic modelling to study potential adjustment to

the established minimum flow and levels for lakes in Northwest Hillsborough

County, Florida.

Eggs: This paper presents an analysis of the flow velocities and turbulent

Reynolds stresses that developed over the surface of each artificial substrate. In

addition, an evaluation of the effectiveness of each substrate to trap and retain

sturgeon eggs is presented.

4. Investigation of Flow and Local Scour Characteristics around a Partially

Submerged Permeable Barb: The study focuses on the flow characteristics

around a submerged permeable barb to understand the flow regimes “formed”

within the vicinity of a barb.

5. Strategies for Cutting Management of Riparian Vegetation: This study

presents the numerical predictions on the detailed hydrodynamic and habitat

quality characteristics of riparian vegetation by using a depth-averaged

two-dimensional flow model.

In addition to above technical sessions, I also attend several Keynote &

Awards Breakfast. The prizemen give lectures about environmental, hydraulics,

watershed and irrigation etc.

II. Sentiment

After I participated in the conference, in the foreign country they pay much

attention in water resource, hydraulics and ocean engineering and environmental

engineering. They not only thought highly of basic research in above fields, but

also in locality application. Therefore, the results of basic research can be

verified by field measure data, and the engineering structure design must based

on basic research. Through combine basic research with field experiment, there

will have much advancement in scholarly research. By comparison with home

research, our research generality emphasized on application, and pay less

attention on basic theory research. Therefore, it will cause laggard in the

development of hydraulic and ocean engineering. So, the foreign experience can

be a good example of our basic theory research. By took part in the international

conference also can increase the opportunity of communicate with foreign

scholar.

III. Suggestion

By took part in the international conference we can communicated with

foreign scholar and exchange the opinions in research. At the same time, we can

introduce Cheng Kung University to foreign scholar, and increase the influence

in academic achievement. The follow are the suggestion of this activity:

1. The register fees of international conference always very expensive, if our

department can offer appropriate for students to join international

conference, it will increase the wish to join the international conference.

2. Our school can take place the international conference more often, it can

Hydraulic Characteristics of Flow over a Highly Permeable Porous Structure

Jan-Mou Leu1

Wei-Che Huang2 Hsun-Chuan Chan3

Abstract

The present study is carry out to investigate the velocity fields and turbulence characteristics of the flow over permeable structures by channel experiment in low water level. Detailed measurements of the time-averaged velocity components, turbulence intensity components of permeable and solid structures are taken by the acoustic doppler velocimeter（ADV）. The characteristic feature of porous medium is permeable, and the vertical distributions of time-averaged velocities above permeable structures are more uniform than solid structure due to the slip velocity at the fluid/porous interface. The turbulence intensity above structure with large porosity are slightly greater than small porosity structure, and the permeable structures have smaller turbulence intensity than solid structure around the structures. The results show that the porous medium reduces the turbulence intensity, and then reduce the scour to structures.

Keywords: turbulence intensity, porous medium, slip velocity

Introduction

Due to take account of environmental protection and conservation in recent years, ecological maintenance and rehabilitation concepts have been added into river engineering, hence ecological engineering methods have been extensively used in river renovate engineering. The main characteristic of the materials used in ecological engineering methods is porosity. Porous medium structures can increase the exchange effect on dissolvable organic particles, inorganic ions, and gas in the water, hence it can improve the self-cleansing ability of the river, and the holes in the structure can also serve as dwelling space for animals and plants in the water. Therefore, porous medium structures are popularly applied to river renovate engineering. Therefore, understanding the differences between the flow fields of permeable and impermeable structures are helpful to estimating the effects of the projects, and can also as a basis for the security of structures.

Leu (2005) and Chan etc. (2006) had experimental study on the velocity fields for permeable and impermeable structures, and categorized the flow condition into four different types according to the water level: (a) submerge flow typeΙ; (b) submerge flow type II;(c) transient flow; (d) subsurface flow, and carried out the experiments to measure the flow fields in submerge flow typeΙ. The results show that due to the slip velocity exists on the surface of porous medium, the time-averaged velocities at the fluid/porous interface of permeable structure are larger than that of impermeable structure. Furthermore, the velocity profile above the permeable structure are more uniform than that above the impermeable structure. In regard to the recirculating zone flow field characteristics of permeable structure, because the penetrating current flows out from the

1

Associate Professor, Department of Hydraulic and Ocean Engineering, National Cheng-Kung University, Tainan 70101, Taiwan. E-mail: [email protected]. Tel: 886-6-275-7575 ext. 63266,

2

Ph.D. Candidate, Department of Hydraulic and Ocean Engineering, National Cheng-Kung University, Tainan 70101, Taiwan. E-mail: [email protected]. Tel: 886-6-275-7575 ext. 63266

3

Postdoctoral Researcher, National Center for Computational Hydroscience and Engineering, The University of Mississippi, 102 Carrier Hall University, MS 38677, USA.

bottom of permeable structure, and the penetrating current pushes the recirculating zone downstream and stretches it, making the recirculating zone behind permeable structure is longer then that behind impermeable structure. The result show that the recirculating zone length of permeable structure is approximately 1.45 times the length of impermeable structure. The above study was performed only on submerge flow type I of high water level conditions, but the other types of flow conditions can be observed in general rivers, therefore the present study aims to investigate the flow fields of submerge flow type II by experiment, and discuss the variation of the flow fields around the structures.

Experiment equipment and setup

The experiments for this study were performed in a rectangular glass flume with adjustable slope. The length of the flume is 15 m, the width is 0.6 m, and the height is 0.6 m. Downstream of the flume, there is a reservoir tank and an electric motor to serve as the discharge provider system. The discharge of the flume is measured by using a calibrated V-notch weir located in the reservoir tank, and the water level in the flume, or the tailwater depth, is controlled by an adjustable tialgate, placed near the downstream end of the flume. The large and small porosity permeable structures made of glass balls with diameter of 2.5 cm and 1.5 cm, respectively. The dimensions of the permeable structures are 15 cm length, 60 cm width, 7.5 cm height, and the porosity γ of permeable structures are 0.475 and 0.349. The structure is placed at 8 m downstream of the flume inlet where the fully develop turbulent flow occurred. The velocity data are collected in the central line of the flume along the vertical lines at different streamwise distances by a NORTEK made three-dimensional sidelooking acoustic Doppler velocimeter. It operated on a pulse-to-pulse coherent Doppler shift to provide instantaneous velocity components at a sampling rate and volume of 25 Hz and 0.22cm3,respectively. Depending on the intensity of turbulence, the sampling durations are 3 to 5 min in order to have a statistically time independent average velocity. The schematic diagram of the experimental setup is shown in Fig. 1.

Experimental conditions and procedure

In this study, the experiments are carried out the at low water level (submerge flow type II) in order to investigate the differences of flow fields between permeable and impermeable structures. Three porosities of rectangular structures are used in the experiment, the porosities are 0.475,0.349 and 0(impermeable structure) The slope of the flume is keep at 1/300, and the average approaching flow velocity U is obtained from the depth-average value of the measured vertical distribution of approaching flow velocity at 8 m downstream of the flume inlet. The experimental conditions are show in Table 1. The turbulence characteristics at each measurement point is calculated according to the following formulas:

u U U = + (1) w W W= + (2) 2 u Tu = (3) 2 w w = T (4)

Where:

U 、W = the instantaneous velocity on the X and Z direction, respectively U、W = the average velocity on the X and Z direction, respectively u、w = the velocity fluctuation on the X and Z direction, respectively

Tu 、Tw = the turbulence intensity on the X and Z direction, respectively

When performing the analysis on the data, normalization of all linear lengths and velocity components are done by the height of structure HP and approaching velocity U, respectively.

Results and discussion

Velocity distributions

The flow conditions of permeable and impermeable are show in Fig. 2. The vertical distributions of normalized time-averaged streamwise velocity component U U₀ of permeable and impermeable structures at different vertical sections are presented in Fig. 3-(A),(B),(C). The differences in streamwise velocity component are small in the region -8≤x H_P ≤-2. In the region x H_P ≥-1, the streamwise velocity component begin to increase due to the contraction of the cross section. Because of water can pass through porous medium, and therefore the contraction effect of permeable structure is less than impermeable structure. Thus, the streamwise velocity component above structure become large with porosity decreased. The vertical distributions of streamwise velocity component above permeable structures are more uniform than impermeable structure due to the slip velocity at the fluid/porous interface.

Fig. 4-(A),(B),(C) shows the vertical distributions of normalized time-averaged vertical velocity component W U₀ at different vertical sections. The vertical velocities are very weak in the region -8≤x H_P ≤-2. Due to the contraction effect, the vertical velocity component begin to increase at the section x H_P =-1. At the section x H_P =0, the water flow upward and the vertical velocity become large with water depth. The maximum vertical velocities above permeable and impermeable structures are occur at the fluid/structure interface (y H_P =1). In the region x H_P ≥1, the vertical velocities above permeable structure are negative, it shows the water flow into permeable structure. Consequently, in the submerge flow type II condition, the discharge above permeable structure will decreased along streamwise.

Turbulent intensity

Fig. 5-(A),(B),(C) exhibits the vertical distributions of normalized streamwise turbulent intensity component Tu U₀ . The streamwise turbulent intensity begin to increase at the section

-1 H

x _P = . The permeable structures have smaller streamwise turbulent intensity, compared to impermeable structure, and the turbulent intensities of large porosity structure are bigger than small porosity structure.

The vertical distributions of normalized time-averaged vertical turbulent intensity component

0

U

Tw of permeable and impermeable structures at different vertical sections are presented in Fig. 6-(A),(B),(C). The tendency of vertical turbulent intensity is the same as streamwise turbulent intensity. In the region -1≤x H_P ≤0, the turbulent intensity increases, and with the porosity decreased the turbulent intensity increased. By comparing the turbulent intensity above the structures, we find the maximum value of turbulent intensity occur at the interface of the structures (y H_P =1), and the turbulent intensities of permeable structure are smaller than impermeable structure. This result shows that the porous medium can effectively decrease the

turbulent intensity at the interfaces of structures.

Conclusion

The flow fields of permeable and impermeable structure in submerge flow type II are detected experimentally by the acoustic Doppler velocimeter in a laboratory flume. Detailed measurements of the time-averaged velocity components, turbulent intensity are taken at different vertical sections around the structures. The vertical distributions of time-averaged velocities above permeable structures are more uniform than impermeable structure due to the slip velocity at the fluid/porous interface. Due to the water flow into permeable structure, the discharge above permeable structure will decreased along streamwise. The streamwise and vertical turbulent intensities of permeable structure are smaller than that of impermeable structure, and the penetration current can rdeuce the turbulent intensities at the downstream of permeable structures. Consequently, the porous medium is effective in reducing the turbulent intensity, and then reduce the scour to the structures.

References

17. Beavers, G. S. and Joesph, D. D. (1967). “Boundary conditions at a naturally permeable wall.” J. Fluid Mech., 30, 197–207.

18. Choi, C. Y. and Waller, P. M. (1997). “Momentum transport mechanism for water flow over porous media.” J. Env. Engrg., 123(8), 792-799.

19. Kuwahara, F., Kameyama, Y., Yamashita, S. and Nakayama, A. (1998). “Numerical modeling of turbulent flow in porous media using a spatially periodic array.” J. Porous Media, 1, 47–55.

20. Masuoka, T. and Takatsu, Y.(1996). “Turbulence model for flow through porous media.” Int. J. Heat Mass Transf., 39, pp. 2803–2809.

21. Mendoza, C. and Zhou, D. (1992). “Effect of porous bed on turbulent stream flow above bed.” J. of Hydraul. Engrg., 118(9), 1222-1240.

22. Prinos, P., Sofialidis, D. and Keramaris, E. (2003). “Turbulent flow over and within a porous bed.” J. of Hydraul. Engrg., 129(9), 720-733.

23. Vafai, K. and Kim, S. J. (1989). “Forced convection in a channel filled with a porous medium: An exact solution.” ASME J. Heat Transfer, 111, 1103–1106.

24. Vafai, K. and Thiyagaraja, R. (1987). “Analysis of flow and heat transfer at the interface region of a porous medium.” Int. J. Heat Mass Transfer, 30, 1391–1405.

25. Venkataraman, P. and Rama Mohan Rao, P. (1998). “Darcian, Transitional, and Turbulent Flow through Porous Media.” J. Hydraul. Engrg. 124(8), 840–846.

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27. Xingwei Chen and Yee-Meng Chiew, M. ASCE (2004). “Velocity Distribution of Turbulent Open-Channel Flow with Bed Suction.” J. Hydr. Engrg., 130(2), 140-148.

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Figure 1. Experimental setup

(a) (b)

Figure 2. Photograph of submerge flow type II: (a) impermeable structure (γ =0); (b) permeable structure (γ =0.475)

Table 1. Experimental condition Test Porosity U0 (cm/s) Fr Re Discharge (cms) A 0.475 37.47 0.3 59953 0.035 B 0.349 37.45 0.29 61418 0.035 C 0 37.45 0.29 61418 0.035 15cm 7 .5 cm 800cm 685cm Porous medium A D V y x head tank flow direction flow straighteners to recirculation tank from recirculation tank

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 0 1 2 3 y /H p 0 1 2 3U/U0 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 y /H p 0 1 2 3 U/U0 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 0 1 2 3 U/U0 (A) (B) (C)

Figure 3. Vertical distributions of streamwise velocity: (A) permeable structure (γ =0.475); (B)permeable structure (γ =0.349); (C) impermeable structure (γ =0)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 W/U0 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 W/U0 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 1 2 3 0 1 2 W/U0 y /H P y /HP y /H P X/HP (A) X/HP X/HP (B) (C)

Figure 4. Vertical distributions of vertical velocity: (A) permeable structure (γ =0.475); (B)permeable structure (γ =0.349); (C) impermeable structure (γ =0)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 0 1 2 3 y /H p 0 0.5 Tu/U0 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 0 1 2 3 y /H p 0 0.5Tu/U0 (A) (B) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 y /H p Tu/U0 0 0.5 (C)

Figure 5. Vertical distributions of streamwise turbulent intensity: (A) permeable structure (γ =0.475); (B) permeable structure (γ =0.349); (C) impermeable structure (γ =0)

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 0 1 2 3 y /H p 0 0.5 1 Tw/U0 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 0 1 2 3 y /H p 0 0.5 1Tw/U0 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x/Hp 0 1 2 3 y /H p Tw/U0 0 0.5 1 (A) (B) (C)

Figure 6. Vertical distributions of vertical turbulent intensity: (A) permeable structure (γ =0.475); (B) permeable structure (γ =0.349); (C) impermeable structure (γ =0)