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Characteristics of Turbulent Open-Channel Flow with Smooth Boundary
mean velocity profiles
本研究包含二維與三維光滑明渠紊流流場量測資料之分析。二維部分乃應用楊(1998)以光纖雷射杜普勒測速儀(FLDV)量測所得之陡坡光滑明渠紊流流場資料，進行全斷面資料之分析，並尋求其水流特性及物理機制。二維實驗條件為: 渠床坡度S = 0.3%、1% 與2%；寬深比B/H介於4.55與11.36之間；流場均為超臨界流(Fr 1.06~3.16)；雷諾數Re之範圍則介於10157至82900之間。三維資料則同樣利用FLDV進行量測，其實驗條件為: S = 0.05%；B/H = 5.0；Fr = 0.688；Re = 16253。
文中主要分析項目包括：平均流速剖面、紊流強度及雷諾應力分佈等水力特性。就2-D量測資料而言，在平均速度剖面分析方面，提出了陡坡最大速度發生位置之分佈規律式，於無因次主流紊流強度及垂向紊流強度亦各提出一經驗分佈式，且整體而言，與實測資料之一致性尚稱良好。值得一提的是:(1)紊流強度於陡坡時近液面區皆有反曲點之產生；(2)無因次垂向紊流強度之值多集中於1附近；(3)雷諾應力於近液面附近亦出現負值區。此外，3-D量測資料中顯示:(1)於本研究實驗條件中，就大部分區域而言，三個方向之無因次紊流強度大小依序為u''/ U*3-D>w''/U*3-D >v''/U*3-D ；(2)本試驗條件下，近床區無因次紊流強度沿水深方向呈線性變化之範圍，在y、z與x方向具有δy > δz > δx 之關係。|
River regulation and water resources planning are difficult in Taiwan due to the geographical reasons. The previous studies concentrated on the two-dimensional (2-D) flow structure that is fundamental and essential to an understanding of open-channel turbulence. Real flows in the natural rivers are often too complex to be represented as 2-D flows. Consequently, understanding the characteristics of 3-D open channel turbulent flow is necessary for many hydraulic engineers in the world. This study analyzed data measured by both 2-D & 3-D FLDV systems for turbulent open channel flows with a smooth boundary. The 2-D data were measured in a steep open-channel with a smooth boundary using a fiber-optic laser Doppler velocimter (FLDV) by Yang (1998). The experimental conditions were: channel bed slope of 0.3%, 1% and 2%, aspect ratio varied from 4.55 to 11.36, Froude number (Fr) ranged from 1.06 to 3.16 (supercritical flow), and Reynolds number (Re) varied from 10157 to 82900. As regards to the 3-D data, the channel bed slope of 0.05%, aspect ratio of 5.0, Froude number (Fr) of 0.688 (subcritical flow), and the Reynolds number (Re) of 16253 were selected. The objectives of this research were to study the mean velocity profiles, the turbulence intensities, and the Reynolds stress for all experimental conditions. For the 2-D measurements, a semi-empirical formula was derived to predict the location of the maximum velocity. Two dimensionless semi-empirical formulas were also derived to predict the two dimensional turbulence intensities for steep open channel flows. Resonably good agreement between the measured and the predicted data was obtained. It was found that there was an inflection point on the turbulence intensity profile near the water surface. The dimensionless vertical turbulence intensity had an average value of about one. There was a region of negative values for Reynolds stress near the free surface. As regards to the 3-D experimental data, the relative magnitude of the dimensionless turbulence intensities were u''/ U*3-D>w''/U*3-D >v''/U*3-D, which was consistent with the earlier hot film measurements. The relative magnitude of the depths (δy, δz and δx in the y, z and x directions) with linear variations of the dimensionless turbulence intensities (v''/U*3-D, w''/U*3-D and u''/ U*3-D ) in the flow depth direction (y) was δy > δz > δx .
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