探討水下地形變化與表面流速關係之研究

Model tests on the relationship between surface velocity and bathymetry

陳昕妤(Hsin-Yu Chen)

指導教授 ： 何昊哲

國立臺灣大學/工學院/土木工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202201858

摘要

近年來極端降雨事件對世界各國造成不少災損，為提升洪水期間之災害應變能力，有效的河川流量監測顯得格外重要。考量觀測安全性及儀器自身限制，目前在高洪峰期間的流量量測仍多使用率定曲線進行推估。然而在高含砂水流的衝擊下，利用此種方式推算流量會增添許多不確定性。目前許多研究嘗試以非接觸式的方法量測流速與水深推估流量，本研究選擇大規模粒子影像測速法測量流速，再結合數值方法以淺水波方程式模擬水下地形，期能以安全性高、效率高及成本低的方法精進洪水期間之現地流量觀測。
本研究分為流速量測及地形數值模擬兩步驟執行。實驗於長30 m、寬1 m、高1 m之室內循環水槽進行，利用變換流速、突起物個數及突起物配置，設計五組不同的案例。實驗過程中先透過錄影記錄觀測區域內的示蹤粒子，再使用大規模粒子影像測速法辨識流速。考量數值模擬需依賴表面流速資料作為初始條件，因此將實驗所得流速與聲波都卜勒流速儀之擬合結果進行驗證，用以衡量數據可靠度；另外在數值模擬上，運用有限差分法搭配Arakawa C型網格對淺水波方程式離散，便能一次性地計算出流場內之二維水深，在假設水面高程不隨時間變化的前提下，間接推估出水下三維地形。根據實驗結果指出，與聲波都卜勒流速儀擬合結果相比，各組計算之平均表面流速誤差為3.9%；從變因分析發現，即使提升流速、增加突起物個數及縮短突起物間距會造成模擬誤差，但水下地形模擬之精度仍有95%。研究結果證實，在室內試驗條件下運用大規模粒子影像測速法與淺水波方程式推算水下地形是可行的，建議未來研究可進一步將此方法學擴展至更大尺度的水槽或現地進行驗證。

關鍵字

大尺度粒子影像測速法 ； 淺水波方程式 ； 有限差分法 ； 水下地形模擬

並列摘要

Extreme climate events, such as heavy rainfall, cause damage to many countries around the globe in recent years. Thus, effective river discharge monitoring is an integral part of enhancing the emergency response ability during flooding. Due to safety concerns and equipment limitations, the rating curve method is often used to estimate the discharge in high flow period; however, the high river sediment concentration generates uncertainties of the river discharge estimation. Therefore, a study of discharge estimation method without physical contact with the water is essential.
The study conducted a series of model tests in a circulating water tank to investigate the bathymetry by various flow velocity and hump configuration. The test procedure can be divided into two steps, namely, velocity measurement and numerical simulation of the terrains. The surface flow velocity was identified by Large Scale Particle Image Velocimetry (LSPIV) method and verified with the fitting result of Acoustic Doppler Velocimetry (ADV). In addition, the finite difference numerical simulation analyzed 2D depths in the flow field by discretizing the shallow water equations with the Arakawa C-grid. The bathymetry was then estimated under the assumption of a time invariant system. The experimental results show that the deviation of measuring surface velocity is 3.9%. The estimation accuracy of a bathymetry is higher then 95%. Based on the results, it is feasible to determine the bathymetry in physical model tests using LSPIV method and the shallow water equations.

並列關鍵字

Large Scale Particle Image Velocimetry ； Shallow water equations ； Finite difference method ； Bathymetry

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