三維光滑明渠紊流流場之量測與分析

Abstract

前人文獻中，關於三維明渠紊流流場之精確量測與模擬誠屬有限。本研究除針對前人二維量測結果進行全斷面流場之分析及探討外，並以Fluent計算流體力學軟體之雷諾應力模式（Reynolds-Stress-Model, RSM）進行數值模擬。最後，再配合三維光纖雷射杜卜勒流速儀（3-D Fiber-optic Laser Doppler Velociemetry, 簡稱3D-FLDV），針對二次流對直線渠道光滑明渠流場之影響，進行量測試驗，以深入瞭解其水流特性及物理機制。 本研究利用楊（1998）二維光纖雷射杜卜勒流速儀（2D-FLDV）之光滑底床量測結果，進行全斷面流場資料分析。在底床剪應力方面，以Knight（1984）及Rajaratnam（1969）之試驗資料重新分析，獲得矩形斷面之底床及邊壁剪應力分佈。就平均速度剖面而言，以Yoon（1970）、邱（1986）及胡（1995）三家流速分佈理論，針對垂線最大流速發生於液面及液面下之物理現象，進行預測結果之比較探討。另外，根據實測資料經由迴歸分析，得出直線矩形斷面渠道之全斷面主流向及垂直向紊流強度分佈式，並以平均速度剖面分佈式推求雷諾應力之分佈，擬供紊流流場之分析參考。 數值模擬部分，針對楊（1998）試驗資料中之陡坡（臨界水深大於正常水深）流況，以RSM模式進行明渠紊流之數值模擬。其中，平均速度剖面之模擬結果與實測資料大致相符，惟近邊壁與近液面區速度剖面折回之現象無法反應。一般而言，主流向紊流強度模擬之結果較實測值稍低，垂直向紊流強度除靠邊壁外，其模擬結果與實測資料頗為一致。此外，陡坡橫向紊流強度與主流向及垂直向紊流強度之相對大小，大體上與緩坡實測結果一致。 在三維量測方面，本研究建構一套三維光纖雷射杜卜勒流速量測系統，克服空間上量測點會焦及時間上之同步量測等問題，獲得一有效之三維紊流同步量測方法。研究結果顯示，二次流主要係紊流之非等向性及雷諾應力在空間上分佈不均所造成，且雷諾應力項與生成項對二次流之貢獻度約略相當。

Reliable measurements and models for 3-D turbulent open channel flow are limited. In this study, both experimental investigations and numerical simulations were performed to increase our understanding of the flow structure (including secondary current) for the straight, fully developed turbulent open channel flows. First, data collectioned by Yang (1998) with 2D-FLDV (fiber optic laser Doppler velocimeter) for steep (supercritical) turbulent open channel flows over a smooth boundary were re-analyzed. Several dimensionless semi-empirical formulas were derived for the predictions of mean velocity profiles, turbulence intensities, and Reynolds stresses. A sophisticated Reynolds-Stress-Model (RSM) was chosen to simulate the fully developed steep turbulent open channel flow over a smooth boundary. The computed mean velocities were consistent with the measured data except for the regions near the side walls and water surface. In general, the simulated longitudinal turbulence intensities were slightly lower than the experimental results, and the simulated vertical turbulence intensities were fairly consistent with the measured data except for the regions near the side walls. The relative magnitude of the longitudinal, vertical and transverse turbulence intensities simulated from RSM was consistent with that for hot film measurements under mild slope conditions. For the 3-D measurements, all velocity components were measured by making use of an innovative six beams and two probes laser Doppler velocimeter system. All terms in the vorticity equation were investigated with high accuracy. It was found that the secondary current was cause by the anisotropy of the turbulence and the non-homogenious distribution of the Reynolds stress. In addition, the Reynolds-Stress term and the generation term in the vorticity equation have a tendency to balance each other.