底泥再懸浮引起密度層化現象的大渦流模擬

Large-eddy simulation of suspension-induced density stratification in turbulent flow

邱繼儒(Ji-Ru Chiu)

指導教授 ： 周逸儒

國立臺灣大學/工學院/應用力學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201603741

摘要

本研究使用大渦流模擬(LES)結合動力混合模型(DMM)模擬次要網格，來探討一等壓力梯度驅動的水平剪力所造成之泥沙密度層化流體運動，我們於底床引入掏刷函數(pick-up function)來模擬掏刷的現象，藉由掏刷率與泥沙沉降速度的大小作為分層效應強弱的控制參數。
由模擬結果發現當掏刷率較大時，分層效應會較強烈，使紊流動能相較於無密度層化效應之流動具有某程度上的衰減，造成垂直底床方向的質量及動量的傳輸受到抑制，甚至在極大掏刷率的情況下，流場中的紊流動將會完全受到抑制，流動進而發展成層流(laminar flow)；當沉降速度越大，泥沙在水域當中的影響時間較短，故紊流動能受分層效應的影響相對較弱，並且透過理想的數學模型加以分析沉降速度與濃度分布間的關係，並同時透過梯度及通量理查森數(Rig、Rif)來分析層流化與否的關鍵。

關鍵字

大渦流模擬 ； 密度分層效應 ； 理查森數 ； 剪力分層流 ； 層流化流

並列摘要

In this study, we use large-eddy simulation (LES) with a dynamic mixed model (DMM) to investigate the stratified channel flow due to sediment resuspension. The flow is driven by a constant pressure gradient. We apply a pick-up function at the bottom to simulate the erosional phenomenon. The empirical erosion rate and settling velocity are chosen as parameters to control the strength of density stratification.
Based on our results, we found that if the erosion rate is greater, it enhances density stratification, suppressing the vertical transport of mass and momentum. In this case, turbulent kinetic energy decays to a certain degree. In the case of the greatest erosion rate, the turbulent kinetic energy is totally damped, and the flow eventually becomes the laminar flow. For the larger settling velocity, the time sediment is retained in water column is shorter, and the influence of density stratification is relatively weak. The analysis of Richardson number is presented. Moreover, we analyze the relation between settling velocity and sediment concentration profiles using the self-similarity analysis.

並列關鍵字

large-eddy simulation ； density stratification ； Richardson number ； stratified shear flow ； turbulence suppression.

參考文獻

1 Richardson, L. F. (1920). “The Supply of Energy from and to Atmospheric Eddies.” Proc. Roy. SO 97(686): 354-373.

2 Taylor, G. I. (1931). “Effect of Variation in Density on the Stability of Superposed Streams of Fluid.” Proc. R. Soc. 132: 499-523.

3 MILES, J. W. (1961). “On the stability of heterogeneous shear flows.” J. Fluid Mech. 10: 496-508.

4 Abarbanel, H. D. I., et al. (1984). “Richardson Number Criterion for the Nonlinear Stability of Three-Dimensional Stratified Flow.” Physical Review Letters 52(26): 2352-2355.

5 Deardorff, J. W. (1973). “An Explanation of Anomalously Large Reynolds Stresses Within the Convective Planetary Boundary Layer.” Journal of the Atmospheric Sciences 30: 1071-1076.