擬似三維異重流及沉滓運移模式之發展與測試

Abstract

水庫泥砂運移型態可分為三角洲堆積、異重流與渾水層型態，較粗的顆粒因流速減 緩落淤形成三角洲，其餘渾水因清渾水比重之差異，在適當的條件下將潛入水面形成異 重流，沿庫底向壩前運行。三角洲淤積型態，其理論較為成熟，已有許多輸砂模式可進 行模擬分析；而泥砂異重流運移之模擬相對困難，目前異重流數值模式發展大致以垂直 二維模式為主，但上游河道進入庫區後河寬與水深均向壩前方向持續擴張，其流場與泥 砂運移實屬三維現象，對於異重流運移特性、動量交換與沿程落淤等現象，有必要藉助 三維模式進行瞭解。 過去在國科會支持下，洪(2007)以層內部二次形狀函數與層介面速度與剪力連續條 件概念發展結構網格之擬似三維分層積分水理模式，簡化三維計算並增加模式穩定性， 本計畫將此一概念推廣至非結構網格(unstructured grid)，並於垂直方向導入σ-座標，以 適應不規則地形，同時以混合長度計算垂向紊流黏滯係數，並進一步建立渾水濃度與密 度差之關係以反應異重流運移現象，與細顆粒沉滓沈降機制以反映異重流沿程落淤、能 量耗散現象等機制；模式嘗試進行庫區流場與濃度分佈模擬，與前人相關試驗結果及石 門水庫泥砂濃度量測結果作比較，期進一步瞭解異重流特性，提供水利單位排砂策略研 擬參考。

The sediment transport behavior in reservoirs can be classified into delta build-up, density current and turbidity layer. The sediment-laden flow entering into the reservoirs behaves like a jet shooting into a stilling basin, and the sediment deposits to form a delta at the entrance due to sudden deceleration. The numerical models for delta formation have been well developed and frequently used to simulate and analyze the flow phenomenon. In addition to the delta formation, the silt and clay plunging beneath the clear water due to density difference and moving toward the dam, is recognized as density current. Most of the numerical models being developed for density current were vertical 2D. However, the behaviors of flow and density current in reservoirs are indeed three dimensional. Transport behaviors of density current and its characteristics including marching speed of head, momentum exchange, sediment deposition should be analyzed by using 3D models. Under the past support of National Science Council, Hung (2007) proposed a pseudo-3D layer-integrated model in which a quadratic shape function used to approximate the velocity distribution in layer ensures the continuity of velocities and shear stress at interfaces. The water depth solved directly without the need of 2D sub-models, whereas the computation is simplified and stable. In this study, Hung’s model will be extended to cover the properties including the unstructured grid and σ-coordinate, and therefore, to allow the numerical grid adapting to complex geometries and terrains. The mixing length concept predicting vertical turbulent viscosities will be embedded into the flow model. The state function for density variation and transport mechanisms including sediment deposition, momentum exchange will be also adopted in this model. In lieu of simulation study performed for some published laboratory data and measured data from Shi-Men Reservoir, the transport mechanism of density current will be intensively analyzed as the basis for planning sediment sluicing strategies.