二維水深平均模式應用於彎道水流與泥沙運移模擬之研究

Abstract

本文之研究目的主要乃擬發展二維水深平均模式用以模擬彎道與直線渠道之流場與泥沙之運移行為。針對模式中水理子模式而言，本研究提出新的數值方法來求解淺水波控制方程式並加入彎道中二次流計算之考量；就輸砂子模式而言，本研究著重於推移載與懸浮載分離計算之建立。 本研究之控制方程式係建立在正交曲線座標系統上，並以本研究所提之新數值方法──雙階分割操作趨近（two-step split-operator approach）法求解水理控制方程式，此數值方法有別於一般之分割操作趨近法如投射法（Projection method, Chorin 1968; Fortin et al. 1971），於演算流程中第二步驟（傳播步驟）同時考量壓力梯度及底床剪應力，此一修正可使水利問題的數值模擬具有更高的彈性度與良好的收斂速度。 本研究之彎道定床模擬中所建立之二次流子模式係採用de Vriend（1977）彎道流速剖面之假設，計算因水深平均（depth averaging）所產生之延散剪應力（dispersion stress）以近似二次流效應之模擬，數值之模擬結果與 de Vriend and Koch （1977）緩彎渠道 與Rozovskii（1961）急彎渠道二組模型試驗資料進行比對，以探討水流流經平床彎道時之水理現象，同時，本研究也針對延散剪應力項作進一步之分析，發現延散剪應力對側向動量之傳遞（由內岸傳遞至外岸）扮演極重要之角色。 至於泥沙運移之模擬，本研究著重於推移載與懸浮載之分離計算（Holly and Rahuel 1990; Spasojevic and Holly 1990）以替代總載（total load）計算之考量，其中懸浮載源項（source-term of suspended-load）代表泥沙之運移在局部之流場中是處於懸浮載運移還是為推移載運移。本研究除了參考Spasojevic and Holly的輸砂傳輸觀念外，也針對輸砂輔助方程式之斜坡上輸砂量及懸浮載源項進行修正，以求得合理之模擬結果。最後將本研究之動床數值模式應用於Struiksma et al.（1985）之彎道動床模型試驗，模擬結果顯示計算值與實驗值存有誤差，本文亦針對此誤差來源進行討論與提出未來改善模式之建議。

A 2-D depth-averaged modelling, is developed for the calculation of flow field and sediment movement in straight and curved channels. For the establishment of flow submodel, the study proposes a new methodology for solving shallow water flow equations and the computation of secondary-flow effect by considering the dispersion stresses. For the sediment transport submodel, it focuses on the concept of coupling the suspended-load transport with the bedload transport. In this study, the shallow water flow equations, in terms of orthogonal curvilinear coordinate system, are computed numerically by the two-step split-operator approach. This newly proposed method, rather than just the conventional Projection method (Chorin 1968; Fortin et al. 1971), considers the effects of pressure gradient and bed friction in the second step (propagation step). This treatment is suitable for solving shallow water flow equations. It can increase the flexibility, the efficiency and the applicability of the numerical simulation for the various hydraulic problems. As for the bend-flow simulation with fixed bed, the influence of secondary flow is taken into account through the calculation of the dispersion stresses, which arisen from the integration of the products of the discrepancy between the mean and the true velocity distributions. Two sets of experimental data from de Vriend and Koch (1977) and Rozovskii (1961), respectively, are used to demonstrate the model's capabilities. The former data set was from a mildly curved channel, whereas the latter was from a sharply curved channel. The simulated results considering the secondary flow effect agree well with the measured data. Furthermore, an examination of the dispersion stress terms shows that the dispersion stresses play a major role in the transverse convection of the momentum shifting from the inner bank to the outer bank for flows in both mild and sharp bends. In regard to the sediment movement, the separated computations between the suspended-load and bedload transports (Holly and Rahuel 1990; Spasojevic and Holly 1990) is used instead of a total-load concept. The source-term of suspended-load is defined to represent the sediment movement either in suspension or as bedload, depending on local hydraulic conditions. Besides, this study follows the Spasojevic and Holly's concept, some auxiliary relations appeared in the sediment transport equations, such as bedload flux on the steep slope and suspended-load source, are modified to obtain the reasonable results from specific test applications. Finally, the present model is applied to the mobile-bed simulation in a bend. Although some discrepancies appear in the computed results comparing with the measured data obtained from Struiksma et al. (1985), the discussions and the suggestions of improvement are mentioned to be referred for the further study.