二次流效應影響下湧波傳遞之模擬研究

Abstract

本研究旨在分析二次流效應對彎道湧波模擬之影響。模式在發展過程中，採用de Vriend (1977) 的速度剖面假設以求解延散剪應力考量二次流之效應。在數值處理上，採用雙階分割操作趨近法，將水理控制方程分割成延散步驟和傳播步驟求解，分別採用顯示和隱示差分式求解。比較混和型上風法、MacCormack法和總變量削減法（TVD）三種方法後，移流項數值方法採用較合適的MacCormack法。本研究採用Bell等(1992)所作的實驗來作比較，驗證模式的正確性。本研究採用的二次流速度剖面的假設為非急彎的條件，因此較小二次流強度因子案例之模擬結果會較接近實驗值。另外，在不同二次流強度因子案例中，考慮二次流效應之模擬結果均會較不考慮二次流效應之模擬結果更接近實驗值。

The purpose of this study is to numerically analyze the effect of the secondary flow on the surge propagation through a bend. The secondary flow effect was embedded in the dispersion stress terms of the flow momentum equations by adopting the vertical velocity profile proposed by de Vriend (1977). Based on the two-step split-operator approach, the momentum equations were decomposed into dispersion and propagation steps and were solved by using both explicit and implicit techniques. Compared with hybrid upwind scheme and TVD (Total Variation Diminishing) scheme, the MacCormack scheme is most suitable for solving the advection term on simulating the positive surge. The experimental data conducted by Bell al. (1992) was compared with simulating results to examine the accuracy of the proposed model. The vertical shape functions embedded in the model is not appropriate for the flow simulation in the sharp bend. Contrarily, results of the case with the smaller secondary intensity show the better agreement. Results indicate that the simulations either in a sharp bend or not, the simulation considering the secondary flow effect shows better agreement.