Development and Application of 2-D Finite Analytic Model of Water and Sediment Movements in Open Channel
|關鍵字:||水深平均二維模式;顯式有限解析法;非耦合演算;非正交貼壁座標系統;紊流模式;非均勻沈滓;懸浮載濃度剖面;沈滓交換速率;depth-averaged 2-D model;explicit finite analytic method;uncoupled algorithm;non-orthogonal body-fitted coordinates system;turbulence model;non-uniform sediment;suspended sediment concentration profile;sediment exchange rate|
For irregular natural channels, there exist longitudinal and lateral variations in flow field and channel bed evolution. A depth-averaged horizontal 2-D model has the capability of simulating the long-distanced longitudinal variations of flow characteristics, as well as the lateral variations of channel cross sections. The purpose of the study is to develop a depth-averaged horizontal 2-D hydraulic and sediment transport model. The main special features of the model include: (1) Considering the irregular cross-sectional geometry of natural channel, a non-orthogonal body-fitted coordinates system is constructed, and the depth-averaged hydraulic and sediment transport equations are derived on the coordinates. The computational grids are then generated by one of the grid generation methods, which is suitable for the flow geometry characteristics. (2) Aiming at the steep channel slope and high flow velocity of Taiwan’s rivers, the hydraulic model considers the dominating convection effects. The explicit finite analytic method is adopted to discretize the governing equations of flow. This numerical method is suitable for the hyperbolic-type partial differential equation; thus it is expected to be applicable to the general open channel flows. (3) The sediment model is uncoupled with the hydraulic model. The incipient shear stress for individual sediment particle is modified to account for the interaction among nonuniform sediments. In view of the strong convection character of suspended load, the suspended load and bed-load transport are separately computed. In addition, the method for estimating the sediment exchange rate near bed between suspended load and bed load in the vertical 2-D models is examined to see whether it is still applicable to depth-averaged horizontal 2-D models. By utilizing the sediment concentration profile developed by van Rijn, a new approach, which is suitable for use in the depth-averaged models and named integral approach, for estimating the sediment exchange rate near the channel bed is proposed to make more accurate prediction of channel scour or deposition mechanism. In this study, the proposed model is applied to various fixed-bed flow and mobile-bed aggradation/degradation simulations. Experimental data are used to verify the applicability and accuracy of the model. For the hydraulic model, case studies include: steady backwater flow, unsteady floodwater flow, flows with strong convection and with separation and circulation in a storage basin and in a flume with Groyne, and dam-break and hydraulic jump flows with sub-critical and supercritical regimes occurring simultaneously and sequentially, and with strong curvature of the free surface. For the sediment transport model, the accuracy of the integral approach for estimating the sediment exchange rate is first verified by a scouring experiment with clear water entering in the inlet. The predicted sediment concentration profiles are compared with the experimental measurements and generally good agreements are obtained. This fact shows that the integral approach with appropriate concentration profiles could compensate for the missing mechanism of vertical settling and diffusion of sediment in the depth-averaged model. In addition, for further understanding of its capability for predicting the channel bed evolution and the change of composition of bed material, the model is applied to simulate the cases with aggrading and degrading beds, respectively, with uniform or nonuniform sediment, and the more complex cases with aggrading and degrading bed alternatively. Comparisons against the experimental data show that the explicit finite analytic method is applicable to the open channel flows with strong convection, and the newly-proposed integral approach, which considers the non-equilibrium sediment concentration profiles on the exchange rate between suspended load and bed load, improves the inherent limitation of the depth-averaged model and increases the accuracy of predicting the channel bed evolution. In future, on the basis of the available field data of Taiwan’s rivers, the model parameters can be calibrated, and numerical simulations and necessary modifications of the model can proceed to enhance the model’s practical value.