【摘要】 对Li&Cheng的势流模型在数值方法、床面平衡条件及冲刷床面调整技术做出了3方面的改进。采用边界元法代替差分法求解Laplace方程,前者可以准确地拟合地形与管道边界,因而可以准确反映固壁边界对流态的影响,此外,还具有数据准备简单,降低计算维数,计算速度快等优点。Li&Cheng模型以床面水流切应力等于泥沙起动切应力,τ_b=τ_c,作为床面平衡条件,这只适用于清水冲刷。以沿程输沙相同作为平衡剖面条件,理论上,将模型推广到了动床冲刷。此外,为了提高模型的收敛性,提出了最速下降法与牛顿迭代法相结合的床面调整技术。采用实验资料对模型进行了检验,计算的冲刷深度与实验结果符合良好。更多还原

【Abstract】 The potential flow model proposed by Li & Cheng is improved in the aspects of numerical method, bed surface equilibrium condition and scoured bed surface adjustment technique. The boundary element method(BEM), instead of the method of difference, is used to solve the Laplace equation. The BEM can accurately fit the terrain and pipeline boundary, so that the influence of solid wall boundary on flow pattern can be reflected accurately. In addition, the BEM also has the advantages of simple data preparation, reducing computational dimension, fast calculation speed and the like. In Li and Cheng model, the bed surface equilibrium condition is that the shear stress of water flow on the bed surface is equal to the starting shear stress of sediment, that is, τ_b=τ_c. However, this is just valid for the clear-water scouring. In the present paper, the constant sediment transport along the way is taken as the criterion of bed surface equilibrium, which has, in theory, extended the potential flow model to the moving bed scour. Besides, in order to improve the convergence of the model, a seabed surface adjustment technique is proposed, which is a combination of steepest descent method and Newton iteration technique. This model has been tested by using experimental data, showing that the scouring depth calculated by the model is in a good agreement with the results from experiments.更多还原