Flow in Open Channel with Complex Solid Boundary

Abstract

A two-dimensional steady potential flow theory is applied to calculate the flow in an open channel with complex solid boundaries. The boundary integral equations for the problem under investigation are first derived in an auxiliary plane by taking the Cauchy integral principal values. To overcome the difficulties of a nonlinear curvilinear solid boundary character and free water surface not being known a priori, the boundary integral equations are transformed to the physical plane by substituting the integral variables. As such, the proposed approach has the following advantages: (1) the angle of the curvilinear solid boundary as well as the location of free water surface (initially assumed) is a known function of coordinates in physical plane; and (2) the meshes can be flexibly assigned on the solid and free water surface boundaries along which the integration is performed. This avoids the difficulty of the traditional potential flow theory, which seeks a function to conformally map the geometry in physical plane onto an auxiliary plane. Furthermore, rough bed friction-induced energy loss is estimated using the Darcy-Weisbach equation and is solved together with the boundary integral equations using the proposed iterative method. The method has no stringent requirement for initial free-water surface position, while traditional potential flow methods usually have strict requirement for the initial free-surface profiles to ensure that the numerical computation is stable and convergent. Several typical open-channel flows have been calculated with high accuracy and limited computational time, indicating that the proposed method has general suitability for open-channel flows with complex geometry.