Numerical models and theoretical analysis of supercritical bend flow

The flow pattern of supercritical flow in bend channels is complicated due to the shock wave phenomenon, which creates difficulties with regard to research and design of bend channels. Using the spillway of an actual project as an example, a three-dimensional numerical investigation was conducted to simulate the flow in a steep-slope bend based on the renormalization group (RNG) k-ε turbulence flow model and the volume of fluid (VOF) method. The validity of the numerical simulation was demonstrated by comparison between the results of numerical simulation and physical model tests. An optimal scheme of setting vertical vanes in the bend channel is presented. The results of numerical simulation and physical model tests are in agreement, which demonstrates the effectiveness of optimization of vertical vanes and the validity of the three-dimensional numerical simulation. Water depths along both bend walls were analyzed numerically and theoretically. The formula for calculating supercritical water depth along either bend wall was derived, and the critical condition of flow separation from the inner wall was determined.