Hydrodynamic Model of Hydraulic Engineering Based on Trigonometric Function Relation Equation

In order to explore the application of fluid mechanics technology in water conservancy and hydropower stations, the author proposes the study of hydraulic engineering fluid mechanics model based on trigonometric function relationship equation. According to standard k- ε Double equation and Reynolds time average (N-S) equation, given the runner boundary conditions, establish the mathematical model of the internal flow of the hydraulic turbine. Through CFD simulation technology, the runner of hydraulic turbine is numerically simulated to obtain the velocity distribution and blade pressure distribution inside the runner, movable guide vane and fixed guide vane, the reliability of the design is improved, and the application of CFD technology in hydropower project is analyzed with an example. The results show that, when the diameter of guide vane distribution circle is 4760mm, the scheme is optimal, and the relative efficiency under the optimal working condition is 96.35%. The flow of the modified runner from the inlet of the volute to the outlet of the draft tube is very stable under the optimal working condition, and there is no obvious vortex, especially there is no obvious vortex belt and vortex at the outlet of the runner; There is no obvious vortex in the draft tube, the flow on both sides of the pier is very uniform, and the flow on one side is not significantly greater than that on the other side, which fully shows that the flow performance of the modified runner is good. After reconstruction, the runner outlet flow field is good, and the internal flow line of the draft tube is smooth. The application prospect of hydrodynamic algorithm for hydraulic engineering is relatively broad.