A simple scheme for calculating the added mass of hydraulic gates

In gate research and design, added mass calculations serve to establish resonance frequencies, vibration modes and the magnitude of flow-induced self-excitation and damping. The fluid boundary geometries vary strongly with gate position and water level variation. A relatively simple and versatile computation scheme is presented which is based on two-dimensional potential flow without wave radiation. Only small amplitude vibrations are considered. A square mesh grid is used, and the potential flow problem is solved by use of finite differences and the classical pointwise Gauss-Seidel iteration (relaxation) method. When the spread-sheet type calculation is used, boundary conditions and boundary locations can easily be varied; this makes it suitable for demonstration purposes. Presented are the boundary conditions, and how they are introduced in the computation scheme. The accuracy of the results is discussed for some cases for which analytical solutions exist: the vibrating strip and the vibrating wall. The number of relaxations needed, the use of overrelaxation and the introduction of an automatic stop of the calculation are other elements of the paper.