| Abstrakt: |
This research paper addresses essentially a numerical simulation of a hydraulic jump in a rectangular channel. The hydraulic jump properties were determined as the length, height, position, and produced energy dissipation. Such characteristics are vital to the study and dimensioning of hydraulic systems in open channel flows. The Shallow Water Equations, named 1D Saint–Venant (continuity equation and motion quantity equation), were used in matrix form in the application of the discretization technique by finite elements in combination with the weighted residual method. The corresponding 1D mathematical model was applied to compute a shockwave referring to the simplifying hypotheses (dynamic calculation of the shockwave under certain practical simplifying hypotheses). The finite element method and the channel boundary characteristics method were used to obtain a numerical solution of the pair of hyperbolic partial derivative equations. The finite element model was then developed using mixed elements with two and three nodes, taking into account the nature and type of the field. One-dimensional model was obtained for each field, based on average speeds on the vertical. The position of the free surface is obtained from a given configuration of rectangular channel (slope condition, upstream, etc.). The results allowed the prediction of the dynamic profile of the free water surface following downstream flow monitoring and the steady state of the channel jump. A very good agreement was found compared to experimental and numerical measurements of other researchers. Interestingly, the hydraulic jump dissipated approximately 10.84% of the flow kinetic energy. |
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