Two-dimensional flow movement in the area of protective regulatory structures

Abstract

Abstract The article discusses the results of numerical studies of the flow movement with a sharp change in the parameters of the channel. Basically, the results of the study using the system of two-dimensional equations of hydrodynamics-Saint-Venant are analyzed. The divergent form of two-dimensional equations describing the movement of a water stream at a site of regulation of a channel by protective and regulatory dams is given. The influence of the length step on the results of numerical experiments is investigated numerically. Graphs of the time variation of the longitudinal velocity component behind the sudden double expansion of the channel are compiled. The flow was unsteady all the time and had the character of stationary pulsations, and the finer the grid, the richer the spectrum of these pulsations. It was noted that in numerical calculations, the time step in the calculations was always much less than the minimum pulsation period, therefore, these pulsations were not associated with difference oscillations that can arise when approximating by central differences. It is concluded that, according to the authors from the following and the present work, they collectively show that the pulsations on different grids differ significantly, the average values of the velocities are close, and thereby the solution for the average values is well converged, this shows that the pulsations are a property source equations of Saint-Venant. The applicability of the numerical model, consisting of two-dimensional shallow water equations, the vector equation of momentum conservation and the scalar equation of mass conservation, in description the flow with the presence of circulation zones, which is typical when water flows are constrained by protective-regulatory structures. In this case, the solution pulsates around a certain average value, and the average length of the circulation zone behind the sudden expansion of the open flow is in good agreement with the laboratory experiments of G.L. Mazhbits.