Simulation of the process of free spreading of a two-dimensional water flow behind pressure-free holes

Abstract

Introduction. Construction of hydraulic structures must meet high reliability requirements applicable to water supply channels, free-flow pipes, and open spillways. Any analysis of hydraulic structures must take account of the dynamic properties of flows that the structures accommodate. The theory of one-dimensional free flows, used in practice, has a number of general guidelines, but lack any details. The co-authors take advantage of the theory of two-dimensional free flows, namely, the method of characteristics proposed and developed in the works of I.A. Sherenkov.
 Materials and methods. In her works, B.T. Emtseva suggests that a uniform flow can be coupled with a general flow only with the help of an intermediate “simple wave” flow, but this statement has no proof. We identified and analyzed a general flow in the plane of the hodograph. Thereafter, characteristics of the first family of the flow were determined. A transition to the physical plane of the flow allowed to determine the coordinates of the points of characteristics of the second family. This allowed to find the coordinates of the points of the extreme streamline and to determine its geometry.
 Results. The proposed mathematical model complied with the system of equations, describing the flow, and the boundary conditions when it was applied to the boundary problem of the free spreading of a stormy, potential, two-dimensional in plan, free, stationary water flow and its free inflow into a wide horizontal smooth channel.
 Conclusions. The concept of a general flow (previously unknown) and equations of motion in the plane of the velocity hodograph made it possible to theoretically prove its applicability to the problem of free flow spreading. A simple analytical solution is obtained in the plane of the velocity hodograph. The theoretical significance of this mathematical model consists in the possibility of its step-by-step application to practical problems and its complication from the identification of the main regularities of a simplified model of a potential flow to the practical use of simulation results. The implementation of the methodology in the form of software will make it usable by designers of hydraulic structures. This is the first stage of problem solving, and at further stages resistance will be taken into account.