Abstract

A two-dimensional numerical simulation of the water flow in a rectangular channel with submerged obstacles distributed alternately along its banks is presented. The governing equations of flow are the shallow water equations, which will be solved by the Boltzmann
lattice method (LBM) with multiple relaxation times (MRT). The non-slip bounce-back scheme was used on walls and obstacles, constant discharge at the inlet and fixed depth at the outlet of the channel. Due to the characteristics of the problem to be simulated, a large eddy simulation (LES) technique was incorporated into the computational code, which allows to obtain results
that are closer to the actual behavior of the flow. In addition, the stability of the simulation at all points of the mesh is evaluated for each step of time and, together with the property of the consistency of the LBM, the convergence of the solution is obtained. The simulation
provides the depth, velocities in the x and y directions, and the magnitude of water vorticity.

Abstract

This paper analyzes the ability of the Lattice Boltzmann method (LBM) with multiple relaxation times (MRT) in the simulation of flow in practical engineering problems. The case study covered refers to the first section of the initiation channel, which is part of the piracema channel, located in the Itaipu Hydroelectric Power Plant. The initiation channel has submerged obstacles distributed from one margin to the other, in order to reduce water velocity and allow the piracema cycle to occur. The governing equations of flow are the shallow water equations, which will be solved through the LBM-MRT. The non-slip bounce-back scheme was used on walls and obstacles, constant discharge at the inlet and fixed depth at the outlet of the channel. Due to the characteristics of the problem to be simulated, a large eddy simulation (LES) technique was incorporated into the computational code, which allows to obtain results that are closer to the actual behavior of the flow. In addition, the stability of the simulation at all points of the mesh is evaluated for each step of time and, together with the property of the consistency of the LBM, the convergence of the solution is obtained. The simulation provides the depth, velocities in the x and y directions, and the magnitude of water vorticity.