Abstract

In many situations ranging from geophysics to chemical engineering, turbulent drag moves particle clouds. I will present and compare various numerical approaches. On the one hand the mean velocity profile above ground is systematically constructed subtracting momentum loss; on the other hand the intrinsic spatio-temporal fluctuations are imposed from empirical distributions on point-like fluid particles. Various applications are explored. One is saltation, i.e. Aeolian transport of sand, discovering that the onset of particles flux exhibits a first order transition with hysteresis. The inclusion of mid-air grain collisions is found to increase the flux considerably due to the formation of a floating “soft bed” that screens energy-rich grains (saltons) from hitting the ground. Solving the fluid motion with the Lattice Boltzmann Method the effect of particle-particle collisions on preferential concentration is also investigated. Another application is powder mixing in a channel due to turbulent fluctuations. Following A.M. Reynolds (2003), a stochastic differential equation is solved for the motion of fluid particles that are attached to real particles. The dependence of the observed diffusive behaviour on Reynolds and Stokes number is monitored. Finally, also spatial correlations in the velocity field are imposed by a Heisenberg-type Hamiltonian. 

Abstract

The pseudopotential method has grown as a powerful tool for multiphase fluid flow simulations within the lattice Boltzmann method framework. We consider that due to its simplicity and computational efficiency, the pseudopotential method could be explored also inside the framework of more traditional Computational Fluid Dynamic methods such as Finite Difference, Finite Volume or Finite Element methods. Following this idea, in this work we start from the macroscopic equations resulting from the pseudopotential lattice Boltzmann method and discretize it by a simple Finite Difference scheme. This pseudopotential based finite difference method is then tested in different benchmark problems such as a planar interface, a smooth droplet oscillation, and a single droplet evaporation. Excellent results were obtained in all tests. One of the advantages of the proposed method is that mesh refinement is straightforward, and converged solutions can be used as a tool of validation for the lattice Boltzmann method. Results indicate that the pseudopotential method is suitable to be used with standard discretization methods such as Finite Difference and that in future works more robust discretizations can be used to further enhance the pseudopotential method application.

Abstract

Derived from simplifications of the Saint-Venant equations, the kinematic wave model has the ability to describe the behavior of surface runoff in watersheds. This paper aims to obtain the numerical simulation of the flow routing in a natural watershed, by using lattice Boltzmann method. In the computational model, the surface of the basin will be represented by a V-shaped segmented in two lateral planes and one main channel. The simulation considers the effective precipitation flowing on the watershed per unit of width at the exit of each of the planes that represent the surface of the basin. The water flowing from the planes enters the main channel in the form of lateral contribution. Hydrograms of two rain events are obtained, which present the volume drained in the outlet corresponding to the whole basin in each event. Two equilibrium distribution functions were developed by Chapmann-Enskog expansion at time scales and model D1Q3, one suitable for flow on the basin surface and another for the main channel, in order to obtain the variables of interest in each case. The numerical results obtained were compared with the KINEROS2 hydrological model. 

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

Abstract

The immersed boundary method has attracted growing interest in CFD research community due to its simplicity in dealing with moving boundaries. In the diffused interface immersed boundary method, a discrete delta function is introduced to account for the boundary effects on the fluid, which causes the diffusion of the boundary interface. Therefore, the diffused interface immersed boundary method requires higher grid resolution in the vicinity of the immersed boundaries to get a better representation of the boundary. A strategy for the application of diffused interface immersed boundary-lattice Boltzmann method is introduced in the simulation of stenosis. The developed numerical method has been examined in the simulation of stenosis. Results show that the current solver is able to accurately predict the velocity profile within the stenosis.

Abstract

Investigou-se o escoamento superficial em bacia hidrográfica por meio da simulação numérica unidimensional utilizando o método do reticulado de Boltzmann (LBM). Desenvolveu-se um modelo computacional onde a bacia hidrográfica é representada pela junção de nove sub-bacias. Para isto, foram estabelecidas duas funções de distribuição de equilíbrio obtidas por meio da expansão de Chapmann-Enskog e utilizando o reticulado D1Q5, uma adequada para o escoamento na superfície da bacia e outra para o canal principal, obtendo a profundidade da água na superfície da bacia e a área da seção transversal nos canais. Além disso, estabeleceu-se a condição de contorno na passagem de fluxo de uma sub-bacia para outra, levando em consideração a conservação da massa e, para se obter uma simulação mais próxima da realidade, considerou-se uma vazão inicial que ocorre no rio (escoamento de base), em cada trecho de canal. Os resultados numéricos obtidos pelo LBM foram comparados com dados medidos em campo.

Abstract

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.

Abstract