Numerical simulation of flow past a square obstacle with Lattice Boltzmann Method (original) (raw)
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Lattice Boltzmann Simulation of Flow around Bluff-Bodies
2004
In this work, results from a 2-D Lattice Boltzmann (LB) solver are presented simulating flow past rectangular square cylinders at low Reynolds numbers (< 250). The LBGK equation is a hyperbolic equation that approximates the Navier Stokes equations in the nearly incompressible ...
New applications of numerical simulation based on lattice Boltzmann method at high Reynolds numbers
Computers & Mathematics with Applications, 2019
In order to study the flow behavior at high Reynolds numbers, two modified models, known as the multiple-relaxation-time lattice Boltzmann method (MRT-LBM) and largeeddy-simulation lattice Boltzmann method (LES-LBM), have been employed in this paper. The MRT-LBM was designed to improve numerical stability at high Reynolds numbers, by introducing multiple relaxation time terms, which consider the variations of density, energy, momentum, energy flux and viscous stress tensor. As a result, MRT-LBM is capable of dealing with turbulent flows considering energy dispersion and dissipation. In the present paper, this model was employed to simulate the flow at turbulent Reynolds numbers in wall-driven cavities. Two-sided wall driven cavity flow was studied for the first time, based on MRT-LBM, at Reynolds numbers ranging from 2 × 10 4 to1 × 10 6 , and employing a very large resolution2048 × 2048. It is found that whenever top and bottom lids are moving in the opposite directions, and the Reynolds number is higher than 2 ×10 4 , the flow is chaotic, although some quasi-symmetric properties still remain, fully disappearing at Reynolds numbers between 2 × 10 5 and 3 × 10 5. Furthermore, between this Reynolds numbers range, 2 × 10 5 <Re< 3 × 10 5 , the quasi-symmetric structures turn into a much smaller and fully chaotic eddies. The LES-LBM model implements the large eddy simulation turbulent model into the conventional LBM, allowing to study the flow at turbulent Reynolds numbers. LES-LBM combined with Quadruple-tree Cartesian cutting grid (tree grid) was employed for the first time to characterize the flow dynamics over a cylinder and a hump, at relatively high Reynolds numbers. In order to construct the macroscopic quantities in the virtual boundaries separating two different grid levels, a set of new schemes were designed. The coupling of the LES-LBM and tree grid drastically reduced the computational time required to perform the simulations, thus, allowing to minimize the hardware requirements. LES-LBM model is shown to be much more efficient when combined with the tree grid instead of using the standard Cartesian grid.
Numerical Simulation of Viscous Flow over a Square Cylinder Using Lattice Boltzmann Method
ISRN Mathematical Physics, 2012
This work is concerned with the lattice Boltzmann computation of two-dimensional incompressible viscous flow past a square cylinder confined in a channel. It is known that the nature of the flow past cylindrical obstacles is very complex. In the present work, computations are carried out both for steady and unsteady flows using lattice Boltzmann method. Effects of Reynolds number, blockage ratio, and channel length are studied in detail. As good care has been taken to include appropriate measures in the computational method, these results enjoy good credibility. To sum up, the present study reveals many interesting features of square cylinder problem and demonstrates the capability of the lattice Boltzmann method to capture these features.
International Journal for Numerical Methods in Fluids, 2009
The present paper deals with the application of the multiple-relaxation-time lattice Boltzmann equation (MRT-LBE) for the simulation of a channel flow with a bi-partition located upstream of a square cylinder in order to control the flow. Numerical investigations have been carried out for different heights and positions of the bi-partition at Reynolds number of 250. Key computational issues involved are the computation of fluid forces acting on the square cylinder, the vortex shedding frequency and the impact of such bluff body on the flow pattern. A particular attention is paid to drag and lift coefficients on the square cylinder. The predicted results from MRT-LBE simulations show that in most cases, the interaction was beneficial insofar as the drag of the square block was lower with the bi-partition than without it. Fluctuating side forces due to vortex shedding from the main body were also reduced for most bi-partition positions.
A volume penalization lattice Boltzmann method for simulating flows in the presence of obstacles
Journal of Computational Science
The LBM is combined with the Volume Penalization (VP LBM) approach to simulate flows in the presence of obstacles. The single relaxation time LBM and the multiple relaxation time LBM are used. For cases where the fluid motion is enhanced by moving boundaries, the comparison of our results with analytical results is satisfactory. The flow around a cylinder at a relatively high Reynolds number is also calculated. For that case, the VP LBM method was parallelized. A comparison of our results with those found in the literature, demonstrates the reliability of the VP LBM to treat complex flows.
Simulation of Free Surface Flow Over Trapezoidal Obstacle with Lattice Boltzmann Method
Han'gug jeonsan yuchegong haghoeji, 2014
An air-water free surface flow simulation by using the Lattice Boltzmann Method(LBM) has not been studied a lot compared with the done by the Navier-Stoke equation. This paper shows the LBM is as one of the application tools for the free surface movement over an obstacle. The Mezo scaled application tool has been developed with two dimensional and nine discretized velocity direction using conventional lattice Bhatnagar-Gross-Krook model. Boundary conditions of a halfway-based for solid wall and a kinematic-based for interface are adopted. A validation case with a trapezoidal shape bump to make a comparison between freesurface movements from computational results and experimental ones was described with grid size dependency.
2014
Numerical calculations of flow around a square cylinder are presented using the multi-relaxation-time lattice Boltzmann method at Reynolds number 150. The effects of upstream locations, downstream locations and blockage are investigated systematically. A detail analysis are given in terms of time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficient, vorticity contours visualizations and phase diagrams. A number of physical quantities mean drag coefficient, drag coefficient, Strouhal number and root-mean-square values of drag and lift coefficients are calculated and compared with the well resolved experimental data and numerical results available in open literature. The results had shown that the upstream, downstream and height of the computational domain are at least 7.5, 37.5 and 12 diameters of the cylinder, respectively.
2015
In this research numerical simulations are performed, using the multi-relaxation-time lattice Boltzmann method, in the range 3 ≤ β = w[d] ≤ 30 at Re = 100, 200 and 300, where β the blockage ratio, w is the equispaced distance between centers of cylinders, d is the diameter of the cylinder and Re is the Reynolds number, respectively. Special attention is paid to the effect of the equispaced distance between centers of cylinders. Visualization of the vorticity contour visualization are presented for some simulation showing the flow dynamics and patterns for blockage effect. Results show that the drag and mean drag coefficients, and Strouhal number, in general, decrease with the increase of β for fixed Re. It is found that the decreasing rate of drag and mean drag coefficients and Strouhal number is more distinct in the range 3 ≤ β ≤ 15. We found that when β > 15, the blockage effect almost diminishes. Our results further indicate that the drag and mean drag coefficients, peak value...
Lattice Boltzmann method (LBM) has been receiving enormous attention from researcher to solve fluid related phenomena. LBM in fluid dynamics simulation, one meet some difficulties, for instance it becomes unstable for high Reynolds number flows and requires computational time and memory for large scale simulations. To avoid this, we used here the Entropic LBM (ELBM) of Karlin's group [7] and implemented parallel code on graphical processing units (GPU). For parallel computation, we used GPGPU system of Nagaoka University of technology, which is equipped with Tesla M2050 processors. To verify accuracy and stability, we have solved double periodic shear layer flow in serial computation. The accuracy and stability of simulation by ELBM were superior to the simulation of standard LBM. Simulations of flow past a circular cylinder is carried out by parallel ELBM, where Reynolds number varies up to 140000. Using the GPU in simulation, computation time speeds up until 10 times faster than that of using central processing units (CPU). The results show that the parallel code of ELBM can solve two-dimensional turbulent flow in arbitrary geometry at the higher stability condition without using any other stabilization techniques. 1. Introduction The simulation of traditional computational fluid dynamics deals with Navier-Stokes equation (NSE). Unlike this, lattice Boltzmann method (LBM) solves the discrete Boltzmann kinetic equation in its simplified form, known as Bhatnagar-Gross-Krook (BGK) equation. Founded in the eighties of last century, LBM become recently a widely used method of computational fluid dynamics (CFD). In LBM, the fluid is simulated by molecular velocity distribution functions with discrete velocities on regular lattice. There are two operations on the distribution functions: streaming and collision. The fluid molecules propagation is described by streaming, which is non-local operation against the local collision operator, describing the collision between molecules [1]. LBM has its intrinsic feature: easy to parallelize on computer [2]. On the other hand, one of long standing problem in fluid flow simulation is the simulation of turbulent flow at high Reynolds number. In CFD, the turbulent flow simulations are usually performed either by computationally expensive direct numerical simulation of NSE or by solving averaged NSE [3, 4, 5, 6]. Direct application of the LBM for the turbulent flow simulation leads to instability of computation, because of the low viscosity of fluid. Laminar flows at low Reynolds number (Re) become turbulent when Re reached the value of Re=300 in the case of flow past a bluff body. One of the promising method of stabilizing the LBM turbulent computation is the entropic LBM (ELBM) of Karlin's group, in which, the distribution functions are straightened to satisfy the maximum condition of the entropy at the every time step of simulation. In this paper, first we confirm accuracy and performance of the ELBM solving double periodic shear layer flow. Then we perform the calculations of high Reynolds number turbulent flow past a circular cylinder using the ELBM of Karlin et al [7, 8] in parallel algorithm.