Wake Interaction Using Lattice Boltzmann Method

FLOW EFFECT AROUND TWO SQUARE CYLINDERS ARRANGED SIDE BY SIDE USING LATTICE BOLTZMANN METHOD

Gap ratio effect on flow characteristics behind side-by-side cylinders of diameter ratio two

In recent years, the Lattice Boltzmann (LB) method has become a powerful numerical \ntool for simulating complex fluid flows and modeling physics and chemistry in \nfluids. Derived from the continuum Boltzmann equation used in statistical \nmechanics, the LB method has the advantage of describing non-equilibrium dynamics, \nespecially in fluid-flow applications involving interfacial dynamics and complex \nboundaries, without simplifying the physics. In addition, the parallel structure \ninherent in the LB method makes it extremely suitable for parallel computing. \nBecause of these features, the LB method affords the most comprehensive pore-scale \napproach to systematically investigate fundamental issues involving flow and \nreactive transport in porous media. In this paper, the state of the art of this \nmethod is discussed. Specifically, a multi-component LB model for simulating \nreactive transport in porous media at the pore scale is presented. In the model, a \nset of distribution functions is introduced to simulate fluid flow and solute \ntransport. The LB equation for flow recovers the correct pore-scale continuity and \nNavier-Stokes equations. The LB equations for solute transport are modified to \nrecover advection-diffusion equations for total concentrations at the pore scale. \nThe model takes into account advection, diffusion, homogeneous reactions among \nmultiple aqueous species, heterogeneous reactions between the aqueous solution and \nminerals, as well as changes in solid and pore geometry. Homogeneous reactions are \ndescribed through local equilibrium mass action relations. Mineral reactions are \ntreated kinetically through boundary conditions at the mineral surface. Simulation \nexamples presented include injection of carbon dioxide saturated brine into a \nlimestone rock with pore geometry derived from a thin section, crystal formation \nfrom a supersaturated solution without flow, and crystal formation during carbon \ndioxide sequestration in oceanic sediments.

The major purpose of the present research is developing the Lattice Boltzmann (LB) method as an extremely efficient computational technique in the pragmatic field of fluid-structure interactions. Hence, the LB method is employed in simulating the incompressible flow past a square unit of four equal diameter circular cylinders. The simulation is conducted at Re of 200 and the spacing ratio (L/D) increases from 1.5 to 5 in 0.5 steps to cover all closely, moderately and widely spaced cases. Accordingly, the effects of the spacing ratio on the shear layer’s behaviour and vortex shedding pattern are studied in detail. Furthermore, its effects on the main force characteristics, i.e., lift and drag coefficients and also the Strouhal number are fully investigated. The observations and results obtained by the LB method employed in the current work are in strict accordance with experimental evidence of other researchers and other existent numerical data in the literature.

In this paper, the low-Reynolds number (Re= 80) flow around a row of nine square cylinders placed normal to the oncoming flow is investigated using the lattice-Boltzmann method. The effects of the cylinder spacing on the flow are studied for spacing to diameter ratios of 0.3 to 12. No significant interaction between the wakes is observed with spacings greater than six times the diameter. At smaller spacings, the flow regimes as revealed by vorticity field and drag coefficient signal are: synchronized, quasi-periodic and chaotic. These regimes are shown to result from the interaction between primary (vortex shedding) and secondary (cylinder interaction) frequencies; the strength of the latter frequency in turn depends on the cylinder spacing. The secondary frequency is also related to transition between narrow and wide wakes behind a cylinder.The mean drag coefficient and Strouhal number are found to increase rapidly with a decrease in spacing; correlations of these parameters with spacing are proposed. The Strouhal number based on gap velocity becomes approximately constant for a large range of spacings, highlighting the significance of gap velocity for this class of flows. It is also possible to analyse the vortex pattern in the synchronized and quasi-periodic regimes with the help of vorticity dynamics. These results, most of which have been obtained for the first time, are of fundamental significance.

Fluid-structure interaction using lattice Boltzmann method: Moving boundary treatment and discussion of compressible effect

PurposeThis study aims to investigate lattice Boltzmann (LB) simulation of the fluid flow and heat transfer characteristics of a heated porous elliptic cylinder in uniform flow based on the two-domain scheme. In the present research, the effect of axis ratio (1 ≤ AR ≤ 2), Reynolds number (5 ≤ Re ≤ 40) and Darcy number (10−4 ≤ Da ≤ 10−2) are studied.Design/methodology/approachTo perform the LB simulation based on the two-domain scheme, the nonequilibrium extrapolation method is modified to model the heat transfer interfacial conditions required at the curved interface.FindingsThe results show that the axis ratio as well as Reynolds and Darcy numbers significantly affect the fluid flow and heat transfer characteristics of the porous elliptic cylinder. It is shown that for AR > 1, the phenomenon of detached recirculating zone occurs at much higher Darcy numbers compared with the case of the porous circular cylinder (AR = 1). The results show that the location of maximum temperature within the cylinder moves downstream when the Reynolds number, Darcy number and axis ratio increase. It is also concluded that the average Nusselt number of a porous elliptic cylinder is always lower than that of a porous circular cylinder.Originality/valueThe LB simulation of forced convection from a porous cylinder in uniform flow with a curved interface based on the two-domain scheme has not been studied yet.

Body-fitted and Cartesian grid methods are two typical types of numerical approaches used for modelling fluid–structure interaction problems. Despite their extensive applications, there is a lack of comparing the performance of these two types of approaches. In order to do this, the present paper presents benchmark numerical solutions for two two-dimensional fluid–structure interaction problems: flow-induced vibration of a highly flexible plate in an axial flow and a pitching flexible plate. The solutions are obtained by using two partitioned fluid–structure interaction methods including the deforming-spatial-domain/stabilized space–time fluid–structure interaction solver and the immersed boundary–lattice Boltzmann method. The deforming-spatial-domain/stabilized space–time fluid–structure interaction solver employs the body-fitted-grid deforming-spatial-domain/stabilized space–time method for the fluid motions and the finite-difference method for the structure vibrations. A new mesh update strategy is developed to prevent severe mesh distortion in cases where the boundary does not oscillate periodically or needs a long time to establish a periodic motion. The immersed boundary–lattice Boltzmann method uses lattice Boltzmann method as fluid solver and the same finite-difference method as structure solver. In addition, immersed boundary method is used in the immersed boundary–lattice Boltzmann solver to handle the fluid–structure interaction coupling. Results for the characteristic force coefficients, tail position, plate deformation pattern and the vorticity fields are presented and discussed. The present results will be useful for evaluating the performance and accuracy of existing and new numerical methodologies for fluid–structure interaction.

A strong-coupled method combined finite element method and lattice Boltzmann method via an implicit immersed boundary scheme for fluid structure interaction

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 limit. It is a system of 9 one dimensional partial differential Hamiltonian-Jacobian equations, consisting of an advection and diffusive portion. The LB method is an alternative computational fluid dynamics (CFD) method used to numerically predict incompressible viscous flow. The current LB method uses a statistical mechanics formulation to solve the Boltzmann equation. The LB model captures the nonlinear Navier Stokes advection terms using linear streaming operators. In this thesis, the LB model is classified as an explicit, Lagrangian, finite-hyperbolicity and weakly compressible approximation of the Navier Stokes equations. The momentum flux tensor is captured locally as opposed to a pressure field eliminating the need to solve the Poisson equation. This allows the fluid structure interactions (FSI) behavior to be calculated elegantly at the interface through the mesoscopic momentum transfer between the fluid and structure. At this level, the forces are simultaneously calculated. The LB equations are discretized both in time and phase space using a standard D2Q9 lattice model. Validation tests for flow around single square cylinders at different aspect ratio at low Reynolds numbers are presented. Good agreement with other investigators is achieved. Flow past multiple bluff bodies (representing building in a city) is also presented. The vortex shedding simulations presented provide preliminary indications in terms of St that the LB method can be used to simulate high Re flow.

PurposeThe purpose of this paper is to investigate the laminar flow and heat transfer characteristics in a two‐dimensional horizontal channel with two square blocks placed side‐by‐side using a numerical scheme based on a coupling between the lattice Boltzmann method and the finite difference method.Design/methodology/approachThe multiple‐relaxation‐time (MRT) lattice Boltzmann equation model coupled with the finite difference method are used to predict numerically the velocity and the temperature fields.FindingsA complex structure of the fluid flow was observed for various dimensionless block separation distance (G). An unsteady flow was found when the two blocks are placed side by side (G = 0). For G &lt; 1.5, the presence of each block develops the street of Van Karman which generates complex binary vortex street. In the opposite case (G &gt; 1.5), the effect of this parameter (G) on the fluid is reduced, whereas, the distance between the blocks and the nearest walls have a great influence on the fluid flow and the heat transfer. When the obstacles are posed on the walls (G = 3), an important heat exchange between the blocks and the nearest walls is noted.Originality/valueThis study offers more knowledge on natural convection in an obstructed channel. Furthermore, this work shows the effectiveness of the MRT lattice Boltzmann equation model for this kind of geometry.

SUMMARY: Realizing the potential of geothermal energy as a cheap, green, sustainable resource to provide for the planet’s future energy demands that a key geophysical problem be solved first: how to develop and maintain a network of multiple fluid flow pathways for the time required to deplete the heat within a given region. We present the key components for micro-scale particle-based numerical modeling of hydraulic fracture, and fluid and heat flow in geothermal reservoirs. They are based on the latest developments of ESyS-Particle—the coupling of the lattice solid model (LSM) to simulate the nonlinear dynamics of complex solids with the lattice Boltzmann method (LBM) applied to the nonlinear dynamics of coupled fluid and heat flow in the complex solid-fluid system. The coupled LSM/LBM can be used to simulate development of fracture systems in discontinuous media, elastic stress release, fluid injection and the consequent slip at joint surfaces, and hydraulic fracturing; heat exchange between hot rocks and water within flow pathways created through hydraulic fracturing; and fluid flow through complex, narrow, compact and gouge- or powder-filled fracture and joint systems. We demonstrate the coupled LSM/LBM to simulate the fundamental processes listed above, which are all components for the generation and sustainability of the hot-fractured

Fluid-structure interaction (FSI) is a very common physical phenomenon which extensively exists in nature, human daily life and many engineering applications. The lattice Boltzmann method (LBM) is an alternative of solving Navier–Stokes equations to obtain complex fluid dynamics. Since the proposal of lattice Bhatnagar–Gross–Krookmodel, the LBM has been improved and applied to various complex flows ranging from laminar flow to turbulent flow and Newtonian flow to non-Newtonian flow. To handle the associated FSI, the bounce-back scheme was proposed and then the immersed boundary method (IBM) was incorporated into the LBM for the simplicity and robustness of IBM in handling complex and moving geometries and the significant efficiency of LBM in solving fluid dynamics. In recent years, the combined frameworks of LBM, that is, bounce-back–lattice Boltzmann method and immersed boundary–lattice Boltzmann method have witnessed a significant development and the successful applications can be found in a range of physical problems such as flow around bluff bodies, flapping wings, wind turbines, aeroacoustics, sea wave modelling and et al. In this paper, the recent progress of LBM and some typical applications involving FSI are reviewed.

The purpose of the present work is simulating cross flow around four cylinders in a square configuration by using a Lattice Boltzmann method. The effective parameters such as Reynolds number and spacing ratio L/D are chosen on the basis of former researches of other authors which have been done experimentally or by using traditional numerical schemes like finite volume method to provide the opportunity for comparing Lattice Boltzmann results with those obtained from experimental and CFD studies. Hence, the Reynolds number is set at Re = 100 and the spacing ratio is chosen to be 1.5, 2.5, 3.5, 4.5. It is shown that final results such as flow pattern, velocity and vorticity field are in accordance with those obtained by former researchers via experimental efforts or by use of finite volume method. This good agreement beside other important qualities such as efficient code, not having mesh tangling associated with other common numerical approaches, high convergence speed and nondimensional velocity and pressure field indicate this fact that in comparison with other numerical methods, Lattice Boltzmann method is very capable of analyzing a broad variety of fluid flows.

In this study, we simulate the process of crystal growth under fluid flow by using Lattice Boltzmann Method (LBM). LBM is one of the numerical simulation methods for the fluid flow. In order to simulate the crystal growth, we adopt the first kinetic reaction model for boundary condition at fluid –solid interface. We performed two simulations. The first one is to simulate the crystal growth in following steps. At each time step, the crystal mass increases according to the solubility of the material. When the crystal mass becomes twice of the initial mass, we place a new crystal seed next to the initial one. In this way, crystal grows and increases. In addition, we adopt the Damkohler number (Da) in order to control the precipitation speed of the crystals. As the Damkohler number increases, the crystal shape changes from round shape to fractal. At the second simulation, the fluid flow is considered. The fluid flow is given from the left side of the numerical model. When Da is 2.0, the crystal shape is little changed by the fluid flow. however, when Da is 600, the crystal seed grows toward the left. These show fluid flow and the the Da number have influenced the crystal shape.