Takaji Inamuro

A non‐slip boundary condition for lattice Boltzmann simulations

A non‐slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine‐velocity model to demonstrate the accuracy of the present boundary condition.

Accuracy of the lattice Boltzmann method for small Knudsen number with finite Reynolds number

The asymptotic theory proposed by Sone [in Rarefied Gas Dynamics, edited by D. Dini (Editrice Tecnico Scientifica, Pisa, 1971), p. 737] is applied to the investigation of the accuracy of the lattice Boltzmann method (LBM) for small Knudsen number with finite Reynolds number. The S-expansion procedure of the asymptotic theory is applied to LBM with the nine-velocity model and fluid-dynamic type equations are obtained. From the fluid-dynamic type equations it is found that by using the LBM we can obtain the macroscopic flow velocities and the pressure gradient for incompressible fluid with relative errors of O(e′2) where e′ is a modified Knudsen number which is of the same order as the lattice spacing and is related to a dimensionless relaxation time. In two problems, the Couette flow with flow injection and suction through porous walls and a three-dimensional flow through a square duct, the accuracy of LBM is examined for relaxation times between 0.8 and 1.7 and the validity of the asymptotic theory for LB...

LATTICE BOLTZMANN SIMULATION OF FLOWS IN A THREE-DIMENSIONAL POROUS STRUCTURE

The lattice Boltzmann method (LBM) with the fifteen-velocity model is applied to simulations of isothermal flows in a three-dimensional porous structure. A periodic boundary condition with a pressure difference at the inlet and outlet is presented. Flow characteristics at a pore scale and pressure drops through the porous structure are calculated for various Reynolds numbers. It is found that at high Reynolds numbers, unsteady vortices appear behind bodies and the flow field becomes time-dependent. Calculated pressure drops through the structure are compared with well-known empirical equations based on experimental data

Flow between parallel walls containing the lines of neutrally buoyant circular cylinders

The motions of a single and two lines of neutrally buoyant circular cylinders in fluid between flat parallel walls are numerically investigated over the range of the Reynolds number of 12 < Re < 96, the ratio of the diameter of the cylinder Ds to the channel width D of 0.25≤Ds/D≤0.5, and the ratio of the streamwise spacing of the cylinders L to the channel width of 0.75≤L/D≤2. The lattice Boltzmann method is used for computations of the fluid phase and the cylinders are moved according to Newton’s law of motion. The Segre–Silberberg effect is found for both a single and two lines of cylinders. It is also found that for two lines of cylinders with Ds/D=0.25 and L/D=1, the equilibrium positions of the two lines are arranged to be staggered with respect to each other in the flow direction. The effects of the Reynolds number Re, Ds/D, and L/D on the equilibrium position of the lines of cylinders and on the friction factor of the cylinder–fluid mixture are presented and discussed.

A Galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy approach

A Galilean invariant model of the lattice Boltzmann method (LBM) for multiphase fluid flows using free-energy approach is proposed. The asymptotic theory proposed by Sone (1971) is applied to the LBM model for multiphase fluid flows using the free-energy approach developed by Swift et al. [Phys. Rev. Lett. 75 (1995) 830] and governing equations for macroscopic variables of the model are obtained. From the governing equations the condition of a Galilean invariant LBM model is identified. In two problems, moving droplet and drop deformation and breakup in a shear flow, Galilean invariance of the proposed model is demonstrated.

A lattice kinetic scheme for incompressible viscous flows with heat transfer

A lattice kinetic scheme for incompressible viscous flows with heat transfer is developed based on the lattice Boltzmann method. In the new scheme, macroscopic variables are calculated without velocity distribution functions. Thus, the scheme can save computer memory because there is no need to store the velocity distribution functions. Governing equations for the macroscopic variables are obtained by applying the asymptotic theory. The continuity equation, the Navier-Stokes equations, and the convection-diffusion equation for fluid temperature are obtained with relative errors of O(ϵ), where ϵ is a small parameter that is of the same order as a lattice spacing and is related to a relaxation parameter. In order to verify the accuracy of the scheme, natural convection flows in a square cavity are simulated, and the calculated results are in good agreement with available standard results.

Numerical simulation of bubble flows by the lattice Boltzmann method

A lattice Boltzmann method for two-phase immiscible fluids with large density ratios is proposed. The difficulty in the treatment of large density ratio is resolved by using the projection method. The method can simulate two-phase fluid flows with the density ratio up to 1000. The method is applied to the simulations of a single rising bubble in liquid and many bubbles rising in a square duct. The terminal shapes and the terminal Reynolds numbers of the single bubble for various Morton and Eotvos numbers are in good agreement with available experimental data. The complicated unsteady structures of the interface and the flow field are illustrated in many bubbles rising in a square duct.

Lattice Boltzmann methods for moving boundary flows

The lattice Boltzmann methods (LBMs) for moving boundary flows are presented. The LBM for two-phase fluid flows with the same density and the LBM combined with the immersed boundary method are described. In addition, the LBM on a moving multi-block grid is explained. Three numerical examples (a droplet moving in a constricted tube, the lift generation of a flapping wing and the sedimentation of an elliptical cylinder) are shown in order to demonstrate the applicability of the LBMs to moving boundary problems.

Molecular Dynamics Simulation of Hydrogenated Amorphous Silicon with Tersoff Potential

A Molecular dynamics method with a Many-body Tersoff-type interatomic potential has been being applied to analyses of hydrogenated Amorphous silicon ( a-Si:H ) thin-film growth processes. As a first step toward film growth simulations, Molecular dynamics simulations of SiH3 radical, which would be a significant precursor for the a-Si:H thin-film growth processes, and a-Si:H formation with a rapid quenching method have been performed by developing new Tersoff-type interatomic potential between Si and H in this study. Visualization of SiH3 radical dynamics by computer graphics has made it possible to observe the inversion and rotation of SiH3 radical, which had been predicted by infrared diode-laser spectroscopie measurement in other group. In addition, visualization of the a-Si:H sample has helped us to find that there are some microcavities in the sample and that there are two kinds of hydrogen in the sample, gathering closely together while lying scattered, which had been predicted in IR absorption experimental results.

Free flight simulations of a dragonfly-like flapping wing-body model using the immersed boundary-lattice Boltzmann method

Free flights of the dragonfly-like flapping wing-body model are numerically investigated using the immersed boundary-lattice Boltzmann method. The governing parameters of the problem are the Reynolds number Re, the Froude number Fr, and the non-dimensional mass m, and we set the parameters at Re = 200, Fr = 15, and m = 51. First, we simulate free flights of the model without the pitching rotation for various values of the phase lag angle ϕ between the forewing and the hindwing motions. We find that the wing-body model goes forward in spite of ϕ, and the model with 0 and 90 goes upward against gravity. The model with goes almost horizontally, and the model with goes downward. That is, the moving direction of the model depends on the phase lag angle ϕ. Secondly, we simulate free flights with the pitching rotation for various values of the phase lag angle ϕ. It is found that in spite of ϕ the wing-body model turns gradually in the nose-up direction and goes back and down as the pitching angle increases. That is, the wing-body model cannot make a stable forward flight without control. Finally, we show a way to control the pitching motion by changing the lead–lag angle . We propose a simple proportional controller of which makes stable flights within and works well even for a large disturbance.