Fumimaru Ogino

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.

Turbulence structure in stably stratified open-channel flow

The effects of stable stratification on turbulence structure have been experimentally investigated in stratified open-channel flow and a theoretical spectral-equation model has been applied to the stably stratified flow. The measurements were made in the outer layer of open-channel flow with strongly stable density gradient, where the wall effect was small. Velocity and temperature fluctuations were simultaneously measured by a laser-Doppler velocimeter and a cold-film probe. Measurements include turbulent intensities, correlation coefficients of turbulent fluxes and coherence–phase relationships. These turbulent quantities were correlated with the local gradient Richardson number and compared with the values calculated using a spectral-equation model and with other laboratory measurements. In stable conditions, turbulent motions approach wavelike motions, and negative heat and momentum transfer against the mean temperature and velocity gradient occurs in strongly stable stratification.

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.

An experimental study of vertical turbulent jet with negative buoyancy

A jet discharged upward into an ambient of higher temperature than that of the jet fluid was investigated experimentally.The width of the upflow spread linearly to the distance from the nozzle exit, whereas the width of the whole jet was almost constant. The height of top of jet varied in proportion to the square root of the discharge Froude number.The time-averaged velocities and temperatures as well as the intensities of their fluctuations at the jet axis were well correlated with the same scaling law as that used for the buoyant jet. The radial distributions showed no similarity profiles for the timeaveraged velocities and temperatures, and the intensities of their fluctuations.ZusammenfassungEin Freistrahl, der in eine Umgebung mit höherer Temperatur als die der Strahlflüssigkeit ausströmt, wurde experimentell untersucht. Die Breite der Aufwärtsströmung nahm linear mit der Entfernung der Düse zu, während die Breite des ganzen Strahls nahezu konstant war. Die maximale Eindringhöhe des Strahls war proportional zur Quadratwurzel der Abström-Froude-Zahl. Sowohl die mittleren Geschwindigkeiten und Temperaturen als auch die Intensitäten der Schwankungsgeschwindigkeiten und-temperaturen in der Achse wurden mit dem ähnlichkeitsgesetz gut korreliert, das auf den Auftriebsstrahl angewandt wurde. Die radialen Verteilungen zeigten keine ähnlichkeitsprofile für die mittleren Geschwindigkeiten und Temperaturen sowie für die Intensitäten der Schwankungsgeschwindigkeiten und -temperaturen.

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.

Turbulent heat and mass transfer between wall and fluid streams of large Prandtl and Schmidt numbers

Abstract The expression for eddy diffusivity in a previous analysis was revised. By using the revised expression, good agreement was obtained between the predicted and experimental results for mass transfer at Schmidt numbers between 800 and 15,000. Both the predicted and experimental results showed that the Sherwood number varies with 1 3 power of the Schmidt number and about 0·9 power of the Reynolds number at Sc = 800−15,000 and Re = 3000−80,000.

Mass transfer from hot dry rock to water flowing through a circular fracture

Numerical simulation of heat and mass transfer from hot dry rock to flowing water in a circular fracture was conducted to estimate the concentration of the dissolved silica at the production well. The local mass transfer coefficients between the rock and the fluid, obtained by using the electrochemical method during the laboratory experiments, were used in the calculation. The results of the simulation indicate that the concentration of the silica at the production well increases with increasing distance between the injection and the production wells, increasing fracture diameter and increasing pressure. It decreases with increases in flow rate and porosity in the fracture. The concentration of silica at the production well first increases and then decreases with increasing initial rock temperature due to the decrease in the solubility of silica at high temperatures. Finally, the mass transfer by forced convection of flowing water plays an important role in the variation in the concentration of silica in water, and the assumption that the concentration of dissolved silica is equal to that at the fracture surface is not valid for estimation of the concentration at the production well.