Tadashi Sakaguchi

Effects of Eötvös Number and Dimensionless Liquid Volumetric Flux on Lateral Motion of a Bubble in a Laminar Duct Flow

Experiments and numerical simulations on lateral migration of a single bubble in stagnant liquids and laminar flows were conducted in the present study to examine the effects of the Eotvos number Eo and dimensionless liquid volumetric flux on lateral forces. It was confirmed that (1) a lateral force due to the existence of the wall acts on a bubble and (2) a lift force due to the net circulation of liquid strongly depends on Eo. Empirical models for the wall and lift forces were also proposed and their validity was confirmed by comparing measured and calculated bubble trajectories.

Numerical analysis of bubble motion with the VOF method

Abstract Numerical analyses of a two-dimensional single bubble in a stagnant liquid and in a linear shear flow were conducted in the present study using the volume of fluid method, which is based on the local-instantaneous field equations. It was clarified that this method gives qualitatively appropriate predictions for the effects of the Morton number and the Eotvos number on fluctuating bubble motion in a stagnant liquid. Calculated velocity and pressure distributions indicated that the Karman vortex causes a sinuous movement of the bubble. As for the bubble motion in a linear shear flow, calculated bubbles migrated in a lateral direction. The direction of the lateral migration agreed to available experimental data. It was also confirmed that (i) the direction or the magnitude of the lateral migration is affected by the Eotvos and the Morton numbers, and (ii) the interaction among the internal flow of the bubble, the wake of the bubble and the external shear flow plays an essential role for the lateral migration.

A three-dimensional particle tracking method for bubbly flow simulation

Abstract A numerical method for solving a three-dimensional bubbly flow was proposed. The method is based on a two-way particle tracking method, which takes into account the effect of bubbles on the liquid phase and vice versa. In order to demonstrate the potential of the method, laminar bubbly upflow in a vertical duct was simulated using the Eotvos number and bubble size distribution as parameters. As a result, we could obtain typical bubble distributions in a bubbly flow and a void wave in the flow direction as well. It was also confirmed that the method can give good predictions for bubble-induced liquid velocity fields, provided that the bubble size is greater than the size of the computational cell for calculating the liquid phase.

Flow instabilities in parallel-channel flow systems of gas-liquid two-phase mixtures

Abstract Parallel-channel two-phase flow systems with compressible capacities and the negative-slope characteristics of the pressure drop vs flow rate curve suffer from a non-uniform flow distribution and/or pressure drop oscillation, depending on the pressure drop characteristics of each channel, under certain operating conditions. The modes of flow distribution are quite similar to those observed in boiling channels. Pressure drop oscillations are subdivided into two types: relaxation oscillation and quasi-static oscillation. The modes of oscillation observed in the parallel-channel system are a single-channel mode, a U-tube mode and a multi-channel mode. These modes of oscillation are closely related to the type of oscillation. Upstream compressibility in the gas feed pipe has a destabilizing effect on the oscillation. On the other hand, upstream compressibility in the liquid feed pipe has a stabilizing effect on the oscillations of the gas flow rate and the pressure drop between the headers of parallel channels, but induces a small oscillation of the liquid flow rate. These non-uniform flow distribution and oscillation patterns are analyzed; the results of the analysis are found to be in good agreement with the experimental results. Thus, the characteristics of the non-uniform flow distribution and the oscillation can be estimated by the method of analysis presented in this paper.

A Simple Numerical Method for Solving an Incompressible Two-Fluid Model in a General Curvilinear Coordinate System

A simple numerical method for solving an incompressible isothermal two-fluid model was proposed in the present study. A general curvilinear coordinate system was adopted in this method in order to predict transient multi-dimensional gas-liquid two-phase flow in complex geometry. The simplicity of the method was achieved by making use of the governing equations expressed in a tensor form in terms of contravariant components and covariant derivatives. It was demonstrated that this method gives good predictions for transient multi-dimensional bubbly flows.

Analysis of the impact force by a transient liquid slug flowing out of a horizontal pipe

Abstract An abrupt increase in the gas flow rate in a horizontal gas-liquid two-phase stratified or wavy flow induces a transient slug flow. When this transient liquid slug flows out of a pipe, it applies a large impact force by its impingement on a structure located outside the pipe. The shape of this impact force-time curve is characterized by such quantities as initial impact force, maximum force, acting period of force and total momentum. The influences of each volumetric flux of two phases and of the pipe diameter on the impact force-time curves and the dynamic behavior of the transient liquid slug are experimentally studied and theoretically analyzed on the basis of Dukler-Hubbards model by applying equations of the integral balance of mass and momentum to the transient liquid slug. The calculated results agree well with the experimental results of the dynamic behavior of the transient liquid slug and of the impact force.

Modeling the mechanical interaction between the velocity fields in three-phase flow

Abstract The predictions of IVA3 computer code models describing the mechanical interactions between the velocity fields in liquid-gas, liquid-solid, and liquid-solid-gas bubble flows are systematically compared with Sakaguchis experimental data for upward pipe flows. For better understanding of the physics of the experiments, a simple model, describing especially the conditions observed in the experiments, was derived by simplifying the theory on which the IVA3 code relies. The model describes an adiabatic, steady-state, three-phase, three-component flow with thermal equilibrium, mechanical nonequilibrium between the velocity fields, and the condition for critical flow. Ishii and Chawlas correlations for calculation of drag forces for bubbles or solid particles in liquid are checked against the experimental data obtained by Sakaguchi et al The model developed by Kolev for computation of the drag forces when solid particles are free in the flow and the volume fraction of the space among the particles if they were closely packed is larger than the liquid volume fraction was checked against data obtained by Sakaguchi et al for three-phase bubble flow. The agreement obtained between the IVA3 predictions and the data for two- and three-phase flow shows the ability of the Ishii-Chawla correlation and the method proposed by Kolev to predict successfully the drag forces for two- and three-phase flows and the correctness of the mathematical modeling technique incorporated in the IVA3 computer code, the so-called partial resolution of local velocity coupling.

Pressure Drop in Gas-Liquid-Solid Three Phase Bubbly Flow in Vertical Pipes

Pressure drops in air-water-particles three phase bubbly flows were measured in vertical straight pipes of three different inside diameters: 20.9, 30.8 and 50.4 mm. Their heights were about 10 m. Experimental data on the pressure drops were presented. Effects of the volumetric flux, particle diameter and pipe diameter on the total, gravitational and frictional pressure drops were discussed. A method estimating the frictional pressure drop was proposed based on a multiplier method. The correlations predicted the experimental data on frictional pressure drop with a deviation of ±13.9%.

Flow Pattern of Gas-Liquid Two-Phase Flow in a Horizontal U bend Pipe

In some horizontal steam generators or refrigerators, a gas-liquid two-phase flow is observed in horizontal U bend pipelines which consist of U bends, upper horizontal pipes and lower horizontal pipes installed just under the upper horizontal pipes. Liquid is generated due to condensation of steam in pipes if they are used as condensers. It is supposed that flow patterns in the horizontal parts of these pipelines are different from those in the horizontal pipes without U bend. Hence, it is necessary to study and observe the flow pattern in horizontal parts and U bend part. In the present study, an experimental investigation was carried out using a horizontal U bend pipeline which has a water supply section at midway of lower horizontal pipe. Flow patterns were observed at four parts including U bend part and horizontal parts. The effects of radius of the U bend on the flow pattern were made clear. The flow patterns and the presented maps were compared with those in the previous studies.

Pressure drop in gas-liquid-solid three-phase slug flow in vertical pipes

Abstract Experimental results related to the pressure drop in steady and fully developed gas-liquid-solid three-phase slug flows in vertical pipes are presented. The experiment was carried out in pipes of 20.9, 30.6, and 50.8 mm I.D. and with solid particles of 2.57 mm mean diameter. Air and water were used as the gas and liquid phases, respectively. An estimating method for the pressure drop in three-phase slug flow is proposed based on a model that devides a slug unit into six regions. A momentum equation is applied to each region and to each boundary between regions. The volumetric fraction and the velocity of each phase in each region are estimated, using the volume balance equations and some correlations. The pressure drop is estimated, using these values. The estimated results of the pressure drop are compared with the measured values, and it is confirmed that this method is useful in estimating such a pressure drop.