Tadashi Watanabe

Translational and radial motions of a bubble in an acoustic standing wave field

The dynamic responses of a spherical bubble in an acoustic standing wave field are studied numerically. The equations of motion in the translational and the radial directions are solved simultaneously. It is shown that a bubble which is larger than the resonance size moves to a node of the pressure field and its radial oscillations become small. A sufficiently small bubble is shown to move to an antinode and radially oscillates under the maximum pressure amplitude. It is found using Poincare maps and power spectra that a bubble which is slightly smaller than the resonance size oscillates chaotically in both the radial and the translational directions. It is demonstrated that the range of the equilibrium bubble size which shows chaotic motions broadens with the pressure amplitude. Finally, the radial responses of the bubble are shown to be dependent not only on the pressure amplitude but also on the drag force in the translational direction.

Study on the bubble motion control by ultrasonic wave

Abstract The behavior of a bubble in an acoustic wave field was investigated experimentally and analytically. Ultrasonic transducers were used to set up acoustic standing waves to control the bubble motion and position in a liquid column under normal and reduced gravity conditions. A single ultrasonic transducer was first used in a liquid column with a free surface to hold a bubble between a node and a loop under normal gravity. The motion and equilibrium position of the bubble were predicted numerically by solving the Rayleigh–Plesset equation and bubble motion equation in the translational direction. By using a pair of ultrasonic transducers and varying the node and loop positions in the acoustic standing wave field, the equilibrium bubble position could be changed at will. Finally, the applicability of the ultrasonic bubble control technique to the reduced-gravity condition was confirmed by conducting experiments aboard NASAs KC-135 aircraft flying parabolic trajectories. The equilibrium position of the bubble was confirmed to be at the node of the acoustic pressure field in the absence of gravity.

Numerical simulation of coalescence and breakup of rising droplets

Abstract Rising droplets with coalescence and breakup are numerically simulated using the lattice BGK method. It is shown for single droplet that the rising velocities are in good agreement with those obtained by two types of empirical correlations. The coalescence of droplets is shown when two droplets are placed vertically in line at different elevations. The breakup of droplet is observed in some cases after the coalescence. It is found that the breakup of coalesced droplet occurs when the Weber number at the coalescence exceeds a critical value, and the critical Weber number agrees well with that given by the empirical correlation.

The effect of the virtual mass force term on the numerical stability and efficiency of system calculations

Abstract A simplified virtual mass force term has been implemented into TRAC-PFI. The coefficient of the virtual mass force term was determined so as to obtain the reasonable sound speed in two-phase flows. Implementation was easily accomplished without changing the basic solution method of SETS. Sample calculations and a small-break LOCA calculation were performed. The virtual mass force term was found to stabilize basic equations and numerical calculations. It was also found that a large amount of CPU time could be saved in the system calculation.

Flow pattern and heat transfer rate in Rayleigh–Bénard convection

The three-dimensional Rayleigh–Benard convection is simulated numerically using the lattice Boltzmann method. Flow patterns are observed and the heat transfer rate is estimated in terms of the Nusselt number. The dependence of the Nusselt number on the Rayleigh number is shown to agree well with that obtained by the two-dimensional calculations of the Navier–Stokes equations. It is shown that several roll patterns with different wave numbers and heat transfer rates are established even though the ratio of the horizontal size to the vertical size is a multiple of 2. Two types of oscillatory roll patterns are shown: one is with oscillatory heat transfer rate and the other is with the constant heat transfer rate. It is found that the square pattern is possible under the same condition for the stable or oscillatory roll pattern. The heat transfer rate decreases with decreasing wave number.

The effect of the virtual mass term on the stability of the two-fluid model against perturbations

Abstract The effect of the virtual mass term on the stability of the two-fluid model against perturbations is studied. Three types of virtual mass term in the momentum equation are discussed: two types of objective form and a simplified form. The differential equation system with no virtual mass term is ill-posed and the solution is unstable against perturbations. By introducing an objective form of the virtual mass term derived by Drew et al., it is shown that the equation system is rendered to be well-posed. The equation system is shown to be ill-posed, however, when a more recent definition of virtual mass acceleration of Drew and Lahey is applied. With a simplified form of the virtual mass term, which is composed only of temporal acceleration terms, the equation system is well-posed or ill-posed depending on velocities. A linear stability analysis is also performed for the implicit upwind finite difference scheme. A hypothetical accelerated flow problem is then numerically simulated by solving the discretized equation systems. It is shown that the solution can be numerically unstable even for the cases when the differential equation system is well-posed. The numerical stability of the solution must therefore be judged based on the spectral radius of the discretized equation system.

Numerical evaluation of interfacial area concentration using the immiscible lattice gas

Abstract The phase separation in a Couette flow and the mixing of two phases in a cavity flow are simulated numerically using the immiscible lattice gas, which is one of the discrete methods of using particles to simulate two-phase flows. The interface is defined as the lattice sites between two phases, and the interfacial area concentration is evaluated in the steady state. In the Couette flow, the interfacial area concentration increases slightly with an increase in the wall speed. It is shown in the cavity flow that the interfacial area concentration increases largely with an increase in the wall speed. Macroscopic velocity fields in the two flows are in good agreement with analytical or numerical solutions of the Navier–Stokes equations. The interfacial area concentration is found to be correlated with the wall speed for the two flows, and the applicability of particle simulation methods to the numerical evaluation of the interfacial area concentration is indicated.

Improvement of Passive Safety of Reactors

A new subsystem called the passive safety and shutdown system (PSSS) is proposed to improve nuclear reactor safety. The subsystem can be added to the existing reactor coolant system (RCS) by a slight modification. To exemplify how the subsystem improves pressurized water reactor safety, anticipated transient without scram under loss of normal ac power is analyzed. The result indicates that the proposed subsystem is very effective in putting an end to the accident. The PSSS not only improves passive reactor safety, but also simplifies RCS and its control and surveillance systems. Items needing further investigation with regard to PSSS design are also discussed.

Numerical study on shock phenomena and void wave propagation in horizontal stratified flow

Abstract Void wave propagation and the related numerical instability in the two-fluid model of horizontal stratified flow have been investigated, focusing on the interfacial pressure force. First, shock phenomena, which are predicted by the two-fluid model when taking into account the interfacial pressure force, are discussed to clarify their physical meaning. Second, numerical instability is investigated through the calculation of void disturbance propagations. The Von Neumann stability analysis is applied to these problems. It has been found that the results explain the nature of the instabilities produced in the calculations. The relationship between the stability limit of the discretized equation set and the ill-posed limit of the field equation set is clarified.

Simulation Monitoring System Using AVS

A simulation monitoring system has been developed to visualize ongoing numerical simulations on supercomputers or workstations. The output data for visualization are transferred from the calculation server to the visualization server and visualized automatically by the monitoring system. Visualization is performed by AVS on UNIX or WINDOWS environment. Modification of simulation program is not necessary, and the monitoring system is applied for both interactive and batch process of numerical simulations