Ryu Egashira

Linear Analysis of Dispersive Waves in Bubbly Flows Based on Averaged Equations

One-dimensional linear dispersive waves in water flows containing a number of small spherical air bubbles are analytically studied on the basis of a set of averaged equations recently derived by the present authors. The set of equations consists of the conservation laws for gas and liquid phases and the equation of motion of bubble wall. In addition to the volume-averaged pressure in each phase, the surface-averaged liquid pressure at the bubble wall is incorporated. The compressibility of water is taken into account as well as that of gas in bubbles, and a model of virtual mass force is included, although the Reynolds stress, viscosity, heat conductivity, and the phase change across the bubble wall are disregarded. The results are summarized as follows: (i) the waves are decomposed into the fast mode, slow mode, and convection mode (void wave). (ii) In the uniform flows, the three modes stably exist for all real wave numbers. (iii) In the limit of infinitesimal void fraction, the explicit representation of the elementary solution is obtained. (iv) The instability does not appear in the range where the present averaged equations are applicable.

A Pressure-Based Two-Phase Flow Method for Computation of Bubble Cavitation Flows

A pressure-based two-phase flow method is proposed for computation of high-speed cavitation flows by coupling a Two-Fluids Three-Pressure bubble dynamics model and a compressible two-phase flow computation. The fluid mixture of two-phase media is composed of a liquid and spherical gas bubbles, those are supposed to disperse in the liquid phase uniformly. State equations of the liquid and gas phases are employed to relate their density with pressure, and the flow of two-phase mixture is then calculated by employing Navier-Stokes equations. Cavitation is evaluated by the volume fraction of gas phase and the average radius of cavitation bubbles in a local flow field is calculated by applying Rayleigh-Plesset equation. For simultaneous computation of above equations, a pressure-based predictor-corrector procedure is developed by applying CCUP method. As an example, flows in an orifice nozzle are treated and the reliability of computation is estimated by comparison with experimental data.Copyright