Kosuke Hayashi

Interface Tracking Simulation of Mass Transfer From a Dissolving Bubble

An interface tracking method for predicting bubble dissolution process is proposed. A non-diffusive scheme for advecting species concentrations is adopted to accurately compute the volume change due to mass transfer. The applicability of the proposed method is examined through several benchmark tests, i.e. mass transfer from stationary bubbles and that from free rising bubbles. Dissolution of single carbon dioxide bubbles rising through a vertical pipe filled with water is also simulated to examine its applicability to high bubble Reynolds number and high Schmidt number conditions. The bubble initially consists of carbon dioxide only, whereas nitrogen and oxygen are dissolved in water. The volume change due to dissolution of carbon dioxide from the bubble and evaporation of nitrogen and oxygen from water are also accounted for. A high spatial resolution is used in this simulation to capture a thin concentration boundary layer in the vicinity of the bubble surface. As a result the following conclusions are...

Countercurrent Flow Limitation at the Junction between the Surge Line and the Pressurizer of a PWR

An experimental study on countercurrent flow limitation (CCFL) in vertical pipes is carried out. Effects of upper tank geometry and water levels in the upper and lower tanks on CCFL characteristics are investigated for air-water two-phase flows at room temperature and atmospheric pressure. The following conclusions are obtained: (1) CCFL characteristics for different pipe diameters are well correlated using the Kutateladze number if the tank geometry and the water levels are the same; (2) CCFL occurs at the junction between the pipe and the upper tank both for the rectangular and cylindrical tanks, and CCFL with the cylindrical tank occurs not only at the junction but also inside the pipe at high gas flow rates and small pipe diameters; (3) the flow rate of water entering into the vertical pipe at the junction to the rectangular upper tank is lower than that to the cylindrical tank because of the presence of low frequency first-mode sloshing in the rectangular tank; (4) increases in the water level in the upper tank and in the air volume in the lower tank increase water penetration into the pipe, and therefore, they mitigate the flow limitation.

Effects of fluid properties on CCFL characteristics at a vertical pipe lower end

The purpose of this study is to derive a counter-current flow limitation (CCFL) correlation and evaluate its uncertainty for steam generator (SG) U-tubes in a pressurized water reactor (PWR). Experiments were conducted to evaluate effects of the liquid viscosity on CCFL characteristics using air–40 wt% or air–60 wt% glycerol water solution and saturated steam–water at atmospheric pressure with vertical pipes simulating the lower part of the SG U-tubes. The steam–water experiments confirmed that CCFL characteristics could be expressed in terms of the Wallis parameters (JG* and JL*) for the pipe diameters of D = 14, 20, and 27 mm. A CCFL correlation was derived using the ratio μG/μL of the viscosities of the gas and liquid phases, μG and μL, as a correction term representing effects of fluid properties, where JG*1/2(μG/μL)−0.07 was expressed by a cubic function of JL*1/2(μG/μL)0.1. In the correlation, the constant C indicating the value of JG*1/2(μG/μL)−0.07 at JL* = 0 was (1.04 ± 0.05), and this uncertainty of ±0.05 would cover most of the previous experimental data including the ROSA-IV/LSTF data at 1, 3, and 7 MPa.

Condensation experiments for counter-current flow limitation in an inverted U-tube

In this study, we measured counter-current flow limitation (CCFL) characteristics in an inverted U-tube (18.4 mm diameter and 1.0 m straight-part length) simulating steam generator (SG) U-tubes under conditions of steam condensation at pressures of 0.1–0.14 MPa. Differential pressure ΔP between the top of the inverted U-tube and the lower tank was measured, and the flow patterns wave estimated by comparing the waveforms of ΔP with those in air–water experiments. As a result, we classified the flow patterns under CCFL conditions into CCFL-P, CCFL-L and CCFL-T. The falling water flow rate under CCFL conditions slightly increased as the pressure increased and the cooling water temperature decreased (subcooling of cooling water increased). In the case of CCFL-L, CCFL characteristics in the inverted U-tube were between those in air–water and saturated steam–water experiments at 0.1 MPa. Furthermore, we derived a Wallis type CCFL correlation and its uncertainty from CCFL data, including previously measured data, i.e., J*1/2G + 0.88JL*1/2 = 0.76 ± 0.05.

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part I: Experiments

Lack of local void fraction data in a rod bundle makes it difficult to validate a numerical method for predicting gas–liquid two-phase flow in the bundle. Distributions of local void fraction and bubble velocity in each subchannel in a 4×4 rod bundle were, therefore, measured using a double-sensor conductivity probe. Liquid velocity in the subchannel was also measured using laser Doppler velocimetry (LDV) to obtain relative velocity between bubbles and the liquid phase. The size and pitch of rods were 10 and 12.5 mm, respectively. Air and water at atmospheric pressure and room temperature were used for the gas and liquid phases, respectively. The volume fluxes of gas and liquid phases ranged from 0.06 to 0.15 m/s and from 0.9 to 1.5 m/s, respectively. Experimental results showed that the distributions of void fraction in inner and side subchannels depend not only on lift force acting on bubbles but also on geometrical constraints on bubble dynamics, i.e. the effects of rod walls on bubble shape and rise velocity. The relative velocity between bubbles and the liquid phase in the subchannel forms a non-uniform distribution over the cross-section, and the relative velocity becomes smaller as bubbles approach the wall due to the wall effects.

Effects of Numerical Treatment of Viscous and Surface Tension Forces on Predicted Motion of Interface

Effects of numerical treatment of viscous and surface tension forces on predicted motion of an interface are investigated. The viscous force and tangential surface tension force (Marangoni force) are treated in two different ways: one is a smeared-out interface method and the other is a ghost fluid method. In the smeared-out interface method, the arithmetic mean and harmonic mean are tested for evaluation of the viscous stress. Linear shear flows, single oscillating drops and surface tension waves are simulated using these methods. These benchmark tests show that the ghost fluid method gives the most accurate evaluations of the viscous and the Marangoni forces. The harmonic mean can give good evaluations of the tangential viscous stress at clean interface, whereas large errors in the viscous stress are caused for contaminated interface. Although the arithmetic mean causes some errors for clean and contaminated interfaces compared to the ghost fluid method, the error can be reduced by increasing spatial re...

Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

An immersed boundary-lattice Boltzmann method (IB-LBM) using a two-relaxation time model (TRT) is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. Adirect-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1) the...

Mass Transfer From a Bubble in a Vertical Pipe

Mass transfer from single carbon dioxide bubbles in a vertical pipe is measured using a stereoscopic image processing method to develop a mass transfer correlation applicable to a wide range of bubble and pipe diameters. The pipe diameters are 12.5, 18.2 and 25.0 mm and the bubble diameter ranges from 5 to 26 mm. The ratio, λ, of bubble diameter to pipe diameter is therefore varied from 0.2 to 1.8, which covers various bubble shapes such as spherical, oblate spheroidal, wobbling, cap, and Taylor bubbles. Measured Sherwood numbers, Sh, strongly depend on bubble shape, i.e., Sh of Taylor bubbles clearly differs from those of spheroidal and wobbling bubbles. Hence two Sherwood number correlations, which are functions of the Peclet number and the diameter ratio λ, are deduced from the experimental data: one is for small bubbles (λ 0.6). The applicability of the proposed correlations for the prediction of bubble dissolution process is examined through comparisons between measured and predicted long-term bubble dissolution processes. The predictions are carried out by taking into account the presence of all the gas components in the system of concern, i.e. nitrogen, oxygen and carbon dioxide. As a result, good agreements for the dissolution processes for various bubble sizes and pipe diameters are obtained. It is also demonstrated that it is possible to evaluate an equilibrium bubble diameter and instantaneous volume concentration of carbon dioxide in a bubble using a simple model based on a conservation of gas components.Copyright

Interface Tracking Simulation of Drops Rising through Liquids in a Vertical Pipe Using Three Coordinate Systems

Interface tracking simulations of single drops rising through a vertical pipe are carried out using three coordinate systems, i.e. cylindrical, general curvilinear and Cartesian coordinates, to investigate the effects of coordinate system and spatial resolution on the accuracy of predictions. Experiments of single drops in a vertical pipe are also conducted to obtain experimental data for comparisons with simulations. The drop shape observed are spheroidal and deformed spheroidal at low values of the diameter ratio, λ, of the sphere-volume equivalent diameter of a drop to the pipe diameter, whereas they take bullet-shapes at large λ. The conclusions obtained are as follows: (1) the effects of coordinate system on drop shape are small at low λ. At large λ, the effects are also small for drops in a low viscosity system, whereas non-physical shape distortion takes place when the Cartesian coordinates are used with low spatial resolution for drops in a high viscosity system, and (2) the drop terminal velocity...

EVALUATION OF VOLUME TRACKING ALGORITHMS FOR GAS-LIQUID TWO-PHASE FLOWS

Qualitative and quantitative evaluations of volume tracking algorithms such as DA, FLAIR, MARS, CIP and VTEMC were conducted. Wide variety of two-dimensional test problems including (1) a circle transported in simple translation and rotational field, (2) a bubble rising in 45° slanted gravity field, (3) zigzag motion of a bubble in a vertical channel, and (4) a bubble rising in a stagnant liquid in axissymmetric cylindrical coordinate were chosen in the present study. As a result of these tests, the superiority of the cell-centered piecewise linear algorithm with the divergence treatment in operator split and especially with embedded micro cells was confirmed. Applicability of these algorithms to three-dimensional problems has to be examined in the future works.Copyright