Seiichi Koshizuka

Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid

AbstractA moving-particle semi-implicit (MPS) method for simulating fragmentation of incompressible fluids is presented. The motion of each particle is calculated through interactions with neighboring particles covered with the kernel function. Deterministic particle interaction models representing gradient, Laplacian, and free surfaces are proposed. Fluid density is implicitly required to be constant as the incompressibility condition, while the other terms are explicitly calculated. The Poisson equation of pressure is solved by the incomplete Cholesky conjugate gradient method. Collapse of a water column is calculated using MPS. The effect of parameters in the models is investigated in test calculations. Good agreement with an experiment is obtained even if fragmentation and coalescence of the fluid take place.

NUMERICAL ANALYSIS OF BREAKING WAVES USING THE MOVING PARTICLE SEMI-IMPLICIT METHOD

SUMMARY The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave.

Numerical analysis of deterioration phenomena in heat transfer to supercritical water

Abstract Deterioration in heat transfer at supercritical water cooling in a vertical pipe is numerically analyzed. The calculation is based on a parabolic solver for steady-state equations in r−z two dimensions, a k−ϵ model for turbulence and a steam table library for physical properties of supercritical water. Calculation results agree with the experimental data of Yamagata et al. It is found that heat transfer deterioration is caused by two mechanisms depending on the flow rate. When the heat flux is increased much above the deterioration heat flux, a violent oscillation is observed in the temperature distribution.

Direct calculation of bubble growth, departure, and rise in nucleate pool boiling

Abstract A mesh-free numerical method (MPS–MAFL) is presented for the analysis of gas–liquid two-phase flows. In this method, a particle method (MPS) is combined with a gridless method (MAFL) for an arbitrary-Lagrangian–Eulerian calculation. Gas–liquid two-phase flows are calculated directly by the present method with and without the phase change. As an isothermal flow, a gas bubble rising in viscous liquids is simulated numerically and the results are compared with the empirical correlation. The energy equation is coupled with the equation of motion for the calculation of nucleate pool boiling. Numerical results are provided for the bubble growth rate, departure radius, and the heat transfer rate, which show a good agreement with experimental observations. The heat transfer mechanism associated with nucleate pool boiling is evaluated quantitatively and discussed with previous empirical studies.

Numerical Analysis of Jet Breakup Behavior Using Particle Method

The numerical method used in this study is Moving Particle Semi-implicit (MPS) method which is based on moving particles and their interactions. Grids are not necessary. Large deformation of fluids can be calculated without grid tangling. A surface tension calculation model is developed to analyze droplet breakup. This model is verified by the simulation of vibration of an ethanol droplet. Two-dimensional numerical analyses of droplet breakup in liquid-liquid and gas-liquid systems are carried out. The correlation between the Weber number and the breakup mode observed in the calculations agrees with that in the experiments. Breakup behavior of a droplet surrounded by a vapor film is analyzed. Flow in the vapor film is considered, though boiling of water and solidification of the melt droplets are ignored. It is found that the breakup of a droplet is suppressed by the vapor film. The critical Weber number in the vapor film is obtained as 50. Molten core coolability is considered by using this result. The median diameter of stable droplets of the molten core is expected as 5 mm in a typical condition, which is consistent with FARO experiment. This result shows that in Advanced Boiling Water Reactor (ABWR) the debris bed up to 40% of the core can be cooled down in the lower head of the reactor pressure vessel.

Numerical analysis of fragmentation mechanisms in vapor explosions

Abstract Fragmentation of molten metal is the key process in vapor explosions. However, this process is so rapid that the mechanisms have not yet been clarified in experimental studies. In addition, numerical simulation is difficult because we have to analyze water, steam and molten metal simultaneously with boiling and fragmentation. The authors have been developing a new numerical method, the moving particle semi-implicit (MPS) method, based on moving particles and their interactions. Grids are not necessary. Incompressible flows with fragmentation on free surfaces have been calculated successfully using the MPS method. In the present study, numerical simulation of the fragmentation processes using the MPS method is carried out to investigate the mechanisms. A numerical model to calculate boiling from water to steam is developed. In this model, new particles are generated on water–steam interfaces. A two-step pressure calculation algorithm is also developed. Pressure fields are separately calculated in both heavy and light fluids to maintain numerical stability with the water and steam system. The new model and algorithm are added to the MPS code. Water jet impingement on a molten tin pool is calculated using the MPS code as a simulation of collapse of a vapor film around a melt drop. Penetration of the water jet, which is assumed in Kim–Corradini’s model, is not observed. If the jet fluid density is hypothetically larger, the penetration appears. Next, impingement of two water jets is calculated. A filament of the molten metal is observed between the two water jets as assumed in Ciccarelli–Frost’s model. If the water density is hypothetically larger, the filament does not appear. The critical value of the density ratio of the jet fluid over the pool fluid is ρ jet / ρ pool =0.7 in this study. The density ratios of tin–water and UO 2 –water are in the region of filament generation, Ciccarelli–Frost’s model. The effect of boiling is also investigated. Growth of the filament is not accelerated when the normal boiling is considered. This is because normal boiling requires more time than that of the jet impingement, although the filament growth is governed by an instant of the jet impingement. Next, rapid boiling based on spontaneous nucleation is considered. The filament growth is markedly accelerated. This result is consistent with the experimental fact that the spontaneous nucleation temperature is a necessary condition of vapor explosions.

A particle–gridless hybrid method for incompressible flows

A particle–gridless hybrid method for the analysis of incompressible flows is presented. The numerical scheme consists of Lagrangian and Eulerian phases as in an arbitrary Lagrangian–Eulerian (ALE) method, where a new-time physical property at an arbitrary position is determined by introducing an artificial velocity. For the Lagrangian calculation, the moving-particle semi-implicit (MPS) method is used. Diffusion and pressure gradient terms of the Navier–Stokes equation are calculated using the particle interaction models of the MPS method. As an incompressible condition, divergence of velocity is used while the particle number density is kept constant in the MPS method. For the Eulerian calculation, an accurate and stable convection scheme is developed. This convection scheme is based on a flow directional local grid so that it can be applied to multi-dimensional convection problems easily. A two-dimensional pure convection problem is calculated and a more accurate and stable solution is obtained compared with other schemes. The particle–gridless hybrid method is applied to the analysis of sloshing problems. The amplitude and period of sloshing are predicted accurately by the present method. The range of the occurrence of self-induced sloshing predicted by the present method shows good agreement with the experimental data. Calculations have succeeded even for the higher injection velocity range, where the grid method fails to simulate. Copyright

Refinement of Transient Criteria and Safety Analysis for a High-Temperature Reactor Cooled by Supercritical Water

Abstract In past designs of supercritical water-cooled reactors, the core flow rate has had to be kept high enough to satisfy the minimum deterioration heat flux ratio criterion where the deterioration heat flux is a function of the core flow rate. Refinement of transient criteria related to the fuel rod design is undertaken, and new dominant transient criteria are proposed in which the cladding temperature is <610°C for Type 316 stainless steel and <840°C for Inconel 700 to reduce the balance of the plant and improve the thermal efficiency. The safety analysis for the high-temperature core using these new criteria is carried out. All the analyzed events satisfy the new criteria. A new formula for the heat transfer correlation at supercritical pressure is proposed based on numerical simulation.

Supercritical-pressure, Once-through Cycle Light Water Cooled Reactor Concept

The purpose of the study is to develop new reactor concepts for the innovation of light water reactors (LWR) and fast reactors. Concept of the once-through coolant cycle, supercritical-pressure light water cooled reactor was developed. Major aspects of reactor design and safety were analysed by the computer codes which were developed by ourselves. It includes core design of thermal and fast reactors, plant system, safety criteria, accident and transient analysis, LOCA, PSA, plant control, start up and stability. High enthalpy rise as supercritical boiler was achieved by evaluating the cladding temperature directly during transients. Fundamental safety principle of the reactor is monitoring coolant flow rate instead of water level of LWR. The reactor system is compact and simple because of high specific enthalpy of supercritical water and the once-through cycle. The major components are similar to those of LWR and supercritical thermal plant. Their temperature are within the experiences in spite of the high outlet coolant temperature. The reactor is compatible with tight fuel lattice fast reactor because of the high head pumps and low coolant flow rate. The power rating of the fast reactor is higher than the that of thermal reactor because of the high power density.

Numerical Analysis of Jet Injection Behavior for Fuel-Coolant Interaction using Particle Method

The numerical method used in this study is Moving Particle Semi-implicit (MPS) method which is based on moving particles and their interactions. Grids are not necessary, so that large deformation of fluids can be calculated without grid tangling. Particles move in fully Lagrangian description. Thus, convection terms are not necessary to discretize and numerical diffusion does not arise. To understand the behavior of jet penetration, water jet injection into a pool of a denser fluid under non-boiling and isothermal conditions is analyzed using the MPS method. The density ratio of the denser fluid (Fluorinert) to water is 1.88. This is categorized to the coolant injection (CI) mode where the coolant is assumed to be injected into the melt pool. The calculation results are compared with experiments which were conducted by Park et al. in Japan Atomic Energy Research Institute (JAERI) for visualization of basic processes in fuel-coolant interaction (FCI). The jet penetration behavior of the three-dimensional calculation agrees with the experiment. It is found that the jet penetration process is divided to two stages and, at the first stage, the coolant jet penetrates deeper than existing correlations of the breakup length in the CI mode.