Takeshi Shimizu

A Numerical Study on Faraday-Type Electromagnetic Flowmeter in Liquid Metal System, (I): A Numerical Method Based on Magnetic Field and Electric Potential Field: FALCON Code

To predict the three-dimensional steady-state structure of electromagnetic phenomena in the Faraday-type Electromagnetic Flowmeter (EMF), a numerical simulation method using the Galerkin finite element method has been adopted and formatted as a computer code, FALCON. As the induction equation for the induced magnetic field that is important in a liquid metal system, we have presented B-φ formulation for the induced magnetic field and the electric potential field and A-φ formulation for the vector potential field and the electric potential field, and compared the computational efficiency of both formulations. We have selected the B-φ formulation. The computer simulation of the EMF of the MONJU secondary cooling system has been performed and the calculations have shown a good agreement with the calibration test data. We have investigated qualitatively how far the influence of the end effect extends and the characteristics of the voltage response. Overall, this study has indicated that the present method can be applied to the estimation of the characteristics of an EMF and the design of a new EMF.

Analysis on the Dynamic Load in a Water Pool during Air Discharge from Submerged Sparger

This paper presents a study of the applicability of the VOF (volume of fluid) method to estimation of dynamic load in a water pool induced by oscillation of bubbles that are ejected through sparger holes. We choose the VOF method to simulate this phenomenon, and the pressure of a bubble is given by entropy change in order to consider the compressible effect of the bubble and the effect of gas coming into the bubble. In calculation of the airflow rate passing through the holes, the effect of two-phase pressure drop is incorporated. in order to investigate applicability of this method, a simplified blowdown test is carried out. According to the numerical results, the pressure-rime history inside the sparger and that in a water pool are both generally reproduced well with analysis, except that the magnitude of first peak pressure in a water pool is overestimated. The most likely reason is that the bubble cloud has especially low void fraction at the early stage of bubble formation, anti mail bubbles around a major bubble work as a buffer, which is discussed, in detail, in this paper.

Analysis on the Dynamic Load in a Water Pool During Air Discharge From Submerged Sparger

This paper presents a study of the applicability of the VOF (Volume of Fluid) method to estimation of dynamic load in a water pool induced by oscillation of bubbles that are ejected through sparger holes. We choose the VOF method to simulate this phenomenon, and the pressure of a bubble is given by entropy change in order to consider the compressible effect of the bubble and the effect of gas coming into the bubble. In calculation of air flow rate passing through the holes, the effect of two-phase pressure drop is incorporated. In order to investigate applicability of this method, a simplified blowdown test is carried out. According to the numerical results, the pressure-time history inside the sparger and that in a water pool are both generally reproduced well with analysis except that the magnitude of first peak pressure in a water pool is overestimated. The most likely reason is that the bubble cloud has especially low void fraction at the early stage of bubble formation, and small bubbles around a major bubble work as a buffer, which is discussed in detail in this paper.Copyright

A Numerical Study on Faraday-Type Electromagnetic Flowmeter in Liquid Metal System, (II) Analysis of End Effect due to Saddle-Shaped Small-Sized Magnets with FALCON Code

In the design of the electromagnetic flowmeter (EMF) in the main cooling loop of the Japanese Prototype Fast Breeder Reactor “MONJU”, large-sized flat permanent magnet was adopted in order to make the end effect of the magnet as small as possible. For an EMF of a future large LMFBR, it is difficult to adopt such a large-sized magnet because of problems of a large space requirement and a tolerance against earthquake. Therefore, it is necessary to develop a novel EMF with small-sized magnets. It has been feared that the decrease of magnetic field and the end effect make the EMFs performance worse, but we have no detailed information about the end effect due to such small-sized magnets. By using the three-dimensional steady- state electromagnetic analysis code FALCON, we have studied numerically on the end effect of an EMF with saddle-shaped permanent magnets, the size of which is smaller than the pipe diameter. Consequently, it has been clarified that the performance of an EMF can be improved by utilizing the effect of the downstream end of magnets and by combining the inclined-electrodes and the effect of circumferential ends of magnets.

Secondary Flow Characteristics in Cubical Piping with Multi Bends

An experimental and numerical investigation of the characteristics of swirling flow produced by a double or multi right-angle bends has been carried out in order to examine the effect of upstream arrangements of pipes and bends in an electro-magnetic flow meter. Swirling flow profiles were compared in both cases of the multi right-angle bends in one flat plane and the multi righ-angle bend in two perpendicular planes which are typical arrangements in a sodium cooled fast breeder reactor power plant. The swirling flow profiles obtained through numerical analysis agreed with the experimental results for the single and double swirling flow in bends in one flat plane and in bends in two perpendicular planes, respectively. Unsteady or oscillatory flows were also discussed based on the experimental observations and numerical results.

Incomplete Discrete Wavelet Transform and Its Application to a Poisson Equation Solver

Recently there have been many developments and new applications of mathematical techniques for describing complex functions and analyzing empirical continuous data derived from many different types of signals. The wavelet theory would be the most important and rapidly developing among these techniques. Wavelets have provided a new method for decomposing a function or signal, just like a Fourier expansion. Several articles on wavelets exhibit the wide variety of applications of wavelet analysis and present many of the key developments of the theory. Daubechies[1] proposed families of compactly supported wavelets with certain degrees of smoothness which are constructed by using multiresolution analysis[2].

Effect of Swirling Flow on Electro-magnetic Flow Meters.

In general, liquid metal fluid flow in externally applied magnetic fields produces induced currents. A study was carried out on the electro-magneto-hydraulic effect of the induced currents on the characteristics of liquid metal electro-magnetic flow meters. Both theoretical analysis and corresponding experimental measurements have been conducted to investigate swirling flow profiles which are produced by upstream arrangements of pipes and bends. The results showed that these arrangements produced two types of flow profiles ; single swirling and double swirling. Based on such flow profiles, the distortion of a potential field was evaluated and the influence on voltage output was estimated with the two-dimensional electro-magnetic analysis code FALCON-2D developed for this study. The analyis showed that the single swirling flow had a larger effect on the voltage output than the double swirling flow.