Fumio Inada

Thermo-Hydraulic Instability of Boiling Natural Circulation Loop Induced by Flashing (Analytical consideration)

An analytical study is presented on the thermo-hydraulic stability of a boiling natural circulation loop with a chimney at low pressure start-up. The effect of flashing induced by the pressure drop in the channel and the chimney due to gravity head on the instability is considered. A method to analyze linear stability is developed, in which a drift-flux model is used. The analytical result of a stability map agrees very well with the experimental one obtained in a previous report. Instability does not occur when the heater power is too low to generate voids in the chimney and only natural circulation of single phase can be induced. Instability tends to occur when boiling occurs only near the chimney exit due to flashing. This instability phenomenon has some similarities with density wave oscillation, such as the phase difference of temperature between the boiling region and non-boiling region, and the oscillation period which is near to the time required for fluid to pass through the chimney. However, there are also some differences from density wave oscillation, such as the boiling region is very short, and pressure fluctuation can affect void fraction fluctuation.

A study on leakage-flow-induced vibrations. Part 1: Fluid-dynamic forces and moments acting on the walls of a narrow tapered passage

Leakage-flow-induced vibrations (instabilities) have been observed in many fields of engineering, but there remain many points to be clarified as to the mechanism of the instability. In the present paper, the viscous fluid-dynamic forces and the moments acting on the walls of a one-dimensional, narrow, tapered passage when one wall is vibrating in coupled translational and rotational modes are analyzed, and fluid-dynamic mass, damping and stiffness matrices are determined, by which the mechanism of instability generated from the flow through a narrow passage is examined. In the case of a single-degree-of-freedom translational or rotational system, only diagonal components of the fluid-dynamic matrices are estimated, and it is found that both negative fluid-dynamic damping caused by the phase delay due to the fluid inertia and negative fluid-dynamic stiffness can occur. In the case of a single-degree-of-freedom translational system, if the passage is divergent, both negative fluid-dynamic damping and fluid-dynamic stiffness can occur. In the case of a single-degree-of-freedom rotational system, the area increment ratio of the passage, at which negative fluid-dynamic damping and fluid-dynamic stiffness can occur, changes remarkably with the location of the pivot. In the case of a two-degree-of-freedom translational and rotational system, it is difficult to conclude directly from the fluid-dynamic matrices whether the fluid-dynamic forces stabilize the system or not. Therefore, in Part 2 of this study the stability of a plate which can vibrate in a coupled mode of translational and rotational motion in a one-dimensional, narrow, tapered passage will be examined.

CFD Simulations and Experiments of Flow Fluctuations Around a Steam Control Valve

Under certain opening conditions (partial opening) of a steam control valve, the piping system in a power plant occasionally experiences large vibrations. To understand the valve instability that is responsible for such vibrations, detailed experiments and CFD calculations were performed. As a result of these investigations, it was found that under the middle-opening (partial opening) condition, a complex three-dimensional (3D) flow structure (valve-attached flow) sets up in the valve region leading to a high pressure region on a part of the valve body. As this region rotates circumferentially, it causes a cyclic asymmetric side load on the valve body, which is considered to be the cause of the vibrations.

A study on leakage-flow-induced vibrations. Part 2: Stability analysis and experiments for two-degree-of-freedom systems combining translational and rotational motions

The stability of a rigid, thin plate able to execute coupled translational and rotational vibrations in a one-dimensional, narrow, tapered passage is studied, and the critical flow rates, natural frequencies and modes on the stability boundaries determined both theoretically and experimentally. The theoretical values correspond very well to those obtained from experiments. The types of flutter are also analysed theoretically. Both divergent- and flutter-type instabilities can occur; the flutter-type is classified as single-degree-of-freedom flutter, which can also occur in single-degree-of-freedom systems, and two-degree-of-freedom flutter, which can occur only in two-degree-of-freedom systems. The single-degree-of-freedom flutter hardly ever occurs when the passage is convergent or when the pivot of rotation is near the inlet of the passage, but the two-degree-of-freedom flutter tends to occur whether the passage is convergent or not and the pivot close to the inlet or not.

Evaluation of Acoustic- and Flow-Induced Vibration of the BWR Main Steam Lines and Dryer

The boiling water reactor (BWR-3) steam dryer in the Quad Cities (QC) Unit 2 Nuclear Power Plant was damaged by high-cycle fatigue due to acoustic-induced vibration. The cause of the dryer failure was considered as flow-induced acoustic resonance at the stub pipes of the safety relief valve (SRV) in the main steam lines (MSLs). The acoustic resonance was considered to be generated by the interaction between the sound field and an unstable shear layer across the closed side branches of SRVs. We have started a research program on BWR steam dryers to develop methods of evaluating the loading. Moreover, it is necessary to evaluate the dryer integrity of BWR-5 plants, which are the main type of BWR in Japan. In the present study, we conducted 1/10-scale BWR model tests and analysis to investigate the flowinduced acoustic resonance and acoustic characteristics in MSLs. The test apparatus consisted of a steam dryer, a steam dome, and 4 MSLs with 20 SRV stub pipes. Computational fluid dynamics (CFD) analysis was conducted to evaluate the acoustic source in MSLs. Finite element method (FEM) was applied to calculate the three-dimensional wave equations for acoustic analysis. We demonstrated that large fluctuating pressure occurred in the high- and low-frequency regions. The high-frequency fluctuating pressure was generated by the flow-induced acoustic resonance in the SRV stub pipes. We evaluated the acoustic source (that is, the fluctuating pressure) in MSLs by unsteady CFD calculations, and we evaluated the pressure propagation by acoustic analysis. These results were verified by comparison with the results of scale-model tests, and they showed good agreement with the experimental results. The effects of the difference between the properties of air and steam were numerically investigated, and it was found that the effects on the acoustic resonance in the SRV stub pipes were not significant.

Characteristics of Type-I Density Wave Oscillations in a Natural Circulation BWR at Relatively High Pressure

Experiments were conducted to investigate two-phase flow instabilities in a boiling natural circulation loop with a chimney at high pressure. The SIRIUS-N facility was designed to have non-dimensional values which are nearly equal to those of a typical natural circulation BWR. The observed oscillations are found to be density wave oscillations, since the void fractions in the chimney inlet and exit are out of phase. They belong to the Type-I category, since they occur at low flow qualities, according to the Fukuda—Koboris classification. Moreover, the oscillation period correlates well with the passing time of bubbles in the chimney section regardless of the system pressure, the heat flux, and the inlet subcooling. Two distinct phenomena are found in relation between the oscillation period and liquid passing time in the chimney, indicating that the driving mechanisms of the instabilities are different between low and high pressures. Stability maps were obtained in reference to the inlet subcooling and the heat flux at the system pressures of 1, 2, 4, and 7.2 MPa. The flow became stable below a certain heat flux regardless of the channel inlet subcooling. The stable region enlarges with increasing system pressure. Thus, the stability margin becomes larger in a startup process of a reactor by pressurizing the reactor sufficiently before withdrawing the control rods. The obtained stability map demonstrates that the nominal operating condition of the ESBWR has a significant stability margin to the unstable region.

Fluctuating Pressure Generating in BWR Main Steam Lines Acoustic Excited by Safety Relief Valve Stub Pipes and Dead Legs

During operation, the BWR-3 steam dryer in the Quad Cities Unit 2 Nuclear Power Plant was damaged by high cycle fatigue. The dryer failure was attributed to flow-induced acoustic resonance at the stub pipes of safety relief valves (SRVs) in the main steam lines (MSLs). The acoustic resonance was considered to be generated by interaction between the sound field and an unstable shear layer across the closed side branches with SRV stub pipes. We HITACHI and CRIEPI have started a research program on BWR dryers to develop their loading evaluation methods. Moreover, it has become necessary to evaluate the dryer integrity of BWR-5 plants in particular which are the main type of BWR in Japan. In the present study, we used 1/10-scale BWR tests and analyses to investigate the flow-induced acoustic resonance and characteristics of fluctuating pressure in MSLs. The test apparatus consisted of a steam dryer, a steam dome and 4 MSLs with 20 SRV stub pipes. A finite element method (FEM) was applied for the calculation of three-dimensional wave equations in acoustic analysis. We demonstrated that remarkable fluctuating pressures occurred in high and low frequency regions. Intensity of three peaks observed in the spectrum of fluctuating pressure in MSLs was increased with St. High frequency fluctuating pressures were generated by the flow-induced acoustic resonance in the SRV stub pipes. Low frequency fluctuating pressures were excited by the acoustic resonance in the dead leg. Frequency of fluctuating pressure generating in the SRV stub pipe was changed with St. On the other hand, frequency of fluctuating pressure excited by dead leg was almost constant. Fluctuating pressure in low frequency range increased gradually with flow velocity and its intensity was roughly proportional to the square of flow velocity. The flow-induced acoustic resonance did not occur for St larger than 0.6 in the BWR MSLs for both low and high frequency ranges. Operating conditions of the BWR-5 from 100 to 115% were in the range of St larger than 0.6, so intense acoustic resonance would not occur in the BWR MSLs.Copyright

Regional Stability Estimation of Natural Circulation BWRs using SIRIUS-N Facility

The SIRIUS-N facility was designed and constructed for highly accurate simulation of core-wide and regional instabilities of the BWR. A real-time simulation was performed in the digital controller for heat conduction in a fuel-rod and modal point kinetics of reactor neutronics using measured void fractions in reactor core sections of the thermal-hydraulic loop. In order to estimate decay ratios, an auto-regressive method has been successfully applied for time series data of the core inlet flow rate. Experiments were conducted with the SIRIUS-N facility for the rated operating condition of 3.13GWt natural circulation BWR. Channel and regional stability decay ratios were determined to be 0.38 and 0.54, respectively, which indicates sufficient margin for the instabilities. Experiments were extended to evaluate the stability sensitivity of design parameters such as the power profile, void reactivity coefficients, core inlet sub-cooling, and the fuel rod time constant.

Flow Induced Vibration of a Steam Control Valve in Middle-Opening Condition

In some cases, a steam control valve in a power plant causes a large vibration of the piping system under partial valve opening. For rationalization of maintenance and management of a plant, it is favorable to optimize the valve geometry to prevent such vibration. However, it is difficult to understand the flow characteristics in detail only from experiments because the flow around a valve has a complex 3D structure and becomes supersonic (M>1). Therefore, it is useful to combine experiments and CFD (Computational Fluid Dynamics) for the clarification of the cause of vibration and optimization of valve geometry. In previous researches involving experiment and CFD calculation using “MATIS” code, we found that an asymmetric flow attached to the valve body (named “valve-attached flow”) occurs and pressure increases where the valve-attached flow collides with the flow from the opposite side under the middle opening condition. This high-pressure region rotates circumferentially (named “rotating pressure fluctuation”) and causes cyclic side load on the valve body. However, because we assumed the valve support is rigid, we cannot clarify the interaction between the rotating pressure fluctuation and the valve vibration when the valve stiffness is small. Thus, in this paper, we conducted flow-induced vibration experiments on a valve with a very weak support and investigated the characteristics of the vibration mode under the middle-opening condition. As a result, under the specific lift condition of the region where rotating pressure fluctuation occurs, lock-in phenomena between the rotating pressure fluctuation and the valve vibration occur and large-amplitude vibration can be seen.Copyright

Evaluation of Hydraulic Factors Affecting Flow Accelerated Corrosion and Its Verification With Power Plant Data

Flow Accelerated Corrosion (FAC) is well known as a complex phenomana of hyraulics and electro-chemicals. Among the two, this study focused on the hydraulic factors affecting FAC. FAC experiments with small rectangular flow duct were conducted in PWR condensate condition. Flow field for the experiment was calculated with numerical simulation using LES (Large Eddy Simulation) turbulence model. From both experimental and numerical results, new model of mass transfer coefficient, as the essential parameters of hydraulics, was proposed considering local turbulent velocity, so as to evaluate the effect of eccentric flow on FAC. To verify the applicability of the model, FAC plant data of actual PWR (Pressurized Water Reactor) condensate line (146 degC) and BWR (Boiling Water Reactor) condensate line (35 degC) were referred. Mass transfer coefficients for each pipe lines were calculated from flow numerical analysis. The new proposed model showed good correlation with the data of FAC thinnng rate, and its applicability was confirmed. In addtion, comparing the two plant cases, electro-chemical effect could be estimated as a similar level, which suggests the possibility of low-temperature FAC in BWR condensate lines.Copyright