中村 友道

This paper is concerned with the dynamics of a so-called fluid balancer; a hula hoop ring-like structure containing a small amount of liquid which, during rotation, is spun out to form a thin liquid layer on the outermost inner surface of the ring. The liquid is able to counteract unbalanced mass in an elastically mounted rotor. The paper derives the equations of motion for the coupled fluid-structure system, with the fluid equations based on shallow water theory. An approximate analytical solution is obtained via the method of multiple scales. For a rotor with an unbalance mass, and without fluid, it is well known that the unbalance mass is in the direction of the rotor deflection at sub-critical rotation speeds, and opposite to the direction of the rotor deflection at super-critical rotation speeds (when seen from a rotating coordinate system, attached to the rotor). The perturbation analysis of the problem involving fluid shows that the mass center of the fluid layer is in the direction of the rotor deflection for any rotation speed. In this way a surface wave on the fluid layer can counterbalance an unbalanced mass. (C) 2014 Elsevier Ltd. All rights reserved.

This paper is concerned with the dynamics of a so-called fluid balancer; a hula hoop ring-like structure containing a small amount of liquid which, during rotation, is spun out to form a thin liquid layer on the outermost inner surface of the ring. The liquid is able to counteract unbalanced mass in an elastically mounted rotor. The paper derives the equations of motion for the coupled fluid-structure system, with the fluid equations based on shallow water theory. An approximate analytical solution is obtained via the method of multiple scales. For a rotor with an unbalance mass, and without fluid, it is well known that the unbalance mass is in the direction of the rotor deflection at sub-critical rotation speeds, and opposite to the direction of the rotor deflection at super-critical rotation speeds (when seen from a rotating coordinate system, attached to the rotor). The perturbation analysis of the problem involving fluid shows that the mass center of the fluid layer is in the direction of the rotor deflection for any rotation speed. In this way a surface wave on the fluid layer can counterbalance an unbalanced mass. (C) 2014 Elsevier Ltd. All rights reserved.

The in-flow instability of cylinder arrays corresponds to the in-plane instability of U-bend tubes in steam generators. This rarely occurring phenomenon has recently been observed in a nuclear power plant in the U. S. For this reason, the importance of studying this instability has recently increased. The fluidelastic instability of a cylinder array caused by cross-flow was found to easily occur in air-flow and hardly in water-flow in our previous report. The present report introduces the results of this phenomenon in several patterns of triangular cylinder arrays in air-flow. The pitch spacing between cylinders is one of the parameters, which varies from P/D = 1.2 to 1.5, for a five-by-five cylinder array. The instability is examined both in the in-flow direction and in the transverse direction. The test cylinders are supported with thin plates to move in one direction. The number and the location of the flexibly supported cylinders are the other parameters. Differences between the instability in the in-flow and in the transverse direction are found. Among these differences the most important is the fact that the fluidelastic instability has not been observed for a single flexible cylinder in the in-flow direction, although it is observed in the transverse direction. However, the present preliminary results suggest that the in-flow instability may be estimated with the Connors' type formula as likely as in the transverse direction case.

The in-flow instability of cylinder arrays corresponds to the in-plane instability of U-bend tubes in steam generators. This rarely occurring phenomenon has recently been observed in a nuclear power plant in the U. S. For this reason, the importance of studying this instability has recently increased. The fluidelastic instability of a cylinder array caused by cross-flow was found to easily occur in air-flow and hardly in water-flow in our previous report. The present report introduces the results of this phenomenon in several patterns of triangular cylinder arrays in air-flow. The pitch spacing between cylinders is one of the parameters, which varies from P/D = 1.2 to 1.5, for a five-by-five cylinder array. The instability is examined both in the in-flow direction and in the transverse direction. The test cylinders are supported with thin plates to move in one direction. The number and the location of the flexibly supported cylinders are the other parameters. Differences between the instability in the in-flow and in the transverse direction are found. Among these differences the most important is the fact that the fluidelastic instability has not been observed for a single flexible cylinder in the in-flow direction, although it is observed in the transverse direction. However, the present preliminary results suggest that the in-flow instability may be estimated with the Connors' type formula as likely as in the transverse direction case.

An evaluation method for estimating the damping of loosely supported single U-bend tube used in a steam generator colliding with a support plate is proposed. First, we performed experimental modal analysis and obtained natural frequencies, modes and damping without collision by Impulse Modal Test and then analysed natural frequencies, modes and damping with collision employing FEM analysis taking account of the collision force. In modelling the characteristics of the collision force, we applied Bijlaard's model for the spring constant and assumed hysteresis. After that, we performed experiments for measuring the damping ratio by changing the gap size and the support plate position. Comparison between calculated and experimental results is made which shows good agreement. Experimentally observed fact showing damping coefficient increases with the initial amplitude is well explained by theoretical model.

An evaluation method for estimating the damping of loosely supported single U-bend tube used in a steam generator colliding with a support plate is proposed. First, we performed experimental modal analysis and obtained natural frequencies, modes and damping without collision by Impulse Modal Test and then analysed natural frequencies, modes and damping with collision employing FEM analysis taking account of the collision force. In modelling the characteristics of the collision force, we applied Bijlaard's model for the spring constant and assumed hysteresis. After that, we performed experiments for measuring the damping ratio by changing the gap size and the support plate position. Comparison between calculated and experimental results is made which shows good agreement. Experimentally observed fact showing damping coefficient increases with the initial amplitude is well explained by theoretical model.

The importance of the in-flow oscillation of a single cylinder in cross-flow has been in the spotlight since an accident in a FBR-type reactor. However, in-flow oscillations can also be observed in heat exchanger tube arrays. Previous reports show some interesting phenomena on the oscillation of cylinder arrays. In this paper, detailed observation on the effect of the pitch ratio for pairs of cylinders, in parallel and in tandem, is highlighted in the range of low flow velocities, where each cylinder can move only in a given direction. The motion of the cylinders is measured by attached strain gages and by a high-speed digital video camera. As a result, it is found that the response of cylinders is greatly affected by their pitch ratio due to the separated vortex, and that the symmetric vortex is restricted when the motion of cylinder is restricted.

The importance of the in-flow oscillation of a single cylinder in cross-flow has been highlighted since an accident in a FBR-type reactor. In-flow oscillations have also been observed in tube arrays. This report is an experimental study on this phenomenon using a maximum of nine cylinders in a water tunnel. Six patterns of cylinder array, one single cylinder, two & three cylinders in parallel and in tandem, and a nine cylinder bundle, are examined. The cylinders are constrained to move only in the in-flow direction. The cylinder motion is measured by strain gages and by a high-speed digital video camera. The results of these motions are compared with the visualized vortex motion. As main results, two excitation mechanisms, symmetric vortex shedding and alternate vortex shedding, are observed. A transition range is found between these two mechanisms where large amplitude vibrations are observed. An additional test has been done to determine the root cause of the large vibrations in the transition range.

The authors have studied the in-flow vibration phenomena of cylinder arrays caused by cross-flow in the low Reynolds number range around Re=800. This Reynolds number range has been studied because it is the range where symmetric vortex shedding occurs. This report is our first trial to study the in-line fluidelastic vibration of cylinder arrays. In initial tests, the flow velocity was increased up to the maximum achievable level by the test equipment. However, it was found that the array's cantilever tube supports resulted in large static tube deflections due to static drag forces. The cylinder array tube supports have therefore been replaced by thin plates supported at both ends. The cylinders are set to be flexible both in the streamwise direction and the direction transverse to the flow. The obtained results of these two patterns are also compared with previous cantilevered data. The origin of the observed vibrations whether a self-induced mechanism or vortex shedding is discussed in detail. Copyright © 2011 by ASME.

The importance of the in-flow oscillation of a single cylinder in cross-flow has been highlighted since an accident in a FBR-type reactor. In-flow oscillations have also been observed in tube arrays. This report is an experimental study on this phenomenon using a maximum of nine cylinders in a water tunnel. Six patterns of cylinder array, one single cylinder, two & three cylinders in parallel and in tandem, and a nine cylinder bundle, are examined. The cylinders are constrained to move only in the in-flow direction. The cylinder motion is measured by strain gages and by a high-speed digital video camera. The results of these motions are compared with the visualized vortex motion. As main results, two excitation mechanisms, symmetric vortex shedding and alternate vortex shedding, are observed. A transition range is found between these two mechanisms where large amplitude vibrations are observed. An additional test has been done to determine the root cause of the large vibrations in the transition range.

The authors have studied the in-flow vibration phenomena of cylinder arrays caused by cross-flow in the low Reynolds number range around Re=800. This Reynolds number range has been studied because it is the range where symmetric vortex shedding occurs. This report is our first trial to study the in-line fluidelastic vibration of cylinder arrays. In initial tests, the flow velocity was increased up to the maximum achievable level by the test equipment. However, it was found that the array's cantilever tube supports resulted in large static tube deflections due to static drag forces. The cylinder array tube supports have therefore been replaced by thin plates supported at both ends. The cylinders are set to be flexible both in the streamwise direction and the direction transverse to the flow. The obtained results of these two patterns are also compared with previous cantilevered data. The origin of the observed vibrations whether a self-induced mechanism or vortex shedding is discussed in detail. Copyright © 2011 by ASME.

The importance of the in-flow oscillation of a single cylinder in cross-flow has been spotlighted since an accident in a FBR-type reactor. However, the in-flow oscillation can be observed in tube arrays of heat exchangers. Previous reports show some interesting phenomena on the oscillation of cylinder arrays, which have a same pitch between cylinders. This paper shows the effect of the pitch ratio of a cylinder array on the characteristics of those phenomena, especially in in-flow direction, where every cylinder can move only in this direction. The motion of cylinders is measured by attached strain gages and by a high-speed digital video camera

The importance of the in-flow oscillation of a single cylinder in cross-flow has been spotlighted since an accident in a FBR-type reactor. However, the in-flow oscillation can be observed in tube arrays of heat exchangers. Previous reports show some interesting phenomena on the oscillation of cylinder arrays, which have a same pitch between cylinders. This paper shows the effect of the pitch ratio of a cylinder array on the characteristics of those phenomena, especially in in-flow direction, where every cylinder can move only in this direction. The motion of cylinders is measured by attached strain gages and by a high-speed digital video camera

Laboratory experiments were conducted to determine the flow-induced vibration response and fluidelastic instability threshold of model heat exchanger tube bundles subjected to a cross-flow of refrigerant 11. Tube bundles were specially built with tubes cantilever-mounted on rectangular brass support bars so that the stiffness in the streamwise direction was about double that in the transverse direction. This was designed to simulate the tube dynamics in the U-bend region of a recirculating-type nuclear steam generator. Three model tube bundles were studied, one with a pitch ratio of 1.49 and two with a smaller pitch ratio of 1.33. The primary intent of the research was to improve our understanding of the flow-induced vibrations of heat exchanger tube arrays subjected to two-phase cross-flow. Of particular concern was to compare the effect of the asymmetric stiffness on the fluidelastic stability threshold with that of axisymmetric stiffness arrays tested most prominently in literature. The experimental results are analyzed and compared with existing data from literature using various definitions of two-phase fluid parameters. The fluidelastic stability thresholds of the present study agree well with results from previous studies for single-phase flow. In two-phase flow, the comparison of the stability data depends on the definition of two-phase flow velocity.