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Flow visualization tests and fluid force measurements were conducted in a water tunnel to investigate flow around and fluid forces on a cross-shaped tube (CST) in a cross-flow. The following results were obtained. Flow around a CST is classified into two patterns. One is perfect-separation flow for small incidence angle and the other is reattached flow for large incidence angle. The critical incidence angle where the flow pattern changes from the former to the latter is about 7.5°∼15°. At the critical angle, the mean drag and lift coefficients reach their minimum while the Strouhal number attains to the maximum. The amplitude of the fluctuating lift decreases as the incidence angle increases. These features of flow around and fluid forces on a CST are quite similar to those of a square prism. These results imply that one-degree-of-freedom galloping and vortex-induced vibration possibly occur for small incidence angle while ILEV (impingement of leading edge vortices) vibration might be caused for large incidence angle when a CST is elastically supported in a cross-flow.

The local fluid excitation force acting on a rotated square tube bundle having transverse pitch-to-diameter ratio of T∕D=3.1, in a single-phase cross-flow was measured, and the normalized power spectral density (NPSD) and correlation length in the axial direction of a tube were examined. The fluid excitation force acting on the interior tube was from three to ten times larger than that acting on the upstream tube. The fluid force was almost fully developed after the third row. NPSD of the fluid excitation force could be almost plotted on a single universal curve. Regarding the lift direction, there was a peak in NPSD at fD∕u∼0.3 caused by vortex shedding. Regarding the drag direction, there could be another peak in NPSD around twice the vortex shedding frequency. In the region of fD∕u>0.5, where the effect of the vortex shedding was assumed to be small in the lift direction, the correlation length of the lift direction was ∼1.1D. NPSD was a little larger than previous results for tube bundles of relatively small pitch to diameter ratios summarized by Axisa, Antunes, and Villard (1990, J. Fluid Struct., 4, pp. 321–341).

A cross-shaped tube bundle is proposed for the lower plenum structure in next-generation LWRs. The vibration response of the cross-shaped tube bundle in cross-flow has been measured in water tunnel tests. First, a small-scale test was conducted. Tests were conducted with 3×3 flexible tubes as well as a single flexible tube in a rigid tube bundle. The flexible tubes could vibrate in the lift, drag, and torsional directions. The effect of the arrangement of the tube bundle and the natural frequency ratio of translational and torsional vibrations were considered. Second, a large-scale test was conducted for only one case to check the effect of Reynolds number, in which the Reynolds number was 10 times larger than that of the small-scale test. In all the cases, large-amplitude vibration appeared when the flow velocity became larger than a critical value, and self-excited vibration was found to occur. The nondimensional critical gap velocity of the large-scale test agreed well with that of the small-scale test, which suggested that the effect of Reynolds number was not so large. A design guideline to prevent self-excited vibration is proposed for the cross-shaped tube bundle.

A cross-shaped tube bundle with small ratio of the gap width to tube diameter may be designed for the lower plenum structure in a next-generation BWR, though the characteristics of flow-induced vibration of this type of tube bundle remain virtually unknown. In this study, fluid dynamic forces acting on a cross-shaped tube bundle in a normal arrangement with small ratio of the gap width to tube diameter subjected to cross-flow were measured by water tunnel tests with two types of scale model. One was a small-scale model to measure local fluid dynamic forces and their correlation length in the lift and drag directions. The other was a large-scale model to investigate the effect of the Reynolds number on fluid dynamic forces in the lift, drag and torsional directions. Free oscillation tests with another small-scale model were also conducted to measure vibration amplitude by random excitation force. The following results were obtained. The measured fluid dynamic drag, lift and torque acting on the cross-shaped tube bundle in cross-flow were successfully compiled into the correlation equations, which include the nondimensional power spectral density (NPSD) of the local fluid dynamic force and the spanwise correlation length. The Reynolds effects on the NPSD can be considered negligible at least in the range of Reynolds number 6 . No remarkable spectral peaks of vortex shedding appeared in the NPSD, and the ratios of the correlation lengths to the tube diameter for the cross-shaped tube bundle were much shorter than that of the random excitation force acting on circular tube bundles. It is considered that this was because the ratio of gap width to tube diameter was small for the tested arrangement.

A tube in a square tube bundle of P/D=1·42 was oscillated in the lift direction in air–water two-phase cross-flow, and fluidelastic forces acting on the oscillated tube were measured. First, the tube amplitude was fixed to 3 mm (=0·136 D), and added mass, damping, and stiffness coefficients were obtained as a function of two-phase mixture characteristics such as nondimensional gap velocity and void fraction. When reference mixture density and velocity were estimated, the drift–flux model, in which the relative velocity between the gas and liquid phases was estimated, generated better results than the homogeneous model. The added mass coefficient was obtained from quiescent two-phase flow as a function of void fraction. Using the added mass coefficient, the added stiffness coefficient converged to zero with decreasing nondimensional gap velocity. This overcame the contradiction in the added stiffness estimation without added mass, in which the added stiffness coefficient did not converge to zero with decreasing nondimensional gap velocity. Next, the effects of the vibration amplitude on the fluidelastic force coefficients were considered. When the tube amplitude was 3 mm (=0·136 D) or less, the equivalent added stiffness and damping coefficients were almost constant and nonlinearity was small. This showed the validity of the fluidelastic force coefficients obtained based on the data of amplitude of 3 mm. The linearity did not exist when the tube displacement amplitude was 4·5 mm (=0·205 D) or more; a remarkable nonlinearity appeared in the equivalent added damping coefficient. A method to estimate the limit-cycle amplitude of the fluidelastic vibration was proposed when only one tube in the tube bundle was able to vibrate in the lift direction. The amplitude could be obtained from the amplitude at which the equivalent added damping coefficient changed from negative to positive with increase in the tube amplitude.

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of JG

Bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of JG

Thermo-hydraulic instabilities of a boiling natural circulation loop with a chimney under high pressure were investigated using linear stability analysis. Drift-flux model was used for two-phase flow model. The instability regions as well as the thermo-hydraulic characteristics in the chimney such as wavy feature were examined, which were compared with the characteristics in low pressure. Instability could occur when exit quality was relatively low, which was the same manner as the characteristics in low pressure. In high-pressure, void was generated near channel exit, and void wave propagated in the chimney. In low pressure, steam was generated only near the chimney exit due to gravity induced flashing, and single-phase enthalpy wave, that is, temperature wave propagated in single-phase flow region. Though flow could be very stable in the high pressure and high power condition, the decay ratio of higher mode could be larger than that of lower mode.

Experiments have been conducted to investigate an effect of inlet restriction on the thermal-hydraulic stability. A Test facility used in this study was designed and constructed to have non-dimensional values that are nearly equal to those of natural circulation BWR. Experimental results showed that driving force of the natural circulation at the stability boundary was described as a function of heat flux and inlet subcooling independent of inlet restriction. In order to extend experimental database regarding thermal-hydraulic stability to different inlet restriction, numerical analysis was carried out based on the homogeneous flow model. Stability maps in reference to the core inlet subcooling and heat flux were presented for various inlet restrictions using the above-mentioned function. Instability region during the inlet subcooling shifted to the higher inlet subcooling with increasing inlet restriction and became larger with increasing heat flux.

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.

In many shell and tube heat exchangers such as steam generators, baffle plates are located at appropriate intervals to support the heat transfer tubes. In the heat exchangers, the secondary coolant streams through the channels such as the flow hole nozzles of the baffle plates in the form of jets, and flows in parallel with the tube bundle. This turbulence induces vibrations which could cause fretting wear and fatigue of the tubes. In this paper, basic characteristics of tube vibration were experimentally investigated in air-water two phase flow to evaluate the jet effect on the relationships between hydrodynamic mass, damping ratio, and excitation force on a vibrating tube and void fractions.

In many shell and tube heat exchangers such as steam generators, baffle plates are located at appropriate intervals to support the heat transfer tubes. In the heat exchangers, the secondary coolant streams through the channels such as the flow hole nozzles of the baffle plates in the form of jets, and flows in parallel with the tube bundle. This turbulence induces vibrations which could cause fretting wear and fatigue of the tubes. In this paper, basic characteristics of tube vibration were experimentally investigated in air water two phase flow to evaluate the jet effect on the relationships between hydrodynamic mass, damping ratio, and excitation force on a vibrating tube and void fractions.

Fluid-elastic forces acting on a square tube bundle (P/D=1.42) in air-water two-phase cross flow were considered experimentally. A tube in the tube bundle was oscillated in the direction perpendicular as well as parallel to the two-phase flow, and fluid elastic forces acting on the oscillated tube as well as tubes surrounding the oscillated tube were measured. Measured fluid elastic forces were separated into coefficients of accleration, velocity, and displacement of the oscillated tube, and the coefficients were nondimensionalized with two-phase mixture characteristics, which were obtained using the drift flux model. It was found that the fluid elastic force coefficients could collapse very well as a function of void fraction and/or nondimensional gap velocity. These coefficients were used to estimate the critical gap velocity of fluid elastic vibration. The results agreed qualitatively with previous experimental results.

Instability of a boiling natural circulation loop with a chimney at low pressure and low heater power was investigated by linear stability analysis and experiment. A homogeneous and thermodynamic equilibrium model for two-phase flow was used. The effect of flashing induced by pressure drop in the heated channels and the chimney was considered. The effects of coupling between two boiling channels were investigated. It was found that in-phase-mode instability was apt to occur when channel inlet subcooling was large and boiling began in the chimney. In-phase-mode instability easily occurred when channel length became short and the chimney became long. Out-of-phase-mode instability was apt to occur when chimney length became small and boiling began in the channel. It was suggested that in-phase-mode instability was density weve oscillation induced by flashing in the chimney and out-of-phase-mode instability was density wave oscillation induced by boiling in the channels. The analytical results agreed qualitatively with experimental results.

For heat exchangers with a small-pitch tube bundle, it is important to evaluate the vibration of the tube due to strong turbulence of fairly high-speed cross-flow. In this study, statistical quantities of fluid force were obtained experimentally to numerically evaluate the turbulent-flow-induced vibration. A tube bundle of 0.0254-meter-diameter and 0.032-meter-pitch tubes was installed in an experimental test section. Specifically, local fluid force acting on a tube was measured using 0.013-meter-wide force sensors installed along the axial direction of the measured tube, and the correlation length was deduced from the fluid forces of the two adjacent sensors. Vibration levels evaluated analytically using the fluid force correlation were compared with the levels obtained from several experiments. The analytical results agreed well with the experimental vibration levels.

In this paper, the feasibility of higher power rates for natural-circulation boiling water reactors (BWRs) is studied with the objective of examining the flexibility of the plant power rate in constructing such plants to cope with the increasing demand for electricity. By applying existing one-dimensional design codes, the riser heights necessary to meet two major thermal-hydraulic requirements, i.e., critical power and core stability, are systematically calculated. Several restrictions on the maximum diameter and height of the pressure vessel are also considered because these restrictions could make construction impossible or drastically increase the construction costs. A very simple map of the dominant parameters for higher power rates is obtained. It is concluded that natural-circulation BWRs of {gt}1000 MW (electric) will be feasible within the restrictions considered here.

Wear damage of heat transfer tubes should be avoided in order to improve the integrity of heat exchangers and steam generators. Tube wear is the result of tube/support impacting and rubbing motion caused by flow-induced tube vibrations. Evaluation of the relationship between the tube vibration and the tube-to-support interaction is a prerequisite for understanding tube wear. In this paper, tube-to-support interaction characteristics were investigated on a tube excited by flow turbulence. The results show that by using the magnitude of tube vibration under conditions free from tube/support contact and parameters representing tube setting condition in the tube support plate such as tube/support clearance and eccentricity, the characteristics of the interaction can be systematically evaluated.

A cross-shaped tube bundle is proposed for the lower plenum structure in the next-generation LWR. The effect of tube bundle arrangement on the flow-induced vibration characteristics of the cross-shaped tube bundle in cross flow was considered experimentally. Regarding random vibration, the power spectral density of the fluid force of the staggered arrangement as well as the correlation length was measured and those of the normal arrangement were compared with those of the staggered arrangement. Regarding self-excited vibration, vibration response was compared. The trend of the power spectral densities, correlation length, and the critical velocity of the normal arrangement were similar to those of the staggered arrangement.Copyright © 2003 by ASME

A cross-shaped tube bundle with dense arrangement may be designed for a lower plenum structure in a next generation LWR, though the characteristics of flow-induced vibration of this type of tube bundle remain virtually unknown. In this study, turbulence-induced fluid dynamic forces acting on a cross-shaped tube bundle with a dense arrangement subject to cross flow were measured by water tunnel tests with two types of scale models. One is a small-scale model to measure local fluid dynamic forces and their correlation length in the lift and drag direction. The other is a large-scale model to investigate the effect of the Reynolds number on fluid dynamic forces in the lift, drag and torsional directions. Free oscillation tests with another small-scale model were also conducted to measure vibration amplitude by random excitation force. In conclusion, the following results were obtained. Vortex-induced vibration cannot arise in the cross-shaped tube bundle, since a typical peak corresponding to periodic vortex shedding was not observed in power spectral density for fluid excitation force. Power spectral densities of fluid dynamic forces in the drag, lift and torsional directions have mutually similar properties and they are hardly dependent on the Reynolds number. The experimental results were compiled into dimensionless correlation equations composed of the power spectral density for the local fluid excitation force and its correlation length. They are useful for evaluating the random vibration amplitude. The estimated amplitudes of turbulence-induced vibration by the correlation equation coincide with those of the experimental results obtained by the free-oscillation tests.Copyright © 2002 by ASME

Cross-shaped tube bundle is proposed for a lower plenum structure in a next generation LWR. Vibration response of cross-shaped tube bundle in cross flow has been measured in water tunnel tests. First, small-scale test was conducted. Tests were conducted with 3×3 flexible tubes as well as single flexible tube in rigid tube bundle. The flexible tubes could vibrate in lift, drag, and torsional direction. The effect of arrangements of tube bundle and the natural frequency ratio of bending and torsional vibrations were considered. Second, a large-scale test was conducted for only one case to check the effect of Reynolds number, in which Reynolds number was 10 times larger than that of small-scale test. In all the cases, large amplitude vibration could appear when the flow velocity became larger than a critical value, and a self-excited vibration was found to occur. The nondimensional critical gap velocity of the large-scale test agreed well with that of the small-scale test, which suggested that the effect of Reynolds number was not so large. A design guideline to prevent self-excited vibration was proposed for cross-shaped tube bundle.Copyright © 2002 by ASME

Fluid-elastic forces acting on a square tube bundle (P/D = 1.42) in air-water two-phase cross flow were considered experimentally. A tube in the tube bundle was oscillated in the direction perpendicular as well as parallel to the two-phase flow, and fluid elastic forces acting on the oscillated tube as well as tubes surrounding the oscillated tube were measured. Measured fluid elastic forces were separated into coefficients of acceleration, velocity, and displacement of the oscillated tube, and the coefficients were nondimensionalized with two-phase mixture characteristics, which were obtained using the drift-flux model. It was found that the fluid elastic force coefficients could collapse very well as a function of void fraction and/or nondimensional gap velocity. These coefficients were used to estimate the critical gap velocity of fluid elastic vibration. The results agreed qualitatively with previous experimental results of Nakamura et al. (1986a,b).

This paper is concerned with the fluid force acting on a tube placed in a parallel steam-water two-phase flow. Based on experiments on the tube vibration induced by the turbulence of two-phase flow, the relationships between the hydrodynamic mass, damping ratio, excitation force, and the fluid flow conditions were evaluated. Mass flow rate, pressure, and void fraction were varied in the experiment to measure random vibration of the tube caused by turbulence in the stream. The hydrodynamic mass and damping ratio were derived by analyzing the vibration data. The excitation force was calculated using a transfer function to represent the relationship between the intensity and excitation force of the vibration given by random statistical theory. It was found that the hydrodynamic mass and damping ratio are little affected by the mass flow rate and pressure but are significantly affected by the void fraction and frequency. In contrast, the vibration excitation force is affected by the pressure as well as the effects of void fraction and frequency. The relationships between them were evaluated.

In some heat exchangers and steam generators, the flow is predominantly axial, and the external fluid flows between baffled compartments through enlarged holes in the baffles around the heat exchanger tubes. Thus, the tube is subjected to relatively high flow velocities over small portions of its length, in the baffle locations. In this paper, the dynamics of such an idealized system is investigated, involving a cylindrical beam with pinned ends in axial flow, going through a baffle plate of finite thickness at some intermediate point, with small radial clearance. The fluid forces along the tube are formulated in a manner reminiscent of the transfer-matrix technique, since the character of these forces changes drastically along the tube. The fluid forces are determined approximately by means of potential flow theory, and viscous effects are taken into account only in a global sense. It was found that if the flow passage through the baffle plate is diffuser-shaped, negative fluid-dynamic damping is generated therein, destabilizing the system and leading to flutter at relatively low flow velocities. The instability depends critically on the shape of the hole through the baffle and on the clearance; thus a convergent-type flow passage does not lead to instability. The negative fluid-dynamic damping is linearly proportional to the flow velocity through the baffle.

In the multi-tube type of heat exchanger, baffle plates are located at appropriate intervals to support the heat transfer tubes. Depending on the baffle plate type employed, the flow field in the tube bundle will consist of a mixture of the cross flow (the fluid flows at right angles to the tube bundle along the baffle plate surfaces) and the parallel jet flow (the fluid streams through channels such as the flow holes of the baffle plates in the form of jets and flows in parallel with the tube bundle). Vibrations induced by the flow can cause fretting wear and fatigue of the heat transfer tubes. Therefore, it it essential to establish a method of evaluating heat transfer tube vibrations induced by the mixed flow for the purpose of evaluating the integrity of heat exchanger tubes. In this paper, three different flows, that is, cross, parallel jet and mixed flows, were simulated in order to clarify the relationships between the flow conditions and vibration of the tube bundle, and to study a method for evaluating tube bundle vibrations induced by turbulence in the mixed flow field by using the vibration characteristics in the cross flow field and the parallel jet flow field.