Fluidelastic Instability Of Tube Bundles Research Articles

Experimental investigation of in-flow fluidelastic instability for rotated triangular tube bundles subjected to single-phase and two-phase transverse flows

The in-flow fluidelastic instability of tube bundles prompted renewed interest since the recent unanticipated failure of the replacement steam generators at the San Onofre nuclear power station. A literature review on the topic discloses contrasting views, depending on the tube bundle and flow configuration addressed. In a recent paper, the authors reported experiments using square bundles, subjected to single and two-phase flows. No streamwise instability was observed, for the tested bundle configurations and the flow velocity ranges explored. In the present paper, experimental results obtained at CEA-Saclay for a rotated triangular tube bundle are presented, providing new in-flow fluidelastic data for both single-phase and two-phase transverse flows. The bundle consists of 50 tubes, with reduced pitch P/D = 1.44 and tube diameter D = 30 mm. It was subjected to single-phase (air or water) and two-phase air-water (with homogeneous void fraction in the range 40% to 98%) transverse flows. In the upper region of the bundle, several different flexibility configurations were tested, with up to 15 flexible tubes, mounted using anisotropic supports, which allow for in-flow vibrations. Results presented in the paper include in-flow fluidelastic stability data obtained for both single-phase and two-phase transverse flows. A detailed complex modal identification of the bundle under natural turbulence excitation was performed, at several flow velocities, highlighting the modeshapes which are prone to in-flow instability. Moreover, local void fraction and identified flow regimes are also presented. These results are discussed and compared to those obtained by previous authors, for similar tested configurations.

Experimental Study on Fluidelastic Instability of Tube Bundles With Asymmetric Stiffness Using Visual Image Processing System

Abstract This technical brief is an experimental study, which used a water tunnel to investigate the fluidelastic instability of tube bundles with asymmetric stiffness. The natural frequency ratios (streamwise/transverse) of the tubes are 50%, 60%, 70%, and 80%, respectively. Flexible tubes are set as the following two patterns: a single flexible tube and a cluster of seven flexible tubes. The vibration data of tube bundles are collected and analyzed by a self-designed Visual Analysis System. The results show that the fluidelastic instability only occurs in the transverse direction. In the streamwise direction, the coupling effect of vibrations in both directions of the tube causes the increase of vibration amplitude, no matter in the single-flexible-tube case or the seven-flexible-tube cluster. Furthermore, reducing the natural frequency of the streamwise direction will not change the transverse critical velocity but leads to an amplitude increase caused by vortex-induced vibration. Compared to the single flexible tube, vortex-induced vibration is more likely to occur in the tube cluster with larger amplitudes.

Experimental and theoretical study on fluidelastic instability of tube bundles subjected to cross-flow in the parallel direction

Fluidelastic instability is an important security issue for the steam generator tube bundles subjected to cross-flow. Lots of studies have been conducted on the fluidelastic instability of the tube bundles in the transverse direction. Recently, the streamwise fluidelastic instability of the tube bundles in cross-flow has been observed in some experimental studies. However, the mechanism of the fluidelastic instability in the parallel is not clear. Thus, in this paper, experimental and theoretical studies were performed to investigate the fluidelastic instability of a rotated triangular tube array subjected to cross-flow in the parallel direction. The influences of the boundary constraint condition and the void fraction of two-phase flow on the threshold of the streamwise fluidelastic instability of the tube bundles were discussed.

Modelling of fluidelastic instability in tube bundles under two-phase bubbly flow conditions

One of the major factors affecting the integrity of tube bundles in a steam generator undergoing excessive vibrations is fluidelastic instability. Currently, a comprehensive model for predicting fluidelastic instability in tube bundles under two-phase cross flow has not been developed. Accurate design guidelines on fluidelastic instability in tube bundles is crucial to avoid tube failure due to tube vibrations. Therefore, this study presents a model for the fluidelastic instability (FEI) of a two-phase flow in a normal square tube bundle. The model focuses on the bubbly flow regime of a two-phase flow. This complex flow across the bundle is simplified as a one-dimensional inviscid flow in channels. The liquid is treated as a continuous phase while the gas bubbles are treated as compressible dispersed particles. The motion of each individual bubble is tracked in time domain simulations. Bubble-to-bubble interaction, bubble break-up, and bubble coalescence mechanisms are considered in the current model. The continuity equation is solved using the local instantaneous void fraction. The momentum equation is then solved to calculate the fluid forces on the tube. Using this technique, it was possible to calculate the change in the flow density around the tube. Prediction of the stability threshold showed very promising results when compared with the experimental data.

Investigation on fluidelastic instability of tube bundles considering the effect of slip ratio of air-water two-phase flow

This paper investigates the fluidelastic instability of a rotated triangular tube array subjected to two-phase crossflow considering the effect of the slip ratio of air-phase and water phase. We first established a Computational Fluid Dynamics model to determine the two-phase flow parameters. Then, a dynamic model of the tube motion while considering the effect of the slip ratio of the air phase and the water phase was developed. The eigenvalue problem of fluidelastic instability of the tube bundles for five void fraction conditions was studied. The results indicate that the slip ratio of the air phase and water phase is an important factor to predict the threshold of fluidelastic instability of a rotated triangular tube array in the transverse direction. The critical velocities of fluidelastic instability of the tube bundles obtained from the separated flow model are much lower those obtained from the Homogeneous Equilibrium Model.

Numerical study on fluidelastic instability of tube bundles in two-phase flow considering the effect of tube boundary constraint

This paper investigates fluidelastic instability of a tube array in two-phase crossflow considering the effects of tube constraint conditions. We first established a theoretical model of tube bundles subjected to two-phase flow. Then, we wrote a numerical calculation program and verified the validity. The following three types of boundary constraints of the tube bundles were concerned in this study: cantilever, simply-supported, and fixed-end tube bundles. We calculated the eigenvalues, the critical velocities, and the instability modes of these three types of tube bundles within the void fraction ranging from 0% to 80%. The results show that the tube constraint conditions could change the critical velocity of the tube bundles, while may not affect the critical reduced velocity and the fluidelastic instability factor of the Connors equation. It is also found that the structural boundary constraint could not change the instability mechanism of the tube bundles in two-phase crossflow.

Numerical simulation of streamwise fluidelastic instability of tube bundles subjected to two-phase cross flow

This work aims to develop and validate a numerical model to simulate the flow-structure interaction in tube bundles subjected to two-phase flow. The model utilizes a mixture multiphase module in which a drift flux formulation is used to account for the slip between the phases. Two methods of numerical flow-structure interaction are used to predict the onset of fluidelastic instability (FEI) in the streamwise direction for a two-phase air–water flow mixture in parallel triangular tube bundles. These models are the hybrid analytical-flow field model and the direct numerical flow/structure coupling model. This work investigates the effects of void fractions in the range of 20% to 80% and several pitch-to-diameter ratios (P/D) in the range of 1.3 to 1.7. The results of the fluidelastic forces and the stability threshold are validated against the experimental data available in the literature and show an excellent agreement. The streamwise FEI threshold shows a significant dependency on the pitch-to-diameter ratio while the void fraction exhibits a lesser effect. Generally, the stability threshold increases as the pitch-to-diameter ratio increases. The model that was developed paves the way for devising of more reliable prediction tools for FEI in steam generators.

Design guidelines for fluid-elastic instability of tube bundles subjected to two-phase cross flow

Fluid-elastic instability of tube bundles is the main cause of vibration failure of heat exchangers. To establish more reasonable and reliable design guidelines for fluid-elastic instability of tube bundles subjected to two-phase cross flow, we investigated experimentally the effects of the flow conditions of the two-phase flow and the geometrical characteristics of the tube bundles on damping, vibration, and fluid-elastic instability. Moreover, we proposed recommended values of the instability constant based on the conductivity difference measurement (CDM) model and the classification of tube bundle arrangements. The reliability of these values was also verified. The results indicated that the damping ratio in the lift direction was smaller than that in the drag direction and fluid-elastic instability was more prone to occur. The order of stability of the four tube bundle arrangements from high to low was normal triangular, normal square, rotated square, and rotated triangular. Thus, to avoid fluid-elastic instability, the normal triangular tube bundle is recommended for large shell-and-tube heat exchangers subjected to two-phase cross flow. In addition, for normal square and normal triangular tube bundles, the recommended instability constant is 4.0. For rotated square and rotated triangular tube bundles, the recommended instability constant is 1.1 when the mass damping parameter is less than or equal to 0.54, otherwise the value is 1.5.

On modeling fluidelastic instability in tube arrays subjected to two-phase cross-flow

An experimental program was undertaken in order to improve our understanding of the mechanism of fluidelastic instability in two-phase flows and to provide practical design guidance to avoid vibration problems in heat exchangers. Different ways of defining the traditional parameters, such as void fraction, damping, velocity, and 2-phase fluid density, were examined. It was found that the damping in quiescent fluid combined with the gamma densitometer measured void fraction and the interfacial velocity, collapses the available data well and provides the expected trend of two-phase flow stability data over the void fraction range from liquid to gas flows. The resulting stability maps represent a significant improvement over existing maps for predicting fluidelastic instability of tube bundles in two-phase flows. This result also tends to confirm the hypothesis that the basic mechanism of fluidelastic instability is the same for single and two-phase flows, providing that the parameters are properly defined.

Fluidelastic instability of a tube array in two-phase cross-flow considering the effect of tube material

Abstract Fluidelastic instability of a tube array is a key factor of the security of a nuclear power plant. An unsteady model of the fluidelastic instability of a tube array subjected to two-phase flow was developed to analyze the fluidelastic instability of tube bundles in two-phase flow. Based on this model, a computational program was written to calculate the eigenvalue and the critical velocity of the fluidelastic instability. The unsteady model and the program were verified by comparing with the experimental results reported previously. The influences of void fraction and the tube's material properties on the critical velocity were investigated. Numerical results showed that, with increasing the void fraction of the two-phase flow, the tube array becomes more stable. The results indicate that the critical velocities of the tube array made of stainless are much higher than those of the other two tube arrays within void fraction ranging from 20% to 80%.

Mechanism analysis on fluidelastic instability of tube bundles in considering of cross-flow effects

Abstract Fluidelastic instability is a key issue in steam generator tube bundles subjected in cross-flow. With a low flow velocity, a large amplitude vibration of the tube observed by many researchers. However, the mechanism of this vibration is seldom analyzed. In this paper, the mechanism of cross-flow effects on fluidelastic instability of tube bundles was investigated. Analysis reveals that when the system reaches the critical state, there would be two forms, with two critical velocities, and thus two expressions for the critical velocities were obtained. Fluidelastic instability experiment and numerical analysis were conducted to obtain the critical velocity. And, if system damping is small, with increases of the flow velocity, the stability behavior of tube array changes. At a certain flow velocity, the stability of tube array reaches the first critical state, a dynamic bifurcation occurs. The tube array returns to a stable state with continues to increase the flow velocity. At another certain flow velocity, the stability of tube array reaches the second critical state, another dynamic bifurcation occurs. However, if system damping is big, there is only one critical state with increases the flow velocity. Compared the results of experiments to numerical analysis, it shows a good agreement.

Large Eddy Simulation of Fluid-Elastic Instability in Square Normal Cylinder Array

Large eddy simulations (LES) are performed at low Reynolds number (2000–6000) to investigate the dynamic fluid-elastic instability in square normal cylinder array for a single-phase fluid cross flow. The fluid-elastic instability is dominant in the flow normal direction, at least for all water-flow experiments (Price, S., and Paidoussis, M., 1989, “The Flow-Induced Response of a Single Flexible Cylinder in an in-Line Array of Rigid Cylinders,” J. Fluids Struct., 3(1), pp. 61–82). The instability appears even in the case of single moving cylinder in an otherwise fixed-cylinder arrangement resulting in the same critical velocity (Khalifa, A., Weaver, D., and Ziada, S., 2012, “A Single Flexible Tube in a Rigid Array as a Model for Fluidelastic Instability in Tube Bundles,” J. Fluids Struct., 34, pp. 14–32); Khalifa et al. (2013, “Modeling of the Phase Lag Causing Fluidelastic Instability in a Parallel Triangular Tube Array,” J. Fluids Struct., 43, pp. 371–384). Therefore, in the present work, only a central cylinder out of 20 cylinders is allowed to vibrate in the flow normal direction. The square normal (90 deg) array has 5 rows and 3 columns of cylinders with 2 additional side columns of half wall-mounted cylinders. The numerical configuration is a replica of an experimental setup except for the length of cylinders, which is of 4 diameters in numerical setup against about 8 diameters in the experiment facility. The single-phase fluid is water. The standard Smagorinsky turbulence model is used for the subgrid scale eddy viscosity modeling. The numerical results are analyzed and compared to the experimental results for a range of flow velocities in the vicinity of the instability. Moreover, instantaneous pressure and fluid-force profiles on the cylinder surface are extracted from the LES calculations in order to better understand the dynamic fluid-elastic instability.

Experimental Research on Fluid-Elastic Instability in Tube Bundles Subjected to Air-Water Cross Flow

Fluid-elastic instability is the major factor in causing the vibration of tube bundles. Design guidelines on fluid-elastic instability in tube bundles is necessary to avoid damage due to excessive tube vibration. However, the design guidelines on fluid-elastic instability in tube bundles subjected to two-phase cross flow have no consistent conclusions. Accordingly, this technical note researches the vibration characteristics of three tube bundle distributions, namely, normal square tube bundles with pitch-to-diameter ratios of 1.28 and 1.32 and a normal triangular tube bundle with a pitch-to-diameter ratio of 1.32. Comparison of the present fluid-elastic threshold results with previously published data shows good agreement in single-phase flow. The effects of pitch-to-diameter ratio and tube bundle configurations on fluid-elastic instability induced by air-water cross flow were also compared and analyzed by measuring unstable behavior of tube bundles. It was found that fluid-elastic instability is more prone to occur with a decrease of pitch-to-diameter ratio and that the normal square tube bundle is more stable than the normal triangular tube bundle. From the perspective of the tube bundle configurations, it was recommended that the instability constant K in normal triangular and normal square tube bundles be 3.4 and 4.0, respectively.

Fluid-Elastic Instability Tests on Parallel Triangular Tube Bundles with Different Mass Ratio Values under Increasing and Decreasing Flow Velocities

To study the effects of increasing and decreasing flow velocities on the fluid-elastic instability of tube bundles, the responses of an elastically mounted tube in a rigid parallel triangular tube bundle with a pitch-to-diameter ratio of 1.67 were tested in a water tunnel subjected to crossflow. Aluminum and stainless steel tubes were tested, respectively. In the in-line and transverse directions, the amplitudes, power spectrum density functions, response frequencies, added mass coefficients, and other results were obtained and compared. Results show that the nonlinear hysteresis phenomenon occurred in both tube bundle vibrations. When the flow velocity is decreasing, the tubes which have been in the state of fluid-elastic instability can keep on this state for a certain flow velocity range. During this process, the response frequencies of the tubes will decrease. Furthermore, the response frequencies of the aluminum tube can decrease much more than those of the stainless steel tube. The fluid-elastic instability constants fitted for these experiments were obtained from experimental data. A deeper insight into the fluid-elastic instability of tube bundles was also obtained by synthesizing the results. This study is beneficial for designing and operating equipment with tube bundles inside, as well as for further research on the fluid-elastic instability of tube bundles.

An unsteady model for fluidelastic instability in an array of flexible tubes in two-phase cross-flow

The streamtube model for fluidelastic instability in single-phase flow was extended to two-phase flow by two kinds of two-phase flow model. One was the traditional HEM, and the other was the slip ratio model. The model based on slip ratio can represent the effect of velocity difference between gas and liquid phases, and was verified with the experimental data from the literature. Comparing to the conventional HEM model, the slip ratio model and the introduction of interfacial velocity could collapse the stability data from various studies, which is beneficial for predicting the fluidelastic instability of tube bundles from existing stability maps and methods.

A single flexible tube in a rigid array as a model for fluidelastic instability in tube bundles

Fluidelastic instability is considered the most critical flow induced vibration mechanism in tube and shell heat exchangers, and as such has received the most attention. The present study examines the concept of using a single flexible tube in a rigid array for predicting fluidelastic instability. The experimental work published in the open literature involving the use of a single flexible tube in a rigid array is critically reviewed. Based on this, an experiment is designed to facilitate precise control of the system parameters and to study tube response at different locations in the array. Experiments were conducted using a fully flexible array as well as a single flexible tube in the same rigid array. It is found that a single flexible tube located in the third row of a rigid parallel triangular array becomes fluidelastically unstable at essentially the same threshold as for the fully flexible array. However, when the single flexible tube is located in the first, second, fourth, or fifth rows, no instability behavior is detected. Thus, tube location inside the array significantly affects its fluidelastic stability behavior when tested as a single flexible tube in a rigid array. It is concluded that, in general, fluidelastic instability in tube arrays is caused by a combination of the damping and stiffness mechanisms. In certain cases, a single flexible tube in a rigid array will become fluidelastically unstable and provide a useful model for fundamental research and developing physical insights. However, it must be cautioned that this behavior is a special case and not generally useful for determining the stability limit of tube arrays.

2 상 횡 유동장에 놓인 관군의 유체탄성불안정성

Experiments have been performed to investigate fluid-elastic instability of tube bundles, subjected to twophase cross flow. Fluid-elastic is the most important vibration excitation mechanism for heat exchanger tube bundles subjected to the cross flow. The test section consists of cantilevered flexible cylinder(s) and rigid cylinders of normal square array. From a practical design point of view, fluid-elastic instability may be expressed simply in terms of dimensionless flow velocity and dimensionless mass-damping parameter. For dynamic instability of cylinder rows, added mass, damping and the threshold flow velocity are evaluated. The Fluid-elastic instability coefficient is calculated and then compared to existing results given for tube bundles in normal square array.

공기-횡 유동장에 놓인 유연성 실린더 관군의 유체탄성 불안정

Using wind tunnel, experimental approaches were employed to investigate fluidelastic instability of tube bundles, subjected to uniform cross flow. There are several flow-induced vibration excitation mechanisms, such as fluidelastic instability, periodic wake shedding resonance, turbulence-induced excitation and acoustic resonance, which could cause excessive vibration in shell-and tube heat exchanges. Fluidelastic is the most important vibration excitation mechanism for heat exchanger tube bundles subjected to cross flow. The system comprised of cantilevered flexible cylinder(s) and rigid cylinders of normal square array, In order to see the characteristics of flow in tube bundles, particle image velocimetry was used. From a practical design point of view, Fluidelastic instability may be expressed simply in terms of dimensionless flow velocity and dimensionless mass-damping. The threshold flow velocity for dynamic instability of cylinder rows is evaluated and the data for design guideline is proposed for the tube bundles of normal square array.

Methods for numerical study of tube bundle vibrations in cross-flows

In many industrial applications, mechanical structures like heat exchanger tube bundles are subjected to complex flows causing possible vibrations and damage. Part of fluid forces are coupled with tube motion and the so-called fluid-elastic forces can affect the structure dynamic behaviour generating possible instabilities and leading to possible short term failures through high amplitude vibrations. Most classical fluid force identification methods rely on structure response experimental measurements associated with convenient data processes. Owing to recent improvements in Computational Fluid Dynamics, numerical simulation of flow-induced vibrations is now practicable for industrial purposes. The present paper is devoted to the numerical identification of fluid-elastic effects affecting tube bundle motion in presence of fluid at rest and one-phase cross-flows. What is the numerical process? When fluid-elastic effects are not significant and are restricted to added mass effects, there is no strong coupling between structure and fluid motions. The structure displacement is not supposed to affect flow patterns. Thus it is possible to solve flow and structure problems separately by using a fixed nonmoving mesh for the fluid dynamic computation. Power spectral density and time record of lift and drag forces acting on tube bundles can be computed numerically by using an unsteady fluid computation involving for example a large Eddy simulation. Fluid force spectra or time record can then be introduced as inlet conditions into the structure code providing the tube dynamic response generated by flow. Such a computation is not possible in presence of strong flow structure coupling. When fluid-elastic effects cannot be neglected, in presence of tube bundles subjected to cross-flows for example, a coupling between flow and structure computations is required. Appropriate numerical methods are investigated in the present work. The purpose is to be able to provide a numerical estimate of the critical flow velocity for the threshold of fluid-elastic instability of tube bundle without experimental investigation. The methodology consists in simulating in the same time thermohydraulics and mechanics problems by using an arbitrary Lagrange Euler (ALE) formulation for the fluid computation. A fully coupled numerical approach is suggested and applied to the numerical prediction of the vibration frequency of a flexible tube belonging to a fixed tube bundle in fluid at rest or in flow. Numerical results turn out to be consistent with available experimental data obtained in the same configuration. This work is a first step in the definition of a computational process for the full numerical prediction of tube bundle vibrations induced by flows.

Dependence of Post-Stable Fluidelastic Behavior on the Degrees of Freedom of a Tube Bundle

Several experimental studies of fluidelastic instability in tube bundles have revealed the existence of post-stable hysteresis behavior. The objective of the present study was to determine the dependence of this behavior on the number of degrees of freedom of the bundle. We tested two different bundle geometries in air cross-flow. We controlled both the number of flexible tubes in the bundle and, using highly asymmetric beams, the number of degrees of freedom per flexible tube. We also varied tube mass within the mass-damping parameter range of mδ/pd2 = 1·9?23, and we varied the number of tube rows upstream of the flexible tubes of interest.We found that a dominant tube typically controls the fluidelastic instability and post-stable behavior of a fully flexible bundle. Furthermore, a single-degree-of-freedom system (a tube constrained to move transverse to the flow) can display similar post-stable behavior as that of the entire bundle. Thus, for the arrays investigated, the fluidelastic mechanism requires neither fluid coupling between tubes nor coupling between streamwise and transverse motion of a single tube to generate hysteresis. However, the exact details of the post-stable behavior (e.g., hysteresis effects, limit cycle amplitudes) depend quite strongly on array misalignment and the number of upstream tube rows. Amplitude-dependent dampimg measurements reported here suggest that finite limit cycles result from fluidelastic, not structural, nonlinearity. Also, transient excitation tests indicate that turbulence may be substantially more likely than previously thought to excite instability of an array operating just inside a hysteresis region. For broad hysteresis regions, such reductions in critical velocity are as significant to heat-exchange design as array pitch and pattern effects. The present work suggests that a nonlinear, single-degree-of-freedom model would be a good first step towards their prediction.