Fluidelastic Instability Research Articles

Fluid-elastic instability of inverted cantilevered cylinders in axial flow

This paper describes and analyzes water-tunnel experiments involving flexible cantilevered cylinders in reverse axial flow, i.e. flow directed from the free towards the fixed end of the cylinder. It was found that the cylinder is subjected to small amplitude motion due to turbulent buffeting prior to first-mode flutter at relatively low flow velocities, followed eventually by an abrupt static divergence at higher flows. The observed flutter was quite unsteady and sometimes near-intermittent. The flutter amplitude increased with flow, prior to the onset of static divergence. The onset of static divergence displayed strong hysteresis, suggesting a subcritical bifurcation. The static divergence amplitude for very flexible cylinders could be very large, such that the free end of the cylinder would face downstream. The influence of some system parameters was investigated, such as cylinder flexural rigidity, slenderness and free-end shape. The dynamics was found to be only marginally affected by the free-end shape, in sharp contrast to the dynamics of cylinders subjected to flow directed from the clamped towards the free end. Finally, the mechanisms underlying the onset of flutter and static divergence are discussed briefly.

Stability of a Cross-Flow Heat-Exchanger Tube With Asymmetric Supports

Abstract Heat-exchanger tubes subjected to cross-flow experience a fluid elastic instability (FEI) at a critical flow velocity. Baffle plates are often used to provide additional stiffness to long tubes. A cladding is provided between the baffle plates and the tubes to allow for thermal expansion, and the cladding acts like a soft spring. In this paper, we study the contact between the cladding and the tube when the stiffness of the cladding is asymmetric. The tube is modeled as a cantilever Euler–Bernoulli beam, and the fluid forces are represented using an added mass, added damping and a time-delayed displacement term. This results in a partial delay differential equation model for the tube vibration. Using the Galerkin approximation and considering only a single mode, a delay differential equation (DDE) model is developed. However, due to the presence of the delay, the single mode model is also infinite-dimensional. This model contains sign function nonlinearity due to the asymmetry in the contact stiffness of the cladding. The DDE model is essentially nonlinear—that is, no linear approximation exists. However, its solutions are scalable: if q(t) is a solution, then α q(t) is also a solution for any α>0. By exploiting this scalability property of solutions, we use Lyapunov-like exponents to probe the stability of the nonlinear DDE. Further, by numerical continuation, we numerically demonstrate the existence of periodic solutions on the stability boundary. Our stability charts will be beneficial to the designers of heat-exchangers.

Investigation on vibration parameters in aluminum finned tube arrays subjected to water cross flow

PurposePredicting the critical velocity is crucial at the instability threshold for shell and tube heat exchangers in order to prevent tube failure due to vibrations. In this study, the vibration response of an aluminum tube bundle subjected to water cross flow was analyzed experimentally. Aluminum tubes are preferred over steel tubes because of aluminum tubes' excellent corrosion resistance, ease of manufacture, and high thermal efficiency.Design/methodology/approachThe fluid elastic instability and vortex shedding mechanisms in a finned tube array of aluminum tubes with a base tube diameter of 19.05 mm and pitch of 34 mm were investigated. The current study considers parallel triangular finned tube arrays with fin heights of 3 mm and 6 mm with a uniform fin thickness and fin pitch. The plain tube array was tested to compare the finned tube array results. The tube vibration response was measured using an accelerometer mounted on the middle tube of the third row. In order to define the fluid elastic instability behavior of various tube arrays, the critical velocity at the instability threshold is measured. By finding the Strouhal number at the small peaks before instability, the vortex shedding behavior of the tube arrays is examined.FindingsThe results reveal that the critical velocity at instability for coarse finned tube arrays increases as the fin height increases. The effect of the tube material is evaluated by comparing the results with those previously reported for parallel triangular tube arrays made of steel. Finally, the occurrence of vortex shedding in a tube array is confirmed based on the Reynolds number and Strouhal number relationship. The instability constant K for the plain tube array of steel and aluminum material are 4.97 and 4.87, respectively.Originality/valueThis paper provides the research findings on the effect of fin height on coarse density finned tube array. This will add substantial knowledge to the literature in the field of fluid elastic instability and vortex shedding, which is needed for the safe functioning of shell and tube heat exchangers.

Experimental study and analysis of design parameters for analysis of fluidelastic instability for steam generator tubing

In this paper, the evaluation method of fluidelastic instability (FEI) of newly designed steam generator tubing in pressurized water reactor (PWR) nuclear power plants is discussed. To obtain the parameters for prediction of the critical velocity of FEI for steam generator tubes, experimental research is carried out, and the design parameters are determined. Using CFD numerical simulation, the tube array scale of the model experiment is determined, and the experimental device is designed. In this paper, 7 groups of experiments with void fractions of 0% (water), 10%, 20%, 50%, 75%, 85% and 95% were carried out. The critical damping ration, fundamental frequency and critical velocity of FEI of tubes in flowing water were measured. Through calculation, the total mass and instability constant of the immersed tube are obtained. The critical damping ration measured in the experiment mainly included two-phase damping and viscous damping, which changed with the change in void fraction from 1.56% to 4.34%. This value can be used in the steam generator design described in this paper and is conservative. By introducing the multiplier of frequency and square root of total mass per unit length, it is found that the difference between the experimental results and the calculated results is less than 1%, which proves the rationality and feasibility of the calculation method of frequency and total mass per unit length in engineering design. Through calculation, the instability constant is greater than 4 when the void fraction is less than 75%, less than 4 when the void fraction exceeds 75% and only 3.04 when the void fraction is 95%.

Thermal hydraulic design and evaluation of the solid microencapsulated fuel in light water reactors

Solid Microencapsulated Fuel (SMF) is a kind of solid fuel rod design that disperses TRISO coated fuel particles directly into a kind of matrix. Without cladding tube and associated failure mechanisms, this type of new fuel design is expected to provide improved performance under normal and even accident conditions. The purpose of this paper is to analyze the thermal hydraulic performance of SMF based on a single channel, compared to the traditional fuel in the 200 MW Nuclear Heating Reactor (NHR200-II). Two kinds of specific SMF by dispersing TRISO particles into Zirconium or SiC matrix were investigated. Thermal margin to DNB was assessed and confirmed by determining the heat transfer capacity under normal condition. Two-phase pressure drop was evaluated by using the homogeneous equilibrium boiling assumption. The centerline temperature of SMF rod was calculated by using effective thermal conductivity of two-phase composite. The analysis of flow instability and flow-induced vibration were also included and compared. This study showed that SMF has a better thermal transfer capacity, a higher margin from vortex shedding and fluid-elastic instability, and a lower fretting wear rate, while a higher sliding wear rate because of a higher Young’s modulus and fundamental frequency, which is compensated by a higher hardness for SiC matrix.

Galloping of circular cylinder induced by downstream strip-plate in cruciform arrangement

It has been reported that two longitudinal vortices are periodically shed from a cruciform two-cylinder system in a uniform flow. These depend on the gap, s, between the two cylinders and can induce a vibration called the “longitudinal vortex-induced vibration”. In previous studies, the authors showed that stationary longitudinal vortices are formed by a cruciform circular-cylinder/strip-plate (CC/SP) system when the upstream cylinder is moving along the downstream strip plate, and that one of these longitudinal vortices, the necklace vortex (NV), generates a lift force that acts on the cylinder in the direction of the motion. The “stationary” position of the NV is believed to make the system unstable, leading to fluid-elastic instability vibration. This study measured the fluid force acting on the rotating upstream circular cylinder blade in a wind turbine-type CC/SP system, and the vibration behavior of a pendulum-type CC/SP system was investigated through wind-tunnel experiments. The lift force coefficient, together with the ranges for the gap ratio (s/d) and velocity ratio (λ=V/U) needed to achieve stationary positions, were obtained (d: diameter of the upstream circular cylinder, U: flow velocity, V: rotational velocity of cylinder). It was confirmed that a cross-flow vibration of the cylinder in the pendulum-type CC/SP system was induced, and an analytical method to predict the vibration amplitude was proposed based on the quasi-steady hypothesis. The vibration amplitude of the pendulum device was well predicted by the method using the lift coefficient, obtained through the wind turbine-type CC/SP experiment. In conclusion it was verified that the vibration was caused by the stationary formation of the NV. It was classified as galloping, although it did not occur for an isolated circular cylinder because of its axisymmetric cross-sectional geometry.

Experimental Study on Fluid Elastic Instability of Concentric Circular Arrangement Heat Exchanger Tubes

In the industrial production, there exists the phenomenon of structure vibration caused by flow, which will cause the deformation and failure of the structure and lead to the economic loss, and even cause the industrial accident and great danger. In this paper, the one mechanism of fluid-induced vibration, namely fluid elastic instability, of the concentric circle arrangement tube bundles in the sodium-sodium heat exchanger is studied experimentally. According to different central angle positions, three kinds of tubular plates are designed, which are approximately triangle arrangement, approximately square arrangement and transitional arrangement respectively. In the small-size water tunnel non-contact graphic measurement is adopted to obtain the critical flow rate Ucr when the tube bundle is unstable. The experimental results show that the flow induced vibration resistance of the transitional arrangement is better, and the critical flow velocity is about 3.78.

Fluidelastic instability research of tube bundles by a two-way fluid-structure interaction simulation

Fluidelastic instability (FEI) could cause serious damage to the tube bundle, and streamwise FEI has attracted more attention in recent years. Water tunnel experiments have been conducted to investigate streamwise and transverse FEI in a parallel triangular tube bundle with a single elastic tube in center. RMS displacement-reduced velocity relationship diagram, vibration time-history curve and frequency spectrum response in streamwise and transverse directions are obtained. A Two-way fluid-structure simulation method was developed to calculate the streamwise and transverse FEI. The motion of the elastic tube was controlled by a User-Defined Function (UDF) coupled with dynamic mesh. The FEI tendency of simulation is consistent with experiment results but the values of predicted critical reduced velocities are more conservative. The process of FEI was analyzed. Finally, the model was extended to explore the effect of pitch diameter ratio, elastic tube arrangement and natural frequency ratio of streamwise and transverse.

Experimental analysis of the influence of the number of rows of a tube bank on the FIV critical velocity

The present study investigated experimentally the influence of the number of rows and the position of a free-to-vibrate monitored cylinder in a tube bank on the critical reduced velocity and compared it with literature models. The experiments were conducted in an aerodynamic channel with a test section assembled with one cylinder free to vibrate in the transversal direction and additional fixed rigid cylinders. The tests were conducted for one, two, three, four, and five rows with the cylinder free to vibrate in different positions along the central line. Models presented in the literature for one row and five rows were used to compare with the instability response for the studied configurations. The experimental results showed that the position of the cylinders is relevant due to the number of rows that will be positioned downstream it and if it is in the first row. The models presented in the literature consider the damping and reduced velocity in the analysis without additional parameters, just the factor associated with the arrangement and space ratio. It was observed that the critical velocity changes with the number of rows: a reduction in the velocity of fluid-elastic instability results with the increase in the number of rows when the cylinder was free to vibrate in the second or third row. The positions in the second and third rows presented the lower critical reduced velocities. An increase in the rate of occurrence of fluid-elastic instability was observed with an increase in the number of rows for the same mass and damping parameters when the cylinder was free to vibrate in the first row. The comparison of the results with models to predict the critical reduced velocity showed that, in general, they did not well predict the instability occurrence due to the lack of parameters and the conservative approach adopted in the model development.

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.

Some Comments on Added Mass Modeling for Tube Bundles Under Two-Phase Cross Flow

Abstract Within the study of fluid-elastic instability in heat exchangers tube banks, a considerable theoretical and experimental effort has been produced for understanding fluid–structure coupling in two-phase flow. This communication discusses the commonly accepted added mass modeling and proposes some ways of further improvement. Notably, it turns out that added mass may be overestimated in a two-phase flow. Taking into account this phenomenon improves the collapsing of flow-induced forces data.

Fluidelastic instability of tube arrays in nonuniform flow: Effect of multimode coupling

Fluidelastic analysis of a tube array usually considers a transverse vibration mode and a streamwise vibration mode for each tube. The underlying effect of multimode coupling is often neglected. For an array of multi-span tubes with closely spaced modes exposed to nonuniform flow, the effect of multimode coupling on fluidelastic instability may be non-negligible but the effect remains unclear. To fill this gap, this paper analyzes the effect of multimode coupling on the fluidelastic instability of tube arrays in a nonuniform flow. The main purpose is to quantify the multimode coupling effect on the instability threshold and figure out conditions under which the multimode coupling effect becomes significant. Equations of motion for the fluidelastic vibrations of an array of multi-span tubes in general nonuniform flow are presented. A mode-by-mode tracing method is introduced to iteratively search for the critical mode (i.e., the mode that initiates the instability) and determine the critical flow velocity. Two case studies involving the fluidelastic analyses of different tube arrays demonstrate the effects of multimode coupling. It is concluded that the multimode coupling may affect the critical flow velocity and the vibration mode and hence the wear pattern due to fluidelastic vibrations. For the considered two case studies, the reductions of critical flow velocities due to multimode coupling can become as high as 40%. The overall effect depends on the mode that initiates the instability and the modal velocity integrals and frequency ratios of the coupling modes. For an array of flexible tubes, the multimode coupling effect on the critical flow velocity is insignificant if the tubes’ natural frequencies are perfectly tuned. However, the multimode coupling effect contributes to affect the critical flow velocity if there is a detuning between natural frequencies of respective tubes, and/or between the streamwise and transverse frequencies of every single tube. These conclusions highlight the necessity to consider the multimode coupling effect in fluidelastic analysis of tube arrays with closely spaced modes.

Equivalent Theodorsen Function for Fluidelastic Excitation in a Normal Triangular Array

Abstract Fluidelastic instability (FEI) remains the most important mechanism of flow-induced vibrations that can potentially cause large amplitude vibrations and early failure of nuclear steam generator tubes. In the present work, experimental tests are conducted to measure the unsteady and quasi-steady fluid forces acting on a normal triangular tube array of P/D=1.5 subjected to single-phase (water) cross-flow. The quasi-steady forces together with unsteady fluid forces are then used to estimate the time delay between the central tube motion and fluid forces on the tube itself. The time delay effect for the quasi-steady fluidelastic instability model is derived in the frequency domain in the form of an Equivalent Theodorsen Function. The results are compared to the first Equivalent Theodorsen function developed for rotated triangular array by Li and Mureithi [1]. Using the Equivalent Theodorsen Function, a stability analysis is carried out to predict the critical velocity for fluidelastic instability in a normal triangular array subjected to single-phase flow. The predicted stability threshold is consistent with previous published experimental data. The results show that the normal triangular array is more stable than the rotated triangular array.

The Flow-Structure Couplings of Fluidelastic Instability and the Effect of Frequency Detuning in Triangular Tube Bundles Subjected to a Two-Phase Flow

Abstract For decades, fluidelastic instability (FEI) has been known to cause dramatic mechanical failures in tube bundles. Therefore, it has been extensively studied to mitigate its catastrophic consequences. Most of these studies were conducted in controlled experiments where significant simplifications to the geometry and flow conditions were utilized. One of these simplifications is the assumption that all tubes have the same dynamic characteristics. However, in steam generators with U-bend tube configuration, the natural frequencies of tubes are nonuniform due to manufacturing tolerances and tubes' curvature in the U-bend region. Thus, this investigation aims to understand the rule of frequency variation (detuning) on FEI in two-phase flow. This includes investigating the effect of detuning on transverse and streamwise FEI for air–water mixture flow. The role of FEI damping and stiffness couplings was investigated over the entire range of air void fraction, or equivalently, the mass-damping parameter. It was found that frequency detuning could elevate the stability threshold caused by either coupling at high air void fraction in the case of transverse FEI. Furthermore, the frequency detuning had a marginal effect on the stability threshold for water flow. It was observed that the mass-damping parameter has a critical impact on FEI under detuning conditions.

Flow-Induced Vibrations of a Rotated Square Tube Array Subjected to Single-Phase Cross-Flow

Abstract This paper investigates the flow-induced vibration (FIV) and possibility of fluidelastic instability occurrence in a rotated square geometry tube array through a series of experimental tests. All experiments presented here were conducted in water cross-flow. The array's pitch spacing ratio of approximately P/D = 1.64 is somewhat larger than that commonly found in typical steam generators. The stability of a single flexible tube as well as multiple flexible tubes was investigated. The tubes were free to vibrate purely in the streamwise direction or the transverse direction relative to the upstream flow. A single flexible tube, in the otherwise rigid tube array, was found to undergo large amplitude vibrations (up to 40% D) in the transverse direction. Tube vibration frequency analysis indicated the presence of two frequency components related to vorticity shedding in the array. This potential vorticity-induced vibration (VIV) and potential coupling between VIV and fluidelastic instability (FEI) are discussed in the paper. Test results for streamwise flow-induced vibrations are also presented. Results in water flow show a possible effect related to flow periodicity at low velocity. At significantly high flow velocities, the tubes are found to fully restabilize. This restabilization after VIV locking has not been previously reported as an unlocking result. The present results suggest that the flow-induced vibration of tubes in a rotated square array configuration is significantly more complex than in other geometries, particularly for the streamwise vibration case.

Turbulence-induced vibration of tube bundles subjected to cross-flow and loose support

Flow-induced vibration of the tube bundles is an important issue in the security of a steam generator. Several investigations were performed to study the fluidelastic instability of the tube subjected to cross-flow. It should be noted that turbulence-induced vibration of the tube bundles subjected to cross-flow and loose support may cause a potential tube fretting wear and fretting fatigue when the flow pitch velocity is lower than the threshold of the fluidelastic instability. However, there is seldom theoretical analysis to study the vibration characteristics of the tube bundles considering the effect of the loose support. Therefore, a mathematical model of a single flexible tube in tube bundles subjected to turbulence random force and loose support was presented in this paper. An experiment was carried out to obtain the turbulence random forces acting on the tube bundle both in the entrance and intermediate regions. The influences of the turbulence force on the vibration characteristics of the tube were investigated.

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.

Pitch and Pattern Effects on Streamwise Fluidelastic Instability in Tube Arrays

Abstract Fluidelastic instability (FEI) is well known to be a critical flow-induced vibration concern for the integrity of the tubes in nuclear steam generators. Traditionally, this has been assumed to occur in the direction transverse to the direction of flow but the tube failures at San Onofre Nuclear Generating Station (SONGS) in Los Angeles proved that this assumption is not generally valid. A simple tube-in-channel theoretical model was previously developed to predict streamwise as well as transverse FEI in a parallel triangular tube array. This predicted that this array geometry was particularly sensitive to streamwise FEI for high mass-damping parameters and small pitch ratios, the conditions in which the SONGS failures occurred. The advantage of this simple modeling approach is that no new empirical data are required for parametric studies of the effects of tube pattern and pitch ratio on FEI. The tube-in-channel model has been extended to in-line square, normal triangular, and rotated square tube arrays and the stability of these geometric patterns are analyzed for the effects of varying pitch ratio and the mass-damping parameter. The results are compared with the available experimental data and conclusions are drawn regarding the relative vulnerability of these different tube array geometries to streamwise FEI.

Numerical Simulation and Modeling Convention of Unsteady Fluidelastic Forces of Tube Arrays

Abstract This paper presents a numerical investigation on the unsteady fluidelastic forces of tube arrays. The key focus is on the consistency between the unsteady fluidelastic force model and the quasi-steady model for tube arrays at large reduced flow velocities, as well as comparing two well-known conventions for the unsteady model. Two-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) simulations are used to prove that the viscous damping coefficients of Tanaka's convention approach their quasi-steady values as the reduced flow velocity approaches infinity, whereas the hysteretic damping coefficients of Chen's modified convention always approach zero and hence result in low-resolution data plots as the reduced flow velocity becomes large. The nonconstant viscous damping coefficients of Tanaka's experimental data at high reduced flow velocities (which motivated the introduction of Chen's modified convention) might be induced by a systematic identification error in the phase of the fluidelastic force. A row of three flexible cylinders is used as a numerical example to analyze the effect of systematic phase error on the predicted stability boundary of the fluidelastic instability. Although identical fluidelastic forces are simulated by using the two conventions, Tanaka's convention is recommended due to its compatibility with the quasi-steady theory and optimal resolutions of data plots over any range of reduced flow velocities.

Flow-excited membrane instability at moderate Reynolds numbers

In this paper, we study the fluid–structure interaction of a three-dimensional (3-D) flexible membrane immersed in an unsteady separated flow at moderate Reynolds numbers. We employ a body-conforming variational fluid–structure interaction solver based on the recently developed partitioned iterative scheme for the coupling of turbulent fluid flow with nonlinear structural dynamics. Of particular interest is to understand the flow-excited instability of a 3-D flexible membrane as a function of the non-dimensional mass ratio ( $m^{*}$ ), Reynolds number ( $Re$ ) and aeroelastic number ( $Ae$ ). For a wide range of parameters, we examine two distinct stability regimes of the fluid–membrane interaction: deformed steady state (DSS) and dynamic balance state (DBS). We propose stability phase diagrams to demarcate the DSS and DBS regimes for the parameter space of mass ratio versus Reynolds number ( $m^{*}$ - $Re$ ) and mass ratio versus aeroelastic number ( $m^{*}$ - $Ae$ ). With the aid of the global Fourier mode decomposition technique, the distinct dominant vibrational modes are identified from the intertwined membrane responses in the parameter space of $m^{*}$ - $Re$ and $m^{*}$ - $Ae$ . Compared to the deformed steady membrane, the flow-excited vibration produces relatively longer attached leading-edge vortices which improve the aerodynamic performance when the coupled system is near the flow-excited instability boundary. The optimal aerodynamic performance is achieved for lighter membranes with higher $Re$ and larger flexibility. Based on the global aeroelastic mode analysis, we observe a frequency lock-in phenomenon between the vortex-shedding frequency and the membrane vibration frequency causing self-sustained vibrations in the dynamic balance state. To characterize the origin of the frequency lock-in, we propose an approximate analytical formula for the nonlinear natural frequency by considering the added mass effect and employing a large deflection theory for a simply supported rectangular membrane. Through our systematic high-fidelity numerical investigation, we find that the onset of the membrane vibration and the mode transition has a direct dependence on the frequency lock-in between the natural frequency of the tensioned membrane and the vortex-shedding frequency or its harmonics. These findings on the fluid-elastic instability of membranes have implications for the design and development of control strategies for membrane wing-based unmanned systems and drones.