Vibration Of Tube Bundles Research Articles

Numerical study on two-phase flow instability in multi-parallel channels of helical-coiled once-through steam generator of lead-cooled fast reactor

The helical-coiled once-through steam generator (H-OTSG) has the advantages of compact structure and strong heat transfer ability, and is appropriate for lead-cooled fast reactor. The two-phase flow instability may cause mechanical vibration and thermal fatigue of heat transfer tube bundles, posing a serious threat to the safe operation of the H-OTSG. In this work, the secondary side of the H-OTSG characterized as multi-parallel channels is modeled by RELAP5/MOD3.4 code, and the oscillation behavior during start-up and the influence of structural and operating parameters on system stability are studied based on time-domain method. The results indicate that the pressure, flow rate, and temperature of the secondary fluid exhibit density wave oscillations at the heating section in a (n-2,2) pattern. In addition, increasing inlet throttling, reducing outlet throttling, controlling subcooling within an appropriate range and avoiding operation under low loads are all beneficial for improving the system stability of the helical-coiled once-through steam generator.

A semi-analytical time-domain model with explicit fluid force expressions for fluidelastic vibration of a tube array in crossflow

It is widely acknowledged that fluidelastic instability (FEI), among other mechanisms, is of the greatest concern in the flow-induced vibration (FIV) of tube bundles in steam generators and heat exchangers. A range of theoretical models have been developed for FEI analysis, and, in addition to the earliest semi-empirical Connors' model, the unsteady model, the quasi-steady model and the semi-analytical model are believed to be three advanced models predominant in the literature. The unsteady and the quasi-static models share the merits of having explicit fluid force expressions and ease of being implemented but require more experimental inputs, whereas the semi-analytical model requires fewer parameters due to its analytical nature but is hard, if not prohibitive, to derive explicit fluid force expressions. Since the fluid force formulations set in the core of development of FEI models, the understanding and in particular the implementation of the semi-analytical model has been impaired by the nonexistence of explicit fluid force expression. This issue becomes more profound in time-domain analysis whereby the simple harmonic assumption is discarded. Here we report a new semi-analytical time-domain (SATD) FEI model with explicit fluid force expressions. The new model allows a consistent frequency-domain stability analysis and more importantly a truly time-domain response analysis. The theory was validated by calculating linear stability thresholds of two typical tube array patterns and comparing against reported experimental data. We then present a nonlinear time-domain analysis of a single loosely-supported tube with piece-wise linear stiffness. The nonlinear and nonsmooth dynamics was probed in details by utilizing various techniques, playing an emphasis on characterizing and distinguishing the chaotic vibration. We found that the system follows a quasi-periodic route to chaos. Such an in-depth study of the nonlinear dynamics of tubes in crossflow has never been reported in the context of SATD model. Our results enrich the theory and provide a different approach for linear and nonlinear dynamics of tube bundles, which are essential for the subsequent fretting wear analysis.

Numerical study on lead–bismuth cross-flow induced vibration in the elastic tube bundle

The physical properties of liquid lead–bismuth eutectic fluid are quite different from that of water or air. It needs to be verified whether the cross-flow vibration mechanism and the empirical prediction model of fluidelastic instability in conventional media are applicable to lead–bismuth. In this work, for an in-line elastic tube bundle with pitch ratio P/D = 1.5, the flow excitation of lead–bismuth at 200 °C is studied and compared with that of water in uncoupled flow field. Then, two cases of lead–bismuth flow-induced vibration with different mass-damping parameters are simulated and studied by fully coupled numerical simulation considering fluid viscous damping. The tube bundle experiences the process from turbulence-induced vibration in low flow velocity to fluidelastic instability in high velocity. The results of flow excitation show that the pressure coefficient distribution of the front row tube in lead–bismuth is basically consistent with that in water, while the inconsistency of the pressure coefficient distribution for the back row tube is caused by the bi-stable deflective flow. The results of lead–bismuth flow-induced vibration show that, in fluidelastic instability, the vibration of tube bundle and the vortex shed from tube bundle are dominated by the frequency close to the first wet modal frequency of tube bundle. The different deflective directions of lead–bismuth and water, caused by bi-stable characters, have less effect on the onset of fluidelastic instability. The instability points of lead–bismuth agree with the experimental results of other media and the Connors prediction model considering fluid viscous damping. The prediction model is suggested to predict the onset of fluidelastic instability induced by lead–bismuth cross-flow in the tube bundle.

A hybrid proper orthogonal decomposition and next generation reservoir computing approach for high-dimensional chaotic prediction: Application to flow-induced vibration of tube bundles.

Chaotic time series prediction is a central science problem in diverse areas, ranging from engineering, economy to nature. Classical chaotic prediction techniques are limited to short-term prediction of low- or moderate-dimensional systems. Chaotic prediction of high-dimensional engineering problems is notoriously challenging. Here, we report a hybrid approach by combining proper orthogonal decomposition (POD) with the recently developed next generation reservoir computing (NGRC) for the chaotic forecasting of high-dimensional systems. The hybrid approach integrates the synergistic features of the POD for model reduction and the high efficiency of NGRC for temporal data analysis, resulting in a new paradigm on data-driven chaotic prediction. We perform the first chaotic prediction of the nonlinear flow-induced vibration (FIV) of loosely supported tube bundles in crossflow. Reducing the FIV of a continuous beam into a 3-degree-of-freedom system using POD modes and training the three time coefficients via a NGRC network with three layers, the hybrid approach can predict time series of a weakly chaotic system with root mean square prediction error less than 1% to 19.3 Lyapunov time, while a three Lyapunov time prediction is still achieved for a highly chaotic system. A comparative study demonstrates that the POD-NGRC outperforms the other existing methods in terms of either predictability or efficiency. The efforts open a new avenue for the chaotic prediction of high-dimensional nonlinear dynamic systems.

Coupling vibration analysis of heat exchanger tube bundles under different stiffness conditions

A two-dimensional tube bundles fluid–structure coupling model was developed using the CFD approach, with a rigid body motion equation and the Newmark integral method. The numerical simulations were performed to determine the vibration coupling properties between various tube bundles of stiffness. Take the corner square tube bundles with a pitch ratio of 1.28 as the research object. The influence of adjacent tubes with different stiffness on the vibration of the central target tube was analyzed. The research results show that the vibration characteristic of tube bundles is affected by the flow field dominant frequency and the inherent frequency of tube bundles. The vibration of adjacent tube bundles significantly impacts the amplitude and frequency of the central target tube. The equal stiffness and large stiffness tubes upstream or downstream inhibit the vibration displacement of the target tube to some extent. The low-stiffness tubes upstream or downstream significantly enhanced the amplitude of the target tube. The findings can be used to provide a basis for reasonable design and vibration suppression of shell-and-tube heat exchangers.

Tube bundle vibration analysis and optimization design

The shell-and-tube heat exchanger is an important equipment in various applications. However, the bundle vibration and low heat transfer efficiency are the main shortcomings. In this article, ANSYS platform was used to simulate and analyze the shell-and-tube heat exchanger, the natural frequency was calculated, and the dominant factors affecting the vibration were determined. The theory of inventive problem solving was used to design the heat exchanger for anti-vibration. The results show that the improved heat exchanger's natural frequency is much larger than the fluid excitation frequency, as a result, the resonance is avoided.

Numerical study on the effect of baffle structure on the heat transfer performance of elastic tube bundle heat exchanger

To make up for the research gaps in the existing literature on the effect of baffle structural parameters on the vibration and heat transfer of elastic tube bundle (ETB) heat exchangers, and improve the comprehensive heat transfer performance (HTP) of heat exchangers, based on an improved elastic tube bundle (I-ETB) heat exchanger used in previous studies, using the bi-directional fluid-structure interaction calculation method, the effects of the baffle structure improvement (height and curvature) on the comprehensive HTP of the I-ETB heat exchanger at different inlet velocities (Uin) were numerically studied. The results show that: while the height factor increases from 0.70 to 0.80, the vibration amplitude of I-ETBs decreases maximum by 10.05 %, and the heat transfer coefficient (h) of I-ETB increases maximum by 5.50 %. Increasing the baffle height improves the comprehensive HTP while suppressing the vibration of the I-ETBs. While the baffle curvature is 10°, the vibration of I-ETBs is the most intense, with the amplitude of the I-ETBs improving maximum by 10.79 %. The Nusselt number per unit pressure drop Nu/ΔP and performance evaluation criteria PEC and JF (a dimensionless number related to Colburn factor j and Fanning friction factor f) values of the heat exchanger all reach the maximum while the baffle curvature is 10°. The increase of baffle curvature has a positive effect on the vibration-enhanced HTP of the I-ETBs, and when the curvature is 10°, the comprehensive HTP of the heat exchanger is better.

The interaction between cross-flow induced vibration and convection heat transfer in tube bundle at subcritical Reynolds number

This work numerically investigates the interaction between flow-induced vibration (FIV) and forced convection heat transfer in tube bundle with a pitch ratio of 1.5 at subcritical Reynolds number (Re = 5 × 103-3 × 104). The range of reduced velocity is 0.53 ≤ Vr ≤ 2.71. The mass-damping parameter of coupling system is 0.07. The three-dimensional refined FIV simulation considering fluid viscous damping has been validated by the literature experiment to capture three continuous FIV mechanisms, namely turbulence-induced vibration, vortex-induced resonance and fluidelastic instability. The heat transfer and pressure drop in tube bundle are validated by the experiment. The coupling of Navier-Stokes equations, energy equations and vibration equations is solved by under-relaxation algorithm. The results of vibration response, the change of damping for the coupling system, flow field and temperature field, heat transfer and pressure drop are presented and delineated in this paper. The results show that for the low velocity turbulence-induced vibration, the interaction between FIV and flow heat transfer is negligible due to the weak fluid–solid interaction. In vortex-induced resonance region, the wall heating makes each row tube be out of phase by affecting the vortex shedding and reduces the positive feedback of resonance, which reduces the amplitude. The wall heating reduces the damping of coupling system, which causes an earlier transition from vortex-induced resonance to fluidelastic instability and a faster increase of amplitude in fluidelastic instability. In both vortex-induced resonance and fluidelastic instability, the vibration of tube bundle dominates the vortex shedding by the natural frequency, and further dominates the change of heat transfer. The best performance of enhanced heat transfer induced by FIV is located in vortex-induced resonance region, in which the time–space averaged Nusselt number is increased by 8.83%. Due to the redistribution of flow field and the elimination of deflective flow pattern, compared with vortex-induced resonance, the increasing ratio of heat transfer induced by FIV is lower and the increasing ratio of pressure drop induced by FIV is higher in the fluidelastic instability.

Experimental Analysis of Flow Induced Vibrations in Heat Exchanger Tube Bundles with P/D of 1.54 Subjected to Crossflow

This paper presents an experimental analysis of flow-induced vibrations in a heat exchanger tube bundle subjected to crossflow. The study focuses on the characterization and insights gained from the investigation. The tube bundle configuration consists of plain tubes with a single flexible tube, arranged in a squared pattern. The primary objective is to assess the flow-induced vibration behavior and identify any potential instabilities within the system. To analyze the flow-induced vibrations, various parameters were considered, including the P/D ratio (tube pitch to tube diameter ratio), which was found to be 1.54. The experiments were conducted under different flow velocities, and the vibration responses of the tube bundle were measured using suitable sensors. The results revealed that the third row of tubes in the bundle exhibited the highest level of instability compared to the other rows. This finding suggests that the positioning of the tubes within the bundle significantly influences the flow-induced vibrations. The vibrations were observed to vary with the flow velocity, indicating a strong fluid-structure interaction. It can be concluded that the squared arrangement of tubes in the tube bundle, along with the specific P/D ratio, contributes to the flow induced vibration characteristics. Understanding these effects is crucial for optimizing the design and operation of heat exchanger systems, as excessive vibrations can lead to mechanical failures and reduced heat transfer efficiency.

Incremental harmonic balance method for multi-harmonic solution of high-dimensional delay differential equations: Application to crossflow-induced nonlinear vibration of steam generator tubes

Diverse science and engineering problems are governed by delay differential equations (DDE). Seeking periodic solutions of DDEs is crucial for many nonlinear dynamic systems. The incremental harmonic balance (IHB) method is an efficient semi-analytical approach for periodic solutions of DDE. Among various DDE systems, flow-induced vibration (FIV) of tube bundles with loose support is unique, in the sense that the added damping cancels out structural damping in the vicinity of critical velocity, making it extremely slow to retain a convergent solution if numerical integration (NI) is utilized. Despite the efforts of developing IHB for various mechanical vibration problems with time-delay, no attempt has been made to employ IHB to nonlinear FIV problems. Here we fill this blank by separately combining two spatial discretization strategies, i.e., discretization via linear vibration modes or via finite element method (FEM), with IHB to capture limit cycle solutions after the onset of instability. Within the range of gap velocity of interest, the IHB demonstrates excellent convergence by increasing harmonic terms, and good agreement is obtained between IHB results and the results by NI method. An 18 degree-of-freedom (DOF) nonlinear DDE system was readily dealt by integrating FEM and IHB, each DOF being approximated by three harmonics. This is the first attempt to employ IHB for multi-harmonic solution of high-dimensional FIV problems, which opens a door for solutions of other DDEs. All the codes used in this paper could be downloaded via: https://github.com/XJTU-Zhou-group/IHB.

Numerical Analysis of Flow-Induced Vibration of Heat Exchanger Tube Bundles Based on Fluid-Structure Coupling Dynamics

According to the needs generated by the industry, there is an urgent need to investigate the flow vibration response law of the elastic tube bundle of heat exchangers subjected to the coupling effect of shell and tube domain at different inlet flow velocities. In this paper, based on the continuity equation, momentum equation, turbulence model, and dynamic grid technology, the vibration response of the elastic tube bundle under the mutual induction of shell and tube fluids is studied by using pressure-velocity solver and two-way fluid-structure coupling (FSC) method. The results show that the monitoring points on the same connection block have the same vibration frequency, while the vibration amplitude is different. Monitoring point A is the most deformed by the impact of fluid in the shell and tube domain. When the inlet velocity( v shell = v tube = 0.15 , 0.4, 0.5 m/s) of shell and tube is low, the amplitude of tube bundle vibration in the Y direction is greater than that in X and Z direction, and the tube bundle produces periodic vibration in the vertical direction. The vibration equilibrium position of the tube bundle along the shell flow direction gradually moves up with the increase of the inlet velocity. The amplitude in the Y -direction of the elastic bundle decreases with the increase of shell-side and tube-side velocity. The relationship between the vibration amplitude in the Y direction and the entrance velocity is a linear function.

Analysis of the effect of baffles on vibration and heat transfer characteristics of elastic tube bundles

For improving the performance of heat exchangers by effectively utilizing the flow-induced vibration, a presence baffle elastic tube bundle heat exchanger, is proposed according to the absence baffle elastic tube bundle heat exchanger. Heat transfer and vibration characteristics of them at different velocities, using flow-solid coupling calculation, are studied and compared. The results show that baffle can improve flow uniformity of shell-side fluid and fully excites the elastic tube bundle vibration to improve its heat transfer performance. When inlet velocity becomes 1.0 m/s from 0.7 m/s, the maximum amplitude of two monitoring points on elastic tube bundle increased by 25.40% and 25.92% for absence baffle elastic tube bundle heat exchanger and by 42.44% and 42.97% for presence baffle elastic tube bundle heat exchanger; in non-vibration and vibration conditions, average heat transfer coefficient of the elastic tube bundle increased by 32.46% and 30.48% for absence baffle elastic tube bundle heat exchanger and by 31.16% and 31.36% for presence baffle elastic tube bundle heat exchanger. Compared to absence baffle elastic tube bundle heat exchanger, heat transfer performance and vibration-enhanced heat transfer of presence baffle elastic tube bundle heat exchanger are generally improved. And at low flow velocities, the improvement is more significant.

Research on enhancement of heat transfer by vortex-induced vibration of heat exchange tube bundles with elastic joints

In the field of fluid-induced vibration enhanced heat transfer in heat exchangers, the elastic tube bundle structure currently cannot reach the ideal state of fluid-induced vibration enhanced heat transfer and is prone to fatigue failure. In response to this problem, this article proposes to make full use of the shell-side fluid vortex-induced elastic tube bundle vibration to achieve the purpose of enhancing heat transfer, and innovatively design heat transfer tube bundles with elastic joins that can adapt to large-amplitude vibration and be not damaged by structural fatigue. Here, the dynamic modal characteristics and the fluid–solid coupling vibration heat transfer characteristics of the single heat transfer tube bundle with elastic joints are studied by numerical calculation. The results show that the low-order modes of this tube bundle include one-dimensional mode, two-dimensional mode, and three-dimensional mode. When the flow velocity is 0.1 m/s≤ u≤ 0.2 m/s, the fluid vortex-induced tube bundle produces a two-dimensional vibration response with a maximum amplitude of 9.2 mm. At the same time, the tube bundle vibration enhances heat transfer significantly. When the flow velocity u= 0.12 m/s, compared with the static circle tube under the same working condition, the heat transfer coefficient is increased by 11.8%. When the flow velocity u > 0.2 m/s, the fluid can stimulate the three-dimensional vibration response of the tube bundle, but the circular tube vibration no longer has the function of enhancing heat transfer. The research in this article will enrich the development of fluid-induced vibration enhanced heat transfer theory and promote its engineering application.

Calculation of Flow Field and Vibration Analysis of Heat Exchanging Tube in Low Temperature Multi-effect Seawater Desalination Evaporator

Abstract In this paper, a 1000t/d low-temperature multi-effect seawater desalination pilot plant (MED) is taken as the research object, a multi-phase flow (VOF) model is selected to describe the shell side flow field of the evaporator, and the overall direct simulation of the flow field on the shell side of MED is carried out by using the fluid mechanics calculation software Fluent. The vapor velocity field distribution around the evaporator tube bundle is obtained by calculation under stable test conditions. The influence of seawater spray density and evaporation temperature on flow field distribution and the vibration of tube bundle under different working conditions are researched. Research result shows that the spray density has little effect on steam velocity, but the maximum steam velocity is significantly affected by evaporation capacity of seawater. At the same time, when the evaporation capacity reaches a certain value, the phenomenon of flow resonance will occur in some areas of the evaporator, which will cause damage to the heat exchange tube bundle.

Numerical Simulation of Flow-Induced Vibration of Three-Dimensional Elastic Heat Exchanger Tube Bundle Based on Fluid-Structure Coupling

The reliability of the heat exchanger tube bundle not only affects the economic efficiency of production but also relates to the normal development of production safety and health. To study the flow-induced vibration of tube bundles, a three-dimensional finite element model of heat exchange tubes and watersheds inside and outside the tubes was established to explore the flow-induced vibration characteristics of tube bundles and analyze the natural frequencies of single-span and multispan heat exchange tubes. Considering the randomness of the effective support between the tube bundle and the support plate of the heat exchanger, the natural frequency and vibration mode of the four-span tube with failure of the tube bundle support are analyzed. On this basis, the vibration caused by the two-way coupling flow between tube and tube outflow is calculated. Finally, the flow-induced vibration characteristics of the five-tube bundle with two different pitch-diameter ratios are analyzed. The calculation results show that the error between the calculated natural frequencies and the theoretical values is less than 3%, and within the allowable error range, the natural frequencies of the same order decrease with the increase of the number of support failures. The vibration frequencies of single-span and multispan tube bundles are consistent with the lift and drag frequencies, the vibration displacement curves show typical Strouhal modes, and the amplitude increases with the increase of fluid velocity. Vibration displacement curves of symmetrical spans of multispan tube bundles are similar in shape and amplitude. With the increase of tube bundle spacing, the vibration characteristics become more obvious.

Study on Behavior of the Heat Exchanger with Conically-Corrugated Tubes and HDD Baffles

Baffles with holes in different diameters (or HDD baffles) and conically-corrugated tubes are respectively longitudinal flow baffle and high-efficiency heat exchange tubes proposed by the author. In this paper, vibrations of tube bundles with HDD baffles and fluid flow as well as heat transfer inside conically-corrugated tubes were numerically simulated, and the heat exchanger with conically-corrugated tubes and HDD baffles was tested for the heat transfer efficiency. It is found that compared with the traditional segmental baffles, tube bundle vibrations in heat exchangers, if using the HDD baffles, can be significantly reduced. Regarding heat transfer efficiency, conically-corrugated tubes are much better than smooth tubes and even better than other high-efficiency heat transfer tubes. Compared with the traditional heat exchangers, heat exchangers constructed with conically-corrugated tubes and the HDD baffles can provide better heat transfer efficiency and less tube bundle vibration.

Numerical Analysis of Flow-Induced Vibration of Heat Exchanger Tube Bundles Based on Fluid-Structure Coupling Dynamics

Numerical Analysis of Flow-Induced Vibration of Heat Exchanger Tube Bundles Based on Fluid-Structure Coupling Dynamics

Analysis of the Effect of Baffles on Vibration and Heat Transfer Characteristics of Elastic Tube Bundles

Analysis of the Effect of Baffles on Vibration and Heat Transfer Characteristics of Elastic Tube Bundles

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.

Analysis on Fluid-Induced Vibration and Heat Transfer of Helical Elastic Tube Bundles

The study on fluid-induced vibration of helical elastic tube bundles (HETBs) to enhance heat transfer is of great significance in industrial production and energy utilization. The fluid-induced vibration response and the heat transfer property of a HETB heat exchanger were analyzed by using a two-way fluid–solid coupling method. The vibration frequency, displacement amplitude, and heat transfer coefficient were computed while considering varying entrance velocities and helix diameters. Numerical results demonstrate that the middle of the HETB vibrates the most violently, and the vibration is mainly in the vertical direction. There are a large number of vortices in the gaps between the tubes and the inner cavity of the heat exchanger. The vibration amplitude and heat transfer coefficient of the HETB increase significantly when the entrance velocity or helix diameter increases. The effect of vibration-enhanced heat transfer improves with the increase in entrance velocity. The mean value of the heat transfer coefficient at the upper side of the HETBs is 2.205 times that at the lower side.