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An experimental analysis on the characteristics of a dynamic structure for the study of multiphase flow induced vibrations in tube bundles
Abstract
Flow-Induced Vibration (FIV) is probably the most critical dynamic issue in the design of heat exchangers. This fluid-structure phenomenon may generate high amplitude vibration of tubes or structural parts, which leads to clashing between internal components or even its fatigue failure. Many test benches have been constructed to study this phenomenon, however, some vibration mechanisms, mostly those related to multiphase flow, are not yet fully understood. Therefore, in this work, an experimental study on the characteristics of a dynamic structure devoted to the study of multiphase flow-induced vibrations in tube bundles under vertical counter gravity cross flow is presented. The dynamic structure used for this project is composed of a system of tensioned piano wires that allow the first natural frequency of the tube to be calibrated. The test section consists of a triangular tube bundle, presenting 19 mm OD tubes and transversal pitch per diameter ratio of 1.26. It counts with one flexible tube, while the remaining tubes are rigidly fixed. This paper presents tests in air environment aiming at addressing the mode shapes and resonance frequencies of the dynamic structure. Also, damping in air was calculated by using the Maximum Frequency Spacing method in combination with the Eigensystem Realization Algorithm. Subsequently, experiments for water single-flow were performed and analyzed. Finally, tests for two-phase air-water flow were carried out; the influence of void fraction on vibration amplitude, resonance frequencies and damping was checked; damping results were compared with published results of previous FIV experimental tests performed. Keywords: flexible mounted tube, flow-induced vibration, multiphase flow, void fraction, resonance frequency NOMENCLATURE f = frequency, Hz H = distance between attachment point, m I = moment of inertia, kg − m 2 K = stiffness matrix L = piano wire length, m M = mass matrix m = tube mass, kg T = tension in piano wires, N U = pitch flow velocity, m/s Greek Symbols α = void fraction, dimensionless ζ = viscous damping ratio, dimension-less η = damping loss factor, dimensionless τ = pitch-to-diameter ratio, dimension-less ψ = mode of vibration, dimensionless ω = circular frequency, rad/s Subscripts 0 = relative to the center of the tube 1,2 = relative to half-power bandwidth points r = relative to rth mode of vibration 2ϕ = relative to two-phase flow
This paper presents a summary of the studies recently performed at EESC-USP, concerning external two-phase flows across tube bundles. Experiments were performed for vertical air-water flow across a triangular tube bundle counting with 19 mm OD tube and transverse pitch of 24 mm. Flow patterns were identified based on visual observations through side windows and using the k-means clustering method based on signals of a differential pressure transducer and a capacitive sensor. Void fraction measurements were performed for bubbly flow using a capacitive probe. Accurate pressure drop results were obtained for liquid and gas superficial velocities ranging from 0.02 to 1.50 m/s and 0.20 to 10.00 m/s, respectively. A tube mounted in cantilever (within the bundle), instrumented with two accelerometers, perpendicularly aligned, mounted in the free tip were used to measure the tube dynamic responses and estimate parameters such as hydrodynamic mass and damping ratios. The results were compared against predictions methods and theoretical models from literature. When the agreement between experimental data and predictions was unsatisfactory, new methods were developed in order to be used as heat exchangers designing tools.
Flow-Induced Vibration (FIV) is probably the most critical dynamic issue in the design of shell and tubes heat exchangers. This fluid-structure phenomenon may generate high amplitude vibration of tubes or structural parts, which leads to fretting wear between the tubes and supports, noise or even fatigue failure of internal components. Many test benches have been constructed to study this phenomenon, however, some vibration mechanisms, mostly those related to multiphase flow, are not yet fully understood. Therefore, in this work, an experimental study on the vibration induced by a two-phase air-water vertical upward crossflow in a tube bundle is presented. For this purpose, a 19mm OD stainless steel tube was flexibly mounted as a cantilever-beam in a test section. The dynamic response of the tube was measured by using piezoelectric microaccelerometers installed at its free-end. The surrounding rigid tubes were installed in order to complete a normal triangular configuration with pitch-to-diameter ratio of 1.26. This paper presents tests in air and water single-phase flows aiming at addressing the resonance frequencies of the dynamic structure. Also, damping was calculated by using the half-power bandwidth method. The influence of flow velocity on vibration amplitudes and frequencies was analyzed. Finally, tests for two-phase air-water flow were carried out; the influence of void fraction on vibration amplitude, resonance frequencies and damping was checked; the results were compared with the data available in the open literature.
Fluid-elastic instability in an air-water two-phase cross-flow has been experimentally investigated using two different arrays of straight tube bundles: normal square (NS) array and rotated square (RS) array tube bundles with the same pitch-todiameter ratio of 1.633. Experiments have been performed over wide ranges of mass flux and void fraction. The quantitative tube vibration displacement was measured using a pair of strain gages and the detailed orbit of the tube motion was analyzed from high-speed video recordings. The present study provides the flow pattern, detailed tube vibration response, damping ratio, hydrodynamic mass, and the fluid-elastic instability for each tube bundle. Tube vibration characteristics of the RS array tube bundle in the two-phase flow condition were quite different from those of the NS array tube bundle with respect to the vortex shedding induced vibration and the shape of the oval orbit of the tube motion at the fluid-elastic instability as well as the fluid-elastic instability constant.
Two-phase cross-flow exists in many shell-and-tube heat exchangers, such as condensers, reboilers and nuclear steam generators. An understanding of damping and of flow-induced vibration excitation mechanisms is necessary to avoid problems due to excessive tube vibration. Accordingly, we have undertaken an extensive program to study the vibration behavior of tube bundles subjected to two-phase cross-flow. This paper presents the results of experiments on four tube bundle configurations; namely, normal triangular of pitch over diameter ratio, p/d, of 1.32 and 1.47, and parallel triangular and normal square of p/d of 1.47. The damping characteristics of all tube bundles are generally similar. Damping is maximum between 40 and 80 percent void fraction where the damping ratio reaches about 4 percent. The effect of mass flux is generally weak. Design guidelines are proposed for hydrodynamic mass and for damping.
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.
Heat exchanger tube bundles may fail due to excessive vibration or noise. The main failure mechanisms are generated by the shellside fluid that passes around and between the tubes. This fluid may be a liquid, gas or multi-phase mixture. The most severe vibration mechanism is a fluidelastic instability, which may cause tube damage after only a few hours of operation. Clearly, such extreme causes of vibration must always be avoided. In contrast buffeting due to flow-turbulence causes very little vibration. However, after many years of service such remorseless low level vibration will produce tube wall thinning, due to fretting, which may be unacceptable in a high-integrity heat exchanger. Consequently, the issues of life cycle and integrity must frequently be included in heat exchanger specification. This paper reviews the various mechanisms that cause vibration and noise. Particular attention is given to methods for achieving good tube support arrangements that minimize vibration damage. References to the most recent sources of data are given and good working practice for the design and operation of standard and high-integrity heat exchangers is discussed.
Many shell-and-tube heat exchangers operate in two-phase flows. This paper presents the results of a series of experiments done on tube bundles of different geometries subjected to two-phase cross flow simulated by air-water mixtures. Normal (30 deg) and rotated (60 deg) triangular and normal (90 deg) and rotated (45 deg) square tube bundle configurations of pitch-to-diameter ratio of 1.2 to 1.5 were tested over a range of mass fluxes from 0 to 1000 kg/(m(2)s) and void fraction from 0 to 100 percent. The effects of tube bundle geometry on vibration excitation mechanisms such as fluidelastic instability and random turbulence, and on dynamic parameters such as damping and hydrodynamic mass are discussed.
Flow induced vibrations in heat exchanger tubes have led to numerous accidents and economic losses in the past. Efforts have been made to systematically study the cause of these vibrations and develop remedial design criteria for their avoidance. In this research, experiments were systematically carried out with air-water and steam-water cross-flow over horizontal tubes. A normal square tube array of pitch-to-diameter ratio of 1.4 was used in the experiments. The tubes were suspended from piano wires and strain gauges were used to measure the vibrations. Tubes made of aluminum; stainless steel and brass were systematically tested by maintaining approximately the same stiffness in the tube-wire systems. Instability was clearly seen in single phase and two-phase flow and the critical flow velocity was found to be proportional to tube mass. The present study shows that fully flexible arrays become unstable at a lower flow velocity when compared to a single flexible tube surrounded by rigid tubes. It is also found that tubes are more stable in steam-water flow as compared to air-water flow. Nucleate boiling on the tube surface is also found to have a stabilizing effect on fluid-elastic instability.
Flow-induced vibration is an important concern to the designers of heat exchangers subjected to high flows of gases or liquids. Two-phase cross-flow occurs in industrial heat exchangers, such as nuclear steam generators, condensers, and boilers, etc. Under certain flow regimes and fluid velocities, the fluid forces result in tube vibration and damage due to fretting and fatigue. Prediction of these forces requires an understanding of the flow regimes found in heat exchanger tube bundles. Excessive vibrations under normal operating conditions can lead to tube failure.
Two-phase flow regimes in tube bundles have been determined in vertical upward cross-flow of air and water in horizontal tube bundles. Experiments were conducted using staggered and in-line tube bundles with a pitch-to-diameter ratio of 1.47, containing respectively 26 and 24 rows of five 12.7 mm O.D. tubes in each row. A resistivity void probe was used to measure the local void fraction and the probability density function (PDF) of local void fraction fluctuations was used in an objective statistical method to determine the two-phase flow regimes. For the in-line tube bundle, a bubbly flow regime occurred for JG<0.4–0.8 m/s and an intermittent flow regime for JG between 0.4–1.0 m/s and 3.9 m/s at all liquid flow rates tested (JL<1.0 m/s). An annular flow regime occurred for JG>3.9 m/s at only low liquid flow rates (JL<0.25 m/s). Compared to the previous flow regime maps, the intermittent flow regime was found to persist up to much higher liquid flow rates, and this was attributed to the difference in the flow regime identification methods used. The limitation of the visual observation technique for flow regime identification in tube bundles became evident as significantly different amplitudes of void fluctuations were measured and different flow regimes were shown to exist near the shell wall and inside the tube bundle. For the staggered tube bundle, the results were similar except for bubbly-intermittent flow regime transition which occurred at higher gas flow rates compared to the in-line tube bundle, possibly due to more efficient break-up of large gas slugs.
The flow-induced vibrational response of a single flexible cylinder positioned in a seven-row rotated square array of rigid cylinders, with pitch-to-diameter ratio of 2·12, and subject to a cross-flow has been investigated. Experiments have been done with the array in both air- and water-flow. The parameters varied during the experiments include the reduced flow velocity, the upstream flow turbulence, the cylinder non-dimensional mass, the cylinder mechanical damping and the row in which the flexible cylinder is positioned. Measurements were made of the cylinder vibration amplitudes in the in-flow and cross-flow directions; in addition, turbulence measurements were made both upstream and within the array of cylinders.In general, it is found that a single flexible cylinder in this array does not become fluidelastically unstable. It does, however, suffer vibrations both from turbulent buffeting and from resonance with array-induced flow periodicities. Results show that three Strouhal numbers are detected in different parts of the array, with all three occurring for some locations. It was also found that, provided no other excitation mechanism was present, a very good correlation between the upstream flow velocity and the cylinder vibration due to buffeting existed.
An experimental wind-tunnel facility which was developed specifically to study cross-flow induced vibrations in heat exchanger tube banks is described. Nineteen tubes in the centre of the closely packed array were flexibly mounted in order that their response and interaction with the flow could be studied. The surrounding 116 tubes were fixed and could be easily removed to study the effect of tube bundle size on flow phenomena and tube response. Results are presented in this paper for vortex shedding while those for turbulent buffeting and fluid elastic instability will be presented in the sequel to this paper.
Design guidelines were developed to prevent tube failures due to excessive flow-induced vibration in shell-and-tube heat exchangers. An overview of vibration analysis procedures and recommended design guidelines is presented in this paper. This paper pertains to liquid, gas and two-phase heat exchangers such as nuclear steam generators, reboilers, coolers, service water heat exchangers, condensers, and moisture-separator-reheaters.Generally, a heat exchanger vibration analysis consists of the following steps: (i) flow distribution calculations, (ii) dynamic parameter evaluation (i.e. damping, effective tube mass, and dynamic stiffness), (iii) formulation of vibration excitation mechanisms, (iv) vibration response prediction, and (v) resulting damage assessment (i.e., comparison against allowables). The requirements applicable to each step are outlined in this paper. Part 1 of this paper covers flow calculations, dynamic parameters and fluidelastic instability.
Contenido: Elementos de transferencia de calor; Ecuación de conducción del calor; Conducción constante del calor; Conducción transitoria del calor; Métodos numéricos en la conducción del calor; Fundamentos de convección; Convección externa forzada; Convección interna forzada; Convección natural; Evaporación y condensación; Fundamentos de radiación térmica; Transferencia de calor por radiación; Intercambiadores de calor; Transferencia de masa; Enfriamiento de equipo electrónico; Apéndices.
Projeto e análise de um dispositivo dinâmico para o estudo das vibrações induzidas por escoamentos bifásicos
- R Alvarez
Alvarez, R., 2014. "Projeto e análise de um dispositivo dinâmico para o estudo das vibrações induzidas por escoamentos
bifásicos". M.Sc. dissertation, University of São Paulo, São Carlos.