M. J. Pettigrew

Vibration Behavior of Rotated Triangular Tube Bundles in Two-Phase Cross Flows

The results of a series of tests describing the vibration behavior of several rotated triangular tube bundles subjected to two-phase cross flows are presented. Tube bundles with a pitch-to-diameter ratio of approximately 1.5 were tested over a broad range of void fractions and mass fluxes. Fluidelastic instability, random turbulence excitation, hydrodynamic mass, two-phase damping and local void-fraction were investigated. Well-defined fluidelastic instabilities were observed in continuous two-phase flow regimes. However, intermittent two-phase flow regimes had a dramatic effect on fluidelastic instability lead-ing to lower than expected threshold flow velocities for instability, This effect was more pronounced in Freon two-phase flow than in air-water, and appeared well correlated to the transition between continuous and intermittent flow regimes. Generally, random turbulence excitation forces were much lower in Freon than in air-water. Although very dependent on void fraction, as expected, damping was quite similar in air-water and Freon.

Vibration excitation force measurements in a rotated triangular tube bundle subjected to two-phase cross flow

Two-phase cross flow exists in many shell-and-tube heat exchangers. Flow-induced vibration excitation forces can cause tube motion that will result in long-term fretting-wear or fatigue. Detailed vibration excitation force measurements in tube bundles subjected to two-phase cross flow are required to understand the underlying vibration excitation mechanisms. An experimental program was undertaken with a rotated-triangular array of cylinders subjected to air/water flow to simulate two-phase mixtures over a broad range of void fraction and mass fluxes. Both the dynamic lift and drag forces were measured with strain gage instrumented cylinders. The experiments revealed somewhat unexpected but significant quasi-periodic forces in both the drag and lift directions. The periodic forces appeared well correlated along the cylinder with the drag force somewhat better correlated than the lift forces. The periodic forces are also dependent on the position of the cylinder within the bundle.

Fluidelastic Instability of an Array of Tubes Preferentially Flexible in the Flow Direction Subjected to Two-Phase Cross Flow

Almost all the available data about fluidelastic instability of heat exchanger tube bundles concerns tubes that are axisymmetrically flexible. In those cases, the instability is found to be mostly in the direction transverse to the flow. Thus, the direction parallel to the flow has raised less concern in terms of bundle stability. However, the flat bar supports used in steam generator for preventing U-tube vibration may not be as effective in the in-plane direction than in the out-of-plane direction. The possibility that fluidelastic instability can develop in the flow direction must then be assessed. In the present work, tests were done to study the fluidelastic instability of a cluster of seven tubes much more flexible in the flow direction than in the lift direction. The array configuration is rotated triangular with a pitch to diameter ratio of 1.5. The array was subjected to two-phase (air-water) cross flow. Fluidelastic instability was observed when the flexible tubes were located at the center of the test section and also when the seven flexible tubes were placed over two adjacent columns. No instability was found for a single flexible tube in a rigid array nor for the case where the seven flexible tubes were placed in a single column. Tests were also done with tubes that are axisymmetrically flexible for comparison purposes. It was found that fluidelastic instability occurs at higher velocities when the tubes are flexible only in the flow direction. These results and additional wind tunnel results are compared to existing data on fluidelastic instability. Two-phase flow damping results are also presented in this paper.

Correlation Between Vibration Excitation Forces and the Dynamic Characteristics of Two-Phase Cross Flow in a Rotated-Triangular Tube Bundle

Two-phase cross flow exists in many shell-and-tube heat exchangers. Flow-induced vibration excitation forces can cause tube motion that will result in long-term fretting wear or fatigue. Detailed flow and vibration excitation force measurements in tube bundles subjected to two-phase cross flow are required to understand the underlying vibration excitation mechanisms. Some of this work has already been done. The distributions of both void fraction and bubble velocity in rotated-triangular tube bundles were obtained. Somewhat unexpected but significant quasiperiodic forces in both the drag and lift directions were measured. The present work aims at understanding the nature of such unexpected drag and lift quasiperiodic forces. An experimental program was undertaken with a rotated-triangular array of cylinders subjected to air/water flow to simulate two-phase mixtures. Fiber-optic probes were developed to measure local void fraction. Both the dynamic lift and drag forces were measured with a strain gage instrumented cylinder. The investigation showed that the quasiperiodic drag and lift forces are generated by different mechanisms that have not been previously observed. The quasiperiodic drag forces appear related to the momentum flux fluctuations in the main flow path between the cylinders. The quasiperiodic lift forces, on the other hand, are mostly correlated to oscillations in the wake of the cylinders. The quasiperiodic lift forces are related to local void fraction measurements in the unsteady wake area between upstream and downstream cylinders. The quasiperiodic drag forces correlate well with similar measurements in the main flow stream between cylinders.

Quasi-Static Forces and Stability Analysis in a Triangular Tube Bundle Subjected to Two-Phase Cross-Flow

Although almost half of the process heat exchangers operate in two-phase flow, the complex nature of the flow makes the prediction of fluidelastic instability a challenging problem yet to be solved. In the work reported here, the quasi-static fluid force-field is measured in a rotated-triangle tube bundle for a series of void fractions and flow velocities. The forces are strongly dependent on void fraction, flow rates and relative tube positions. The fluid force field is employed along with quasi-steady models [1, 2], originally developed for single phase flows, to model the two-phase flow problem. Stability analysis is performed using the single flexible tube model [1] as well as constrained mode analysis [2]. The results are compared with dynamic stability tests [3] and show good agreement. The results of single flexible tube analysis and multiple flexible tubes tend to coincide at low structural damping as expected. The present work uncovers some of the complexities of the fluid force field in two-phase flows. The data are valuable since they are the necessary inputs to the class of quasi-static, quasi-steady and quasi-unsteady fluidelastic instability theoretical models. This database opens a new research avenue on the feasibility of applying quasi-steady models to two-phase flow.Copyright

Fluidelastic Instability and Work-Rate Measurements of Steam-Generator U-Tubes in Air–Water Cross-Flow

The dynamic response of U-tubes to two-phase cross-flow has been studied in tests involving a simplified U-tube bundle with a set of flat-bar supports at the apex, subjected to air-water cross-flow over the mid-span region. Tube vibration and the interaction between tubes and supports were measured over a wide range of void fractions and flow rates, for three different tube-to-support clearances. The vibration properties and tube-to-support work-rates could be characterized in terms of the relative influence of fluidelastic instability and random-turbulence excitation. For the first time, in a U-bend tube bundle with liquid or two-phase flow, fluidelastic instability was observed both in the out-of-plane and in the in-plane direction. This raises the possibility of higher-than-expected tube-to-support work-rates for U-tubes restrained by flat bars, particularly if fluidelastic instability, random turbulence and loose supports combine adversely.

Two-Phase Flow-Induced Forces on Piping in Vertical Upward Flow: Excitation Mechanisms and Correlation Models

Momentum variation in two-phase flow generates significant low frequency forces, capable of producing unwanted and destructive vibrations in nuclear or petroleum industries. Two-phase flow-induced forces in piping were previously studied over a range of diameters from 6 mm to 70 mm in different piping element geometries, such as elbows, U-bends, and tees. Dimensionless models were then developed to estimate the rms forces and generate vibration excitation force spectra. It was found that slug flow generates the largest forces due to the large momentum variation between Taylor bubbles and slugs. The present study was conducted with a 52 mm diameter U-bend tube carrying a vertical upward flow. Two-phase flow-induced forces were measured. In addition, two-phase flow parameters, such as the local void fraction, bubble size and velocity, and slug frequency were studied to understand the relationship between the force spectra and the two-phase flow patterns. A new two-phase flow pattern map, based on existing transition models and validated using our own local void fraction measurements and force spectra, is proposed. This paper also presents a comparison of the present dimensionless forces with those of previous studies, thus covers a wide range of geometries and Weber numbers. Finally, a dimensionless spectrum is proposed to correlate forces with large momentum variations observed for certain flow patterns.

Fluidelastic Instability in a Normal Triangular Tube Bundle Subjected to Air-Water Cross-Flow

This paper presents the results of tests on the vibration of a normal triangular tube bundle subjected to air–water cross-flow. The pitch-to-diameter ratio of the bundle is 1.5, and the tube diameter is 38 mm. The tubes were preferentially flexible in one direction. Both the lift and the drag direction were tested. A wide range of void fractions and fluid velocities was tested. Fluidelastic instabilities and tube resonances were observed. The resonances induced significant vibration amplitudes at high void fractions in the lift direction. The results are compared with those obtained with a rotated triangular tube bundle. They show that the normal triangular configuration is more stable than the rotated triangular configuration.

Dynamic Interaction Between a Straight Tube and an Anti-Vibration Bar

Fretting-wear is a known problem in steam generator U-tubes. These tubes are supported by flat bars called anti-vibration bars (AVB) in the plane of the U-bend. Clearances between the tubes and the bars are designed to be minimal, but cumulative tolerances and manufacturing variations may lead to clearances larger than expected. Large clearances may result in ineffective support leading to in-plane and out-of-plane motion causing fretting-wear and impact abrasion. In the present work, the problem is investigated with a single two span tube, an anti-vibration bar at mid-span and a local excitation force. The dynamic behavior of a tube with simple supports at both ends and an anti-vibration bar at mid-span is characterized. The influence of clearance, preload and tilt of the support on the dynamics of the tube are investigated experimentally. The results indicate that the fretting-wear work-rate is very low with preloads, reaches a maximum around a zero clearance and diminish again for larger clearances. The tilt of the anti-vibration bar in our experiments seems to change the dynamic behavior of the tube.Copyright

Two-Phase Damping in Vertical Pipe Flows: Effect of Void Fraction, Flow Rate and External Excitation

Predicting vibration effects in steam generators requires good knowledge of two-phase damping ζ2φ. The purpose of this work is to correlate two-phase damping in axial flow with tube transversal excitation frequency and magnitude. The test section consists of a stiff square tube subjected to internal axial flow of air-water mixture. The hydraulic diameter is 3 inches. The tube is supported with linear bearings and fitted with flexible tubing on both ends to allow motion in the transverse direction. Compression springs allow setting the natural frequency of the tube oscillation. A motor provides transverse sinusoidal excitation to the tube assembly. ζ2φ is determined from the frequency response function. As a result of this study, ζ2φ is represented as a function of excitation frequency and amplitude, void fraction and flow rate. Specific information is gained through high frame rate videos of the oscillating tube, including bubble transverse velocity and size for low void fraction, and flow pattern transitions. Indeed, it is suspected that two-phase damping is partly caused by the work rate of virtual mass forces of the gas phase. Better knowledge of the physical process involved in two-phase damping will allow better modeling and prediction of tube behavior.© 2014 ASME