This paper re-examines the available experimental data to investigate the random excitation forces that affect tube bundles exposed to two-phase cross flow. Much of the experimental data generated over the past four decades has been gathered in an attempt to understand the parametric dependence of the random two-phase forces. The data includes air-water, steam-water and various Freons used in a variety of test sections with either strain gauges to measure the tube amplitude or force tranducers to measure the reaction forces. A review of previous work in this area finds that some authors claim a strong flow regime dependence, while others suggest that this dependence is weak. This work takes a detailed look at this discrepancy and finds that a single design guideline does not adequately bound all flow regimes. As a result, two dimensionless upper bounds are proposed.

The problem of fretting-wear damage between a vibrating structure and its supports is discussed in this paper. Typical components of concern are piping systems and pipe-supports, multispan heat exchanger tubes and tube supports, and nuclear fuel bundles and fuel channels. Fretting-wear damage is related to the dynamic interaction between a structure and its supports. This interaction is conveniently formulated in terms of a parameter called “work rate” to predict fretting-wear damage. Work rate is simply the integral of contact force over sliding distance per unit time. Fretting-wear damage may be investigated from an energy point of view. It is essentially the mechanical energy or power dissipated through contact forces and sliding that causes fretting-wear damage. Development of a simple formulation that relates tube vibration response and fretting-wear damage is reviewed in this paper. Some new practical examples and simple calculations are discussed.

Detailed unsteady fluid force and phase measurements for a single tube oscillating purely in the streamwise direction in a rotated triangular tube array subjected to air-water two-phase cross-flow have been conducted in this study for homogeneous void fractions between 0% and 90%. Additionally the streamwise steady forces were measured in two-phase flow at a Reynolds number (based on the pitch velocity), Re = 7.2 × 10 4 . The results are compared to those previously obtained for transverse direction oscillations. The measurement results show that the magnitude of the force coefficients for both directions (drag and lift) is comparable both in trend and quantitatively. However, the phase in the drag direction is negative while that for the lift is positive. The range of variation of the phase is also significantly smaller for the drag direction. Noting that negative phase corresponds to positive damping and vice versa, this observation confirms previous findings of lack of instability in the drag direction for a single flexible tube in a rotated triangular tube array. The drag steady fluid force coefficients were found to increase with dimensionless displacement in the flow direction for the entire range of void fractions considered. The derivative of the measured steady fluid force coefficient, which is an important factor in fluidelastic instability study using the quasi-steady model, was found to remain positive in the drag direction. The effect of void fraction on the unsteady fluid force coefficient and other dynamic parameters such as hydrodynamic mass and damping are also discussed.

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.

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.

Excessive flow-induced vibration causing fretting-wear damage can seriously affect the performance of process equipment such as heat exchangers, condensers, nuclear steam generators, nuclear fuels, reactor internals, and piping systems. Fretting-wear damage generally takes place between a vibrating structure and its supports. It can be predicted with a fretting-wear coefficient obtained experimentally and a parameter called work-rate that formulates the dynamic interaction between structure and support. The work-rate is essentially the rate of mechanical energy dissipated at the support. On the other hand, the total available mechanical vibration energy in a structure is related to its mass, vibration frequency, mode shape, damping, and vibration amplitude. This leads to the development of a simplified formulation based on energy considerations to relate the vibration response of a structure to fretting-wear damage at its supports. The basic energy equations and the formulation of a simplified energy relationship to predict fretting-wear damage are outlined in this paper. The relationship is verified against experimental data for a multi-span heat exchanger tube. The energy approach is also compared to time domain calculations performed with a non-linear finite element code. The results indicate that the simple energy approach may be very useful to estimate fretting-wear damage in practical situations. Finally, the application of the method is illustrated for a typical heat exchanger tube and for nuclear fuels.

While steam generators operate in two-phase flow, the complex nature of the flow makes the prediction of flow-induced fluidelastic instability of steam generator tubes a challenging problem yet to be solved. In the work reported here, the quasi-static fluid force-field, which is the important unknown for two-phase flows, is measured in a rotated-triangle tube bundle for a series of void fractions and flow velocities. The forces are shown to be strongly dependent on void fraction, flow rates and relative tube positions. The fluid force field is then employed along with quasi-steady vibration stability models, originally developed for single phase flows, to model the two-phase flow problem and predict the critical instability velocity. The results are compared with dynamic vibration stability tests and are shown to be in good agreement. The present work uncovers some of the complexities of the fluid force field in two-phase flows. The database provides new potential to designers to estimate expected fluid dynamic loads under operating conditions. The force field data may also be applied in dynamic computations for tube wear simulations, replacing the simple Connors’ model which is currently used.

The fluidelastic instability behaviour of flexible cylinders subjected to internal single-phase (liquid or gas) flows is now reasonably well understood. Although many piping systems operate in two-phase flows, so far very little work has been done to study their dynamic behaviour under such flows. This paper presents the results of a series of experiments to study the fluidelastic instability behaviour of flexible tubular cylinders subjected to two-phase internal flow. Several flexible cylinders of different diameters, lengths and flexural rigidities were tested over a broad range of flow velocities and void fractions in an air-water loop to simulate two-phase flows. Well-defined fluidelastic instabilities were observed in two-phase flows. The existing theory to formulate the fluidelastic behaviour under internal flow was developed further to take into account two-phase flow. The agreement between the experimental results and the modified theory is remarkably good. However, it depends on using an appropriate model to formulate the characteristics of the two-phase flows.

Severe in-plane vibrations were observed in a series of 20-mm dia. PVC vertical U-tubes of different elbow geometries subjected to air-water internal flow. An experimental study was undertaken to investigate the excitation mechanism. Vibration response, excitation forces and fluctuating properties of two-phase flow were measured over a wide range of flow conditions. The experimental results show that the observed vibrations are due to a resonance phenomenon between periodic momentum flux fluctuations of two-phase flow and the first modes of U-tubes. The excitation forces consist of a combination of narrow-band and periodic components, with a predominant frequency that increases proportionally to flow velocity. For a given void fraction, the force spectra for various flow velocities and elbow geometries coincide generally well on a plot of the normalized power spectral density as a function of a dimensionless frequency. The predominant frequencies of excitation agree with recent results on the characteristics of periodic structures in two-phase flow.

Two-phase flow is common in the nuclear industry. It is a potential source of vibration in piping systems. In this paper, two-phase damping in the bubbly flow regime is related to the interface surface area between phases and, therefore, to flow configuration. Two sets of experiments were performed with a vertical tube clamped at both ends. First, gas bubbles of controlled geometry were simulated with glass spheres let to settle in stagnant water. Second, air was injected in stagnant alcohol to generate a uniform and measurable bubble flow. In both cases, the two-phase damping ratio is correlated to the number of bubbles (or spheres). Two-phase damping is directly related to the interface surface area, based on a spherical bubble model. Further experiments were carried out on tubes with internal two-phase air-water flows. A strong dependence of two-phase damping on flow configuration in bubbly flow regime is observed. A series of photographs attests to the fact that two-phase damping increases for a larger number of bubbles, and for smaller bubbles. It is highest immediately prior to the transition from bubbly flow to slug or churn flow regimes. Beyond the transition, damping decreases. An analytical model is proposed to predict two-phase flow damping in bubbly flow, based on a spherical bubble model. The results also reveal that the transition between bubbly flow and slug/churn flow depends on tube diameter. Consequently, the tube diameter also has an effect on two-phase damping. The above results could lead to some modifications of existing flow regime maps for small diameter tubes.

Two-phase internal flow is present in many piping system components. Although two-phase damping is known to be a significant constituent of the total damping, the energy dissipation mechanisms that govern two-phase damping are not well understood. In this paper, damping of vertical clamped-clamped tubes subjected to two-phase air-water internal flow is investigated. Experimental data is reported, showing no dependence of two-phase damping on tube natural frequency, and a strong dependence on void fraction, flow velocity and flow regime. Two-phase damping increases with void fraction, reaches a maximum, and decreases beyond that point. The maximum damping ratio is roughly 3% for all flow velocities. It is reached at around 50% void fraction for high velocities, and 25% void fraction for low velocities. Data points plotted on two-phase flow pattern maps indicate that damping is greater in a bubbly flow regime than it is in a slug or churn regime. The maximum two-phase damping is reached at the highest void fraction before the transition to a slug or churn flow regime. It appears that two-phase damping may depend on the interface surface area between phases.

In nuclear power plant steam generators, the vibration response of tubes in two-phase cross-flow is a general concern that in some cases has become a very real long-term wear problem. This paper summarizes the results of the most recent U-bend vibration-response tests in a program designed to address this issue. The tests involved a simplified U-tube bundle with a set of flat-bar supports at the apex, subjected to two-phase air-water cross-flow over the mid-span region of the U-bend. Tube vibration properties and tube-to-support interaction in the form of work-rates were measured over a wide range of flow velocities for homogeneous void fractions from zero to 90%, with three different tube-to-support clearances. The measured vibration properties and work-rates could be characterized by the relative influence of the two most important flow-induced excitation mechanisms at work, fluidelastic instability and random-turbulence excitation. As in previous similar tests, strong effects of fluidelastic instability were observed at zero and 25% void fraction for pitch velocities greater than approximately 0.5 m/s, whereas random turbulence dominated the tube vibration and work-rate response at higher void fractions. In both cases, a link between vibration properties and the effect of the flat-bar supports could be established by comparing the vibration crossing frequency, extracted from time-domain vibration signals, to the participation of the lowest few vibration modes and to the measured work-rate. This approach may be useful when fluidelastic instability, random turbulence and loose supports all combine to result in high work-rates. Such a combination of factors is thought to be responsible for excessive U-tube fretting-wear in certain types of operating steam generators.

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: 1) flow distribution calculations, 2) dynamic parameter evaluation (i.e. damping, effective tube mass, and dynamic stiffness), 3) formulation of vibration excitation mechanisms, 4) vibration response prediction, and 5) 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, dynumic parameters and fluidelastic instability.

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. Part 2 of this paper covers forced vibration excitation mechanisms, vibration response prediction, resulting damage assessment, and acceptance criteria.