New Experimental Data and Analysis for Two-Phase Flow-Induced Vibration of Tube Bundles: Preliminary Results

In the past, fluid-elastic instability in two-phase flow has been largely investigated with air-water flow. In this work, new experiments are conducted in air-water cross-flow with a fully flexible 5 × 3 normal square array having pitch-to-diameter ratio of 1.4. The tubes have a diameter of 0.016 m and a length of 0.21 m. The vibrations are measured using strain gages installed on piano wires used to suspend the tubes. Experiments are carried out for void fractions from 0%–30%. A comparison of the results of the current tests with previous experiments conducted in air-water cross-flow shows that instability occurs earlier in a fully flexible array as compared to a flexible tube surrounded by rigid tubes in an array. An attempt is made to separate out the effects of structural parameters of three different experimental datasets by replotting the instability criterion by incorporating the instability constant K, in the reduced velocity parameter.

Use of Redundant Sensors to Determine the Acoustic Transfer Matrix of a Pump

A series of tests in a small-scale loop containing a centrifugal pump was carried out to develop practical acoustic test and analysis techniques to be used in a manufacturer’s pump test facility during pump qualification testing. To determine the pump transmission characteristics, the effect of high noise levels due to the flow was reduced by driving an external source repeatedly with a swept-frequency signal and performing synchronous, time-domain averaging. A new multi-sensor technique is shown to provide accurate estimates of the pump acoustic transfer matrix. Results confirm that the pump transfer matrix is similar whether the pump is running or not. This indicates that the full-scale pump transfer matrix may be determined with the pump off using a relatively weak external acoustic source and a pump loop system with no cavitation.

A Theoretical Series Solution for the Dynamics of Finite-Length Bearings and Squeeze-Film Dampers

In this paper we develop a non-linear dynamical solution for finite length bearings and squeeze-film dampers based on a Spectral-Galerkin method. In this approach the gap-averaged pressure is approximated, in the lubrication Reynolds equation, by a truncated double Fourier series. The Galerkin method, applied over the residuals so obtained, generate a set of simultaneous algebraic equations for the time-dependent coefficients of the double Fourier series for the pressure. In order to assert the validity of our 2D–Spectral-Galerkin solution we present some preliminary comparative numerical simulations, which display satisfactory results up to eccentricities of about 0.9 of the reduced fluid gap H/R. The so-called long and short-bearing dynamical solutions of the Reynolds equation, reformulated in Cartesian coordinates, are also presented and compared with the corresponding classic solutions found on literature.

Study of Fuel Rod and Grid Supports Interaction

In order to predict the dynamic response of a nuclear fuel rod and its supports (spring and dimples) a non-linear model has been developed. The non-linearities arising from the supports are defined as a function of the rod motion and incorporated in the differential equation as generalized pseudoforces. This approach allows the use of modal analysis and preserves the physical understanding of rod frequencies and modes. The modal equations were written with the help of the Laplace transformation and integrated using an Ordinary Differential Equation (ODE) solver. The model determines the rod natural frequencies and motion, the support impact forces and the normal work rate. The paper describes the model predictions for a single span rod and compares them to experimental data.

Severed Tubes in Operating Nuclear Steam Generators: Case Analysis — I

During a routine inspection in October 2001, it was discovered that a plugged tube in one of the steam generators at a nuclear station was completely severed at the upper tubesheet. The severed surface appeared to be fresh, clean, 360-deg. and with no evidence of necking down, ductile failure or visible flaws. Eddy current inspection revealed that the four neighboring tubes downstream of the severed tube each had wedge-shaped wear marks starting from the tubesheet end. However, there was no visible mid-span impact wear marks. Furthermore, the tube was visibly swollen due to over-pressurization. This tube was plugged in 1986 with no indications of flaw or wear marks. It was replugged later. The tube was not stabilized because there was no apparent potential for a circumferential sever to occur anywhere in the tube. Flow-induced vibration based on classic linear theory showed that this tube should have wide margin against fluid-elastic instability, turbulence or vortex-induced fatigue failure. However, it also was found that if for any reason the tube was laterally restrained (clamped) at the support plates, the margin against fluid-elastic instability would be reduced significantly. Still, this tube should have been stable and turbulence or vortex-induced vibration alone, as predicted by the classic linear theory without fluid-structure interaction, should not have caused fatigue failure. This study points out a deficiency in the classic linear turbulence-induced vibration analysis without taking into account the effect of fluid-structure coupling. When the cross-flow gap velocity is near the critical velocity, fluid-structure coupling would greatly increase the vibration amplitude over what is predicted by the classic acceptance integral approach. It is this increase in turbulence-induced vibration that caused this particular tube to fail by fatigue.

Damping of Steam Generator Tubes

The flow-induced vibration (FIV) analysis is one of the most critical evaluations needed to ensure long-term operation of steam generator. Original design hardware is usually based on experience and testing. Performance changes, such as an increase in power with increased feedwater flow, or tube repairs including plugs, stabilizers, and sleeves are best evaluated analytically. A critical factor in an FIV analysis is damping. The effective damping for a steam generator tube is a function of the structural support configuration, vibration amplitude, and the void fraction of the shell-side fluid. Numerous tests have been performed in the nuclear industry to determine appropriate damping ratios for the analysis of steam generator tube bundles. As part of the root-cause analysis for a recent plugged tube sever in a Once-Through Steam Generator (OTSG), Framatome ANP performed damping tests on tubes that were swollen due to internal pressure. Damping tests were performed on virgin tubes. The tests were repeated after swelling the tube into the tube supports and again after the swollen tube was severed and stabilized. Tests were performed with air or water inside the tubes. The tests results showed a damping ratio of 2% to 5% for both a virgin tube and a tube that was swollen and locked into the tubes supports. Stabilization increased the damping ratio to greater than 8%.

Flow-Induced Vibration of Cross-Shaped Tube Bundle: The Effect of Tube Bundle Arrangement

A cross-shaped tube bundle is proposed for the lower plenum structure in the next-generation LWR. The effect of tube bundle arrangement on the flow-induced vibration characteristics of the cross-shaped tube bundle in cross flow was considered experimentally. Regarding random vibration, the power spectral density of the fluid force of the staggered arrangement as well as the correlation length was measured and those of the normal arrangement were compared with those of the staggered arrangement. Regarding self-excited vibration, vibration response was compared. The trend of the power spectral densities, correlation length, and the critical velocity of the normal arrangement were similar to those of the staggered arrangement.

On-Site Evaluation of Bending Stresses at the Root of Small Bore Pipes by Accelerometric Measurements

Several vibration-induced failures at the root of small bore piping systems occurred in French nuclear power plants in past years. The evaluation of the failure risk of the small bore pipes requires a fair estimation of the bending stress under operating conditions. As the use of strain gauges is too time-consuming in the environmental conditions of nuclear power plants, on-site acceleration measurements combined with numerical models are easier to handle. It still requires yet a large amount of updating work to estimate the stress in multi-span pipes with elbows and supports. The aim of the present study is to propose an alternate approach using two accelerometers to measure the local nozzle deflection, and an analytical expression of the bending stiffness of the nozzle on the main pipe. A first formulation is based on a static deformation assumption, thus allowing the use of a simple analog converter to get an estimation of the RMS value of the bending stress. To get more accurate results, a second method is based on an Euler Bernoulli deformation assumption: a spectral analyzer is then required to get an estimation of the spectrum of the bending stress. A better estimation of its RMS value is then obtained. An experimental validation of the methods based on strain gauges has been successfully performed.

Probabilistic Assessment of Fretting Wear in Steam Generator Tubes Under Flow Induced Vibrations

Successful life management of steam generators requires an ongoing operational assessment plan to monitor and address all potential degradation mechanisms. A degradation mechanism of concern is tube fretting as a result of flow-induced vibration. Flow induced vibration predictive methods routinely used for design purposes are based on deterministic nonlinear structural analysis techniques. In previous work, the authors have proposed the application of probabilistic techniques to better understand and assess the risk associated with operating power generating stations that have aging re-circulating steam generators. Probabilistic methods are better suited to address the variability of the parameters in operating steam generators, e.g., flow regime, support clearances, manufacturing tolerances, tube to support interactions, and material properties. In this work, an application of a Monte Carlo simulation to predict the propensity for fretting wear in an operating re-circulation steam generator is described. Tube wear damage is evaluated under steady-state conditions using two wear damage correlation models based on the tube-to-support impact force time histories and work rates obtained from nonlinear flow induced vibration analyses. Review of the tube motion in the supports and the impact/sliding criterion shows that significant tube damage at the U-bend supports is a result of impact wear. The results of this work provide the upper bound predictions of wear damage in the steam generators. The EPRI wear correlations for sliding wear and impact wear indicate good agreement with the observed damage and, given the preponderance of wear sites subject to impact, should form the basis of future predictions.

A Perforated Conical Strainer as an Example of an Acoustic Noise Generator

It is customary to insert a perforated conical strainer into the suction piping of the turbo-compressor that boosts the pressure in natural gas transportation systems. Conical strainers prevent foreign objects, left in the pipeline after its construction, from falling into the compressor impellers. In addition, the strainers are believed to be effective permanent scrubbing devices in most services requiring infrequent cleaning, such as dry and sweet natural gas transportation systems. The strainers that ‘substitute’ scrubbers offer remarkable construction and design savings for the pipeline gas operators, hence, they are often installed in today’s gas transportation systems. A conical perforated strainer could be installed as close as few meters from the compressor nozzle or at a distance of ten to fifteen pipe diameters from it. However, the convenience of strainer installation rather than consideration of its acoustic behaviour frequently dictate its location in the piping system. Therefore, the strainers are usually inserted at the flange sets that are installed for a different purpose, for example, at the spool piece flange sets or at the orifice plate flanges. The strainer location is rarely analysed although it frequently contributes to the acoustical fatigue of piping attachments, strainer disintegration, and spectacular noise generation. In this study, a case of noise generation by a conical strainer is illustrated by noise and vibration measurement results, which were carried out at several different locations of the studied piping system. Noise and vibration spectral components are identified and mitigated by the proposed recommendations.