An Excitation Spectrum Criteria for the Vibration-Induced Fatigue of Small Bore Pipes

The purpose of the study is to determine an easy-to-use criterion to evaluate the risk of vibration induced fatigue of small bore pipes. The failure mechanism considered is the resonant amplification of a stationary broadband excitation of the main pipe by natural modes of the small bore pipe, leading to bending stresses above the fatigue limit of the steel. Based on the Euler beam theory, a simple model is built up for the natural mode shapes of the small bore pipe close to its root. It is shown that the velocity spectrum at the root of the small bore pipe is equal to the RMS value of the bending stress multiplied by a function of the natural frequency, the damping coefficient, the speed of elastic waves in the steel, the Young modulus and a non-dimensional factor weakly depending on the geometry of the small bore pipe. A maximum velocity spectrum can then be deduced, assuming that a small bore pipe vibrates mainly on its natural mode shapes. The maximum excitation spectrum is defined for each frequency ƒ as the one which would generate a maximum bending stress equal to the endurance limit of the steel, would the small bore pipe have a natural frequency equal to ƒ. Using envelope values of the dimensional factor, the stress intensification factor, the peak factor and the endurance limit of the steel, one obtains the following maximum velocity spectrum for the stainless steel: v<6mm/s/sqrt(ƒ) and the following maximum velocity spectrum for the ferritic steel: v<2.7mm/s/sqrt(ƒ) The velocity spectrum criterion appears less penalizing than the 12 mm/s criterion and more conservative than the strict enforcement of the ANSI-OM3 standard. Comparisons with former studies show that the velocity spectrum criterion leads to the correct fatigue diagnosis.

Excitation by Flow Over an Obstructed Opening

The effect on flow-induced cavity resonance of the presence of an obstruction, or a grid made up of regularly spaced obstructions, in the cavity opening is considered. The presence of a single obstruction or of a grid generally alters the flow so that the excitation occurs on the smaller length scale created by the obstruction. However, discussion of resonant excitation on the length scale encompassing the obstructions has not been found in the literature. For this study, measurements of cavity pressure due to flow over a cavity with obstructions or grids of varying dimensions in the opening were made. Measurements of the flow field around a single obstruction were also made. The cavity pressure measurements show that flow over an opening with a grid does result in the occurrence of classical resonant excitation at the large length scale. The frequency of the excitation and the amplitude of the response at the large length scale are reduced, depending on the dimensions of the obstruction. Flow field results show the effects that an obstruction has on the flow, including effects on the vortex convection velocity and the energy production distribution.

A Harmonic Balance Approach for Modeling Three-Dimensional Nonlinear Unsteady Aerodynamics and Aeroelasticity

Presented is a frequency domain harmonic balance (HB) technique for modeling nonlinear unsteady aerodynamics of three-dimensional transonic inviscid flows about wing configurations. The method can be used to model efficiently nonlinear unsteady aerodynamic forces due to finite amplitude motions of a prescribed unsteady oscillation frequency. When combined with a suitable structural model, aeroelastic (fluid-structure), analyses may be performed at a greatly reduced cost relative to time marching methods to determine the limit cycle oscillations (LCO) that may arise. As a demonstration of the method, nonlinear unsteady aerodynamic response and limit cycle oscillation trends are presented for the AGARD 445.6 wing configuration. Computational results based on the inviscid flow model indicate that the AGARD 445.6 wing configuration exhibits only mildly nonlinear unsteady aerodynamic effects for relatively large amplitude motions. Furthermore, and most likely a consequence of the observed mild nonlinear aerodynamic behavior, the aeroelastic limit cycle oscillation amplitude is predicted to increase rapidly for reduced velocities beyond the flutter boundary. This is consistent with results from other time-domain calculations. Although not a configuration that exhibits strong LCO characteristics, the AGARD 445.6 wing nonetheless serves as an excellent example for demonstrating the HB/LCO solution procedure.

Numerical Modelling of the Three-Dimensional Slamming Problem

This paper deals with the slamming phenomenon for deformable structures. In a first part, a three-dimensional hydrodynamic problem is solved numerically with the Finite Element Method. The results for a rigid body are successfully compared to the analytical solutions. After the numerical analysis, an experimental investigation is presented. It consists in series of free fall drop-tests of rigid, deformable cones shaped models with different deadrise angle and thickness. Distribution of the pressure and its evolution are analyzed. Numerical and experimental results are compared and present good agreement.

Study of the Acoustic Oscillations by Flows Over Cavities: Part 1 — Internal Flows

We present a study of acoustic oscillations induced by an internal airflow over a shallow and a deep cavity. The Kelvin-Helmholtz instability is interacting with an acoustic mode of the duct, leading to a resonance which produces a very high sound level. The influence of upstream boundary layer thickness and neck thickness is studied. Some results obtained by modifying the upstream lip shape, by crenel addition, are also given. It is also shown that the numerical simulations using a lattice-gas method give relatively good results by comparison with the experiments. Especially the resonance with the duct acoustics was qualitatively reproduced.

Surface Roughness Effects on Circular Cylinders at High Reynolds Numbers

The problem of flow-induced vibration has been studied extensively. However, much of this research has focused on the smooth cylinder to gain an understanding of the mechanisms that cause vortex-induced vibration. In this paper results of an investigation of the effect of surface roughness on the cross-wind forces are presented. Measurements of the sectional RMS fluctuating lift forces and the axial correlation of the pressures for Reynolds numbers from 1 × 105 to 1.4 × 106 are given. It was found that surface roughness significantly increased the axial correlation of the pressures to similar values found at high subcritical Reynolds numbers. There was little effect of the surface roughness on the sectional lift forces. The improved correlation of the vortex shedding means rough cylinders will be subject to larger cross-wind forces and an increased possibility of vortex-induced vibration compared to smooth cylinders.

Upgrading of Tubular Heat Exchangers by the Helical Spacer Method and Evaluation

The tubular heat exchangers described exhibited a sensitivity to flow-induced tube vibration at about 50% of their design shell-side flow. Following a detailed theoretical analysis, the heat exchangers were modified by the helical spacer method providing additional tube supports in-between the existing support plates and in the U-bend. This modification aimed at allowing the heat exchangers to operate safely and reliably at full load, including a 25% overload. Post modification sound and vibration testing was performed which confirmed the adequacy of the modification. The test results showed however, that at the overload condition, an unusual acoustic wave inside the shell was developing. It was determined that this wave would not be harmful to the safe operation of the heat exchangers. The paper will discuss the findings in more detail.

Nonlinear Sloshing in Fixed and Vertically Excited Containers

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

Flow Induced Vibration and Fretting Wear: An Integrated Approach

Fuel assemblies are exposed to severe thermal, mechanical and radiation loads during operation. Global core and local fuel assembly flow fields typically result in fuel rod vibration. Under certain conditions, this vibration, when coupled with other factors, might result in excessive cladding fretting wear. This phenomenon is of the concern for nuclear fuel designers, especially in light of the need for higher burnup, longer cycle lengths, and operational safety margins in fuel designs. Understanding of (1) the fretting wear margins for a particular nuclear fuel design, (2) the probability of a fuel assembly exposed to a particular set of thermal, mechanical, flow and radiation conditions being at risk of excessive wear, and (3) the factors affecting fretting wear resistance, are important in order to better guide design, testing, and operational flexibility. In this paper, an integrated method to estimate fretting margin of nuclear fuel is presented, including its formulation, benchmark against experimental data and example application to in-core conditions. The major features of the method are as follows: • flow and rod vibration response are coupled through a linear structural analysis model, • flow field is determined using a sub-channel thermal-hydraulic code, • wear progression is treated as a time-dependent process, through taking into account impact of resulting rod-to-support clearance, • a possibility of a fluid-elastic instability is accounted for. Supporting data on basic wear mechanisms, flow field and fuel assembly fretting wear behavior obtained at a number of experimental facilities at Westinghouse Electric Company and Atomic Energy of Canada Limited are also presented. These facility include: • VIPER hydraulic test loop data where vibration response and wear are measured under prototypical flow conditions, and • autoclave fretting-wear machine steam employed to determine fretting-wear coefficients of fuel rod and grid-support designs.

On a Circular Cylinder in a Uniform Planar Shear Flow at Subcritical Reynolds Number

An experimental investigation was conducted of a circular cylinder immersed in a uniform planar shear flow, where the approach velocity varies across the diameter of the cylinder. The study was motivated by some apparent discrepancies between numerical and experimental studies of the flow, and the general lack of experimental data, particularly in the subcritical Reynolds number regime. Of interest was the direction and origin of the steady mean lift force experienced by the cylinder, which has been the subject of contradictory results in the literature, and for which measurements have rarely been reported. The circular cylinder was tested at Reynolds numbers from Re = 4.0×104 − 9.0×104, and the dimensionless shear parameter ranged from K = 0.02 − 0.07, which corresponded to a flow with low to moderate shear. The results showed that low to moderate shear has no appreciable influence on the Strouhal number, but has the effect of lowering the mean drag coefficient. The circular cylinder develops a small steady mean lift force directed towards the low-velocity side, which is attributed to an asymmetric mean static pressure distribution on its surface. The reduction in the mean drag force, however, cannot be attributed solely to this asymmetry.