Random Forces Resulting From Internal Two-Phase Flow on Bends and Tees

The time dependent forces resulting from a two-phase air-water mixture flowing in an elbow and a tee are measured. Their magnitudes as well as their spectral contents are analyzed. Comparison is made with previous experimental results on similar systems. For practical applications a dimensionless form is proposed to relate the characteristics of these forces to the parameters defining the flow and the geometry of the piping.

Evaluation of Non-Vibrating Utility Burner/Furnace Systems for Resistance to Thermoacoustic Oscillations

Six burner/furnace systems which operated successfully without vibration are evaluated for resistance to thermoacoustic oscillations. The evaluation is based on the Rijke and Sondhauss models representing the combined burner/furnace (cold/hot) thermoacoustic systems. Frequency differences between the lowest vulnerable furnace acoustic frequencies in the burner axial direction and those of the systems’ Rijke and Sondhauss frequencies are evaluated to check for resonances. Most importantly, the stability of the Rijke and Sondhauss models is checked against the published design stability diagram of Eisinger [1] and Eisinger and Sullivan [2]. It is shown that the resistance to thermoacoustic oscillations is adequately defined by the published design stability diagram to which the evaluated cases generally adhere. Once the system falls into the stable range, the frequency differences or resonances appear to play only a secondary role. It is concluded, however, that in conjunction with stability, the primary criterion, sufficient frequency separations shall also be maintained in the design process to preclude resonances. The paper provides sufficient details to aid the design engineers.

Vortex-Induced Vibrations of a Rigid Cylinder on Non-Linear Elastic Supports

The dynamics of vortex-induced vibrations of a rigid circular cylinder with structural non-linearities, introduced by means of discontinuities in the support system, are studied experimentally. The analysis of the measurements is carried out using non-linear vibration tools, i.e phase-flow portraits, frequency spectra, Lyapunov exponents and correlation dimensions, to provide an insight into the dynamical changes in the system brought about by restricting the motion. We show that chaotic motions can occur due to the structural non-linearities.

Effects on Pipe Vibrations of Cavitation in an Orifice and in Globe-Style Valves

A piping system of French nuclear power plants displays large amplitude vibrations in particular flow regimes. These troubles are attributed to cavitation generated by single-hole orifices in depressurized flow regimes. Real scale experiments on high pressure test rigs and on-site tests are then conducted to explain the observed phenomenon and to find a solution to reduce pipe vibrations. The first objective of the present paper is to analyze cavitation-induced vibrations in the single-hole orifice. It is then shown that the orifice operates in choked flow with supercavitation, which is characterized by a large unstable vapor pocket. One way to reduce pipe vibrations consists in suppressing the orifices and in modifying the control valves. Three technologies involving a standard trim and anti-cavitation trims are tested. The second objective of the paper is to analyze cavitation-induced vibrations in globe-style valves. Cavitating valves operate in choked flow as the orifice. Nevertheless, no vapor pocket appears inside the pipe and no unstable phenomenon is observed. The comparison with an anti-cavitation solution shows that cavitation reduction has no impact on low frequency excitation. The effect of cavitation reduction on pipe vibrations, which involve essentially low frequencies, is then limited and the first solution, which is the standard globe-style valve installed on-site, leads to acceptable pipe vibrations. Finally, this case study may have consequences on the design of piping systems. First, cavitation in orifices must be limited. Choked flow in orifices may lead to supercavitation, which is here a damaging and unstable phenomenon. The second conclusion is that the reduction of cavitation in globe-style valve in choked flow does not reduce pipe vibrations. The issue is then to limit cavitation erosion of valve trims.

Annular Axial Flow-Induced Vibration of Cylindrical Shells by Flu¨gge’s Shell Theory

The unstable phenomena of thin cylindrical shells subjected to annular axial flow are investigated. In this paper, the analytical model is composed of an elastic axisymmetric shell and a rigid one which are arranged co-axially. Considering the fluid structure interaction between shells and fluid flowing through an annular narrow passage, the coupled equation of motion is derived using Flu¨gge’s shell theory and Navier-Stokes equations. The unstable phenomena of thin cylindrical shells are clarified by using the root locus based on the complex eigenvalue analysis. The numerical parameter studies on the shells with a freely supported end and a rigid one, and with both simply supported ends, are performed taking the dimensins of shells, the characteristics of flowing fluid so on as parameters. The influence of these parameters on the threshold of instability of the coupled vibration between thin cylindrical shells and annular axial flowing fluid are investigated and discussed.

A Full Scale Test for Acoustic Fatigue in Pipework

Gas flow through a corrugated pipe can produce unacceptable levels of noise. The occurrence of such noise gave rise to concerns about vibration induced fatigue of small-bore subsea pipework in the Schiehallion oil field. In order to check that the subsea pipework was free from noise-induced vibration a full scale replica of the subsea equipment containing the small-bore pipework was built and tested. The test required the generation of acoustic pressures with a 1 bar amplitude and a frequency range of 80 to 800Hz. It was also necessary to arrange for resonant conditions within the pipework and for acoustic nodes and anti-nodes to be swept though a range of possible locations. The test was conducted with full-scale conditions of methane at a static pressure of 170bar and with a range of gas flow rates. Particular attention was given to achieving the correct acoustic and structural natural frequencies together with the correct acoustic and structural damping ratios. The subsea equipment was found to be vulnerable for one operating condition. This vulnerability was removed by retro-fitting a brace to the existing subsea pipework.

On the Pressure and Force Field on a Circular Cylinder Oscillating in the Lock-In Region at Sub-Critical Reynolds Number

The vortex induced vibration of a rigid cylinder has been studied in the subcritical Reynolds range in terms of motion parameters and also in terms of instantaneous pressure distribution on the cylinder surface. The resulting force field has been analyzed as a function of the fundamental parameters z* (non-dimensional amplitude) and Un (critical velocity ratio) showing a possible systematic modelization of the force component synchronous with the oscillation frequency, responsible for the power input in the lock-in region. The magnitude and the phase of the synchronous force component have been studied analyzing build-up events as well as steady state constant amplitude oscillation events. A very close correspondence has been highlighted among the two different analyzed cases, confirming that a quasi-steady model of the force field is a robust and reliable representation of the flow-cylinder interaction force field. This interaction is responsible for the typical transient build-up oscillations of technical interest. The pressure distribution monitored at different locations along the oscillating cylinder axial coordinate allowed finally to show a direct link between the incoming flow velocity distribution and the correlation characteristics of the vortex shedding force distribution along the cylinder axis.

Damping Measurements in Tube Bundles Subjected to Two-Phase Cross Flow

An experimental study was conducted to investigate two-phase damping in tube arrays. The objective was to compare different measurement methodologies in order to obtain a more reliable damping estimate. This will allow for improved guidelines related to failures due to fluidelastic instability in tube bundles. The methods compared were the traditionally used half-power bandwidth, the logarithmic decrement and an exponential fitting to the tube decay response. The working fluid used was Refrigerant 11 (Freon), which better models the real steam-water problem, as it allows for phase change. The void fraction was measured using a gamma densitometer, introducing an improvement over the traditional Homogeneous Equilibrium Model (HEM) in terms of velocity and density predictions. The results obtained by using the half-power bandwidth method agree with data previously reported for two-phase flow. The experiments showed that the half-power bandwidth produces higher damping values than the other two, but only up to a certain void fraction. After that point, the results obtained from the three methods are very similar. The exponential fitting proved to be more consistent than the logarithmic decrement, and it is not as sensitive as the half-power bandwidth to the frequency shifting caused by the change in added mass around the tube. By plotting the damping ratio as a function of void fraction, pitch mass flux and flow regime, we were able to verify that damping is more dependent on void fraction and flow regime than on mass flux.

Spectrographic Analysis for the Modal Testing of Nonlinear Aeroelastic Systems

The spectrograph is a signal processing tool often used for the frequency domain analysis of time-varying signals. When the signal to be analyzed is a function of time, the spectrograph represents the frequency content of the signal as a sequence of power spectra that change with time. In this paper, the usefulness of the technique is demonstrated in its application to the analysis of the time history response of a nonlinear aeroelastic system. The aeroelastic system is modeled analytically as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap is used to provide the forcing input to the system. The nonlinear system is obtained by introducing a freeplay type of nonlinearity in the pitch degree-of-freedom restoring moment. The airfoil is immersed in an aerodynamic flow environment, modeled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion are solved using a fourth-order Runge-Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. Time-histories are obtained for the nonlinear responses of the linear and nonlinear aeroelastic systems to a sine-sweep input. The time-histories are analyzed using the spectrographic technique, and the frequency content of the response is plotted directly as a function of the input frequency. Results show that the combination of the sine-sweep input with the spectrographic analysis permits a unique insight into the behaviour of the nonlinear system with a minimum of testing. It is shown that the frequency of the nonlinear system response is a function of the input frequency and one other characteristic frequency that can be associated with the limit cycle oscillations of the same nonlinear system subject to a transient input.

Flow Excitation of Diametral Acoustic Modes of Axisymmetric Cavities

Flow-excited resonances of the acoustic diametral modes of a cylindrical pipe housing an axi-symmetric shallow cavity are investigated experimentally. The aeroacoustic response of the cavity-pipe combination is studied up to a Mach number of 0.4 and for several ratios of cavity length to its depth. Although the diametral modes do not have a preferred orientation because of the system axi-symmetry, they are found to be strongly excited by any of the first three instability modes of the cavity shear layer. Intense acoustic pressure levels, up to 170 dB, and wide lock-in resonance ranges have been observed. The acoustic pressure and its phase are measured along the cavity circumference to examine the orientation of the excited diametral modes within the un-preferential domain of the axi-symmetric cavity. Preliminary results suggest that the excited modes are stationary at low flow velocities, but they switch to spinning mode pattern at higher velocities.