An experimental scale model study was conducted to investigate the onset of fluidelastic instability in a tube array subjected to axisymmetric jet flow. A tube array was constructed using aluminum tubes with 44.45 mm outer diameter, $D$, which were arranged in a square pattern with 88 mm pitch, $P$. The pitch to diameter ratio, $P/D$, was approximately 2.0. The tubes were flexibly mounted using threaded rod and tuned to a first mode natural frequency, $f_n$, of 9 Hz. Auxiliary damping devices were added to each tube, and tuned, to achieve a damping ratio, $\zeta$, of 1 % of critical. The mass damping parameter, $m(2 \pi \zeta)/(\rho D^{2})$, of the tube array was 27.9. The tube array was tested under uniform flow conditions in McMaster University's 2 ft wind tunnel to establish the critical reduced velocity, $V_{cr}/(f_n D)$, of 30.0 at the onset of fluidelastic instability. The uniform flow test established a basis for comparing the results with the existing literature and evaluating the validity of the proposed partial admission calculation. The tube array was also tested in open air using an axisymmetric jet, with two different physical arrangements, the first with the jet aimed between tubes and perpendicular to the tube spans and the second with the jet aimed at a tube face and perpendicular to the tube spans. In each case the jet flow velocity was incrementally increased to characterize the onset of fluidelastic instability. To characterize the flow dispersion through the tube array a series of velocity profile measurements were also collected. The measured velocity profiles were used to estimate the spanwise function of transverse average gap velocity, $\bar{V}(x)$, which was used to predict the equivalent critical uniform gap flow velocity, $V_{cr}$, using the concept of partial admission. The predicted $V_{cr}$ values showed reasonable agreement with the experimental results. However, the prediction method did indicate instabilities in tube rows where instability was not actually observed. A simplified prediction approach was developed which was based on using a predicted three dimensional velocity profile, $V(x,y)$, at the $z$ location of the first row tube gap, under the assumption of free field conditions, to calculate an estimate of the spanwise function of transverse average gap velocity, $\bar{V}(x)$. Although the predictions of $V_{cr}$ agreed reasonably well with the experimental results, first row instabilities were not observed in any of axisymmetric jet flow experiments. Therefore, this method can be used to estimate the the critical uniform gap velocity, $V_{cr}$, but not the spatial location of the instability. Based on the results of the experiments and calculations, adoption of the modified partial admission formula is recommended and possible avenues for further investigation and verification are suggested. / Thesis / Master of Applied Science (MASc)

The study of fluidelastic instability in tube arrays has been ongoing for four decades. Although much research has been conducted, a full understanding of the mechanisms involved is still not available. Designers of cross-flow heat exchangers must depend on experience and empirical data from laboratory studies. As new designs are developed, which differ from these experimental facilities, there is an increased risk of failure due to fluidelastic instability. An experimental program was conducted to examine fluidelastic instability in inline and rotated square finned tube arrays. Three arrays of each geometry type were studied; two with serrated, helically wound finned tubes of different fin densities, and the third, a bare tube which had the same base diameter as the finned tubes. The tube pitch was kept constant to reduce the number of test sections required under this investigation. As a result, the bare tube array has a larger tube pitch ratio than that of previous researchers. The finned tubes under consideration were commercial fmned tubes of a type typically used in the fossil and process industries. The addition of fins to tubes in heat exchangers enhances heat transfer due to the increased surface area and the turbulence produced by the flow moving over the fins. The resulting flow pattern/distribution due to the fins is therefore much more complicated than in bare tube arrays. Previous research has shown that an effective diameter of a finned tube is useful in the prediction of vortex shedding. This concept is used to compare the finned tube results with the existing bare tube array guidelines for fluidelastic instability. All of the tube arrays in the present study have the same tube pitch, and have been scaled to have the same mass ratio. Results for the rotated square arrays show that the use of an effective diameter is beneficial in the scaling of fluidelastic instability and the finned tube results are found to fit within the scatter of the existing data for fluidelastic instability. For in-line square arrays, the results indicate that fins significantly increase the stability threshold. / Thesis / Master of Applied Science (MASc)

<p>An experimental study was conducted to investigate damping and fluidelastic instability in tube arrays subjected to two-phase cross-flow. The purpose of this research was to improve our understanding of these phenomena and how they are affected by void fraction and flow regime. The model tube bundle had 10 cantilevered tubes in a parallel-triangular configuration, with a pitch ratio of l.49. The two-phase flow loop used in this research utilized Refrigerant 11 as the working fluid, which better models steam-water than air-water mixtures in terms of vapour-liquid mass ratio as well as permitting phase changes due to pressure fluctuations. The void fraction was measured using a gamma densitometer, introducing an improvement over the Homogeneous Equilibrium Model (HEM) in terms of void fraction, density and velocity predictions. Three different damping measurement methodologies were implemented and compared in order to obtain a more reliable damping estimate. The methods were the traditionally used half-power bandwidth, the logarithmic decrement and an exponential fitting to the tube decay response. The decay trace was obtained by "plucking" the monitored tube from outside the test section using a novel technique, in which a pair of electromagnets changed their polarity at the natural frequency of the tube to produce resonance. The experiments showed that the half-power bandwidth produces higher damping values than the other two methods. The primary difference between the methods is cam,ed by tube frequency shifting, triggered by fluctuations in the added mass and coupling between the tubes, which depend on void fraction and flow regime. The exponential fitting proved to be the more consistent and reliable approach to estimating damping. In order to examine the relationship between the damping ratio and mass flux, the former was plotted as a function of void fraction and pitch mass flux in an iso-contour plot. The results showed that damping is not independent of mass flux, and its dependency is a function of void fraction. A dimen~; ional analysis was carried out to investigate the relationship between damping and two-phase flow related parameters. As a result, the inclusion of surface tension in the form of the Capillary number appears to be useful when combined with the twophase component of the damping ratio (interfacial damping). A strong dependence of damping on flow regime was observed when plotting the interfacial damping versus the void fraction, introducing an improvement over the previous result obtained by normalizing the two-phase damping, which does not exhibit this behaviour. The interfacial velocity model was selected to represent the fluidelastic data in two-phase experiments, due to the inclusion of the tube array geometry and density ratio effects, which does not exist for the pitch velocity approach. An essential component in reliably establishing the velocity threshold for fluidelastic instability, is a measure of the energy dissipation available in the system to balance the energy input from the flow. The present analysis argues that the damping in-flmv is not an appropriate measure and demonstrates that the use of quiescent fluid damping provides a better measure of the energy dissipation, which produces a much more logical trend in the stability behaviour. This value of damping, combined with the RAD density and the interfacial velocity, collapses the available data well and provides the expected trend of two-phase flow stability data over the void fraction range from liquid to gas flows. The resulting stability maps represent a significant improvement over existing maps for predicting fluiclelastic instability of tube bundles in two-phase flows. This result a1so tends to confirm the hypothesis that the basic mechanism of fluidelastic instability is the same for single and two-phase flows.</p> / Doctor of Philosophy (PhD)

<p>Of the various excitation mechanisms causing excessive tube vibrations in tube and shell heat exchangers, fluidelastic instability is the most dangerous, and therefore has received the most attention. The objective of this research is to advance the current understanding of the fluidelastic instability in tube arrays through a fundamental investigation of the phenomenon experimentally, numerically and analytically. The concept of using a single flexible tube in a rigid array to investigate fluidelastic instability has been critically reviewed. It was found that the fluidelastic instability threshold in tube arrays is significantly affected by array geometry, pitch ratio, mass ratio and tube row location in the array. The results showed that, in general, fluidelastic instability in tube arrays is caused by a combination of the damping and the stiffness mechanisms. It was concluded that while the use of a single flexible tube in a rigid array provided a useful model for fundamental research and physical insights, it must be cautioned that it is not generally adequate for determining the experimental stability limits of tube arrays. The outcomes of this critical review helped in the design of a new experiment which facilitated precise control of the system parameters, and provided more comprehensive measurements.</p> <p>Experimental investigation of the interaction between tube vibrations and fluid forces was conducted using surface pressure measurements at the tube surface. The results showed that, there is a finite time delay between tube vibration and the associated fluid forces acting on the tube. The resulting phase lag was found to increase as the mean gap velocity increased, and ultimately the fluid forces became in phase with the tube velocity during the onset of instability. Velocity measurements of the interstitial flow perturbations associated with tube vibrations were carried out along the flow path in the array. It was found that the flow perturbation amplitude is most pronounced at the flow separation point from the vibrating tube, and that the flow perturbation amplitude decays continuously to a negligible amplitude at about one and a half rows upstream. This suggests that the flow perturbations are caused by the flow separation from the tube and the associated vorticity shedding and convection. The phase lag measurements between tube vibrations and flow perturbations support this conclusion, and show that the flow perturbations propagate upstream and downstream at different rates. Computational Fluid Dynamics modeling of the tube array was developed to assist in understanding the experimental results. The CFD models were validated using experimental data from both the literature and from the present research. It was found that there are two propagation mechanisms for the flow perturbations associated with tube vibrations. The first mechanism is caused by the pressure pulsation due to tube vibrations. This mechanism is dominant at lower reduced velocities, and propagates at the speed of sound. The second mechanism is caused by the flow separation and the associated vorticity shedding, and this mechanism is dominant at higher reduced velocities. The transition between the two mechanisms occurs at a reduced velocity of about (U_r≈2). Mathematical models of the flow perturbation phase lag and amplitude decay were developed. The new models were coupled with the semi-analytical model after modifying its geometrical parameters according to the flow visualizations in the literature. The resulting stability maps show a significant improvement to the current prediction of the fluidelastic instability data in the literature. The outcomes of the present work can contribute to improve the future design guidelines for tube and shell heat exchangers to achieve extended service time with higher efficiency.</p> / Doctor of Philosophy (PhD)