A constrained-mode analysis of the fluidelastic instability of a double row of flexible circular cylinders subject to cross-flow: A theoretical investigation of system parameters

Abstract

A new method of solution is proposed for a previously developed stability analysis of a double row of flexible cylinders subject to a fluid cross-flow. The double row of flexible cylinders may either be by itself or positioned in an array of rigid cylinders, the latter case being more representative of heat exchanger tube arrays. This new method of solution enables a long double row of fluid-dynamically coupled flexible cylinders to be adequately represented, from a stability viewpoint, by a two-cylinder kernel. This is done by prescribing a specific inter-cylinder modal pattern, and this is the reason for calling this the constrained-mode solution. A comparison of the critical flow velocities obtained via (i) this solution and (ii) the more complete long-row solution shows that the agreement between them is excellent. It is also shown that for some combinations of cylinder array geometry and mass-damping parameter the theoretical stability boundary of a single flexible cylinder surrounded by rigid cylinders is sensibly the same as that for a full array of flexible cylinders, the instability mechanism for these cases being virtually entirely due to negative fluid damping. However, for other cases where fluidelastic-stiffness effects are important, the flexibility of adjacent cylinders has a significant effect on the stability. The constrained-mode solution is capable of dealing with both of these instability mechanisms. By using the constrained-mode analysis, theoretical stability boundaries are obtained and compared with experimental data from similar cylinder arrays, plotted in terms of the critical reduced flow velocity versus the mass-damping parameter. Although the shape of the theoretical curve agrees well with the experimental data, theory consistently under estimates the experimental data points, by a factor of approximately 2. It is shown that the discrepancy may be partly due to small frequency differences between cylinders, which will inevitably be present in any cylinder array, raising the critical flow velocity of the experimental data points and bringing them closer to the theoretical values. This effect of frequency detuning is particularly important for high values of the mass parameter and low cylinder mechanical damping; however, it becomes less important for low values of the mass parameter and high values of cylinder mechanical damping.