A generalized constrained-mode analysis for cylinder arrays in cross-flow

Abstract

For cylinder arrays subject to cross-flow, the fluid dynamic and mechanical coupling between cylinders has an important effect on the fluidelastic stability of the array, especially for high values of non-dimensional mass-damping, mδ / ρd 2 . Due to the large number of cylinders in heat exchanger tube banks, this coupling results in coupled matrices prohibitively large from a computational point of view. To overcome this problem, the constrained-mode method of analysis was developed, which allows a very large array of cylinders to be represented in a stability analysis by a kernel of a small group of cylinders. The disadvantage of this constrained-mode method is that it assumes adjacent cylinders to be moving either in-phase or out-of-phase with each other, but nothing intermediate. In the present paper the above restriction is relaxed, such that adjacent cylinders can have any phase angle between their respective displacements. Using this form of the constrained-mode analysis, the stability of in-line square, rotated square and rotated triangular arrays has been investigated. It is shown that for sufficiently high values of mδ / ρd 2 (the exact value depending on the type of array) the phase angle between the displacements of adjacent cylinders can have an important effect on the stability. Not only can it change the flow velocity at which instability will occur, but for some arrays it can also change the inter-cylinder mode shape from being predominantly in the cross-flow direction to being predominantly in the in-flow direction.