Torsional wake stiffness and the dynamic response of tethered tandem cylinders in the subcritical and critical regimes

Abstract

This study experimentally investigates the stationary and dynamic characteristics of a tandem cylinder configuration in which the downstream cylinder is confined to rotate about a pivot point centered at a fixed upstream cylinder with a specified cylinder-to-cylinder spacing. Results were obtained for Reynolds numbers 1.3 × 10 4 ≤ Re ≤ 1.4 × 10 5 , cylinder spacings ℓ = L / D = 2 , 4 , and, for the dynamic case, mass ratios 0.5 ≤ m * ≤ 2. The positional dependence of the quasi-static moment of the fluid forces on the downstream cylinder about the pivot point was determined by measuring the torque required to hold the downstream cylinder stationary. This moment data were subsequently used to evaluate the validity of using a torsional wake stiffness model to predict the frequency response of a freely oscillating tethered cylinder. This model assumes the wake of the upstream cylinder acts as a linear torsional spring, generating a restorative moment that drives the downstream cylinder to the upstream cylinder’s wake centerline. In the subcritical regime, 1 × 10 4 ≲ Re ≲ 9 × 10 4 , the wake stiffness model predicts the system frequency with reasonable accuracy, with results being best for larger mass ratios. A fundamental change occurs for the critical regime with Re ≳ 1.0 × 10 5 . For ℓ = 4 , the frequency response drops off and then becomes negligible for Re ≳ 1.2 × 10 5 . For ℓ = 2 , the slope of the stationary moment changes sign, creating a regime of “negative stiffness” near the wake centerline, and the dynamic system maintains robust, high-amplitude limit-cycle oscillations, in contrast to the ℓ = 4 case. For both spacings, the wake stiffness model is not accurate in the critical flow regime. These findings suggest that for Re ≳ 1 × 10 5 , the wake-structure interaction may be governed by unsteady, motion-dependent fluid dynamics that necessitate a fully dynamic energy approach for accurate prediction.