Experiments on the flow around two tandem circular cylinders from sub-up to transcritical Reynolds numbers

Abstract

Measurements were taken on two tandem circular cylinders in cross flow for Reynolds numbers from subcritical up to transcritical values (2 · 105 ≤ Re ≤ 6 · 106). The tandem arrangement with small spacing S = 1.56 d (d: diameter of the cylinders) represented a twin cable assembly of the main cable of the Messina Bridge. The tests were carried out in a special facility for high Reynolds numbers, the DNW High Pressure Wind tunnel in Göttingen. The steady forces on both cylinders were measured using a two-sided strain gauge balance. The wake profiles were taken by a pressure rake. At the angle of incidence α = 0◦ the appearance of the drag-curve Cd1 depending on Re for the front cylinder is similar to the behavior of a single smooth circular cylinder. The shape of the corresponding curve Cd2 of the downstream cylinder resembles the inverse of the upstream one with negative drag in the subcritical and transcritical Rerange. The critical Reynolds number regime is around Rec ≈ 4· 105. Here, the drag on the second cylinder changes sign from Cd2 ≈ -0.4 to +0.4. Further, asymmetric flow, reflected in steady lift Cl2 ≈ 1, was observed. The supercritical regime is followed by the upper transition, after that, the transcritical range begins at Re ≈ 3.5· 106. In that case a second drag inversion occurs, that is coupled with a change of the topological structure of the flow and thus can be a source of instability. In all relevant Reynolds number ranges for both cylinders curves of the force/moment coefficients were created, i.e. the dependence of these coefficients upon α. These curves for the sub-, super-, and upper transition as well as for transcritical Reynolds numbers are strongly nonlinear in nature with a curved character, pronounced extrema, and zero-crossings. In the subcritical case there are, in addition, hysteretic jumps of lift and drag. For all Reynolds number ranges investigated, we found that for the rigidly coupled tandem cylinders, the derivative of the global lift (around α = 0◦) is negative and the corresponding Den Hartog criterion indicates instability.