Session: 08-06-02: VIV of Flexible Risers and Cables

Paper Number: 79469

79469 - Flow Around Curved Tandem Cylinders 

Curved cylindrical bodies are an important part of offshore technology. Curved cylinders, a simplified representation of catenary risers, has been the object of several studies in recent years, but little effort has been directed towards the investigation of multiple curved cylinders. In the present study, the flow around two curved cylinders in tandem has been investigated at a Reynolds number of 500, by means of direct numerical simulations (DNS). To our knowledge, this is the first investigation of curved tandem cylinders.

The upstream cylinder has a radius of curvature of rc=12.5 diameters (D). In order to ensure a constant gap ratio along the entire geometry,a steeper curvature of rc= 9.5 D was chosen for the downstream cylinder. However, one of the challenges of a curved tandem cylinder setup is that regardless of the inflow direction, the effective gap ratio will vary along the curved part of the cylinders. To avoid influence of the domain boundaries, the curved cylinders were fitted with straight extensions of 7 D and 15 D in the vertical and horizontal directions, respectively. The convex configuration was chosen, with uniform inflow perpendicular to the vertical extension. For validation, single curved cylinders at the same rc’s were also studied.

 

Our results show that there is a variation of flow regimes, even along the straight vertical extension, which is induced in part by the variation of effective gap ratio and in part by the induced axial velocity due to the curvature. The flow varies from a hybrid overshoot/reattachment type at the top of the straight extension to co-shedding in the curved part of the gap.

 

At this Reynolds number, the wake is turbulent and highly three-dimensional. Similar to straight tandem cylinder arrangements, the Strouhal number (St) is the same for both cylinders, based on the crossflow force spectrum, as well as spectra of velocity time traces in the gap and wake. But, whereas the downstream cylinder has a clear dominant peak at St, the upstream cylinder force spectrum does not. It is characterized by several low frequency peaks of the similar magnitude as the St peak, which in itself has significantly lower energy than its downstream cylinder counterpart.

 

Although there is a variation of regimes along the cylinders, the drag coefficients share the overall trend with straight tandem cylinders in the reattachment regime. This means that the upstream cylinder Cd is positive and significantly larger than the downstream cylinder Cd. Due to recirculation in parts of the gap region, the pressure forces on the downstream cylinder are negative. However, contribution from viscous forces, mainly on the horizontal extension, yields a positive, albeit very small, Cd.

 

The wake is bounded by the curved cylinder and its straight horizontal extension on one side, which influences the development of the large-scale vortices and their orientation. Slanting of the vortices in the vertical direction is seen, similar to curved single cylinders. There seems to be a stronger presence of vortex dislocations in the tandem arrangement than for the single curved cylinder validation cases. At this Reynolds number, the wake is characterized by a mode B instability, causing streamwise vortices to develop in the regions between the large scale vortices. Comparing with the single curved cylinders, we see that there are less of these structures in the tandem wake, due to enhanced diffusion induced by the presence of the downstream cylinder.

Vortices are shed from the upstream cylinder curved section into the horizontal part of the gap, and these interact with both cylinders as they are convected downstream. This flow exhibits strongly three-dimensional swirling eddy patterns.

 

 

Presenting Author: Tale Aasland The Norwegian Unversity of Science and Technology

Authors:

Tale Aasland The Norwegian Unversity of Science and Technology
Bjørnar Pettersen The Norwegian University of Science and Technology - Department of Marine Technology
Helge I. Andersson The Norwegian University of Science and Technology - Department of Energy and Process Engineering
Fengjian Jiang SINTEF Ocean - Department of Ships and Ocean Structures