Hydrodynamic Forces On Various Multiple-Tube Riser Configurations
Authors: Sarpkaya T. 
Published: October 2008

ABSTRACT
The interference effect in steady and time-dependent flows is briefly reviewed and the drag and inertia coefficients for two particular riser configurations subjected to harmonic flow are presented.

INTRODUCTION
A body's resistance to flow is strongly affected by what surrounds it. When two bodies are in close proximity, not only the flow about the downstream body but also that about the upstream body may be influenced Examples include condenser tubes in heat transfer, variety of columns in pressure suppression pools of nuclear reactors, risers, piles, and other tubular structures in offshore engineering, turbine and compressor blades in mechanical or aerospace engineering, and high-rise buildings, cooling towers, and transmission lines in civil engineering. The quantification of the interference effects in terms of the pressure distribution, lift and drag forces on individual members, vortex shedding frequency, and the dynamic response of members of the array in terms of the governing flow and structural parameters constitute the essence of the problem.
There are infinite numbers of possible arrangements of two or more bodies positioned at right or oblique angles to the approaching flow direction. Numerous experiments, often prompted by the need to solve problems of immediate practical interest, provide data on the force transfer coefficients. But the intrinsic nature of the phenomenon still remains a mystery.
A careful review of flow interference between two circular cylinders in various arrangements in steady flow has been presented by Zdravkovich where an extensive list of references may be found. Numerous studies have shown that the changes in drag, lift and vortex shedding are not necessarily continuous. In fact, the occurrence of a fairly abrupt change in one or all flow characteristics at a critical spacing is one of the fundamental observations of flow interference in cylinder arrays.
For the tandem arrangement (one cylinder behind the other), it has been shown that at relative spacings SID &lt; 3.5 there is a strong mutual interference between the two cylinders. This critical distance increases with the bluffness of the cylinders. For two plates in tandem, the critical spacing is about 10 times the plate width.2 In general, the tandem arrangement has a strong effect on the drag and is sensitive to spacing. The upstream cylinder takes the brunt of the burden and the total drag for the group is smaller than the sum of the drag forces acting on each cylinder in isolation in a tunnel with the same blockage. The drag coefficient for the downstream cylinders is reduced partly by shielding and partly by the occurrence of earlier transition in the boundary layers due to the turbulence in the approaching flow.
The side-by-side arrangement exhibits a discontinuity in the flow and measured forces for spacing ratios smaller than a critical value (SID &lt; 2.2 for two circular cylinders and about 4 for two plates). The observed discontinuity (a switching phenomenon and bistable nature of the flow between the plates) results in two values of the drag coefficient.