Results from numerical simulations of flow at high Reynolds numbers around cylinders and associated forces are presented. The numerical model is based on the discrete vortex model combined with an integrated boundary layer model. Hereby it has become possible to include the influence of the pipe roughness on the flow and the associated forces. The paper summarizes the theoretical basis for the model, including the boundary layer part and a simple approach for including the diffusion of rotation. Results obtained from the simulations with arrays of 2, 4 and 8 cylinders are presented. Steady flow and oscillatory flow cases are covered.
An extensive amount of experiments to determine hydrodynamic loads on single cylinders has been carried out and reported in the literature. Within the last decade or so, increasing attention has been given to the determination of forces on more complex structures, such as riser bundles (Ottesen Hansen et al /1/, Overvik et al /2/), conductor arrays (Heideman and Sarpkaya /3/), and the complex joints of steel jackets (Velk and Sterndorff /4/).
When a cylinder is located in the downstream wake of another the force on the rear cylinder is typically smaller than on the one in front. This phenomenon is often referred to as 'shielding effect'. If, on the other hand, the same two cylinders are placed side by side in close proximity, the total force on the two becomes larger than the sum obtained from two isolated cylinders. This is referred to as 'blockage effect' or 'negative shielding effect'.
Model tests and full scale measurements on jacket type structures have clearly demonstrated the shielding effects in steady current flows, see e.g. Lambrakos et al /5/, and Cuffe et al /6/. Reductions in total loads of up to 40 - 60 percent were found for structures with large conductor arrays. In wave flows, the shielding effects may be less significant, Cuffe et al /6/, Sterndorff et al /7/.
The blockage effect was demonstrated for the simple 2 cylinder case by Jacobsen et al /8/. A system with a small and large pipe in close proximity resulted in load increases of up to 85 percent as compared to a 25 percent increase in exposed area for the side by side arrangement. For the tandem arrangement the total load was smaller than the load on the large pipe alone.
For groups of cylinders it is not trivial to evaluate whether the total force becomes smaller or larger compared with the situation where the cylinders are separated. Depending on the flow conditions and flow angle a group of cylinders may exhibit increase as well decrease in load compared to the separated cylinder case. Individual cylinders in a group will experience reduced load, others increased load. Detailed analyses and testing are required to assess the loads on cylinder groups.
In the present paper numerical results are presented for total and individual loads for systems containing 2, 4 and 8 cylinders.