Interaction In Deep-Sea Riser Arrays
Authors: Huse Erling 
Published: October 2008

SUMMARY
When designing tension leg platforms (TLPs) for very deep waters the current force cm the risers may become an important aspect of the design considerations. The present paper describes a simple calculation procedure, based on wake and momentum considerations, for predicting the current force on each individual cylinder in an array of cylinders. The procedure is verified quite well by comparison with available experimental result.
As a next stage the procedure is used for calculating the mean (static) deflection of each riser in the riser system of TLPs. A typical application is to determine necessary pretension or spacing to prevent the risers from colliding with each other. Based on systematic calculations criteria for the on-set of collision between risers of equal diameter and pretension are formulated and expressed in a single formula. Interaction between risers of different diameters, such as a drilling riser operating in between the production risers, can also be studied by the calculation procedure.

1. INTRODUCTION
Practical evaluation of drag forces on arrays of cylinders has so far been based on experiment data, see for instance Refs. 1 and 2. Considerable efforts have in recent years been spent cm developing numerical procedures based on calculating the shedding and development of individual vortices in the wake flow and corresponding forces on cylinders. survey of such methods see for instance Ref.3. In spite of recent progress these methods are still far from representing suitable tools in practical engineering work with TLP riser arrays, which may contain as many as 50 or more individual risers.
As a stage in between the purely empirical data and the vortex methods we have a group of methods based on considering the wake as a turbulent flow field, neglecting the effect of individual vortices. Such considerations have been applied in Refs.4, 5, 6, and 7 with considerable success, in some cases even for oscillatory flow.
The objective of the present publication is to present and verify a simple calculation procedure for predicting current loads on individual cylinders in an array of cylinders. The procedure is based on the theory of turbulent wakes together with momentum considerations. Such a method is expected to work very well at large spacings between the cylinders. For very dense arrays (center-to-center spacings of for instance 2 to 3 diameters) one would expect the wake consideration alone to fail due to potential flow effects as well as the effect of individual vortices. A correction for the potential flow effect is therefore incorporated in the method.
The basic principles of the procedure were first published in Ref.8, then limited to in-line force and rigidly supported cylinders in fixed positions. In the present paper the theory is extended to include the mean transverse force on the cylinders. Furthermore the calculation procedure is extended to include calculation of the static deflection of each riser in the array. Typical applications are determination of necessary pretension and spacing to prevent collision between individual risers, optimization of the pretension of a drilling riser operating within an array of production risers, position stability of individual risers, etc.