The drag coefficient for long-slender structures that is typically provided in design guidance has been determined from test specimens of sufficient length that they are unaffected by the aspect ratio (L/D), whereby they are considered to be of “infinite” length. However, it is apparent from the literature that aspect ratio does have a significant non-linear effect at short L/D ratios. DNV provides guidance on the aspect ratio effect on the drag coefficient of a cylinder, for which no experimental source data has been cited. The DNV design guidance has wide usage in the offshore industry and merits critical evaluation. This paper critically reviews the literature and presents the results of a series of tow tank experiments performed by the authors. A series of tow tank tests of a surface-piercing cylinder has been undertaken using a range of aspect ratios as well as testing the effect of various end conditions, where the effects of VIV and ventilation has been deemed insignificant. Correlation of the various data sets of the literature and the experimental test programme provides the basis for developing an alternate design guidance curve for the effect of aspect ratio on the drag coefficient of cylinders.

The prediction of Vortex-Induced Vibration (VIV) of cylinders under fluid flow conditions depends upon the eddy shedding frequency, conventionally described by the Strouhal Number. The most commonly cited relationship between Strouhal Number and Reynolds Number for circular cylinders was developed by Lienhard [1], whereby the Strouhal Number exhibits a consistent narrow band of about 0.2 (conventional across the sub-critical Re range), with a pronounced hump peaking at about 0.5 within the critical flow regime. The source data underlying this relationship is re-examined, wherein it was found to be predominantly associated with eddy shedding frequency about fixed or stationary cylinders. The pronounced hump appears to be an artefact of the measurement techniques employed by various investigators to detect eddy-shedding frequency in the wake of the cylinder. A variety of contemporary test data for elastically mounted cylinders, with freedom to oscillate under one degree of freedom (i.e. cross flow) and two degrees of freedom (i.e. cross flow and in-line) were evaluated and compared against the conventional Strouhal Number relationship. It is well established for VIV that the eddy shedding frequency will synchronise with the near resonant motions of a dynamically oscillating cylinder, such that the resultant bandwidth of lock-in exhibits a wider range of effective Strouhal Numbers than that reflected in the narrow-banded relationship about a mean of 0.2. However, whilst cylinders oscillating under one degree of freedom exhibit a mean Strouhal Number of 0.2 consistent with fixed/stationary cylinders, cylinders with two degrees of freedom exhibit a much lower mean Strouhal Number of around 0.14–0.15. Data supports the relationship that Strouhal Number does slightly diminish with increasing Reynolds Number. For oscillating cylinders, the bandwidth about the mean Strouhal Number value appears to remain largely consistent. For many practical structures in the marine environment subject to VIV excitation, such as long span, slender risers, mooring lines, pipeline spans, towed array sonar strings, and alike, the long flexible cylinders will respond in two degrees of freedom, where the identified difference in Strouhal Number is a significant aspect to be accounted for in the modelling of its dynamic behaviour.

This project investigates a cantilevered cylinder projecting down into the water column moving at high velocity through still water, as is applicable to submarine masts. Surface-piercing cylinders differ from fully submerged cylinders due to the generation of surface wakes and under increasing flow speeds the formation of a ventilated pocket in the lee of the cylinder, both of which grow with increasing velocity, with concomitant effects on the hydrodynamic loading. The relative length of submergence, or immersed aspect ratio (L/D) and end conditions of the cylinder with respect to tip vortex drag effects may also impact the hydrodynamic loads and wake formation. Laboratory testing of surface-piercing cylinders to date has predominantly been confined to characterising the wakes shed from a rigid cylinder cantilevered down into the water from a towing tank carriage, which under certain test conditions will also exhibit significant Vortex-Induced-Vibration (VIV), though not adequately identified and accounted for in its magnification of drag and wake.