Strouhal Number for VIV Excitation of Long Slender Structures

Abstract

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.

State-of-the-Art Review of Vortex-Induced Motions of Floating Offshore Wind Turbine Structures

“…The Strouhal number is sensitive to the Reynolds number and surface roughness ratio. Figure 4 presents the Strouhal number versus Reynolds number relationship for a circular cylinder [12]. The so-called 'camel hump' (abrupt increase of St) develops in the high Re (Re > 1 × 10 5 ) region.…”

“…The original St versus Re curve as collated by[13] seen in the background in gray. The open circles denote the bulk of the data discussed and presented in[12,14] relating to Strouhal number, where the squares are some of the data, which were referenced by Lienhard in the development of the St versus Re curve. Figure from[12,14].…”