The prediction of Vortex Induced Motion (VIM) of compliant offshore structures such as Spars is one of the most challenging areas in the offshore industry. It has been observed that though, numerous experimental and numerical studies have been conducted in an effort to improve the understanding of this phenomenon, the outcomes still often appear incoherent. Models and data, where available, are often proprietary and understandably being kept confidential (because of the cost involved). Presented here is a new Semi-Empirical Method, a wake oscillator model derived assuming span-wise constant flow velocity, in which attempts were made to replicate or capture the flow phenomena observed in VIV experiments. The model involves coupling, through a displacement parameter, two non-linear equations namely, the Duffing equation and the Van der Pol equation. Steady state harmonic solutions were sought for the resulting system of non-autonomous nonlinear differential equations through Multiple Scale (Many- Variable/Derivative Expansion Procedure approach) Perturbation theory, an asymptotic method developed by Nayfeh (1968). Three scenarios usually encountered in VIV were examined in this work, (1) for a Cylinder mounted rigidly, (2) for a Cylinder mounted elastically [i.e. free], and (3) for a Cylinder mounted elastically and forced externally. Of most interest is the unforced rigid cylinder mounted elastically, as it forms the basis of VIV/VIM problem formulation for floating structures such as Classical and Truss Spars. Among other analysis carried out, the new model was used to investigate the effect of nonlinearity in the stiffness coefficient of the system of an elastically mounted rigid cylinder and to study its contribution to the hysteresis (jump) phenomenon. Over all the model demonstrated adequate qualitative and quantitative results for phenomena A Semi-Empirical Model for Vortex Induced Motion of a Cylinder normally observed in a VIV experiment, such as a clear resonance peak, a lock-in range, and the structure phase lag(φ) passing through lock-in with an overall phase jump of π. The uniqueness of the present model could be stated as follows: Firstly it is not dependent on lift and drag coefficients data as usually obtained from forced VIV experiments, demerits of which have been clearly stated in this work. Secondly, inputted Strouhal parameter has not been fixed to the subcritical value of 0.2, as have been done in all the other VIV models. But rather in the present model it has been obtained from a well established Strouhal-Reynolds relationship estimated from the data of Morkovin (1964) and Lienhard (1966) which have been expanded to an extremely high range of Reynolds number regime of Re = 4.5 x 10 7 based on vortex shedding data obtained from the Space Shuttle Solid Rocket Motor during re-entry, therefore making the model to be directly applicable in real engineering scenario. Thirdly, all the empirical parameters used have been clearly defined with expressions linking such parameters to the physical mass and damping parameter that governs the oscillatory response. The present model has been successfully utilized in the prediction of other systems resulting in very good qualitative and quantitative correlations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:578551 |
| Date | January 2011 |
| Creators | Aboyeji, Ayodele Oluseye |
| Publisher | University of Newcastle Upon Tyne |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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