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Wake oscillator models |
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Wake oscillator models |
OrcaFlex includes two wake oscillator models: the Milan model and the Iwan and Blevins model. These are two of many different wake oscillator models that have been proposed by many different authors. We selected these two models after reviewing the literature and testing a number of different models.
We found that there are errors in some of the published models and that many of the wake oscillator models contain disguised references to frequency domain concepts. This makes them difficult to implement in a true time domain analysis, unless additional assumptions are made.
A typical wake oscillator model is a heuristic model that uses a single degree of freedom, Q say, to represent the wake behind a rigid cylinder. It models the oscillation of the wake by Q being a function of time that obeys a differential equation that we will call the wake equation of motion.
The oscillation of the wake generates a lift force, i.e. a force that is normal to the cylinder axis and normal to the flow direction. The model gives the lift force magnitude as a function of Q, and this force is applied to the cylinder and so affects the motion of the cylinder. In return, the wake equation of motion involves terms that depend on the motion of the cylinder. This couples the wake equation of motion to the cylinder equation of motion, so together the two form a coupled nonlinear system.
The wake equation of motion is typically a nearly linear, second order, ordinary differential equation. It is not usually derived from physical laws, but is chosen to be one whose qualitative characteristics are known to be similar to VIV. For example there are differential equations that are known to have solutions that are oscillatory, self-generating and self-limiting.
The wake equation of motion involves parameters whose values are calibrated to match empirical results. This sort of modelling ethos is commonly known as an inverse method, by which one attempts to reproduce empirical data without recourse to the fundamental physics of the system. Rather, one simply writes down a system of equations that have the right sort of characteristics and then adjusts parameters in the equations to tune them to best match the empirical data.
Almost universally, wake oscillator models only give the lift force and say nothing about the effect of VIV on the drag force. The main aim behind the wake oscillator paradigm is to model the oscillating lift force.
Wake oscillator models are time domain models, so can only be used in an OrcaFlex time domain dynamic analysis. To apply a wake oscillator model to a line, select the model for that line's dynamics VIV.
When the simulation is run OrcaFlex creates and attaches a wake oscillator, of the selected model, to each node in the line. Each such oscillator then obeys the equations of the selected model. There is no linkage between the wake oscillators except through the structure. It is therefore effectively being assumed that the interaction between VIV at different levels occurs predominantly through the structure, not through the fluid.
The wake oscillator models have only a single degree of freedom: they only consider the transverse direction. Note that the transverse direction can change during the simulation, either because the line orientation changes or through wave motion changing the fluid velocity direction. When this happens the wake oscillator model is effectively being rotated; we make the assumption that this rotation does not significantly affect the wake.
The wake oscillator models require the flow velocity as input. In OrcaFlex this is taken to be the fluid velocity minus the filtered node velocity. This allows non-VIV motion, e.g. in a towed case, to contribute to VIV, providing its period is significantly longer than the filter period. The filtering is necessary to prevent the VIV motion itself feeding back into the input to the wake oscillator.
The input flow velocity includes the fluid velocity due to both current and any waves specified. The models can therefore in principle be used to model the effect of waves on VIV. However please note that the models were developed and calibrated for steady state conditions, so unsteady flow is outside their intended area of application.
The effect of inline drag amplification can be modelled by means of a table relating amplification factor to transverse A/D.
Both the Milan and the Iwan and Blevins models have various parameters that determine their properties. You can choose to use either the default set of values for these parameters or your own specified values.
Except for the initial value parameter, the default values are those given in the original Milan and Iwan and Blevins papers. If you choose to specify the parameters, then you have complete control over their values.
| Warning: | The specified parameters option has been provided principally to allow calibration of the model against other experimental results. If you are not doing this then we strongly recommend that you use the defaults. |
The following two model parameters are common to both wake oscillator models.
Any wake oscillator model is very heavily tied to the data set used to calibrate it. One must ensure that the relevant fluid dynamical and structural dimensionless parameters (for example, the Reynolds number) of the experimental set-up used to generate the data are sufficiently similar to that of the situation that one wants to model. Otherwise, one is relying on luck to provide the right answer. For example, to model the VIV of telephone wires in air, the data set should be obtained from a wire vibrating in a wind tunnel. The experimental data are usually obtained from a system with a constant fluid in-flow speed, so one cannot expect the model to be applicable for currents that vary over the same time scale as that due to VIV. If the current variation is sufficiently slow then the model should be valid.
In general, the authors of wake oscillators make no attempt to model the start-up of VIV. This is due to the nature of the devised mathematical model. The modelling method used exploits the fact that the solution phase space of the system contains limit cycles that correspond to stationary VIV. The parameters are set so that the limit cycles have the right radius and that the system state tracks around them with the right frequency. To find the non-stationary dynamical behaviour of the system far away from such critical regions in the phase space is extremely difficult without simply integrating the equations of motion.