Vortex tracking models: Data and results

Data

The vortex tracking models require the following data. See also the data common to all the time domain VIV models.

Maximum number of vortices logged

The maximum number of vortices that will be displayed and logged, for each side of the line. This only affects the display of vortices and does not influence the actual calculation. Its purpose is to give you some control over the size of the simulation file and the speed of drawing the 3D view. It takes the following values.

0 is the default value: vortices will not be logged or drawn. The simulation file is then as small as possible, and the replay as fast as possible. However the drawback of doing this is that you will not see any vortices on the 3D view.
'~' means 'log and draw all vortices'. There are typically up to several hundred vortices generated per node, and each vortex needs to log its position and strength so that it can be drawn on the 3D view, so this value can result in large simulation files and slow drawing.
An intermediate value, 30 say, allows you to see the youngest 30 vortices per side of the line: as new vortices are generated at the separation points, you will see the oldest vortices (typically now downstream) disappear from view. They have not been destroyed and are still accounted for in the calculation, but their position and strength are no longer available to the 3D view.

Model parameters

You can choose to use either the appropriate default set of values for these parameters or your own specified values. 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.

Vortex smear factor

This setting controls the degree to which vortices are smeared. The original Sarpkaya and Shoaff model used point vortices, i.e. the vorticity was concentrated at a single point. This is what arises in the formal mathematical solution of the inviscid Navier-Stokes equations (i.e. those ignoring fluid viscosity) but it means that each vortex is a singularity, since the vorticity density at the point itself is actually infinite. In reality, viscosity in the fluid spreads the vorticity to some extent, and we have found that the model is more stable if the vortices are smeared to reflect this.

The smear factor is non-dimensional. Very small values concentrate each vortex, while larger values spread the vorticity over a region surrounding the point. The default value is 0.1 and in our experience this gives reasonable performance; too high a value would be unrealistic. OrcaFlex will warn you if this value is more than 0.2.

Creation clearance

A non-dimensional value used only by model 2. At each time step the model creates two new vortices, one at each of the two separation points: this value controls how close to the disc surface these newly-created vortices are placed. They are positioned at the separation angle determined by the boundary layer model, and at a distance $\lambda r$ from the disc surface, where $\lambda$ is the specified creation clearance and $r$ the disc radius (= half the line outer diameter).

Creation clearance can also be set to '~', in which case the new vortices are placed using the model 1 algorithm. This sets the value of $\lambda$ such that the tangential velocity contribution of the new vortex at the separation point just cancels out the previous tangential velocity at that point.

Coalesce same, coalesce opposite

These are non-dimensional thresholds that are only used for coalescing in model 2. They control how close to each other two vortices have to be before they are allowed to be coalesced into one combined vortex.

There are separate threshold values for pairs of vortices with the same sign and opposite signs of vorticity. So if one of the two vortices is clockwise and the other is anti-clockwise, then the coalesce opposite threshold will be used; if they are both clockwise or both anti-clockwise, the coalesce same threshold is used.

Reducing the thresholds means that vortices will coalesce less often, so the model will have to keep track of more vortices and the simulation will therefore be slower. Conversely, increasing the thresholds makes the model coalesce more readily, so fewer vortices need to be tracked and the simulation is faster, but less accurate.

Our experience so far is that the default values of 0.04 for both thresholds gives a reasonable balance between performance and accuracy. If the mass ratio (= mass of line / mass of water displaced) is low then the fluid forces are more significant, and in these cases lower coalescing thresholds may be needed so that the fluid behaviour is more accurately modelled.

Vortex decay constant, vortex decay threshold 1, vortex decay threshold 2

These set the rate of vortex strength decay in both vortex tracking models. The decay model is described below. It is as in Sarpkaya and Shoaff's report (page 79) and the default values for these data are as given in that report. We therefore recommend that the default values be used unless you wish to experiment with other values, for example to calibrate the model.

Vortices are created with an initial strength determined by the tangential velocity at the separation point. The strength of each vortex then decays at a rate that depends on how far the vortex is away from the centre of the disc, in the relative flow direction.

Let $r$ be the disc radius (= half the line outer diameter) and $d$ be the distance, measured in the relative flow direction from the centre of the line to the vortex. In model 1, at each time step the vortex strength is scaled by a factor $\lambda$ which depends on $d$ as follows:

if $d \leq \text{DecayThreshold1}{\times}r \text{ then }\lambda = 1{-}\text{DecayConstant}$
if $d \gt \text{DecayThreshold2}{\times}r \text{ then }\lambda = 1$
if $\text{DecayThreshold1}{\times}r \lt d \lt \text{DecayThreshold2}{\times}r$ then $\lambda$ varies linearly with $d$, from $(1{-}\text{DecayConstant})$ to $1$

The effect of this is that while the vortex is less than DecayThreshold1 radii downstream then the vortex loses proportion DecayConstant of its strength (e.g. DecayConstant=0.01 means 1% decay) per variable time step. While the vortex is between DecayThreshold1 and DecayThreshold2 radii downstream its rate of decay falls linearly (with $d$) to zero. And when the vortex is more than DecayThreshold2 radii downstream then there is no decay.

Clearly DecayConstant must be in the range 0 to 1, and DecayThreshold1 must be less than DecayThreshold2. Note that DecayThreshold1 and DecayThreshold2 can be set to infinity. If either of them is infinity then $\lambda$ = 1-DecayConstant always, so the vortices always lose DecayConstant of their strength per variable time step.

The same decay model is used in model 2, except that the factor $\lambda$ is adjusted to allow for the fact that model 2 uses the outer time step instead of model 1's variable time step. The adjustment results in the same rate of decay per unit time.

Drag coefficients

The vortex tracking models include the drag effects in both the transverse and inline directions, but not in the axial direction. When either vortex tracking model is used, OrcaFlex therefore suppresses the components of the usual Morison drag force in the transverse and inline directions, but not in the axial direction. The drag coefficients for the normal directions are therefore not used, but the axial drag coefficient is used.

Results

The vortex force is available as a line force result which reports the total lift and drag force. This is the sum of the force generated by the vortex tracking model (which is in the inline and transverse directions and already includes the drag force in those directions) and the standard Morison drag force in the axial direction.

The stagnation and separation points are available as line angle results and transverse VIV offset as a line position result.