Line data: Fluid loads

Drag formulation

A number of authors have proposed formulae to model the way in which drag force on a line varies with the incidence angle. OrcaFlex offers a choice of three formulations, standard, Pode and Eames, which are described in detail under line theory. All use the drag coefficients defined on the line types data form.

The drag formulation chosen applies to the whole line. The remaining data on this page are specified on a section-by-section basis so they can, if required, be applied to only particular parts of a line. Sea state disturbance and wake interference effects can be rather demanding in computational terms; by enabling them only for sections of line where you expect them to be significant, you can make large savings in simulation time.

Disturbance vessel

Determines whether a line section will experience sea state disturbance generated by a particular vessel.

Line wake interference

To model wake interference you must first define one or more wake interference models. You then choose which line sections to include in wake modelling: each section may

define a wake generated (an upstream section)
be defined to react to wake (a downstream section)
do both of these (a downstream section that reacts to wake generated further upstream, but also generates its own wake that further downstream sections might react to).

These data items are defined in more detail below.

Note:

Wake modelling does not include the wake effect of one part of a line on another part of the same line – it only includes wake effects on other lines. To model the wake effect of one part of a catenary on another part beyond the sag bend, for instance, you need to model the catenary as two distinct lines, joined at the sag bend.

How wake effects are modelled

Wake is generated downstream of an upstream cylinder, representing an OrcaFlex line segment, when there is fluid velocity relative to the upstream cylinder. Both fluid motion and upstream cylinder motion can therefore contribute to the wake. The steady relative velocity $\vs$ is given by \begin{equation} \vs = \text{[undisturbed current velocity vector at upstream cylinder centre]} - \text{[model starting velocity]} \end{equation} The wake models are steady state models of wake effects. They do not, for instance, model the time taken by wake to convect downstream, nor do they include any effects of wave motion or of any changes in upstream cylinder velocity during a simulation. The only effect of the upstream cylinder velocity comes from any steady starting velocity.

Note:

OrcaFlex does not model combined wake effects. If a given downstream node is in the modelled wake of more than one upstream node, then OrcaFlex chooses to apply the wake effects of the upstream node that gives the strongest wake effect at that downstream position when the wake effects from other upstream nodes (which give weaker wake effects at that point) are ignored. So if you are modelling riser arrays, for example, then the wake effects at any given point are modelled as if they came from the upstream wake-generating node that gives largest wake effect in isolation, i.e. as if the other upstream nodes were absent.

The strength of a given node's wake decays with distance downstream and with distance in the transverse direction, as defined by the specific wake model. In addition, OrcaFlex reduces the wake strength in the axial direction of the upstream line, so that the strongest wake selected comes from the upstream node that is axially closest to the downstream node. More details are given in the paper by wu et al.

Line wake interference data

Wake generated

Choose here one of the defined wake models to have OrcaFlex model wake generated by that line section acting as an upstream line, or select (none) to have no wake generated by that line section.

Three types of wake model are available.

The Huse model is an analytic wake model that models the velocity reduction and hence drag reduction on the downstream object, but does not include any lift effects.
Blevins' is an analytic model that models the both the drag reduction and the wake lift force that tends to draw the downstream object into the centre of the wake.
A user specified model allows you to define your own drag and wake lift coefficients as a function of position of the downstream object relative to the wake of the upstream object.

See wake models below for more details of each of these models.

Reacts to wake

If a line section reacts to wake, then each node in the section will act as a downstream cylinder in the wake model. Each node will be subject to the strongest wake effect (i.e. strongest at that downstream position) from any upstream nodes on other lines that generate modelled wake. Sections with reacts to wake turned off will ignore any modelled wake generated by upstream sections.

So to summarise, the wake modelling will include the strongest wake effects on downstream sections that react to wake turned on, due to modelled wake from upstream nodes in sections of other lines for which a wake model is selected for wake generated.

Notes:

While a line section is allowed to be both a downstream section (reacts to wake) and at the same time act as an upstream section (generates wake), the wake effect will be based on the undisturbed steady relative flow velocity, so the wake effects of this wake-generating section will not take into account any velocity reduction due to it in turn being subject to the wake of another wake-generating section further upstream.

OrcaFlex does not model multiple wake effects. If a given downstream node is in the modelled wake of more than one upstream node, then OrcaFlex chooses to apply the wake effects of the single upstream node that gives the strongest wake effect at that downstream position. So if you are modelling riser arrays, for example, then the wake effects at any given point are modelled as if they came from the upstream wake-generating node that gives largest wake effect in isolation, i.e. as if the other upstream nodes were not generating any wake.

Wake models

The wake model data form enables you to define one or more models of wake interference. You can open this data form with the wake models button on the line data form or, once you have at least one wake model defined, from the model browser.

Each wake interference model defines the way in which the flow velocity, wake drag reduction and wake lift force on a downstream cylinder vary as a function of the $(x,y)$ position of the downstream cylinder centre relative to the wake frame of reference of the upstream cylinder.

You can define more than one wake model. You might, for example, want to use different wake models for different lines. A wake model that is not used by any line in the model will simply be ignored, so you can define wake models and then decide later which (if any) to use to model wake generation.

Wake frame of reference

The wake models use a frame of reference based on the steady relative fluid velocity vector, $\vs$, at the upstream cylinder, defined as follows:

origin at the upstream cylinder centre
$x$-axis in the direction of $\vs$
$z$-axis obtained by projecting the upstream cylinder axial direction normal to $\vs$. It is therefore the direction normal to $\vs$ and in the plane formed by $\vs$ and the cylinder axis. $z$ is positive towards end B of the upstream line.
$y$-axis in the direction that completes the orthogonal right-hand triad of wake axes $x,y,z$, so normal to the plane formed by $\vs$ and the cylinder axis

Wake model data

Each wake model is given a name, and is defined as being one of the available types, Huse, Blevins or user-Specified, described below.

Huse model

Huse (1993) proposed a model for wake velocity reduction, and hence drag reduction, but which does not give any wake lift force. The model uses the following key variables. Upper case subscript $\mathrm{D}$ denotes drag, lower case subscripts $\mathrm{u}$ and $\mathrm{d}$ indicate upstream and downstream, and subscript $0$ denotes undisturbed, i.e. ignoring any wake effects.

$v_\mathrm{d}(x,y)$ is the disturbed fluid velocity vector at downstream position $(x,y)$ relative to the upstream cylinder wake, allowing for wake effects.
$v_\mathrm{d0}(x,y)$ is the undisturbed fluid velocity vector at position $(x,y)$.
$v_\mathrm{u0}$ is the undisturbed fluid velocity at the upstream cylinder centre.
$d_\mathrm{u}$ and $C_\mathrm{Du}$ are, respectively, the normal drag diameter and undisturbed drag coefficient of the upstream cylinder, as given on the line type data form. Note that the wake modelling does not allow for any non-isotropic aspects of the drag coefficients. If the $x$ and $y$-drag coefficients differ, the $x$-value is used for the wake model.

The disturbed velocity $v_\mathrm{d}(x,y)$ is then given by \begin{equation} v_\mathrm{d}(x,y) = v_\mathrm{d0}(x,y) - k_2 v_\mathrm{u0} \left(\frac{C_\mathrm{Du} d_\mathrm{u}}{x_\mathrm{s}}\right)^{1/2} \exp\left( -k_3 \left(\frac{y}{b}\right)^2 \right) \end{equation} where

$x_\mathrm{s} = x + 4 d_\mathrm{u}/C_\mathrm{Du}$

$b = k_1\left(C_\mathrm{Du} d_\mathrm{u} x_\mathrm{s}\right)^{1/2}$

The constants $k_1$, $k_2$ and $k_3$ are user-editable non-dimensional model parameters. They should normally be left as the default values to represent the original Huse model. Changing these model parameters from their default values will give a variant of the Huse model. (The parameter $k_3$ was misprinted in Huse, 1993 as 0.639 and was corrected in a later paper to 0.693.)

Blevins model

The Blevins model is an analytic model that models velocity and drag reduction, and also includes the wake lift force that tends to draw the downstream object into the centre of the wake. See the appendix of Blevins OMAE 2005 paper for the theory of the model, which we do not reproduce here.

Blevins' model has three non-dimensional model parameters $a_1$, $a_2$ and $a_3$, and these are user-editable. They should normally be left as the default values, since these are the values given by Blevins; changing these values from their defaults will give a different model.

User specified model

As an alternative to these analytic models, you may instead define a model (incorporating both wake drag reduction and wake lift effects) by specifying drag and lift coefficient factors as a function of the position of the downstream object relative to the wake of the upstream object.

The wake effects are defined in a table of drag and lift coefficient factors for the downstream cylinder, as a function of the downstream cylinder position relative to the upstream cylinder wake, as follows. Here, we again use $d_\mathrm{u}$ to represent the normal drag diameter of the upstream cylinder, and we introduce $C_\mathrm{Dd}$, the undisturbed (or reference) drag coefficient of the downstream cylinder, and $C_\mathrm{Ld}$, the reference lift coefficient of the downstream cylinder.

The position columns of the table define, in non-dimensional form, a number of downstream positions relative to the upstream cylinder wake frame of reference. These positions are given by non-dimensionalised distances $\mathbf{L/d_u}$ (downstream) and $\mathbf{T/d_u}$ (transverse) from the upstream cylinder centre.
The coefficient factor columns of the table define the wake effects at the given $(L/d_\mathrm{u}, T/d_\mathrm{u})$ positions, in terms of coefficient factors for drag and lift. These are scaling factors, not the drag and lift coefficient values themselves. The drag scaling factors are applied to the reference drag coefficient $C_\mathrm{Dd}$ of the downstream cylinder, as given on the line type data form. The lift factors are signed scaling factors that are applied to the reference wake lift coefficient $C_\mathrm{Ld}$ given on the wake models data form. A positive lift coefficient factor means a lift force in the positive wake frame $y$-direction, so (since wake lift effects are normally towards the centre line of the wake) the lift coefficient factor at a given $T/d_\mathrm{u}$ position will normally have the opposite sign to the $T/d_\mathrm{u}$ value.

OrcaFlex uses linear triangular interpolation to obtain drag and lift coefficient factors for wake frame positions between those specified in the table.

Note:

The drag coefficient factors can be negative, representing flow reversal at that position in the wake. This can happen, and indeed the Blevins model can predict flow reversal just behind the upstream cylinder. The drag factors must not be greater than 1, however, and so flow enhancement cannot be modelled.

Wake drag effects are normally symmetric, and wake lift effects anti-symmetric, either side of the wake centre line. So, to avoid the need to supply both positive and negative values of $T/d_\mathrm{u}$ in the table, you can tell OrcaFlex to reflect data. In this case you must only give table rows for one half of the wake plane, i.e. either for $T/d_\mathrm{u} \geq 0$ only, or for $T/d_\mathrm{u} \leq 0$ only. OrcaFlex will then automatically reflect all your data points that are not on the wake centre line, by internally duplicating them and negating $T/d_\mathrm{u}$ and the lift coefficient, and will then interpolate over that new combined data set, which now covers both sides of the wake centre line.

Note:

Data reflection will not in general give perfectly symmetric response characteristics: the interpolation involves triangulation of the data, and that triangulation might not be symmetric either side of the wake centre line. However any lack of symmetry will be proportional to the spacing of the points you specify in the data - the closer the data points, the better the symmetry.