OrcaFlex Manual - Orcina

System Modelling: Data and Results, 6D Buoys
Drag Coefficients for Translational Motions
408
w
These are obtained from ESDU 71016, Figure 1 which gives data for drag of isolated rectangular blocks with one
face normal to the flow. The dimensions of the block are
a in the flow direction
b and c normal to the flow direction (c>b).
The figure plots drag coefficient, Cx against (a/b) for (c/b) from 1 to infinity (2D flow). Cx is in the range 0.9 to 2.75
for blocks with square corners.
Note: ESDU 71016 uses Cd for the force in the flow direction; Cx for the force normal to the face. For
present purposes the two are identical.
Drag Properties for Rotational Motions
There is no standard data source. As an approximation, we assume that the drag force contribution from an
elementary area dA is given by
dF = ½.ρ.V 2 .Cd.dA
where Cd is assumed to be the same for all points on the surface.
Note: This is not strictly correct. ESDU 71016 gives pressure distributions for sample blocks in uniform
flow which show that the pressure is greatest at the centre and least at the edges. However we do
not allow for this here.
Figure: Integration for rotational drag properties
O
Z
Consider the box rotating about OX. The areas Ay and Az will attract drag forces which will result in moments about
OX. For the area Ay, consider an elementary strip as shown:
For an angular velocity ω about OX, the drag force on the strip is
dF = ½.ρ.(ωz).|ωz|.Cd.x.dz
and the moment of this force about OX is
dM = ½.ρ.(ωz).|ωz|.Cd.x.dz.z = (½.ρ.ω.|ω|.Cd).x.z 3 .dz
Total moment is obtained by integration. Because of the V.|V| form of the drag force, simple integration from -Z/2 to
+Z/2 gives M = 0. We therefore integrate from 0 to Z/2 and multiply the answer by 2. The result is
M = (½.ρ.ω.|ω|.Cd).(x.z 4 /32)
OrcaFlex calculates the drag moment by
so we set
M = (½.ρ. ω.|ω| .Cdm).(AM)
z
dz
X