Tower, nacelle and kernel widths

Tower and nacelle forces are off unless asked for, in either rotor mode. Each kind of point has its own kernel width, in cells of the anchor level’s dx, and each body has its own set.

Tower

With num_force_points_tower > 0 OpenFAST is asked for that many tower force nodes, base to top.

• AeroDyn computes the drag from the velocities ERF samples at the tower nodes. TwrAero must be on. The stub applies a cylinder drag with its own tower_diameter and tower_cd.

• ERF spreads each node’s force with width epsilon_tower, so the tower wake and its shadow on the rotor appear in the flow.

• AeroDyn’s TwrShadow would count the shadow twice. ERF reads it and warns when it is not 0.

Nacelle

With nacelle_cd > 0 and nacelle_area, ERF adds one drag point at the hub node:

\[\mathbf{f} = -\tfrac{1}{2}\,\rho\, c_d\, A\, |\mathbf{u}_c|\,\mathbf{u}_c, \qquad \mathbf{u}_c = \mathbf{u} \Big/ \left(1 - \frac{c_d A}{4\pi\epsilon_n^2}\right).\]

• \(\rho\) is the body’s air_density, \(c_d A\) = nacelle_cd × nacelle_area and \(\epsilon_n\) = epsilon_nacelle in metres.

• \(\mathbf{u}\) is sampled at the hub node, also with sampling = upstream.

• A Gaussian force of width \(\epsilon_n\) lowers the velocity at its own centre by the factor \(1 - c_d A/(4\pi\epsilon_n^2)\), so the sampled velocity is divided by it. This is the correction Kynema applies with its own nacelle width.

• The run stops when the factor is under 0.5.

The tower force and the nacelle drag are logged with the thrust. The integrated momentum source equals minus their sum.

Choosing the widths

Key	Applies to	Guidance
epsilon	Line nodes, disk rings, ct_disk points	Line: fixed length, 0.035 D. Corrected disk: \(\epsilon \le 0.5 R\). The FLLC and the disk correction both use this width.
epsilon_tower	Tower force nodes	About \(2.8\, c_d d\) keeps the drag about 10 % low (some 23 m for an 8 m tower).
epsilon_nacelle	Nacelle drag point	Factor \(1 - c_d A/(4\pi\epsilon_n^2) \ge 0.8\) on two or more cells.

Unset, epsilon_tower and epsilon_nacelle take epsilon. Bodies may use different widths, for example a narrow actuator line beside a wide actuator disk; their sources add on the same fields. The widths are part of the restart record.

Tower width

A tower node samples a velocity its own drag has already lowered. A line of drag \(\tfrac{1}{2}\rho c_d d U^2\) per unit length, spread with width \(\epsilon\), slows the flow on its axis by the fraction

\[\frac{c_d\, d}{4\sqrt{\pi}\,\epsilon}\]

in linear theory. For an 8 m tower (\(c_d = 1\)) that is about 11 % at 10 m and 6 % at 20 m; with the drag taken from the lowered velocity, the drag comes out about 18 % and 10 % low. No correction is applied. epsilon_tower lets the tower keep a wide kernel while the blades are narrow. The start-up audit warns when the tower’s force points lie farther apart than its kernel.

Nacelle width

For a 60 m² nacelle with \(c_d = 1\) the factor is 0.24 at 2.5 m and 0.81 at 5 m.

Why the factor must stay above 0.5, and why 0.8 is recommended

The correction is a linear estimate. Along the axis Bernoulli gives a sampled speed of \(U\sqrt{1 - 2 c_d A/(4\pi\epsilon_n^2)}\), which stagnates where the linear factor reaches 0.5. Below that, the drag fed back through the corrected velocity is no longer a small change. The run therefore stops when \(c_d A > 2\pi\epsilon_n^2\) (about 3.1 m is the least width for the nacelle above).

That limit is where the correction stops making sense, not a target:

• Near it the linear factor and Bernoulli part ways: their drag differs by 44 % at a factor of 0.6 and 5 % at 0.81.

• The velocity interpolated at the hub sees only part of the deficit, depending on where the hub sits in its cell: 60 to 100 % with the kernel one cell wide, 88 to 100 % at two. The corrected drag can then come out up to about twice the true one at the limit on one cell, and 25 % high on two.

A factor of 0.8 or more on two or more cells keeps both effects to a few per cent. Kynema’s choice \(\sqrt{2 c_d A/\pi}\) gives a factor of 7/8 (6.2 m for that nacelle).

For the IEA 15 MW (\(c_d A\) about 50 to 60 m²) a 2 m blade width gives a factor between about 0 and −0.19, which aborts; the nacelle then needs its own width (two 2.5 m cells give 0.81 to 0.84). The recommended 8.4 m blade width gives 0.93 to 0.94, so one width serves both.

Width keys given without their force

With mode adm or alm, a width given for a tower or nacelle aborts when its switch (num_force_points_tower, nacelle_cd) was never set, and warns when it was set to zero. With mode = none, which forces nothing, it warns.