Damping & Sizing

02 · The measured surface

Equivalent damping over period and roll amplitude

Twenty-one forced-roll CFD cases, one per cell, identical geometry, mesh and solver settings throughout. Damping is not a property of the tank alone: it rises steeply with roll amplitude at every period, which is what a quadratic conduit loss does and a linear-viscous one cannot.

ζ is a linearisation of a quadratic loss and is valid at the amplitude it was measured at — it is not a material constant. The 13 s column is the least reliable: it sits closest to resonance, where the extraction is numerically ill-conditioned.

03 · What the grid proves

The natural period does not move; the response peak does

A single-amplitude sweep cannot separate these two. The grid can, and the separation is decisive: the exchange period is an inertial property and holds to under 2 % across a four-fold change in roll amplitude, while the amplitude peak doubles over the same range.

The 10° peak sits at the edge of the tested period range, so its amplification is a lower bound.

04 · The laws, and what tested them

Predictions made before the runs, not fitted after

Two numbers are fitted, both at one conduit area and one fill: an effective conduit length, and a loss coefficient. Everything else is geometry. The cases below were then placed where the resulting predictions are falsifiable — at the predicted resonance of conduit areas and fills the model had never seen.

The loss law needed correcting by this test, and the correction is instructive. Derived as a form drag it scales as 1/A_c, which reproduced the calibration area but failed in opposite directions either side of it — under by 55 % at the smaller conduit, over by 108 % at the larger. Fitting the exponent rather than assuming it gives n = 2.14, and rms error over 35 cases at three conduit areas falls from 36.5 % to 8.6 %.

The moment adds two static terms the redistribution estimate omits — the weight moment of the whole fluid mass about the roll axis, and the within-leg free surface. Below about 20 s the closed form degrades, because the legs’ own sloshing modes begin to participate.

05 · Conduit sizing

Roll reduction against conduit area

With every link validated, the chain runs from geometry to roll response, and the design question becomes answerable: for a given hull, which conduit area returns the most roll reduction?

Two results matter more than the peak value. The optimum is deliberately detuned — the tank period sits below the roll period, which is correct for a heavily damped absorber. And the optimum is broad: 5 and 6 m² are within one percent of each other, so the as-built routing uncertainty that worries a tuned device is survivable here.

Hull damping roughly halves the benefit at every conduit area. It is a property of the vessel, not of the tank, and it moves the answer by more than any sizing choice does.

06 · Limits

What this does not establish

• One geometry family. Conduit area is validated over 3.4–13.5 m² and fill over 25–70 %; the loss exponent rests on two off-calibration conduit areas and should be treated as provisional until a third tests it.
• The closed-form moment is validated for forcing periods of 20 s and above. Where the coupled peak falls just below that, the table says so.
• A connected tank worsens long-period roll through the free-surface penalty it imposes. That is present in the same model and is not a small effect.
• Nothing here is a vessel result. The hull enters only as roll period, hull damping and tank authority; applying it to a ship requires that vessel’s own values.

Provenance

Every case and derived value on this page is published in the immutable release — digest 1034bb4efc5d9b39…, pinned dataset revision 51ba5ddbca8d…. That release grew from 24 to 57 cases and 133 to 441 derived metrics to carry this work, and all 47 declared source files resolve on the pinned revision.

Three of the 33 new cases are flagged, not clean. fill-f25-t12-a5, fill-f25-t13p95-a5 and grid-t10-a10 exceed the declared 2 % exchange cycle-change limit (2.25 %, 2.30 % and 3.24 %). They are published with status accepted_with_exception and counted in the release’s dispositions table rather than dropped, because they are real runs and because where they fall is informative: the two lowest-fill cases and the largest-amplitude shortest-period cell are the most nonlinear conditions in the set, and the slowest to settle. Statistics that assume every cell is equally converged should exclude them.

No time series were published. The samples table stands at 9,933 rows against a declared limit of 10,000, so adding series would breach the release’s own limit; the raw histories stay in the pinned private source.

Generated by scripts/generate_sloshing_damping_page.py, which regenerates this page from the reviewed analysis files — no value here is hand-transcribed, and --check fails the build if the page drifts from its sources. Sources:

• review_output/damping/response_surface.json
• review_output/damping/prediction_checks.json
• analytical/loss_scaling.json
• analytical/moment_model.json
• analytical/design_sweep.json