digitalmodel · CFD verification suite · case 7 · marine · interactive

Floating-Body Heave Free Decay: 6-DOF Rigid-Body Motion vs Hydrostatics

A buoyant box released below its equilibrium heaves freely on a VOF free surface with mesh morphing (interFoam + sixDoFRigidBodyMotion, heave-constrained). Equilibrium draft validated against Archimedes; decay period against the hydrostatic period with the difference reported as added mass. Issue #1169, epic #1161.

VERIFIED — draft +1.1% vs Archimedes; 11 damped cycles; Ca = 0.39 (physical)

SolverinterFoam + sixDoFRigidBodyMotion, v2312

Body0.3×0.2×0.5 m cuboid, ρ = 500 kg/m³ (15 kg)

Draft0.2532 m vs 0.2505 m (+1.1%)

Heave period1.149 s = 1.18 × T_hydrostatic

Implied added massCa ≈ 0.39

Regression testtests/solvers/openfoam/validation/test_floating_body.py

1 Objective

Verify the coupled rigid-body/free-surface machinery: a half-density cuboid is cut out of a 1 m³ tank mesh, released ~0.054 m below its hydrostatic equilibrium, and heaves freely under sixDoFRigidBodyMotion with mesh morphing (constrained to pure heave: line + orientation constraints, so the decay is cleanly one-dimensional). Two known answers gate the result: the Archimedes draft (m/ρA_wp = 0.2505 m) and the hydrostatic heave period T = 2π√(m/k), k = ρgA_wp corrected for the closed tank. Case derives from the shipped floatingObject tutorial with the motion solver switched to sixDoF and the asymmetric water lump removed for a clean release.

What this gates in real work

This is the suite's first moving-body free-surface case — rigid-body 6-DOF coupled to VOF. The heave free decay is the exact numerical twin of the free-decay test every floating structure gets at model-test commissioning (FPSOs, semis, spars, floating-wind platforms): release from an offset, read off the natural period and damping. Verifying it qualifies:

Heave natural periods and added mass — the measured period exceeds the waterplane-stiffness value by exactly the added-mass ratio; here the implied Ca ≈ 0.39 falls in the published range for rectangular sections. The same mechanics set semi/spar heave periods that must avoid wave energy.
Motion decay & damping — the log-decrement extraction used here is how viscous damping is fed to frequency-domain RAO models (see the diffraction dashboards under /hydro/).
Wave-body interaction next — combine with the verified wave tank (#1170) for wave-excited motions, the path to CFD RAO spot-checks against the OrcaWave/AQWA pipeline.

2 The decay — animated

Heave free decay (mid-plane slice): the half-density box is released ~0.054 m below its equilibrium and oscillates to rest at the Archimedes draft (dashed line = measured equilibrium CoM height).

3 Heave decay vs hydrostatics

Quantity	Measured	Reference	Error / band	Status
Equilibrium draft	0.2532 m	Archimedes 0.2505 m	+1.1% (gate ≤ 5%)	PASS
Decay envelope	11 cycles, monotone	damped oscillation	δ = 0.34/cycle	PASS
Heave period	1.149 s	T_hyd = 0.973 s (no added mass)	ratio 1.18 ∈ [1.0, 1.6]	PASS
Implied added-mass coefficient	Ca ≈ 0.39	rectangular-section range ~0.3–0.8	∈ [0.1, 1.5]	PASS

Why the period is 18% above the waterplane-stiffness value — and why that is correct physics. The hydrostatic period T = 2π√(m/k) ignores the water the body drags along; the true period is 2π√((m+m_a)/k). Solving the measured period for m_a gives Ca = m_a/(ρ∇) ≈ 0.39, inside the published range for heaving rectangular sections. A solver that missed the radiation/added-mass physics would land on the hydrostatic period — the offset is evidence the coupled hydrodynamics is working, so it is gated as a band, not hidden as an error.

4 Numerical model

Item	Setting
Tank / body	1×1×1 m tank; cuboid 0.3×0.2×0.5 m cut by topoSet + subsetMesh, bottom at z = 0.2333 m
Mesh	20×20×30 background (11,640 cells after body cut); morphing via `dynamicMotionSolverFvMesh`
Motion	`sixDoFRigidBodyMotion`, Newmark; heave-only (line + orientation constraints); accelerationRelaxation 0.7
Fill	Still water at 0.5368 m; closed-tank stiffness correction k/(1−A_wp/A_tank) applied to the reference period
Solver	interFoam (VOF) + kEpsilon RAS (tutorial numerics), maxCo = 1
Recorder	`sixDoFRigidBodyState` function object (CoM history every time step)
Fast variant	3.5 s (~3 min): 2 cycles, period within 0.3% of the 14 s run, draft within 1.3% — the regression test

The case is generated by digitalmodel.solvers.openfoam.validation.build_floating_body_case; the runner grew topoSet/subsetMesh stages so it runs end-to-end via OpenFOAMRunConfig(run_topo_set=True, subset_mesh_set="c0", subset_mesh_patch="floatingObject", run_set_fields=True). Archived copy: docs/api/cfd/cases/floating_body_decay/.

5 Conclusion

The 6-DOF/VOF coupling reproduces floating-body hydrostatics and free-decay dynamics: Archimedes draft to +1.1%, eleven monotonically damped cycles, and a heave period whose added-mass content (Ca ≈ 0.39) is physically consistent. The moving-body foundation for floating-structure RAO and wave-drift work is verified.

References

OpenFOAM ESI v2312 tutorial multiphase/interFoam/RAS/floatingObject (base case; motion solver switched to sixDoFRigidBodyMotion with heave-only constraints).
Newman, J.N. (1977). Marine Hydrodynamics, MIT Press — hydrostatic stiffness, natural periods and added mass.
digitalmodel issue #1169 under epic #1161; regression test tests/solvers/openfoam/validation/test_floating_body.py.

Generated from a real OpenFOAM v2312 solve. All chart data and animation frames are computed directly from the solved fields and body-state history — no values are hand-entered.