Engineering summary · OpenFOAM VOF · free decay + forced roll
The completed campaign verifies the first sloshing mode against theory, resolves the forced-roll response from 16–26 seconds, adds a stationary baseline and sectional wall loads, and publishes complete-cycle fields plus pressure-resolved QA near the response maximum.
01 · Study question
A partially filled rectangular tank was evaluated with VOF CFD. Seven free-decay cases test mesh and timestep sensitivity against the analytical first-mode frequency. Thirteen forced-roll records cover 16–26 seconds, targeted 21–25 second refinement, medium/fine comparison, pressure QA, and sectional loads. One no-roll run establishes the numerical baseline.
02 · Executive findings
Across the published mesh and timestep cases, measured frequency differs from the analytical target of 0.758054 Hz by 0.2964–0.3264%. The finest 25,600-cell case gives 0.755807 Hz.
Use: this supports the VOF model for natural-frequency prediction. The convergence sequence is monotonic but not demonstrably asymptotic, so the residual should not be represented as a formal high-order grid-convergence result.
Normalized liquid-level response increases from 0.190 m/deg at 16 s through 0.22071 at 22 s to 0.22119 m/deg at 23 s, then decreases to 0.22074 at 24 s, 0.21946 at 25 s, and 0.217 at 26 s. The fine 24 s case gives 0.22145 m/deg, confirming mesh sensitivity is comparable to the small period-to-period differences.
Use: treat 22–24 seconds as a broad governing region; 23 seconds is the sampled medium-mesh maximum, not a universal tank optimum.
Roll-moment amplitude normalized by roll angle rises from 1.49 MN·m/deg at 16 s to approximately 1.94 MN·m/deg at 24–26 s. The level-response maximum and moment maximum therefore need not occur at exactly the same period.
Use: period selection depends on the response quantity governing the engineering decision.
At 24 seconds, the medium and fine cases give liquid-level amplitudes of 1.1037 m and 1.1124 m, while aggregate roll moment changes from 9.673 MN·m to 9.815 MN·m.
Use: response magnitude is relatively stable across the published medium/fine comparison, but this single comparison does not replace a full asymptotic convergence study.
03 · Forced-roll response
The principal result is present directly in the page, so it remains visible without JavaScript or external data loading.
| Period | Level response | Roll-moment response | Engineering reading |
|---|---|---|---|
| 16 s | 0.190 m/deg | 1.495 MN·m/deg | Lower end of published response band |
| 18 s | 0.205 m/deg | 1.687 MN·m/deg | Response increasing |
| 20 s | 0.216 m/deg | 1.821 MN·m/deg | Approaching broad maximum |
| 21 s | 0.21882 m/deg | 1.86463 MN·m/deg | Targeted refinement |
| 22 s | 0.22071 m/deg | 1.89958 MN·m/deg | Broad plateau |
| 23 s | 0.22119 m/deg | 1.92120 MN·m/deg | Sampled medium-mesh level maximum |
| 24 s | 0.22074 m/deg | 1.93463 MN·m/deg | Fine, pressure, and sectional comparisons available |
| 25 s | 0.21946 m/deg | 1.94061 MN·m/deg | Level response descending |
| 26 s | 0.217 m/deg | 1.937 MN·m/deg | Level response reduces; moment remains high |
Values are derived from the immutable release’s final-three-cycle harmonic metrics. Open the interactive study to select curves and export plots.
04 · Visual evidence
These are case-specific CFD snapshots and synchronized response graphs. The new 22 s and fine 24 s media cover one complete final forcing cycle with no temporal interpolation; legacy 16 s and 26 s media remain shorter final-window context.
05 · Validation and QA
The mesh and timestep series remains within approximately 0.3% of the analytical target. This is the strongest validation statement supported by the public release.
Open validation →The new pressure-resolved fine case reduced the observed maximum Courant number from 0.478 to 0.326. It completed and converged, but still exceeded its tighter configured target of 0.25.
Open detailed QA →Inputs, QA, bounded histories, complete-cycle media, pressure envelopes, and sectional loads are published where case-specific evidence exists. Simpler validation cases remain intentionally concise.
Review coverage →06 · Conclusions and limits