Report APPL-HRC-01 rev A is issued in full on request. The abstract is published online at advikprotofab.com/publications, and the complete report, ready to print, is sent by Advik Protofab Private Limited to anyone who asks for it.
Technical report · Model-scale hull CFD
Hull Resistance CFD
A four-level grid study of a single-screw merchant hull at model scale, from 1.65 to 21.3 million cells, with viscous resistance verified by the ASME V&V 20 procedure.
1Abstract
The viscous flow around a single-screw merchant hull, Case 1, was computed at model scale as a double-body half model, with steady Reynolds-averaged equations and the k-ω SST closure, in OpenFOAM on in-house hardware. Four meshes were generated from one specification, every length scaled by the same factor, and solved from 1.65 to 21.3 million cells. Resistance was assessed by Richardson extrapolation over the three finest meshes. Base-cell and first-cell ratios agree to 0.17% across the family, against a 2% tolerance, so the measured order of accuracy belongs to the discretisation and not to a change in the meshing script.
The report gives the grid-convergence index, the split of resistance into friction and pressure, a face-by-face audit of the wall treatment, and the iterative orbit, reported as a mean over whole periods. The hull, its owner and its builder are not identified.
2Headline findings
| Figure | Quantity | Finding |
|---|---|---|
| 0.223% | Grid-convergence index | Resistance on the finest mesh is 97.537 N. Richardson extrapolation to zero cell size gives 97.363 N. The grid uncertainty is ±0.217 N at a factor of safety of 1.25. |
| 2.93 | Observed order of accuracy | Measured across the three finest meshes, against a formal second order for the scheme. The sequence is monotonic. The same procedure on the three coarser meshes alone returns an order of 0.83, an extrapolation 2.1% lower, and a grid-convergence index of 3.18%. |
| 88% | Skin friction | Skin friction is 88% of the model resistance. The share moves from 86.96% to 88.04% across a fivefold change in cell count, with the pressure part converging in the same direction. |
| Phase mean | Iterative orbit | On the two finest meshes the resistance orbits with a period locked to the iteration count. The reported value is the mean over whole periods. On the fine mesh that mean sits 0.017 N from the final iteration, and a record written every iteration bounds the sampling bias at about 10⁻⁵ of the resistance. |
3Terms used above
The report defines the terms used above as follows, so that a figure is read as the report means it.
- Grid-convergence index
- The ASME V&V 20 estimate of the discretisation error remaining on the finest mesh, from the change between three systematically refined meshes and a stated factor of safety.
- Observed order
- The order of accuracy measured from those three meshes. It is a result, not the formal order assumed for the scheme.
- Double body
- The hull reflected about the waterline, so the still-water surface becomes a plane of symmetry and waves are excluded.
- Phase mean
- The mean of a reported force over a whole number of periods of an iteration-locked orbit, used where the final iteration is one phase of that orbit.
4Evidence base
Case 1 is a single-screw merchant hull with a conventional stern and a centreline propeller, computed at model scale at a Froude number of 0.256 and a Reynolds number of 1.58 × 10⁷, as a double-body half model. The hull, its owner and its builder are not identified.
5Fitness for use
| Application | Status | Basis |
|---|---|---|
| Ranking hull, appendage or skeg variants against each other | Ready | A grid uncertainty of ±0.22% on one mesh family, common to every variant and therefore largely cancelling in the comparison. |
| Model-scale viscous and form resistance, absolute | Ready, with stated tolerance | 97.54 N on the finest mesh, with a grid uncertainty of ±0.22%. |
| Stern boundary layer on the same solutions | Ready, with stated tolerance | On the finest mesh, 713 774 of 713 776 hull faces lie in the validity band of the wall treatment. The fraction in band improves as the mesh is refined. |
6Contents of the full report
- Summary
- The capability
- The demonstration case
- The mesh family
- Near-wall resolution
- Grid convergence of resistance
- The value of the fourth mesh
- Iterative convergence
- Uncertainty budget
- Readiness by application
- Guidance for owners and designers
7Revision record
| Revision | Date | Description |
|---|---|---|
| A current | 2026-10-23 | First issue. Supersedes APPL-HW-01, a three-grid study to 8.4 million cells whose resistance had not been shown to lie in the asymptotic range. |
Obtaining the full report
Report APPL-HRC-01 rev A carries the method, the derivations, the complete reference tables and the uncertainty budget. It is issued on request.
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