Author Contributions
Conceptualization, A.Y., T.T. and T.K.; methodology, A.Y.; software, A.Y.; validation, A.Y.; formal analysis, A.Y.; investigation, A.Y., T.T. and T.K.; resources, A.Y.; data curation, A.Y.; writing—original draft preparation, A.Y.; writing—review and editing, A.Y., T.T. and T.K.; visualization, A.Y.; supervision, T.T. and T.K.; project administration, A.Y., T.T. and T.K.; funding acquisition, A.Y. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Coordinate system and location of two rigid wing sails on the hull.
Figure 1.
Coordinate system and location of two rigid wing sails on the hull.
Figure 2.
Left and middle: the shape and the sectional view of a rigid wing sail, right: the computational domain for the single wing sail.
Figure 2.
Left and middle: the shape and the sectional view of a rigid wing sail, right: the computational domain for the single wing sail.
Figure 3.
CFD results of
CL and
CD for a rigid sail compared with the results of Kanai et al. [
12].
Figure 3.
CFD results of
CL and
CD for a rigid sail compared with the results of Kanai et al. [
12].
Figure 4.
Maximum Cx and α at the maximum Cx of the single rigid sail.
Figure 4.
Maximum Cx and α at the maximum Cx of the single rigid sail.
Figure 5.
Body plan of the hull designed by Akane Yasuda.
Figure 5.
Body plan of the hull designed by Akane Yasuda.
Figure 6.
Configuration of the hull and the sail.
Figure 6.
Configuration of the hull and the sail.
Figure 7.
Grid of the computational domain (γ = 60°, α = 16°).
Figure 7.
Grid of the computational domain (γ = 60°, α = 16°).
Figure 8.
Input the vertical distribution of UA.
Figure 8.
Input the vertical distribution of UA.
Figure 9.
Maximum Cx and α at the maximum Cx of a rigid sail with/without the hull.
Figure 9.
Maximum Cx and α at the maximum Cx of a rigid sail with/without the hull.
Figure 10.
Cx of the rigid sail with/without the hull (γ = 120°).
Figure 10.
Cx of the rigid sail with/without the hull (γ = 120°).
Figure 11.
Configuration of the hull and the two sails.
Figure 11.
Configuration of the hull and the two sails.
Figure 12.
Optimized α1 and α2.
Figure 12.
Optimized α1 and α2.
Figure 13.
Maximized Cx(ave.) of the two sails attached to the hull.
Figure 13.
Maximized Cx(ave.) of the two sails attached to the hull.
Figure 14.
Cx(ave.) of two sails for γ = 0°.
Figure 14.
Cx(ave.) of two sails for γ = 0°.
Figure 15.
Cx(ave.) of two sails for γ = 60°.
Figure 15.
Cx(ave.) of two sails for γ = 60°.
Figure 16.
Cx(ave.) of two sails for γ = 90°.
Figure 16.
Cx(ave.) of two sails for γ = 90°.
Figure 17.
Cx(ave.) of two sails for γ = 120°.
Figure 17.
Cx(ave.) of two sails for γ = 120°.
Figure 18.
of the two sails ( = 26°, = 150°).
Figure 18.
of the two sails ( = 26°, = 150°).
Figure 19.
of the two sails ( = 60°, = 150°).
Figure 19.
of the two sails ( = 60°, = 150°).
Figure 20.
Pressure distribution and streamlines at 25 m above from the hull deck (γ = 150°).
Figure 20.
Pressure distribution and streamlines at 25 m above from the hull deck (γ = 150°).
Figure 21.
of two sails for = 150°.
Figure 21.
of two sails for = 150°.
Figure 22.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 150°, optimized and ).
Figure 22.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 150°, optimized and ).
Figure 23.
, , and of the two sails ( = 150°, , = 32°, = 60°).
Figure 23.
, , and of the two sails ( = 150°, , = 32°, = 60°).
Figure 24.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 150°, , = 32°, = 60°).
Figure 24.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 150°, , = 32°, = 60°).
Figure 25.
, , and of the two sails ( = 180°).
Figure 25.
, , and of the two sails ( = 180°).
Figure 26.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 180°).
Figure 26.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 180°).
Figure 27.
, , and of the two sails ( = 90°, = 180°).
Figure 27.
, , and of the two sails ( = 90°, = 180°).
Figure 28.
of the two sails for = 180°.
Figure 28.
of the two sails for = 180°.
Figure 29.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 180°, optimized and ).
Figure 29.
Pressure distribution and streamlines at 25 m above from the hull deck ( = 180°, optimized and ).
Table 1.
Nomenclature.
Symbol | Unit | Meaning |
---|
| m | chord length of a rigid sail |
| – | drag coefficient of a rigid sail |
| – | drag coefficient of the fore side sail, Sail-1 |
| – | drag coefficient of the aft side sail, Sail-2 |
| – | |
| – | lift coefficient of a rigid sail |
| – | lift coefficient of the fore side sail, Sail-1 |
| – | lift coefficient of the aft side sail, Sail-2 |
| – | |
| – | thrust coefficient of a rigid sail |
| – | thrust coefficient of the fore side sail, Sail-1 |
| – | thrust coefficient of the aft side sail, Sail-2 |
| – | |
| – | of a single rigid sail with hull for a certain apparent wind direction |
| N | drag of a rigid sail |
| m | height of a rigid sail |
| m | wind reference height |
| N | lift of a rigid sail |
| m | length of hull |
| – | the origin of the coordinate system |
| – | Reynold’s number |
| m/s | apparent wind speed |
| m/s | reference wind speed |
| m/s | apparent wind speed at 10 m above water |
| m2 | area of a rigid sail |
| m | hull-fixed coordinate axis, aligned with the hull’s forward direction |
| m | fixed spatial coordinate axis, parallel to the water surface, in the direction of the incoming wind |
| m | hull-fixed coordinate axis, aligned with the hull’s width direction |
| m | fixed spatial coordinate axis, parallel to the water surface, perpendicular to the direction of the incoming wind |
| – | dimensionless thickness of boundary layer |
| m | fixed spatial coordinate axis, vertical and upward relative to the water surface |
| ° | angle of attack of a rigid sail |
| ° | angle of attack of the fore side sail, Sail-1 |
| ° | angle of attack of the aft side sail, Sail-2 |
| ° | apparent wind direction |
| m | spacing between two rigid sails along hull length |
| | kinematic viscosity of the air |
| kg/m3 | density of the air |
Table 2.
CFD calculation setting for the single-wing sail.
Table 2.
CFD calculation setting for the single-wing sail.
CFD solver | FINETM/Marine 10.1 [14] |
Time configuration | Steady |
| |
Turbulence model | k-ω SST |
Number of grid points | about 0.5 million |
Grid structure | unstructured grid |
Table 3.
Principle particulars of the hull.
Table 3.
Principle particulars of the hull.
Specifications | Unit | Value |
---|
Length | m | 300.00 |
Breath | m | 50.00 |
Depth | m | 25.00 |
Draft | m | 16.50 |
Table 4.
The number of cells and the results of for each grid.
Table 4.
The number of cells and the results of for each grid.
Grid Name | Coarse | Medium | Fine |
---|
number of cells | 913,795 | 1,435,379 | 2,420,830 |
| 1.445 | 1.397 | 1.384 |
Table 5.
The calculated values for the grid convergence study.
Table 5.
The calculated values for the grid convergence study.
| | | | | | | |
---|
0.286 | 0.014 | 0.005 | 3.616 | 2.502 | 0.008 | 1.370 | 0.60 |