Table 2, Summary of mesh dimensions xmax
xmin ymax ymin -4.318
z max
zmin
m m m m m m 7.974 -2.059 4.318
3.1 TETRAHEDRAL MESH
For the tetrahedral mesh, two volumes were created around the hull. The inner volume, close to the hull had a constant mesh size at all the boundaries. The outer volume had larger mesh elements at the outer surface than at the inner surface. The geometry
for the
tetrahedral mesh is shown in Figure 4 for the mesh on the hull surface and the nominal waterline. The total number of elements within the mesh was 2,170,899.
3.2 HEXAHEDRAL MESH
The surface file used to create the hexahedral mesh was the same as the one used for the tetrahedral mesh. For the hexahedral mesh the additional step of creating new surfaces so that the hull could be defined completely in four-sided elements was required. This was done within Gambit.
Again the mesh was divided into two regions. One region was close to the hull surface, and one was sufficiently far from the hull surface that flow conditions were not changing significantly. The hull and fluid volume were defined using a more elaborate system of construction planes along the length of the hull, especially close to the bow and the stern. Once the inner mesh was successfully defined, the cells in the planes were extruded to the inlet, outlet and bottom wall boundaries. The mesh was symmetrical about the centreline of the ship. The total number of elements within the mesh was 986,984, which was less than one half of the number used for the tetrahedral mesh. The hexahedral mesh is shown in Figure 5, for the hull surface and the nominal free surface.
3.3 CFD SOLVER
For both meshes the boundary conditions were set as velocity inlets on the two upstream faces, and pressure outlets at the two downstream faces. The upper and lower boundaries were set as walls with zero shear force. The hull surface was set as a no-slip wall boundary condition.
The CFD solver used was FLUENT 6.1.22. Uniform flow entered the domain through a velocity inlet on the upstream boundaries and exited through a pressure outlet on the downstream boundaries. Flow speed magnitude was set at 0.728 m/s, which corresponded to 6 knots at 1:18 scale, based on Froude length scaling. The fluid used was fresh water.
4. COMPARISON OF CFD PREDICTIONS WITH EXPERIMENT DATA: FORCE COEFFICIENTS
4.1 HULL ONLY
Force components and non-dimensional coefficients derived from the results of the CFD simulations for the tug hull (without the fin) are given for the tetrahedral and hexahedral meshes in Table 4. The results of the simulations are compared with the experiments in Figure 6.
0.000 -2.159
The angle between the incoming flow and the hull (yaw angle) was set by adjusting the boundary conditions, so that the velocity at the inlet planes had two components. The cosine component of the angle between the steady flow and the centreline of the hull was in the positive x direction for the mesh and the sine component in the positive y direction. The pressure outlet planes were set so that the backflow pressure was also in the same direction. The advantage of this approach was that one mesh could be used for all the yaw angles. Yaw angles from 10 degrees to 45 degrees were simulated.
The selection of the turbulence model was based on discussions with experienced users of Fluent and other CFD codes (Rhee 2005, Turnock, 2006,). The turbulence model used was a model with the default parameters given in Table 3. Turbulence intensity and turbulent viscosity ratios were set at 1% and 1 respectively. The flow was solved for the steady state case. The non- dimensional residual for each of the solution variables (continuity, x, y and z velocity components, and were set to 10-3 (default values). All flow conditions reported came to a solution within these tolerances. Results were presented as forces acting on the hull (including the fin if it was present) and as flow vectors within the fluid. Table 3, Parameters for turbulence model
*
0
*
i
R *
M t 0
TKE Prandl number SDR Prandl number
1.0 0.52
0.111 0.09
0.072 8
1.5
0.25 2
2
B-44
©2008: Royal Institution of Naval Architects
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68