Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014
equations were decreased by a minimum of 3-4 orders of magnitude for each time step. Time steps were set so that, for all cases, the propellers were limited to 6 degrees rotation or less. This limitation on the level of propeller rotation per time step was found to be sufficient in a study of towed-water power generators
[10],
particularly since the results are nearly steady in a frame of reference rotating with the propeller.
3.
COMPUTATIONAL GEOMENTRY, BOUNDARY CONDITIONS, AND MESH
The propellers Introduction
section.
investigated were described in the In
terms of computational
geometry, the propellers were imbedded within a cylindrical domain of radius 2 m and length 4 m. This resulted in a blockage ratio, based on the propeller diameter, of 0.58%. Slip-wall boundary conditions were employed on the outer walls to eliminate the formation of a boundary layer. A uniform velocity was specified at the inlet (ranging from 1 m/s to 4 m/s) and a constant pressure boundary condition was specified at the outlet. The inlet turbulent viscosity ratio was set to 10.
values were of order unity, permitting the turbulence quantities to be integrated to the wall (rather than the use of wall functions).
Table 1. Summary of grid resolution results. Propeller
Fine, Medium, Coarse Cell Counts (millions)
Sailer 2 locked
Sailer 2 freewheel
Sailer 3 locked
Sailer 3 freewheel
B-Series 2-blade 10 inch locked
B-Series 2-blade 10 inch freewheel
B-Series 3-blade 6 inch locked
B-Series 3-blade 6 inch freewheel
B-Series 2-blade 6 inch locked
B-Series 2-blade 6 inch freewheel
4.
Figure 1. Surface mesh on B-Series locked condition propeller.
Three levels of mesh density were employed for several of the cases to assess grid convergence. This effort is discussed in the Results section.
However, all results
presented in subsequent figures were obtained using the finest level of mesh for each of the different configurations as specified in Table 1. As a representative example, the surface mesh for the B-Series, 3-blade, locked-condition propeller is shown in Figure 1.
(Fine-level blade mesh
densities were similar for the other propellers.) In addition, clustering of cells toward propeller surfaces was performed for the finest level meshes such that the average resultant y+
B-82
Percent Drag Variation Fine/mediu m
6.1, 3.4, 2.4 0.12 6.1, 3.4, 2.4 0.45 7.1, 4.6, 3.1 0.18 6.5 ,4.3 ,2.7 0.39
4.9, 3.0, 1.7 0.29 7.1, 4.7, 3.0 3.4 5.6, 3.6, 2.1 0.11 8.2, 5.7, 2.1 1.4 4.0, 2.4, 1.3 0.94 6.4, 3.9, 2.3 1.5
0.6 1.3
0.29 1.33
0.52 4.3 0.38 0.39 1.63 4.0
Percent Drag Variation Fine/coarse
RESULTS
The results to be presented primarily involve drag or drag coefficients as a function of speed for the different propellers.
Note that the drag reported is that of the blades only; the drag on the hub is not included.
Shown in Figure 2 are drag levels as a function of velocity for each of the propeller designs under locked conditions. As expected, at a given speed the drag for propellers with similar projected areas are nearly indistinguishable. That is, over the range of velocities the Sailer 2 and the 2-blade, 6- inch-pitch B-Series propellers have nearly identical drag, as do the Sailer 3 and the 3-blade, 6-inch-pitch B-Series propellers. In addition, the drag of the 3-blade propellers is approximately 66% greater than that of the
2-blade ©2014: The Royal Institution of Naval Architects
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