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4.1 During straight-ahead motion
Figure 4 shows the results of wake distribution calculations for the AP section at the center of the rudder, during straight-ahead motion (no propeller), using a Reynolds number of 106 (equivalent to a scale model ship). For the model ship Reynolds number, a large wake is generated behind the ship in the vicinity of the rudder.
Fig.4 |
Wake distribution calculated at A.P. section (β=0deg., δ=0deg., without propeller) |
Next, we investigated the effects of changes in rudder direction during straight-ahead motion on the rudder normal force behind the ship, using rudder angles of O°, ±5°, and ±10°.
Fig.5 Rudder normal force without propeller (β=0deg.)
Figure 5 compares the rudder normal force calculations (during straight-ahead motion) to captive model tests[2] . Note that the rudder normal force FN on the vertical axis is expressed as a dimensionless parameter. L is the length of the ship, and d is the draft.
As Figure 5 shows, the CFD calculation results are consistent with actual observations with respect to the small rudder angles used extensively during course keeping. Figure 6 shows the wake coefficient (1-wR) at the rudder position, calculated using the rudder normal force matching method. The rudder normal force model is designed in accordance with the expressions given in sections (2) and (3) above.
Figure 6 indicates that the calculation results for the effective rudder inflow velocity at a rudder angle of 10° are consistent with the experimental results[2].
Fig.6 Effective rudder inflow velocity (β=0deg.)
We also calculated the lateral forces and turning moments acting on the ship hull that are generated by steering operations during straight-ahead motion, as shown in Figures 7 and 8.
Fig.7 |
Lateral force induced by steered rudder (β=0deg., Calculated) |
Fig.8 |
Yaw moment induced by steered rudder (β=0deg., Calculated) |
Table. 2 |
Comparison of rudder-to-hull interaction coefficients between present calculation and experiment (without propeller) |
| Items |
aH |
xH/L |
| Calculated |
0.811 |
-0.247 |
| Exp.(HIROSHIMA UNIV.) |
0.991 |
-0.269 |
|
Table 2 contrasts the calculated and experimental results for the coefficient of interaction by the rudder acting on the ship hull aH and the adherence force position xH/L. Table 2 indicates that the CFD results describe with adequate precision the lateral forces and turning moments acting on the main ship hull generated by steering operations.
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