Trans RINA, Vol 153, Part A1, Intl J Maritime Eng, Jan-Mar 2011


hull, the horizontal components of the side force and bending moment are a consequence of non-uniform inflow in the tangential direction to the propeller disc due to in-plane velocity to the propeller disc from the oblique inflow. Higher oblique inflow gives bigger side force and bending moment.


Contrary to other components, in positive heading


angles, the horizontal side force and bending moment are slightly higher for the open water condition than when the propeller works behind the hull. The reason for this relationship is the higher arm of the eccentric thrust in the z coordinate system in the open water condition, leading to larger bending moment in the y direction (see Figure 9), even though the thrust in the behind condition is slightly higher than in open water conditions (see Figure 3).


0.06 0.04 0.02 0 -40 -30 -20 -10 -0.02 -0.04 Heading angle -0.06


Figure 8: Comparison of the horizontal component of the bending moment


coefficient condition and behind the hull 20 10 0 -50 -40 -30 -20 -10 0 10 20 30 40 50 -10 -20 -30 -40 Heading angle


Figure 9: Centre of the eccentric thrust in the propeller disc in z coordinate system as a percentage of the propeller radius


J=0.2 J=0.2-Hull J=0.6-Hull J=0.6 J=1-Hull J=1


between open water 0 10203040


J=0.2-Hull J=0.6-Hull J=1-Hull J=0.2 J=0.6 J=1


It seems that the tangential wake component is not


dominant in positive heading angles, and therefore not only the tangential wake but also the axial wake component influences these components of the side force and bending moment. When the axial wake varies over the propeller disc it should induce the bending moment and lateral force. The axial wake into the propeller disc depends on the thruster azimuth angle, with the axial wake being larger and closer to the hull (inner and upper part of propeller disc). So, the location of the centre of the propeller disc relative to the hull in different azimuth angles is considered to be important. The location of the propeller centre in different azimuth angles is shown in Figure 10. It is worth mentioning that it is common to decompose the total wake into three components:


 Potential wake without considering the steady wave pattern made by the hull


 Viscous wake due to the viscous nature of the boundary layer





Wake component due to action of the waves set by the hull (steady wave pattern)


It is believed that the viscous wake is the main contribution of the total wake (80-90% of total wake) [14]. It is known that a single screw propeller mainly operates within the viscous wake where the wake effect is important, while a twin screw propeller to a larger extent operates outside of the viscous wake (mostly in the potential wake) so the viscous effect is therefore less important twin propeller arrangements.


Thus, for a ship


with twin azimuth thrusters there will be a more significant potential wake effect experienced by the propeller when the thruster is azimuthed outward from the ship centreline, while when the thruster is azimuthed inward the viscous wake is dominating. It is possible that when turning the thruster towards the hull, there will be larger differences in axial wake over the propeller disk than when the thruster is turned outwards, leading to a larger change in the arm of the off-axis thrust. The effect of axial wake is observed in the horizontal component of force and moment in positive heading angles such that propeller gives less horizontal bending moment and side force


in behind conditions than in open water


conditions. The effect of only the ship hull wake from the comparison


between


components of force and moment is seen at zero heading angles


open


in all the water


condition results and when propeller works behind the ship hull. However, it should be noted that the wake at the propeller changes with heading angle, since a change of heading changes the propeller position relative to the hull. More detailed knowledge of wake velocities in both axial and tangential directions is necessary to see the contribution of both components of the wake hull in relation to the change of results.


A-14


©2011: The Royal Institution of Naval Architects


Arm of the ecentric thrust in z coordinate divided by propeller radius


Horizental bending moment Kmy


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