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# lec12 - 12 12.1 PROPELLERS AND PROPULSION Introduction We...

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12 PROPELLERS AND PROPULSION 12.1 Introduction We discuss in this section the nature of steady and unsteady propulsion. In many marine vessels and vehicles, an engine (diesel or gas turbine, say) or an electric motor drives the (Continued on next page)

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12.2 Steady Propulsion of Vessels 51 propeller through a linkage of shafts, reducers, and bearings, and the effects of each part are important in the response of the net system. Large, commercial surface vessels spend the vast majority of their time operating in open-water and at constant speed. In this case, steady propulsion conditions are generally optimized for fuel eﬃciency. An approximation of the transient behavior of a system can be made using the quasi-static assumption. In the second section, we list several low-order models of thrusters, which have recently been used to model and simulate truly unsteady conditions. 12.2 Steady Propulsion of Vessels The notation we will use is as given in Table 1, and there are two different ﬂow conditions to consider. Self-propelled conditions refer to the propeller being installed and its propelling the vessel; there are no additional forces or moments on the vessel, such as would be caused by a towing bar or hawser. Furthermore, the ﬂow around the hull interacts with the ﬂow through the propeller. We use an sp subscript to indicate specifically self-propulsion conditions. Conversely, when the propeller is run in open water, i.e., not behind a hull, we use an o subscript; when the hull is towed with no propeller we use a t subscript. When subscripts are not used, generalization to either condition is implied. Finally, because of similitude (using diameter D in place of L when the propeller is involved), we do not distinguish between the magnitude of forces in model and full-scale vessels. R sp N R t N T N n e Hz n m Hz n e n p Hz η Q e Nm Q p Nm g P e W P p W D m U m/s U p m/s Q m Nm f kg/s f m kg/s f hull resistance under self-propulsion towed hull resistance (no propeller attached) thrust of the propeller rotational speed of the engine maximum value of rotational speed of the propeller gear ratio engine torque propeller torque gearbox eﬃciency engine power propeller shaft power propeller diameter vessel speed water speed seen at the propeller maximum engine torque fuel rate (or energy rate in electric motor) maximum value of Table 1: Nomenclature
52 12 PROPELLERS AND PROPULSION 12.2.1 Basic Characteristics In the steady state, force balance in self-propulsion requires that R sp = T sp . (150) The gear ratio η is usually large, indicating that the propeller turns much more slowly than the driving engine or motor. The following relations define the gearbox: Q n e = ηn p (151) p = g ηQ e , U and power follows as P p = g P e , for any ﬂow condition. We call J = U p /n p D the advance ratio of the prop when it is exposed to a water speed U p ; note that in the wake of the vessel, p may not be the same as the speed of the vessel U . A propeller operating

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