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Are there theories that assert about the ideal shape (i.e., ignoring structural constraints) of a propeller?

Just looking at the shapes that emerge in practice, it appears that both the fluid speed relative to the propeller and the fluid's viscosity are factors that radically affect the optimal shape. Are there any laws that relate these factors?

From what I have observed in practice, I would conclude that a ducted fan with blade angles matched to the desired Mach number, and diameter matched to the desired power, is a maximally efficient propeller, meaning that it converts rotational energy into the maximum possible mass flow to its rear. Is this (or some statement like it) correct?

And if so, does it apply across the full range of viscosity and flow speeds – from hypersonic air flight to trawling under water at just a few knots?

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  • $\begingroup$ When Brunel designed the SS Great Britain, he designed the propeller. Apparently, they have run a simulation to optimise the propeller and his design is 95% compared to optimal - he did not have computers... $\endgroup$ – Solar Mike Oct 22 '18 at 5:30
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  1. Propeller Diameter It is observed that the speed of the shaft and the propeller diameter are very closely related. A low shaft speed (given diameter) is very beneficial from efficiency point of view. However, it leads to high shaft torque subsequently large shafts and gearboxes. Therefore, while designing the propeller a balance must be found to ensure its performance.

Generally, propulsive efficiency can be increased by installing propellers with large diameters. However, the diameter behind the ship is limited by the draught of the vessel. Optimization of propeller design is done to meet the balance.

marine propeller

  1. RPM Selection of RPM of the ship plays a very important role in the propeller design. The rotational speed chosen for the vessel must be different from the resonant frequencies of the shaft, hull and other propulsion machinery. It is often seen that low RPM design increases the propulsive efficiency by 10 to 15 percent.

  2. Number of blades The number of blades chosen has an effect on the level of unsteady forces acting on them. Considering the efficiency point of view, optimum open water efficiency increases with increase in the number of blades.

  3. Blade Outline Blade outline plays a very important role in propulsive efficiency. Research and experiments using propellers with various blade areas have shown that efficiency increases by decreasing the blade area. This is because the frictional drag increases with increased blade area. However, it should be kept in mind that the strength of the propeller cannot be compromised by decreasing the area to large extent. Tip of the propeller has to be kept narrower in order to ensure efficient flow of water through the blade.

  4. Angle of Attack & Camber The design of angle of attack of the propeller and its corresponding chamber depends on the design lift which has to be determined by the naval architect. If a larger angle of attack is chosen then the section designed would be less susceptible to pressure side cavitation and more susceptible to suction side cavitation. The reverse also holds true if the angle of attack is decreased.

  5. Pitch/Diameter ratio To achieve the best propulsive efficiency for a given propeller diameter, an optimum Pitch/Diameter ratio is to be found, which again corresponds to a particular design rate of revolution.

Apart from the conventional changes in the parameters of the propeller in order to achieve higher efficiency, there are certain external components which help in improving the flow around the propeller, hence, improving propulsive efficiency. They are as follows –

  1. Stern Tunnels These devices help in reducing the wake peak effect for ships having V-shaped sterns, thus reducing the effect of vibration. They are horizontal hull appendages placed above the propeller, they deflect the water towards the propeller ensuring even flow through the propeller.

  2. Schneekluth ducts These type of devices redirect the flow to the upper portion of the propeller disk thus equalising the effect of wake and improving hull efficiency. These are also capable of accelerating the flow by means of the aerofoil shape cross section. This is done by creating a low pressure area in front of the duct which is achieved through its design.

design of propeller Image Credits: schneekluth.com

  1. Grouches Spoilers Their function is to redirect the flow horizontally in towards the propeller. They are small curved triangular plates welded in front, top and side of the propeller. These were designed to prevent the formation of keel vortices for U-shaped stern ships.

propeller design for u shaped stern ships Image Credits: schneekluth.com

  1. Rudder Bulb System Kappel propeller comprises of smoothly curved extended blade tip towards the suction side of the blade which reduces the energy loss from the tip vortex flow. Integrating a rudder bulb and flaring the Kappel propeller hub cap will provide additional reduction in the energy loss from hub vortex and drag from the hub-rudder profile. The rudder bulb system also reduces cavitation increasing the total efficiency of the propeller assembly. A Kappel propeller and a rudder bulb system is designed for a target ship and accordingly engine is selected as per the power/ rpm requirement. It is important to properly optimize these two parts to achieve improvement in fuel saving, efficiency and reduction in emission.

Source: http://seq.vindicatrix.com/newsletters/17-%20Aug%202016.pdf

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  • $\begingroup$ Is this for "pulling" or "pushing" propellers? $\endgroup$ – Solar Mike Dec 21 '18 at 12:41
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There are several parameters youd need to decide on first.

  1. What is the viscosity of the fluid? More viscous fluid favors larger propellers with more power to surface area.
  2. How how big is the vehicle? Smaller vehicles would generate a smaller wake for a given speed and allow correspondingly propellers before turbulence takes over.
  3. What is the speed? Higher speeds result in greater cavitation and work against multi bladed or complex propellers where cavitation interactions could occur.
  4. Materials strength limits the rpm of the propeller. An infinitely strong propeller with unlimited fuel would go to lightspeed.
  5. (1), (2) and (4) determine the gear ratio and pitch.

Once you answer these questions and specificy the fluid properties then one could assume an optimal propeller shaped such that the blade length is that point where material stress exceeds strength.

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  • $\begingroup$ If true this is an interesting answer to a variant of my question in which structural strength is a factor. But your statement #4 can't be correct – not least because, given any finite flow speed and viscosity, above some rotational rate any propeller will "freewheel" in the flow medium (i.e., not be able to produce additional thrust). $\endgroup$ – feetwet Oct 22 '18 at 15:21

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