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Numerical calculations of propeller shaft loads on azimuth propulsors in oblique inflow

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Abstract

This paper evaluates various computational methods used to compute propeller performance, hydrodynamic side force and bending moment applied to an azimuth propulsor propeller shaft in oblique inflow. The two non-viscous models used are the BEM method and the blade element momentum theory (BEMT). RANS calculations are used to compute the loads on the propeller and the nominal wake velocity from the thruster body to be used in the BEMT model. The effect of the ship hull is also considered in the calculation by implementing the measured nominal wake of a ship hull at different propeller azimuthal positions. All the models are compared and validated against the experimental results, and the discussions are presented.

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Abbreviations

D p :

Propeller diameter

f z :

Vertical force on propeller

f y :

Lateral force on propeller

\( K_{T} = \frac{T}{{\rho n^{2} D_{\text{p}}^{4} }} \) :

Propeller thrust coefficient

\( K_{Q} = \frac{Q}{{\rho n^{2} D_{\text{p}}^{5} }} \) :

Propeller torque coefficient

\( K_{{f_{y} }} = \frac{{f_{y} }}{{\rho n^{2} D_{\text{p}}^{4} }} \) :

Propeller lateral force coefficient

\( K_{{f_{z} }} = \frac{{f_{z} }}{{\rho n^{2} D_{\text{p}}^{4} }} \) :

Propeller vertical force coefficient

\( K_{{m_{y} }} = \frac{{m_{y} }}{{\rho n^{2} D_{\text{p}}^{5} }} \) :

Propeller lateral moment coefficient

\( K_{{m_{z} }} = \frac{{m_{z} }}{{\rho n^{2} D_{\text{p}}^{5} }} \) :

Propeller vertical moment coefficient

\( m_{y} \) :

Propeller lateral moment

\( m_{z} \) :

Propeller vertical moment

n :

Shaft rotational speed

Q :

Propeller torque

R :

Propeller radius

r :

Blade element radial distance

T :

Propeller thrust

u 0 :

Propeller average axial induced velocity

u i :

Blade element axial induced velocity

V a :

Advance velocity

χ:

Wake skew angle

\( J = \frac{{V_{\text{a}} }}{{nD_{\text{p}} }} \) :

Advance coefficient

ψ:

Propeller circumferential angle

F t :

Blade tangential force

k l :

Lift coefficient empirical factor

k d :

Drag coefficient empirical factor

L :

Lift force

\( \bar{T} \) :

Annular ring thrust

\( \bar{u}_{0} \) :

Annular ring average axial induced velocity

β:

Inflow angle

η:

Blade element camber

V R :

Resultant velocity

c :

Blade element chord

C p :

Pressure coefficient

c f :

Frictional coefficient

C D :

Drag coefficient

C L :

Lift coefficient

D :

Drag force

δ:

Propeller heading angle

References

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Acknowledgments

This research is sponsored by The Research Council of Norway at The University Technology Centre of Rolls Royce at NTNU through the research project SeaPro. This project was partially supported by the Norwegian HPC project NOTUR that granted access to its computer facilities. The assistance of Dr. Vladimir Krasilnikov with performing the BEM method calculations is appreciated.

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Authors and Affiliations

  1. Department of Marine Technology, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway

    Hamid Amini, Lucia Sileo & Sverre Steen

Authors
  1. Hamid Amini
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  2. Lucia Sileo
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  3. Sverre Steen
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Correspondence to Hamid Amini.

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Amini, H., Sileo, L. & Steen, S. Numerical calculations of propeller shaft loads on azimuth propulsors in oblique inflow. J Mar Sci Technol 17, 403–421 (2012). https://doi.org/10.1007/s00773-012-0176-z

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  • DOI: https://doi.org/10.1007/s00773-012-0176-z

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