Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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On the Optimization, Including Viscosity Effects, of Ship Screw Propellers with Optional End Plates
On the Optimization, Including Viscosity Effects, of Ship Screw Propellers with Optional End Plates
Pages 585-606
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From page 585... ...
ABSTRACT For ship screw propellers an optimization theory is discussed, that can be applied to propellers with and without end plates. The method differs from the classical optimization in that for the derivation of the optimum circulation distributions the sum of kinetic and viscous energy loss of the propeller is minimized instead of kinetic energy loss only.
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From page 586... ...
Some conclusions from the numerical results given in sections 8 and 9 are as follows. Combination of the iterative numerical method with the optunization including viscosity gives somewhat different optimum distributions of circulation, chord length and maximum profile thickness along blades and end plates than combination with the classical optimization gives.
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From page 587... ...
Chord lengths at blade and end plate are denoted by ci(ai) , while the maximum thickness distributions of the profiles are denoted by titai)
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From page 588... ...
We want to consider screw propellers which concur to the desire to spread evenly the cavitation danger over all values of ~' (i = b, p,s) , at the propeller.
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From page 589... ...
. concentrated vortex line segment occurs at the propeller, because, following the law of Blot and Savart, such segment would induce at the propeller velocities which are inversely proportional to the distance from the segment.
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From page 590... ...
However a good insight can be obtained in this way. For the three types of considered screw blade planforms it is seen that at the blade tip there are ranges of Xb in which the free vorticity strength does not vanish /(ab,e,Xb)
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From page 591... ...
For this type of end plate we have no concentrated vortex line segment at the junction of blade and end plate and because the free vorticity at the two symmetric end plate parts is of equal strength at their connection, also there exists no discontinuity in the vorticity field of the type of Figure 4. Aside we remark that experiments in a cavitation tunnel showed that the more or less concentrated blade tip vortex, which normally arises for propellers without end plates that have a square root singularity in the circulation distribution at the blade tip (see for instance Figure 14)
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From page 592... ...
. Obviously, shorter chord lengths will cause smaller viscous losses, and min~rnization of the viscous loss especially is important for the end plates, because they have a relatively large velocity with respect to the water.
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From page 593... ...
o The dependence of EWC on the circulation distributions is a complicated one, when we realize that the skin friction drag coefficient C: depends via the Reynolds number Reyi and the chord length ci on the circulation loci, see formulae (28)
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From page 594... ...
Then we want to find the optimum circulation distributions PiPt (i = b, p,s) , belonging to the given quantities, from which follow automatically the optimum chord length distributions coins by relation (13~.
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From page 595... ...
| if vx still changes to some extent, then 1 1 Fig. 7 Iteration scheme for the optimization including viscosity when the given quantities are prescribed.
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From page 596... ...
For instance a strength calculation based upon simple beam theory is incorporated in this step. In the strength calculation the considered force fields acting on the beams representing the screw blades and end plates, are the potential theoretically induced lift forces, the centrifugal forces and the viscous forces.
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From page 597... ...
To obtain some insight into how the difference between optimization including viscosity and classical optimization affects in our theory the corresponding - screw propellers, we give in Figure 8 for the propellers of Tablet with k=0.5 the corresponding circulation distributions. It is seen from these figures that in the linearized theory for the optimization including viscosity there occur somewhat smaller values of circulation at large radii than for the classical optimization.
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From page 598... ...
/~Ti(a`) ~ has unjustly been taken equal to one, at the spanwise stages of negative circulation Pb there can occur viscous energy gain EWC and thrust production TVUIC due to viscosity, instead of viscous energy loss and thrust deductum due to viscosity.
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From page 600... ...
, 4= ~ cn o no 11 ~ :' Is ~ o a)
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From page 602... ...
This is a logical conclusion because end plates can help to decrease the relatively large kinetic energy loss which occurs for screw propellers which are heavily loaded or have a small number of screw blades. On the influence of the type of end plate planform Here we compare the application of some different types of end plate planforms.
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From page 603... ...
_ o 1 .q ~ ~.~ Io , ol 17 0 W.- 3 Fig. 18 The opti~num propeller ~ of Table4 with one-sided end plates at of screw blades; a~b = A~3 = 0.
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From page 604... ...
REFERENCES t71 ill de Jong, K., "On the Optimization, Including Viscosity Effects, of Ship Screw Propellers with Optional End Plates", International Shipbuilding Progress, to be published.
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From page 605... ...
It turned out that tip vortices could not be made visible, which is an indication that the basic principle of minimizing kinetic energy loss seems to work. Indeed, open water tests showed that the efficiency of the propeller with end plates for larger thrusts was significantly better than the efficiency of a corresponding B-screw propeller, even though it concerned model scale experiments, see [2]
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