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Early theoretical analysis applied to propellers was based on momentum theory. In 1910, Bctz was the first to fonnally fonnulate thc circulation theory ofaircraft wings for using with screw propellers [2]. The Vortex theory ofpropellers was developed with the basic assumption that certain geometric qualities ofthc flow in which a propeller operates must eKist ifthe energy losses are to be minimized. In 1929, Goldstein developed this theory, showing that the flow past a vorteK sheet could be calculated by relating the two theoretical cases of a propeller with a finite number ofblades and a propeller with an infinite number ofblades [3]. Goldstein formulated Betz's vorteK theory for propellers for real cases ofpropellers with a finite number ofblades. He showed that the velocity characteristics changed substantially by removing the assumption ofthe infinite blade number. His analysis was done for the case ofoptimum circulation distribution ofa propeller with minimum energy loss. By calculating the ratio of the circulation with infinite and finite number ofblades. the Goldstein coefficient, K, was derived for periodic flow [3]. In 1947, Glauert published that the individual airfoil sections along the blade span could be included directly into a liOing line calculation to design a propeller owing to certain characteristics of lift and drag. He used momentum theory to detennine the average induced velocity at the lifting line [4]. In 1952, Lcrbs simplified the calculations by introducing the concept ofinduction factors [5]. The induction factors depend only on helix geometry and therefore can be calculated
dependent of loading. To achieve this, Lerhs made two assumptions. One, that the radial induced velocity is assumed to be negliglble in the cases of light to moderate loading; the other, that the calculated hydrodynamic pitch approximates the shape ofthe streamlines in the wake. These are assumed to depend only on the axial and tangential velocity components [5]. Lerbs extended Glauert's methods to calculate element contributions to thrust and torque along the blade span. The results were integrated over the propeller blades to give overall performance ofthe propellers. He effectively produced the first practical numerical propeller design method applied under various non-optimum conditions of loading [5]. Lerbs' method became known as the lifting line method for marine propellers, because the force produced by the circulation is assumed to act along radial lines in place ofthe blades, similar to the theory ofairscrews r6]. In 1955, Eckhardt and Morgan developed an engineering approach to the lifting line method. They assumed an optimum distribution ofcirculation, and a reduced thrust, proportional to the Goldstein factor due to the number ofblades, and proceeded to calculate induced velocities. This greatly reduced the amount ofcalculations. They also showed that their method produced only small errors under light and moderate loading conditions and therefore it is a very useful design tool [7]. In 1976, panel method was initially developed as lower-order method for incompressible and subsonic nows [8]. In 1985, Hess and Valarezo introduced the panel method for marine propcl1ers that allowed them to vary the pitch values and distributions and take into account the inflow wake distribution and cavitation effects [9]. The panel method
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Page 7 and 8: Table of Contents Abstract ... Ackn
Page 9: List ofTables Table I: Required Inp
Page 12 and 13: Figure 46: Surface Dynamic Pressure
Page 14 and 15: a long time to analyze, draw, fabri
Page 16 and 17: Simulation work is now commonly don
Page 20 and 21: ------------------------- provides
Page 22 and 23: As can be secn in Table I, the lift
Page 24 and 25: propeller geometry has to be entere
Page 27: avoid cavitation; however, it decre
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Page 34: Table 2: Advantages and Disadvantag
Page 41 and 42: trend for many companies to reduce
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Page 47 and 48: Table 3: Prototyping Technology Mat
Page 49: quite accuratc for a testing level.
Page 54 and 55: For given values ofJ, Fn, Rn, En, t
Page 56: propeller geometry for impon into t
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3.3 Simulations using CosmosFloWork
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simulation domain are set to 6m and
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CosmosWorks can be used to check th
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Figure 33: Dynamic Pressure Distrib
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Chapter 4 Case Study: Simulation of
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The plots of RPM and thrust from ou
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Figure 46: Surface Dynamic Pressure
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Figure 48: Deflection ofthe AUV Pro
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In this simulation, two nose cones
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Chapter 6 Propeller Fabrication by
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Figure 60: Stratasys rDM 2000 After
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Material options for Stratasys Fusi
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Chapter 7 Conclusions and Future Wo
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References III Burtner, E., 1953, "
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[20] D'Epagnier, P.K., 2005, "A Com
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Appendix 1\: The Part ofOpcnPVL_SW
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Create all of the function commands
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Appendix B: SolidWorks Macro lor th
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'create loft swModcl.ClearSelcction
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