Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Propulsor Design Using Clebsch Formulation
Propulsor Design Using Clebsch Formulation
Pages 284-300
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From page 284... ...
ABSTRACT A three dimensional invense design method is presented for the design of marine propulsors This method makes use of the Clebsch representation of the rotational part of the ve ocity held for modeling both the bound vorticity of blade surfaces and the free stream vor city The blade shape is detemmined by imposing the flow tangency condition for a given loading specihcation This technique is demonstrated here for the design of a ducted pod propulsor operating in a unifomm stream and a ducted propulsor mounted on the tail of an axisymmetnc body operating in a shear onset Row For the case of ducted propulsor design, both mixed and axial flow conhqurabons are presented to demonstrate the use of mixed flow concept for cavitation perfommance improvement INTRODUCTION The problem of propulsor design has aroused considerable the reheal interest for over half a century For examp e, the lining line [1 ] and limbo surface theories [2]
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From page 285... ...
that the vo~baty vector lies on the surface of Bernoulli surface Therefore the hrst Clebsch potential to m c de the free stream shear can be identhed as the total head H The second Clebsch potential requires a time scale representati on i n order to m ake the vorti a ty dehnition The deft function [15] provides such representation and is consistent with the overall scheme of the fommulabon The drip function can be interpreted, as the bme required for a fluid particle to trove hrom a reference position to reach a particular point in the nc :: he d and it can written as
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From page 286... ...
fbisthemeanof(7) Appropnate Clebsch potentials for both blade effect and free stream shear effect have been identified and can be applied to the propulsor flow modeling The velocity held has to satisfy continuity condition by taking the divergence of (1)
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From page 287... ...
It was vended and further enhanced at Naval Surface Warfare Center Carderock Division (NSWCCD) so that it can be used for practical propulsor design The code can perfomm inverse blading design for a given body and duct geometry Upstream inflow velocity and static pressure distributions must be preach bed The blade loading is specified by prescnlzn3 span ::lse swirl velocity distribubons at the leading and trailing edges of the blade rows The code has two modes of blade design with a given duct and body geometry The hrst mode is to design the blades according to the given loading and duct geometry in this case, the mass nc :: rate is a calculated parameter The second mode is to design for a given mass nc :: rate and the load distnbubon will be scaled accordingly to achieve the required mass nc :: rate for a heed duct and body geometry The second mode also allows vanabon of duct geometry by increasing or decreasing duct radius for a heed load distribubon A generalized load distribution algorithm has been incorporated so that different chordwise load distnbubons can be specified along different streamlines The new capability enables hne tuning in blade design which is partculary useful for Made section design near the end:.
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From page 288... ...
can predict the above mentioned effect with fairly good results it is shil notvery time and cost ehectve to incorporate RAMS in the design iteration RAMS is used only to analyze selected design candidates Use of RAMS as analysis tool in propulsor design has been proven to be very effective However it is highly desirable to incorporate in the love se design mode as much physical phenomena as possible The be Eat is that the candidate design for RAMS analysis should be very close to the best comprc mised design The Clebsch approach provides a base for incorporation of of her ehects during the design calculation The secondary flow is intrinsically captured using the fully three dimensional fommulation Theoretically, the boundary layer developed on the lower surface of the duct can also be modeled in the
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From page 289... ...
The stacking positions for both rotor and stators are at the leading edge of the blades. Only the zero harmonic or the circumferential averaged design calculations were performed to evaluate different blade load distributions.
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From page 290... ...
115852 0.0719415 0.0270212 0.0178991 .0528194 Figure 6 Pressure Distribution with Force Vortex Loading for the Pressure Side I,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, -1 -0 75 -0 ~ -0 25 0 0 25 0 ~ 0 75 1 1 25 Or rid CPNON 0.4SS108 0.S82827 0.SS2545 0.2822ti5 0.2S1 984 0.18170S 0.1S1422 0.0811 41 0.0S08ti .019421 0.059702 0.1 1998S .170254 0.220545 0.27082ti Figure 7 Pressure Distribution with Force Vortex Loading for the Suction Side The effect of hub unloading is clear by comparing the pressure distributions depicted in Figures 2 to 7. The negative pressure peak and the adverse pressure gradient near the rotor root region have been greatly reduced.
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From page 291... ...
The next two design examples show the effective use of mixed flow concept for cavitation improvement if manipulation of loading is not adequate for desired improvement in cavitation. DESIGN EXAMPLE 2 - AXIAL PRESWIRL A preswirl propulsor is defined as a Figure 10 Rotor Blade Shape ducted propulsor with a set of preswirl stators in front of the rotor.
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From page 292... ...
The resultant pressure distributions on suction and pressure sides and the net pressure distribution are shown in Figures 16, 17 and 18. O .g: n is O BE no 1 _ _1-: 5 .~ l l l l l l l l l l 0.O 0.7 on ~ = l l l l l l l l l l l l l l l l l l l l OH O9 1 1 1 Figure 14 Inflow Meridional Velocity Distribution a ~ n r; n ~ Figure 15 Loading Distributions for the rotor and stator CPNON 0.173783 0.142552 0.11 1S2 0.080088B 0.0~88574 0.01 7Ei259 - 0.01 3ti05E - 0.0~48371 -0.076OE86 -0.1073 - 0.138532 o.
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From page 293... ...
The intent here is not to optimize the present design, but to demonstrate the idea of mixed flow in propulsor design for cavitation performance improvement under the same design requirements. Figure 1 9 shows the pressure distributions on the duct upper and lower surfaces and on the stern surface.
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From page 294... ...
A notional mixed flow propulsor design is presented here to illustrate the use the present design code for such propulsor design and to show the potential gains in performance as compared with that for an axial unit. The body configuration and the inflow conditions are the same as the previous axial preswirl example.
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From page 295... ...
1 or -or. UPPER BIDET it ~ \, 81~ 1 X Figure 27 Pressure Distributions for the Duct and Stern The duct and the stern axial forces as a percentage of rotor thrust for the mixed flow Preswirl is different from that for the axial preswirl.
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From page 296... ...
The duct lower surface boundary layer development is quite different as compared with that for an axial flow. Its interaction with the rotor tip gap and effect of flow passage geometry on the tip gap physics is still unclear for mixed flow propulsor design.
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From page 297... ...
Hladk, S D and Diggs, J G " A or upled Viscous/Potential Flow Design Method for Wake Adapted, Multi Stage, Ducted Propulsors Using Generalized Geometry ", Trans SNAME, Vd 102, pp2 1 2 28,1994 8 Renick D H " An Analysis Procedure for Advanced Propulsor Design " Master of S ci ence Thesi s M assacll usetts I nsti tute of Technolonv, May 1999 9 McHnde, M W " The Design and Analysis of Turbomachinery in an incompressible, Steady Flow Using the Streamline Curvature Method " Technical Memorandum TM 79 Fe 1nsvl. area State University, February, 1979 10 Tan, C S
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From page 298... ...
15 Lighthill, M J " Drift" J Fluid Mech Vol 1' pp 3153 1956
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From page 299... ...
e wifih Frofessor Ke win's commentthat designfoods need to be fast enough so the designers c m evaluate different propulssr types Ed explore design space in m efficient meaner The computational model based on the Clebsch Fommubtion is extremely fast bee mse of its mmmerical 1 oilman on of decomposing 9 th ee-dimffnsionsl problem into 9 series of two-dimensionsl calculations Use of potential flow models in propulsor design requires the k owledge of effective wake Ed th ust deductions The use of either sxisymmetric RA! dS or Eid r Salvers wifih 9 Lifting Su—-.
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From page 300... ...
vorticity such that She vorticity may not be small in ce thin region of the flow passage he on -l l shear Assumption ma. not be valid mdbkding designhas to take into account She distortion of the free stream vo ticity due to blade deflection The Clebsch fommubtion provides s theoretical framework that is not rein limed to the w ok shear as mmption In principle, the Clebsch formulation represents s design theory based on ire -isc id rotation theory model it c m be degenerated to s special case that is equivalent to She Euder/Liftmg Surface Model by only accounting for the shear in the zero harmonic solution We have not pe formed s simulation for m open propeller md are pkmomg to perform such simulation in the future The convergence properties for the openpropeller wil l definitely be e- chatted In regard to Dr 5 mchezCsjs's comment on She large hub design The Clebsch formulation does not make use of the image m odel that potential flow m od is ha ve to use The use of mgukr momentum as design variable does not impose my constraints on She large hub boundary The challenge for the large hub design is merely the question of prescribing good losdmg dish ibution for such design application
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