1Propeller Design for Minimum Induced VibrationsMosaad, M. A., Mosleh, M., El-Kilani, H., and Yehia,W.

ABSTRACT

Propeller skew is the single most effective design parameter which has significant influence onreducing propeller induced vibration without sacrificing the efficiency. Up to date applications ofpropeller skew for a certain propeller almost does not has a specified criteria. In this paper aproposed concept design criteria for propeller skew is presented. Computational results for the flowpatterns of skewed propellers with different skew angles, for cavitating and non- cavitatingpropellers are presented. The simulation work is carried out by FLUENT software usingunstructured grids, based on Reynolds-Averaged Navier-Stokes computational fluid dynamicsmethod. The selection of the best propeller skew angles is based on comparative analysis of thesenumerical results. The overall results of the proposed approach may be considered practical forpropeller designs with minimum induced vibrations.

Key-Words: - Propeller skew, Vibrations, Cavitations

1. INTRODUCTION

During recent years Computational Fluid-Dynamics (CFD) models have demonstrated torapidly become effective tools to analysemarine propeller single-phase flows. Incontrast to this, cavitation presents complextwo-and multi-phase flow phenomena that arestill difficult to accurately simulate [1].Cavitation occurs on nearly all ship propellers.It may lead to expensive problems if notacknowledged in an early design stage. Thetwo most frequently occurring problems arevibrations and noise in the afterbody due tocavitation-induced pressure fluctuations on thehull, and cavitation erosion on propeller bladesand appendages. Early recognition of theseadverse effects is important, not only to ensurecompliance with contract requirements, butalso because often cavitation has to becontrolled at the cost of propeller efficiency[2]. To ensure that the propeller meets therequirements that relate to comfort (vibrationand noise) and safe and economic operation(erosion), model scale experiments orcomputations that address cavitation are to beconducted prior to construction [2].Due to high operational costs of experimentalinvestigations it is highly desirable to be ableto study cavitation with reliable CFDtechniques [3].

The paper presents optimum skew range basedon RANS comparative study of flow patterncharacteristics of two new families of skewedpropellers. These propellers are characterized bythe presence or absence of cavitation inception.The first family is a skewed propeller family ofDTMB-P4119 to be studied as non-cavitatingpropellers. The second is a family of INSEAN-E779A as cavitating propellers.2. NUMERICAL SETUP AND COMPUTATIONALAPPROACH

General conservative form of the Navier Stokesequation is presented as the continuity equation

Continuity equation,

mii

Suxt

?? )(???

???

(2.1)Where:?? = density, [kg/m3]

iu = is the velocity component in the ith direction,m/s (i =1, 2, 3) andS m = source terms.

In case of incompressible flows the density isconsidered to be constant. Since the propeller flowhas been considered as steady and incompressible,the continuity equation gets modified as,

0)( ?ii

ux

???

(2.2)

The momentum equation will be,

DRSticky NotePublished by the Port Said Engineering Research Journal, PSERJ, Port Said University, 2011.

DRHighlight

2iij

ij

i

jij

i

Fgxx

p

uux

ut

????

??

????

??

?????

? )()( (2.3)

Where:

ijl

l

i

j

j

iij x

uxu

xu ??

????

????

32)]([ ??? , (2.4)

ij? = is the Reynolds stress tensorp = static pressure, [N/m2]gi = gravitational acceleration in the ith direction ,[m/s2]Fi = external body forces in the ith direction and, N?ij is the Kronecker delta and is equal to unity wheni=j; and zero when i ? j.The Reynolds-Averaged form of the abovemomentum equation including the turbulent shearstresses is given by:

? ? ? ?

? ?jiji

i

i

i

j

j

i

j

jij

i

uuxx

p

xu

xu

xu

x

uux

ut

??????

???

???

????

?????

????

??????

????

?????

???

?????

?

?

??

??

32

(2.5)Where:

'iu = is the instantaneous velocity component, m/s (i

= 1,2, 3).In the present work, the SST (Shear StressTransport) k- ? turbulence model is chosen forturbulence closure. The SST k-? model iscurrently one of the most widely usedturbulence models for propeller flowsimulation [4].For the cavitating propeller cases, thecavitation model was activated, using a multi-phase CFD setup with water and water vaporunder normal conditions as the workingfluids.[3]Regarding the Boundary Conditions forcavitation cases were set in the same way asfor the non-cavitating cases. The onlydifference was at the exit boundary, where aconstant exit pressure was set to match thegiven cavitation number (?) [5].

The outlet boundary condition with a static

outlet pressure based on the cavitation number

can be calculated as given in [3]:

(2.6)Where:Pout= outlet pressure,[ pa]Pv= vapour pressure, [pa]?n = rotation cavitation number

(2.7)

D =Propeller diameter, [m]

N= Rate of revolutions of propeller, [rps]

P= Static pressure at point of interest, [pa]

3. PROPOSED CONCEPT DESIGN FOR MINIMUMPROPELLER INDUCED VIBRATION

In this concept design three elements wereidentified as being influential in determiningpropeller vibratory response. The three elementsof importance are pressure fluctuation, propellerloading, and cavitation inception. The objectivesof the proposed concept design are:

Minimize pressure fluctuation, within theneighbourhoods of the propeller flowfield.

Blades elements unloading throughoutminimized pressure distribution ofchordwise elements along the span of thepropeller blades.

Avoid cavitation inception whichdramatically magnifies the propellerinduced vibratory forces

The achievement of the three objectives indesign will result in many successful propellers.4. NON-CAVITATING PROPELLER

This study aims to analyze a family of skewedpropeller of different skew angle to assess theinfluence of skew in the objectives of theconcept design. The selected propeller geometryis DTMB-P4119 which is a right handed, three-bladed fixed-pitch propeller with pitch diameterratio of 1.084 of typical diameter D=0.305 m,the full details of geometry data for thispropeller was given in [6].The original design of this propeller is withoutskew, i.e. skew angle=zero. Different propellergeometries of the same propeller dimensions

3have been modeled with only difference in theskew angles. Skew angles ( S? ) applied from15:75 degrees with increment of 15 degree.The geometries of these propellers are shownin Fig.1. For the simulation purpose, designadvance coefficient J=0,833 was selected.

.deg0.0?S? .deg15?S?

.deg30?S? .deg45?S?

.deg60?S? .deg75?S?Fig. 1 Skewed Propeller Family of DTMB-

P4119

4.1 Spanwise Pressure DistributionThe pressure distribution on the blade surfacesis an important factor for blade designs,considering the cavitation suppression andmaterial strength issues [7, 8].

(4.1)

Where:Cp= pressure coefficientP= Static pressure at point of interest, [pa]Po=Reference Pressure at infinity, [pa]

Figures 2, 3 present comparison of spanwisepressure distribution expressed in terms ofpressure coefficient Cp versus distance fromthe leading edge non-dimensionalized by thechord length (X/C) at 0.7 R, 0.9 R as examples

for the Skewed Propeller Family of DTMB-P4119.

4.2 Pressure FluctuationThe predominant factor for propeller vibrationsis pressure fluctuations. In the present study ofDTMB-P4119 family of skewed propellers thenumerical results of pressure fluctuation havebeen predicted.Figure 4 shows a direct comparison between theresultant circumferential pressure fluctuations at0.7 R of the studied geometries.

4.3 Influence of Skew on Tip SpeedThe logic resultant consequence of skewapplication which plays role in reducing theblade pressure loading and fluctuation is theincrease in tip speed. Figure 5 shows results ofthe circumferential speeds on the propellers tipsfor different skew angles. The velocity analysiswas that the propeller's skew angle has only aninsignificant influence on the mean values of thetip flow velocity

4.4 Discussion of non cavitating propellerResultsApplication of propeller skew has been shown tobe effective in reducing blade loading along thespan of propeller blade. This reduction can beeasily investigated along the applied skew rangeof 0:60 degree (Figures2, 3) Skew of 75 degreesresults in increase of the negative pressure i.e.the propeller back in the tip region at 0.9 R.Concerning the pressure fluctuation the increaseof propeller skew almost improve the pressurefluctuation in the propeller flow fieldneighborhoods (Figure 4).The increased velocity as a direct consequenceof pressure reduction has been also investigated.Fig. 5 shows the slight increase in the propellertip speed which might be negligible.Finally, based on the aforementioned analysis, amoderate skew range of 45:60 degree isrecommended from hydrodynamic and vibrationpoints of view.

4Fig. 2 Chordwise Distribution of pressure coefficient for DTMB-P4119 Skewed Family at 0.7 R, J=0.833

Fig. 3 Chordwise Distribution of pressure coefficient for DTMB-P4119 Skewed Family at 0.9 R, J=0.833

5Fig. 4 Pressure Fluctuation of DTMB-P4119 Skewed Family at 0.7 R, J=0.833

Fig. 5 circumferential Tip Speeds of DTMB-P4119 Skewed Family, J=0.833

65. CAVITATING PROPELLER

The purpose of this study is to examine theproposed concept design and the criteria ofskew application for attest case of cavitatingpropeller with different number of blades. Thepropeller model selected for the present studyis INSEAN (Italian Ship Model Basin) E779Awhich is a four blade propeller, 4.5 degreeskewed, with a uniform pitch (pitch/diameter =1.1), a forward rake angle of 4 3 and adiameter of 227.2 mm.Three other geometries have been alsomodelled by skew angles of 45, 60, and 75degrees to apply and examine the proposedconcept design. This was to build a family ofskewed E779A propeller. Figure 6 shows thesegeometries.

.deg5.4?S? .deg45?S?

.deg60?S? .deg75?S?

Fig. 6 Skewed Propeller Family of E779A

For the simulation purposes, the followingoperating condition is considered: Uniformflow at speed V = 5.808 m/s and propellerrotational speed n = 36.0 rps, (advancecoefficient J = 0.71); cavitating number of?n = 1.763 [1].

5.1 Cavitating FlowCavitating flow condition is simulated at thedesign advance coefficient and cavitationnumber. Figure 7, 8 compares the predictedextensions of cavitating regions on thepropeller face and back.

.deg5.4?S? .deg45?S?

.deg60?S? .deg75?S?Fig. 7 Back Cavitation on Skewed Propeller

Family of E779A

.deg5.4?S? .deg45?S?

.deg60?S? .deg75?S?Fig. 8 Face Cavitation on Skewed Propeller

Family of E779A

5.2 Spanwise Pressure DistributionFigures 9: 11 show a chordwise distribution ofcavitating pressure at 0.6, 0.7, and 0.9 R for thepurpose of comparison of the application of theproposed concept design for the SkewedPropeller Family of E779A propeller.

7Fig. 9 Chordwise Distribution of pressure coefficient for E779A Skewed Family at 0.6 R,J=0.71

Fig. 10 Chordwise Distribution of pressure coefficient for E779A Skewed Family at 0.7 R,J=0.71

Fig. 11 Chordwise Distribution of pressure coefficient for E779A Skewed Family at 0.9 R,J=0.71

85.3. Pressure FluctuationFigure 12 shows the pressure fluctuation at 0.7R for the family of E779A skewed propellers..

Fig. 12 Pressure Fluctuation of E779A Skewed

Family at 0.7 R, J=0.71

5.4. Influence of skew on tip SpeedFor the cavitated propeller test case Figure 13shows measurements of the circumferentialspeeds on the propellers tips for different skewangles. As shown in the figures, the increase inthe mean value of tip flow velocity is small andcan be also negligible.

Fig. 13 Circumferential Tip Speeds of E779A

Skewed Family, J=0.71

95.5. Discussion of cavitating propeller Results

The analysis of non-cavitating propeller resultscame with a recommended beneficial skewrange of 45:60 degree. The efficiency of thisrange examined for a cavitating propeller andhas shown success in the objectives of theconcept design. This recommended skew rangedecreases the propeller blade elements loadingalong the cavitated propeller diameter (Figures5.4: 5.6). This unloading reduces the cavityvolumes developed on the propeller back(Figures 5.2, 5.3). The sheet cavitationdeveloped on the original design of thepropeller model with 4.5 degree skew has beentransferred to only slight tip cavitation by 60degree skew. While 75 degree skew results inexcessive negative pressures on the propellerback, and reproduced higher cavity volume onthe propeller tip region. The pressurefluctuation also decreased by implementing theproposed skew (Figure 5.7). Regarding theeffect of skew on the tip speed slight incrementhas been visualized (Figure 5.8).9. CONCLUSIONS

The proposed propeller concept design of skewshows a beneficial effect in reduction of thepressure fluctuation and blade hydrodynamicunloading, and achieving higher marginagainst cavitation inception. Increase in skewangles over 60 degree can result in higherhydrodynamic loading of blades negativepressure near tip regions. It is concluded thatthis rise in the propeller skew has been resultedin reproducing cavitation volumes on thepropeller reloaded blade elements. From thevibration point of view cavitation inception isdramatically magnifies the induced vibratoryeffects. To minimize propeller inducedvibration, the propeller design should be ingood balance between blades loading and skewangle. The increase in the mean velocities forthe applied skew angles shows insignificantinfluence on propeller tip loading. Tosummarize, a moderate skew of 45:60 degree isproposed from a hydrodynamic and vibrationpoints of view.

10. REFERENCES:[1] Francesco Salvatore1, F., Streckwall, H.,

Propeller Cavitation Modelling by CFD -Results from the VIRTUE 2008 RomeWorkshop, First International Symposiumon Marine Propulsors smp09, Trondheim,Norway, June 2009

[2] Tom, J.C., Terwisga, Van. CavitationResearch on Ship Propellers- A Review ofAchievements And Challenges, SixthInternational Symposium on CavitationCAV2006, Wageningen, The Netherlands,September 2006

[3] Lifante,C., Frank, T., Investigation ofPressure Fluctuations Caused by TurbulentAnd Cavitating Flow Around A P1356 ShipPropeller, ANSYS Germany GmbH,Otterfing, Germany, NAFEMS Seminar:Wiesbaden, Germany, 2008

[4] Krasilnikov, V., Jiaying, S., CFDInvestigation in Scale Effect on Propellerswith Different Magnitude of Skew inTurbulent Flow, First InternationalSymposium on Marine Propulsors smp09,Trondheim, Norway, June 2009

[5] Shin, R, Kawamura, T. PropellerCavitation Study Using an UnstructuredGrid Based Navier-Stokes Solver, ASMEJournal of Fluids Engineering, September2004

[6] Brizzolara, S., Villa, D., A systematiccomparison between RANS and PanelMethods for Propeller Analysis, 8thInternational Conference onHydrodynamics, Ecole Centrale, Nantes,2008

[7] Validation of RANS Predictions of OpenWater Performance of A Highly SkewedPropeller with Experiments, Proceedingsof the Conference of Global ChineseScholars on Hydrodynamics, Vol 18, Issue3, July 2006, Pages 520-528

[8] Abdel-Maksoud, M., Menter, and F.,Wuttke, H., Viscous Flow Simulations forConventional and High-Skew MarinePropellers, Ship Technology Research,Vol. 45, No. 2, 1998.