Cavitation inception tests on a systematic series of two bladed propellers

September 2006

G. Kulper, T.3.C. van Terwisga, e.a. Deift University of Technology

Ship Hydromechanics Laboratory, TU Deift

Mekelweg 2, 26282 CD Deift

TUDeift

Deift University of Technology

Cavitation inception tests on a systematic

serles of two bladed Propellers

by

G. Kuiper, T.J.C.. van Terwisga,

G-3. Zondervan, S.D. 3essup and M. Krikke

Report No. 1565-p

₂₀₀₆

Presented at the 26th Symposium on Naval Hydrodynamics, Rome, Italy 17-22 September 2006

Page lof 1/2

26th Symposium on Naval Hydrodynamics

_{Page 1 of i} Forward Opening Speech Group Photo Keynote Lectures Cavitation Drag Reduction

Fast or Unconventional Ships Fluid Dynamics in the Naval Context Hydro-Structural AcoustIcs

Maneuvering

Nonlinear Wave-Induced Motions and Loads

Optimization

Propulsor Hydrodynamics Ship Wave Hydrodynamics Viscous Ship Hydrodynamics Wake Dynamics

Participants

26th Symposium on Naval

Hydrodynamics

Hotel Palazzo Carpegna

Rome, Italy

September 17-22, 2006

A portion of the work done to prepare this document was performed under Department of the Navy Contract N0001404D0564 issued by the Office of Naval Research under contract authorIty NR 201-124. However, the content does not necessarily reflect the position or the policy of the Department of the Navy or the government, and no official endorsement should be Inferred. The United States Government has at least a royalty-free, nonexciusive, and irrevocable lIcense throughout the world

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Copyright 2007 by Strategic Analysis, Inc. All rights reserved.

Printed in the United States of America.

26th Symposium on Naval Hydrodynamics

Page 1 of I

Forward Opening Speech Group Photo Keynote Lectures Cavitation Drag Reduction

Fast or Unconventional Ships Fluid Dynamics in the Naval Context Hydro-Structural Acoustics

Maneuvering

Nonlinear Wave-Induced Motions and Loads

Optimization

Propulsor Hydrodynamics Ship Wave Hydrodynamics Viscous Ship Hydrodynamics Wake Dynamics

Participants

file://X:\Lndex.htm

8/28/2007

Cavitation Inception Tests on a Systematic Series of Two-Bladed Propellers

Kuiper i G., Van Terwisga i T.J.C, Zondervan i Jessup 2 S.D. Krikke M.

'MARIN, NL; 2NSWCCD, US; 3Royal _{Netherlands Navy, NL} Discussion

Effect of Gas Diffusion on Bubble Entrainment_and Dynamics Around a Propeller

Hsiao C.-T., Jam A., Chahine G.L. Dynaflow Inc., US

Dynamics and Noise Emission of Vortex Cavitation Bubbles Choi _{J., Hsiao 2 C.-T., Chahine 2 G.L., Ceccio 1 S.}

1University of Michigan, US; 2Dynaflow _{Inc. US} Computation of Turbulent Super andTPartially _Cävitating

r Flows Beneath a Free Surface

Kinzel M.P., Lindau 1W., Paterson E.G., Kunz R.F., Ñoack R.W., BogerD.A., Trujillo M.F.

Applied Research Laboratory/Pennsylvania State University, US

Discussion

Identification of Large Scale Structures in the. Wake of Cavitating Hydrofoils Using LES and Time-ResolvedPIV

Wosnik 'M., Arndt

R.E.A., Qin 2

1University of Minnesota, US; 2WhiteDrive Products,. US Discussion

Modeling of Cavitation Inception in High-Reynolds_Number Circular Jets Using Detached-Eddy Simulation

Edge B.A., Trujillo M.F., Paterson E.G.

Applied Research Laboratory/Pennsylvania State University1 US

Discussion

Bubble Interaction with a Propeller Flow Pereira ' F., CastafioGraff 2 E., Gharib 2 M.

1INSEAN, IT; 2CALÏECH US

Computation of the Unsteady Two-Phase Flow Around a

Maneuvering Surface Ship

Hyman 'M.C., Moraga 2 F.J., Drew 2 D.A,, Lahey 2 R.T. 1Naval Surface Warfare Center-Panama City, US;

2Rensselaer Polytechnic Institute, US Discussion

Effect ôf Unsteady Turbulent Fluctuationson Vortex/Vortex/Nuclei Interaction

Hsìao C.-T., Chahine G.L. Dynaflow Inc., US

ABSTRACT

The paperaimsat propellerdesign techniques Which suppress inception of tip vortex cavitation. Model tests provide insight in the phenomena associated with tip vortex cavitation inception on propeller blades and the important parameters are systematically varied and investigated. Theapplication ofthis work is primarily directed to improvements onnavál propellers. However, lessons learned are also useful in thedesign of propellers formerchantships, wherethere is a risk of cavitation hindrance dueto vibrations or noise.

A systematicseries of propeller blade designs has been made, based around an :existingstate ofthe art controllablepitchNaval propeller design Geometric parameters were varied in the tip region including thickness, planform, skew, chord distribution and rake. All theseparameters Were varied While maintaining a constant radial loading distribution.

The results of the cavitation inception tests are presented in the form of inception diagraÑs for the distinct types of tip vortex cavitation that can be distinguished (trailing, local tip and' leadingedge vortex cavitation). Cavitation inception performance is quantified .bythe width Of the non cavitatingrangeof operating conditions at constant a,referred toas the cavitation bucket. The systematic tests indicate that the blade contour isan irnportant,parameterin tip vortex inception.

Using the resultsofthesystematic tests a seriòs of propeller models were designed in an effort to improve the results furtherby combinationsof the parameters in the systematic tests. The results showed nosignificant improvements, but indicated the pitfalls

26th

Symposium on NavaF Hydrodynamics

Rome, Italy, 17-22 September 2006

Cavitation inception tests on

_{a systematic series of two}

bladed propellers

G.Kuiper, TJ.C. Van Terwisga, G-J. Zondervan

MAR1N, Wageningen, The Netherlands),

S. D. Jessup NSWC-Carderock Division, USA),

M.Krikke (Royal Netherlands Navy)

and problems which have to be avoided. A low skew planform was finally désigned aiming at the delay of cavitation inception. The model test results confiEmed thedesign guidance derived from the systematic tests. Recent full scaleobsCrvátjonsconfirmed themodel test resultsand provide an illûstrationofthepotential of the new design technique.

Panel Method: analysis was used to assist in thedesign ofthevarióus; tip variants. The possibilities and shortcomings in application of inviscid computations for the analysis of tip: flow arequantified.

INTRODUCTION

Investigations into delay of the onset of cavitatiOn on low noise propellers have traditionally been focused on inceptiOn of sheet type cavitation. The principal

design objective Was the "bucket width" of the

propeller blade sections. The so-called cavitation 'bucket' relates the minimum pressure on the blade sectiOn to the angle of attack. This has led to sections

with a wide cavitation bucket, such as the Eppler

sections. (Eppler and Shen, 1979, Shen and Eppler,

1981) The replacement of the traditional NACA

sectiOns with alternate section families was followed by a design method, where sections were designed with a bucket width adapted to the variations in angle of attack which Were experienced. This technique was developed in a combined research program iñ Which the US Navy, The Royal Netherlands Navy(RNN)and Marin cooperated. ( Kuiper and Jessup, 1993) . As a

result of the suppression of inception of sheet

cavitation 'inception were investigated aiming at

developing propeller design tools for this purpose. This paper is based on some of the findings of this research effort.

Numerous 'ideas have been :proposed to suppress tip vortex cavitation inception on propellers or foils.. A review wasP given in 1979 by Platzer and Souders (1979). Most devices, however, imply sharp cornersor edges in the tip region and experience has shown that possible benefits in suppression of the tip vortex are mostly overshadbwed by promotion of cavitation inception on those edges. The only method applied generally to delay tip vortex inception has therefore beena reduction of the tip loading.

LP

MAI

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CITAyANft,

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Fig. 1.From Platzer ans Souders, 1979.

Tools for the prediction of tip vortex strength are

scarce. For example the relation between the blade loading from O.9R to the tip as a measure for the strength of the'tip vortex has' been used. This relation

could provide a qualitative indication of a vortex

strength, useful for comparing the strength of the tip vortex

at various propellers or at various radial

loading distributions, but it is far from a predictión of the inception conditiòns.

From comparisons between tip vortex inception at model and full scale it has become clear that viscous effects are strong. The minimum pressure in a non-cavitating voEtex is strongly dependent on a Reynolds number and a more or less 'empirical scaling law is

generally used (McCormick,1962) in which the

inception index of a vortex is taken proportional to the Reynolds number to a certain power. Depending on the facility used this power varies between 0.2 and

05.

For the prediction or scaling of tip vortex inception a viscous calculation could provide valúable insights. Süch a viscous calculation method is not yet readily available. Early efforts with RANS codeswere

carried out on

foils (Dacles-Mariani and Zilliac,

1005), and nowadays viscous calculations on

propellers in uniform conditions are being performed (e;g in the EC project Leading Edge). Unsteady tip vortex calôulations are possible, but veiy time

consuming and the convergence and grid

independency remains very problematic. These

calculations are still far from being used as a design tool. 'During the start of the TIPVOR project the only design tool available with a certain degree of accuracy and stability was the non-cavitating, fully wetted panel code for propellers.

TYPES OFTIP VORTICES ON PROPELLERS The TIPVOR research project started with a detailed investigation on the physics of the tip vortex near inception of cavitation in the vortex core Attention was given' to the accuracy of the determination of inception at model scale and it was concluded that the blade geometry was a major factor in this.. Since

model propellers today are manufactüred with

numerically controlled tools, the variation in tip

geometry and thus the variation between blades has been significantly reduced This also proves that the geometry has a major influence on the inception of cavitation Instead of investigating the devices as' in Figure 1, it was therefore decided to investigate the geometry of a faired conventional propeller tip and to develop design methods for this geometry.

Closer examination of various inception conditions showed that three types of tip vortices could be distinguished: the trailing tip vortex, the local tip vortex and the leading edge tip vortex. (Terwisga et al,

1999)

Trailing

type of vortex

cavitation is generally

associated with a vortex, building up strength

in

downstream direction. The physical mechanism

involved 'is the roll-up process of the trailing vorticity behind the blades. Cavitation inception occurs away from the blade (detached inception), but very often

cavitation develops up to the blade or cavitation

attention has been given in literature to this type of tip vortex cavitation.

Fig. 2 Trailing tip vortex.(attached)

Leading-edge vortex cavitation

is another form of

vortex cavitation that can be observed on propeller blades. Similar to the development of a tip vortex on a delta wing, a cavitating vortex can be seen breaking away from a propeller blade. A Navy propeller will

have a strongly unloaded tip in order to delay tip

vortex cavitation. lt will have a reduced loading at the

blade hub to avoid hub and root cavitation, and

consequently it will have it's loading concentrated in

the middle of the blade. This leads to

a vortex originationg at the leading edge, passing the tip at some distance. The behaviour of the leading-edge vortex can be veiy dynamic, depending on the blade loading and will not cavitate if not sufficiently strong.

Fig. 3 Leading edge tip vortex

Local tip vortex cavitation originates from separation of the flow at the very tip of the propeller blade. The pressure distribution on the tip and the geometry of the tip play an important role. At a light tip loading this type of cavitation is not related to the roll-up of the tip vortex. At moderate tip loading it may coincide with trailing vortex cavitation.

Local and leading edge vortex formation can also merge. A local tip vortex occurs downstream of the blade tip, a leading edge vortex originates upstream of

the tip and in the limit they coincide. Distinction

between the two is useful, however, because in many cases the two types of vortices occur simultaneously. They can often be distinguished more clearly froma

paint test in steady (open water) conditions (Fig.5).

Fig. 4 Local tip vortex

Fig. 5 Paint test on pressure side of parent propeller

at low loading (KT=O.05)

The inception conditions of a propeller are of course dependent on the first type of tip vortex inception which occurs. It is important to distinguish between

them because the parameters influencing their inception, and therefore the ways to improve a design, are quite different. Inception of the trailing vortex can

be controlled by the loading distribution of the

sections at the tip. Inception of a leading edge vortex can be influenced by the leading edge contour and its loading. Inception of the local tip vortex depends both on tip loading and geometrical details of the blade tip..

POTENTIAL FLOW ANALYSIS

As mentioned in the introduction, viscous codes are

still

_{insufficient for design purposes and in the}

of the wake panels equal to the local pitch of the Sections at the same radius No contraction or roll-up was considered. In these calculatiOns the focus is on the pressure distribution on the blades, but also on :the

pressure gradients near the tip and the leading edge, because these pressure gradients are the locations where separation may occur and where vortex formation can start. In later stages also the direction of the streamlines on the propeller surface was considered, mainly to see if the streamlines in the design condition would not cross the leading edge or the tip. Such a crossing will also cause a low pressure peak, but the direction of the streamlines may be a more;clear indicatorof problem areas.

Since in the calculations there is no separation the minimum pressure in the tip region is taken as a criterion for cavitation inception. This is of course a

major simplification of the pressure distribution in the viscous core ofa vortex.

A radial grid distribution was used. This leads to a

singulare grid element in the tip. This, however,was not the major limitation of the panel calculations. The most importantproblem was singular behaviour of the pressure at the trailing edge in the tip regiàn. Grid refinement was no solution, on the contrary (Fig. 5) The cause of this singularity may be the prescribed

location of the wake, which is not necessarily force free in the prescribed position.

Investigations have been made to improve this by adjusting the position of the

first row of wake

elements or by allowing a force acting on them. But these investigations are outside the scope of this paper.

01

0.2

.02 0 0.2 0.4 08

Fig 5 Calculated pressure distribution at O.97R radius.

08 1 12

At O99R the pressure distribution was very scattering due to this.effect. So O.97R is used as a reference, with neglect of the trailing edge singular behaviour. Apart from the fact that it proved to be very difficült to predict the minimum pressure in the tip region reliably, this singularity was sometimes so strong that it affected the radial loading distribution. This was

especially the case with some highly skewed propellers

DEVELOPMENT 0F A SYSTEMATIC TWO

BLADED PROPELLER SERIES

In finding relevant parameters describing the propeller blade geometry, the distinction between the mentioned types of tip vortices plays an important role. The parameters chosen fór optimisation are often dictated by the propeller design method. Design parameters sch as camber, thickness and angle of attack of the blade thickness are parameters because. they are used in the design of the propeller.

In the present investigation the focus was on the pressure distribution near the tip, as calculated by the panel code. This makes it possibleto use more integral variables involving also the radial distribution of the sectional characteristics. The parameters chosen were:

the shape of the blade:contour, the shapeof the tip geometry the rake at the tip.

These are more general features of a propeller blade design and are more difficult to quanti1i in a single geometry parameter. Therefore the following approach was chosen: systematic variation ofa parent propeller. In this way the possibilities of the panel code in treating the difficult problem of tip-vortex development was investigated and design criteria could be deduced for improvement of tip vortex cavitation inception..

To investigate the cavitation inception characteristics

as accurately as possible by means of model experiments, the inflöw conditions have to be defined and have to be repeatable. _{This is very difficult in} non-uniform inflow, because of the interaction between the wake generating structitre (a hull, a dummy model or a wake screen) and the propeller. Therefore propellers were used in open water, witha

accumulation of large amounts of gas ¡n the tip vortex. The risk of gaseous cavitation was further reduced by using the experimental procedure of calling inception first, _{while determining desinence of the vortex} cavitation immediately after that. In case of strong hysteresis the desinent inception conditions were used in combination with a short duration of the cavitation. The inception conditions_{were determined in the Large} Cavitation Tunnel of Marin and insome cases also in the 36" tunnel of the David Taylor Model _{Basin in} Carderock, USA. A hub was manufactured in which two blades could be inserted. The diameter of the two bladed propeller was 40 cm, large enough to ensure geometric accuracy when the blades were manufactured with a numerically controlled milling machine. The selection of a two bladed propeller simplified the calculations because of a reduction of the blade to blade interference.

THE PARENT PROPELLER DESIGN

A 2 bladed parent propeller was designed to have the same blade sections and radial loading distributionas

a typical high quality navy propeller. The inception characteristics measured for the various tip _vortex types are presented in the inception diagram in Fig. 5.

suction side cavitation, the curveson the left hand side

are the inception conditions of pressure side cavitation. Only the curves of tip vortex cavitationare

given here. A propeller with optimum inception conditions has all types of cavitation incepting _{at the} same time.

A propeller that is optimum from a cavitation inception point of view has a bottom of the bucketas

low as possible while the operationalcurve crosses

through the lowest point of the bucket. Such an

optimisation criterion can lead, however, to a very narrow bucket, which in practice is useless because the propeller is never operating exactly along its operational curve (e.g. due to added resistance dueto wind and waves or pitch variations in case of controllable pitch propellers). Therefore the width of the bucket near the bottom is even more important. In the present investigation the width of the bucketat a cavitation index of 2 has been used as a criterion. This width is indicated in Fig. 5 and is expressedin the range of the thrust coefficient K1 _{. The bucket} width of the parent propeller was 0.095 and trailing vortex inception was the critical type, very close to local vortex inception. The purpose of the present investigation is to increase this bucket width.

VARIATION OF THE TIP LOADING

To achieve the highest possible cavitation inception speed the operating curve of the propeller has _to intersect the lowest point of the cavitation bucket. The pitch of the propeller, and especially the pitch of the tip, plays an important role here. It is not possibleto simply adjust the pitch of the parent propeller, because in that case also the radial loading distribution varies strongly. To veri1' that the tip loading_{can adjust the} cavitation bucket to bring it in line with the operating curve a separate two bladed propeller was designed with a more unloaded tip.

The loading from 0.8R towards the tip was decreased, the loading around 0.6R was increased, _to maintain the same power vs. rpm relationship _{as the} parent propeller. From panel code calculations itwas found that such a change would result inan increased suction peak at the leading edge near the tip, so the camber of the tip sections was adjusted. _{After a} number of iterations the pressure peak _{near the} leading-edge at 0.97R was designed in such a way that it matched the minimum pressure at the pressure side (Fig.6). The tip loading was significantly reduced with only a positive loading in the forward part of the section.

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Fig.7. Cavitation bucket of unloaded

tip variant.

(dotted lines are from the parent propeller)

VARIATION OF TIP THICKNESS

The flow around the propeller tip is highly

three-dimensional and sectional considerations are losing their hydrodynamic significance very close to the tip. The idea is that a thicker tip causes a lower pressure gradient along the contour, thus suppressing boundary layer separation and subsequent vortex formation.

The maximum thickness in the tip region was varied using several variants in the design stage, as shown in Fig. 8. The gray area indicates the final increase in tip thickness which was applied for the model propeller with a thicker tip.

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Fig.6 Pressure distributions at 0.97 R on parent and unloaded tip variant

In this way the pressure gradient perpendicular to the leading edge was minimized. The resulting unloaded tip propeller had the same open water performance as the parent propeller. The thrust coefficient and the efficiency in the inception region (around Kt=0.I) were less than 1% different from the parent propeller. This is to illustrate that even a change in loading of the tip requires a complete redesign of the propeller. All the subsequent variations in this project were the result of a series of calculations in which a variant was optimized.

The resulting cavitation bucket of the unloaded variant is shown in Fig. 7. There is a difference between local

and leading edge inception at the pressure side,

indicating that the shape of the tip can probably be further improved. The bucket width of the unloaded tip propeller was 0.085, slightly, but not significantly

less than the parent propeller. But the shift of the

bucket is considerable and illustrates that with a

proper choice of the tip loading the bucket can be adjusted to the operating curve without significant loss of bucket width.

0.6 07 08 0.9 i 11

nR

Fig.8 Variations of the radial distribution of the

maximum thickness.

As can be seen the parent propeller already had an increased thickness at the tipi The chordwise position

of the maximum thickness was varied in order to

decrease: the pressure gradient perpendicular to the blade contour in the tip region while delaying as much as, possible the formation of low pressure peaks at = 2. In all cases the radial loading distribution at the tip was maintained.

The influence of the applied thickness variations on the pressure distribution wasP most pronounced at higher blade loadings,

but remáined very small

Although a reduction of the presÑure gradient at the leading edge, upstream of the tip, could be obtained, the effect on the bucket width was small., The type of inception found on the thicker tip was local tip vortex cavitation,, both at. the pressure and the suction side. The thicker leading-edge suppresses leading edge. vortex formation, and the increased surface area at the

tip apparently also decreases the strength of the

trailing vortex, but at the expense of local vortex

formation. The bucket width of this variant was 0.08

and no improvement over the

parent could be

obtained.

VARIATION OF THE CHORDLENGTH

T THE TIP

A traditional way, to reduce tip vortex cavitatión is to increase the chord length of the tip. The idea is to redüce, the pressure gradient perpendicular to the tip contour while maintaining the loading Since 'also the skew at the leading edge was used as a parameter, the increase of the chord length was obtained using the same leading edgecontour, thus creating:a strong 'tail' at the tip. The length of the sections above 0.7 R was increased upto 50%.

Here the panel code 'gave severe complicatiOns,

because of numerical errors'that occured at the.trailing edge of the outer' sections. The pressure peaks were so strong that the sectional lift and thus the propeller thrust could nótbecal'culated reliably. The loading at

the trailing

edge was

subsequently reduced by adapting the camber. The non-dimensional pressure coefficients are given 'in Fig8 for the parent and in Fig.9 for the chord variant.

Fig. 9

Figs.8 and 9. Pressure distributions on parent propeller and on the increased chord length variantat Kt"0.l'5

The pressure gradient near the tip could be reduced signilicantly, which leads to the expectation that tip vortex iñception otild be significantly reduced 'The

result of the

inception

test was more complex,

however. Inception of the the 'leading edge tip vortex was' delayed, resulting in a move to the right in the

inception diagram. But the local' tip vortex at the

suction side remained unchanged The net result was a considerable narrowing of the width of the cavitation

bucket from 0.095 to 0062. This might still

be

improved by also shifting the local inception curve, e.g 'by altering the camber distribution of the sections, but this would: still lead to a bucket width which is comparable to the parent 'propeller and not to any significant improvement. Based on these results any positive, effect on the inception of the tip-vortex of an elongationofthechord 'length coult not be confirmed.

VARIATION OF THE TIP RAKE

In a previous project (AFDEASR) it was found that

rake towards the pressure Side was effective

in

widening the cavitation bucket (Kuiper,1994). Tip

rake has also been applied to increase the efficiency (Anderson and Anderson, 1986). This is applied in the so-called "Kappel":propeller (Anderson et al, 2002), but in that case the rake is towards the suction sideand

the blade tip is loaded! Here the efféct of tip rake

towards the pressure side in combination with the loading distributión of the parent propeller (which has

an unloaded tip) is investigated, with the goal of

widening the cavitatión bucket.

The rake which was investigated is given in Fig.l0

The applied tip rake to the pressure side is rather

extreme and approaches the geometry of atip plate.

Fig. 10 Rakevariant.

The design

of such a blade

requires accurate

prediction of the flow directions, because at the tip strong curvatures are created and the flow should be aligned properly so that the flOw is not be forced to separation over these curved surfaces .Therefore the

flow direction was also shown in panel code results as shown iñ Figl 1 Such calculations were carried out

for a range of blade loadings A criterion for the

severity of the cross flow is difficult to determine, however.

The inception measurements showed a trailing vortex coming of the comerof the raked tip. Apparently there

was still

too much cross-flow over the

strong

curvature, leading to separation and vortex formation. Local and leading edge vortex inception were delayed and without the vortex on the corner of the raked tip the bucket width was increased from 0.0985 of the parent to 0.10.4, a moderate but significant increase. The prematureoccurrence of the trailing vortex on the

raked tip reduced this width to 0.085, a moderate

reduction. This confirms that strong curvatures in the tip region should be avoided. Rake with a smoother curvature, as used in Kuiper (1994) may therefore increase the bucket width, especially the width of the bucket of local and leading edge vortex cavitation.

Fig.1 i Pressure distribution and direction of wall

velocity ofrake variant at Kt0. 15

VARIATION OF THE LEADING EDGE SKEW Skew is generally defined in terms of the midchord position of the blade sections Since leading edge vortex formation takes place oñ the leading edge, the skew of the leading edge was drastically changed. Instead of a highly skewed leading edge the leading edge was made nearly straight. This leads to a strong curvature between leadingedge and tipand this corner requires attention.

In the calculations skew turned out to have significant effect on the ràdial loading distribution. It required drastic changes in camber and pitch at the tip to arrive at the same radial loading distribútión as the parent propeller. In many cases which were investigated numerically, the numerical problems at the very tip prevented an accurate determination of the loadiñg

and the pressure distribution at the tip. The skew

variant that was chosen, with a nearly straight leading edge, still had a slightly lòwer tip loading than the parent propeller. Again, this is a completely new design. Using the panel code the minimum pressure peaks in the inception region have been maximized

and as a secondary criterion the pressure gradient

perpendicular to the contourihas been minimized.

parent propeller. Also the low pressure region at the tip near the trailing edgewas considerably smaller. So the pressure gradients were not reduced.

The design condition was at Kt=0.l2, but the development of the pressure distribution is more clearly seen at Kt=O.15 as shown in Fig. 12. There is a low pressure peak at the leading edge near the tip, which is expected to give sheet cavitation , and one at the tip near the trailing edge, which is expected to give local vortex cavitation.

Fig. 12 Pressure distribution on the suction side of the skew variant at Kt=O.15.

The big surprise came with the inception diagram of this skewed variant, as shown in Fig.13.

The inception data of the parent propeller have again been inserted in the diagram. The position of the bucket reveals its lighter tip loading compared to the parent propeller. But the width is considerably larger (0.113), especially due to the shift of thepressure side local tip vortex inception. At the suction side the trailing vortex is the first to come in, indicating thata

slight further reduction of the tip loading might even improve the bucket width. Local inception at the tip is second at the suction side and occurs in the same

condition as on the parent propeller.

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AN INTERMEDIATE EVALUATION

At this point the following evaluation was made. As to the panel code as a tool it was concluded that the singularity at the tip was a serious handicap to assess and optimize certain shapes. The risk of local tip vortex inception could not be predicted using the minimum pressure in the trailing edge region of the tip. These numerical errors should be investigated further.

The assessment of the risk of trailing vortex inception using the loading of the tip region can be used in a

comparative sense. Absolute prediction of trailing vortex inception on the basis of panel code calculations is not possible or inaccurate. The tip loading can be used to shift the inception bucket of trailing vortex cavitation, but not without redesigning the sections.

The panel calculations are especially useful to avoid premature sheet cavitation and bubble cavitation. The avoidance of leading edge peaks in the pressure distribution is a necessary condition for the avoidance of sheet cavitation, but also for vortex cavitation. For the prediction of vortex cavitation the pressure gradient perpendicular to the tip has been used, but the results of this criterion are indicative at best.

was difficult to optimize further with conventional changes. Only the lengthening of the chord at the tip and application of rake _{showed the potential of a} moderate improvement of the cavitation bucket, but this would require further (experimental) optimization cycles because the improvement

_{was beyond the}

capabilities of panel code predictions.

The only significant improvement was found on the

skew variant. This parameter has therefore

been

investigated further.

FORWARD SKEW VARIANT

As a consequence of the previous results a variant was designed with forward skew. Again this was a variant

with the same loading distribution as the parent

propeller, and the blade sections in terms of pitch, camber and thickness distribution have been_adjusted

to minimize leading edge pressure peaks in the

inception region of the thrust coefficient.

The application of skew influences the boundary layer development over the propeller blades. For backward skewed propellers the combined effect of flow retardation inside the boundary layer and centrifugal forces working on the boundary layer flow particles cause a redirection of retarded vortical flow towards the tip. This results in an accumulation of vorticity in this region of the propeller and in a increase of the tip-vortex strength. In the case of forward skew, the hypothesis is that due to the shape of the leading-edge the radial flow components near the leading-edge will

be in the direction of the hub rather than the tip. It is supposed that forward skew helps in redirecting the vorticity away from the tip and therefore prevents the accumulation of vorticity into a tip-vortex.

The forward skew variant had a trailing edge with little skew and unfortunately this resulted again in numerical problems in the panel code. The tip loading from 0.95R showed an increase of the loading relative to the parent propeller, but this was considered due to the numerical difficulties.

The experimental results for the forward skewed

propeller are given in Fig.14. The bucket width is determined at the suction side by trailing tip vortex

inception. Even then the bucket width

is 0.113,

comparable with the variant with the straight leading edge. The fact that the trailing vortex cavitates first at

the suction side confirms that the tip loading

was

indeed higher than the parent propeller. This can in principle be corrected by adjusting the pitch at the tip, but this requires a new design. When the trailing tip vortex is ignored the bucket width is indeed very large

with a value of 0.16 compared to 0.095 of theparent

propeller!

KT

Fig. 14. Inception diagram of forward skew variant.

This forward skew variant was also tested at a slightly lower pitch setting (PfD (0.7R)=: 1.4 instead of 1.6). This reduces the tip loading. The result_{was a shift of}

the

_{bucket, but the bucket width, including the}

position of the trailing vortex inception line, was not changed. This illustrates that the shift of the trailing vortex line requires a new radial loading distribution at the same loading, and therefore a new design. With such a new design the bucket width could be increased

further.

The effect of skew on the bucket width, and especially on the local pressure side inception, lead to further variations.

RAISED FOREHEAD VARIANT

Forward skew may be one step too far for most ship owners and therefore an alternative blade contour was tried nick-named the 'raised forehead' contour,as

4

Fig.

15. Contours of parent propeller and raised

forehead variant.

In this variant the skew of the leading edge was

reduced only over the outer 10 percent of the radius to reduce the flow in radial direction, which seems to be contributing to the development of the tip-vortex. This gives a sharp curve of the contour near the tip, which requires further attention.

The contour as in Fig.! 5 has the same chord length distribution as the parent propeller. A variant with a shorter chord length at the tip was also designed and investigated, but with disastrous results. The bucket width nearly disappeared! This shows that skew reduction is not a panacea that can be applied without care, but should be closely integrated into the design while giving attention to the occurrence of local pressure peaks that trigger cavitation.

In order to ensure a smooth flow at the leading edge of

the raised forehead an increased thickness was

applied, forming a bulbous shape. The thickness

distribution is given in Fig. 16.

Fig. 16. Thickness distribution of raised forehead variant.

The 'raised forehead' variant of Fig.15 was designed again with the same radial loading distribution as the parent propeller and without low pressure peaks at the suction side at inception loading.

The experimental result

is shown in Fig.17. The

critical

type of inception was

local tip vortex

inception. an 3.00 100 o j.. 003 OEl OtO 02

Fig. 17 Local tip vortex inception on raised forehead

The result is not spectacular, because the bucket width is slightly smaller than that of the parent propeller. The suction side inception has slightly improved, but the expected improvement at the pressure side has disappeared.

Given these results a further analysis was made using computed pressure distributions and streamline plots in an effort to gain more insight in the flow.

Figure 18 shows the pressure distribution and the streamlines computed for the loading condition near inception at the suction side of the blade. It is shown that the streamlines follow the tip contour.

025

--t

:t-

sedr

Fig. 18 Example of correct flow lines at the suction

side.

The direction of the flow lines near the trailing edge indicate that no local tip vortex is developing here giving rise to inception of cavitation. The cavitation pattern in Fig 19 illustrates that vorticity developing at the trailing edge may leave the blade at O.9R instead of at the tip.

The local tip vortex inception at the tip is determined by the local flow near the raised forehead. A sheet is formed at the raised forehead, but vortex cavitation is delayed on the suction side, as shown in Fig. 19.

Fig. 19 Cavitation pattern on the suction side of the raised forehead variant.(a=2.0)

The local tip vortex at the pressure side, however, was observed to develop much earlier than expected. An observation of this vortex is given in Fig.20.

Fig.20 Local tip vortex inception at the pressure side of the raised forehead variant.

Figure 20 shows that the local tip vortex on the

pressure side develops directly at the leading-edge, so at the very end of the raised forehead contour. For this condition (at a lower loading) computations were also made. The pressure distribution and streamline traces for the pressure side inception condition are shown in Figure 21.

I.-P4J1

'8

Fig. 21. Streamlines at raised forehead at low loading.

Clearly visible is the strong cross flow in this loading condition occurring in the tip region. This cross flow

is likely related

to the development of a local

loading was increased, resulting in a small bucket width.

Fig.22. Streamlines at higher loading (suction side inception)

In the condition of inception at the suction side (similar as in Fig.18) such a cross flow was not present, as shown in Fig.22.

The described results illustrate the complexity ofthe

design for delayed inception of the tip vortex. The major influence of the skew of the leading edge has

been identified. However, a straightforward application of the 'raised-forehead' blade contour is no guarantee for success. Not only the pressure peaks and the gradient of the pressure distribution, but also the direction of the cross-flow has to be carefully considered and controlled.

FULL SCALE VALIDATION

In the TIPVOR project there was no time available any more to make a raised forehead variant with a wide bucket. A full scale design was then made fora

supply vessel

of the

Royal Netherlands Navy. Although the conclusions were positive, this vessel had many restrictions on the operating conditions, complicating a straightforward validation of the raised forehead concept.

The design method and criteria developed from the systematic design study so far were put to practice in

the design of a

frigate propeiJer for the Royal Netherlands Navy. The design of propellers for open-shaft arrangements usually concerns the adaptation to a wake field dominated by the wake of the struts and the influence of the inclined shaft.

On the resulting propeller full scale observations_were made. Fig.23 shows the maximum extent of the cavitation when the propeller operates at nearly full power!

4

Fig 23. Cavitation observation near full power on a

frigate propeller

There is sheet cavitation at the raised forehead, just as

in Fig.! 9, but the blade sections at the inner radii, that have been optimised for optimum tolerance for inception of cavitation, are such that sheet cavitation is absent at inner radii.

Fig.24. Detail of tip cavitation on raised forehead of a frigate propeller.

In comparison with

the performance of similar

propeller designs it can be concluded that this was the propeller with a very small amount of cavitation in full

power condition. A very clear indication of the

success of the applied approach is the fact that a tip vortex could not be observed, even at the highest ship

speeds.

The experiences with this propeller show that a raised forehead can lead to a wide cavitation bucket, but that the calculations of the inception conditions have to be carried out very carefully. Experimental validation at model scale still is absolutely required.

CONCLUDING REMARKS

In the numerical and experimental study described in this paper progress has been made in understanding the tip vortex cavitation phenomenon and criteria have been devised and tested to delay the onset of this type of cavitation.

A significant problem that was encountered during the numerical design evaluations has been the singular behaviour of the employed panel code near the trailing edge at the tip. Efforts to solve this problem, e.g. to neglect the Kutta condition at the trailing edge near the tip, will result in a lower resolution in that region. A solution to this problem has to be found or at least

the effect of this singular behaviour on the radial

loading distribution has to be avoided.

The design criteria used in this numerical exercise

were:

Avoid low pressure peaks at the blade

sections in the estimated inception conditions Minimize the pressure gradient

of the

pressure perpendicular to the tip

Ensure that the calculated flow lines do no cross the contour

Application of these

criteria is by

no means

straightforward. In

the design

process, first the

inception conditions, governed by operational

conditions, have to be set and then a blade design meeting these requirements has to be made.

Application of the criteria is far from clear in some cases and gains that are made regarding one criterion often deteriorates the other. Propeller design still is an art with many constraints.

A result of this study is

the experience that the

distinction between the origin of the tip vortex at

inception is very useful. The trailing tip vortex can be optimized rather independently from the others. Local tip vortex inception can be minimized using the panel code results. Leading edge vortex cavitation cannot be estimated by the panel code. All types have to be

determined experimentally,

where the

distinction

between them is not always easy.

The main result of the exercises has been the increased bucket width which can be obtained when, using the mentioned design techniques, the blade contour is adjusted. The forward skewed propeller remains an interesting option

, which has to be investigated

further. The raised

forehead is an intermediate

solution, which has shown to be effective, but which was found to require very careful design calculations.

ACKNOWLEDGEMENTS.

REFERENCES.

ANDERSON, S.V., ANDERSON, P.," Hydrodynamic Design of Propellers with Unconventional Geometry". Trans. RINA, 1986.

ANDERSON, P., FRIESCH, J., KAPPEL, J." Development and lidi

scale evaluation of a new

marine propeller type", 97th Hauptversammlung der SIG. Hamburg, 2002

DACLES-MARIANI, J., ZILLIAC,G.G. ," Numerical/Experimental Study of a Wingtip Vortex in the Near Field", AIAA Journal. Vol.33 NO.9, 1995, pp!56 l-1568

EPPLER,R.,SHEN,Y.I. "Wing Section for Hydrofoils-Part i:SymmetricaI Profiles", J. Ship

Research, Vol. 23,1979,pp 209-2 17

KUIPER, G., JESSUP, S.D. ,"A Propeller Design Method for Unsteady Coñditions", Trans. SNAME,

1993.

KUIPER, G. "Effects Of Skew and Rake on Cavitation Inception for Propellers with Thick Blade Sections", 20th Symposium on Naval Hydrodynamics Santa

Barbara, USA, 1994

MCCORMICK, J. , "On Cavitation Produced by a Vortex Trailing from a Lifting Surface", ASME J. Basic Ene., 1062, PP369-379

PLATZER, G.P, SOUDERS, W.G., "lip Vortex

Cavitation Delay with Application to Marine Lifting Surfaces", DTNSRDC REP. 79/051, 1 979

SI-IEN,Y.T.,EPPLER,R., "Wing Section for

Hydrofoils -Part 2": Nonsymmetrical Profiles-, J. Ship Research, VOL 25, !981,PP39-45

TERWISGA, T. VAN, KUIPER, G., RIJSBERGEN, M.X.VAN ," On Experimental Techniques for the

Determination of Tip Vortex Cavitation on Ship