The Propeller as a Source of Noise and Vibration

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M A R I T I M E R E S E A R C H I N S T I T U T E

MUtiNilWil'H The propeller as a source of noise and vibration

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THE P R O P E L L E R A S A SOURCE

OF NOISE AND VIBRATION

A lecture on ways to treat the propulsor as a

source of noise and vibration in the various stages

of design

b y

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nuj!ij=iwii.H The propeller as a source of noise and vibration

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CONTENTS Page

1 INTRODUCTION 3 1.1 Vibration of ships 3 1.2 Objectives 5 2 PHYSICAL ASPECTS OF PROPELLER INDUCED HULL PRESSURES 6

3 BACKGROUND to hull excitation forces 10 3.1 Reducing the hull excitation pressures 10

3.1.1 Reducing shaft rate 13 3.1.2 Reducing volume acceleration 13

3.1.3 Increasing Clearances 16 3.1.4 Reducing Volume Variation 16 3.2 Increasing phase relationships 28 3.3 Reducing the solid boundary factor 29 3.4 Reducing wetted surface area 31 3.5 Mode profile adaptation 31 4 TREATMENT OF HULL PRESSURES IN THE VARIOUS DESIGN STAGES 32

4.1 Stage I: Concept design 33 4.2 Stage II: Preliminary design 34

4.2.1 Design specification 34 4.2.2 Hull form design 35 4.2.3 Wake estimation 35 4.2.4 Propeller design 35 4.2.5 Performance assessment 36

4.2.6 Design selection 36 4.3 Stage III: Detailed design 36

4.3.1 Design specification 37 4.3.2 Hull form design 37 4.3.3 Hull flow assessment 37 4.3.4 Ship effective wake 38 4.3.5 Propeller design 39 4.3.6 Loading distribution 40

4.3.7 Skew 40 4.3.8 Chord-length and thickness 41

4.3.9 Propeller assessment 41 4.4 Stage IV: Final design 43

4.4.1 Final design analysis 43 4.4.2 Propeller assessment 43 4.5 Stage V: Remedial measures 44

4.5.1 Definition of the problem 44 4.5.2 Finding a solution 44

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HUJiiJiiwji.H The propeller as a source of noise and vibration

1 INTRODUCTION

1.1 Vibration of sfiips

It is practically impossible to build a ship that is entirely free from vibration. Fortunately, in most cases this is not a serious problem. Vibration becomes a problem, however, when it causes

1) fatigue damage to important structural elements in the ship;

2) serious impairment to the proper functioning and increased maintenance of essential machinery components and equipment;

3) annoyance and discomfort to the ship's personnel (and guests) and interference with the efficient performance of their duties.

The vibration level necessary to cause fatigue cracks in a structure is approximately 10 times that causing complaints from the crew. Such damages are therefore mostly experienced close to the excitation sources and particularly in the aft peak. So, usually the third consequence occurs before the other ones. Its importance relative to other causes of human annoyance and discomfort follows clearly from table 1.

Causes of discomfort During working time During leisure time

High sea states 24% 24%

High noise levels 2 2 % 2 2 %

Climate 22% 13%

Vibration 17% 34%

Other 15% 7%

Table 1: Causes of human annoyance and discomfort on board ships

The frequency range for the phenomena termed vibration on board ships is approximately 0.5-50 Hz. Broadly speaking, the vibration level depends on three parameters, being 1) the magnitude of the excitation forces;

2) the flexibility of the structure;

3) the dynamic magnification factor at different frequencies.

From this it follows that in order to reduce the risk of excessive vibrations one should 1) keep the excitation forces as small as possible;

2) avoid fiexible structures;

3) avoid structural resonance conditions.

Possible solutions to alleviate vibration problems for ships already in operation are often costly and time consuming. Doing the appropriate investigations in the correct sequence relative to the various design stages is therefore a necessity. Unfortunately this is difficult

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The propeller as a source of noise and vibration

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N E T H E R L A N D S

to realise, because of the ship's complexity as a vibrating structure. One has to consider all excitation sources and response types. A n overview of the most important ones is given in table 2, where also the coupling between the above excitation and response items is indicated.

Excitation source

Response types Excitation source

Hull girder resonance Superstructure resonance

Forced afterbody vibration

Propeller Excitation only when

number of blades and RPM are very low Possible Possible Slow running Diesel engine Vertical vibration possible

Not expected Possibly caused by

hull girder resonance Shafting vibration Longitudinal vibration

possible

Possible Not expected

Table 2: Relation between excitation sources (vertically) and response types (horizontally)

The annoying vibration of the superstructure is the primary object to keep under control and the corresponding most important source of excitation is the propeller. This is clearly shown in table 3 below. The table groups vibration problems in the superstructure of 47 ships as collected by Det norske Veritas.

Excitation source

Type of vibration

Total Excitation source

Global Local Global / Local Total

Propeller 10 27 37

Engine 4 4

Propeller / Engine 3 2 5

High sea states 1 1

Total 15 30 2 47

Table 3: Occurrence of vibration problems on 47 ships as a function of excitation source.

In dealing with the propeller as a main excitation source, the resulting pressure impulses need to be assessed. Figure 1 gives an indication of the importance of keeping the pressure impulses from the propeller low regarding the risk of fatigue damages in the afterbody. The figure is based on reported cracks in the aft peak in 20 ships where pressure impulses had already been measured. According to this investigation, 6 0 % of the ships with pressure amplitudes of the order of 10 kPa, at a frequency equal to the blade frequency, had reported fatigue damages. Another 2 0 % of the ships with pressure amplitudes of about 5 kPa had similar cracks. The maximum allowable pressure of 8 kPa that is indicated in the figure should only be regarded as an indication.

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M A R I T I M E R E S E A R C H

I N S T I T U T E

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1.0 0 . 5 / / _{8( DOO} p 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 A ( N / m 2 ) 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 A O O O O A P J O T ( N / m 2 )

• ruvMAGF RICK I FVFi f N O O F S H I P S W I T H C R A C K S . D A M A G E R I S K L E V E L ( T O T A L N O O F S H I P S

. P R E S S U R E I M P U L S E O F B L A D E F R E Q . . T O T A L P R E S S U R E I M P U L S E

Figure 1 Recommended upper limit for the single and total pressure impulse with

reference to the probability of cracks in the aft peak structure

1.2 O b j e c t i v e s

In this lecture we will confine ourselves to the study of the propeller as the main source of vibration and more specifically to the study of the hull pressures the propeller induces. Vibration transferred to the shaft (the so-called shaft induced vibration) is not treated. In the remainder of the lecture notes the physics behind propeller induced hull pressures is treated (chapter 2 ) ; a possible approach of the problem relative to the various design stages is presented (chapter 3); and finally some background to guidelines for measures for reduction of hull pressures are given (chapter 4).

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BSESaSES The propeller as a source of noise and vibration

2 PHYSICAL A S P E C T S O F P R O P E L L E R INDUCED HULL P R E S S U R E S

In the introduction it is indicated that of all the main excitation sources on board a ship (cf. figure 2) the propeller through the induction of a fluctuating hull surface pressure field, is the most important.

Figure 2 Illustration of main excitation sources on board a ship

In this chapter the physical aspects of the origination of the hull surface pressure field are investigated.

T h e operation of a propeller in the spatially varying wake field of a ship gives rise to a varying thrust and torque on each blade due to the different inflow velocities encountered at different angular positions in the wake. For the majority of hull forms, the axial wake field dominates the thrust generating component. Local turbulence levels in the inflow due to the boundary layer and propeller-hull interaction, give rise to thrust variations, while ship motions also give thrust variations. Strong interaction between the propeller and the flow feeding from the hull can cause large variations in the velocities incident to the propeller.

The above variations in blade thrust are caused by variations in the angle of attack with the incident flow at each propeller radius. These cause variations in the lift of each blade section through changes in the pressure distributions across each section. Hence, as each blade rotates, it carries with it a varying pressure field that is due both to the lift of each section and to the fluid displacement effects caused by the section thickness. This cyclic pressure field gives rise to hull excitation forces; however, their effect is small when clearances are greater than 1 5 % of the diameter, and the blades are free from cavitation.

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l.'l:AJ!N:IM!l»l The propeller as a source of noise and vibration 7

Dominating propeller excitation may arise due to pressure impulses acting on the hull, induced by the growth and collapse of the cavities on the propeller blades. The relative importance of the cavitation in this respect can be seen in figure 3.

Figure 3 The effect of propeller cavitation in relation to the non-cavitating propeller

There are significant differences between the pressure field induced by the non-cavitating propeller and that induced by transient cavitation, both with regard to phase angle changes and in the manner in which the pressure impulses diminish with distance from the propeller. Thus, at the hull surface area close to the propeller, total pressure impulses consisting of the contribution from both the non-cavitating propeller and cavitation should be included. This may be important for consideration of fatigue problems in the after peak. For hull girder and superstructure response calculations, however, only the total integrated hull surface excitation forces are of importance. In that case the contribution from the non-cavitation pressure impulses may be neglected.

The basic reasons for this are the following:

1) The pressure from a non-cavitating propeller is (approximately) proportional to the second inverse power of the distance to the propeller as opposed to a cavitating propeller where the pressure decreases (approximately) inversely proportionally to the distance;

2) The phase angles of the pressures due to cavitation are almost constant over large parts of the hull while the phase angles of the pressure from a non-cavitating propeller will vary along the hull.

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uiAJ!iJiHJii.ia The propeller as a source of noise and vibration 8

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In figure 4 a schematised hull surface pressure distribution is drawn, with both contributions from non-cavitating and cavitating propeller.

Figure 4 Example of an idealised pressure distribution due to the cavitating (index c)

and the non-cavitating propeller (index o)

The total force distribution along the hull is depicted schematically in figure 5 for both loaded and ballast conditions.

1 UNIT LENGTH

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Given the fact that this total force is primarily made up of the cavitating contribution, knowing the types of cavitation causing this is important. Different types of cavitation occur in practice. From the point of view of hull excitation, the following types have been identified as major contributors:

1) Suction side sheet cavitation on the blade;

2) Tip vortex and collapsing sheet cavitation off the blade; 3) Propeller-hull vortex cavitation.

In general, the hub vortex does not contribute significantly to hull vibration unless it is very strong and excites the rudder. Face cavitation, although contributing to high frequency noise, does not contribute significantly to hull excitation. Except for ships requiring a low radiated noise signature, the majority of excitation problems from cavitating propellers are associated with well-developed cavitation.

The formation of significant volumes of cavitation, and their subsequent growth and collapse as each blade traverses the wake peak, gives rise to violent pressure pulses (or rather shock waves) that excite the nearby plating of the hull.

Due to the shock nature of the pressure wave, the hull experiences an almost instantaneous pressure pulse over the aft area of the hull plating; hence maximum force is exerted. This contrasts with the non-cavitating case in which the plating experiences large differences in the phase of the pressure peak; hence a smaller force is generated. For single screw hull forms with relatively short stern overhangs, the dominating phenomenon is the dynamic suction-side sheet cavity and its extension into the wake.

The pulsating pressures interacting with the hull give rise to vibration of the ship's structure, that in turn generates a reactive pressure field. The mode profile of the hull affects the dynamic loading and hence the level of response of a given structure to the excitation pressure distribution that emanates from the propeller. Pressure applied at, or near node-points has little or no dynamic effect while the reverse is true at anti-nodes.

Experience gained from scaled model tests and full scale observations indicate that midchord cavitation, cloud, foam and streak cavitation and sheet cavitation on the face of the propeller blade are the prime reasons for propeller erosion, whereas extensive sheet cavitation on the back of the blade (covering 5 0 % or more of the blade area) is responsible for thrust breakdown. Within the context of cavitation induced hull excitation, sheet and vortex cavitation have attracted most attention and are assumed to be responsible for a large part of the induced pressure. These two types of cavitation may form either on the blades or off the blades of a propeller. In general, cavitation on the blade is responsible for the blade passage frequency component and its first few harmonics, whereas cavitation off the blade often collapses in a semi-random manner mainly giving rise to pressures at higher harmonic multiples of the blade passage frequency.

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The propeller as a source of noise and vibration 10

3 BACKGROUND TO HULL EXCITATION F O R C E S

Hull excitation forces due to partially cavitating propellers have been shown experimentally and theoretically to derive from rapid growth and collapse of the cavities, both on and off the blades. This rapid variation gives rise to a near-instantaneous pressure pulse per blade passage which acts (in phase) over the whole of the wetted surface of the stern. The response of the hull structure to a distributed pressure field depends on the local panel stiffness and resonances, and to the global response of the hull (i.e. its mode profile).

In mathematical terms the exciting force is given by:

F H U L L = j M p S B F n , p e'("'-<P) dS (1) WA

where:

FHULL = Hull Excitation Force;

Mp Mode Profile;

S B F = Solid Boundary Factor;

P Pressure Amplitude;

CO Excitation Frequency;

t Time;

(p Phase Angle;

nz Unit normal in the vertical direction;

dS Wetted Surface (Elemental) Area;

W A = Wetted Area.

Hence, the hull excitation force due to cavitating propellers may be reduced by: Reducing the hull excitation pressures (section 4.1);

Increasing the phasing relationships between surface locations (section 4.2); Reducing the solid boundary factor (section 4.3);

Reducing the effective wetted surface area on which the pressure field acts (section 4.4);

Adapting the longitudinal distribution of force to the mode profile of the hull (section 4.5).

These items will be addressed in the following sections.

3.1 R e d u c i n g the hull excitation p r e s s u r e s

From this understanding of the primary elements which influence the generation of hull excitation forces it is possible to reduce the magnitude of the force by reducing the contribution from each of the basic elements.

A model for hull pressure generation due to cavity dynamics (i.e. volume variation) was proposed by Huse (1975). This model assumes a system of N cavities of volume Vj each at a distance ai from the hull point. By representing the volume by a point source, and

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using Bernoulli's equation (neglecting a velocity dependent term) the pressure at a hull point is obtained as:

Pcw(t) = S B F p7t 4 2

3t i=i

1 a v

47ta, 3t (2)

Assuming constant shaft rotation this reduces to

Pcw(t) = SBF PTC n^ I

i=i

1 3^Vi 3V 3 1 / a

3(1)2

+

3()) 3^ (3)

where pcw is the pressure due to the dynamic activity of the cavity and ^ is the angular position co-ordinate in the propeller disc.

On the assumption that this model is valid, deductions may be made concerning shapes of these Vj distributions (with angular position) which contribute to low excitation pressures. Such data is available from physical and numerical experiments. However, relatively little data exists from Stereogram analysis of cavity history either at ship or model scale. Numerical estimates of cavity topology from lifting surface analysis are derived from a model of the real situation.

Examination of the available measured and computed cavity topology data indicates that:

1) 2^Vi((|)) varies as shown in Figure 6 2) Vi(r) varies as shown in Figure 7

Cavity Volume

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The propeller as a source of noise and vibration 12

Thus there is a tendency for the maxinnum volume to occur just after the wake peak with the outer radial locations concentrating the volume. Cavity collapse occurs as the blade enters the high velocity region.

1.0 ' 0.85R ta 3 o Cavity Volume

Figure 7 Radial Variation of Cavity Volume

Some full-scale observations show that the main volume of cavitation appears to grow and collapse as a knot of cavitation, which is relatively stationary in space (hence appearing to sweep across each blade as a 'hill' which extrudes into a tip vortex). Figure 8 illustrates the volume variation associated with this appearance.

Cavity Volume \ Collapse \ P h o 9 e Growth / P h o c e / Angle ^ TDC

Figure 8 Principal Regions Giving Rise to Excitation Pressure

Inspection of the above equation (3) shows that the hull pressure is reduced when: 1) The shaft rate, n, reduces (section 4.1.1)

2) The volume acceleration decreases (section 4.1.2) 3) The clearances, a i , increase (section 4.1.3) 4) The volume velocity decreases (section 4.1.4)

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BSESnBZES The propeller as a source of noise and vibration 13

3.1.1 R e d u c i n g shaft rate

Tills is tiie dominant propeller design parameter since it amplifies ttie pressure, for a given cavity history, as the square of the revs/second.

The cavitation regime susceptibility of a propeller is dependent on the relative velocity at each section, and the immersion depth of the section (for a given angular orientation, (j)). The principal component of the relative velocity is the rotation velocity, hence it is common to construct the cavitation number:

Po - Pv

0 . 5 p ( 7 m D f

a n = - - (4)

where

Po = static pressure

Pv = saturated vapour pressure

n = revs/sec

D = diameter

P = specific density

TinD : = propeller tip speed (m/s)

Reducing n, and selecting an optimum propeller (increased diameter) can be shown to decrease nD, and hence increase the cavitation number. This gives a consequent increase in the margin against cavitation, and a reduction in cavity volume, Vi in a given wake field.

Increased diameters generally lead to higher propulsive efficiencies and, consequently, lower thrust requirements. This factor also contributes to lighter propeller loadings and higher margins against cavitation flare-up.

3.1.2 R e d u c i n g volume acceleration

Figure 9 shows four curves, taken from Raestad (1986), involving components of equation (3):

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14 - o . l - o . a - 0 . 3 - 0 . 4 - O . B I 1 _ 140

Figure 9 Example 1 of Variations in Terms of Equation (3)

Curve A : Total volume (SVj) variation witii angular position in the disc Curve B : ai - distance between cavity volume and hull point

Curve 1 : (1/ai). {d^\/Jd<\)^) (Term 1 of equation (3)) Curve 2 : (av/Bcj)). a(1/ai)/9^ (Term 2 of equation (3))

For the "normal" distribution of S V j s h o w n , and considering a point 2 5 % of diameter to starboard on a section at 45° to the vertical, as shown, curve 1 is observed to be at least an order of magnitude larger than curve 2. The dominance of term 1 over term 2 derives from the fact that:

* 3(1/ai)/9(t) is two to three orders of magnitude smaller than Ma-, * dy/di? is only one order of magnitude greater than d'^V-Jdif Thus the character of the function

E (1/ai) 3'Vi/a(t)' i=i

determines the character of the pressure trace acting on the hull, due to a cavitating propeller.

Figure 9 shows that a pulse occurs in the angular interval 150° to 180° due to the growth phase of the cavity, while in the interval 180° to 220° the collapse phase of the cavity contributes a second pulse, the amplitude of which is greater than the first.

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Figure 10 gives comparable data for the same propeller operating in a more non-uniform wake. Again, the first term of equation (3) predominates, and the collapse phase of the cavity is more severe than the growth phase.

1 • t . 4 t.» 1.0 0.« 0 • 0.4 0.8 0 0 -0.8 - 0 . 4 - O . a - o . l - I . e

Figure 10 Example 2 of Variations in Terms of Equation (3)

The curves further show that the maxima in term 1 (hence pressure) are coincident with regions of minimum radius of curvature of the Vi((})) curve A.

Hence, peak to peak variations in curve 1 may be reduced if, for curve A:

* The whole X V j curve is scaled down.

* The total volume SVid(t) is maintained, but the Vj variation is more gradual (i.e. the minimum radius of curvature is increased).

These deductions are based on the assumption that the discrete volumes, Vj, comprising the instantaneous total volume, act in phase.

In reality, however, the volume of cavitation on a blade at any instant in time is composed of expanding, stable and collapsing sub-volumes. In addition, the growth phase of the cavity appears to occur as the leading edge enters the w a k e peak region, while the collapse phase occurs as the blade trailing edge leaves the wake peak. Hence, by designing-in highly swept leading edges, the growth and/or collapse phases of cavitation on sections at adjacent radial locations (near the tip) may be used to reduce the peak-to-peak variations in the pressure signal (time domain):

A

1

1 4 0 " 180» 2 2 0 "

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BSmnSSES The propeller as a source of noise and vibration 16

No published design experience exists for determining the required degree of leading edge sweep. Figure 9 suggests that only a 10° to 15° sweep is necessary between (say) the 0.85 radius and 0.975 radius in o r d e r t o facilitate some cancelling effects.

In addition, highly skewed blades exhibit much shorter angular and linear distances between leading edges of outer radii, and mid to trailing edges of adjacent inner radii. In these configurations the peaks created by the growth of the outer, leading-edge cavitation may partially cancel the troughs generated in the collapse phase of cavitation at adjacent inner radii.

3.1.3 I n c r e a s i n g C l e a r a n c e s

In the above model of cavity pulsations, ai is the distance from a portion of the pulsating cavity to the reference location on the hull. Figures 9 and 10 (curve B) show the variation of a\ for the tip radius point as it sweeps past a V-shaped hull section. The magnitude of ai is dominated by the tip clearance and the section angle, ag.

An increase in ai can be obtained by spreading the cavity volume over a larger radial extent, or reducing as by incorporating steeper V-shaped afterbody sections.

3.1.4 R e d u c i n g Volume Variation

For a given design instance in which the thrust, revs/min and diameter of the propeller are fixed, the principal means by which the cavity volume and its variation may be reduced fall into three categories:

* W a k e Distribution - axial - tangential - radial * Propeller Geometry - skew distribution - blade area - pitch

- section thickness distribution - camber

- blade number

* Propeller Loading Distribution - circulation distribution

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Ad Wake Distribution:

As shown in Figure 11 the variation in local wake fraction, at any given radius, gives rise to an angle of attack variation of similar character. This in turn causes suction pressure peaks, in the leading edge region of the blade sections, which can give rise to cavity development. Reducing the wake variation reduces the angle of attack variation and hence the tendency for sheet cavitation to develop.

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Axial component: Influences volume and volume-variation

T l i e angle of attack is determined primarily by the axial component of w a k e and the loading distribution on the blade. The tangential wake component is less important for single screw ships. The importance of the axial component derives from the fact that the pitch angle is small for the outer radii:

P/D

Pitch Angle (Degrees) P/D

r/R = 0.8 r/R = 1.0

0.8 17.7 14.3

1.0 21.7 17.7

1.2 25.5 20.9

Table 6: Pitch angle at the outer radii

Axial wake peaks of the order of 5 0 % of the mean velocity ratio are often encountered. Variations in the advance angle (3, however, result in smaller angle of attack variations due to the induction effect of the propeller.

Considering the above table, one may expect maximum angles of attack in the range 4 to 8 degrees which are larger percentages of the low P/D designs than the high P/D designs. Such variations cause the formation of sharp suction peaks at the leading edges of profiles which are typically less than 3 % thick in the outer 2 0 % of the blade. Thin sections have narrow cavitation buckets (see Figure 11), and, in a non-uniform flow, have lower margins against suction and pressure side cavitation.

Typical axial wake distributions are shown in Figure 12 together with suggested improvements.

Tangential Component: Influences Volume-Variation

The tangential velocity component is less important for single screw ships than the axial component because it is relatively small compared to the rotational velocity of the propeller blade section. It does, however, introduce an asymmetry into the distribution of Ap - the advance angle variation - due to the difference in sign of the component on port and starboard sides of the hull.

The major effects of this asymmetry are to produce the maximum angle of attack on the starboard side (for a right hand rotating propeller), and to create a steeper slope in the 3as/3(t) curve, thus encouraging more rapid collapse of sheet cavitation.

Radial C o m p o n e n t

Little data exists concerning the influence of the radial velocity component on the growth and collapse of cavitation. It is likely to be most influential in de-stabilising the tip vortex and tip sheet cavitation, hence may contribute to higher harmonics. Radial velocity variation is obviously minimised with tunnel fins and ducts.

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»i^jiiJ:HJii.H The propeller as a source of noise and vibration 19

Ad Propeller Geometiy:

The selection of the radial distribution of skew and chord-lengths, together with the type of camber line and section thickness profiles is crucial for the reduction of cavity volume variation, and hence pressure and exciting force.

Pitch is not considered to be an explicit design parameter, since the normal design process requires the circulation distribution to be prescribed, and the pitch corresponding to this to be subsequently derived.

• L O W W E > N • H I G H P E A K 0 ) • S T R O N G G R A D I E N T / ' u - J y . r ^ M E A N O R I G I N A L . \ I M P R O V E M E N T \ s y I E • LOW MEAN • HIGH P E A K S (2) • STRONG GRADIENT / \ (LOCAL) / X • aiLGE VORTEX / OR SEPARATION / / / MEAN

Ï 7

ORIGINAL / \ IMPROVE-V / ' M E N T .0' • HIGH WEAN • HIGH PEAK 0 ) / • WEAK GRADIENT / • SHARP LOCAL PEAK L

I, ^

ORIGINAL V i M P R O V E M E N T MLAN 10' F i g u r e 1 2 G u i d e l i n e s : Higii Sl<ew ( E f f e c t on C a v i t y D y n a m i c s )

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S k e w : Influences Volume-Variation

Numerous research projects in the USA, Europe and Japan (Valentine 1975, Ken/vin 1978b, Sasajima 1983, Holden 1983, Yamasaki 1981-86) have shown that skew, alone, gives reductions in hull pressure.

Figure 13 shows that, even where the area under both curves is approximately the same, the larger angular interval in which the cavitation exists, causes the regions A' ,B' and C' to have larger radii of curvature (hence lower d\JJd<^ than the less skewed propeller (A, B and C)). T h e ordinate of Figure 13 represents the total volume at each angular position of the blade generatrix. However, at each radial location, the elements of cavitation are in different stages of growth and collapse.

Covlty Volyms

Port 180*

(Disc Angit)

Stord.

Figure 13 Guidelines: High skew (effect on cavity dynamics)

A highly skewed propeller, with strong leading edge sweep (related to skew) gives greater opportunity for components in the pressure equation to cancel each other:

p(t) = C Z {Mad{d'Wdi>^) i=1

The effect of skew on the reduction of hull pressures has been found experimentally by various research groups and a c o m m o n trend has been deduced as shown in Figure 14.

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I M E T H E R L A N D S _{The propeller as a source of noise and vibration} ₂₁

0 - 2 0 ' 4 0 - 6 0 '

S K E W A N C L E : ^ 0 . 9 6 R ) - * S ( 0 . 6 R )

Figure 14 Guidelines: Effect of Skew on Pressure Distribution

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Since pitch reduction at the outer radii is a consequence of applying skew, (Morgan 1968, Gumming 1972) there is a similar trend involving pitch ratios at 0.6R and 0.95R. This is shown in Figure 16. = change In e f f i c i e n c y I r e f " P r o p e l l e r E f f i c . ^ a t Reference P t . e j ae a? aa a9 i.o i.i P i t c h B a t i o P O . 9 5 R / P O . 4 E = r e f at a? as ag i.o i.i P i t c h R a t i o P O . 9 S R / P O . 4 R ( a ) (b) (See y i g . 4 . 1 0 ) Kp (See Tig. 4 . 1 0 ) ( c ) « f s

"

0.0") 10 20 *o so P r o p e l l e r Skew E f f e c t s on P r e s s u r e E l u c t o a t i o n s (BOLDEN 83)

Figure 16 Guidelines: Effect of pitch, skew and wake on pressure reduction and

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Figure 16(c) gives practical guidance with regard to the amount of skew (Os) required for a given w a k e variation (Aw) in order to reduce pressure amplitudes at blade passage frequency.

Within MARIN'S CRS/CAV activities, propeller re-design incorporating skew and chord-length increases have been performed [Raestad 1 9 8 6 d ] . One of these screws, for a twin skeg C P application, has been evaluated experimentally at model scale [Van der Meulen, 1987c]. The screw has been designed with:

50° skew (78% increase)

Blade area increase of 4 . 3 % weighted towards the tips (+13.5% chord at 0.95R)

The following table summarises the principal results with regard to pressures and forces. These data are used in Figures 14 and 15.

PROP = 5394 6064 COMMENTS

Pt,8 (Meas). (Meas). * Wake Aw = 0.445 (50% of VxA/m)

* Blade Area increased by 4.3%

PZ (kPa) 9.5 0.9

P2Z 4.8 3.2 * Chord at 0.95R increased 13.5%

P3Z 0.3 2.7 * Chord at 0.90R increased 6%

P4Z 0.4 0.7 * Skew increased by 22° (i.e. by 78%)

FZ (kN) 71 7 * BF FORCE REDUCES by 9 0 %

F2Z 29 19 * 2BF FORCE REDUCES by 3 4 %

F3Z 6 24 * 3BF FORCE INCREASES by 300%

F4Z 1 5 * 4BF FORCE INCREASES by 400%

Table 7: Blade amplitudes of pressure and force

T h e blade amplitudes of pressure and force for the highly skewed propeller reduce by 9 0 % of their previous level at blade rate, and by 3 4 % at twice blade rate. This result is excellent with regard to main hull vibration and low modes of panel vibration. However, due to the increased pressures and forces at three and four times blade rate, the consequences for higher modes of panel vibration, and for internal noise are increased with the new pressures and forces at three and four times blade rate.

These results relate to model scale cavitation and wake phenomena. At ship scale the distribution of force among the various harmonics will change; however, no definite statement can be made regarding the levels of harmonic content at ship scale.

B l a d e area: Influences volume a n d volume variation

Lifting line design methods (e.g. Lerbs 1952) compute the radial distribution of the ratio C l . c / D , required to satisfy the design specification of thrust or torque loading. T h e designer then must identify a radial distribution of c / D which, together with a radial distribution of thickness, will satisfy strength, back-bubble and erosion constraints, as well as avoid thrust breakdown and high levels of vibratory excitation.

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RESEARCH l ^ ^ j l f A ^ t j j C I

m:tJ!ij=n,ni.H The propeller as a source of noise and vibration 2 4

Increased area (i.e. chord-length) leads to a reduced C L requirement, and hence to reduced incidence angle and camber ratio. Increased chord-length, without a proportional increase in thickness, implies a reduced cavitation bucket width, and hence lower margins against cavitation inception (Kruppa 1968). However, the lower lift requirement results in a blade section pressure distribution which is less conducive to cavity growth; hence cavity volumes and hull pressures should decrease.

Increased blade area has been investigated by the CRS/CAV group (Raestad 1986b,c Fitzsimmons 1987a,b and Van der Meulen 1986,87a), in two wake fields, formed by alternative hull forms for the same Ro-Ro design study. In this investigation the blade section pitches, thicknesses and leading edge contour were c o m m o n , while the area was increased by 2 0 % . The skew angle increased by 4 degrees (23%) as a consequence of holding constant the leading edge contour.

The following table illustrates the principal results with regard to the first four blade rate harmonics of hull pressure and vertical force.

B L A D E A R E A E F F E C T AND W A K E

(Model scale experiment data) [Van der Meulen 1986 & 1987a]

PROP P5963 P5969

(AE/AO) (0.726) (0.877)

Component Orig. Mod. Orig. Mod.

hull hull hull hull

Highest pres PZ (kPa) 4.9 2.4 5.3 2.2 P2Z 3.8 1.2 2.2 0.6 P3Z 4.0 0.5 0.8 0.4 P4Z 4.4 0.3 0.6 0.5 (Fz)Z(kN) (Fz)2Z 131 58 140 54 (Fz)3Z 143 57 81 30 (Fz)4Z 138 23 27 14 153 16 32 26 Aw 0.55 0.45

Table 8: Blade area ratio and rake (Note: A decrease in Aw of 0.1 is more effective than

an increase in area of 0.15.)

Increased blade area, for wake fields in the range Aw = 0.45 to 0.55, show a slight increase in blade rate components, and 4 0 % to 5 0 % decrease in twice blade rate components. For the components at three and four times blade rate, the severity of the wake non-uniformity determines whether or not a significant improvement is possible. For a given target hull excitation pressure, reduced blade area (hence increased efficiency) could be considered if the skew angle were to be increased. Holden (1983) also investigated this effect, by reducing blade areas from 0.76 to 0.55, 0.45 and 0.35 on

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IJIJJÜJ1IWM.H The propeller as a source of noise and vibration 25

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alternative propellers. Gains of 5 % predicted at model scale, realised only 2 % gain at ship scale, thus leading to the conclusion that scale effects, as well as interaction effects, require more effort.

Pitch: Influences volume variation

Van Oossanen (1972) and Holden (1983) have demonstrated that pitch distribution plays an important role in the generation of hull excitation pressures. The tendency in propeller design in the late 1960's, when vibration was a common problem, w a s to produce constant pitch variation, or pitch increasing at the tips.

Such features tend to generate high angles of attack on the outer blade sections, which in turn cause violent flare-up and collapse in the wake peak at the 12 o'clock position.

T h i c k n e s s Distribution: Influences Inception and Volume

Much of our current thinking with regard to the design of blade section profiles derives from model testing and potential flow analysis of isolated two-dimensional section profiles in steady (or quasi-steady) irrotational inflow.

In reality, the sections comprising a propeller blade operate in a cascade of low aspect ratio wings rotating in a shear layer. Sections near the blade tips (0.85R to 1 .OR) are influenced by end-effects, including the roll-up of the tip vortex sheet.

Many propellers operating today have sections such as the Japanese "AU" and "MAU" series and the Stone Manganese "Scimitar" series, in which proprietary camber line and thickness distributions have been derived such that the section face is relatively flat, lift is generated by camber and incidence, and nose radii are small.

Propellers designed with the aid of the MIT, PBD-codes generally incorporate NACA section thicknesses which have been modified by increasing the leading edge offsets to accommodate a larger nose radius. Small nose radii lead to early onset of cavitation in a non-uniform flow due to their tendency to generate sharp pressure peaks at incidence. Moderate increases in section thickness have little effect on hull pressures and forces [Van der Meulen 1986].

Camber: Influences volume

Camber lines, like thickness distributions in use today, fall into the proprietary and NACA categories.

Two dimensional potential flow theory indicates that camberlines (like the NACA a=0.8 mean line) provide smooth pressure distributions with moderate gradients at the nose and the tail of the section. These characteristics aid blade sections to resist the onset of cavitation, and minimise drag. T h e NACA a=0.8 camber line is generally adopted in high skew designs.

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i i u j ! i j j w j i . « The propeller as a source of noise and vibration 26

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Blade number: Influences excitation frequency

Clianges in blade number primarily affect ttie frequency of excitation, rattier than the magnitude of the exciting force due to a cavitating propeller. This is due to the fact that cavitation flare-up and collapse occurs generally in an angular interval which is less than the blade angle for 4, 5 and 6 bladed propellers. Hence the primary mechanism - cavity volume variation - is not reduced.

Some benefit may be derived from other factors associated with the change in blade number, such as thinner sections, longer chord lengths, higher skew etc.

Ad Propeller Loading:

The majority of propellers designed today use (in the initial stages) a lifting line representation of the propeller's action. The radial distribution of circulation (or lift) on this line, determines the thrust and torque of the propeller at its design point, and hence its efficiency.

Circulation distribution: Influences volume and v o l u m e variation

An optimum distribution of circulation may be derived in the design process by specifying a condition of minimum energy loss in the far, downstream wake. Figure 17(a) compares an optimum distribution with a tip and hub-unloaded distribution. Theoretically, the optimum circulation distribution gives highest efficiency in unbounded flow.

Optimum loading is characterised by strong gradients near the hub and tip, which tend to form hub and tip vortices which become visible under cavitating conditions, even in uniform flow.

In non-uniform flow no condition for optimum loading exists, and in fact the strong circulation gradients can lead to high levels of hull pressure as well as strong interaction with the hull flow field which may lead to reduced total propulsive efficiency.

Since model scale and full scale wakes differ in non-uniformity, and radial variation of the circumferential m e a n , the best (or optimum) propeller at model scale may not be the best at ship scale.

For wake distributions having high levels of non-uniformity a moderate degree of tip off-loading may be necessary - even with a highly skewed propeller. Figure 17(b) illustrates the effect of moderate tip unloading on components of the propulsive efficiency a n d hull excitation pressures for a wake in which the (WT)max exceeded 0.8.

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C i r c u l a t i o n . (Schematic)

0.5 1.0 r/R (a) Radial Circulation Distributions.

C i r c u l a t i o n (Sciiematic) C3PT njL 0.707 0.703 _{n °} 1.031 1.018 0.713 0.692 n -6.100 6.000 4.300 3.500 0.5 • 1.0 r/R (b) Radiol Orculotlen Oistrlbutïons.

Figure 17 Guidelines: Effect of Tip Loading on Efficiency and Pressure

Proportion of lift due to incidence: volume variation

Holden (1983) gives hull excitation pressure results for two propellers having the same loading and chord-length distributions, but with different camber and pitch distributions. The alternative propeller was designed with negligible pitch and camber differences at the 0.4R and 0.95R locations, while camber variations in this interval showed a maximum of 5 0 % increase in camber at 0.65R.

Subsequent model tests in the Trondheim cavitation tunnel have shown negligible differences in the blade rate pressure amplitude, while the twice blade rate amplitude increased by approximately 4 0 % (1 kPa in absolute magnitude).

This result should be treated as a specific case. However, it is reasonable to conclude that, from a basis propeller design involving shockfree orientation (pitch) of the sections, the alternative design strategy of increasing the camber/chord ratio involves a reduction in pitch (hence section incidence), and hence less stable cavitation is generated in a non-uniform flow. This reduced stability may be the cause of the higher amplitude of pressure at twice blade passage frequency.

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The propeller as a source of noise and vibration 28 N E T H E R L A N D S

3.2 Increasing p l i a s e relationships

Equation (1) above defines thie contributions of pressure, phiase, etc. to the surface force exciting the hull. From this equation it can be seen that the surface force is the result of a vectorial summation of elemental forces p exp(i(cot+(p)). Hence, as shown in Figure 18, the more in-phase the pressures are at different locations, the greater is the surface force. The in-phase nature of propeller cavitation-related pressure pulses derives from the fact that the cavities grow and collapse within a short angular inten/al - corresponding to the region of highest wake. The pressures from a pulsating cavity and a rotating cavity, as experienced at a point above the propeller, are shown in Figure 19.

a

i

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m:*j!ij;iwii.M The propeller as a source of noise and vibration 29

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Figure 19 Guidelines: Examples of Types of Cavity Dynamics Modelling

3.3 R e d u c i n g the s o l i d boundary factor

The S B F considered within this text is a composite factor which combines the influence of both the hull shaping (Sb) in so far as it differs from the idealised infinite flat plate, a n d the proximity of the free surface (Sf) on which a constant pressure exists. The dominant factor has been shown to be the free surface component, Sf.

SBF = SbSf

Huse (1982) gives empirical relationships for Sb and Sf for a propeller and hull configuration on which the equivalent clearance ratio is 0.439:

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»ijj!N;H.ni.ia The propeller as a source of noise and vibration 30

where a is the transverse inclination of the section with respect to the horizontal axis (i.e. 90 degrees minus Og

Sf = 9.341 5 - 3 0 . 1 4 3 8^ + 33.19 5^ for 0<8<0.35 Sf = 1.0 for 0>0.35

where 5 is the ratio of the field point immersion depth to the shaft immersion depth. Figure 20 illustrates the variation of S B F with respect to the immersion of the propeller tips and the immersion of the hull point at which propeller excitation pressures are applied.

Figure 20 Total Boundary Factor (Stot) Dependency on Free-surface Proximity and

Tip-Submergence Ratio (az/Z)

These results show SBF values well below the theoretical flat-plate value of 2.0 a n d which fall to zero at the hull and free-surface interface.

This data suggests that maximum benefit can be obtained from transverse hull section shaping which lie close to the free surface (C/Z is large). This conclusion, however, fails to account for the possibility that ship motions and following seas could greatly increase the immersion of the hull above the propeller (hence increased SBF) in addition to increasing the wetted surface area.

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liiiiiHiiTini'hi The propeller as a source of noise and vibration 31

3.4 R e d u c i n g wetted s u r f a c e a r e a

Equation (1) stiows tiiat as tiie area over wiiicti tlie pressure acts is reduced, ttie total surface force is reduced. There is danger, however, in attempting to design to extremes of exposed surface area, since the phenomena at full-scale are more complex than can be expressed in a simple relationship such as our equation.

Wetted surface area increases at ship-scale due to ship motions and following seas. The time periods involved are of the order of 100 seconds of blade passages, and hence should be taken into account when estimating the mean and standard deviations in pressures and forces for in-service operation.

Wide, shallow transom sterns (e.g. Ro-Ro and container vessels) provide the most effective transfer mechanisms for propeller excitation of the hull. Rolling, pitching and following seas, can increase the effective area for surface excitation, by a factor of 2. Ideally V-shaped transverse sections with angles (to the horizontal) in excess of 30 degrees should be adopted where possible. In terms of the equation, the designer should try to minimise the quantity n^dS.

For twin screw forms, the transverse excitation may also be important, hence nydS will also require consideration.

3.5 Mode profile adaptation

Adapting the hull form and propeller location is complex from the view point of the hydrodynamics of the hull boundary layer and propeller- hull interaction, it is also difficult in terms of vibration response.

A hull form, in each of its design loading conditions, will be excited into vibration by sea states and by the operating propeller and main machinery. The modes of vibration are numerous. It is important to establish the frequencies of these modes and to identify their associated node-points. The latter is important for cavitation excitation, since locating the propeller close to a node of a dominant mode can reduce the main hull vibration.

This section is included for completeness of the above mathematical modelling approach. No ships have been designed specifically to this option.

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N E T H E R L A N D S The propeller as a source of noise and vibration 32

4 TREATMENT O F HULL P R E S S U R E S IN T H E VARIOUS DESIGN

S T A G E S

As already mentioned in the introduction, performing investigations in the correct sequence relative to the design stage is considered appropriate. For this reason we have to take a closer look at the role that cavitation induced hull pressure excitation plays in the various stages of the design. For the purpose of this lecture the traditional design stages are simply defined as in table 3.

Design Stage

Description Output of design stage

1 Concept design Limiting ranges of principal design parameters.

II Preliminary design Alternative configurations falling within the ranges defined in stage 1.

III Detailed design One configuration selected from stage II, and including detailed specification of geometry and performance based on advanced analytical methods and model tests. IV Final design Definition of final detailed geometry and prediction of

trials performance based on results from stage III.

V Re(medial)-design Definition of the nature of the problem. Specification of hull and/or propeller modifications. Repetition of stages III and IV.

Table 3: Definition of the design stages.

In the concept design stage general guidelines and simple empirical methods and formulas can be used. In the preliminary and detailed design stages analytical methods and more or less advanced computational tools are used. In the final design stage these methods and tools can be completed by experimental probing. The re-design stage focuses on the origins of an excitation problem and possible remedial measures such as retro-active modifications that may alleviate the problem.

It is assumed that no substantial hull or shaft resonances exist close to the design R P M and that any noise or vibration is the result of forced excitation due to the dynamics of back side cavitation as blades pass through a wake peak.

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The propeller as a source of noise and vibration 33

4.1 S t a g e I: C o n c e p t d e s i g n

Ttiis design stage utilises the 'broad-brush' approach for determining the principal design parameters. At this stage, the major data available to the designer are:

1) Historical data (similar ships, wake non-uniformities, achieved levels of vibration and pressure);

2) Guidelines, rules and empirical methods; 3) Design specification.

The design specification gives the limits for target performance. At this stage, any specification relating to vibration limits should be translated into a limiting distribution of surface forces within a range of excitation frequencies.

T h e historical data-store may then give initial estimates of hull shape and wake non-uniformity, which together with the first estimate of thrust from propulsion estimates will allow initial estimates of R P M , diameter and propeller-hull clearances to be made.

This design stage is characterised by a small number of design parameters that are well-defined, while the remainder may be determined within a wide range of values.

Initial estimates of excitation quantities thus require evaluation at the extremes of range as well as the mean value. Thus the results of this stage cannot be regarded as precise, they merely indicate a range of possible solutions.

Propulsive performance and engine choice are the primary influences at this stage. Fortunately, the tendency towards slower shaft speeds and larger diameters has reduced the incidence of cavitation excitation problems by increasing the cavitation number, as R P M (or n) reduces. For optimum propellers, D increases more slowly than n decreases. Hence the product nD reduces as n reduces, causing the cavitation number to increase, and by that increases margins against excitation forces.

Since an increase in propeller efficiency is also associated with lower shaft R P M and larger diameters, reduced propeller excitation and fuel consumption are compatible goals. Empirical and semi-empirical methods represent attempts to rationalise and generalise the experience and data obtained from specific design and experiment studies. Empirical methods involve the regression of large amounts of data against geometric or quasi-hydrodynamic variables. Semi-empirical methods involve the introduction of simplified theoretical models as the kernel variables in order to make the results more sensitive to the underlying physics of the phenomenon. Using such methods is possible for

1) Wake parameters 2) Solid boundary factors 3) Hull pressures

4) Hull forces

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If the design specification (including a margin of safety) is not satisfied during initial estimates, then the empirical methods may be used in an inverse way (or by trial and error) to arrive at sets of design values which fully satisfy the specification. These values become the design options and target values that are passed to the next design stage.

4.2 S t a g e II: Preliminary d e s i g n

The preliminary design stage, involves working the concept design stage options into hull form geometries and performing (or subcontracting) propeller designs. This stage is driven from the target levels and design parameter ranges identified in the concept stage.

This stage seeks to produce one or more specific viable, alternative configurations of hull form, propeller geometry, propeller location and operating conditions, from which one option will be selected and passed to the detailed design stage.

Analytical methods and semi-empirical methods are required tools. The design stage involves the subjects, depicted in Table 4 .

Subject Work involved

Design Specification Elaboration of the target parameter ranges identified in stage 1. Hull Form Design Consideration of features that are crucial for satisfying the target

levels of wake and clearances and wetted surface area. Wake Estimation Use of semi-empirical methods rather than similar ship data. Propeller Design Hydrodynamic design (lifting line) involving skew, radial loading

and wake data.

Performance Assessment Use of semi-empirical or analytical methods for estimating pressure and force levels.

Design Selection Choice of the most viable alternative.

Table 4: Type of work possible in the preliminary design stage

The above subjects will be worked out below.

4.2.1 D e s i g n s p e c i f i c a t i o n

The specification for the preliminary design stage, as evolved from stage I, delivers estimated quantities that serve as global parameters that require to be satisfied through specific design configurations.

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4.2.2 Hull form d e s i g n

Ttie tiull form is botti ttie wal<e generating body, wtiicti affects ttie severity of cavity dynamics, and ttie force-transfer meclianism for sucti cavity-induced pressure fields. Tiie target levels of wake parameters and pressure levels derived in stage I, have been derived in order to give compatibility with target pressure and force amplitudes. It is also possible to use these data togetherwith general guidelines, to determine a compatible hull form definition, that is by inverse design.

Thus the designer is required to:

1) Generate afterbody shaping with clearances a^/D and aJD; section x-values and waterline angles (j), which are in accordance with stage I requirements for wake non-uniformity;

2) Build-in general guidelines for hull form development;

3) Generate the hull form in a numerical format suitable for wake assessment.

4.2.3 Wake estimation

Empirical methods have been presented for estimating wake contours and wake non-uniformity parameters, which require an afterbody form definition. The alternative configurations generated above may be assessed by such methods, in order to confirm that the complete design satisfies the target wake parameters.

The wake contours estimated may also be passed fonward to the propeller design and assessment blocks within this stage once they have been converted from nominal wake at model scale to effective wake at ship scale.

4.2.4 Propeller d e s i g n

For preliminary design, where several options may be in the process of evaluation, it is advisable to use lifting line design and analysis tools to generate data for the selection process prior to the detailed design stage. Such tools, together with the target performance from stage I and specific guidelines, may be used as follows:

1) Derive the mean circumferential effective wake distribution.

2) Select a distribution of balanced skew, based on maximum skew angle indicated by stage I.

3) Select a radial distribution of either:

- circulation (with attention to tip loading), or

- pitch ratio based on ratios from empirical method from stage I. 4) Select a thickness distribution to satisfy a classification society class.

5) Design using a lifting line method with lifting surface correction factors for pitch and camber ratios.

6) Check final pitch ratios with those suggested from stage I. 7) Re-design the propeller, adjusting:

- chord-lengths to satisfy cavitation margins, and efficiency; - pitch or circulation distribution to satisfy efficiency requirements.

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E S E I i n m The propeller as a source of noise and vibration 36

4.2.5 Performance a s s e s s m e n t

Once a design geometry has been derived for the mean effective circumferential wake distribution, a quick assessment can be made using the simple empirical methods of stage I. In addition, where lifting line analysis systems exist, then a more refined estimate of pressures, phases and hull excitation forces may be made.

The use of lifting line methods is advised at this stage:

- Their accuracy is consistent with the accuracy of the input wake data. - They are quick, and require only moderate computing power.

- They generate sufficient data for informed redesign.

- They are sensitive to the major factors influencing excitation forces.

The elapsed time for one such design and analysis exercise may take as little as 30 minutes, thus allowing several options to be evaluated by one person in a standard working day.

4.2.6 D e s i g n selection

The design selection procedure involves consideration of propulsive performance estimates, structural response estimates (from parallel design and analysis effort) and construction costs f o r t h e hull and the propeller.

An essential concept in modern design practice is the inverse-design process.

Within this phase, any non-compliance identified from the performance estimation phase may be used together with the propeller geometry, hull form and analysis tools to determine new combinations of local wake peak structure and propeller details that will give compliance with the design specification. The effective solution thus obtained may then pass to the detailed design stage.

4.3 S t a g e III: Detailed d e s i g n

The detailed design stage involves the definition of hull form and propeller geometry to model manufacturing standard. At this stage, flow disturbances caused by appendages and inlets on the hull should be considered.

This stage also requires model testing in order to define the tangential and radial components of the nominal wake (the semi-empirical methods supplying only estimates of the axial wake) and total inflow components for propeller and hull configurations that experience significant propeller-hull-interaction. LDV techniques may be used to define total inflow velocity fields.

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₃₇

A proposed sequence of events witfiin tfiis stage comprises the subjects collected in Table 5.

Subject Work involved

Design Specification Extended and refined through stages 1 and II.

Hull Form Design Consideration of appendages and details affecting local flows to the propeller and hull manufacture.

Wake Estimation Use of model tests, and hull (nominal) flow computations,

where applicable.

Propeller Design Estimation, using measured or calculated axial wakes and

available methods.

Performance Assessment Use of lifting surface methods.

Design Selection Use of lifting surface methods, giving estimates for model scale test environment and ship scale environment.

Table 5: Type of work possible in the detailed design stage

On completion of this stage, the propeller definition may be sent for manufacture.

4.3.1 D e s i g n s p e c i f i c a t i o n

As a result of the investigation into alternative hull and propeller configurations performed in stage II, the number of free variables, in the design will have reduced, as will have the estimate acceptable ranges of these parameters.

4.3.2 Hull form d e s i g n

Following from the selected option in stage II, the influence of appendages and inlets (mainly thruster tunnels) on flow disturbances at the propeller should be assessed, and, in conjunction with good design practice, geometries should be defined. The major, main-hull requirements are to avoid local and large scale separated flow entering the upper disc region of the propeller. Attention to the details of waterline shaping, waterline endings and clearances fonward and above the propeller is essential if acceptable wake structures are to be achieved.

4.3.3 Hull flow a s s e s s m e n t

The simplest types of hull form assessment are the standard wake and flow visualisation tests, which have been performed routinely in towing tanks throughout the world for the past decades. Recently, LDV and PIV systems have permitted measurement of flow fields in the vicinity of operating propellers (total wake), although their use has generally been confined to research projects. This allows an alternative effective wake to be deduced (the TMI wake, Total Minus Induced).

Computational methods have evolved in the last decade from double body potential flows, through free surface flows with boundary layers to Navier Stokes solvers such as Marin's P A R N A S S O S code. Codes of these types may be used to give more refined estimates of the wake than given by empirical methods. These may also indicate specific hull regions

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M A R I T I M E

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R E S E A R C H

that may contribute to high wake peaks caused by strong decelerating flow along streamlines passing into the upper half of the propeller disc.

At present such methods have been used predominantly to predict nominal flows, for which there is some degree of correlation on axial component levels. No large amount of significant computations of total inflow to the propeller have been performed yet, hence, configurations in which there are strong propeller-hull interactions may not be predicted well by these systems. However, significant progress in this field is being made and so this situation may change in the near future.

4.3.4 S h i p effective w a k e

An estimate of the ship scale effective wake is required in order to facilitate a detailed design of propeller, and subsequently to estimate its cavitation performance.

However, the effective wake cannot be measured and is not unique; it is dependent on the influence of the propeller on the hull flow, and the hull flow's reaction at the propeller plane. A schematic representation of the system is:

W,o, = W i + Wef, = W i + [ W p h + Whp + W n ]

where:

n = Nominal flow; ph = Propeller to hull; hp = Hull to propeller; eff = Effective inflow;

i = Induced by the propeller, tot = Total.

Nominal wakes for the same hull form show variations when tested in different model tanks. This is due to the use of different flow turbulence stimulators, types of pitot tube or LDV/PIV device, sizes of model and methods of interpolation and smoothing. In order to minimise these random errors, the same test facility should be used throughout the total design cycle.

Whether starting from the nominal flow or the total inflow, the effective wake is obtained by processing it through a numerical model for propeller flow. The effective wake is, therefore, strongly dependent on the propeller flow model.

Estimates of ship scale wake may be made by modifying the model effective flow in the ratio of the ship and model effective wakes, derived in the conventional way from propulsion tests at model scale.

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4.3.5 Propeller d e s i g n

Witiiin tiiis piiase of tiie detailed design stage, a detailed blade surface is defined such that requirements set out in the design specifications for thrust, efficiency, strength and margins against cavitation are met.

The process requires the designer or group to have: - Experience;

- Design Tools;

- Knowledge of the limitations of the design tools;

- Basic design data (e.g. section thickness and camber distributions); - Specific design data (e.g. thrust, power, wake distribution, RPM). The major design parameters to be fully defined are:

- radial distribution of loading; - radial distribution of skew;

- radial distribution of chord-length and thickness.

A suggested portfolio of computation tools to facilitate design choices, is as follows: - Lifting Line Design package

This tool is in common use throughout the world, and is capable of allowing the assessment of radial distributions of loading on the requirements for efficiency, chord-lengths and camber and thickness.

Skew is not treated explicitly in the hydrodynamic design part.

T h e principal output is the radial distribution of C L - C / D .

T h e choice of c/D therefore determines the value of C L , which in turn is achieved by a combination of camber and incidence.

- Cavitation Inception

Cavitation bucket charts (or a program for blade sections comprising standard camberlines and thickness) may be used to determine the best combination of chord-length, thickness and camber.

Alternative nose radii to be assessed, as well as non-standard thickness and camber distributions.

- Lifting Surface Design

MIT propeller design programs (such as PBD10) are in regular use throughout the western world. At MARIN the ANPRO-package is used for this purpose. It is essential for the design of highly skewed propellers.