The choice of propeller design parameters with respect to cavitation control

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3 SEP. 138t

ARCHIEF

SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

HØVIK OUTSIDE OSLO, MARCH 20. 25., 1977

"THE CHOICE OF PROPELLER DESIGN PARAMETERS WITH RESPECT TO CAVITATION CONTROL"

By

P. van Oossanen, Netherlands Ship Model Basin, Wageningen, the Netherlands

SPONSOR: DET NORSKE VERITAS

PAPER 811 - SESSIONX

3 (.3)

Lab.

y.

Scheepsbouwkunde

Tech&sche Hogeschool

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1) Netherlands Ship Model Basin, Wageningen, The Netherlands. NETHERLANDS SHIP MODEL BASIN

WAGENINGEN

1.

THE CHOICE OF PROPELLER DESIGN PARAMETERS WITH

RESPECT TO CAVITATION CONTROL

BY P. VAN OOSSANEN'

SUMMARY.

In this paper results are given of a study how the type and

extent of cavitation on screw propellers, working in wake flows,

are influenced by different values of propeller geometry and

propeller-operation parameters. The rtethod developed by the

author for the theoretical prediction of cavitation is employed

to calculate the extent of cavitation on face and back of the

blades of a systematic series of propellers. This propeller series is derived by varying the main geometry parameters around a centre - or reference - propeller. To determine the dependence of the extent of cavitation on different types of non-uniform velocity fields, the cavitation characteristics of

the reference propeller is also calculated for a systematic series of wake field parameters. The results of these calcula-tions indicate that the cavitation performance of a propeller can be significantly affected by changing values of geometry

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NETHERLANDS SHIP MODEL BASIN WAGENINGEN

INTRODUCTION.

In the past, the prediction of cavitation on screw propellers has

been based primarily on experimental methods. These methods have

increased in sophistication over the years. Recently, however,

successful attempts have also been made in theoretically pre-dicting the extent of cavitation. Previously, such theoretical

predictions were unsuccessful due to a number of shortcomings,

particularly connected with the calculation of cavitation from

the approximate pressure distribution [1, 2, 3] 1)

Cavitation was always assumed to occur in the region on the blades in which the pressure is less than the value of the

vapour pressure. More recent approaches constitute an improvement

in this regard [4, 5, 6, 7] . In the method developed by the

author [7, 8, 9] , recently obtained results of fundamental

cavitation studies are employed to overcome some of the

ob-stades associated with real fluid effects. The adopted calcu-lation procedure leads to satisfactory correcalcu-lations with observed

cavitation patterns for lightly- and moderately - loaded

propellers. For heavily-loaded propellers in very non-uniform wakes, the predicted results are less satisfactory. Evidence

exists which indicates that thís is mainly due to a lack of knowledge regarding the change in the wake flow dueto the

working propeller. Nevertheless, the results obtained for these

cases are still useful in a qualitative sense.

In this paper the method developed by the author for the

theoretical prediction of cavitation is employed to calculate the extent of cavitation on face and back of the blades of a

systematic series of propellers. This propeller series is

derived by varying the main geometry parameters around a centre-or reference-propeller. To determine the dependence of the

extent of cavitation on different types of non-uniform velocity fields, the extent of cavitation on the reference propeller is also calculated for a systematic series of wake field parameters.

PAGE

2.

1) Numbers in parentheses refer to the references listed at the end of this paper.

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In the paper the derivation of the systematic wake field

para-meters and the definition of the reference propeller is first

considered.

DERIVATION OF SYSTEMATIC WAKE FIELD PARAMETERS.

In a plane vertical to the axis of the propeller shaft, at the location where the axis intersects the generator line of

the propeller blades r the axial component of the flow (in the

direction parallel to the propeller shaft) can approximately be expressed in terms of polar coordinr.tes as:

6

11

1

V(x,O)

I

[O

a + a. cos

j

üI I i + b x V

i

j[

ojs

i i

in which x = non-dimensional propeller radius (=r/R),

r = local propeller radius,

R radius of propeller,

e = angular polar coordinate (see Fig. 1)

V = ship speed,

a , a ----a , b = constants.

o i b o

Here a linear dependence of the constants a on x is assumed.

A reason for choosing only the first 6 terms of an even Fourier

series is that the theory developed for the calculation of cavitation on a propeller blade is a quasi-steady theory which disregards effects associated with high harmonics of the

wake field. Various effects associated with the propeller

inflow along the blades are averaged along the chord, thereby rendering useless the inclusion of Fourier series terms which have a period smaller than about half of the chord length of the blade sections. In addition, it should be noted that due to the effect of the suctiaiof the propeller on the ship's boundary layer, the use of the measured wake field in absence

3.

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F

of the propeller (the so-called nominal wake field) , in itself

probably leads to larger differences with respect to predicting the cavitation behaviour on the propeller than those due to

omitting the higher order terms of the Fourier series. The

same argument can be made with regard to the inaccuracies associated with approximate wake-scaling procedures which are used to derive the full-scale wake characteristics based on model wake surveys.

In equaLion (1) a cosine series is adopted because the nominal

wake field of single-screw ships is symmetric with respect to the vertical plane through the ship's centre line. For twin

screw ships this is not the case. Here the tangential component

of the flow is usually more important since the axial compo-nent. is generally very uniform except in a small sector of the propeller disc behind shaft brackets, struts and in the

"shadow" of the propeller shafts.

The tangential component of the flow can approximately be expressed in terms of polar coordinates as:

V(x,e) =

I _c _{+ c1x +} (d + d x) sin e1 V

[o

o i J s

in which c ,c d d _{= constants.}

o 1' o' 1

In deriving this relation it is assumed that the tangential flow component is primarily due to the existence of a dif-ference between the inclination of the propeller shaft: and the general inclination of the flow into the propeller. Again, a linear dependence on x is assumed. The tangential

flow component is considered positive if the direction of this flow component is clockwise when looking upstream (see

Fig. 1).

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NETHERLANDS SHIP MODEL BASIN PAGE

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NETHERLANDS SHP MODEL BASIN WAGENINGEN

From expression (1) for the distribution of the axial wake

component over the screw disc, it follows that the average axial velocity into the propeller can be determined by inte-gration, viz.: 2 1.0 V (x,0) xdüdx a

V =v

f

A s O _Xh (1

_{- xh)}

s 2 o _Xh

_{(1_xh)}

f f 2iî 1.0 a (1+b x) xd0dx o o

in which xh = non-dimensional hub radius.

The integration is to be performed from the hub radius to the propeller tip since no flow can pass through the hub. In relation

(3) the cosine terms have been left out since the integration

thereof, with respect to O, between the limits O and 271, is zero.

After carrying out the integration the following relation is obtained:

V=v

la

+a b

R I A s o 3 o o (1_xh2) j (1-xh3) i (4)

In relation is the volumetric, average axial velocity

into the propeller between the hub and the blade tip radius. On

using the relation:

7A = s (1w) (5)

where w is the wake fraction, it follows that:

3 2

lXh

= 1- a -a b

R o

300

2 1- Xh 5. (3) (6

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It follows that the average radial distribution of the axial wake velocity can be found from:

V 2

V (x) =

-

f a (1+b x) de

a o o

2 o

from which follows:

V(x)=a

(1+bx)V

a o o s

Since the adopted theory for the calculation of cavitation on propeller blades does not account for effects associated with radial wake components, it follows that the wake field para-meters which, together with geometry and operational parapara-meters, approximately determine the cavitation properties of a screw propeller are:

a, a1, a2, a3, a4, a5 and a6

b o c and c o d

_andd

o

To determine the values of these 12 parameters for a given wake field, it is necessary to carry out a harmonic analysis of the

wake component values at each radius. The amplitudes of each

harmonic can then be drawn as a function of x. The coefficients of the equation of the straight line which fits the drawn curve best then correspond to the values of the required parameters. If the harmonic analysis of the wake components at a specific radius is carried out according to the formulas:

WAGENINGEN 6.

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V ()

N a = A + A

cos (mOB

in in V rn=l s Ve(0) N = C + C sin (mO-D o in in V m=1 s

it then follows that:

a + a b x =

A (x)

0

00

0 a + a b x = A (X); B (x) = O 1

lo

1 i a + a b x = A (x); B2(x) = O 2

2o

2 a + a b x =

A (X);

B3(x) =0

3

30

3 a + a b x = A (X); B4(x) = O 4

4o

4 a + a b x = A (X); 135(x) = O 5

5o

5 a + a b x = A (x); B6(x) = O 6

6o

6

c +cx

=C (x);

0 1 0

± dx

= C1(x); D1(x) = O

DERIVATION OF PROPELLER GEONETRY PARAMETERS.

The centre, or reference propeller around which the propeller

series is derived is a 5-bladed propeller with an expanded blade

area ratio of 0.75, a constant pitch-diameter ratio of 1.0 and a hubdiameter ratio of 0.2. The blade sections are composed of

NACA 66 (modified) basic thickness sections [io) and a

NACA a =

0.8 basic camber distribution.

Table 1 gives the non-dimensional geometric properties of the

blades of this propeller, which has zero skew and zero rake.

and

NETHERLANDS SHIP ÑODEL BASIN

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Table 1. Non-dimensional values of geometric parameters of

reference propeller.

The calculations with this reference propeller were carried out

for a diameter of 4.0 meter.

RESULTS OF PERFORMANCE AND CAVITATION CALCULATIONS.

The performance and cavitation calculations were carried out

by means of the method developed by the author [7, 8, 9J . These

calculations were performed for the 12 radii at which the propeile geometry is specified and 12 angular blade positions (0, 30,

60 ...) . Interpolation and integration procedures are then

adopted to calculate the total extent of cavitation on both

back and face of all the blades at the same instant, as a

function of the angular blade position of one of the blades of the propeller. This permits the calculation of the following quantities: A cav(back) (11) A o max PAGE 8. c(x) t(x) (x) !(X)

-(x)

0.200 0.2115 0.04200 0.2000 0.025 1.0 0.01792 0.00665 0.300 0.2528 0.03590 0.1420 0.025 1.0 0.00903 0.00473 0.400 0.2882 0.03190 0.1107 0.025 1.0 0.00549 0.00369 C.500 0.3164 0.02690 0.0850 0.025 1.0 0.00324 0.00283 0.600 0.3357 0.02200 0.0655 0.025 1.0 0.00192 0.00218 0.700 0.3431 0.01720 0.0500 0.025 1.0 0.00112 0.00167 0.800 0.3330 0.01240 0.0372 0.025 1.0 0.00062 0.00123 0.850 0.3170 0.01000 0.0315 0.025 1.0 0.00044 0.00105 0.900 0.2907 0.00765 0.0263 0.025 1.0 0.00031 0.00088 0.950 0.2774 0.00532 0.0192 0.025 1.0 0.00016 0.00063 0.975 0.1956 0.00416 0.0213 0.025 1.0 0.00020 0.00103 0.990 0.1136 0.00300 0.0264 0.025 1.0 0.00031 0.00089

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and A (face) A o max A cay (total) A o max íd A

I-

cav(total) A L o max

where A = area ccicred by cavitation on the back of

cay (back)

all the blades at the same instant,

Acav(face) = area covered by cavitation on the face of

all the blades at the same instant,

Acav(total)= area covered by cavitation on face and back

of all the blades at the same instant,

A0 propeller disc area (= R2)

The maximum value of expressions (11) to (13) are a representative measure of the amount of cavitation on the blades for use in

propeller design studies for the purpose of minimizing the extent

of cavitation, etc.

Relation (14) represents the maximum absolute value of the

derivative of the total area covered by cavitation with respect to the angular coordinate. This quantity can he considered to

be a representative measure for the unsteadiness of the

cavita-tion (i.e. the rate of change of cavity sizes) . A high value

for expression (14) indicates that high vibration-exciting

pressures on the hull above the propeller can occur.

In addition to these cavitation characteristics, the propeller performance characteristics were also calculated. These

per-formance characteristics are best represented by the following

coefficients:

T

the thrust coefficient: KT

= 2 4

pn D NETHERLANDS SHIP MODEL BASEN

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the advance ratio

and the behind" efficiency: flß

= '1oR =

where is the relative rotative coefficient. When the

calcula-tions are performed in open water, the above coefficients become the well-known open water performance coefficients, in which

case

R =

To obtain insight into the dependence of the extent of cavitation

on each of the 12 wake field parameters, calculations were carried

out in which each of the wake parameters was varied separately.

The basic or reference values of the 12 wake parameters were chosen

to be:

a = 0.7,

o

a1-a2-a3-a4-a5-a6-b0-c0-c1-d-d1

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In these calculations the values of the propeller operation

para-meters, were chosen to be: diameter (D) = 4.0 meter, ship speed

(V) = 10 rn/sec., propeller shaft speed (N) = 2.5 revs./sec., and the effective static pressure at centre line of shaft, minus the

vapour pressure = 150,000 Newton/rn2.

EFFECT OF WAKE PARAMETERS.

The results of varying a0, a1, a2, a3, a4, a5 and a6 are given

in Figs. 2 to 8. The results of varying b, co, d and d1

are shown in Figs. 9 to 13.

WAGENINGEN 10

Q

the torque coefficient: KQ =

2 5 pn D V j = nD KT.J (18) 2 KQ

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NETHERLANDS SHIP MODEL BASIN

WAGEN IN GE N

11.

Figure 2 indicates that for the basic - or reference-value-of

a0 = 0.7, no cavitation occurs on the reference propeller. As

a0 is decreased, the wake fraction is increased (see equation (6)) resulting in lower inflow velocities, which lead to cavitation on

the back of the blades. When a 0, the bollard condition is

o

attained, for which case the maximum amount of cavitation on all the blades, at the same instant, is 20 percent of the propeller disc

area. On increasing a, the wake fraction is decreased, resulting

in higher inflow velocities. When the wake fraction is 10 percent

(a = 0.9) cavitation on the face of the blades starts to occur,

the amount of which keeps increasing with the value of a0.

Due to the fact that on varying a0, only the average speed of the

propeller inflow is influenced, the extent of cavitation on a

blade is only a result of the variation in static pressure between

different angular blade positions. The maximum values for the rate of change of the amount of cavitation with 1espect to the

angular blade position is therefore only small.

Figures 3 to 8 show the results obtained for each of the

coef-ficients a1 to a6. As follows from equation (1) , these coefficients

are the amplitudes of a circumferential cosine-variation of the axial velocity. On comparing the extent of cavitation on the reference propeller at equal values for the respective

coeffi-cients (amplitudes) , it is seen that the extent of cavitation

increases with harmonic order, until for a5 a maximum extent is

obtained. The extent of cavitation shown in Fig. 8 for

corres-ponding values of a6 is appreciably less. The rate of change of the extent of cavitation with angular blade position is also ap-preciably larger for a5 than for all other harmonics. To explain this phenomenon the chord lengths must be compared with the arcs of length corresponding to the period of each harmonic at the

various radii. When this is done it will be found that for the 5th

harmonic, the chord lengths of all blade sections are of the order

of one-half to one complete period (1.2566 radians). This indi-cates that the advance angle of the flow along the blade, at any one instant,has both a maximum and a minimum value somewhere on each blade section. When this occurs, the curvature of the flow

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along the blade sections is nearly the largest possible for a

given amplitude . It follows that the induced camber due to the

nominal, circumferential - varying flow across the blade is

also nearly the largest possible. The procedure adopted for the

calculation of this induced camber, which is found to be of

sig-nificant importance in the analysis of performance and cavitation

characteristics of propellers in a non-uniform flow, is given

in Refs. 7 and 9. In this particular case, the effective

camber-chord length ratio of the blade section at 0.7R varies between

about -0.01 and +0.06 during one revolution for a5 = ± 0.25. These

variations in effective camber are primarily responsible for the

increase in the extent of cavitation on both the back and face of

the blades for a3, a4 and a5 with respect to the values for a1,

a2 and a6.

From the above analysis of the results shown in Figs. 3 to 8

an important conclusion can be drawn with respect to the choice

of the expanded blade area ratio and the number of blades since

2)

these determine the order of magnitude of the chord length If possible, the chord lengths of the blade sections should be

chosen such that their projected lengths in the propeller plane

are never in the region of the lengths corresponding to the

period of the wake harmonics with large amplitudes. Analytically

this can be expressed as:

2n P(x) 2i

0.5

. - .

xR > c(x) cos arctan -

> 1.5 - .xR

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m xrrD m

where m is the order of the harmonics possessing the largest

amplitudes.

. Actually, the largest curvature of the flöw occurs when the

chord length is exactly contained in one complete period of the

harmonic with the largest amplitude.

. The chord length is in fact equal to:

c (x)

= k(x)

AE/AO

D z

where k(x) is a constant for a particular type of blade

contour.

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WAGEN INGEN 13.

In a previous study carried out by Oosterveld et al [ii] it was

also found that high camber-chord length ratios lead to large

unsteady cavities on the blades, giving rise to much higher

vibration-exciting forces on the hull above the propeller.

It is quite possible that a re-analysis of results of

investi-gations such as carried out by Van Oossanen and Van der Kooy [12]

in which it is found that the vibration-exciting pressures on the hull above the propeller (due to cavitation) increase with the number of blades, is due to the existence of a dominant

harmonic in the wake field. The existence of such a dominant

harmonic will cause the effective camber to increase as the chord lengths of the blade sections àpproach the lengths corres-ponding to the period of this harmonic. From analyses of wake

fields such as given in Ref. 13, it is clear that the rnplitude

of one of the first 6 harmonics of either the axial or the tangential wake component can be significantly larger over a part of the radius than the amplitudes of other harmonics.

The effect of a1, a2, a3, a4, a5 and a6 on the performance characteristics is also shown in Figs. 2 to 8. For increasing

harmonic order, up to a5, the I\T ValUes become lower and the

hQvalues become higher for a specific value of the parameters

a1 to a5. The effect on the behind efficiency, _B' is

signifi-cant. This result is also found to be due to the fact that in a circumferentially-varying propeller inflow, the effective camber distributions of the blade sections vary with angular

blade position, and differ considerably from the geometric camber

distributions. The largest difference, for the subject calculations,

occurs for the 5th harmonic (a5) as explained above. The resulting changes in the lift and drag properties of the blade sections are

responsible for the unfavourable differences in and KQ between

the "open-water" and "behind" performance.

The different trend in the KT, KQ and riB-values for a6 (see

Fig. 8) is due to the fact that the 6th harmonic of the axial

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asvm-metric with respect to the mid-chord position 1)

Hence the ideal angle of incidence is changed (see Ref. 9)

which results in different lift-to-drag ratios of the blade

sections. From Fig. 8 it is apparent that when a6 assumes

po-sitive values the nR-values are larger than unity, resulting in

behind efficiencies which are larger than the respective open-water efficiencies.

In Fig. 9 the results for b0 are shown. This parameter describes

systematically the effect of different radially-varying axial

velocity distributions. For h0 = O the same performance and

cavitation characteristics are obtained as for a = 0.7 in Fig. 2.

o

It is seen that when comparing the results of Fig. 2 to those of

Fig. 9, for equal KT-valuesf only small differences occur in both the performance and the cavitation characteristics.

In Fig. 10 the results for c0 are shown. This parameter describes the effect of a constant tangential wake velocity over the pro-peller disc. This parameter is therefore a measure of the "rotation in the incoming flow. For negative values of co, the rotation of the flow is opposite to that of the propeller (in the subject

calculations) . For decreasing values of

c0,

KT and K0 increase such

that the behind efficiency increases. This result is well-known

(see for example Ref. 14) . When c0 is less than about -0.05,

cavitation on the hack of the blades starts to occur.

The effect of a linear, radially-varying rotation of the inflow over the propeller disc is shown in Fig. 11. This type of inflow

is described by the parameter c1. Once again it is seen that for negative values of c1, the KT and KQ_values increase such that the behind efficiency also increases. For values less than about -0.175 cavitation on the back of the blades occurs, the amount of which increases considerably with decreasing values of c1. The rate of change of the extent of cavitation with angular blade position is negligible due to the fact that this velocity is

constant in a circumferential direction.

1) The distribution of the effective camber of the blade sections for the higher harmonics, for which the arc lengths correspondirìq to the period of the harmonics are shorter than the chord lengths, has at least two points of inflection.

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The effect of a circumferential variation in the tangential

velocity component is described by the parameters d and d1

The effect of d and d1 on the performance and cavitation

characteristics is shown in Figs. 12 and 13. Figure 12 gives the results for d, which represents the amplitude of a constant sine-variation with angular blade position, independent of the

radius. Figure 13 shows the results for d1, which represents

the amplitude of a sine-variation with angular blade position which is linearly dependent on the radius x. The small increases

in KT, KQ and for increasing absolute values for both d and

are again due to changes in the effective camber during a propeller revolution which, for the subject propeller, leads to more efficient lift to drag ratios. Both back and face cavitation occur on the propeller during a revolution for larger absolute

values of d and ¿I

o 1

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Effect of Reynolds Number.

The results of calculations for different propeller sizes, ranging from 0.25 to 7 meters, are shown in Fig. 14. In these

calculations the geometric dimensions, with respect to the diameter of 4 meters, were scaled linearly, while the speed

of advance was divided by. the square root of the scale ratio and the number of revolutions was multiplied by the square root of the scale ratio, i.e. the advance ratio was kept

con-stant. The static pressure at the propeller shaft was also

scaled linearly, decreasing with decreasing propeller size, ensuring that the cavitation number remained constant. The

static pressure for the 4 meter proeller was chosen to be

2

99400 Newton/rn , because for the reference value of 150,000

Newton/rn2 _{no cavitation occurred on any,of the propellers in}

the range considered.

From Fig. 14 it is c'ear that with increasing Reynolds number,

the propeller thrust increases slightly while the torque reduces

appreciably. Hence the efficiency increases with Reynolds

number _{which is a well-known result. In addition, it is}

seen that. for a diameter of 1.1 meter, cavitation starts to

occur on the back of the blades, the extent of which slightly

increases with Reynolds number. Thus the conclusion can be drcwn that scale effects on the extent of çavitation exist over the entire Reynolds number range considered.

Effect of Nmnber of Blades.

The results of calculations for different values of the number

of blades, ranging from 2 to 7, _{are shown in Fig. 15. In these}

calculations the chord lengths were scaled in such _{a way that}

the expanded blade area ratio remained constant _{for all}

pro-pellers. Camber and thickness values were scaled also, so as

to keep the f/c and t/c ratios constant. Also _{the radii of}

NETHUUANDS SHIP MODEL BASEN PAGE

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WAG EN I NG EN

leading and trailing edges were scaled so as to keep the p1/c

and Pt/c values constant. From the results shown in Fig. 15 it appears that with increasing blade number the efficiency in-creases until the maximum efficiency is reached for Z = 4. For

higher blade numbers the efficiency decreases. If the t/c ratios

had been chosen from a strength point of view, than the blades of the propellerswith a low blade number may be respectively thinner, which would then lead to relatively higher efficiencies for decreasing number of blades. At the reference static pressure of 150,000 Newton/rn2 none of the propellers cavitate.

Effect of_Expanded Blade Area Ratio..

When varying the expanded blade area ratio such that all non-dimensional geometry parameters remain constant, the results shown in Fig. 16 are obtained. It is' seen that with increasing

blade area the margin against cavitation decreases, until at

AE/AO = 1.23 cavitation starts to occur on the back of the blades.

Effect of Pitch-Diameter Ratio.

When only the pitch-diameter ratio is varied and all other para-meters are kep constant, the results shown in Fig. 17 are obtained.

Cavitation on the back of the blades is seen to start at a pitch-diameter ratio which is only slightly larger than the reference value of 1.0. Cavitation on the face of the blades starts to

occur for a pitch-diameter ratio of 0.75.

An increment in KT equal to 0.15 can be sustained free of

cavitation.

Effect of Camber-Chord Length Ratio.

The reference propeller has a radially-constant camber-chord

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PAGE

18.

all other parameters constant, the results shown in Fig. 18

are derived. It is f9und that when the camber is too small,

cavitation on the back of the blades occurs which increases

significantly in extent when the camber is only slightly reduced.

When the extent of cavitation is about 10 percent of the disc ratio, however, a further reduction in camber does not influence

the extent of cavitation very much. Ari increment in KT equal to

0.07 can besustained free of cavitation, which is less than

half of the respective value for the pitch-diameter ratio.

Effect of Static Pressure and Depth of Submersion.

The effect of varying the static pressure at the propeller shaft is shown in Fig. 19. Here, the depth of submersion of the

propeller was kept constant. Only the pressure above the water

surface was varied. Froni Fig. 19 it is seen that only cavitation

on the back of the blades occurs in the range of pressures considered. Cavitation starts to occur at a value of 130,000

2 2

Newton/rn (the reference value is 150,000 Newton/rn ). The extent

of cavitation at first only slightly increases with decreasing

pressure. At a value of about 90,000 Newton/rn2 the extent of

cavitation starts to increase at a faster rate with decreasing pressure. At this point also the rate of change of the extent

of cavitation with respect to the angular blade position

be-comes increasingly larger. This is due to the increasing effect of the pressure caused by the water column when the air pressure becomes small in comparison. In that case the variation in the value of the cavitation number between top and bottom blade

positions becomes much larger.

Effect of Ship Speed.

The results of calculations for different ship speeds, while

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Cavitation on the face of the blades occurs for speeds in excess of 14.2 meters/sec. Cavitation on the back of the blades occurs for

speeds lower than 8.7 meters/sec. For zero ship speed (bollard

condition) the maximum extent of cavitation on the back of the

blades is 20 percent of the propeller disc area. Once again, the rate of change of the extent of cavitation with respect to the

angular blade position is negligible due to the uniform propeller

inflow and the nearly constant value of the cavitation number at

a blade section during a revolution. An increment in KT equal to 0.22 can be sustained free of cavitation.

Effect of Shaft Speed.

The effect of varying the shaft speed is shown in Fig. 21. It is

seen that for a shaft speed slightly in excess of 2.5 revs./sec., cavitation on the back of the blades occurs, the maximum amount

of which increases very fast with increasing number of revolutions.

This is due to the significant decrease in cavitation number with

increasing speed of rotation of the propeller. The increment in

which can be sustained free of cavitation is 0.14.

Effect of Dìameter.

When only the propeller size is varied and the speed of advance,

the number of propeller revolutions and the static pressure at

the propeller shaft are kept constant, the results shown in

Fig. 22 are derived. It is seen that for a diameter larger

than 4.65 meters cavitation on the back of the blades occurs,

the amount of which increases considerably on increasing the

diameter. As is the case with increasing shaft speed, this is

due to the decrease in cavitation number with increasing rotative

speed. For a propeller diameter of 5 meters, 30 percent of the prop

1er disc area is covered with cavitation. Cavitation on the face

of the blades occurs when the diameter becomes less than 2.9

meters. An increment in KT equal to 0.22 can be sustained free

of cavitation.

NETHERLANDS SHIP MODEL BASiN

(21)

NETHERLANDS SHIP MODEL BAS!N

WAGENNGEN

CONCLUSIONS.

From the results presented in this paper, the following main conclusions can be drawn:

For the purpose of cavitation control in propeller design,

a subject up t.o now requiring a long-standing experience

in both the design and the testing of propellers in cavita-tion test facilities, a theory for the calculacavita-tion of

cavitation on propellers is a powerful tool. This is because of the possibility of assessing the effect of each of the

many design parameters involved. It is possible to calculate

the type and extent of cavitation- on the blades, thereby allowing for the effects of various parameters involved

in the cavitation control problem to be assessed by assuming specific values for these parameters and calculating the resulting cavitation performance.

In a circumferentially-varying wake field, the extent of cavitation on the blades of a propeller with respect to the angular blade position is often governed by the curvature of the flow over the blades. The curvature of the flow changes the effective camber of the blade sections which results in significantly different lift, drag and chordwise loading distributions compared to those for uniform flow. This

phenomenon is the main cause for the differences in "open

water" and in "behind'T condition. The largest induced camber

occurs when the chord lengths of the blade sections coincide with the arc lengths corresponding to the period of the

harmonic with the largest amplitude. This fact should be

taken into consideration when choosing the number of blades and the expanded blade area ratio in propeller designs.

Significant scale effects on cavitation inception exist up to

a Reynolds number value of about 1x107. (Reynolds number

based on resultant velocity and chord length at r O.7R)

PAGE

(22)

WAGENINGEN 21.

When systematically varying propeller geometry and operational

parameters, in a uniform flow, for the purpose of ascertaining

the importance of different parameters, it is found that the increment in KT which can be sustained free of cavitation is the smallest for the camber-chord length ratio.

In this case the increment in KT is about half of the value obtained for the pitch-diameter ratio and the shaft speed, and about one-third of the value obtained for the advance speed and the propeller diameter.

In a uniform flow, the rate of change of the extent of

cavitation with angular blade position is negligible except when the variation in the value of the cavitation number

(based on the resultant speed and static pressure at a blade

(23)

REFERENCES.

Lockwood-Taylor, J., "Screw Propeller Theory", Trans. of the North East Coast Institution of Engineers and Shipbuilders,

1942.

Burrill, L.C., "Aerodynamics and Marine Propeller Design", Trans. of the North East Coast Institution of Engineers

and Shipbuilders, 1965.

Kafali, K., "An Investigation of the Pressure Distribution

Around the Profiles Suitable for Marine Propellers", Inter-national Shipbuilding Progress, Vol. 12, No. 128, 1965.

Johnsson, C.A., "On Theoretical Predictions of Characteristics

and Cavitation Properties of Propellers", Publication No. 64 of the Swedish State Shipbuilding Experimental Tank, 1968.

Holden, K.O., "Type and Extent of Cavitation on Hydrofoils and Marine Propeller Blades", Det norske Ventas, Report No.

72-2-M, 1972.

Johnsson, C.A., "Correlation of Predictions and Full Scale

Observations of Propeller Cavitation", International Ship-building Progress, June 1973.

Oossanen, P. van, "Calculation of Performance and Cavitation Characteristics of Propellers Including Effects of Non-Uniform Flow and Viscosity", Publication No. 457 of the Netherlands

Ship Model Basin, 1974.

Oossanen, P. van, "Method for the Assessment of the Cavitation Performance of Marine Propellers", International Shipbuilding

Progress, Vol. 22, No. 245, January 1975.

Oossanen, P. van, "Theoretical Prediction of Cavitation on Propellers", Paper presented at the Chesepeake Section of the

Society of Naval Architects and Marine Engineers, 9th February,

1977.

PAGE

(24)

Brockett, T., "Minimum Pressure Envelopes for Modified NACA-66 Sections with NACA a = 0.8 Camber and Buships Type I and

Type II Sections", David Taylor Model Basin, Report No. 1780,

February, 1966.

Oosterveld, M.W.C. et al, "Some Propeller Cavitation and

Excitation Considerations for Large Tankers", Proceedings of the ist European Conference on Marine Technology, May, 1974. Oossanen, P. van, and Kooy, J. van der, "Vibratory Hull Forces Induced by Cavitating Propellers", Trans. Royal Institution of Naval Architects, Vol. 115, 1973.

Gent, W. van, and Oossanen, P. van, "Influence of Wake on Propeller Loading and Cavitation", Paper presented at 2nd

Lips Propeller Symposium, Drunen, Holland, 1973; International Shipbuilding Progress, 1973.

Oossanen, P. van, "Trade-offs in the Design of Sub-Cavitating

Propellers", International Shipbuilding Progress, Vol. 23, No. 264, August 1976.

(25)

NOMENCLATURE.

A

cav(back)

Acav_(face)

A area covered by cavitation on back and face of all

cay (total)

the blades at the same instant,

AE expanded area of propeller blades,

Am amplitude of m th harmonic component of axial

velocity component,

A0 disc area of propeller,

Bm phase angle of m th harmonic component of axial

velocity component,

Cm amplitude of m th harmonic of tangential

velocity component,

D propeller diameter,

phase angle of m th harmonic component of tangential velocity component,

advance ratio,

thrust coefficient, torque coefficient, pitch of blade section,

total static pressure at center line of propeller

shaft,

vapour pressure at prevailing temperature,

area covered by cavitation on the back of all the blades at the same instant,

area covered by cavitation on the face of all the blades at the same instant,

PAGE WAGENINGEN 24. D m J KQ p p o

(26)

NETHERLANDS SHIP MODEL BASIN WAGEN IN GEN b o C

crc

_o d d o' f m n, N s torque, radius of propeller, Reynolds number, thrust,

VA average value of axial inflow velocity over

propeller disc,

local value c'f axial inflow velocity component, average circumferential axial velocity at x,

ship speed,

local value of tangential inflow velocity

componen t,

Z number of propeller blades,

a01a1,a2,a31a41a51a6 wake field parameters,

wake field parameter,

chord length of blade section, wake field parameters,

wake field parameters, camber of blade section,

order of harmonic component of wake field, revolutions per second of propeller,

r polar coordinate,

rh radius of propeller hub,

t maximum thickness of blade section,

25.

Q R R n T V a V a V s Vt

(27)

P

i

Pt

WAGENINGEN

r

w wake fraction,

x non-dimensional radius,

Xh non-dimensional radius of propeller-hub,

no open-water efficiency,

efficiency in "behind" condition,

O angular polar coordinate,

p fluid density,

radius of curvature of leading edge of profile or blade section,

radius of curvature of trailing edge of profile or blade section.

PAGE

(28)

z DIRECTION OF ROTATION AND POSITIVE DIRECTION OF TANGENTIAL VELOCITY COMPONENT

(VIEWED FROM DOWNSTREAM)

CONTOUR OF PROPELLER BLADE

GENERATOR LINE

LIFTING LINE THROUGH QUARTER - CHORD POINTS

OF BLADE SECTIONS

(29)

10 0.8 0.7 0.6 0.5 K1 1OKQ Q4 T'O 0.3 Q2 0.1 - 0.1 -0.2 -0.3

pr

-\[i. (ACAvcro.rAL))J max.

-Lde

V

t i i .1 i 0.8 Va(X B).. - a0 1.0 Vt(xg) VS

(Ac AV( TOTAL )'\

\

A /max. (ACAV( BACK))

\

AO max. (AC AV (FACE ) )

\

A0 max. [d (ACAVToTAL)1 Lcii' A0 "J max.

FIG. 2 EFFECT OF VARYING a0 ON PERFORMANCE AND CAVITATKDN

CHARACTERISTICS

Z:5; Vs=lOrnISeC,

Ns2.5 rejsec;

A0

D=4.Orn D

_P-F,=15O00O

N/rn2 1.4 1.2 0.6 0.4 0.2 o a0

(30)

07 0.6 0.5 _0.2 0.1 O 1)8 d (ACAV(T0TAL?'.l1 [do \ A0 Ii max. 1OKQ (ACAV(T0TAL) A0 J max.

--

(ACAV( FACE )"

\

Aç / max -035 -0.25 -0.15 -0.05 0.05 0.15 0.25 a1, ÍVa(X.G):O75+a1COS8; Vt(X0

[V

FIG. 3 EFFECT OF VARYING

ai ON PERFORMANCE AND CAVITATION CHARACTERISTICS

0.35 0.25 0.20 (ACAV(T0 TAL) '

\

A J max. 0.15 (ACABACK A0

/

max. 0.10 (ACAV(FACE)\

\

A0 J max. r d (ACAVT0TAL] 0.05 [do' AO iJ max.

Z5; V5=1OrnJsec

-O.75; N2.5revs/sec,

Ei0.

D4.Om;

-(x)=O.O25;

_{P-P15OOOO N/rn2}

0.4 1OK 1Jß 0.3

(31)

o

___

-- 1111 (ACAV(FACE \ Acj

/

max. f I f

I. .1

I i -0.35 -0.25 -0.15 -0.05 o.òs 0.15 0.25

IVa(xg)o7cos2e Vt(X9)

a2 L VS 0.35 (ACAV( TOTAL)) A0 max. (ACAv(BACK)) A0 (ACAV (FACE)) AO La P'cAv.T0TAU)1 (d8\ A0 J max. max. max.

Z5

;

Vs=lOrnIsec.

±..LO75.

Ns2.5reVS!SeC;

A0

D=4.Om

--(x)=O.O25;

Po-Pv 150000

N/rn2

FIG. 4 EFFECT OF VARYING a2 ON PERFORMANCE AND CAVITATION

CHARACTERISTICS

(32)

0.7 _{O .} _0.5 K-r 04 i OK B 0.3 0.2 0.1

1i- (AQLJ

lde\

A0 (A CAV(FACEf A0

/

max. o _i i i I i i i I i i i I i i i I i i i i i i I I i i i -Q35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35 I Va(X.6)_07,a3c0s39 Vt(X8)_0 VS VS I

Zz5; Vs1OmIsec;

O.75; N52.5reVS/seC;

D4.Om

(x)O.O25;

P0-Fk15OOOO N1m2

FIG. 5 EFFECT OF VARYING a3 ON PERFORMANCE

AND CAVITATION CHARACTERISTICS

0.25 0.20 (ACAV(TOTAL)

\

A0 max. 0.15 (AV(BACK) A0

/

max. 0:70 (ACAV(FACE )' " AO

I

max. d (ACAV(T0TAL)" o.os [d8 \ AO

I

I I I I I I I I I I ¡

III

I I I I I I

(33)

0.7 0.6 0.5 KT ° 1OKQ rlB 0.3 0.2 0,1 (ACAV(FACE ;) A0 max. C) i i i I i I i i i I i i I i i

Ii

i i I i i i 0.15 0.10 0.05 o (ACAV(T0TAL) A0 max.

Z5; Vs=lOrnlsec;

0. 75 ,

N2.5 revslsec;

A0

D=4.Om

D

.t(X)O.O25

Po-Pv150000 N/rn2

FIG. 6

EFFECT 0F VARYING a4 ON PERFORMANCE AND CAVITATION CHARACTERISTICS

-0.35 -0.25 -0.15 -0.05 0.05 0,15 025 0.35 a4

IVa(X9)07c046

Vt(X9)0]

(ACAV(BACK)

\

max. A0 max. [d(A CAV(T0TAL)'1

\

A0 1J max. I I I I ¡ I I I ¡ I I I 0 25 0.20

(34)

0.7 0.6 0.5 0.4 K0 1B 0.3 0.2 0.1 o I d (ACAVT0TAL1 " A0 Jj (ACAV(TOTAL)"\

\

A0

1mx.

Íw'I

+:-

__._-I /

_I

- - -

(A CAV( FAC E

\

A0 I i i I max. I i i -035 -0.25 -0.15 -0.05 0.05 0.15 0.25 a5 {Va(x

8)0

c0S58 Vt(X8)01 VS

j

FIG. 7 EFFECT OF VARYING a5 ON PERFORMANCE AND CAVITATION

CHARACTERISTICS 0.35 025 0.20 (ACAV (TOTAL) A0 0.15 (ACAV(BAC K) max. 0.10 _o (ACAV(FACE A0 max. max. L (CAV(TOTAL1 o.o Lde \ A0 Ji max.

Z5; VslOmIsec;

Lo

75; N52.5revsjsec

LiO

D4.0m;

l(x)0.025;

P0 -Pv= 150000 N/rn2

(35)

0.7 0.6 0.5 K1 0.4 iO K liB 0.3 0.2 0.1

Ii.

(ACAV( TOTAL)

d0'

AO 10 K KT max. (ACAVCTOTAL )' \ A0

JmaX-(AV(FE)' \

AO

/

max. o i i i I i i i I i i i I i i I i i i I i i I i i i -035 -0.25 -ü15 -0.05 0.05 0.15 0.25 a [Va(xO)..O7.a6CQS68 VS 0.25 0.05 _0.35 [d (ACAVCTOTAL)1 d6 \ A J] max.

Z5 v5iOmßsec

Lo.75 Ns=2.5reVS!SeC;

A0

E!-i.o

D4.Om;

D

(x)O.O25;

_{Fb -Pvl5O°°°}

Nun2

FIG. 8 EFFECT OF

VARYING

6 ON

PERFORMAN AND

CAVITATION CHARACTERISTICS 0.20 0.15 0.10 (ACAV(TOTPL )

/

max. max. max.

\

AO (ACAV(BACK) " AO (ACAV(FACE)

\

AO

(36)

1.0 0.9 0.6 0.6 0.5 0. i OKQ 0.3 0.2 0.1 o _-0.1 _-02 _-0.3

071r.

(AcAv(BAcK) A0 ) max.

V

d (ACAV(TAL) Lde A0 max

/

0.2 0.6 1.0

íVa(XO)O7(ibX)

t(X.8)-[ VS VS 0]

FIG. 9 EFFECT OF VARYING b0 ON PERFORMANCE AND CAVITATION CHARACTERISTICS

ACAV(FACE A0 )max 14

Z5

;

V51Orn!seC

..E.-O.75 Ns:25reVS/SeC;

A0

D4.Om

í.(x)O.O25

FbPv15OOOONIm2

0.25 0.20 (ACAV(TAL) max. \ 0.15 (ACAV( BAC K) max. AO 0.10 (ACAV(FACE max.

\

A d (ACAV(TOTAL)'] 005 d9\ A J] max. -14 -1.0 -0.6 -0.2 b0

(37)

KT 10Ko 1B 07 0.6 0.5 0.4 0.3 0,2 0.1 o

co

-035 -0.25 -015 -0.05 0.05 0.15 0.25 IVa (X9) -o7 ¡

Vt(xØc]

L vs VS 0.35 0.25 0.20 0,15 0.10 (ACAV(TOTAL

\

A0 (ACAV( BACQ

\

A0 (ACAV(FA)

\

Ac

max. max. rna x.

Li. (AcAv.QTAL1 0.05 Lde AO /J max.

Z5; Vs1Om!sec;

.E-O.75. N52.5

revslsec

A0

D4.Om

(x)OO25;

_{Po -Pv=150000 N/rn2}

FIG. 10 EFFECT OF VARYING c

(38)

K1 lo KQ 1B

lo

_0.9 _0.8 0.7 _0.6 _o. 04 ₀₃ ₀₂ _0.1 _0.1 Q2 0.3 ACAV( BACK) O max. 1.0 0.9 _0.6 0.7 0.6 0.5 _0.4 0.3 0.2 0.1 (ACAV( TOTAL) " A0 (AC AV( BACK) A0 (ACAV(FACE)

\

A0

max. _max. _max.

Z5

V1Om1sec

O,75. N2.5 reIsec,

A0

F()J-jo.

D4.Om

D

¿(x)O.O25;

P0 -P1 50000 NJm2

Va(XO) V (XO) C1 0.7 C1X Vs Vs

FIG. 11 EFFECT OF

VARYING c1 ON PERFOMANCE

AND CAVITATION

CHARACTERISTICS fd (ACAV(TOTAL) [d8 AO max _l.4 1 .0 _0.6 _0.2 02 0.6 1.0 1.4

(39)

0.6 0.5 KT 0.4 IOKQ B 0.3 0.1 01 10 K I-o .._i i I t i i I i i i I _j. j I i i i I i i i I i i i -0.35 -0.25 -0.15 -0.05 0.05 0.15 025 0.35 d0 [Va(X -O7 Vt(x9)d SINe] VS VS

Z5

;

Vs=iOmlsec,

O.75; Ns2.5reISeC;

D4.OmIsec

.(x)=O.O25 P0 -Pv15OOOO N1m2

FIG. 12 EFFECT OF VARYING d0 ON PERFORMANCE AND CAVITATION CHARACTERISTICS

0.20 (ACAV(T0TALf AO J max. 0.15 (ACAV( BACK)

\

AO max. 0,10 (A CAV( FACE)'\ Aç

I

max. f d(A CAV(TOTAL?\1 0.05 Lde\ AO JJ max. 07 0.25

(40)

d1 . [ Va(X9) -0.7 VS Vt(x e) -d1X SIN (ACAV(BACK)\

\

AO

I

max. (ACAV(FACE)'\ \. AO

I

max. I d (ACAV(TOTAL) Lde " AO Jj max.

Z5

;

Vs1OmISeC,

-O.75 N2.5 revslsec;

D4.Om

..(x»O.O25

Po-Pv1 50000 N/rn2

FIG.13 EFFECT OF VARYING d1 ON PERFORMANCE

AND CAVITATION CHARACTERISTICS

-14 -1.0 -0.6 -02 0.2 1.0 1.4 max. (A CAV( TOTAL)

'

AO

(41)

0.6 .37 log [Riio.7] 10K0 (AC AV ( BAC K

\

AO I I t I i i i I i i i I i i I i i i ¡ i i I 2 3 D(i-) mtes) 4 1' [ La. (ACAV(TOTAL) LdB \ A0 Ijmax. max. 7

\

A0

FIG. 14 EFFECT OF REYNOLDS NUMBER ON PERFORMANCE AND CAVITATION

C HARACTERT IC S max. 1.L (ACAV(T0TAL o.o Lde \ A 1J max

Z:5

AO

ELl.O.

D N5D

--(x)=O.O25;

PO -R2485co(NIrn2)

0.25 I I I I I I I I I I T I I I I I i I I I I 0.20 (ACA0TAL 9 m ax. 0.15 (ACAV(BACK \ A0 max. 0.10 (AV(FACE) 0.5 KT 0.4 10Ko ho 0.3 B_ log [R n ( 0.1 02 7_ 0.1 5 6 (X.$) -0.7 Vt(xe) -01 VS VS

j

(42)

07 _0.6 0.5 KT 0.4 10k0 )0 0.2 ci o 0.3 -10 K (AvToTAL)

\

Aj

)rnax, 4 5 6 [Va(X O)Q7 Vt(Xp) -L VS VS J I I I I i i t I i i i I i i t I i i i I i i i I i i

FIG. 15 EFFECT OF NUMBER OF

BLADES ON PERFORMAN

(NO CAVITATION OCCURRES)

0 25 V5=lOmlsec Q75 . Ns:2.SrevSISeC,

A0

D=4.Om

..(x)O.O25

P0-R15OOOONJm2

0.20 (ACAYtTOTAL)

\

A0 max. 0.15 (ACAV( BACK) \ A0 max. 010 ACAVFACE)) max

íL

(ACAV(TOTAL) 0.05 de

\

A0 I t r i I I -I J t-i I j I I I t I I o 2 3

z,

(43)

I (ACAV(TOTAL

[de \

A0 .Jjmax. I t t i I i i I i i

rv(0)

-07 Vt(xe) -0

LV3

V 1 .9

FIG.16 EFFECT OF BLADE AREA RATIO ON

PERFORMANCE AND CAVITATION

[ d (ACAVTOTALJ\1 0.05 j.de " A )J max.

Z5

;

V =iOmlsec

N52.5reVSfSeC -)1.Q

D4.Om,

x)O.O25

P0 -P=150000N!m2

max. max. max.

(ACAOTA L)) (ACAVBACK " A (AC AV (FAC E

\

AO 17 0 0.7 0.9 1.1 1.3 1.5

(44)

1 .0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 o _-0.i _-0.2 -0.3 IVa(XO) -0.7 .Vt(X.0) 0] L VS VS 0.4 _0.3

(vc TOTALÍ

\

AO Jrnax.

(tBAcKi

\

AO

Jmax.

(ACAVcFACE )'\ \ A

I

max. - d (ÇA'IJTOTAL1 [c1

\

A

FIG. 17 EFFECT OF

PITCH DIAMETER RATIO

ON PERFORMANCE AND

CAVITATION m X.

Z5

; Vs1OmIsec;

075; Ns2,5revS(SeC.

A0

D4.Om;

-(x)O.O25

P0 -P=l5OOOO N/rn2

1.0 1.2 1.4 1.0 0.4 0.6 0.8 D

(45)

0.7 0.6 KT 0.4 1 OR0 T'O 0.3 _a2 _0.1 o 0.5 0.15

(eAc

\ A Im-x

1__ (AcAv(To)1/

Ido A

.jmx.

0 25 0.20 (ACAV(T0TAL \ Ao

Jmx.

0.10 (ACAV(FACE A0

/

m3x. I (AcAv(ToT1 , [d9 /J

Z:5, Vs=lOmIsec;

-LO.75;

N52.5revsSc;

A D D=4.Om;

PO -P15OOOONIm2

-0.04 -C.0 2 C. 2 001 O.G 0.08 01 [ "a(XO)07

V()]

FIG. 18 EFFECT OF CAMBER CHORD LENGTH RATIO ON

PERFORMANCE AND CAVITATION

max.

(46)

101co 07 -I J -0.5 0.6 0.5 Q4 0.3 0.2 _0.1 i i i I 1 T (ACAV(T0TAL1 " AO JJ

11

10 T i (AcAv( BAC)\

\

AO Jmax. 110003

13O3

po -R AT PROPELLER SHAFT Va(XQjc.7

Vt(XJ,

(Nm2) L o (AcAv(ToTAt A0 mix. (AC/V(BACK) A0 max. Q. (ACAVFACE)' \ A0 J max. -

iL (vLiIALY1

o.i Lde A0 JJ max.

FIG. 19 EFFECT OF STATIC

PRESSURE ON CAVITATION CHARACTERISTICS

Z5

V51OmJsc

N=2.5revsJsec

AO

P(X).10

D=4.Om D -(x):O.O25 o I i i i I i i i I i i i I i i i I i i i I i 70000 T 0.4 0.3

(47)

1 .0 ' ' ' ' ' ' ' -0.1 -0.2 -0.3

AAÇ1

A0 , max. 10 12 14 16 18 20 2 V mjsec. IVa(X 8 - r., VS VS 24 2F. 28 0.4 0.3 _0.2 _0.1 (A CAY TO TAL (ACAV(BACK A0 (A CAV( FACE)

\

A

max. max. max.

1_a.

(çyîor

Lde \

A

Jj max.

Z5

_{4O.75; N2.5 revs/Sec;}

EL-io

D4.Om

D

(x)O.O25;

_{PO -Pv=150000 Njm2}

FIG. 20 EFFECT OF FORWARD SPEED

ON PERFORMANCE AND CAVITATION CHARACTERISTICS

10k0 110

0.9 C .8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

2

4

(48)

10k0 1.0 _0.9 0.8 07 0.5 0.5 0.4 0.3 0.2 0.1 o - 0.1 0.2 - 0.3 1.0 2.0 3.0 4.0 5.0 6.0

Va(X9)

0.7

Vt(X$)

-0

N5(revssec).j vs vs 7.0 8.0

FIG. 21 EFFECT OF SHAFT SPEED ON PERFORMAN AND CAVITATION

CHARACTERISTiCS 1.0 0.9 0.8 0.7 (ACAV(TOTAL)

\

A0 max. 0.6 (A CAV C BAC K 0.5 A0 max. 0.4 (ACAV(FACE)'

\

A0

/

max. 0.3 íd (ACAV(TQTAL)\1 0.2

['

A0 Ji max. 0.1 o

Z5

;

Vs=lOmIseC;

O.75;

A0

2=i.o

D4.Orn;

4x)Qo2;

_{P0 -Pv1 50000 N1m2}

(49)

10k Q n 'O as 0.7 0.5 0.4 Q3 0.2 0.1 o -0.1 -0.2 -0.3 ACAV(FACE)' AO )max. D(in meters) f Va(XO0. L VS 1_t. ACAV(TOTALf1 ¼ Ao IJ max. VS I I ₆ 10 09 0.8 0.7 O 0.5 0.4 0.3 0.2 0.1