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    6.6 Interaction between a hull & a propeller

    So far in the study of the resistance of a ship & itspropellerthetwo have been considered separately. However, in reality the

    propeller has to work behind the ship & in consequence one has an

    interaction upon the other. How does the hull affects the water

    in which the propeller is working? (later we will also study theeffects of a propeller on the hull)

    A ship affects the water near its stern in 3 aspects:

    1) pressure increase at the stern;2) boundary layer (a propeller is in the boundary layer or way

    of the ship);

    3) Water particle velocity induced byship generated waves.

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    Wake fraction: water particle velocity near the propeller isnot the same as the ship velocity.

    ( : ship velocity & flow velocity at its stern)

    : , thus1

    : , thus (1 )

    The relationship between Froude & Tay

    s A s A

    s A s

    F A

    A F

    s A

    T A s T

    s

    w V V V V

    V V Vw V

    V w

    V Vw V V wV

    Froude

    Tay

    wake factor

    wake factorlor

    lor wake factor:

    or1 1

    When wake (most cases, a single screw)

    When , wake (only for high speed ship)

    F TT F

    F T

    A s

    A s

    w ww ww w

    V V

    V V

    positive

    nagative

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    wT & wF, (wake factors) are determined by the measurements

    made in a model test (near a hulls stern) or in a real ship test.

    Nominal wake: wake measured near the stern of a hull in the

    absence of the propeller (using pilot tubes).

    Effective wake: wake measured in the presence of propeller.

    The measurements show that a propeller at a rotating speedn

    behind a hull advancing at velocity, Vs, delivers thrust T. By

    comparing it to the results of the same propeller in the open-watertests, we will find that at the same revolutionsn, the propeller will

    develop the thrust Tbut at a different speed (usually lower),

    known as effective speed of advance, VA. The difference between

    Vs

    & VA

    is considered as the effective wake.

    Relation between nominal wake & effective wake.

    Since propellers induce an inflow velocity which reduces the

    positive wake to some extent, the effective wake factor usually is

    0.03~0.04 lower than the corresponding nominal wake.

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    Wake factor of a

    single screw ship

    Averaged Wake Fraction

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    Wake factor of a

    twin screw ship

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    Relative Rotation EfficiencyThe efficiency of a propeller in open water is called open-water

    efficiency,

    where VA is the advance speed, Tthe thrust, n the rotation speed

    (# of rotations per unit time), & Q0 is the torque measured in the

    open water test when the propeller is delivering thrust Tat therotation speedn.

    In the case the same propeller behind a hull, at the same advance

    speed it delivers the same thrust Tat the same revolutionn butneeds torque Q. In general, Q is difference from Q0. Then, the

    efficiency of the propeller behind the hull,

    0

    02

    AT VnQ

    2

    AB

    T V

    nQ

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    The ratio of behind-hull efficiency to open-water efficiency is

    called the relative rotative efficiency.

    The difference between Q0 and Q is due to

    1. wake is not uniform over the disc area while in open water, the

    advance speed is uniform.2. model and prototype propellers have different turbulent flow.

    (Remember then Reynolds number are not the same)

    1.0~1.1 for single-screw ship

    0.95~1.0 for twin-screw ship

    00

    0

    , thusBR B RQQ

    R

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    The influence of the propeller on the hull

    Thrust-deduction factor (fraction)When a hull is towed, there is an area of high pressure over the

    stern, which has a resultant forward component to reduce the total

    resistance. With a self-propelled hull (in the presence of the

    propeller), the pressure at the stern is decreased due to thepropeller action. Therefore, there is a resistance augment due to

    the presence of the propeller. IfTis the trust of the propeller &RT

    is the towing resistance of a hull at a given speed Vs , then in order

    that the propeller propel the hull at this speed, Tmust be greater

    thanRTbecause of the resistant augment. The normalizeddifference between TandRT, is called the thrust-deduction

    Fraction,and denoted byt.

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    1 , thus 1

    - is the "naked" hull resistance- the thrust after subtracting the resistance of the rudder & other

    stern appendages.

    measured in experiments depends, not

    T TT

    T

    T R Rt R t T

    T T

    RT

    t

    only on the shape of the hull

    & the characteristics of the propeller, but also the type of the rudder.

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    Hull Efficiency

    Hull Efficiency is defined as the ratio of the effective power fora hull with appendages to the thrust power developed by

    propellers.

    1

    1

    where

    - effective horsepower EHP

    - "naked" hull resistance

    - speed of the ship

    - the work done by the propeller in delivering a thrust

    - the speed of

    T sE

    HT A

    E T s

    T

    s

    T

    A

    R VP t

    P T V w

    P R V

    R

    V

    P T

    V

    the propeller w.r.t. the ambient water.

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    Propulsive Efficiency

    Quasi-propulsion coefficient is defined as the ratio of theeffective horsepower to the delivery horsepower.

    0

    0

    0

    2 2

    - delivered horsepower 2

    - efficiency of a propeller in open water,

    - relative rotative efficiency,

    - hull efficienc

    T s T sE A

    D B H R H

    D A

    E T s

    D

    D R H

    R

    H

    R V R VP TV

    P nQ nQ TV P R V

    P nQ

    y.

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    The division of the quasi-propulsive coefficient into three parts is

    helpful in 1) understanding the propulsive problem & 2) in

    making estimates of propulsive efficiency for design purposes.

    ( )

    In the design, usually we let

    (1 )( ) ,

    where is a correlation allowance, (or load factor). It depends

    principally on the hull roughness of the newly

    T

    D

    H R o H R o

    D D H R o

    D

    R VEHPP DHP

    EHPP DHP

    painted ship,

    foaling, weather condition & the length and type of a ship.

    Finally, the ,

    where is the shaft efficiency.

    s

    s

    DHPSHP

    main engine horsepower

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    6.7 Cavitation

    A typical pressure distribution in a blade element is shown below,

    Pressure (+)

    Suction (-)Back VR

    face

    As the pressure on the back of a propeller falls lower and lowerwith the increase in a propellersn, the absolute pressure at the

    back of the propeller will eventually become low enough for the

    water to vaporize and local cavities form. This phenomenon is

    known as cavitation. ( , vapor pressure of water)v

    P

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    Cavitation on a propeller will

    1. lower the thrust of the propeller, & thus decrease its

    efficiency,

    2. cause vibration of hull & the propeller and generateuncomfortable noise, &

    3. cause erosion of the propeller blade.

    Criteria for prevention of cavitation

    Mean thrust loading coefficient21

    2

    c

    R p

    T

    V A

    22 2

    - density of water, - Thrust,

    - project blade area, 1.067 0.229 ,

    - the relative velocity at 0.7 of a propeller

    2 0.7

    p

    p

    D

    R

    R A

    T

    A PA

    A D

    V R

    V V R n

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    Cavitation number

    0

    212

    0 - presuure at some point of a blade

    - vapor presuure of water

    v

    R

    v

    p p

    V

    p

    p

    The cavitation is most likely to occur at the tips of blades where

    the relative velocity is the largest and the hydro-static pressure is

    the lowest when blades rotate to the highest position. It can also

    occur near the roots where blades join the boss of a propellerbecause the attack angle is the largest.

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    6.8 Propeller Design

    Methods of Propeller Designa. Design based upon charts (diagrams). These charts are obtained

    form the results of open-water test on a series of model

    propellers. (also upon software, such as NavCad).

    b. Design using circulation theory and CFD (not studied here).

    Methodical Series

    A model propeller series is a set of propellers in which the principal

    characteristics such as pitch ratio etc are changed in a systematic

    manner. There are many series tested, and their results are

    summarized and presented in the form ofcharts which can be used

    in design. The most extensive model propeller series is Netherland

    Ship Model Basin (NSMB) at Wageningen. This series test was run

    from 1937 to 1964.

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    NSMB Series includeSeries A: narrow blade tips, airfoil sections, high efficiency

    only for light loaded propellers (not widely used)

    Series B: wider tips, airfoil section from blade root to 0.7radius, and circular back from 0.8 radius to tip.

    Scope of series B is shown

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    Given below is the dimensions (outline, thickness) of

    B.4 blade

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    The B series results are presented in the form ofcharts of

    diagrams, known as diagram .

    At upper right corner, the diagram gives 4.40 B. (indicating Btype, 4 blades &AE /A0 = 0.40, t0/D = 0.0045 (blade-thickness

    fraction),d/D = 0.167 (diameter ratio of the boss to the

    propeller), &the Pitch,P.

    At low left corner, it gives the definitions of

    PB

    andP

    B

    0.5

    2.5, and (notice that )

    - revolutions per min, - propeller diameter (ft)

    - delivered at propeller

    (1- ) - speed of advance (knots)

    and are

    D A

    p

    A A

    D

    A s

    p

    n P VnDB J

    V V nD

    n D

    P

    V V w

    B

    horsepower

    dime !nsional

    diB

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    diagram

    Horizontal coordinate:

    Vertical coordinate: ratio of the pitch to diameterP/D

    Two sets of curves , and one optimal ( ) line

    PB

    0&

    PB

    0

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    Propeller Design Based on Charts-The information required for making a propeller design from

    charts are:

    1. Principal dimensions, & main coefficients of a ship used toestimate wake, thrust factors, & relative rotative efficiency.

    2. Speed of a ship

    3. EHP (from model tests or estimated from other available data)

    4. engine power (SHP) & rpm.5. restrictions on the maximum diameter of propeller.

    0.5

    0.5

    D

    -Design Procedures

    ( )1. Calculating , (assuming , for computing )

    From the chart to find , pitch ratio that give the best efficiency.

    (From , & pitch ratio )

    D Ep D D

    A

    n P PB PV

    D P

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    2. This will give a best propeller in open water. Since the

    propeller works behind the hull, it is usually to reduce by

    5%~8%, for single-screw ship, 4% for twin screw ship.

    3.With the same valuep

    D

    B

    0

    a smaller value ( ), use

    the chart again to find efficiency and pitch ratio ( / ).

    4. In the same way, we may use different chart & different

    to see the effects (no. of blades, blade area r

    A

    nD

    V

    P D

    n

    0

    0

    0

    atio) on .5. After determining , we calculate (propulsive coeff).

    1where . Then we re-calculate ( ) .

    1

    D

    ED R H H D

    D

    PtP

    w

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    6. If the newly computed, , is very close to the previous

    assumed one, then we continue to examining the cavitation

    of the propeller. If not, we use the newly computed to

    repeat the above 1-5 ste

    D

    D

    P

    P

    ps again.

    7. Examining the condition of cavitation for the propellers.

    If the condition is not satisfied, choose a propeller with larger

    , or make other adjustments (such as reducing , & using

    mul

    EA n

    tiple screws).

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    Examples

    Example a, Using the B4.40 chart to design a propeller suitable for

    the following conditions. Also determine SHP. (knowing EHP, Vs todetermine , P,D)

    Vs= 16 knots Taylor wake factor w = 0.3075

    EHP = 5000 Hp thrust deduction t= 0.186

    Allowance for appendage 6% Shaft loss = 3%

    Allowance for weather 15% reduction in = 7%

    n = 120 r/min relative rotative effi. 1.0R

    0

    0.5 0.5

    2.52.5

    : EHP(1 ) EHP(1 0.06 0.15) 6050 hp

    Assuming 0.65, (DHP) EHP / 9308 hpAdvance velocity 1 11.08 knots

    120 9308Taylor propeller coeff., 28.33

    11.08

    D D D

    A s

    D

    p

    A

    PV w V

    n PB

    V

    Solution

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    0

    Checking B4.40 chart, 213, 213(1 0.07) 198,

    1 0.8140.597, 0.597 0.597 0.705.

    1 0.6925The previous is assumed to low. New iteration starts.

    Let 0.71, EHP / 8521 hp,

    opt

    o D H R

    D

    D D D p

    t

    w

    P B

    0

    27.1,

    From B4.40 chart, 209, 209(1 0.07) 194.4,

    0.8140.602, 0.602 0.708 0.71

    0.6925

    This time the assumed is very close to the comupted one.

    194.4 11.08, 17.9 ft120

    opt

    o D H R

    D

    A

    A

    VnD DV n

    , 0.85,

    DHP 85210.85 17.9 15.2 ft, SHP 8784 hp

    1 0.03s

    PD

    P

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    Example b. GiveD (due to the restriction of draft) & usingB.4.40 chart to find the optimumn,P/D, and

    A cargo Ship

    L = 86 m Vs = 9 knots

    B = 13 m EHP = 515 hp

    T= 5.66 m w = 0.184

    = 4500 m3 t= 0.125

    = 1.0 = 0.97D = 4m = 13.14 ft = 0.218 (load factor or allowance)

    R s

    D

    1. 1 9 1 0.184 7.34 knots,2. Assuming 0.69,

    1 EHP3. (DHP) 909 hp,

    A s

    D

    D

    D

    V V w

    P

    Solution :

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    4. Try a range of rotation velocities, n

    0.5

    2.5

    ( )D

    p

    A

    N PB

    V

    A

    ND

    V

    1

    1D o R

    t

    w

    No. Name Unit Value

    1 n rpm 90 95 100 105 110

    2 18.6 19.6 20.7 21.7 22.7

    3 161 170 179 188 197

    4 % 64.5 64.6 64.7 64.3 63.8

    P/D 0.95 0.875 0.79 0.75 0.70

    5 P = P/D*D m 3.8 3.5 3.16 3 2.8

    6 0.691 0.692 0.693 0.69 0.688

    0From the chart

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    Based on the results shown in the table, it is found that

    the highest value is 0.693 when 100,

    and it is also closest to the assumed .

    Thus, 100 is the optimal rotation speed.

    Pitch. = 3.16

    D

    D

    n

    n

    P

    m = 10.37',

    (DHP) 909SHP 937 hp.0.97

    D

    s

    P

    A different problem: given the rotation velocity,n, to determine

    the optimal diameter of the propeller.