Ship-Theory Propulsion 2

8/15/2019 Ship-Theory Propulsion 2

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Dimensional Analysis

The thrust of a propeller could depend upon:a) Mass density of water, .

b) Size of the propeller, represented by diameter .

c) Speed of advance, .

d) Acceleration due to gravity, .e) Speed of rotation, .

f) Pressure in the fluid, .

g) Viscosity of the water, .

= (

,

,

,

,

,

,

)

=

1




If the model and ship quantities are denoted by the suffixes M and S,respectively, and if is the linear scale ratio, then =

If the propeller is run at the correct Froude speed of advance, = ,

= /

The slip ratio has been defined as 1 . For geometrically similarpropellers, therefore, the nondimensional quantity must be the same

for model and ship. Thus, as long as and are the same in ship

and model

∝

= ,

= /,

=

∙

=

=

,

=

∙

=1

∙ / =

1

/, = ∙ /




The thrust power is given by = ∙ , so that

=

∙

= .,

=

∙

= . ∙ . =

If the model results were plotted as values of

=

, =

to a base of or , therefore, the values would be directly applicable to theship. But the above coefficients have the disadvantage that they becomeinfinite for zero speed of advance, a condition sometimes occurring in practice.Since or is the same for model and ship, may be replaced by .

=

, =

=

, =

=

2

=

2 ∙

, =

where = ∙ is the thrust power and = 2 ∙ is the delivered power

of the open water propeller.



Propeller-Hull Interaction

Wake: Previously we have considered a propeller workingin open water . When a propeller operates behind themodel or ship hull the conditions are considerably modified. The propeller works in water which is disturbed

by the passage of the hull, and in general the water aroundthe stern acquires a forward motion in the same directionas the ship. This forward-moving water is called the wake,and one of the results is that the propeller is no longer

advancing relatively to the water at the same speed as theship, , but at some lower speed , called the speed of advance.



Propeller-Hull Interaction

Froude wake fraction

=

, =

1 +

Taylor wake fraction

=

, = (1 )

Resistance augment fraction and thrust deductionfraction

=

=

1, = (1 + )

=

= 1

, = 1



Power Definitions

Brake power is usually measured directly at the crankshaft coupling by means of a torsion meter or dynamometer. It is determined by a shoptest and is calculated by the formula = (2), where is therotation rate, revolutions per second and

is the brake torque, ∙ .

Shaft power is the power transmitted through the shaft to thepropeller. For diesel-driven ships, the shaft power will be equal to thebrake power for direct-connect engines (generally the low-speed diesel

engines). For geared diesel engines (medium- or high-speed engines),the shaft horsepower will be lower than the brake power because ofreduction gear “losses.” Shaft power is usually measured aboard ship asclose to the propeller as possible by means of a torsion meter. The shaftpower is given by = (2).



Power Definitions

Delivered power is the power actually delivered to the propeller.There is some power lost in the stern tube bearing and in any shafttunnel bearings between the stern tube and the site of the torsionmeter. The power actually delivered to the propeller is thereforesomewhat less than that measured by the torsion meter. This delivered

power is given the symbol . Thrust power is the power delivered by propeller as it advances

through the water at a speed of advance , delivering the thrust . Thethrust power is = .

Effective power is defined as the resistance of the hull, , times theship speed ,

= .

Propulsive efficiency is defined as

=

=

=

= 1

(1 ) =

( 1 )

( 1 )

= , =( 1 )

( 1 )

, =



Different Design Approaches

Case 1: , , are known and . is required.In this case the unknown parameter may be eliminated fromthe diagrams by plotting / versus instead of versus asfollows.

=

=

= 2

2

=

2

− =

= 0.1739

which are the variables used in charts between pages 192-196. Onthese charts the optimum and 1/ are read off at theintersection of known

− value. Afterwards is

computed using the optimum 1/ value as = /.



Different Design Approaches

Case 2: , , are known and is required.In this case the unknown parameter may be eliminated fromthe diagrams by plotting / versus instead of versus asfollows.

=

=

=

2

2 =

2

− =

= 1.75

which are the variables used in charts between pages 197-201. Onthese charts the optimum and 1/ are read off at theintersection of known

− value. Afterwards iscomputed using the optimum 1/ value as = /.



Typical Propeller Design

Given DataService speed: = 21 = 10.8 /

Effective power with model-ship correlation allowance: = 9592

Estimated propulsive efficiency: = / = 0.75

Immersion depth of propulsion shaft: ℎ = 7.5

Estimated delivered power at 21 : = / = 9592/0.75 = 12789

Empirically determined wake fraction: = 0.20

Empirically determined thrust deduction fraction: = 0.15

Estimated relative rotative efficiency: = 1.05

Design CalculationSelected propeller diameter (with adequate clearance): = 6.4

Selected number of blades (from consideration of vibration forces): = 4

Calculation of velocity of advance (wake speed): = 1 = 10.8(1




Wageningen B-Series charts: ∙ − =

=

∙.∙ . ∙ .

= 0.52039

Using the charts given on pages 197 (B4-40), 198 (B4-55), and 199 (B4-70) for

∙ − = 0.52039 from the optimum propeller efficiency curve we getExpanded blade area ratio: 0.40 0.55 0.70

1/ at optimum efficiency: 1.260 1.275 1.290

= 60 ∙ / ∙ 1/ : 102.1 103.3 104.5

Corresponding /: 1.110 1.090 1.070Open water efficiency : 0.673 0.670 0.663

We proceed to choose the blade area ratio by applying a cavitation criteriongiven by Keller.




The required thrust is

=

1 =

1 =

1 =

9592

(1 0.15) ∙ 10.8 = 1044.9

The Keller area criterion for a single-screw vessel gives

=1 . 3 + 0 . 3 ∙ ∙

∙

+

where = . + ℎ = 98100 1750 + 1025 ∙ 9.81 ∙ 7.5 =171764 / = 171.8 /, and is a constant varying from 0 to 0.2. Taking = 0.2,

=1.3 + 0.3 ∙ 4 ∙ 1044.9

171.8 ∙ 6.4 + 0.2 = 0.571

Interpolating between / = 0.55 and / = 0.70 for / = 0.571 we get = 103.5 , / = 1.087, and = 0.669. Accordingly the value becomes:

=1

1 ∙ ∙ =

1 0.15

1 0.20 ∙ 0.669 ∙ 1.05 = 0.746

This compares well with the value of 0.750 assumed. If a larger difference had been

found, a new estimate of the power would have to be made, using = 0.746.




Another Example of Calculating Optimum A somewhat different example of calculating optimum is given below. Acommon problem for the propeller designer is the design of a propeller when therequired propeller thrust (e.g. from a model test equal to the resistance correctedfor the thrust deduction) and the propeller diameter (e.g. from the availableclearance) are known. The advance velocity of the propeller may be estimated fromthe ship speed and wake fraction. The unknowns are the required power and theengine . Suppose that the following data is given for a container vessel.Thrust: = 142 = 142000 ∙ 9.81 = 1393000 = 1393

Ship speed: = 21 = 10.8 /

Advance velocity (Wake speed): = 21 1 0.2 = 16.8 = 8.64 /

Selected propeller diameter (with adequate clearance): = 7.0

Selected number of blades (from consideration of vibration forces): = 4Immersion depth of propulsion shaft: ℎ = 5.0

Design Calculation We begin by considering Keller’s formula for with = 0 for the given ship

=

=1.3 + 0.3 ∙ 4 ∙ 1393

(98.1 1.75 + 1.025 ∙ 9.81 ∙ 5.0) ∙ 7.0 = 0.485

For single skrew wake field = 0.2, it may be less if the wake field is good.




Obviously is an important parameter affecting the value of . If it wereselected as 0.2, would be 0.685 instead of 0.485. Now that we have taken = 0 and consequently the minimum must be 0.485. To be on the safeside let us select = 0.55. Already we have selected = 4 therefore ourpropeller now is B4-55. Consequently we can use the diagram ofB4-55 series. We know the thrust and the diameter , hence seek for the .

To use the diagram we need to know both and ; however at present we canonly calculate / as follows

=

=

1393000

1025 ∙ 8.65 ∙ 7 = 0.3707

Now when we select a / pair in the diagram it must be such that / =

0.3707. This may be done either by trial-and-error followed by linear iterationor by the graphical method. The graphical method gives the result directly butin order to use it we must draw the curve corresponding to = 0.3707 for arange of values. Wherever this curve crosses a value in the diagram of B4-55, that particular pair corresponding to a definite / ratio in thediagram is a correct pair. Supposing that we have established the

following table for various / ratios using the diagram (B4-55)




Our aim now is to select the propeller with maximum open-water efficiency.The first examination indicates it may be / = 1 but to make sure we try the

close neigborhood of it; / = 0.95 and / = 1.05. From these results wesee that / = 1 really gives the maximum efficiency hence we select it. Thusour final decision for the propeller is B4-55, / = 1, = 0.651, = 0.699 so

that =

=

.

.∙ = 1.768 , = 60 ∙ = 106 . Finally, since the

torque coefficient = 0.0310, = = 1025 ∙ 1.768 ∙ 7 ∙ 0.0310,

= 1669322 ∙ . Power to be delivered = 2/1000 = 18544




Example of Calculating Optimum DiameterIn this example we suppose that from the beginning we have selected theengine and its RPM hence we are to select a diameter for maximum efficiency.

For a fast patrol boat the following data is given.

Advance velocity of propeller: = 28 = 14.4 /

Delivered power : = 440

= 720, = 720/60 = 12

= 5

= / = 0.75




To eliminate the unknown diameter we must use /

as the parameter.

=

=

=

∙

=

=

∙

∙∙.=0.016

Applying any one of the approaches (graphical or interpolative) described in theprevious problem we can establish the following table.

In this case the most efficient choice is / = 1.4 and = 1.19 so that = /, = 14.4/(12 ∙ 1.19) = 1.01 , = 1 . Since = 0.153, = , =23500 . If this thrust is not in accord with the resistance calculations of the boatcalculations must be repeated for a different speed till the convergence is gained.Finally the cavitation possibility must be checked at least by using the Kellerformula. In this case Keller formula gives minimum = 0.59 hence OK.

/ /

1.200 1.085 0.098 0.0237 0.713 0.016

1.300 1.140 0.124 0.0306 0.735 0.016

1.400 1.190 0.153 0.0387 0.747 0.016

1.350 1.165 0.138 0.0346 0.742 0.016

Ship-Theory Propulsion 2

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