chap 7 resistance and powering of ship recall static equilibrium! what are the forces in the x- axis...
TRANSCRIPT
Chap 7 Resistance and Powering of Ship
• Recall Static Equilibrium!
• What are the forces in the x-axis of the ship?– Resistance or Drag– Thrust (Propulsion)– We will first look at propulsion,
then drag in this chapter.
41 knots!
Ship Drive Train and Power
7.2 Ship Drive Train System
Engine ReductionGear
Bearing Seals
ScrewStrut
BHP SHP DHP
THP
Shaft
Brake Horse Power (BHP)
- Power output at the shaft coming out of the engine before
the reduction gears
Shaft Horse Power (SHP)
- Power output after the reduction gears (at shaft)
- SHP=BHP - losses in reduction gear
Horse Power in Drive Train
Ship Drive Train and Power
Delivered Horse Power (DHP)
- Power delivered to the propeller
- DHP=SHP – losses in shafting, shaft bearings and seals
Thrust Horse Power (THP)
- Power created by the screw/propeller (ie prop thrust)
- THP=DHP – Propeller losses
Relative Magnitudes?
BHP>SHP>DHP>THP
E/G R/GBHP SHP Shaft
BearingProp.
DHP THP EHPHull
Ship Drive Train and Power
7.3 Effective Horse Power (EHP)
• EHP : The power required to move the ship hull at a given
speed in the absence of propeller action (related to resistance)
(EHP is not related with Power Train System)
• EHP can be determined from the towing tank experiments at
the various speeds of the model ship.
• EHP of the model ship is converted into EHP of the full scale
ship by the Froude’s Law.
EHP is approximately equal to THP (usually slightly less)
VTowing Tank Towing carriage
Measured EHP
Effective Horse Power (EHP)
0
200
400
600
800
1000
Effe
ctive
Ho
rse
po
we
r, E
HP
(H
P)
0 2 4 6 8 10 12 14 16 Ship Speed, Vs (Knots)
POWER CURVEYARD PATROL CRAFT
Typical EHP Curve of YP
What EHP is required for the 12 knot YP cruise?
Effective Horse Power (EHP)
Efficiencies
• Hull Efficiency
THP
EHPH
- Hull efficiency changes due to hull-propeller interactions.- Well-designed ship : - Poorly-designed ship :
1H1H
Well-designed
Poorly-designed
- Flow is not smooth.- THP is reduced.- High THP is neededto get designed speed.
Screw
Effective Horse Power (EHP)
Efficiencies (cont’d)
• Propeller Efficiency
DHP
THPpropeller
• Propulsive Coefficient (PC) ~ An overall measure of drive train efficiency
SHP
EHPp
propeller designed for well 6.0p
SHPDHP
THP
EHP
7.5 Total Hull Resistance
• Total Hull Resistance (RT) The force that the ship experiences opposite to the motion of the ship as it moves.• EHP Calculation
P
ST
P
s Hft lb
sft
V(lb) R)EHP(H
550 ship of speedV
resistance hull total
S TR
P
ST
Hatts
Wattss
J
s
ftlb
s
ftlbVR
550/1W 1
:
Power
Total Hull Resistance (cont)
• Coefficient of Total Hull Resistance
- Non-dimensional value of total resistance
S V 5.0
RC 2
s
TT
hull submerged theon area surface wetted
ship of Speed
density Fluid
resistance hull Total
watercalm in resistance hull totaloft Coefficien
S
V
R
C
S
T
T
dimension-nonlb
2
2
4
2
ftsft
ftslb
Total Hull Resistance (cont)
• Coefficient of Total Hull Resistance (cont’d)
-Total Resistance of full scale ship can be determined using
ST VSC , , and
TST CSVlbR 25.0)(
speed ship scale Full
form of Curves from obtained
table propertywater from available
test model the by determined
:V
: S
:
:C
S
T
Total Hull Resistance (cont)
• Relation of Total Resistance Coefficient and Speed
0
5000
10000
15000
20000
Tota
l R
esis
tance, R
t (lb
)
0 2 4 6 8 10 12 14 16
Ship Speed, Vs (knots)
TOTAL RESISTANCE CURVEYARD PATROL CRAFT
speed highat 5 o t
speedlow at 2 from
2
n
V
VCRn
S
STT
speed highat 6 to
speedlow at 3 from
2
n
V
VVCVREHPn
S
SSTST
7.6 Components of Total Resistance
• Total Resistance
AWVT RRRR Resistance Viscous: RV
Resistance Making Wave: RWResistance Air: RA
• Viscous Resistance
- Resistance due to the viscous stresses that the fluid exerts
on the hull.
( i.e. due to friction of the water against the surface of the ship)
- Water viscosity, ship’s velocity, wetted surface area and roughness
of the ship generally affect the viscous resistance.
Characterized by the non-dimensional Reynold’s Number, Rn
Components of Total Resistance
• Wave-Making Resistance - Resistance caused by waves generated by the motion of the ship - Wave-making resistance is affected by beam to length ratio, displacement, shape of hull, (ship length & speed)
Characterized by the non-dimensional Froude Number, Fn
• Air Resistance - Resistance caused by the flow of air over the ship with no wind present - Air resistance is affected by projected area, shape of the ship above the water line, wind velocity and direction - Typically 4 ~ 8 % of the total resistance
Components of Total Hull Resistance
• Total Resistance and Relative Magnitude of Components
Viscous
Air Resistance
Wave-making
Speed (kts)
Re
sis
tan
ce (
lb)
- Low speed : Viscous R dominates - Higher speed : Wave-making R dominates- Hump (Hollow) : location is function of ship length and speed.
Hump
Hollow
Coefficient of Viscous Resistance
• Viscous Flow around a ship
Real ship : Turbulent flow exists from near the bow.
Model ship : Studs or sand strips are attached at the bow
to create the turbulent flow.
Coefficient of Viscous Resistance (cont)
• Coefficients of Viscous Resistance - Non-dimensional quantity of viscous resistance - It consists of tangential and normal components.
FF KCC normaltangentialV CCC
• Tangential Component : - Tangential stress is parallel to ship’s hull and causes a net force opposing the motion ; Skin Friction
- It is assumed can be obtained from data of flat plates.
FC
flow shipbow stern
FC
tangential
norm
al
Coefficient of Viscous Resistance (cont)
S
n
nF
FV
LVR
RC
CC
)2(log
075.0
210
of Component Tangential
Semi-empirical equation
watersalt for
water freshfor
/sft101.2791
/sft101.2260
/s)(ft ViscosityKinematic
)Speed(ft/s Ship
(ft)L
Number Reynolds
25-
25-
2
pp
S
n
V
L
R
Coefficient of Viscous Resistance (cont)
• Tangential Component (cont’d)
- Relation between viscous flow and Reynolds number
· Laminar flow : In laminar flow, the fluid flows in layers
in an orderly fashion. The layers do not mix transversely
but slide over one another.
· Turbulent flow : In turbulent flow, the flow is chaotic and
mixed transversely.
Laminar Flow Turbulent Flow
Flow overflat plate
5105about Rn5105 about Rn
• Normal Component
- Normal component causes a pressure distribution along the
underwater hull form of ship
- A high pressure is formed in the forward direction opposing
the motion and a lower pressure is formed aft.
- Normal component generates the eddy behind the hull.
- It is affected by hull shape.
Fuller shape ship has larger normal component than slender
ship.
Full shipSlender ship
large eddy
Coefficient of Viscous Resistance (cont)
small eddy
• Normal Component (cont’d)
- It is calculated by the product of Skin Friction with Form Factor.
23
)(
)(
)()()(
)(ft 19 K
K
ftL
ftB
ftTftBftL
C
CKC
F
Fv
Factor Form
Coeff. Friction Skin
of Component Normal
Coefficient of Viscous Resistance (cont)
• Reducing the Viscous Resistance Coefficient
- Method : Increasing L with constant submerged volume
1) Form Factor K Normal component KCF
Slender hull is favorable. ( Slender hull form will create a smaller pressure difference between bow and stern.)
2) Reynolds No. Rn CF KCF
Summary of Viscous Resistance Coefficient
Wave-Making Resistance
• Definition : refer to the previous note
•Typical Wave Pattern
Bow divergent waveBow divergent wave
Transverse wave
L
Wave Length
Stern divergent wave
Wave-Making Resistance
Transverse wave system : Waves perpendicular to wake
• It travels at approximately the same speed as the ship.• At slow speed, several crests exist along the ship length
because the wave lengths are smaller than the ship length.• As the ship speeds up, the length of the transverse wave
increases.• When the transverse wave length approaches the ship length,
the wave making resistance increases very rapidly.
This is the main reason for the dramatic increase in
Total Resistance as speed increases.
Wave-Making Resistance (cont)
Transverse wave System
Wave Length
WaveLength
SlowSpeed
“Hull”Speed
Vs < Hull Speed
Vs Hull Speed
Hull Speed : speed at which the transverse wave length equals the ship length. (Wavemaking resistance drastically increases above hull speed)
Divergent Wave System: waves that angle out
• It consists of Bow and Stern Waves.
• Interaction of the bow and stern waves create the Hollow or
Hump on the resistance curve.
• Hump : When the bow and stern waves are in phase,
the crests are added up so that larger divergent wave systems
are generated.
• Hollow : When the bow and stern waves are out of phase,
the crests match the troughs so that smaller divergent wave
systems are generated.
Wave-Making Resistance (cont)
Calculation of Wave-Making Resistance Coeff.
• Wave-making resistance is influenced by: - beam to length ratio - displacement - hull shape - Froude number• The calculation of the coefficient is too complex for a simple theoretical or empirical equation. (Because mathematical modeling of the flow around ship is very complex since there exists fluid-air boundary, wave-body interaction)• Therefore model test in the towing tank and Froude expansion are the best way to calculate the Cw of the real ship.
Wave-Making Resistance (cont)
Reducing Wave Making Resistance
1) Increasing ship length to reduce the transverse wave - Hull speed will increase. - Therefore increment of wave-making resistance of longer ship will be small until the ship reaches to the hull speed.
Wave-Making Resistance (cont)
Reducing Wave Making Resistance (cont’d)
2) Attaching Bulbous Bow to reduce the bow divergent wave
- Bulbous bow generates the second bow waves .
- Then the waves interact with the bow wave resulting in
ideally no waves, practically smaller bow divergent waves.
- EX :
DDG 51 : 7 % reduction in fuel consumption at cruise speed
3% reduction at max speed.
design &retrofit cost : less than $30 million
life cycle fuel cost saving for all the ship : $250 mil.
Tankers & Containers : adopting the Bulbous bow
3) Stern flaps - helps with launching small boats, too!
Wave-Making Resistance (cont)
Bulbous Bow
Wave-Making Resistance (cont)
Coefficient of Total Resistance
Allowancen Correlatio : C
CCK)1(C
CCCC
A
AWF
AWVT
Coefficient of total hull resistance: the C’s added
Correlation Allowance
• It accounts for hull resistance due to surface roughness, paint roughness, corrosion, and fouling of the hull surface.• It is only used when a full-scale ship prediction of EHP is made from model test results. • For model,• For ship, empirical formulas can be used.
. 0 smooth is surface model SinceAC
Other Type of Resistances
• Appendage Resistance
- Frictional resistance caused by the underwater appendages
such as rudder, propeller shaft, bilge keels and struts
- 224% of the total resistance in naval ship.
• Steering Resistance
- Resistance caused by the rudder motion.
- Small in warships but troublesome in sail boats
•Added Resistance
- Resistance due to sea waves which will cause the ship
motions (pitching, rolling, heaving, yawing).
Other Resistances
• Increased Resistance in Shallow Water
- Resistance caused by shallow water effect
- Flow velocities under the hull increases in shallow water.
: Increment of frictional resistance due to the velocities
: Pressure drop, suction, increment of wetted surface area
Increases frictional resistance
- The waves created in shallow water take more energy from
the ship than they do in deep water for the same speed.
Increases wave making resistance
7.7 Basic Theory Behind Ship Modeling
• Modeling a ship - Not possible to measure the resistance of the prototype ship - The ship needs to be scaled down to test in the tank but the scaled ship (model) must behave in exactly same way as the real ship. - How to scale the prototype ship ? How to make relationships between the prototype and model data? - Geometric and Dynamic similarity must be achieved.
?
DimensionSpeedForce
prototype Model
prototype ship model ship
Basic Theory behind Ship Modeling
• Geometric Similarity - Geometric similarity exists between model and prototype if the ratios of all characteristic dimensions in model and prototype are equal. - The ratio of the ship length to the model length is typically used to define the scale factor.
Volume :
Area :
:
Factor Scale
3
33
2
22
)(ft
)(ft
)(ftS
)(ftS
(ft)L
(ft)L
λ
M
S
M
S
M
S
Length ModelM
shi scale fullS
:
p:
Basic Theory behind Ship Modeling
• Dynamic Similarity - Dynamic Similarity exists between model and prototype if the ratios of all forces in model and prototype are the same. - Total Resistance : Frictional Resistance+ Wave Making+Others
S
MSM
M
S
S
MSM
M
M
S
S
M
MM
S
SS
nMnSnMnS
nWnV
L
LVV
L
L
v
vVV
gL
V
gL
V
v
VL
v
VL
FFRR
FfCRfC
,
,
)( ),(
,
Basic Theory behind Ship Modeling
• Dynamic Similarity (cont’d)
- Both Geometric and Dynamic similarity cannot be achieved
at same time in the model test because making both Rn and
Fn the same for the model and ship is not physically possible.
)kts(16.3 ft100
ft10)kts(10
L
LVV
S
MSM
)(100
) (assume 10
100)(10
kts
vvft
ftkts
L
L
v
vVV
SM
M
S
S
MSM
Example
Ship Length=100ft, Ship Speed=10kts, Model Length=10ftModel speed to satisfy both geometric and dynamic similitude?
Basic Theory behind Ship Modeling
• Dynamic Similarity (cont’d) - Choice ? · Make Fn the same for the model. · Have Rn different Incomplete dynamic similarity - However partial dynamic similarity can be achieved by towing the model at the “corresponding speed” - Due to the partial dynamic similarity, the following relations in forces are established.
WSWM CC
VSVM CC
Basic Theory behind Ship Modeling
• Corresponding Speeds
M
M
S
SnMnS
gL
V
gL
VFF ,
- Example : Ship length = 200 ft, Model length : 10 ft Ship speed = 20 kts, Model speed towed ?
ktsktsV
LLV
L
LVV
S
MSS
S
MSM
47.4 20
120
1
/
1
(ft)L
(ft/s)V
(ft)L
(ft/s)V
M
M
S
S
1kts=1.688 ft/s
Chap 7.7 Basic Theory Behind Ship Modeling
• Modeling Summary
AWFAWVT CCKCCCCC )1(
AMWMMFMTM CCKCC )1(
)5.0*( 550
)(
)1(
2sSSTSTS
STS
ASWSSFSTS
VSCRVR
hpEHP
CCKCC
AMFMTMWM CKCCC )1(FroudeExpansion
Measured in tank
)calculatedor (given, 0
smooth) is Model( 0
)givenor Calculated .factor scale todue(
d)(calculate ,
)//V ,( S
AS
AM
MS
FSFM
MMSnMnSWMWS
C
C
KK
CC
gLVgLFFCC
1)
2)
3)
7.9 The Screw Propeller
7.9 Screw Propeller
DiameterHubBlade TipBlade Root
Pitch DistancePitch AngleFixed Pitch
Variable PitchControllable Pitch(Constant Speed)
7.9 Screw Propeller
• Variable Pitch (the standard prop):
- The pitch varies at the radial distance from the hub.
- Improves the propeller efficiency.
- Blade may be designed to be adjusted to a different
pitch setting when propeller is stopped.
• Controllable Pitch :
- The position of the blades relative to the hub can be
changed while the propeller is rotating.
- This will improve the control and ship handling.
- Expensive and difficult to design and build
Right and Left Hand Props
Right HandLeft Hand
Pressure Face
Suction Face
Leading Edge
Trailing Edge
Propeller Walk
• Due to a difference in the pressure at the top and bottom of the prop (due to boundary layer), the lower part of the prop works harder.
• This leads to a slight turning moment.
• Right hand props cause turns to port when moving ahead.
Prop Walk Solutions• Twin Screws
• Counter rotating propellers (one shaft)
• Tunnels/shrouds (nozzle)
Shrouded (nozzle) prop
7.9 Skewed Screw Propeller
Highly Skewed Propeller
DDG51
- Reduce interaction between propeller and rudder wake.- Reduce vibration and noise
Advantages
Disadvantages
- Expensive- Less efficient operating in reverse
7.9. Propeller Theory
Propeller Theory
• Speed of Advance
Q
PWake Region
SV WV
0waterV
Swater VV
• The ship drags the surrounding water so that the wake to
follow the ship with a wake speed (Vw) is generated in the stern. • The flow speed at the propeller is,
WSA VVV Speed of Advance
7.9 Propeller Theory
Propeller Efficiency
tpropeller
C
11
2DHP
THPpropeller
~70 % for well-designed prop
oA
TAV
TC 25.0
- For a given T (Thrust),Ao (Diameter ) ; CT ; Prop Eff
The larger the diameter of propeller, the better the propeller efficiency
Maximumdiscpropeller projected theofArea :A
r thrust Propelle:
tcoefficien loadingThrust :
o
T
CT
Chap 7.9.3 Propeller Cavitation
• Cavitation : Definition
- The formation and subsequent collapse of vapor bubbles
on propeller blades where pressure has fallen below the
vapor pressure of water.
- Bernoulli’s Equation can be used to predict pressure.
- Cavitation occurs on propellers (or rudders) that are
heavily loaded, or are experiencing a high thrust loading
coefficient.
1 atm=101kpa =14.7psi
Blade Tip Cavitation
Sheet Cavitation
Navy Model Propeller 5236
Flow velocities at the tip are fastest so that pressure drop occurs at the tip first.
Large and stable region of cavitation covering the suction face of propeller.
Consequences of Cavitation
1) Low propeller efficiency (Thrust reduction)
2) Propeller erosion (mechanical erosion as bubbles
collapse, up to 180 ton/in² pressure)
3) Vibration due to uneven loading
4) Cavitation noise due to impulsion by the bubble
collapse
Propeller Cavitation
Propeller Cavitation
• Preventing Cavitation
- Remove fouling, nicks and scratch.
- Increase or decrease the engine RPM smoothly to avoid
an abrupt change in thrust.
rapid change of rpm high propeller thrust but small
change in VA larger CT cavitation &
low propeller efficiency
- Keep appropriate pitch setting for controllable pitch
propeller
- For submarines, diving to deeper depths will delay or
prevent cavitation as hydrostatic pressure increases.
Propeller Cavitation
• Ventilation
- If a propeller or rudder operates too close to the water surface, surface air or exhaust gases are drawn into the propeller blade due to the localized low pressure around propeller. The prop “digs a hole” in the water.
- The load on the propeller is reduced by the mixing of air or exhaust gases into the water causing effects similar to those for cavitation.
-Ventilation often occurs in ships in a very light condition(small draft), in rough seas, or during hard turns.
Other forms of propulsion
A one horsepower cable-drawn ferry!