Resistance
Ship Resistance
Resistance and Propulsion - Lecture 2
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Resistance
Ship Resistance
•
Resistance of a ship:
– The resistance force of a ship moving at a constant speed is the force
required to tow the ship in calm water at that speed.
– If the hull is not fitted with the appendices, the resistance force is called
the bare hull resistance.
•
Effective power
– The effective power is the power required to overcome the resistance.
PE = VRT
• PE Effective power
• V Ship speed
• RT Total resistance of the ship
Resistance and Propulsion - Lecture 2
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Resistance
Dimensional Analysis
•
The resistance of a ship:
RT = f (V , L, ρ ,ν , g )
– Total Resistance
•
•
•
•
•
V Ship speed
L Ship length
ρ Fluid density
ν Fluid kinematic viscosity
g Gravity acceleration
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Resistance
Dimensional Analysis
•
Dimensional Analysis
– Total resistance coefficient
CT = CT ( Rn , Fn )
• Total resistance coefficient
(S = Wetted area)
RT
CT =
1 / 2 ρV 2 S
V2
ρ
VL
• Reynolds number Rn =
= L
V
ν
µ 2
L
• Froude number
Fn =
V
=
gL
V2
L
ρg
ρ
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Resistance
Resistance Components
•
Resistance Decomposition I:
– Frictional Resistance: Resistance component resulting from the integration
of the wall shear stresses (force tangent to the wall) on the hull surface.
– Pressure Resistance: Resistance component resulting from the integration
of the pressure distribution (force normal to the surface) on the hull
surface.
•
Notes:
– Total Resistance= Frictional Resistance + Pressure Resistance
– Resistance components depend on the Reynolds and Froude numbers.
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Resistance
Resistance Components
•
Resistance Decomposition II:
– Viscous Resistance: Resistance component associated to the energy spent
in the generation of vorticity (wake vortices, turbulence) as a consequence
of the existence of viscosity.
– Wave Resistance: Resistance component associated to the energy spent to
generate the system of gravity waves of the ship.
•
Notes:
– Total Resistance = Viscous Resistance + Wave Resistance
– Resistance components depend on the Reynolds and Froude numbers.
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Resistance
Flow past a body
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Resistance
Resistance in an Ideal Fluid
•
Submerged body (without free surface):
– Resistance Components I
• Frictional Resistance: Zero – Ideal fluid, no shear stresses.
• Pressure Resistance: Zero – d’Alembert paradox.
– Resistance Components II
• Frictional Resistance: Zero – Ideal fluid, no viscosity.
• Wave Resistance: Zero – No gravity wave system. (still water plane)
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Resistance
Resistance in an Ideal Fluid
•
Body at or close to the free surface (with free surface):
– Resistance components I
• Frictional Resistance: Zero – Ideal fluid, no shear stresses.
• Pressure Resistance: Non zero – Pressure resistance due to wave
generation.
•
– Resistance components II
• Viscous Resistance: Zero – Ideal fluid, no viscosity.
• Wave Resistance: Non zero – Pressure resistance due to wave generation.
Note:
– If there are lifting surfaces with vorticity generation, there is induced resistance
(hydrofoils).
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Resistance
Resistance in a Viscous Fluid
•
Submerged body (without free surface):
– Resistance Components I
• Frictional Resistance: Non zero – Viscous frictional resistance.
• Pressure Resistance: Non zero – Viscous pressure resistance.
– Resistance Components II
• Frictional Resistance: Non zero – Viscous frictional and pressure
resistance.
• Wave Resistance: Zero – No gravity wave system. (still water plane)
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Resistance
Resistance in a Viscous Fluid
•
Body at or close to the free surface (with free surface):
– Resistance components I
• Frictional Resistance: Non zero – Viscous frictional resistance.
• Pressure Resistance: Non zero – Viscous and wave pressure resistance.
•
– Resistance components II
• Viscous Resistance: Non zero – Viscous frictional and pressure
resistance.
• Wave Resistance: Non zero – Pressure resistance due to wave
generation.
Notes:
– If wave breaking occurs, there is wave energy transfer to the viscous
dissipation of kinetic energy.
– There is interaction between the viscous and wave resistance components
(viscous effects may affect wave making and vice-versa).
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Resistance
Resistance Components
Total Resistance
Pressure Resistance
Wave Resistance
Energy in the waves
far downstream of the
shop
Frictional Resistance
Viscous pressure
Resistance
Wave-breaking
Resistance
Viscous Resistance
(energy in the wake)
Total Resistance
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Resistance
Other Resistance Components
• Air resistance
– Resistance of the airflow around the emersed part of the ship and its
superstructures.
• Added resistance in waves
–
Additional resistance due to the interaction of the hull with
incoming waves.
• Appendage resistance
– Additional resistance due to the appendages.
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Resistance
Viscous Resistance
•
Resistance and wake:
– The resistance of a ship is originated by the flow around the hull.
– The wake flow downstrean of the ship is originated by the threedimensional flow around the hull.
•
Wake
– The hull resistance is related to the velocity of the wake flow.
– The velocity distribution in the wake depends on the hull form.
– The velocity distribution in the wake is important for the effciency of the
propulsor.
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Resistance
Viscous Resistance
Momentum Balance
Control Volume
Streamline
V
y
y=a
V
y=b
R x
u( y)
y = −b
y = −a
p∞
p∞
Streamline
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Resistance
Viscous Resistance
•
Mass conservation for incompressible flow:
a
– Volumetric flow rate
∫
b
−a
•
∫ u( y)dy
Vdy =
−b
Momentum theorem (Newton’s law)
a
– Momentum balance R =
∫
b
∫
ρV 2 dy − ρu 2 dy
−a
−b
b
– Resistance force
∫
R = ρ u (V − u ) dy
−b
– If
b
V − u = O (ε )
R = ρV
∫ (V − u)dy
−b
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Resistance
Viscous Resistance
Nominal wake
•
Velocity deficit: V − u ( y )
•
Flow rate deficit (volumetric)
b
∫ (V
− u ) dy
−b
•
Nominal wake distribution
wn =
V − u ( y)
u ( y)
= 1−
V
V
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