TS 4001: Lecture Summary 4 - personal.its.ac.idpersonal.its.ac.id/files/material/192-suryo-adji-Resistance.pdf · 20 February 2002 Resistance 4 Froude 1877 •Ships make waves. •Waves

TS 4001: Lecture Summary 4

Resistance

20 February 2002 Resistance 2

Ship Resistance

• Very complex problem:

− Viscous effects.

− Free surface effects.

• Can only be solved by a combination of:

− Theoretical methods.

− Phenomenological methods.

− Experiments.

• Must predict resistance to select propulsion plant.


Speed-Power Trends

• EHP = (Resistance) x (Speed)

• For the horizontal axis:V in knots, L in feet.


Froude 1877

• Ships make waves.

• Waves require energy.

• Energy is spent from the ship’s propulsion plant.

• Therefore, waves = resistance.

• Test with models.

• But, that’s only half the problem – how about fluid friction?

• Unfortunately, viscous fluids were “unknown” to Froude.

• So, he tested with “waveless” models – wooden planks.


Froude’s Early Sketch


Sources of Resistance.

• Since ship resistance is such a complex problem, we have to break it down.

• To understand where it comes from, we have to understand the principal types of fluid flow.

• Look at a submerged body first, then bring in the free surface.


Fluid Flow - Submerged

• Examples of fluid flow for a submerged body (no waves):

D’Alambert’s paradox


Fluid Flow - Surface


Types of Fluid Flow

• Potential flow.

• Viscous flow.

• Wavemaking.

• Flow separation.

• Circulation/Vortex motion.

• Cavitation.

• Hydrofoil flow.

• Elastic/Compressible flow.


Potential Flow

• Ideal, non-viscous or frictionless, streamline flow.

• Unbroken streamlines whose journey is made with no friction.

• Many applications:

− Wave making.

− Bernoulli law.


Viscous Flow

• Real, frictional flow.

• Attachment of innermost fluid particles to surface of body.

• Resistance to shear offered by moving particles in adjacent layers.

• Newtonian fluids.

• No-slip boundary condition.

• Boundary layer.


Wavemaking

• Occurs at the interface of two non-mixing liquids.

• Free surface is disturbed by oscillatory movements giving rise in propagating waves.

• Energy carried away by the waves constitutes the wave making resistance.

• Not to be confused with resistance in waves.

• Gravity plays a very important role.

• Both surface and sub-surface waves.


Flow Separation

• Occurs when streamlines are prevented from following contours of body.

• Vortices (or eddies) with circulatory motion and reverse flow are formed after separation.

• Important for resistance, but also for wake and propeller induced vibration.


Circulation/Vortex Motion

• Circulatory motion of fluid about an axis, in planes perpendicular to that axis.

• Solid body may surround axis, or gas pocket may enter on it.

• Forming a core around which the coil of circulatory motion takesplace.


Cavitation

• Formation of bubbles, voids, or cavities alongside or behind a body moving in a fluid.

• Occurs when fluid pressure at a point on the body is reduced to vapor pressure of fluid.

• Will study it in more detail in the next set.


Hydrofoil Flow

• Combination of two or more flows.

• Relative motion of body and fluid develops drag and lift forces on the body at right angles to the direction of relative motion.

• Very important in special hull forms and in maneuvering and motion control (later).


Elastic Flow

• Traveling pressure – Wave phenomenon.

• Arises from elasticity of fluid.

• Formation of shock pressure waves radiating at high speeds from exciting sources.

• Shock and vibration problem.


Conclusions

• Ship resistance is caused by many different fluid flow phenomena.

• These interact and combine in complex ways.

• Theoretical methods have not yet been developed to the point where model tests are not needed.


Resistance Source Summary

• Friction:− dominant at low speeds,− function of wetted surface area, speed, and roughness.

• Wavemaking:− dominant at higher speeds,− function of hull form and speed,− part of “residual resistance”.

• Eddy/Form:− result of pressure difference,− part of “residual resistance”.

• Air/Appendage:− not always designed for,− can be significant.


Resistance Breakdown

• Different fluid flows generate different resistance components.

• This decomposition has some physical grounds and is used simply because it is convenient.

• Study the major resistance components separately.

• Then find a way to put them together.


Frictional Resistance

• Also known as viscous resistance.

• Aft acting force to set fluid within the boundary layer in motion.

• Depends on wetted surface of body, not its geometry.

• Zero for an ideal fluid.


Wavemaking Resistance

• Part of residuary resistance.

• Energy expended to produce waves is a measure of the work done by the ship on water.

• Nonzero even for an ideal fluid.

• Directly related to wavemaking by the body.

• Related to hull geometry.


Separation Resistance

• Also known as Form Drag.

• Part of residuary resistance.

• Occurs when fluid flow separates from hull, especially near the stern.

• (Residuary) = (Wavemaking) + (Separation)

• (Residuary) = (Total) - (Frictional)


Appendage Resistance

• Very difficult to predict and scale up: Vastly different scale from ship.

• Many causes:

− Eddy making resistance: Inability of water to flow in smooth streamlines around abrupt discontinuities; flow breaks clear and reverses; eddies fill in the void.

− Frictional resistance.

− Cavitation.

• Usually dealt with as a single number, either a total for all appendages, or each individual appendage.


Typical Appendage Resistance

-2-5%2-5%All single propeller ships

-8-14%8-14%Large, medium speed, 2 propellers

-10-23%12-30%Small, medium speed, 2 propellers

10-15%17-25%20-30%Small, fast, 2 propellers

-10-16%10-16%Large, fast, 4 propellers

1.61.000.7

TYPE OF SHIP LV

: i n k n o t s , i n f e e t .V L V L


Air Resistance

• Consists of both frictional and eddy-making resistances caused by relative flow of air around above water part of the ship.

• Usually not designed for, but can be a major component in certain cases.

• Depends on air density, relative wind speed, projected area of above water part of the ship, and some resistance coefficient.

• Wind tunnel tests can be used to evaluate the air resistance coefficient.


Total

(Total Resistance) =

(Frictional Resistance) +

(Residuary Resistance) +

(Appendage Resistance)(1) +

(Air Resistance)(1) +

(Correlation Allowance)(2)

(1): If available.(2): To patch things up.


Correlation Allowance

• All extrapolation methods require an adjustment to achieve correct correlation between model and ship.

• Determined by comparing full scale ship trials to previous modeltest results.

• Must be known in advance.

• Decreases with increasing ship length.


Typical Speed Profile

Ship is “climbing” its own bow wave

Typical ResistanceCharacteristics of

Displacement Vessels

Res

ista

nce

(lbs)

/ D

ispl

acem

ent (

tons

)

Wavemaking resistancedominates at high speeds

Speed/Length Ratio


Summary: Resistance Components

• Frictional− Equivalent to resistance of flat plate being towed

• Form (Eddy/Separation)− Energy lost in the formation of eddies caused by flow separation

• Wave− Energy lost in the making and breaking of waves

• Appendage− Added resistance of bilge keels, struts, shafts, rudders, and propellers

• Air− Drag associated with superstructure and hull above the waterline

• Correlation Allowance− Accounts for hull roughness and scaling differences between model and ship

(Typically runs from 0.0004 to 0.0005)


Sources of Information

• Theoretical Calculations:− Solution of the complete problem (Navier-Stokes with a free surface

at high fluid speeds) is not yet practical.

− Wavemaking can be predicted relatively well, frictional not so.

• Tests:− Full scale would be best but is of course not practical.

− Have to do model scale and then “extrapolate”.

• Preliminary:− Regression analyses of earlier ship data.

− Standard series.


The Main Problem

• How do we extrapolate from model scale to full scale.

• How to “scale up” dimensions, velocities, and forces from model to full scale ship?

• In other words, how do we go …


… from this …


… to this.


Dynamic Similarity

• Consider two geometrically similar ships.

• How do we scale their resistance properties?

• Flows must be similar.

• Resistance depends on:

− Length,

− Water density,

− Kinematic viscosity,

− Ship speed,

− Acceleration of gravity,


Dimensional Analysis

• Assume:

• For this to be dimensionally correct:

• Solving:


The Resistance Equation

• Therefore:

• Since we have geometrically similar bodies:

• Therefore, we can write:


Resistance Coefficient

• The resistance coefficient

is a function of the Reynolds number

and the Froude number


Conclusions

• The two important parameters in ship resistance are:

− The Reynolds number, which physically represents viscous effects, and

− The Froude number, which represents wavemaking.

• Two geometrically similar hull forms (geosims) will have the same wave resistance coefficient if and only if they have the same Reynolds number and Froude number.

• How do we achieve this?


Resistance Calculations

1/ 2 1/ 2

Want to find: (Re, Fn)If subscript corresponds to ship and to model we must have:( ) ( )For that we need:

(Re) (Re) or

and

(Fn) (Fn) or

R

R s R m

m s sm s

s m m

m m mm s

s s s

Cs m

C C

V LV L

V g LV g L

νν

=

= =

= =


Is this possible?

1/ 2

Pick a reasonable model/ship ratio / 1/100Then the previous requirements are:

1100 and 10

In order to satisfy both we must either:(a) perform the experiments on a

m s

m s m m

s m s s

L L

V V gV V g

νν

=

= =

space station with adjustableorbit and adjustable g, or(b) invent an exotic fluid with kinematic viscosity one thousandththat of seawater.Unfortunately, none of these options is feasible.


So which one to choose?

So we can't satisfy both both Re and Fn scaling simultaneously.Which one to choose?Call the ship/model ratio / ( 1).Then we either satisfy

s mL L λ=

This is for the same fluid for ship and model. Since ( 1), Re scaling is highly impractical.Fn scaling is all we can do.

λ


Froude’s Hypothesis

So the problem is how to get (CR)s from measurements of (CR)m assuming Fn scaling only. Strictly speaking, since CR is a function of both Re and Fn, this is not possible.

Froude’s hypothesis is:

CF is the frictional resistance coefficient and this is a function of Re only (assuming that the extra friction due to the waves generated by the ship is small).

CW is the wavemaking resistance coefficient and this is a function of Fn only.

CFORM is the form drag (separation resistance) and we assume that it is a function of hull geometry only.


Froude’s Method

Froude was able to verify this experimentally by pulling wooden planks down Thames and in his basement!


Froude’s Calculations


Total Resistance Coefficient


Frictional Resistance

• Characterized by the Reynolds number, Re.

• From 50% of the overall resistance (high speed streamlined ships) to over 85% (slow speed tankers).

• Flow is laminar for low Re and turbulent for high Re (more typical in full scale ships).


Skin Friction Lines


I.T.T.C. Friction Line


Correlation Allowance

• I.T.T.C. friction line

• Correlation allowance:


Wavemaking Resistance

• Froude’s pattern was explained by Lord Kelvin using the method of stationary phase.


Typical Ship Wave Pattern

• Calculation of wave pattern allows calculation of wave making resistance.


Typical Plots

• Typical wavemaking resistance coefficient plots exhibit multiple peaks and valleys.

• This has led to many optimization studies.


Other Components of Resistance

• Wind resistance.

• Added resistance due to waves.

• Added resistance due to turning.

• Appendage resistance.

• Effects of trim.

• Shallow water effects.

• Subsurface waves.


Operational Factors

• Displacement and Still-water Trim− Resistance sensitive to changes in displacement and trim

• Sinkage and Squat− Caused by bow and stern wave systems− Ship sinks down without trimming at low to moderate speed− Stern begins to “squat” as speed increases

• Shallow Water− Generally increased resistance in shallow water

• Sea Conditions− The heavier the seas, the higher the resistance

• High Winds− Increase ship resistance, especially if rudder is used to maintain course

• Fouling− Can significantly increase resistance if not controlled


Shallow Water Effects

• As the wave pattern changes, the wavemaking resistance also changes.


Shallow Water Effects (cont.)

• Water depth: h


Speed Reduction in Shallow Water

Contours show percent speed loss.

Ax = max cross sectional area of the hull.

h = water depth


Speed in Restricted Channels

For a rectangular channel of width b and depth h:

If a ship with cross sectional area Axand wetted girth p is in the channel:


Resistance Prediction

• If model tests are not available:

− ITTC for frictional resistance.

− Resistance standard series for wavemaking and form drag (residuary resistance).

− Pick the right standard series:

• Taylor series

• Holtrop

• Many, many others.


Standard Series

• Start with a parent hull.

• Build several models by systematically varying key hull geometric parameters.

• Test, measure, and curve fit.

Parent hull form for Taylor standard series.


Taylor Series – Typical Contours


Holtrop’s Method

• See the UM notes and software implementation on the class web notes.

• AUTOHYDRO module of AUTOSHIP implements a number of standard series.


Definition of Standard Speeds

• Maximum− Trial speed measured in calm water with maximum power output from the engines,

with a clean and freshly painted hull− Max speed declines with engine degradation, hull fouling, and sea state− Max power output from engines cannot be sustained for long periods without

suffering engine damage (redlining)• Sustained

− Speed with engines at 80% power and clean hull in calm water− Requirements usually state sustained vs. maximum speed− Can be maintained for long periods as necessary

• Cruise− Speed at which ship is expected to meet range requirement

• Most Economical− Speed and engine combination where fuel usage is least


Effect of Length on Powering

• Hull Speed (Why does a longer ship need less power to make speed?)− Speed at which the ship overtakes its bow wave and “climbs the hill”− If vship is the ship velocity in fps, cwave is the celerity of the transverse wave train in

fps, and Lw is the length of the transverse wave in feet, then:

− By equating the wave length to the ship length (LS), and converting fps to knots, we have the equation for hull speed (VS):

• Since they have higher hull speeds, longer ships have lower wave resistance at the required speed, and thus need less power than their shorter counterparts

v cgL

Lship wavew

w= = =2

2 26π

.

V L LS w S= =2 261 688

1 34..

.


Additional Reading

• 1.4.1 Ship Resistance and Propulsion Notes

• 1.4.2 Reliable Performance Prediction (D. M. MacPherson)

• 1.4.3 Practical Hydrodynamic Optimization of a Monohull(D. Hendrix et al)

Documents

TS 4001: Lecture Summary 4 - personal.its.ac.idpersonal.its.ac.id/files/material/192-suryo-adji-Resistance.pdf · 20 February 2002 Resistance 4 Froude 1877 •Ships make waves. •Waves