2014_ship resistance part 2

7/21/2019 2014_Ship Resistance Part 2

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Ship Resistance 2: ViscousResistance


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Friction Resistance and Shear Stress

Shear stresses in a fuid arise rom the relative motions between thelayers o fuid. Newton made the hypothesis that the shear

stress in a fuid is linearly depending with respect to thetime rate o shear strain.

The rate o change o shear strain o the cell is thus:

n the limit as the si!e o the cell reduces to !ero" the shear strainbecomes

and hence in the case shown:

we consider the fuidoriginally occupying thesmall rectangular volumeindicated" then the shearstrain at some later point in

time is de#ned as:


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Friction Resistance and Shear Stress

$luids which behave li%e this are called Newtonianfuids. &ost fuids inengineering applications are 'ewtonian" including water" air" oil etc.$luids which do not behave li%e this are called non-Newtonianfuids(they are relatively rare( blood is one e)ample.

* unny e)ample o a non+'ewtonian fuid is Oobleck, amixture ocornstarch and water.,oblec% is a non+'ewtonian fuid. -hen someorce is applied it reacts li%e a solid or a short moment beore it returnsto its liuid behaviour.www.sciencelearn.org.n!/Science+Stories/Strange+0iuids/Sci+&edia/Video/,oblec%

The riction resistance on a small area o the ship is simply the shear stress at the interace between the hulland the water multiplied by the area.

1ence the velocity gradient at the surace o the ship is a %ey actor in determining the rictional resistance
http://www.sciencelearn.org.nz/Science-Stories/Strange-Liquids/Sci-Media/Video/Oobleckhttp://www.sciencelearn.org.nz/Science-Stories/Strange-Liquids/Sci-Media/Video/Oobleck


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non-Newtonian fuids

* non-Newtonian fuidis a fuidwhose fow properties dier in any

way rom those o 'ewtonian fuids

viscosity 3the measure o afuid4s ability to resist gradualdeormation by shear or tensilestresses5 o non+'ewtonian

fuids is dependent on shear rateor shear rate history

in a non+'ewtonian fuid" therelation between the shearstress and the shear rate isdierent and can even be time+dependent 6 a constantcoe7cient o viscosity cannot bede#ned.


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I we test a scale model, how does resistancevary with scale ,ne means o estimating resistance o a ship is to test a scalemodel 8 but what conditions do we need to apply to the model scale

tests9

-e ideally need three %ey conditions to be satis#ed

!eometrical Similarity "inematic Similarity

#ynamic Similarity

Geometric similarity means that the model is geometricallysimilar to the ull+si!e ship. This is $relatively% straightorwardwhen we consider the model at a macro-scale3e.g." scalingprincipal dimensions5" but essentially impossi&lei we consider the

micro-scale3e.g." details o s%in roughness5. 1ence at model scalea de#ned surace roughness is typically used" and correctionsapplied later to compensate or realistic #nish. The intermediatescale 3e.g." curvature similarity5 is doable but reuires non-straightorward e'ort.

Kinematic similarity means that ratios o velocities must be


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#ynamic Similarity

Dynamic Similarity means that the ratio o the (ey orce$gravitational, viscous% o interest to the inertial orce

remains constant at di'erent scales" so that the orce o interestresults in the correct acceleration.

-e can consider how properties scale by e)amining the scale ratios$or e)ample the length scale ratio 0 0s/0m where S ship and &

model

we choose a length scale 0 " a velocity scale V " and a density

scale " then other scales are #)ed by these choices. &ore

speci#cally:

Time thought o as length/velocity scales as 0/

V.

*cceleration thought o as velocity/time scales as V2/ 0

&ass scales thought o as volume ) density or ;characteristic

length


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#ynamic Similarity or viscous fow with noree surace we assume an incompressible 'ewtonian fuid with no ree

surace" then the viscous orce can be written as

1ere Sis the wetted surace" is the dynamic viscosity" andis the velocity gradient

1ence the viscous orces scales as ) V/ 0) 02

or ) V) 0

The inertial orce scales as: x )*x +

*

ence or dynamic similarity we want the viscous orceto scale in the same manner as the inertial orce

) V) 0 ) 02) V

2

or ) 0) V


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#ynamic Similarity or viscous fuids with no ree surace$cont% ) 0) V

then

where Sreers to the ship and Mto the model.

hence

or

-here the kinematic viscosity is

3this is what we normally mean by viscosity5

1ence or >ynamic similarity 3Reynolds Number)

must remain constant.


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#imensional nalysis the /-theorem

in ?ngineering" *ppl. &aths and physics" the 0uc(ingham /-theorem is a (ey theorem or non-dimensionalisation

the theorem" due to ?. @uc%ingham 3ABAC5" puts the Dmethod odimensionsE #rst proposed by 0ord Rayleigh in his boo% The Theory ofSoundE 3AFGG5 on a solid theoretical basis" and is based on ideas o

matri) algebra and concept o the Hran%I o rectangular matrices.the result has also appeared earlier in independent publications by *.Vaschy 3AFB25 and >. Riabouchins%y 3ABAA5.

/-theorem states that i there is a physically meaningul

e1uation involving nindependent physical varia&les and kindependent physical unitsthen the original expression is e1uivalent to an e1uationinvolving a set op 2 n 3 k dimensionless parameters constructed rom the

original varia&les


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#imensional nalysis the /-theorem

J+theorem provides a method or computing sets o dimensionlessparameters rom the given variables" even i the orm o the euation isstill un%nown

the choice o dimensionless parameters is not uniue: @uc%ingham4stheorem only provides a way o generating sets o dimensionless

parameters" and will not choose the most Dphysically meaningulE

?)ample: consider a sphere moving with constant velocity Uthrough aviscous fuid o unbounded e)tent. the sphere is smooth" the onlylength scale o the problem is the sphere its diameter d. The drag orce> must be a uniue unction o the diameter d" the sphere velocity U" the fuid density and the the %inematic viscosity v, i.e."

f(D,d,U,,)=0 (1)


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#imensional nalysis the drag o a sphere

Kindependent physical variables:nL ;D


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cademic 5ear *678-79summary o :ee(-* )ecture ;onday


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)aminar and >ur&ulent Flow

n laminarfow the fuid moves in !"#n!or layers.$luid does not mi) between the layers( layers slide

over each other.

n turbulentfow the meanvelocity over aconsiderable period o time may be uniorm" but thevelocity o a given fuid particle has random =>fuctuations. n the presence o a velocity gradient"these mi) fuid between layers.

u

The photoshows laminarturbulenttransition in a

Net o in%

inNected into3clear5 water


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>ur&ulent fows

'ecessary conditions or a fow to be turbulent 3according to: 1.Tenne%es and O. 0. 0umley" First ?ourse in >ur&ulence" M$T %re&&,

ABG25

irregularity or randomness di'usivity large Reynolds num&ers @# vorticity fuctuations

dissipative continuum

tur&ulent fows are F)


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>ur&ulent fows $contBd C 7%

irregularity or randomness: this ma%es a deterministic approachto turbulence problems impossible( instead" one relies on statistical

methods.

di'usivity: rapid mi)ing and increased rates o momentum" heatand mass transer. a fow pattern loo%s random but does note)hibit spreading o velocity fuctuations through the surroundingfuid" it is surely not turbulent.

the contrails o a Det aircrat: e)cluding the turbulent regionNust behind the aircrat" the contrails have a very nearly constantdiameter or several miles. Such a fow is not turbulent" eventhough it was turbulent when it was generated.

diusivity prevents boundary+layer separation on airoils at large3but not too large5 angles o attac%" it increases heat transerrates in machinery o all %inds" it is the source o the resistanceo fow in pipelines" and it increases momentum transerbetween winds and ocean currents.


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>ur&ulent fows $contBd - *%

large Reynolds num&ers: turbulence oten originates as aninstability o laminar fows i the Reynolds number becomes too

large. The instabilities are related to the interaction o viscous termsand nonlinear inertia terms in the euations o motion.

@# vorticity fuctuations: Turbulence is rotational and =>"characteri!ed by high levels o fuctuating vorticity. $or this reason"

vorticity dynamics plays an essential role in the description oturbulent fows. The random vorticity fuctuations that characteri!eturbulence could not maintain themselves i the velocity fuctuationswere 2>" since an important vorticity+maintenance mechanism%nown as vorte) stretching is absent in 2> fow. ?.g."

cyclones in the atmosphere which determine the weather"are not turbulence themselves" even though their characteristicsmay be infuenced strongly by small+scale turbulence 3generatedsomewhere by shear or buoyancy5" which interacts with thelarge+scale fow.

random waves on the surace o oceans are not in turbulent


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>ur&ulent fows $contBd - @%

dissipative: turbulent fows are always dissipative. Viscous shearstresses perorm deormation wor% which increases the internal

energy o the fuid at the e)pense o %inetic energy o theturbulence. >ur&ulence needs a continuous supply o energyto ma(e up or these viscous losses. I no energy is supplied,tur&ulence decays rapidly.

Random motions" such as gravity waves in planetary

atmospheres and random sound waves $acoustic noise%"have insigniEcant viscous losses and" thereore" are nottur&ulent. n other words" the maNor distinction betweenrandom waves and turbulence is that waves are essentiallynondissipative 3though they oten are dispersive5" whileturbulence is essentially dissipative.

continuum: turbulence is a continuum phenomenon" governed bythe euations o fuid mechanics. ven the smallest scalesoccurring in a tur&ulent fow are ordinarily ar larger thanany molecular length scale.


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>ur&ulent fows $contBd - 8%

tur&ulent fows are fows: Turbulence is not a eature o fuids buto fuid fows. &ost o the dynamics o turbulence is the same in all

fuids" whether they are liuids or gases" i the Reynolds number othe turbulence is large enough.

since the euations o motion are nonlinear" each individual fowpattern has certain uniue characteristics that are associatedwith its initial and boundary conditions.

no general 3strong5 solution to the => 'avier+Sto%es euations isyet %nown( conseuently" no general solutions to problems inturbulent fow are available.

Since every fow is dierent" it ollows that every turbulent fow

is dierent" even though all turbulent fows have manycharacteristics in common.


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)aminar and >ur&ulent Flow

The transition between laminar and turbulentfow typically occurs when the Reynolds

Num&er is between APL

and APQ

.

,nce the Reynolds 'umber is high enough"perturbations 3caused by vibration" noiseetc.5 start to grow" generating tiny waves3Tollmein-Schlichtin waves5" which grow

and orm turbulent eddies. These waves"originally discovered by )udwig Grandtl"were urther studied by two o his ormerstudents" -alter Tollmien and 1ermannSchlichting or whom the phenomenon isnamed.

Transitional fow along a sheet withoutlongitudinal pressure gradient

Turbulent fow along a sheet without longitudinalpressure gradient. 3Visuali!ation with liuid dyetracers5.


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0oundary )ayers

The boundary layer is the region o fuidclose to a solid body in which the

transverse velocity gradients are largecompared to the longitudinal gradients"and shear stresses are signi#cant.

$luid velocity at the body surace is !ero3the no' condition5" and increasesrom !ero to the ma)imum value" whichcorresponds to the velocity which wouldoccur in the inviscid fuid fow.

The boundary layer thic%ness is typicallyde#ned as the distance to the point atwhich the speed reaches BB o theinviscid fow value.

0aminar+boundary layer thic%ness can beestimated as

while turbulent boundary+layer thic%ness

P GL ALP 22L =PP

P.PP

P.CL

P.BP

A.=L

A.FP

Turbulent

#istance from leading edge $m%

0) >hic(ness $m%

P P.A P.= P.C P.L P.Q

P.PPP

P.PP=

P.PPL

P.PPF

P.PAP

P.PA=

0aminar $low

#istance rom leading edge $m%

0) >hic(ness $m%


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0oundary )ayers

,ne assumption or the velocity in the laminar boundary layer:

*nd or the turbulent boundary layer:

-ith n typically around A/G or Rn up to about APF

P P.2L P.L P.GL A

P

P.2L

P.L

P.GL

A

uHmax

yHdelta

The local s%in riction resistance

coe7cient is related to the shearstress at the wall 8 and thus thevelocity gradient.

1ence it can be seen that thelaminar s%in riction coe7cient will

be much lower that the turbulentvalue.

1ence i laminar fow can bemaintained or longer" theresistance will be lower.

'ormall transition occurs at local


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cademic 5ear *678-79summary o :ee(-* )ecture Friday


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)aminar Su&-)ayers

?ven in ully turbulent fow there remains a very thin layer ne)t tothe wall surace" %nown as the laminar !or viscous" sub-layer#

The region between the laminar sub+layer and the turbulent layer is%nown as the buer !one.


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)aminar Su&-)ayers

in the literature 2 complementary e)pressions are proposed or thevelocity in the turbulent boundary layer:

the #nner !ro.#"!*#on u/u5=f1(u5y/) is valid in the viscous sub+layer"where u5is the so+called fr#*#on veo#*yu5=675.y(.,0)/8

the ou*er !ro.#"!*#on (U'u)/u5=f2(y/-) is valid in the main portion o the boundary layer"where the Reynolds stresses 5#9are dominant

i u#:denotes the fuctuating part o the velocity component u#:, then 5#9=;7u#:u9:8, here ;7?1, f2=' o+(y/-)>?2, a result due to randtl and vonUrmUn

a simpler velocity distribution" but one that has less empirical support and scienti#c motivation

than the logarithmic pro#le" is the A/G+power relation u/u5=3@(u5y/)^(1/@)


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S(in Friction ?oeJcient

t is possible to use an assumed velocity distribution to calculate thelocal s%in riction coe7cient" and then integrate along the length to

#nd the mean s%in riction coe7cient.

-hilst ormulae derived using this %ind o approach have beenadopted" the coe7cients have oten been adNusted to matche)periment data.

Two well+%nown and widely+usede)amples o s%in riction semi+empirical ormulae areSchoenherr $riction line

and %TT& '()* correlation

line

These give uite dierent resultsat low Rn

A.PP?VPL A.PP?VPQ A.PP?VPG A.PP?VPF A.PP?VPB

P

P.PP2=

P.PPCL

P.PPQF

P.PPB

Schoenherr

Rn

?f


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Roughness and ?orrelation llowance

The riction or correlation lines are usually written to predict the

riction coe7cient o a smooth surace. n practice real ship hulls arenot smooth due to actors such as:

structural roughness 3e.g. plate waviness" welds etc.5local damagecorrosion 3e.g. pitting5

corrosion products 3e.g." rust5paint ailures 8 poorly applied paint" stripped o paint" blisteredpaintmarine ouling3or any o the above ater they have been painted over5

Roughness is measured with apro+lometer# !seehttpwww#hull-rouhness#com"

the roughness is small enough to stay within the laminar sub+layerit has little or no eect on resistance .

Typical mean roughness height or a new ship is around APP microns8 or an old shi it can be as much as APPP microns


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The Worrelation *llowance is determined rom comparison o model andull+scale trial results.

-hen using the ormula or roughness allowance given on previousslide" The ABthTTW recommend the ormula:

-ith these ormula" the combination o roughness and correlationallowance give results which are similar to those in the previousrecommended value or Worrelation *llowance alone.



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The Roughness allowance is calculated here or a =PPm ship travelling

at AQ %nots.The Reynolds 'umber is 2.PF?B.

The #rst graph shows the absolute value o the change in rictioncoe7cient( The second graph shows the same data e)pressed as apercentage increase on the standard DsmoothE value based on the TTW

ABLG correlation line.

Sample ?alculation o Roughness llowance

2014_ship resistance part 2

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