Numerical simulation of scale effect on ship stern flow and hydrodynamic performance

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CHINA SHIP SCIENTIFIC RESEARCH CENTER

Numerical Simulation of Scale Effect on Ship Stçrn Flow And Hydrodynamic Performance

Gao Qiuxin Zhou Liandi

CSSRC Report August 1995 English version95004

P. 0. BOX 116, WUXI, JIANGSU

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ContentS Page Abstract IntroductiOn Governing equat:ioi. Numerical method Test caSe Results Summary ReferenceS

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.lthstract,

The variations of ship stern flow, field

structure

and it.s corresponding hydrodynarnic

performance under full scaie Reynolds number(5*109)

and, model scale

Reynolds

number (5*106) are

investigated numericaily in this paper. The

governing equations for 3-D incompressible

turbulent flow which consist of Reynolds-]veraged

Navier-Stokes ( RT\NS ) equation and K-a two

equation turbulence model are solved b.y finite

difference scheme.. Detailed computational results

are.' presented graphically ... The domparisons

between present calculation ' , . existing

measurementand other calculation are made

1. Introduction '

The accurate prediction of 'ship stern flow is

of great significance not only in the design of

propeller and controlling surface , 'in the study

of. sh'ip vibratidn and noise reduction , but also

in. the understanding, of, flow phenomenon and

capturing, of' flow, structure; Traditionally, ship

stern, flow 'information at' full ' scale Reynolds

number '(up to' billions) are obtained by ship

model towing tank test and data scaling Such procedure is still in wide use in almpst all ship'

performance' research . Because of uncertainty

introduced from data scaling V shortage of

experImental database at full -scale Reynolds

number and iarge demand for research fund ,

manpower and long research circle required by

model . test , the capability Of model, test

research has been greatly -restricted . So , more

effective and reliable . universal shi:p stern

flow research method fo' different Reynolds

number (ranging from 1 million tO b1llion) must

be developed and put intj use .

With the advance of computer , hardware

technique and numerical computal:ional method , it

becomes 'very posibi.e' and hopeful to predict

ship stern flow numerically . This kind of work

has beendone by S'Ju and V. C.

atel [11 .. The

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From the point of view of the present

authors, the, key difficulty for high Reynolds

number flow calcu].,atloEi results from stability

requirement. StabiLity condition is related to

the fluid parameters time: step , mesh size .

physical quantity '( velocity )' and boundary

condition and so on. The higher Reynolds number

is , the thinner l:he corresponding boundary layer

is. That is' to. say , the change of physical

quantity in the bc.undar' layer i more dramatic

and the gradient is very large.So, in order to

resolute the fiow , very fine grid istribution nust be. used. According to the CFL stability

condition, time step must be rathr small if the

explicit scheme i adopted , which is nearly

impossible to realize. Based on the above

analysis, it is not hard to understand why so.

many flow predicting codes become divergent and can not obtain any result when they are applied to high Reynolds number cases.

Thank to the turbulent model ( which is

required to

cloe

the governing equation for

turbulent flow or more accurately which increases

the dissipation feature ) -, the flow parameter;

(effective viscosity) plays .more..impoZTtaflt role

than the, fluid molecular . viscosity. . This

effective turbuient viscosil:y reduces the

stability difficulty significantly.

Apart from. physical consideration, there are

several points which are important and mut be

noticed. The first , implicit scheme for time.

discretization i.s recommended. The second , for

convection term ,. upwinding-bias space

dicretization scheme is adviced. The third , the

wall function approach should be used as possible

And the last Ofle, attention must be paied to the

initial condition and time step mesh size

solution strategy.

In this paper , the variations of ship stern

flow field structure and its corresponding

hydrodynamic performance under full scale

Reynolds number(5*IO!I) arid model scale Reynolds

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-2-number (5*106) are investigated numerically . The governing. equations for :3-D incompressibl.e

turbulent flow which consist of RP.NS equation and

K-e two equation turbulence model are solved by

finite difference scheme [2] The stability

condition is carefully dealt with by. introducing

implIcit upwinding scheme. The execution and

running of the calculating program seem to be smooth and normal.

The calculation of HSVA stern flow for full

scale Reynolds number(5*109) and model scale

Reynpids number (5*106) is conducted in this paper.

Detailed domputatioflal results are presented

graphically . The comparisons between present.

calculation , existing measurement and other

caldulation are made . . .

Governing equation ..

The governing eqUat.ion' for 3-D Incompressible

turbulent flow which consist of RNS equation, and

K-s io' equation turbulence, model can e written

in vectOr form as follows:

V.17=0. . . .

-+VV)1

v.(rv.K)c;,.E .

7o WE V Q(F'VV) +(. ,? K2 I i

where :, / , P , K, .E denote velocity veàtor

.

pressure kinetic energy and its dissipation

rate .repectively . . ...

G, =0.5y, .(VV+VV):(VV+VV7) , is turbulent energy

generatiofl, . . . .

is turbu4ence edd viscosity .

Numerica,l method . .

In this. pape.r , the governing' equations are

first written in physical cylindrical polar

coordinate sysl:em and then transformed into

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-3-computational coordinate system . Here , only

independent variables are transformed and

dependent variables are left

jh

original physical

coordinate system . Three dimensional body-fitted

computational .mf?sh is generated by elliptic grid'

generatibh method . .Staqgered grid layout is

adopted . he coupling of velocity and pressure

are dealt with by using SIMPLEC . Unsteady

governing equations are discretised y implicit

'exponential difference scheme .. The resl4lting

algebraic equation syst:em

is solved by ADI and

TDMA

As we know ,' for high Reynolds number flow

for instance Reynolds number up.to 1 billion, the

gradient of physical quantity in inner region of

boundary layer becomes very lager , which will

result some difficulties in accurate 'resolution

of boündar layer and stability problem if we

choose to use very fine "grid d,istributon . To

overcome these obstacles ', Two-point.. wall

function approach is employed' . Attention must be

paid to

nèure the two inner grids located in

log-law region for high Reynolds nuhiber flow

The detailed .nuñeii'c is given ir' refOrence [21

4.' Test case

HS\)A tanker Is chosen as our test case for

its larger block coefficient and .. documented te.st

data . Because i.t

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very full , weak stern

separation may Occur . Maiy domputer programs

failed, to obtain convergent.' results. So ,'

robustness of, presertL. caiculation'method can be

validated.by selécLion of 'this, 'test case.

5. Results

The' calculation', was conducted on

PC LQ/33

with 2000 timeste.ps (.0.003 s I time step ) .'

Grid resolution along lc)ngitudlr)ai , radial. and

circumferential direction .' is ' 80*30*20

respectively '. Tie. calculation' results for two

Reynolds' numbers ( 5*109,5*lO(' )' are 'presented

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vector , pressure coefficient and friction.

coefficient distribution

Axial velocity iso-bar is given in figure ito

figure 8 ( on the left side is the esu1ts for

Reynolds number 5'iO' ,

on the right sideis

the

results for Reynolds. number 5*109 ,) . Axial

velocity. :reflects the ,thickness of boundary

layer . The çalcu]..ation esults indicate boundary

layer is thin around mid-ship and qradually

becomes thiok when close to ship stern . Very

remarkably, along circuPiferential directior , due

to the convergence of geometry , boundary layer

begins thickening near bilge firStly and then

about at x=0.85i' boundary layer near water line

begins thickening also. keel . boundary layer

remains thin until x =0.9 . When x is gr.eter

than 0.9 , Keel boundary layer is thickening

dramatically and this induces the generation of

bilge vortex arid . the sudden change of

hydrodynamic coefficient ( see figures 9-16 )

The boundary layer corresponding to Reynolds

number 5*109 is pretty similar but rnuch thinner

compared to that of Reynolds number 5*106 for x <

0.9 . When x > 0.9. , 'the thickness of boundary

layer becomes almost identical. which means

there is very. remarkable effect of Reynolds

number on the thickness of. boundary layer only

for x < 0.9 , total boundary layer thickness

nearly kecps iderit:icäl for two ReynOlds number

and is. determined' mainly by localS shape of

geometry ( ñon-visqous effect ) when x > 0,90

So , fOr cei'tain ship hull form ( at. least large

block coefficient ) , it can be deduced. from the

numerically predicted results that there will be

negligible effect of Reynolds number on very

after stern fow f.tel

(x >0.9

) especially in

outer region of boundary layer , but in the

inner region of I:)oundary layer , the effect of

Reynolds number for boundary layer thickness i

very c]r.

. ..

Cross stream vectors ( Figure. 9. - Figure 16 )

graphically show the formation ., develOpment and

dissipation of bilge vortices . It is found from

the comparison for different Reynolds number

prediction that CrOSS flow is dominated ii'ostly by

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significant effedt. of Reynolds nUmber on cross

flow coul.d be fOund , Of course , this conclusion

must be vërifiëd throught further investigation.

Friction coefficieht (C, ) distribution is

given in figures 17 to 22 C, is a important index for det:errnlnat-ion of separatipn point

Calcu]ation results show very strong reliance of

C,. value on Reynolds number similar to axial

velodity . V

In figures 23-24 is pressure, coefficient (C;).

distribution . Calculation resdltsV show : 1.

consistence with measurement at model scale

Reynolds number (*1O) , 2 near after stagnation

point , C,. increase rapidly , 3 corresponding to

V

change of local geometry aid. axial velocity 'V

appear two peaks at keel ; 4.: no severe effect of

Reynolds number OflCp V

V

Included

jfl

the paper. also. are the results

predicted by Ju arid Patel [ 1 ] ( figure 25

It can be .tound from comparison that the general.

agreement between present calculation and theIr

prediction is good .. However , due to the

shortage of experjmental data further

verifiOat.ion of predicte,d

rüts. must

be.

conducted . . . V V ' ' V

The variatiOns of ship stern flow field

structure and its corresponding hydrodynamic

performance under full scale Reynolds' number(5*1Q9)

and model scale Reynolds number (5*1O) ' are

investigated numerically . The comparison between

pr:esent calculation , existing measuremenL anØ

other. calculation is conducted . The results

show numerical prediction of ship stern flow is

of very bright prospect V

7. References

L S. Ju and V.. C. Patel

- _Scale _{Reynolds Numbers}

Research

V

Vol . 3.5 ,. No

101-113 : V

6

-Stern _VOW. at Full.

1' _,Journal

_{of Ship}

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2. GAO Qiu-Xin arid Zhou Lian-Di , " Stern flow

solver by using 3-D unsteady R1\NS equation "

Proceedings of 94' ICHD

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0.00 0.02

FIg. 2(o) Axiol Velocity Contour(x=O.751)

0.04 0.06 .0.08

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Fig. 2(b) AXIQI Velocity Contour(xO.75l)

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8

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Fig. 6(b) Axial Velocity Contour(xrO.95)

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rig. 8(b) Axial Velocity Contour(xrl.000) Fig. 7(b) AxIal Velocity Coñtourx=O.972

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13

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14

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,-

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-Fig22(b) Cf distributlon(xO.952) Fig.22(b) Cf distrlbution<x0.952)

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Axial Pressure distribution

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Axial Pressure distribution

15

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-diS tr;bu ton

Pr e s sure

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Cross-Stream Velocity Veclors _I- U0

I Helicily Density -20 -10 -5 0 -0.02 z -0.04 -0.06

Anal Velocity Contours

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FIg. 25 Vetoclty rield and heticity density In transverse seclions

16

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Aiol Velocity Contours

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CrossSlreOm Velocity Vectors .UO

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