Model test on discharge of fluid with neutral density in the boundary layer of a light ship

Report No. 3814

September 1973

LABORATORI UM VOOR

SCH EEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFI

MODEL TEST: ON DISCHARGE OF L1JID WITH NEUTRAL DENSETY IN THE BOUNDARY lAYER OF A LIGHT SHIP

by

M.C. Meijer and A Gemán

-o:

A method for the estimation of the extent of turbulence in the viscous wake of a ship is given with an eye to its mixing ¿haracteristics. This extent is defined as an area (Aw) perpendicular to the ships direction of travel, which, when multiplied with the considered distance of travel, gives the amount of water that is available to dilute the total amount of chemical to be discharged in order to reach the prescribed

maximum concentration0

The calculation shows the main elements which control 'the growth of the turbulent

extrapolation of The product of a dimensional form where the resùit by a model test.

extrapolated 'to two different ship sizes and' expressed as the nominai wake area relative to the product of beam and draught, are compared with corresponding results obtained from known full scale wake concentration measurements0

It is concluded that the model results line-up very well with the: full scalê results, which is in 'agreement with the theorem that the propeller is not a mixing device.

The effective mixing 'area keeps growing behind the ship 'until at about ₅ length distance the area ratio is about 1.2. After this

point the rate of growt'h is reduced, but at about 500 lengths distance, the area ratio has grown to be _3, after which there is no evidence that the growth stops0

Por the total dilution capability of the ship' s wake the concentration of the effluent discharged is not important..

boundary layer and hich is necessary for the

the results of model experiments to the full scale.0 goup of factors which account for the three

of the ship's hull and the, position in the wake of 'mixing has to be judged, has been established The non-dimensionalized results of the tests,

1, introduction

The basic criteria for harmless disposai into the sea of categoryB - noxious cargo residues - mentioned in Regulation _{5 of Annex II of} the'drft Convention (reference 6) are

i: a dilution of i p.p.m. (10_6) must be obtained directly behind the ship

2: in each tank the volume of the residue should be less than i. in3

or 1/3000 of the taik capacity Whichever is the greatest

in a Norwegian report (reference i) it has been concluded that the discharge should take place ìnthe turbulent boundary layer of the ship of which the extent.couid be taken to be equal to B x T

where: B = vessel' s beam

T = vessel' s' mean draught

In another report haracter and Control of Sea Pollution by. Oil") the cross sectional area is roughly estimated-at 2B x. 2T

or ₄ B T

Most authors consider the propelie as an effective mixer (Abraham et al; F.A.0. sept.

1970):.

A comment was given by Salon & Wicander, who pointed at the. reason to use the cross section of the boundary layer timé.s ship speed as a measure for the available' volume of solvent, These authors, however, advise to use the mass flow of water, passing through the ship's propiier instead, because this should be easier to handle,

The present author believes that a reasonable formula can 'be

designed on the basis of the boundary layer concept, which has the

' Symbols for ship particulars are used. as standardized by

advantage that a good basis for extrapolating results from model experiments is obtained. Also the disadvantage of measurement in the propeller slip stream with its non-stationary chaiacter is - avoided.

In this report the density of the discharged fluid is assumed to be equal to that of the receiving water.

2. Hydrodynamic principles

A body moving through a liquid meets. resistance of a frictioni

nature. The related forces occur in the fluid in a region near

the surface of the body, which region is called the "boundary layer". With low viscosity liquids like water,, high speed and large size

of the body, as. is the case' with ships, the boundary layer is characterized by large. internal forces, instability of flow, causing eddies with sideways transportation of fluid par. tides.

in this region mixing takes place.

If a secondary fluid is added to the boundary layer the mixing motion is addéd to the average longitudinal stream. This means that the boundary layer will not locally or immediately be mixed fully with the added fluid. The mechanism is analogous to the mixing of snioke from a fire in a strong wind.

The flow behind a ship's propeller viewed apart from the hull,, although subject to viscous forces in a minor sense, is

characterized mainly 'by a very stable vortex flow 'and not by turbulence. In fact the ship's propeller does not create much 'turbulence by which a good mixing process will occur. The fact

that much turbulence is found in the screw race of a single screw ship is mostly attributable to the ship's boundary layer passing through the screw disk.

Viscous effects in ship model experiments are subject to scale effect, because the frictional forces are too great relative to the inertia forces in the fluid, which results in ioo thick boundary layers in the model and too optimistic results for the possible dilution may be expected. Por that reason a theoretical approaóh is used which is based on the same principles which are used in naval architecture to calculate the frictional resistance for a model and for the ship. The formulae used in the boundary layer calculation are given in paragraph

_3.

The boundary layer thickness at the stern (aft perpendicular APP) is assumed to be proportional to that which occurs at a flat plate parallel to the stream. The formula is taken from

H. Schlichting (reference _3)' and is 'based on Prand'tl' s 1/7th power velocity distribution In relation to the frictional resistance coefficient such as it was agreed for ships at the international towing 'tank conference

1957.

To this coefficient has been added a roughness allowance according to common practice to take care of differences in the surface of modeland ship (reference

₄₎

and an allowance which is necessary for any additional resisting protubeances like bilge keels set at an angle to the stream., The pertinent formula for C is .a rough estimate. The average

width of the boundary 1ye is assumed proportional to the wetted

girth at midships. '

In order to obtain the nominal sectional area of the wake, a factor must he added to make the quantitative connection between the

calculated wake and the thaxirnum concentration of afluid mixed in it. The combination of factors is established by means of a model test.'

Theoretical estimate of wake at aft perpendicular (A.P.P.)

Boundary layer thickness: = C (Cf + ACf

+ ).L.5

-

0,075

'f (logRn

-VL - 2,

Rn

_{= cjy}

()= approx. 1.2 x 10. in /.sec)

= 0,0004= roughness allowance

bxix(TA - T)

2 bilge keel allowance

L

(B+2T)

m where A where L = length

Boundary layer width: G = C2. (B + 2T) (girth)

where C2 = constant..

= breadth

= actual draught at iiidship

Bundary layer crass_sectional area: A =

Wake sectional area for calculation: Aw= C3

x

G constant

2)2 - plate friction coefficient with

= coefficient to account for relationship between maximum concentration and average concentration

in wake; C3 will depend on distance behind ship and number of discharge ho],es.

4.

The model experiment

Table i shows 'the main particulars of the fl'Oo II lowing tank of the Shipbuilding Laboratory of the Deift University of Technology in which the mixing capacity of a ship model wake has 'been tested. Also in table i the particulars of the model

in the test condition are listed.

The shipmodel had been selected from the available stock of the laboratory, which happened to contain a model of. a coaster of nearly equal speed, dimensions and shape. as those encountered with at least one existing chemical tanker0 The condition at the test has been selected to be light, with trim over the stern, The model had 'ben fitted with bilge keels and was stiffly fixed to the towing carriage..

Two holes connected with a calibrated glas container served to d.ischarge.the measuring fluid. These holes were designed to simulate valves in the forward cofferdam of the ship. With this position most of the mixing will take place in the region with high energy dissipation0 Only thus, a reasonable dilution near the stern could be expected.

The flow rate of the, measuring fluid at discharge was measured with a common' stop-watch0

The concentration of the Rhodamin -B, ised as a tracer in the discharged fluid, was measured in the ship's wake at two fixed

positions behind the ship (0.07 L and 0.84 L aft of APP) by pumping continuously samples through a pitot-tube '('at a speed less than model speed) and through a flúorometer. Calibration was performed afterwards by pumping through in exactly the same manner, fluid of known concentration.

Before the actual measurement started, several runs have been performed to find the flow line with highes concentration below the' stern0 This crosswise position was not changed when the probe was moved, aft to the position 0.84 L aft, of APP.

Results of four runs have been recorded in table 2,

run i gives the concentration below the stern

with a model speed correspondïng with a ship's full speed.

The discharge rate was corresponding to roughly 100 m3 per hour0 In run 2 the model speed has been reduced to correspond with

7 kn. for a coaster. In this case the meter was restless and f].ow visualization' with acoloured discharge indicated insufficient development of turbulence, for which reason the result must he disregarded0

run ₃ was designed to show the influence of reduced discharge flow rate.

in run 4

the sample was taken some distance behind the stern,

Runs 1 and ₃ show that the speed of discharge has had no influence on th mixing capacity of the boundary layer.

5..

Results for full size ships

In table 3 the calculations are carried out for extrapölation of the results according to chapter 3 to ship sizes of respectIvely 25

en 100 times the model (linear scale).

The speed is scaled up according to constant Froude number, in order to represent "full speed'! in both sizes. Table 3A is addêd to

clarify each step in the calculation.

In table ₄ some useful results have been summarized. The most

important result seems to be the one showing the maximum volume of pure residue to be discharged every 100 milestraveling distance to reach 1 p.p.m. concentration. The influence of size and of

distance behind the ship is obvious0

In table ₅ the nominal wake cross sectional area Aw,, its non-dimensiona] ratio with the product of beam and draught aft and the corresponding distance, absolute and relative to the ship's length, are listed for the extrapolated. model results, together with direct full scale

measurement results taken from refernce 1 and _'5. The non-dimensional values have been plotted in:the figures 1 and 2'.

It should be noted, that the distance can be replaced by the product of ship speed and the ime after passage of the ship

z=vt

From t1is t may be calculated if the speed is known.

6. Remarks

Increase of L by 10% increases Aw and _{by 10%}

Increase of Tm(load) by 100% decreases Aw and _{by approx.15%} due to loss of bilge keel pressare resistance at zero trim angle. Increase of Tm by 100% with same trim angle increases

%7 byapprox. 30%.

One tube of suitable design, wide 0.50 m, long 2,00 m, perpendicular to the hull, may add i m2 to Aw. This may be of interest for very small ships. The propeller of the ship. should be designed to take care of the added resistance.

4.

Dilution increases with reduction of discharge flow rate,

it is therefore a tricky means of comparison. In the case of the testa dilution of 12000 (=Ct/Cw) (as in the

Norwegian ests) could have been found with the following discharge flow rate : ( L = 71.25 m, V

6.25

m/sec)

.Qw AwV

2. 6 x 6. 25

-3

3

QO=

_{Ct/Ow Ct/Ow}

-12000 -

1.35 x

10 m /sec

= 4.9 m

5., If more fundamental research is sought on the problem of

mixing in a ship's boundary layer, attention is drawn to the necessity to perform test.s with large size ship mOdels

(L

= 6

to 12 rn). Much knowledge and experience in the field of turbulent boundary layers and propeller flow is availabUe in ship model basins all over the world. As regards the mechanism of mixing within the boundary layer, advise may be sought from aero- and.thermo-.dynamicists, also metheorologists will be. excellent advisers, because in these relatively lcw-spee.d fluid-dynamics there is basically no difference between water and air.

70 Conclusions

From the figures 1 and 2 the following conclusions can be drawn

1. Tk model results line up very well with the full scale results,

which is in agreement with the theorem that the ship' s propeller is not a mixing device. With careful analysis. model tests may. be useful to study ship's boundry layer mixing problems.

-2, The effective mixing aiea keeps growing in the wake behind a

ship at a nearly constant rate, At about ₅ lengths distance the nominal wake area ratio is about 1.2 (time for a 12 knot coaster is about i minute). After this point the rate of

growth is reduced, probably due to decay of turbulence. At about 500 lengths (coaster at 12 knot, t

_{= 96}

min.) the area ratio is ₃ and, is still growing.

For the total dilution capability _{Of the ship's wake it is} not important whether or not a part of the dilution is obtained before disóharge,(Aiso in the formula proposed in reference i, page 27, the discharge flow rate Q times the

concentration i the tank means: flo _{rate of the pure product).}

When the maximum distance traveled, _{or the maximum time elapsed} after passage of the point in which the maximum concentration is prescribed, is fixed, the reciproque of _{he value AX/BTA} derived from the figures _{may be used as a córr'ect±on factor} to the formula for Cw as given in reference 1.

Acknowledgement

The tests have been performed by R. Onnink. Help was given by _the Deift Hydraulics Laboratory and the _{Physics Department of} Rjks-.-waterstaat for the fluorome-Ler

concentratjon_measurernents. The report has been prepared in collaboration with the -Royal 'Netherlands Shipowners' _Association.

(i:) Final Report on Study No. IX - Pollution caused. by the discharge of noxious liquid substances other than oil through normal operational procedure of ships engaged in bulk transport

-submitted by Norway for 1X00 - PCMP/2/7 12 Febr01973 (page 13, .7 and: Annex Iv)

Abraarn et al; "Full scale experiment.s on disposal of waste. fluidS into propel:.er stream of ship".,

FOAQO.., tech0conf. on marine pollution and its effects on living resources and. fishing

Rome, Dec

₁₉₇₀

H0 Schlichting; "Crenzschicht Theorie". G. Braun, Karlsruhe ₁₉₅₁

Comstock (ed); "Principies of Naval Architeeture"

SNAI' New York 1967

Untersuchungen, über die Vermischung von Dünnsüure mit Meerwasser im Schraubenstrahl des Ktistenmotorschiffes

"Kthe-H".

Delft Hydrauiics Laboratory, Report M 939

Draft International Convention for the Prevention of Pollution from Ships, 1973. (INCO pu.blicatio PCMP/8)

List of Symbols

QoxCt

= Nominal cross sectional wake area : Aw -

VxCw

B = beam

b = width of bilge keel

Ct = concentatiofl at discharge

Cw = concentration.ifl a paint in the wake

C.f = plate friction coefficient

C = constants or coefficients

k':

wake area ratio : k = Aw/B x TA

= length between perpendiculars

length of bilge keel

discharge flow rate or capacity Reynolds number = VL/

time after passage 'of the ship, draught aft

draught forward

actual draught at midship Bhip speed

distance aft of APP

8

boundary layer thickness aft

¿Cf = roughness allowance

A

C = allowance for pressure resistance

= kinematic viscosity coefficient

APP aft perpendicular

F'PP = forward perpendicular

V

= volume of pure residue

12. i = Rn = t = TA = Tm = V =

Table 1 : List of Particulars

Dimensions of towing tahk II

Particulars öf model no.0 ₇₇ (condition at test):

length 80 m

breadth 2.80 m

depth 1.20 m

iegth betweeÌi perpendiculars breadth

draught .foiward draught aft

length of bilge keels breadth of bilge keels

rudder present

propeller _absent

conneti.on with carriage fixed

measuring fluid . . . Rhodamin. -B in water concentration 0 = i0 kg/rn3 at d.tschage. LPP = 2,850 m B 0,472 m T = 0,022 m T = _{0., 137} rn :1 _1.24 ni = _{0,435 L} b _{0,0í1 m 0,023 B}

discharge openings nuiiber

diameter dist.ance aft of FPP distance to centre linê

: : : .: 2 0,003 m 0,310 m 0,04.1. ni 0,11 L

0,174 x

(1

Table 2 : Measurement result for model

Probe position at maximum concentration in wake submersion = 0,064 m = 0,47 TA

di.stanc,e from centre plane = 0,012 m= 0,05 x

. speed probe aft discharge concentration wake area

remarks of A.P.P. flow räte reduction rate _ratio

V L _{Q.o Cw}

K=AW

rn/sec m3/se,c BXTA

O _measured o Qo Qo

_{i 5 ,45 Qo}

xTAxVxCw/Ct

0,O647xVxCw/bt.

V x Cw/Òt

140 1

1,25

0,07

2

0,73.

0,07

3 1,25 0,07 4 1,25 0,84 10

_1,3

x 10

.0,095.

105

x 10

_Ò,151

unstable

0,3

10 _0,.4

_{x 10}

₀₀₉₃

10

0,37 x 10

0,334

o

o

V i) _1ogRi (logRn-2)2

c.

f _p C --'C -+Cf f _p. rn/sec rn 2 rn/sec m

i rndel,\= 1

i,5

285

1.ix106

02xiO6 _6.5051 20.25 _{0.0037 0 0.0012}

_O.ÓO9

_0.070

2 ship _{25 6.25 71.25}

_1.4x106

_3.18x108

8.5O4

_{42.20 0.0018 0.0004 0.0012}

0.0034 1.21 (i,i kñ)

Table Calculations (cont.d.) B±2T nl Aw 1C2C3

B x

TA A w/01 C2 03

B x TA

0.685

0,137

0.487

_0.094

0.334

A (table 2) (table 2)

©

C1CC

₂₃

CCC K-.

₁₂₃

_BxT

K-

_BxTA.w

test 1&3

test 4

A A

table .2 table 2. at at 0,0.7 aft 0,8.4L aft

0.065

0.231 312.5

0.057

0.204

>'2À

.2 100 nl

0,631

15.80.

63.10

0.0442 19.10 270 ¿.0646 40.3 646 0.474

t

0.418

QQ mb/sec Conce±itration reduction rate at 0.07L aft Cw/Ct at O.84L aft dilution at 0.07L aft ct/ow 10 (table 2)

0.3: x 10

3.1 x l0

9.3 x 10

1

0.3

at 0.84L aft discharge raté 1.3 x io

0.37 x 10

₇₇₀

₂₇₀₀

0036

0.4 x 10

2500 0. 01 08 1.9 x 10 0.53 x 10 ₅₂₅ 1880 112

0.57 x 10

1750

_33.6

2.2 x 10

0.60 x io

455

i6Ö

₃₆₀₀

0.65 x

₁₅₄₀

1080

Table ₃ Clarification

Column:

A=

linear scale factor

speed according to

= V/tfj

= constant; scale =

'R

L = length

kinematic viscosity coefficient Rn= Reynolds number =

_VL/

logR.n from math. tahis (base 10) from (iogRn - 2)2

= 2)2

Cf = plate friction coefficient = 0,075/(logRn 2)2

AC = roughness allowance from experience in naval architecture

LIC hilge.-keel resistance allowance estimated; 4bl(TA_TI)/L. (B+2T)

total viscous resistance coefficient

= plate boundary layer thickness

_{= 5 x®x}

10 B+2T _{= B+TF±TA} midship wetted girth

fiat plate wake section area Aw/C1C2C3=

(J

_x

_6J BxTA = section of inclined block at A.P.P.

= (k x Cw/Ct)À=.1 : (í conditions I and 3

same : condition 4

4)

dilut.ion= Ct/Cw= 1 :)

same :

i:

(ìDx

3600

t)

_{as if concentration distribution were homogeneous}

18.

constant derived from test=()(of table 2 condition ₁ and ₃₎ same., ((of table 2, condition

₄₎

: 63

k = relatie norninal' wake area cond. i and ₃₎ k = same = ( x (cond.

₄₎

scale factor of flow rate for constant roude number

Q,o

(gx Qo

.A=

i) flow rate of discharge for constant Froude

Lengtr L (and relative speed) _{L = 71,25 m ( V = 12,1 kn) L = 285 m (V =}

_24,3

_kil)

distance aft of A.PQP. ₅ 60 th

20m

_{240 m}

discharge rate (from test) m3/hotir 112 3396 112 3600 1080 3600

dilution Ct/Ow

nominal wake area ratio k _Aw/BxTA nominal wake area Aw m2

525 1750 0,065 2,6 1880 0,231 9,3 455

1540

0,057

36,8 1660 0,204 132

maximum volume of pure residue to be discharged = Cw. Aw. V.t. to reach i pp0m. (Ow = 10 ₎

per 100 mile (0,1852 x io6 m = Voto) 0,48 th3

1,73

_6., rn3 _{24,5 m3}

Increase of.V.for 1 p0p.m0 pei 100 mile per i added wake cross section

'

Table 5

20..

0.07

0.84

0.07

0.84

2.65

5.50

141 363

603

190,

509

470.

Test.

L.

m B rn TA

orT

rn Aw 2 m

ditanceX

rn VAW

BxT

i

Model

71.25

11.80

3.42

2.6

5

0.064

2 U

9.3

60

0,230

3

Model

V V

285

47020

V V

13.70

36.8

20

0.057

4 . .

152

240

0.204

.5. Kthe-H

56,62

11.02

3.39

25.7

150

0.69.

6

(Run.-7)

. V

40

300

1.07

7

Esso-Bergen

.68.30.

11.50

3.47

69

9650

1.72.

8 V 107

24800

268

250

41200.

_6.25

V

iò

. . . 76

13000

V

1.90

V 11 93

21150

2.33

12 V V . .

109

32200

2.73,

.

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