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Wall Effect Correction for Shallow
2C 9P
Water Model Tests
ARCH1E
Synopsis
Thi paper presents a scmiempirical method of all effect correction for shallow water model tcsts and gives diagrams for the determina-tion of cccss resistance due to wall effcct. The diagrams are based on images nicthodcsperiments with the Victory model in deep and shallow waler channels. Analysis shows considerable influence of the channel sidth on model resistance.
Introducf ion
It is well known from experience that walls of the ship model tank can influence model resistance. The wall effect is especially considerable for shallow water model tests and model resistance exaggeration is greatly diIkreiit from that for deep water and the same tank width.
An explanation of the considerable wall effect plieno-menon for a shallow water channel lies in the fact that the viscous resistance of a model in that channel essentially increases and in some cases the pressure redistribution
OU a model hull may lead to boundary layer separation.
The run of a model is accompanied by rising of
wae
heights. Interaction between model waves and walls of the shallow water channel and the pressure redistribution on a model hull induced by the interaction influences
model resistance in a greater degree than for deep channel.
All this leads to the rapid increase of the resistance in
subcritical region.
For shallow water tests it is practically impossible to choose such dimensions of a model to ensure the absence of essential wall effect on model resistance. Ja. I.
Volt-kunsky has shown, for example, that for the relative
water depth hId = 3width of a tank equal to 24 breadths
of a model is patently insufficient even for smaller towing velocities to secure one per cent wall effect of model
resistance (Ref. 1). As appears from the T. Inui data
(Ref. 3), for the relative water depth
h/d = 5
and thetank width equal to 65 lengths of a model the wall effect exaggerates a wave model resistance 60 per cent in com-parison with the same water depth and unrestricted width for the critical speed v = /g/z. The results of experiments with the Arabia model according to the images method have shown considerable influence of the tank width on
model resistance in shallow water not only on high speeds
but also in the non-wave-making region (Ref. 4). M. Kirsch (Ref. 5) computed the wave resistance in shallow water and in a channel of rectangular cross section for certain mathematical ship forms. Calculations are based on L. N. Sretcnsky formulae and are in essence a con-tinuation of the calculations made by Ja. I. Voitkunsky
lab. v.
Technische Hog dl
Deilt
(Ref. 2). Froiii M. Kirsch example it f&llows that in shallow
water channel the wave ;csistancc of a model with relative dimensions b tv = 15 per cent and hid 6 is increased for
about 77 per cent in comparison with the resistance of the same model in unbounded liquid and for the Froude length nutither 037 (rrotidc depth number 0 74).
As it follows from the above there is an imperative need to eliminate the wall effect from the shallow water
model tests.
In the following, a semicmpirical method of wall effect correction for shallow water model tests is presented and diagrams for the determination of excess resistance due to vall effect are given. The diagrams are based on images method experiments with the Victory model in deep and
shallow water channels.
I'ART I
A method of sall effect correction for shallow water model tests
Using the principal idea of Gertler's approach to the-blockage correction for reanalysis of the Taylor standard
by L. S. ARTJUSHKOV
C
Cndidoteof Tech&c& Science
Associate Member
Lecturer of the Leningrad Shipbuilding Institute
Wriite, discussion on this paper is invited
Fig 1Sketch of general correlation beitteen tiodd resisticc in a channel and s/ta//ott nater
series (Ref. 6), we will get the general correlation for a
model nm ing in a shallow water channel. The main
problem is to find resistance of a model for unrestrictcd width if resistance for a shallow water channel is known.
Let (Fig I)
Rt owing resistance of a model for shallow water and unrestricted width
R'towinz resistance for a channel with the same water depth and given h;w ratio
Rrfrictional resistance of a model vmodel speed in unrestricted water v'model speed in restricted water.
In accordance with Froude hypothesis
R=Rr+Rt
Let us assume also that friction resistance increase
caused by combined shallow water and wall effect forms a
part of the residuary resistance increase.
As it appears from Fig 1 there are following relations for any constant value of the resistance R
R=-R'r+R'f=Rr+Rf
. (1)The marks (') or lack of them denote the corresponding speeds for which the quantities are determined. The mark
() is omitted.
From (1) we haveRr = K1 - (R - Kr) = Kr - 6R
(2) where= - R't.
The dimensional quantities given in equation (2) can be converted to nondirnensional, as follows
R'1 =-- c (V)2 . C'r' R1 = - i (i)2 . C
Now it can be written
(v)2 C' = (v')2 . C'r - (v')2 . thus R't =-,-- I (v')2 . Cr' Rr c (i)2 Cr C1
=
(C'1 - Cr)
and (v')2 . C1=
(v)2 . C (i")2 . Cr' orCr = ()2 . C - C'y
The formulae 4 and 5 determine the relation between residuary resistance coefficients of a model mos ing in a shallow \Vatcr with unrestricted width and in a channel with the same water depth and given h/il' ratio. Value of the residuary resistance coefficient for shallow water with
unrestricted width C can be easily determined by formulae
4, if we know the residuary resistance coefficient for a model in a channel C', which is obtained from an experi-ment, and residuary coefficient correction Cr preliminary
calculated.
R =
fi (v')2 . Cr(3)
36
10 (10 that, we have to know the relation between speeds
0' a model in a channel V and in unbounded liquid v for
given water depth.
It seems impossible at prcsci-it to get this speed relation
V/v by theoretical way. It must be derived from syste-matical model tests in shallow water channels.
As far as our knowledge goeS from the available data
the most systematical and extensive model tests in shallow
water channels with variable widths and depths are 1939
experiments by L. Landveher (Ref. 7) and 3. D. Conistock
and C. 1-f. Hancock 1942 work (Ref. 8). Unfortunately, resistance data are omitted in the latter, which hampers
to use it. Owing to this Landweber data are only used in the following analysis.
Landweber tested the Clairton model in the series of channels with varying depths and widths that formed a
total of 42 different channels with rectangular cross
sections.
All model resistance data for each water depth were presented in form of relation between towing resistance
and the relative breadth bfn' for some Froude length
-;
rig 2Resistancerelative breadth presentation of a
model data
numbers. Fig 2 gives an example of such relation for the
relative depth hId 2 '22 as the most typical. As it is
seen, the towing resistance of the model does depend upon
the relative breadth. This dependence is much stronger for higher speeds. For low speeds the relation between
resistance and bjw ratio is nearly linear.
These diagrams gave an opportunity to derive by
extrapolation the model resistance for unrestricted width (l,/w = 0) and given depth. In Fig 2 dotted lines represent the extrapolation parts of the curves.
Further, all model data were again redrawn and tions betccn modcl resistance and speed for some
rela-tive hrcadtlis received (Fig 3). By means of these diagrams
the relations v7v liac been calculated for constant values of the model resit;incc and for the given relative breadth. It was found that for a iiven relative breadth relati n V/v
is nearly constant for all values of resistance, so that a mean
value of the relation may he chosen for each bit' ratio.
40
005 040 020 225 r0
Fig 3Rcsistati cespeed presentation of a model data for relative breadths
in Tabe 1 and presented in Fig 4. For relative depth hid
= 20 and 1
5 the relations v'/v have been received byextrapolation.
-. ,
09 0.8 07 5.2 25 20 37 Table 1Speed relations v'/v for a model in different channels
Further in accordance with formula 5 the residuary coefficient corrections Cr were calculated in the form of
the friction resistance coefficient portions
in order to eliminate the scale effect and to apply correc-tions to modcs of any lengths.
The friction resistance coefficients were calculated from
the Schocnherr extrapolation line.
It was found that relation 6Cr/Cj does not depend
upon speed either, so that a mean value of the relation has been taken for each b/w iatio. Table 2 Contains the mean values of Cr/C'i found in such a way and Fig 5
gives their graphic presentation
()2 9L_1
C' v' C'
(6)
Fig 5Relative residuary coefficient corrections
C'r/C' for a model in different channels
Thus a calculatiot of the residuary resistance cocrncicnt free from wall effect comes to the determination of the
v'!v and C'C'r values from diagrams Figs 4 and 5 for given /z/d and blw ratios and to the computation of C by formula 4. The linear interpolation may be used for
intermediate values of the h,'d ratios.
\ b/v li/il 0G4 008 012 016 020
025 030
15 0968 0933 0894 0849 0795 0699 -2-0 0-976 0950 092! 0886 0843 0-780 068525
0-982 0962 0-938 0-913 0885 0-846 0796 3-0 0-986 0970 0-952 0-934 09t5 0-889 O859 3.5 0-989 0-977 0965 O'952 0.933 0-9!8 0895 4-0 0-992 0-983 0-974 0-9'4 0953 0-937 0-91650
0-9960990 0983
0976 0968 0-957 094160
0-997 0-993 o989 0983 0-977 0967 095480
0999 0-996 0994 0-989 O9S5 0-977 0965 100 09990996 o994
0-990 0987 09S0 0971 01 02 05 k,WFig 4Speed relation v'/vfor a model in different
channels
It is seen that the speed of a model in a shallow water channel is greatly dependent upon width of the channel. Thus, for cxamp!c, speed of a. model with breadth equal to a quarter of the channel width is 30 per cent less than in the case of unrestricted water and the same relative
water depth hId 1 .5
000 004 h/d 222 008 43 3.5 50
Cr
Fr Fr )
PESTP!CTED VTE
WIDTI4 Table 2
Relatk'e residuary coel11cint Corrections
Cr/C't for a
model in different channels.
Speed of a model in unrestricted water can be
deter-mined by expression
v==v': (--)
; (7)for the determination of the total resistance coefficient for unrestricted shallow water it is necessary to calculate the
Reynolds number Re = v -L/u, friction resistance
co-efficient Cr and to get corrected value of the total resistance coefficient C for speed v.
The application of the wall effect corrections to the residuary resistance coefficient C'r is evident from Fig 6.
Fig 6Application of the wall effect corrections to C't
curve
Using the method, the value of the residuary resistance coefficient in a channel C can be easily calculated if the value of Cr is known.
It is clear, that the applicability of the method and its limitation depends on experimental data used for deter-mination of the speed relation v7r. So far as the experi-ments with the Clairton model were carried out up to Froude depth numbers no more than 07, the diagrams can be only used in that speed range commonly called
ubcrjtjcaJ.
38
The method has been ipplicd to correct the resistance experiments with the Arabia model (Ref. 4). The tests Were carried out with one, two and three models in scale = I :2() by method of images in the shallow water
basin of the
Vcrsuclisaiistalt fur Binncnschiffbau atI)uisburg. The basin width was 9-78 m. that gave relative hrcadths equal to 51l, 1022, and 15 33 per cent
respec-tively. Tests with the Arabia model of the same scale were
also carried out in the model basin of the H.S.V.A. at iJaniburg that gave relative breadth equal to 13 -22 per
cent.
As an example, in Figs 7a and 7b in upper parts of the figures the results of the tests are presented in form of the residuary resistance coefficients for different test condi-tions. They 'erc calculated from original measured values of the total resistance coefficients taken from Figs 6b and 6d, Ref. 4 for water depths 5 and 3 m. respectively. As it is seen, the influence of the basin width on model resistance in shallow water is considerable not only at high speeds but also in the non-wave-making region.
The results of the model tests corrected for the wall
effect (lower parts of Figs 7a and 7b) show good agreement
for all conditions for Froude depth number up to 0-7. It
was to be expected because of the limitation of the method mentioned above.
The case of three models for water depth/i = 3 m. is an
exception. 1 I I UNCOPECTED
Petrte
water wdth 3 rrek 42Fr'7
Fig 7aAnalysisof the Arabia model tests at water
dept/i/i = SOn. . bw
\
h'd \ 004 0-os 012 0-16 0-247 0-20 0-25 0-30 0-161 0348 0-482 2-0 0034 00S1 0137 0-203 0279 0-386 0-570 25 0028 0067 0-112 0-162 0-218 0-300 0-418 3-0 0023 0054 O-0S9 0-127 0166 0-225 0-302 3.5 0018 00-11 0068 0096 0-125 0-168 0-223 4-0 0013 00300050 0072
0094 0-126 0-172 5.0 OO)S 0016 0-028 0042 0057 0-082 0-115 6-0 0005 0011 0-020 0-030 0043 0-062 0089 8-0 0003 0-007 0011 0-019 0028 0-015 0066 10-0 0-003 0007 0-011 0-018 0026 0-038 0055 Urestricte I COP PE I CT ED water th A' 3 rriL/
/ /
2rreSho .
/
'."\
.rLet I\.
J
-L
Q.iD 02 020 2 '4 Fr iIz 014 2 C22 024 Cr(CCr)()2
Lr E ST M 7 UESTPICTEJ Fr WATEq WIOTW cc3 4.0 00 23 404.0 so 2.0 4.') 0.06 UNCORRECTED Pestrtcted nater wd Ui h=30 n (lYtj.
=i2
U.g 0.10 042 044 ... 3 uiodcls ...jrnode[ (Flonibur 2 models 4 model. 046 0IFig 7bAnalysis of the Arabia model tests at water dept/i Ii = 3 0 m.
',Vall effect experiments on the Victory Models for deep
and shallow water using the method of images
Experimental investigation of the wall effect influence on a model towing resistance can be carried out by two main
methods.
The first one consists in using the special adjustable walls resting on the bottom of the tank. The walls imitate
a channel of the gi\en width. Variations of the water depths
are usually obtained by changing the water level in the
basin. This method was used by Landweber (Ref. '1),
Comstock and Hancock (Ref. 8), Voitkunsky (Refs. I
and 2) and by some other investigators.
The second method called the method of images
con-sists of joint towing of two, three and so on ruodek.
It imitates, in each case, a channel equal to an interval between the models. The method of images was used in Canada in 1935 (Ref. 9). It was subsequently apphcdhy
Netherlands Ship Model Basin for all effect invcstlg:ttu)U
for deep (Rcf. 10)_and shallow water (Ref. 4).
It is necessary to note that there is a principal difl'ereiit e between these methods. The difThrcnce lies in the coiIcep
tion of "opened" and "closed" channels.
Term "opened channel" means that false walk of thu tank which arc used for a change of the tank WI(ltll, 40'
not carried to the ends of the tank and do not preveiit ihi
020
pressure redistribution on inner and outward sides of the
walls. In this case the resistance of a model can be different
from that for the usual "closed channel".
At the same time for the images method the channel may be treated as "closed".
On the other hand the method of images is not quite accurate because of the fact that condition of adherence
is not realised at the dividing boundary between the
models.
Besides, the influence of the acceleration part of the model run on the resistance may be different for these
methods.
\ValI effect resistance experiments on the Victory models
for deep and shallow water using the method of images were carried out in the 5 5 wide and 24 deep ship model basin of the Leningrad Shipbuilding Institute. The models
were made in scale I
: cr = 1
: 65 and their principaldimensions were:
Length on waterline 2085 m.
Breadth 0291 m.
Draft
Ol34m.
Displacement
547
kg.Five paraffin mo:lcls were made in
all, so that the
relative breadth b/n for successive tests of the series of the models from one to five was as follows (Table 3).
Table 3
Test data
The 20 mm. trip wire stimulator was used located ata
distance of 85 mm. from bow perpendicular. No
correc-tions were applied for the stimulator resistance.
Before the experiments the comparative towing resist-ance tests were carried out v ith all models in deep water to determine the possible difference in resistance of the models. Fig 8 shows the results of the comparative tests.
?30ELS ! tH75C O CONTPDL 03.0 5 t' 55 C ..: 05
r
C '. sr:!'sg 8Results of the co,npara!il'e textsof oil Ire' I ieforr
iii ode/s Unrestricted CORRECTED 4 3 water width 2mode's model modeLs 1mode (nburg) p'
/
-0.7 h3.C) m -t Number of models in a series 1 234
Relatie breadth b/w,% 5.3 1O6 1592ll
264QUa 0.O8 0) 042 0.44 ciS 0.8 0.20
Fr /Ij 60 Cr ffl so 4.0 50 2.0 4°
3.0
2.0
All points practically lie on one curve. The maximum EGO
scatter is not more than ±5 gr.
In Fig 9 the residuary resistance cocflicient C of the
model I for deep vatcr is compared
vith that of the
500Victorymodel in Scale cc = 64 tested by G. Hughes in NPL
tank No. 2 (Ref. 11). Both results arc given as measured
without any corrections. It is necessary to note that plate 4c0
stimulating device used by Hughes was not sufficiently
effective for this model.
300
40
200
0.2 0.4 06 4Q 42
15., ..
Fig 10Towing resistance of the Victory model in
corresponding channels for relative dept/i
h/d=30
600 40; 300 Ouc I00 MAPKS oo 5,3 40.6 . 45,9 21.4 4)(.4 26.4h/r3
MAQKS 000St.
h/d 2,0 0.2 40.6 45.9 24.4 26.4 08 04 06 4.2 li_n .Fig IlTowing recistancc of the Victory model in
corresponding channels for relative dept/i
hld= 20
In Fig 11 these oncs are divided by arrows. Existence of
zones is bound up with the solitary wave which was
clearly observed at that depth.
42 o MoH, °55, 2.0mm trip + + + Huis, J. 64, plotes AS EASUPEO WITHOUT C0PECTIDNS t 'I55 C wire
,tl7.0
11
7<
0 0.40 0.15 020 025 FrFig 9Residuary resistance coefficient for the Victory
models
The gravity type dynamometer was used during the experiments. The models were rigidly fastened on a frame connected \vith the dynamometer and the frame with a series of the models was free for trimming and sinkage.
During the experiments the dividing boundary between the models formed by the wave system interaction of the neighbour models was clearly observed. A field behind tile models was covered with the waves, forming a cell structure with rhombic-shaped cells. The wave system of a model located between the models in the series was in
exact accordance with the wave system between the extreme
model and the basin wall.
The test results were corrected for tile air resistance of the frame. The air resistance was subtracted from total measured resistance of a series of the models and the remainder was divided by the number of the models. So that the resistance was reduced to the resistance of one model tested in a corresponding channel.
The experiments were carried out with the series of models from one to five in deep and in shallow water for
relative depth numbers hid equal to 50, 30 and 20.
The dcep water corresponds to 24 m. water depth that gives h/d ratio equal to 180.
One model was tested without frame.
All tests were carried out in a speed range up to Froude depth number 07.
Figs 10 and Ii show as an example the towing resistance
of the model in corresponding channels for the relative
depthshid equal to 30 and 20 respectively. As it is seen, there is a good analogy with Landschcr's tests (see Fig 3) with the c,sception of tile relative depth hid = 20. here there are two ZOflCS of the constant speed relation V/v.
, r
I
The same approximate niethod as used to derive
tow-in resistance R for unrestricted water, as in the case of the LandvehCr data analysis. Further, using the value of
R the eXCeSS rcsistaiiceR due to wall effect was found
in a form
LR
(8)Rc
The results are given in Figs 12, 13, 14 and 15 for deep
and shallow water. 30
As it is seen. the relative excess resistance for deep water
"oscillates" with the channel width change. It is in
accordance with
theoretical conclusion on the wave
20resistance dependence upon channel width.
For shallow water the oscillating behaviour of the curves disappeared but for all depths there are nearly horizontal parts of the curves. In this region the relative
eccss resistance almost does not increase when the
width of a channel decreases. This typical feature is steady for all depths.
040-024 so 30 20 10 42 DEEP WATER
h/ds
0.05 040 045 022 025 m , 053 w Fig 12Rcla!ive excess resistance due to nail effect fordeep iialcr
rr°10-°24
035 0.10 0.15 020 025
U/W
F'g 13Relative excess resistance due to naIl effect for
Ji/d= 50
41
Fig I 4Rcla:ive excess resistance due to wall effect for
h/d= 3O
II
I0.20 0.25 .j. 050
Fig 15Relative excess resistance due.to wall effect for
hId = 20
It is necessary to note that for rclative depth h'd
= 5 0
the values of the relative excess resistance for small
veloci-tics are slightly hihcr than for h/d = 3 0. This fact needs
subsequent explanation.
Comparison of (lie wall effect experiments with the
Landweher data analysis has shown that there is a definite
excess resisitnec. In connection ss itli this it is ads isablc
for models with Hock coelijeterit 65-0 75 to use the
diagrams of the telat is c excess resistance from Figs 12-15,
and for models with block coellicient O75-0 80 to use the method worked out in previous section.
Conclusion
Aiialvsis of the walt effect on a model resistance for shallow svatcr tests shows considerable influence of the relative channel breadth on the resistance. For example, for relative depth h'd == 20 and Froude length number 0 22, if a model breadth is equal to 20 per cent of a clian-nel width, it is possible to measure the resistance 25
times as much the resistance of the same model for
unrestricted water and the same water depth.
It
is evident that choice of a model dimension for
shallow water tests should be done with a special
careful-ness.
References
Voiikunsky, Ja. I., On the influence of chann.l depth and width on resistance. Sudostroenie, 2, 1950 (In Russian).
Voitkuriskv. Jo. I., Influence of restricted channel width on resistance. Sudostrocnie, 2 1949 (In Russian).
Inui, I., Japanese developments on the theory of wave-making and rave esistance. Sescnth International Conference on Ship
l-lydrodvnanuucs. Oslo, 19-20 August. 1954.
Manen, J. 1).. san; Lammeren, W. I'. A.. van; Model and ship trials in shallow water. International Shipbuilding Progress, Vol. 4, No. 31. March 1957.
Kirsch, NT., Shallow water and channel effects on wave resist. alice. Journal 01 Slup Research. Vol. tO. No. 3, September 19h6.
(icrtkr. M.. A reanalysis of the oriainal tcst data for the
laylor stndaiil SL'Fic'S. The David Taylor Model Basin Report No. tiO(. March 1954.
Land'cber, L.. Tests of a model in restricted channels. US Fxperiirucntal Model Basin Report No. 460. May 1939.
Comstnck. J. P., llauicock, C. ii., 1 lie effect of size of towing tank out model resistance. Trans. SNA\IE, Vol. 50, 1942. Cooibcs, L. P.. l'erring, W. G. A., I3ottle, D. W., Johnston, L.,
Wall interference and depth effcct in the R.A.E. seaplane tank and scale effect tests on hulls of thice sizes. R. and M. 1649, ARC. February 1935.
Lammeren, \V. P. A., van: Manen. J. D., san; Lap, A .J. \V., Scale effect experiments on Victory ship and models. Trans.
INA, Vol. 97, 1955.
hughes, G., Viscous and interference effects deduced from NSMB and NPL Victory model tests. Trans. INA, Vol. 9S,
1956.
42
Subsequent progress ii the wall effect correction is
bound up with the experimental work in shalT'ow water channels for critical and supercritical speed regions.
Acknow ledgenients
This investigation was carijed out as a part of research programme of the Leningrad Shipbuilding Institute and the paper is published with the approval of the Rector of the Institute.
The author wishes to acknowledge with thanks the stall of the ship model basin and especially Jr. V. I. Schetinin for great help with the test work.
The author also gratefully appreciates the warm support
he received from Professor Dr. Ja. I. Voitkunsky for the author's work. Notation Symbols R Rr R AR C Cr L b d H' /i V g a Fr F1h total resistance residuary resistance friction resistance
resistance for unrestricted width and given water depth
excess resistance due to wall effect total resistance coefficient
residuary resistance coefficient friction resistance coefficient length of a model
breadth of a model draft of a model sctted area of a model
idth of a channel depth of water velocity acceleration of gravity mass density kinematic viscosity
= Froude length number = Froude depth number
