Theoretical
and
Experimental
Investigation
of
Resistance of High-Speed Round-Bilge Hull Forms
Prasanta IL Sahoo’, Lawrence J. Doctors*, (M), Martin R Renilson3, (AM)
ABSTRACT
Computational~uid dynamics (CFD) techniques are becoming increasingly popular in analysing jlow problems in almost all branches of engineering, especial~ in resistance prediction of sh@ where complex jluid flow exists. While towing-tank tests provide better absolute accuracy, the knowledge of the importance Qf modification to hull forms is limited. In this respect, CFD techniques and theoretical formulations have an added advantage of permitting rapid modifications to hull forms to be undertaken so that a comparative study of results can be made within a few hours.
In this paper the results of a comparative study on resistance of high-speed round-bilge hull forms using CFD techniques, theoretical analysis and experimental results are presented. This paper provides a study of the following:
● Analysis of calm-water resistance tests of a systematic series of 14 high-speed round-bilge displacement hull forms and the subsequent development of the regression equation.
● The result of modelling the same 14 models in HYDROS, a program which uses robust panel methods to calculate resistance.
● Corresponding results of the 14 models using SHIPFLOW (CFD), a sophisticated ship-resistance program developed by FLO WTECH International of Sweden, which employs a combined potential-jlow bounda@ayer viscous-jlow zonal approach.
This study includes an examination of dl~erent versions of the computer programs in order to determine the importance to transom-stern hulls of the various assumptions, such as j+eedom to rise and trim, and the nature of the fiee-suface boundary conditions.
1 ~c~mr, Depa~~t of Nava]Architecture & Ocean Engineering,AustralianMaritimeCOlh2gG@ pm secondmentto
AustralianMaritimeEngineeringCo-operativeResearchCentre,PO Box 986, Launceston,TAS 7250, Australia
2 He~, ~a~mt of Naval Architecture,The Universityof New SouthWales,Sydney,NSW 2052, Australia.
3 Head, ~a~mt of Naval Architecture& ocean Engineering,AustralianMaritime College,PO BOX986,Launceston,
1. INTRODUCTION 1.1 Background
Over a ten-year period, starting in 1979, a major research project on combatant-vessel design was conducted at the Maritime Research Institute Netherlands (MARIN). This program was initiated as an outcome of the growing belief that a significant improvement in the performance of transom stern, round-bilge monohulls could be obtained, especially with regard to their calm water resistance and seakeeping characteristics. The project was jointly sponsored by the Royal Netherlands Navy, the United States Navy, the Royal Australian Navy “ and MARIN.
Extensive testing in calm water and waves was carried out on a systematic series of high-speed displacement hull forms (HSDHF), as described by Blok and Beukelman (1984), Van Oosanen and Pieffers (1985), MARIN Report 30 (1987) and Robson (1988). The test data for 40 models were analyzed and included in a powerful computer system. However, except for the parent hull, the results of the tests and the analysis were not published.
1.2 AMECRC Systematic Series
The AMECRC systematic series is based on the HSDHF systematic series. The work on this project started in 1992, as described by Rikard-Bell (1992). The parent model is very similar to that of the HSDHF series and has the following parameters: L/B = 8,0, B/T = 4.0 and C~ = 0.396. The series transformation procedure is based on the variation of L/B, B/T and C, and range of parameters for all models are as follows:
.
I
I
I
I
Disp.(kg)I
1 8!4 I 0.396 I 6.321 8.653 I 2 I 6.512 ! 3.51 I 0.395 I 11.455 7.098 i 3 8 2.5 0.447 11.454 7.098 4 8 4 0,447 7.158 8.302 5 4 4 0,395 25.344 5.447I
6 8 I 2.5 I 0.395 I 10.123 I 7.396 7 4 2.5 I 0.396 I 40.523 4.658 ! 8 4 2.5 0.5 51.197 4.308 9 8 2.5 0.5 12,804 6.839 10 8 4 0.5 8.002 7.998 11 414] 0.5 32.006 I 5.039 12 8 I3.25 I 0.497 I 9.846 7.464 1 13 6 3.25 0.45 15.784 6.379 14 6 4 0.5 14.204 6.606Table 1: Systematic Series Parameter Range
This ‘parameter space’ or series ‘cube’ is shown in Figure 1. The parameters of each of the 14 models can be identified from this figure. All models have the same length of 1.6 m and the influence of change of the series parameters on the hull shape is illustrated in Figure 2,
where all the body plans are presented in the same scale. 1.3 Calm-Water Resistance Tests
Two independent performance prediction models, C,-Fn and R,/W-FnV, are presented, evaluated and commented on in this paper. They were developed using the ‘classic’ multiple regression analysis approach and a novel, non-linear estimation approach, which allows use of a loss function different from the least-squares one. On a similar basis, an improved wetted- surface area estimation model was developed. The results of the analysis are implemented as performance prediction software, which incorporates a prediction correction based on the performance of the ‘closest’ series model.
Lo
8.0
Figure 1: AMECRC Systematic Series [ Bojovic and Sahoo (1998), p 54Q
.,, .
9
1
~~gure 2: AMECRC Systematic Series Body Plans [ Bojovic and Sahoo (1998), p 546]
1.4 Multiple Regression Analysis
The general purpose of multiple regression is to analyse the relationship between several independent variables and a dependent variable. In general, multiple regression allows the researcher to ask (and hopefully answer) the general question ‘what is the best predictor of ?’ In the simplest case, one dependent and one ... . .
independent variable, fitting of a regression line to a number of points could be visualized in a scatter plot. In the multivariate case, when there is more than one
independent variant, the regression line cannot be
visualized in the two dimensional space, but can be
computed in the following form
Y=a+bl. X1+ b2. X2+... +bp” Xp (1) It is evident from Equation 1that a linear relationship between variables is assumed. There are virtually no limits on the form that the independent variable may take provided that no variable is directly (linearly) related to
another variable, or the sum of the other variables.
Actually, a common polynomial ‘non-linear’ regression model c;uld also ~ implemented as a linear model (i.e. X2= Xl , X3= Xl and so on...). These types of models, which include some transformation of the independent variable in a linear equation are known as non-linear in the variable (StatSoft, 1994).
1.5. Speed-Dependent Versus Speed-Independent Regression Model
Ship-resistance regression models may be broadly categorized into two groups: speed-independent and speed-dependent models. In speed-independent regression models, ship speed is not included as an independent variable, and separate regression equations must be generated at a series of discrete speeds covering the range of interest.
Fung (1995) discussed the fact that the major shortfall of speed-independent regression models is that the predicted resistance curves do not always vary properly with speed, despite the high statistical correlation, which may be achieved at any individual speed. This is because the resistance computed at one speed is not directly linked to that at another speed since the speed variable is not explicitly included in the regression.
In speed-dependent regression models ship speed is explicitly included as an independent variable, providing direct control over the nature of variation of resistance with speed. Detailed discussion of these two types of models can be found in the paper by Fung (1993).
According to McPherson (1993), the speed-independent model provides a superior analysis as it allows the different contributions of the various hull-form parameters, at different speed, to come into play. A speed-independent model was used in the analysis of the AMECRC Systematic Series results,
2. REGRESSION ANALYSIS OF CALM WATER RESULTS
2.1 Regression Mathematical Models
It was decided to use a speed-independent regression model, as it is simpler than the speed-dependent one, while equally reliable. Speed-independent regression models are usually either of CR-Fn or RRAV- FnV type. Literature study reveals that no advantage is gained by use of any of these models, although some arguments could be found that the residuary resistance, assumed to be independent of viscous effects and therefore wetted surface area, should not be non-dimensionalized using surface area, as in CR. While a clear correlation exists between CR and R~fi, and Fn and FnV, Equations (2) and (3),
(2)
(3)
r—
VI13still these two mathematical models are completely independent. On another note, care was taken to assure the accuracy of wetted surface area (WSA).
2.2. Selection Of Independent Variables
McPherson (1993) and Fung (1991), suggested as a general rule-of-thumb that the number of data points should exceed the symbolic form
Nti > NPa(NPw+3)/2 (4)
in which NPWis the number of parameters incorporated in the regression equation. This is the case for random data and the authors’ belief is that more than the suggested number of parameters could be used in the case of systematic series data. Table 2 presents the parameters considered to have a constant value for all models.
The initial regression analysis, described by Bojovic
1/3
(1995), was conducted using L/B, BiT, C~, L/T and L/V as basic independent variables. Square and reciprocal
LCB I 5.4% aft from amidshivs
c.
I 0.626Table 2: Hull parameters common for all Systematic Series models.
values of the basic variables then extended the set of independent variables. It is obvious that the L/T is de$ved from L/B and B/T. It should also be noted that L/V is a fimction of L/B, B/T ~d CB: L —= ~ 1/3
/()
L*B 3E” T c~ (5)This led to the development of the regression model which had the following form, for FnV between 0.90 and 2.25 at each speed:
1
R#t=bl+
b2UV’’3+b3--“V113 (6)
It is known (Lewis, 1988) that the performance of this type of vessel is best described by length-volume ratio. Initially, it was intended to also include in the regression model the following parameters: half angle of entrance, iE, deadrise amidships, PM, and deadrise at transom PT. While it was expected that inclusion of these parameters could only improve the regression equation, their presence in the equation was found to be impractical as their values might not be known in the initial design stages. Being highly correlated to basic series parameters L/B, B/T and C~, these parameters were considered represented by them and were left out of the independent variables’ set.
Assuming that the previous regression model, Equation 6, actually suggests that the best predictor, has the following form:
(w()
B m2.— .CT
T (7)
A couple of different independent variable sets were tried until the final set consisted of 86 variables of the form presented in Equation 7 where:
It is believed that this selection of variables provided enough freedom for regression analysis to select either separate or coupled influences of basic series parameters. The selection of mi values was such as to enable obtaining of combinations, which correspond to:
(Fa_’kw(+r
(9)This set of independent variables was used for the multiple regression analysis (MRA). The MR4 model was applied both to the CR-Fn and RRAV input values. The regression equation obtained still contained the sum of a few variables at certain Froude numbers. It was believed that this suggests the existence of an even better predictor in the form similar to Equation 7. That is why the non-linear estimation (NLE) was applied in the following fornx
(lo) The NLE method estimated the bi-coefficients by minimizing the loss tlmction which was initially set to be the same as the one built into the MRA model - the least squares finctio~ and is given by:
Loss fimction =(obsewed fiction - predicted fimction)z 2.3. Prediction Evaluation
The Royal Australian Navy (MN) was involved in HSDHF research conducted at MARIN. The outcome of this research was never published, but was implemented as software available to participants only. Naval Engineering Service of Department of Defence kindly provided performance prediction of Model 13 performance using the sotlware developed at MARIN. Actually two predictions were provided, using RINDS and REFDS modules of HOSDES sotlware. RESDS calculates the resistance of a ship based on the MARIN HSDHF series and provides the most suitable comparison for the AMECRC regression methods. REFDS calculates the resistance of a general fast displacement type of ship. Its database is much larger and is based on HSDHF series, NPL series, Series 64, Camdian HSDHF series and selected ships from the MARIN database.
Results of the comparison are presented in Figures 3 and 4. It can be seen that both prediction methods, MRA and NLE, estimate the calm-water performance of Model 13 reasonably well. Their estimates are closer to the interpolated values than HOSDES predictions. The explanation for the considerable difference between these predictions is still uncertain. Reasonably good agreement for Fn>O.40, CRestimation methods (with and without the
05 1 15
1112 25
Figure 3: RR/w-F33V for Model 13- Comparison of
Interpolated values and Prediction [ Bojovic (1996), p 18]. (las CKol 0o17 (Mm Oa
&w
OoB 003. Oon o 02 03 04 ml 06 a7 08 09 I FFigure 4: CR-Fn for Model 13- Comparison of Interpolated values and Prediction [ Bojovic (1996), p 18]
Model 13 included in the database) exhibit a fl’XO relative difference. The following regression equations for wetted surface area (WSA) were obtained from MRA and NLE methods respectively (Bojovic, 1996):
CS = 3.3283+ 0.7449(L/B ‘3 C~-z3+0.352(B/T) x J CB-mJ4.63E-02X (L/B) (B/T)JC~-l -0.0379x (L/B) x CB’ - 1.3672x(B/T) XCB-1’3 (11) CS=-$;O$9+6.669E;~~~L/B)O’35;~B/T)]”477 xCB + 1.644CB x(L/B) (12)
Respective R2 values are 0.99866 and 0.99885. The two following formulas deseribe series geometry related to the position of the initial transverse metacentre (Bojovic,
1996):
KB / T = 0.8986-0.5389 CB (13)
.
BM . C~ T / B<= 0.05567 (14)
3. SHIPFLOW THEORY
A basic overview of the features of the CFD code SHIPFLOW (SHIPFLOW Release Notes, 1997) is provided here. The method is based on a zonal approach where the flow is divided into three different zones with different solution methods, as shown in Figure 5. In Zone 1 the program uses the potential-flow method employing Rankine sources on the hull and part of the free surface where either a f~st-order or second-order discretization is implemented. In the potential flow method the SHIPFLOW code can be run in both linear and non-linear mode.
In Zone 2 the boundary layer is computed using a momentum-integral method similar to the one developed by Larsson (1975). It is based on streamlines, which are automatically traced from the potential-flow solution. Starting at the stagnation point the method fwst computes the laminar flow and checks the stability of the wave-like disturbances in the layer. The program computes the ratio of the amplitude at any point downstream of the point to the amplitude at the point itself. The transition is assumed to occur when the amplitude ratio has reached a certain value of the most unstable frequency amplitude, or a value set by the user.
In Zone 3 the governing equations are the Reynolds-Averaged Navier-Stokes (MNS) equations, obtained by averaging the time dependent Navier-Stokes equations over the entire length and time scales of the turbulent fluctuations. In the present version of SHIPFLOW used, the diffision of momentum longitudinally is neglected and by this the velocity and turbulence are parabolized meaning the solution may proceed from the inlet station, plane by plane downstream. The RANS method has not been used in the present paper since this procedure is used only for slow speed hulls where there is a thick boundary layer (wake region) at the stem.
4. HYDROS THEORY
The computer program used for this research is HYDROS/4, an extensive set of modules developed at The University of New South Wales over the last decade.
=0
4#mAnwtm18mmtwMKa#&Q3
L /
Figure 5: The Zonal approach in SHIPFLOW [ SHIPFLOW 2.3 (1997), figure 1].
The capabilities of HYDROS cover four main areas of Hydrostatics, Statical Stability, Resistance in cahn-water and Performance in Waves. Some sophisticated characteristics of HYDROS are:
● Its ability to handle complicated hullforms, which possess typical naval architecture geometric details, such as chines and transom sterns, as well as sections, which might or not pierce the water surface. In this way, monohulls, catamarans, multihulls, and small-waterplane-area twin-hull (SWATH) vessels can be analyzed.
● The fact that the geometry of the vessel has to be defined only once; thereafter, hydrodynamic computations for different combinations of displacement, draft, and trim can be effected by altering only one or two items of input data (draft and trim). HYDROS automatically re-generates the required underwater geometry for the analysis. . It is highly modularized in nature, in which the
components of I-IYDROS communicate with each other through the file system. This permits the user to combine tlmctions in a large number of ways. For example, one original vessel can be analyzed in a regular wave system in different conditions. The resulting response-amplitude operators from one such condition can be used repeatedly to determine the statistics of operating the vessel in different seaways. The computer program was described fully by Doctors (1995) and Doctors and Day (1997). The resistance module applies traditional thin-ship theory to the vessel, together with the standard modifications for water of finite depth and channel of ftite width (for the purpose of simulating towing-tank tests). Furthermore, the hollow in the water behind the transom stem of the vessel is modelled in a realistic and plausible manner. Finally, a novel technique for applying correction or form factors to both the wave-resistance and the fiictional-resistance components is used.
The application of these correction factors was detailed by Doctors(1998a). Finally, there is an additional improvement in Doctors ( 1998b), in which the case of a partially wetted transom stem is modelled; that is, the hollow can be partly filled with slowly re-circulating water, thus simulating the case of operation at relatively low speeds.
5. RESULTS
In order to maintain uniformity and the make the best of comparison between the various methods adopted here it was decided to present the results of this investigation in the form of RT/W against Fn in model scale. The experimental drag as measured at various speeds were divided by the weight of the model to obtain the experimental RT/W for all 14 models tested. The models were free to trim and sink in all cases. As illustrated in the regression model, CR corrected values were fwst obtained which were added to the corresponding CF (1’I”fC-57 ship-model correlation line) to obtain a set of values for CT at various Fn. The CT values were then converted to corresponding RT/W values.
In the CFD approach used by SHIPFLOW, it must be remembered that it is only a tool to analyze different types of hull forms so as to obtain a hull form with the best wave-resistance characteristics. Potential-flow panel methods like the method included in SHIPFLOW cannot handle wave breaking and spray phenomena that occurs at high Froude numbers. This means that the wave resistance CW$flcomputed by SHIPFLOW, will be smaller than the residuary resistance from experiments, CRexP. The computed results should therefore compare with a wave-pattern resistance flom experiments. Some of the wave energy from wave breaking and spray is however captured in the computations and the computed wave resistance lies between the residuary resistance and the wave-pattern resistance. The only way to directly compute the total resistance from SHIPFLOW results is:
CT,,fl=Cw,,fl+CF,,fl (15)
where CF,,fl is the friction component computed by XBOUND module of SHIPFLOW. The CT,,flvalue is of interest when comparing different design alternatives of a hull or when comparing different positions of the hulls in a multi-hull configuration. In many cases it is enough to study the variation of CW,SOonly. But, since the wave resistance is under-estimated as described above, CT,~fl cannot directly be used for power prediction. It is therefore necessary to make a correction for the difference between CW,,fland CK,W
In the work of Sirvio and Oma (1997) a constant value (C%.XP- Cw,,fl) for the correction was used and this
is probably appropriate for the catamaran hull if the investigations are in the lower ranges of speed. The friction component was therefore computed using the ITTC-57 line and the total resistance computed fiorn CT= CF,lmc57+ Cw,,fl+ (CR,,W - CW,M) (16) Another approach, as suggested by Janson (1998), is to compute a wave-resistance correction factor as :
KW = CR,,XP/ Cw,,fl (17)
from cases where both experimental and computational data are available. The total resistance is then computed fkom:
CT,~== Cw,,flx ~ + CF,,fl (18)
The ~ factor must be estimated from earlier comparisons of CR,,XPand CW,,fl.h varies with Fn ~d may be large at high Fn where wave breaking and spray is a large part of the resistance. G will also vary from one hull to another depending on how much wave breaking and spray is generated. At lower speeds where the transom is not completely dry Cw,,fl will be larger than CR,,~ since the computdions assume that the tiansom is dry. If this is not the case there will be too large a hydrostatic contribution to the wave resistance in CW,,fl.A too steep transom wave will also be computed at low speeds if the transom is not dry.
CT,,fl = Cw,,fl+ CF,,fl (19)
Janson (1998) also commented on the computation of wave resistance for tankers and other ships which operate at low Froude numbers. The wave resistance is a small part of the total resistance at very low Froude number and it is often difficult to compute this small wave resistance value accurately. The computed results can, however, still be used to compare different design alternatives from a wave resistance point of view. The wave-pattern must then be used to investigate the diverging wave system and to determine which design alternative performs best.
In HYDROS all 14 models were subjected to exactly the same simulations as the experiments. As explained earlier a correction factor ~, obtained in Equation 17, was used to calculate the total resistance coei%cients which was transformed to RT/W values in order to compare SHIPFLOW results with other methods. This procedure naturally gives perfect agreement with experimental results for all Froude numbers. To provide a more realistic evaluation of results it was decided to use the form factor of Granville (McPherson, 1993) given by:
(1
2l+k=l+18.7x CBX; (20)
This results in the modified expression for calculating the total resistance coefficient for SHIPFLOW as:
CT,M= cw,,fl + (l+k)CF,,fl (21) o EqmTuim.. Q18 -.,-~~ ....aisbwmffl a —mm,v r-” am ,/ ?, . . f on # ,.,” alz
$
Qm am Q@ 00$ cm? am, am ml WI am 0S3 am Qm am tm tm FL!Figure 6: RTiW vs. Fn results for Model 1.
am 0 ewhwim I I I I I I 1 —HJhwmw am I I I I I I ,,, 0 ,,.“0 ,. an , /. ( , .. .,.. atz . . . . . ,... ..~./ ....! ,.. &
I
...
..
...-
....
am ...” .... j#’- /.J”-. /.J”-. am I I I I I I I I J am am W Q= am amaelam l.m 1* RIFigure 7: RT/W vs. Fn results for Model 2. The Figures 6 to 19 depict the graphical overview of experimental, theoretical, regression and numerical (as per Equation 21) results for all 14 models.
Table 3 presents the root mean square errors of RTAV with respect to experiment for all Fn values between 0.3 and 1.0 in increments of 0.05. As can be seen from the above table, SHIPFLOW consistently under-predicts when compared with regression or HYDROS. It
is to be noted here that regression analysis for Model 7 and 8 have not been carried out beyond Fn=O.55 and 0.5 respectively, hence the high RMS errors when compared with HYDROS. am -0 ~~ as ---mm n . . . . ..aiJLvlRwi at+ . —H@waw .P’” ( $.” au .0.”’ ,,. c-*” .. ...”’ .P”; . ..-” ‘“ $ ‘“ A. .. ... .. .& . .. ...’” ‘ on .. .. .“ . ... .. Om-am m? ?---0 am am n= O.a m ‘Fn am am - ‘m ““
Figure 8: R@ vs. Fn results for Model 3. m 0 mm am -..--~ . ...-.ml?w —I+rhlaw O* ./ ,d’ an V ,.,,.’ i’ “’ alz ,ti .,““” / / .“”’ i?am ..,.r ....’” 2 / ,,..’””” ,/. ... am 7 ,.. P“’,. ..”” . . . Ool ,... am , r #’~”: 0(2 . 0 am m 032 aa ml m Fn ‘m ‘m am 10) lW
Figure 9: RT/W vs. Fn results for Model 4. Actual variations of RT/W in percentage for various methods have been presented in Figures 20 to 23 while varying L/B ratio and slenderness ratio (L/V1n).
It is evident Mm the results of all 14 models that SHIPFLOW has consistently under-predicted the experimental results at higher Fn values and this may be partly attributed to the empirical formula used for the determination of form factor (l+k). From Figures 6 to 19 it is quite clear that predicted values for HYDROS lie closer to experimental values than SHIPFLOW. The same
w . ~~ -..-~~ e au – . . . . ..~mw an – —1.@mmhv ,’
4
P“ .. . @n / / w’ / “.. ./’ ... an - .. ....” =’47-” $ am ,. .-. .. ... . & D“ ,... t’” ,...’”” am # . ..-. ”-,/’” ... m ...-” /“ /...” .“:..” Ml+---
...-Md 1 1 I I I I Wma ana ‘Fnm’’’’w’m’”Figure 10: RT/W vs. Fn results for Model 5.
Oawna amom amomomlm I.*
Fn
Figure 11: RT/W vs. Fn results for Model 6. trend can be recognized from the computed RMS errors presented in Table 3. Figures 20 and 21 depict RT/W errors as a percentage against L/B ratios at Fn=O.30 and Fn=O.50 respectively. At Fn=O.30 both SHIPFLOW and HYDROS exhibit under-prediction by about 5% at higher L/13 ratio, when compared with experimental values. At Fn=O.50 these values increase to about 17% below experimental values at higher L/El ratio.
Figures 22 and 23 present errors in RT/W as a percentage against slenderness ratio (L/Vl’3) at Fn=O.55 and Fn=O.80 respectively. It is interesting to note that regression and numerical calculations show some form of instability at lower values of L/V “3, However the trend appear to be similar for all methods once the slenderness ratio increases beyond 6.5. Here too SHIPFLOW
under-predicts experimental values by at least 17-18% as O.* ,, ;lendemess ;atio increases, whereas in case of HYDROS
it is within 10Yo.Some of the important observations that can be made from this study are:
CFD analysis as an i&portant and powerful tool in the hands of an experienced designer, can provide fmitful guidelines as to the merits of alternative designs based on wave resistance.
The stage has been reached where CFD analysis can stand on its own while evaluating various design configurations. On this aspect it is the most cost-effective solution when compared with traditional tank testing, which could be costly and time consuming.
Although numerical analysis is mature enough it is still not at a stage where traditional tank testing can be entirely ignored or replaced.
Osl Qmm o -..--~ 02! ...-.wmw —W.=xw 0 a!a ~ as , s ....-”” .w’-f ...-an . . . & ,. ...““... /?{ ....-”” am . . . . . ,.. . . . ...-””” .... . am r.1,,.,’ ,.$ ...;..’ M3 ... ...,..Y’.D” ..-0 aw, mom w) m am ammos W tm Fn
Figure 12: R# vs. Fn results for Model 7. ml
“QmaILIcamcL40 o.m am am man mi.m
Fn
Figure 13: RT/W vs. Fn results for Model 8.
0 WRrw an -..-~~ -.-...m~ffl 0 —mm’w au 0,. 0./ . . . :, . au a . . . 9 y“ .“”” 9,. ....” &lo .../ . ...’ ~ 9 -,.- ..-...’ ,.~ ,.. . . ..0 . . ...” .,9.” ‘ . ..-” ..0 . ...”-(W . .. .. ,.*’ “...” ../ ....’ .!.. a.- ‘ f .t~ O.fa #--0 ml. am m?aomm amFn a“ m m ‘m l.m
Figure 14: RT/W vs. Fn results for Model 9. am-Q ~~ 0 -..-~~ am .,..--m~m ,$.’ —l+@t8Fuw au *’”Y< 0,,,” / ,,..’” Qi2 . . ..’ . ...’” D’” “,””’”’ Ow ./ /“’ a w. .,. Ii ~m # . ..” ./ , . ..’” ..-. . . “’-..,” ,Y ..’” am . . . . . . .. . . ,.7’:: ‘“ Ow ~~ P’” #-002 ?--0 Om . Oao.m aa am m Ice tm Fn ‘m a“ m
Figure 15: RT/W vs. Fn results for Model 10. Model Regression SHIPFLOW HYDROS
1 0.00065 0.01474 0.00307 2 0.00646 0.01763 0.00308 3 0.00166 0.01707 0.00929 4 0.00054 0.01417 0.00656 5 0.00180 0.03085 0.00920 6 0.00165 0.01861 0.00412 7 0.12941 0.04467 0.01397 8 0.08907 0.08921 0.04518 9 0.00529 0.01440 0.00659 10 0!00157 0.01389 0.00668 11 0.06192 0.02758 0.00927 12 0.00293 0.01664 0.00822 13 0.00048 0.01734 0.00279 14 0.00119 0.01836 0.00449
Table 3: RMS Errors in RT/W with respect to Experiment.
an ---~ ...9mamw —*RW 0 am ,--/. 0 .+ an ... ,. .u.-.. . ..,’” >.-..P ..-’ k’. ..- . . . . . .. ::: . . . ....” ... . .. .. am
J{
,,.
...
-” ..J ...-QC3 A. .. .,,/”<
Om .,”””‘i am ... p-0 ambVaan aa m am am WI w I.m I.m
l%
Figure 16: R# vs. Fn results for Model 11.
—Hfk+urm 0.!4 .,,’ ..-?.,. .,.. / ,.. au ... .... .. am, /?> ..-””” d’~m 1:..... .,....-/... F
+“”
,,. /..
.“ Ma / ,.g.?~““”-”””
am /. ,,ff am b--- I I I I I I m am am as am am am MU *OI flo mFigure 17: R~/W vs. Fn results for Model 12.
am e -~ -.-~~ am .-..-SP=M 0 —Wmw an— ,,, a12 -.4’” ,...” -m-’ ,,.. ,.. . .. .. .. “ ~ ‘m x . .. .. .’ ,... ,. .-. am R ‘ ...-’ W W F 0 am 02 w am WI amamamasoua tw RI
Figure 18: RT/W vs. Fn results for Model 13.
m m aa am am am am m I:m t.ia
Fn
Figure 19: RT/W vs. Fn results for Model 14.
-., ,.,, s =
‘“’.
‘“4 I I A ‘.\ ‘..., .a *. “..., ‘. .,, [; ~. %.. . . . . ... . .,. . . . . - ..:...5. 5 -.-...-- --- .-7---. .7--- 4 4 5 6 m 7 8Figure 20: RT/W Error (?40)vs. L/Bat Fn=O.30. 6. -a-watie# .+sihwdI*E# ,,*..l$dmlxwlE# --- -WPWQLLS -- .... d ... “%...-,., s ‘.-, ... ... ... ,.,... ... d 4 j .-$ .!5 ---4---”” --- /---a #... ..- ---- --y----. a #---‘ --- #----t 4 5 6m 7 8
! +O!m-’t -*--ax .,, I ..*..* -.. * m t. i I 4 9 6 7 8 9 Sknd- Rstio
Figure 22: R~/W Error (%) vs. L/VIn at Fn=O.55.
i,, ,--.%-..-..., -.-... ., ~.,.?” %. w
I
g=
:
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,1 , .. I I 1 ! ..J I Slenderness SattoFigure 23: R~/W Error (%) vs. L/VIn at Fn=O.80. 6. ACKNOWLEDGEMENTS
The contributions of all industry participants, in supplying the models, conducting the tests and providing valuable guidelines throughout the project are gratefully acknowledged. The authors would also like to extend special thanks to Mr. Predrag Bojovic for the development of the regression equation. The authors are also indebted to Mr. Arninur Rashid for his invaluable help in SHIPFLOW data analysis. We are grateful to Dr. Carl-Erik Janson of FLOWTECH International AB for guiding us through the complexities of SHIPFLOW during the preparation of this paper. Last but not least, the authors would like to thank Australian Maritime College for fmcial support for this research work. In addition the authors would like to express their gratitude to the authorities at the University of New South Wales.
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