Added resistance due to waves, a comparison of model experiments and computer models

DI NORSKE

V RITAS

TECHNICAL NOTE

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-Ship Model Basin

Added resistance due to waves for a 80 000 tdw tanker as estimated by computer models based on the theory presented by Gerritsma/Beukelman/2/ and Faltinsen et al./3/ has been compared to model data.

Reasonable agreement was found in the low frequency region. For a wave-length about equal to the ship length substantial differences between theories as well as experiments were noted. Agreement between model experiments and the

Gerritsma/Beukelman theory and the Faltinsen asymptotic theory was obtained in the near high frequency region. The importance of making the mathematical-model_in. .

accordance with the theoretical assumptions is demon-strated.

Note no.: Divisect.no.-year-no. Date:

FDIV/54-19-81 Nov4, 3rd 1981

Title:

ADDED RESISTANCE DUE TO WAVES, A COMPARISON. OF MODEL EXPERIMENTS AND COMPUTER MODELS

Written by:

List OF

oNtms

page Introduction 3 Results Conclusion . . . . 6 List of reference. 0 Figures - 9

INTRODUCTION

Fuel cost has increased considerably over the last decade, and has created a growing consern for ship resistance characteristics. One such resistance contributor, the Added resistance due to waves, has been shown, in reference

/14

to only cause a minor slowdown for ships operating in a trade between Europe and the Persian Gulf. Hence it seems natural that research resources should by consen-trated in areas where the potential economic and safety gains give a larger pay-off on the invested capital.

This has also been the conclusion of the SBT (Segregated

Ballast Tanker) working group within the. Research.

The originally high priority research on this matter has* been scaled down. However, an already initiated work on added resistance in waves was to be concluded.

Model experiments on added resistance in waves carried out at NSMB on a 80 000 tdw tanker in light ballast condition was to be compared to theoretical models. The two most

relevant theories were that developed by Gerritsma and

Beukelman /2/ -and more recently that developed by Faltinsen et al. 13/.

The Gerritsms/Beukelman method is based on an energy con-sideration, but according to Faltinsen et al. /3/ the rational basis for this method is not quite clear. How-ever the theory is well known, and widely used.

The Faltinsen et al. /3/ method intergrates the 2nd order mean pressure forces to obtain the added resistance due to waves. Since this method already is described in quite some detail in ref. /3/, those interested may consult this reference.

-

4

-In the following we will limit our discussion to the out-come of the comparison between the model experiment and that of the theoretical computations.

RESULTS

The outcome of the comparison is shown in Fig. 1. Both theories seem to agree well in the low frequency region,

but for frequencies where _{we11-77; >} substantial

difference is noticed.

The model experiments indicates a somewhat larger resist-ance than that of the theoretical predictions, in particular for the region where

3 < Z7-4- <4

However, in model experiments one is only able to measure the added thrust which will include the added resistance due to waves, on the hull, and the changes in propeller efficiency due to changes in the wakefield caused by the presence of waves and ship motions.

The relative magnitude of these two effects are uncertain, but the propeller efficiency is believed to be most

in-fluenced when the wave-length is of the order of the ship length, e.g. in this case

3 < 11/7/

<4

which is in the same region where theory and measurements diverge the most.

For co > 4, the model experiments compare fairly well

with the Gerritsma/Beukelman theory. In this region the Faltinsen et al. theory drops off cons/derab/y, and seem to fail to predict the added resistance. For this high fre-quency region the pressure field over the wetted surface is believed to be poorly represented by two dimensional theories, at least not for such blunt bodies as for a ship

with CB = 0.8.

It should be noted that the asymptotic solution given by Faltinsen et al. for the high frequency region,

_weAdg>

6,

seem to compare well with the model experiments.

In Fig. 1 a curve marked Faltinsen et al., model -Fig. 2, is shown. The difference between the Fig. 3 and Fig. - model lies in the hull modelling 'technique.

For the Fig. 2-model, the bow and stern regions, contributincT the most to the added resistance, was divided into a number of equally spaced strips, see Fig. 2. The hull lines are exactly reproduced in the mid section of each strip. The added resistance is estimated from the pressure component in the longitudinal direction acting on the projected area. The projected area is estimated, based on two consecutively defined hull sections. (See Fig. 2).

By the hull definition shown in Fig. 2, the projected area is seriously underestimated, resulting in an equivalent underestimation of the added resistance.

By changing the hull definition to that shown in Fig. 3, the projected area resembles more closely with the true area.

The difference in the computed added resistance by the same method, but based on the before mentioned area re-presentations, can be clearly seen in Fig. I (difference between curve 1 and 2).

Based onour investigations, we have found. that the hull must be defined by strips, where the first and last Strip is placed such that their beam is less than 0.03 times that of the ship beam, e.g.

b/2 ç 0.03 B/2

CONCLUSION

A comparison between model experiments and two different theories for predicting added resistance due to waves for

a C = 0.8, 80 000 tdw tanker show some unusual results as seen in light of previous work done by Faltinsen /3/.

The most destinct difference between the theoretical models is noted in the high frequency region. The difference be-tween the Gerritsma/Beukelman and the Faltinsen method for this example is larger than that previously noted /3/. On the other side in ref. /3/ for ships with large block

coefficients at high frequencies of encounter, both theories diverged substantially from that of model experiments. In

this study, the Gerritsma/Beukelman theory compares fairly well with model data in this region as opposed to the

The validity of the Faltinsen et al. method may be questi-oned in the high frequency region for large block coeffi-cients ships. Three dimensional effects must possibly be accounted for. However, the asymptote developed by

Faltinsen et al. for this region seem to give a more accurate description of the phenomenon.

The importance of a correct mathematical modelling (hull definition) in accordance with the principles utilized in the theory, has been demonstrated. The Faltinsen model is in particular sensitive to the strip definition and when modelling a hull.

This study has not been able to answer any questions with respect to a proper mathematical description of the pheno-menon of added resistance due to waves. However, a need for further comparison between theories and model data is clear, and such work should be encouraged. Further refine-ment of the theoretical models seem to be in need as well.

LIST Of REFERENCE

/1/ LindeMarui,

/2/ Gerritsma,

/3/ Faltinten,

K and Robertston,-St "Am analysis Of the weather slow-down of

a

SIT-tanker in -ballast with special emphasis on.

added resistance".

Pet norSke Veritas Report NO 800641,

September '1980.

J and Beukelman, WI ."Analysis of the:

Resistance Increase in waves of

a

Fast Cargo Ship"...

. Appendix 5 of Report, Seakeeping

Ciminittee, Proc 13th ITTC, Vol 2

(1972)-p. 902, Vol 19 NO 217

.(SepteMber.1972) p. 285.

Liapis1d4;-itnd-SkjOrdal, S.: "Prediction of Resistance and

Pro-pulsion of a Ship in a Seaway". 13th Symp. on Naval Hydrodynamics, October 1980, Tokyo.

8 7 4

2

Added resistance due to waves Faltinsen et al. theory

( model fig.2)

ii

( model f ig.3)

31 Genitsma/Beukelman theory 41'Model experiments, NSMB( Response

trust)

5) Asymp tote ( Fat tinsen )

L = 232m B= 39m C B°8035 Fn= 0,1294 3 ). ₁₀

Weft'

Fl G.1 RAW pg B2/L.a2 6 5

PROJECTED AREA PROJECTED AREA X 5 SECOND ORDER PRESS X 4 X 6 X 5 X 4

FIRST STRIP CHOSEN SMALL. PR OJ EC TED AREA CLOSE TO ACTUAL AREA.

x3

X x1 1 FIG. 3 -Added resistance component Added resistance component

FIRST STRIP IS TO WIDE. UNDERESTIMATED _FIG.2

PROJECTED AREA

SECOND

ORDER