Twenty-Second Symposium on Naval Hydrodynamics (1999) / Chapter Skim
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3 Hydrodynamics in Ship Design
3 Hydrodynamics in Ship Design
Pages 11-109
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From page 11... ...
Present capabilities are Den discussed' and the attainable accuracy in the prediction of waves, wave resistance, local flow, viscous resistance and propeller effects is assessed. Prospects for improvements, based on present research in and generation, free surface flows, turbulence modelling, propeller [lows and full scale predictions are outlined.
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From page 12... ...
2.1 Potential Flow Panel Methods The flow is assumed steady, irrotational and incompressible. A Cartesian coordinate system is employed, where the origin is at the bow and at the undisturbed free surface level, x downstream, y to starboard and z upwards.
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From page 13... ...
and (8) go to zero and the position where the free surface boundary conditions are applied approaches the correct one.
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From page 14... ...
The discussion will address five important areas: wave pattern, wave resistance, wake/local flow, viscous resistance and propeller/hull interaction. Figure 1 presents predicted potential flow waves from two different hulls, the slender Series 60, C~=0.60 hull and the very bluff Dyne tanker, designed as a test case at the 1990 Gothenburg workshop (8~.
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From page 15... ...
By investigating the predicted wave pattern and wave profile, and comparing with the computed pressure distribution on the hull, experienced designers are guided in their optimization process. Good descrip 7W loom o.
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From page 16... ...
A more thorough discussion on free surface RANS methods will be given in Section 4.2. 16 3 Wave resistance
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From page 17... ...
Very frequently, negative values of the wave resistance are found for linear methods and low Froude numbers. There are thus several reasons why resistance calculations are inaccurate in the low speed range.
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From page 18... ...
As pointed out above, transom stern ships, have a relatively thin boundary layer even close to the stern, and bilge vortices are seldom a problem. For such hulls very good viscous flow predictions are possible, an important advantage, since these hulls often have brackets, whose direction can be optimized.
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From page 19... ...
Although reference will be given to research elsewhere, the emphasis will be on the work in the Chalmers/FLOWTECH group. Four areas will be covered: grid generation, free surface boundary conditions, turbulence modelling and propeller blade flows.
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From page 20... ...
4.2 Free surface boundary conditions As mentioned above, the most important result of the 1994 workshop (9) was the breakthrough of the 20
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From page 21... ...
Further, a good Kelvin wave system might not be needed for other predictions of interest, such as wave resistance, sinkage and trim, side forces and other local phenomena. In the first free surface RANS methods of the MAC and VOF types the grid was kept fixed and the free surface tracked in the grid at every time step.
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From page 22... ...
None of them is presently capable of computing an accurate Kelvin wave pattern due to resolution problems, but this problem will be solved as the computer power increases. 4.3 Turbulence modelling An interesting clue in the search for better stern flow prediction methods was presented by Deng et al (54)
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From page 23... ...
more results were presented, which strongly supported the use of their Reynolds stress model. One result is shown in Figure 5 where the prediction of the wake contours in the propeller plane of the HSVA hull is shown.
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From page 24... ...
There is thus a strong influence of rotation and all Reynolds stress components are computed individually. Some results for Svennberg's second test case, two counter rotating vortices in a flat plate boundary layer, have been presented recently in (58)
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From page 25... ...
1+ is typically two orders of magnitude smaller, relative to the hull length, at full scale as compared to model scale. Fortunately, in a Reynolds-averaged method the scale is only important in the direction normal to the hull, where it determines the velocity distribution in the inner part of the boundary layer (neglecting surface roughness effects)
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From page 26... ...
Four different turbulence models were tested in the Reynolds number range 5 x 106 - 1.3 x 109, namely the Cebeci-Smith and Baldwin Lomax algebraic models, Menter's k-mle shear stress transport (SST) model and Chien's low Reynolds number k-£ model.
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From page 27... ...
The normally predict the hull wave profile quite well, but cannot predict the Kelvin wave pattern due to insufficient resolution. This problem will be removed thanks to the increase in computer power.
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From page 28... ...
( 1996) , A solution method for the nonlinear ship wave resistance problem, MARIN, Holland (PhD thesis, Technical University of Delft)
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From page 29... ...
( 1997) A Comparison Between Moving Grid and a Level Set Technique for Solving 2D Free Surface Flows.
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From page 30... ...
(1998) , The scaling of high Reynolds number viscous flow predictions using CFD techniques, 3rd Osaka Colloquium, Osaka (72)
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From page 31... ...
I was required to simultaneously obtain both boundary conditions and solutions since only form, not value, could be produced a priori. Having experienced some convergence difficulties I talked to Prof.
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From page 32... ...
DISCUSSION G Jensen Hamburg Ship Model Basin, Germany The drawback of potential flow panel methods is not only the lack of viscous effects.
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From page 33... ...
Abstract The research reported here builds upon previous efforts which were directed toward improving the correlation between the traditional linearized waveresistance theory and experimental data for the toe tat drag on a marine vessel. It is shown that very simple form factors based on the usual hull geometric parameters can be used to correct the calculations of the ware resistance and the frictional resistance, which leads to a vastly improved prediction of the total resistance of the vessel.
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From page 34... ...
A second meshing, consisting of "pyramidsn or "tents" with a rectangular base, is employed for the purpose of the numerical calculation of the wave resistance. The bases of these tents are chosen in order to match the centerplane area as closely as possible, while their height is the local beam of the deIIiihull or monohull.
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From page 35... ...
Model in Towing Tank 2.2 Modeling of the Hollow The hollow behind the transom stern is modeled by assuming that it Is a geometrically smooth addition to the vessel. Clearly, the water flow passes the transom-stern girth line in a well behaved manner and it is necessary to assume that the longitudinal derivatives of the mathematical body must be continuous there.
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From page 36... ...
for the wave resistance in a channel is Rw = H9 amp x Nevertheless, it is clear that this model To possesses the following realistic and necessary at tributes: X k2k(U2+V2) 2k-kotanh(kd)
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From page 37... ...
(17) Here, a wave-resistance form factor fw has been applied to the computed linearized wave resistance, an idea which is analogous to that behind the traditional (frictional-resistance)
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From page 38... ...
For a standard Wigley hull, it was found that a panel layout of 40 x 8 (in the longitudinal and vertical directions, respectively) results in an estimated discret~ation error of 0.1% in the wave resistance over the range of Eroude numbers of interest.
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From page 39... ...
Doctors (1998) prowded the details of the hull segments from which the ship models were assembled.
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From page 40... ...
We start by illustrating the effectiveness of the straightforward Michell theory together with the ITTC estimate of the fric 40 Figure 2: Sample Ship Models (b) SIHE Series tional resistance, with form factors fw and fF of unity, indicated by F"nc.
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From page 41... ...
= 0 1 0.4 0.6 0.8 Figure 3: Resistance Components for SIHE Series Model 1 (d) s/L = 0.5 Func tion Code Func .
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From page 42... ...
Comp. o o o o T,E Q15 - ~H ~ ~F or T 0.1 0.05 Sent = SIHE Model = 9 0 L/Vl/3 = 9550 ° s/L = 0~ d/L = 1.156 Fund = 0 O 0 02 0.4 0.6 0.8 1 F Figure 4: Resistance Components for SIHE Series Model ~ (b)
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From page 43... ...
Figure 10 shows the resistance components for the pure theory for two conditions, including a 02- Curve ~ Func | Comp | o o o o O T,E OIS~~-~ -- -1S /~ 0.05O- . my' o o o Series = SIHE Model = 1 L/V1/3 = 6289 s/L = 0.2 d/L = 1.156 I l I ~ 0 0 ~0.4 0.6 0.8 1 F Figure 5: Use of Form Factors for SIHE Series Model 1 (b)
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From page 44... ...
T,E T T T T ,~f ~,,' o -"" ~ A., . o','~~ Series = SIHE i,' Model = 9 ,' L/V/ = gyro ~ s/L = 02 d/L = 1.1" l 02 0.4 0.60.8 F Figure 6: Use of Form Factors for SIHE Series Model ~ (b)
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From page 45... ...
s/L = 0 ~: ,§ ~t/ o o Figure 7: Effect of Tr~som-Hollow Factor for SIHE Series Model 1 (b) s/L = 0.2 0~- Curve ~ ~ ~ Comp.
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From page 46... ...
Model 2 1 O.Q5 aP' Comp. | T,E T T ' T of '~f,,~''' / ~Sari - = Lam ^ ~Model = 8 L/V1~ = 8.187 s/L = 0 d/L = 0.~fZ73 - 1 ~ ~ ~ 1 0 02 0.4 0.6 0.8 Figure 9: Use of Form Factors for Togo Series (c)
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From page 47... ...
Model 2, s/L = 0, d/L = 1.0 Sene#l = wig~y Model =2 L/V~/8 = 7.1 I 7 s/L =Q4 d /L =02£, Wo,,,-' 02~1 ' 0.15 0.1 0.05 Curve Fbuc Comp. o o o o T,E Seri" = Wigley Model = 5 z/vl/~= 6.6g7 s/L = 0 d/L = l 0 02 0.4 0.6 0.8 F Figure 11: Use of Form Factors for Wigley Series (a)
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From page 48... ...
Resistance, Propulsion and Vibration, Society of Naval Architects and Marine Engineers, Jersey City, New Jersey, 327+`ri pp (1988) LUNDE, J.K.: "On the Linearized Theory of Wave Resistance for Displacement Ships in Steady and Accelerated Motion", Lana.
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From page 49... ...
AUTHOR'S REPLY Dr. Scragg has correctly noted that the particular functional variations of the form factors presented in this paper relate to geometric parameters alone, even though the possibility of dependence on Froude number was included in the computer program.
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From page 50... ...
These methods are generally preferred to the other ones since require only wave measurements at fixed points, and the wave profiles do intersect only partly the viscous wake region; on the other hand, infinitely long records of the wave height are needed in the application of LCM: suitable corrections for truncation errors were therefore proposed. Several years later, wave pattern analysis was re-examined in the framework of potential flow numerical simulation, to obtain an algorithm for the evaluation of wave resistance more reliable than direct pressure integration on the hull (Nakos, 1991~: in this case, transverse cut technique was preferred.
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From page 51... ...
The 95% confidence interval related to the wave resistance coefficient shows a rather narrow error band and the comparison with the numerical wave resistance as well as with experimental data available in the literature shows a satisfactory agreement. Furthermore, the errors typical of the mathematical model related to LCM were studied; in particular, the wave resistance coefficient dependence on transverse location of the wave profile and the effects of truncation were analyzed by numerical experiments: the wave pattern around a submerged prolate spheroid (conventional hull case)
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From page 52... ...
4. Wave pattern analysis: the Longitudinal Cut Method "...The existence of a far field in which linear theory is valid, breaking absent, and where the Kelvin wave pattern and the amplitude function have meaningful 52
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From page 53... ...
As stated before, in order to investigate on the propagation of precision errors in the determination of wave resistance, we performed LCM elaboration (by means of a computer program developed at INSEAN (Agostini et al., 1997~) for all the measured wave profiles.
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From page 54... ...
For the Catamaran, precision errors propagation was examined in the same way, whereas the effects related to the wave pattern generated by the carriage were studied in two ways: 1. by subtracting the carriage waves, for every probe and every Froude number, to the signals related to the corresponding model towing tests, and by computing the wave resistance in comparison with the wave resistance obtained from the original signals; 2.
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From page 55... ...
The steady wave pattern around a submerged prolate spheroid was computed by a desingularized boundary integral method (Lalli, 1997) and the wave resistance, evaluated by LCM, is compared, for .3~r <.8, with the value obtained by pressure integration.
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From page 56... ...
wave resistance coefficient can be obtained with a reasonable confidence; b' the main error, in the evaluation of wave resistance, is related to wave pattern analysis: it is well known that the longitudinal cut method is sensitive to wave profile truncation; the present analysis, based on numerical experiments, shows that: · generally, only a lower limit is given for the transverse location of the probe: this condition can be misleading; in fact, though along any parallel cut ~(X,yo) - O(X-~/2~, according to (6)
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From page 57... ...
( 19634. "The Determination of Wave Resistance from Wave Measurements along a Parallel Cut," Int.
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From page 58... ...
_ s y/L= .141 }: ~ ~ ~ ~ ~V' -REV 0 1 2 3 x./L 4 5 6 y/L= . 174 -6 -8 -10 -1 0 l 2 3 4 5 6 x/L 8 6 4 2 ~ylL=.223 1 o Em\ ~: 11 ,1' ~-~ -2 4 -6 -10 4 -1 0 1 2 3 4 5 6 V xlL Figure 3 Plot of 10 wave height measurements (Series 60 wave pattern, Froude=.316)
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From page 59... ...
10 12 Carriage waves: U = 3.54 m/s; y/L = .2 time(s) 15 20 25 Figure 5a: Plot of 7 wave height measurement (wave pattern generated by the motion of the camage, U=3.55 nets)
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From page 60... ...
Figure 7a: Comparison between the average waves generated by the towed model (catamaran, Froude=.S) and the average waves generated only by the carriage at the same velocity (U=3.55 m/s)
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From page 61... ...
: without truncation correction, (b) : with truncation correction)
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From page 62... ...
: without truncation correction; (b) : with truncation correction, 62
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From page 63... ...
Osgood 0.001~0 o.ool~ o.col4ao O.C012= o.=aoo o.oa~oo onto Mao o.am2ao owe 0.18 023 o.ao46 o.Oo4 t a~t n~` _ 0.002 .
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From page 64... ...
x In Al 4 Q , o. CO q, 4 -8 1 2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 y/L Figure 17a: Numerical computation of the potential flow past a submerged prolate spheroid: wave resistance coefficient error versus lateral position of the wave profile to to a)
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From page 65... ...
o o lu1 2 o O ~8 x GO ~D 4 Q O a, - 4 _ C)
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From page 66... ...
-3366 panels - - - 4880 panels ~ 6532 panels - - - 8639 panels 0.2 0.4 /L 0.6 0.8 1.0 Figure 18a: Numerical computation of the potential flow past a couple of submerged prolate spheroids: wave resistance coefficient error versus lateral position of the wave profile (b/I,=2.635)
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From page 68... ...
In this work a very deep analysis on the main error sources related to wave pattern analysis is earned out, in particular for the longitudinal cut method. Uncertainty analysis shows that the propagation of the experimental errors in the determination of the wave resistance from a longitudinal cut does not affect significantly the result, also because He precision error decays rapidly in the far field: this is another reason to prefer the method of Sharma with the wave truncation with respect to the transverse cut method, based on wave measurements in a region including He wake, where viscous effects, and therefore flow unsteadiness, are very meaningful, and a more significant spreading of the results can be expected, with respect to figure 13 (at y/L = .2~.
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From page 69... ...
TO numerical wave resistance lots been obtained by both the pressure integration and the wave pattern analysis on a transverse cut downstream the sl~ip. All e.~;tensio~ of the n~nerical ',~etl~od based on a modified Ne`~10n iterative procedure to determine the Inning print and sinkage is preselected, discussed Ad con~parcd ~ ills sorbic of the e.~;perin~e~tal data.
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From page 70... ...
tIle test~`d mo ;lels Tl~e cooperati`~e e.xperin~cntal in~ estig`~tio'~ uas carried o~t on models of tl~rec high speed crafts i', tl~e towing tank of the Uni~ersit~ of Naples ( 146 ',~ .~; t3.() n~ x 4.2 ~, n~a.xi~u',~ carriage speed 6 ~n/s)
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From page 71... ...
3. WAVE PATTERN EXPERIMENTAL ANALYSIS The wave pattern e`;peri~e~tal investigation, As carried omit by using ditTerc~,t tecl~niq~es to verify tl~cir validity with the tested models used in this research.
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From page 72... ...
Talc motivation for the use of such methodology is to ofold. Orient pressure integration is affected by Eric Al errors Lick arise in balancing large pressure forces ilk opposite directions, whereas, probably a more fa~o~r.~ble sit~-~tion e.~;ists in analysing wave records arid ilk deriving the wave resistance from the integration of .~ positive quantity as the squared free wave spcctn~n~.
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From page 73... ...
5. WAVE RESISTANCE EVALUATION WITH NUMERIC TRllVI AND SINKAGE PREDICTIONS The numerical '~etl~od described so far leas Aced extended to the case of l~igl~ speed crafts for `~1,icl~ bloc dynamic si'~k.3g~ rind trills arc, Its Koch v cr`' i~,porta~t Aft.
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From page 74... ...
Roughly a minimum of about 300 plucks over the hull arid 2800 offer the surface for tile transom ~nonol~ull sphere judged to be sufficient; these figures are modified to about 3200 over the surface and double the n~'n~ber over the hull, for the catamaran. For the Wigley simple hull even less panel can be sufficient for ~ stable wave resistance prediction.
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From page 75... ...
1 6 -0.18 -O. 20 ~8 -0.22 I i`'llre 7 - Wigley Catam.: Numeric wave resistance and clyllamic trim all~l si2~-aOe comparisoll with ex~ments of tl~e l~un~ps and hollows of tl~e resistance curve are accurately predicted by tl~e method.
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From page 76... ...
The tendency of tile e.xpenmental wave resistance to stabilise for Fn>() .8 is not followed by the calculations, most probably for the incorrect trim predicted at these speeds.
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From page 77... ...
-no On ns 1 n Is 2s I , .
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From page 78... ...
4E-~ 2E-3 OE+ o 8E-3 o 4E-3 OE+~ dC`v /d ~ Monol~ul I Fly= ()
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From page 79... ...
,.. 0.60 0.70 0.80 0.90 1.00 1.10 1.20 -1.0 -1.2 Figure l2 - CAT1 catamaran configuration: numeric trim, si~;age and wave resistance compar.ison with expe~iments.
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From page 80... ...
6E-1 4E-1 OE+O 8E-2 4E-2 OE+O 2E-2 1 E-2 OE+O Mo',oh~ll Fn = 0.~ E>;p ilarge modell - E>;p t.~;~11 r~c~del Nr'',,crie 1 1 ()
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From page 81... ...
3.5 3.0 2.5 2.0 1.5 ~ .0 0.5 0.0 0.40 0.50 0.60 0.70 0.80 0.90 1.00 t . 10 Figure 16 - CAT2 Cata~narm~: expenmental/num~cal wave resistance comparison `~dcq~atels, positioned both for the catan~aran and for its den~il~'ll.
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From page 82... ...
cx cr Elvis '~lctl~odolog~: At be also improved to be .~doptcd for routine '~l~crical `~'e pattern analysis of Ail speed crafts. 0.20 0 10 0.00 0.15 0.10 0.05 0.00 0.06 82 A it\ Fll = 0.6 hi\ _ 'it ~ _- ~u _ ~ _ 1 1 1 ~ 0 20 40 A Fn=0.7 u _ ~ I l___r~ I 0 20 4 A 0.04 _ /~ _~W `~ _~: u _~ 1 1 1 1 0 20 4 Fll =0.9 Figure 18: Exalllples of free wave spectra for the demillull CAT 2 Solid calve: nlllllerical Dotted curve: experimental
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From page 83... ...
~Funher Development of a Proccd~re for Determination of Wave Resistance from Longit~'di~al-c`~t S~rface-Prof~le Measurements"; Jo~r'~;~l of Slain Research, vol. 19' n.2 dime 1975, pp.
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From page 84... ...
Different existing methods are reviewed and the new Most Likely Extreme Response method is presented. The third is to estimate extreme values, based on the different methodologies presented under point two above, and to demonstrate the sensitivity of these extreme values to the methodologies chosen.
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From page 85... ...
The present paper will focus on the prediction of extreme values, based on the selective use of nonlinear time domain codes. Different methods will be reviewed and applied to vertical hull girder bending moments and shear forces.
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From page 86... ...
showed that, for the midship vertical bending moment of a mono hull with a large flare, typically 36 wave cycles (nH nil ·nt. will be sufficient to estimate the hourly maximum bending moment with approximately 5°/0 error.
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From page 87... ...
Derivation of the underlying wave profile The last step in the procedure is to derive the underlying wave profile, which caused the Most Likely Extreme Response time series according to linear theory. This is achieved using the frequency response Unctions, which were already calculated using SWAN in its linear mode.
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From page 88... ...
The same spectrum has been used in all the irregular wave analyses as described below. In this particular run, the measured maximum midship sagging and hogging bending moment were respectively 4.46-105 kNm and -2.31-105 kNm.
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From page 89... ...
for the Snowdrift at Fn = 0.145 in head waves. Linear transfer functions Figure 3 - Figure 7 show the measured and calculated transfer functions for heave, pitch, midship vertical bending moment and shear forces arnidship and at a quarter of the length aft from the bow.
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From page 90... ...
(1500 seconds) by the mean Nonlinear simulations in random irregular waves A straightforward method to obtain an estimate for the nonlinear maximum midship vertical bending moment in irregular waves, is to perform 'enough' nonlinear simulations in irregular waves and to identify the realized extreme response from the simulated time histories.
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From page 91... ...
Sage Figure 8 Calculated Hermite distributions of extreme 5.Q~1 midship vertical bending moment using different sets of statistical moments, compared with experiments. a Y 2.5x1 MLER calculations The last method which is illustrated here, is the Most Likely Extreme Response method.
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From page 92... ...
Data block 2 3.45.105 -2.01 105 4) Data block 3 3.99 105 -2.15 1 Os Nonlinear simulation of Most Likely Extreme 4.57 105 -2.36 105 Response: Table 3 Measured and calculated extremes in Me 1500 seconds sea state for the Snowdrift at Fn = 0.145 in head waves (Hs = 4.8 m, Tz= 8.0 s)
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From page 93... ...
The regular design wave approach and the Most Likely Extreme Response approach have been used to calculate ULS-values of the vertical shear force at a quarter of the length from the aft perpendicular, and the midship vertical bending moment. In the regular design wave approach, an amplitude of tom and a wave period of 9.5 s was used.
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From page 94... ...
4j , , ~........ 2L """" "~~~~""" o 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 V - e h~quenoy Radish Figure 15 Roll RAO for the trimaran at 5 knots, in bow quartering waves (135°)
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From page 95... ...
30 Figure 21 Snapshots of simulated vertical bending moments in regular waves (period 9.5 s) with different amplitudes for the trimaran (5 knots, head waves)
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From page 96... ...
c108 o _~08 _5.Q) c108 Mo~ lil~ly EXIT VBM Trmlan 5 lowly, head - 4 Girls - ''''1 110 120 rumlSl Figure 24 Simulated nonlinear Most Likely Extreme Response history for the midship vertical bending moment in the trimaran (5 knots, head waves)
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From page 97... ...
For the trimaran, the results as obtained by the regular design wave approach and the Most Likely Extreme Response approach were very close.
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From page 98... ...
Nonlinear ship loads: stochastic models for extreme response, Journal of Ship Research, 42 (1)
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From page 99... ...
The Most Likely Extreme Response method was presented to calculate the non-linear response in a well-def~ned condition, which is known to give the largest response in a linear calculation. The required simulation time depends on the shape of the auto-correlation function of the response.
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From page 100... ...
Numencal simulations using FLUENT software demonstrates We features of the air cavity, and Me reduction in lift simulated compares well win theory and published experimental result for a NACA 0010 foil at zero angle of attach The ventilation number of Me cavity was found to be inversely proportional to Me cavity length. Further work involves testing foils with different vent locations at different angles of attack.
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From page 101... ...
Result Dom this theory were found to correlate well win linear theory for cases where cavity starts fiercer Dom the leading edge. A theory for potential flow past thin airfoils with ventilation was developed by Fabula (1962)
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From page 102... ...
noted that Were appeared to be a relationship between the air flow rate and We cavity length and pressure that depended on the angle of attack It was observed Mat beyond a Certain CQ value IlOminally around 0.0() 4, We · Theory (Uc=1.00001 )
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From page 103... ...
This software has a capability for solving muld-phase flows, tenth options for grid refinement around large pressure gradient locations. The simulations are expected to provide a means of obtaining fairly accurate results for ventilated foils that can be compared against corresponding result from experiments and theory.
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From page 104... ...
Air vent location Water inlet velocity Air inlet velocity Dimensionless air flow rate Ambient pressure 3°/O chord 10 m/s 5 m/s 0.005 1.3 E05 Pa Using a dine step of 0.01 see, the simulations were run up to t =1.9 sec. The simulation was stated with the foil in the Filly wetted condition, and air injection was initiated 0.3 see into the simulation.
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From page 105... ...
Fig 5: Simulation results for NACA 0010 foil at ~ =0O, U,,O= 10 m/s, air flow = 5 m/s at 3% of chord from leading edge.
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From page 106... ...
Relative stadc pressure contou", at various time steps.
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From page 107... ...
This agrees well win Log et al's (1959) results where the least squared straight line fit to Mental C,, data intersects at~.22 for zero angle attach The data also shows that 90°/O of steady state lift value is achieved in less that 1 see aver air injection This response time information is an m~port~t consideration when developing a ride control Syst=L It is of interest to know how this time varies as the operational parameters are changed This will be part of Be future research in this project This simulation has shown conv~c~g evidence as to the Citation of FLUENT for simulation of Be flow of interest 5.
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From page 108... ...
Simulations conducted on the same foil with the commercial software FLUENT have shown good correlation with experimental data for the lift coefficient at zero degree angle of attack. The product of ventilation number and cavity length is found to be roughly a constant for the duration of cavity development.
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From page 109... ...
At die current speeds of high speed craft, most notably catamaran ferries, ride control foils are required to be quite large, thus heavy, to produce the required force without cavitating. Air injection on He surface of He foil gives He ability to greatly adjust the lift of the foil as well as delaying the onset of cavitation.
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