Proceedings of the Sixth International Conference on Numerical Ship Hydrodynamics (1994) / Chapter Skim
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Session 11- Wavy/Free Surface Flow: Ship Motions
Session 11- Wavy/Free Surface Flow: Ship Motions
Pages 559-632
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From page 561... ...
Osborne (Massachusetts Institute of Technology, USA) Abstract A three-dimensional panel method is used to solve the linearized ship motions problem for a ship traveling with steady forward speed through quasi-random incident waves.
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From page 562... ...
, a time history of the incident wave elevation at some prescribed reference point on the free-surface. The ship's inertia matrix is Mjk, and the linearized hydrostatic restoring force coefficients are given 562 '~Yo ~ USE z A ~: X r S b Figure 1: The reference frames and surfaces of the problem.
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From page 563... ...
The simplest choice of a basis flow, and the one that will be used here, is the freestream alone: ~ =-Us. This choice leads to the familiar Neumann-Kelvin linearization of the pressure, the free-surface condition and the body boundary conditions: p = -p (~t - U fat)
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From page 564... ...
3.3 The Integral Equation The foregoing initial-boundary-value problem can be recast as an integral equation by making use of the transient free-surface Green function. The three perturbation problems described above all satisfy the same boundary-value problem, with the exception of the body boundary condition.
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From page 565... ...
· (22) Given the form of the body boundary condition for this problem, it is natural to consider each radiation potential to be the sum of three terms: ¢(n)
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From page 566... ...
,. 12.5 15.0 Figure 2: Wigley hull at Fit = 0.3, impulsive pitch displacement memory function.
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From page 567... ...
bit + bhj = 0 for j ~ k As~pv Some sample calculations of the pitch memory functions due to both an impulsive displacement and an impulsive velocity appear in Figures 2 and 3. Both calculations have been made for a Wigley hull at a Froude number 0.3.
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From page 568... ...
As expected, the results are practically identical. Calculations made using this method are compared to frequency domain calculations using WAMIT at zero forward speed in Figures 5 through 8.
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From page 569... ...
569 n nor n non 1.0 2.0 _~ Figure 16: Wigley hull at Fn = 0.3, pitch-pitch damping coefficient. lion of the ship to a forward speed U
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From page 570... ...
In the following convolution, the exciting forces on the ship due to the wave elevation measured at a fixed point in the earth-fixed reference frame, (o(t) , may be computed by Xj(t)
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From page 571... ...
·10 -5 0 5 t '° Figure 18: Wigley hull at Fn = 0.3, ,l] = fir, the heave exciting force impulse-response function.
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From page 572... ...
<,,,,I 0 50 0.75 1 00 (L'>,) ~g 1 25 1.50 Figure 23: Wigley hull at Fn = 0.3, JIB = or, the heave exciting force phase angle.
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From page 573... ...
The results are identical to graphical accuracy, which is expected as these codes are the time-domain and frequencydomain manifestations of the same theory as long as U = 0. Figures 22 through 25 show a comparison of the magnitude and phase angle of the frequencydomain exciting force coefficients for heave force and pitch moment for the Wigley hull at a Froude number of 0.3.
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From page 574... ...
Asymptotically then, the Green function at forward speed behaves like an oscillation at the critical frequency, which decays at a rate of i`. 574 ASVT DtOIC Ail Figure 26: Comparison of the impulse-response function and the proposed asymptotic tail.
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From page 575... ...
Figures 28 and 29 show the convergence of two radiation impulse response functions with increasing numbers of panels. All the curves are for a Wigley hull at Froude number of 0.3, and each curve which appears in the figures is itself the converged result of a series of calculations using progressively smaller time steps for the same spatial discretization.
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From page 576... ...
This simulation is of a Wigley hull at Froude number 0.3, encountering head seas with a PiersonMoskowitz spectrum corresponding to 5 meters per second wind speed. The top of Figure 32 shows a segment of the time history of the incident wave elevation as measured at the origin of the ship-fixed reference frame.
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From page 577... ...
2 0 1 5 1 n no 1 152 Panel ~-~~~~~ 512 Panel : ~~~~~~ 288 Panel O Journee 1.00 1.25 1.50 (Lil~li2 Figure 34: Wigley hull at F77, = 0.3, ~ = 1r, the pitch response-amplitude operator.
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From page 578... ...
Seakeeping calculations with forward speed using time domain analysis.
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From page 579... ...
Ship motions by a three dimensional Rankine panel method. In Eighteenth Symp.
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From page 581... ...
We study the linearized sea-keeping problem for an elastic body, i.e., the periodic small motions of an elastic structure which floats (without forward speed) at the free surface of the ocean (in the infinite depth case)
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From page 582... ...
We begin by reducing the initial problem to an equivalent one set in a bounded domain, thanks to the socalled coupling method between finite elements and integral representation (introduced by Jami and Lenoir [8~. The reduced problem is then extended to complex frequencies using the analytic continuation of the Green function of the seakeeping problem (Vullierme-Ledard t16~.
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From page 583... ...
In this section, ~ denotes a real positive number. We recall here the coupling method between finite elements and integral representation (Jami and Lenoir A
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From page 584... ...
. It is well-known that any solution So of problem Pv satisfies the integral representation formula ~ = Sand + Did in Q
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From page 585... ...
(16) of Pa, the only difficulty to construct this extension lies in the Green function Go.
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From page 586... ...
r ~ J (Q Su7l~+Q~D~) ~ d~=o, by virtue of the boundary conditions on S
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From page 587... ...
, including the assembly of the matrices of a three-dimensional problem and the computation of eigenvalues using an inverse iteration scheme at each nonlinear iteration, was build in a couple of days by a new user of the code (numerical evaluation of the Green function extended to complex-valued frequency is not included!
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From page 588... ...
for solving wave propagation problems in unbounded domains, two specific tools for their solution have been developped: the computation of the coupling integral terms of the method of coupling of finite element and integral representation t5] and the boundary terms of the localized finite element method (see e.g.
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From page 589... ...
On the lower part of this figure the scattering frequencies (~*
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From page 590... ...
LENOIR. Determination of scattering frequencies for an elastic f eating body.
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From page 591... ...
The method uses a non-linear boundary element approach which treats the free surface deformation and finite amplitude vessel motions in a time-stepping procedure. Boundary layer effects and lifting effects are included in the calculations.
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From page 592... ...
Recent developments based on the three-dimensional Rankine panel method offer a potential improvement relative to the traditional strip theory approach. These developments include both frequency domain methods, e.g., Nakos & Sclavounos (8)
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From page 593... ...
which satisfies Laplace's equation, V2~ = 0 (1} Traditionally, ~ is broken down into a number of component parts to aid in the linearizing of boundary conditions. Here, however, no linearizing assumptions are made, so ~ is left as a whole quantity and therefore encompasses such terms as incident wave potential, diffraction potential, radiation potential, etc.
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From page 594... ...
law is the instantaneous jump in doublet strength across the trailing edge, i.e., ,uw is the newly emerging wake strength. On the free surface, the initial boundary conditions are that the ~ and d<~/8n (i.e., ,u and o)
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From page 595... ...
The 6 DOF response of the vessel to free-surface deformation can therefore be computed by integrating the equations of motion over each time step. The wetted surfaces of surface-piercing objects, hulls, channel walls, etc.
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From page 596... ...
Lnstantaneous surface streamlines are traced over the hull, keel, rudder, etc.; unsteady integral boundary layer calculations then provide boundary layer characteristics, such as dis placement source term and skin friction coefficient, for the next step. The former modifies the boundary conditions (Ed.
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From page 597... ...
The present calculations used a time step increment of .03 seconds. This corresponds to
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From page 598... ...
The present repanelling procedure in the panel model has to be made more robust before such issues can be addressed with the present approach. Some general views of the calculated dynamic pressure distribution on the hull at different stages of a wave encounter are shown in Fig.
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From page 599... ...
9. King, B.W., Beck, R.F., and Magee, A.R., "Seakeeping Calculations with Forward Speed Using Time-Domain Analysis," 17th Symposium on Naval Hydrodynamics, 1988.
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From page 600... ...
11. Nakos, D.E., Kring, D.C., Sclavounos, P.D., "Rankine Panel Methods for Time-Domain Free Surface Flows," to be presented in the Sixth International Conference on Numerical Ship Hydrodynamics, Iowa City, Iowa, August 1993.
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From page 601... ...
, _ ~ \ (6) Streamline/Boundary / LAST: NO ~> Layer Analysis \:TE~ ~ YES ( END )
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From page 603... ...
6. Effect of Wave Steepness on Pitch, Heave, and Acceleration Response Functions for SI75 Model Hull at Froude = 0.275.
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From page 604... ...
7. Computed Dynamic Pressure Contours on S175 Hull During Wave Encounter.
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From page 605... ...
A= Model Length - 4. Sm Beam - 0.496 m Draft - 0.163 m CB ~ 0 ~ 454 Cx- 0.7SS _l I 1/11111 -_ Bow 1 (Decreased Flare)
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From page 606... ...
11. Effect of Wave Length on Pitch and Heave Transfer Functions.
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From page 607... ...
12. Effect of Wave Steepness on Pitch and Heave Transfer Functions.
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From page 608... ...
500 400 o 300 200 1 ' 1 100 RESPONSE OF PARENT vs FLARED: Ha/= 0.034 PARENT -- -- -- FLARED \/L =1.2 , . O 1 1 1 0 2 4 6 250 1 E- 2QO Z 150 100 50 O EM _50 -100 -150 _ EN -4 -6 -8 0.3 0.2 0.1 0.0 -0.1 4 ~ 0 2 :N / \ 0 2 ~10 1 1 1 4 6 TIME (seconds)
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From page 609... ...
15. General Views of Frigate During Wave Encounter Showing Computed Free Surface Elevation Contours, Fr = 0.3, A/L~ = t.2, H/X = .021.
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From page 610... ...
The numerical wave maker is driven by an oscillating velocity potential, and so the precise wave length and wave amplitude are not controlled directly. A number of cases have yet to be run to provide sufficient information for cross-plots to be generated to complete the figures shown in the paper.
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From page 611... ...
2. In general, the code works with the complete unsteady pressure distribution which is integrated at each step to provide the instantaneous force and moment acting on the vessel; the separate contribution of the hydrodynamic, and hydrostatic pressures, have not been examined in detail.
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From page 613... ...
This study presents the design, implementation and application of a Rankine Panel Method for the solution of transient wave-body interactions in three dimensions. At the presence of mean forward speed, the Dee surface and body boundary conditions are linearized about the doubly body flow, as it is outlined in section 2.
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From page 614... ...
The resulting steady-state added mass and damp ing coefficients compare excellently with related predictions by the frequency domain computer code SWAN. Section 8 presents free motion simulations in the presence of constant forward speed, where the rigid-body equations of motion are solved at each time step.
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From page 615... ...
This study employs the doublebody flow as the basis flow, which satisfies the rigid wall condition over the calm free surface, and offsets the mean forward speed over the mean position of the hull below z = 0. The doublebody linearization has been employed successfully in the frequency domain by numerous previous studies and its validity has been demonstrated over a wide range of hull shapes, Froude numbers and frequencies (see ea.
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From page 616... ...
It is worth noting that these spline coefficients are not equal to the value of the respective unknown at the panel centers, although they are linearly related to them. The discrete formulation follows from collocation at all panel centers, Hi, and the employment of a discrete time-marching scheme for the integration of the free surface boundary conditions.
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From page 617... ...
At low mean forward speeds the critical value of the time step scales with the square root of the typical panel size h, while at higher speeds the stability condition imposes a much more restrictive upper bound of At scaling with h312. A remedy to the severe stability criterion of figure 1 may be found in employing a three-step semiimplicit scheme composed of a Leap-frog marching for the kinematic free surface condition and a Trapezoidal approximation of the dynamic condition (see Vada and Nakos (1993~.
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From page 618... ...
Damped tree surface conditions at the presence of forward speed follow from (4.2) by adding the proper convective terms to the B/8t operator.
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From page 619... ...
5. FORCED HARMONIC MOTIONS AT ZERO FORWARD SPEED This section discusses the application of the nu 619 merical solution algorithm, outlined in the previous sections, for the simulation of wave flows due to forced heave and pitch oscillations of a ship without forward speed.
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From page 620... ...
Added mass and damping coefficients for the modified Wigley hull at zero forward speed.
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From page 621... ...
6. STEADY MOTION AT CONSTANT FORWARD SPEED This section presents applications of the proposed solution algorithm for the prediction of wave flows due to the steady forward motion of ships.
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From page 622... ...
The aforementioned "critical" oscillations are much more pronounced in the next simulation which considers the same series-60 hull at Froude number F = 0.2. Figure 8 shows the time history of the resultant forces and moments, as predicted by four different computational domains.
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From page 623... ...
Further numerical experimentation has shown that the precise form of the critical transient oscillation depends, almost exclusively, on YOUT and C,O with the general tendency to decrease as the size of the free surface domain and artificial beach increase. The ~ = 0.25-singularity of the forward speed problem which is the underlying cause of the persistent transient oscillations has been been extensively studied over the years.
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From page 624... ...
Time history for the Serie~60, Cb=0.7, hull in steady motion at a Froude number of 0.2.
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From page 625... ...
40 ;4 Figure 11. Time history for the modified Wigley hull in steady motion at a Froude number of 0.3.
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From page 626... ...
Time history for the modified Wigley hull in steady motion at a Froude number of 0.2.
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From page 627... ...
Added mass and damping for the modified Wigley hull at a Froude number of 0.3.
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From page 628... ...
The wave flow due to the forced harmome heave and pitch motion of the modified Wigley model and the Serie~60, CB-0.7' iS solved by using n ink .
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From page 629... ...
Within this study three cases of free motion simu lation are examined. The first case, illustrated in Figure 16, shows the heave and pitch response of a modified Wigley hull which starts impulsively at t=0 from its calm-water position with a forward speed corresponding to Froude number F = 0.3.
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From page 630... ...
Modified Wigley hull started impulsively and dropped from an initial height, (3/Lw~, = 0.01 at three speeds. Swan- 1 ° Swan-2 15.0 125 10.0 ~ 75 fir 5.0 2.5 0.0 180 120 60 O \1 -60 - 1 20 -180 o / / \ \ 2 r~~~'" ·1 Figure 18.
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From page 631... ...
An artificial waveabsorbing beach is designed and employed for the damping of redactions due to the finite free surface computational domain. Wave flows due to forced and free motions of realistic ship hulls are computed with and without mean forward speed.
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From page 632... ...
Future extensions of the present formulation and solution scheme include relaxation of the body boundary condition linearization, in order to model large-amplitude ship motions, and solution of the wave flow past ships advancing along arbitrary curvilinear paths which addresses the problem of ship maneuvering in the presence of ambient waves. ACKNOWLEDGEMENTS This study has been supported by Det Norske Veritas Research AS.
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