Proceedings of the Sixth International Conference on Numerical Ship Hydrodynamics (1994) / Chapter Skim
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Session 6- Wavy/Free Surface Flow: Viscous-Inviscid Interaction
Session 6- Wavy/Free Surface Flow: Viscous-Inviscid Interaction
Pages 311-364
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From page 313... ...
The procedure is illustrated by applying it to a Wigley form. INTRODUCTION We suppose that a given double body of a ship form is at rest in a uniform stream UOO of an incompressible fluid parallel to its centerplane, and that the vector velocity field v of the mean flow within the boundary layer and wake (BLW)
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From page 314... ...
Obtain a source distribution on the body surface ye and the centerplane of the wake as the numerical solution of an integral equation of the first kind, using given data for the viscousflow velocity field exterior but close to the edge of the boundary layer.
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From page 315... ...
, y = y2(x,z) denote the equations of a given hull surface S0, its displacement thickness surface S1 and a surface S2, near but exterior to BLW, respectively.
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From page 316... ...
when R = 0, is essentially Moore's partial differential equation expressed in rectangular, Cartesian coordinates. CONTINUATION OF OUTER IRROTATIONAL FLOW INTO BOUNDARY LAYER Source Distribution on Body Let ~ denote the velocity potential of the irrotational flow about the displacement body in a uniform stream and ~ that of the disturbance potential.
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From page 317... ...
are taken to extend over the double body and over the centerplane of the wake for an additional ship length L and for z varying from -h to +h. The integral in (14)
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From page 318... ...
[9] have furnished a formulation for calculating the velocity field for a flat quadrilateral panel on which a source distribution of constant strength is distributed.
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From page 319... ...
for 81. Initially, the case R = 0, equivalent to Moore's PDE for thin boundary layers, was treated, i.e., with UOO = 1, PI +Qz = R P = Uo61 - a Q = WO61 - 13 with the boundary conditions 6~ (0, z)
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From page 321... ...
5 0.0 0.5 x/ L Fig. 2 Source distributions on Wigley form at various iterations at z/h =1/26 321 1.0
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From page 322... ...
z/h = 9/26 z/h = 19/26 zl h =9/26 z/h = 19/26 o 2 X/ L Fig. 3a Source distribution on Wigley form and wake centerplane at second and third approximations for two values of z/h 322
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From page 323... ...
0.02 0.01 0 In 3 o In 0.00 · -0.01 -0.02 2nd approx.
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From page 324... ...
Irrotational velocity field in BLOW.
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From page 325... ...
Irrotational velocity field in BEW.
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From page 326... ...
W/UO° at X/=0.5 0.010 0.005 8 0.000 -0.005 -~__ 0.0 0.1 0.2 Y/ L 0.3 Figure 4c. Irrotational velocity field in BLW.
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From page 327... ...
'a ca to u)
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From page 328... ...
The same remark applies to bow flows (free-surface boundary layer, wave breaking, bilge vortices, necklace vortices)
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From page 329... ...
NOMENCLATURE Re = u,,L, Reynolds number 6, B' the wetted ship hull and S free surface its image Sp free surface ~ Dp fluid domain Sv free surface ~ Dv DP potential flow domain u = (?
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From page 330... ...
In both cases, the boundary of the potential flow domain is determined by the displacement body. This kind of approach may cause some difficulties when dealing with full-form hulls and transom sterns, where the definition of the displacement thickness is not an easy task, especially when boundary layer separation occurs.
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From page 331... ...
1~. Overlapping zone Potential Flow Figure 1: Com putational sub-dom ains and overlapping zone We assume a body-fixed reference frame with the x-axis oriented along the uniform stream U and the z-axis positive upwards.
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From page 332... ...
On the free surface, the boundary conditions to be satisfied are the following: b! Bud +v~ =w [xz = 0 Tyz =0 NUMERICAL MODEL Potential Solver or z = 0 (17)
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From page 333... ...
A finite volume technique is used to discretize equation (12~. The inner region Dv is divided in hexahedra Vijk.
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From page 334... ...
, a non-overlapping domain decomposition scheme was used. The values of the tangential component of the velocity and the pressure of the potential field at the matching surface were used as boundary conditions for the Navier-Stokes solver, while the normal component of the viscous solution was used as Neumann condition in the potential flow.
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From page 335... ...
In fact, as mentioned before, the potential flow field is expressed as the sum of a double model potential ~ and a wave potential ~ . This linearized form t3]
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From page 336... ...
3, is consistent, in the sense that the discrete problem can be solved with any desired accuracy, up to roundoff errors. The jump, clearly recognizable in the plot, is experienced when the free surface flow computation begin, starting from the converged double body flow.
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From page 337... ...
. Regarding to the location of the matching surface, the viscous domain should be chosen as narrow as possible to improve Figure 8: Top view of the boundary layer and the wake for the double model case r .~_ Figure 9: Top view of the boundary layer and the wake for the free surface flow the efficiency of the numerical scheme in practical applications.
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From page 338... ...
Further numerical experiments are needed to analyze the dependence of the solution on the grid refinement and on the thickness of the viscous region. Moreover, in the viscous region, the wave amplitude is rather underestimated: this problem might be solved by a grid refinement, or by a more accurate implementation of the free surface boundary conditions for Navier-Stokes equations.
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From page 339... ...
[2] Tahara, Y., Stern, F., "An Interactive Approach for Calculating Ship Boundary Layer and Wakes for Nonzero Froude Number", Proc.
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From page 340... ...
In response to the first question, on the free surface boundary of the inner region one of the unknown velocity components can be simply obtained by the continuity equation. The combination of this with the boundary conditions (17)
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From page 341... ...
The MANS method in the near field resolves the turbulent boundary layer, the wake flows, and the nonlinear waves around the ship hull. The kinematic and dynamic Ire - surface boundary conditions are satisfied on the exact free surface in the RANS solution domain.
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From page 342... ...
and developed an interactive approach to calculate ship boundary layers, wakes and wave field for a Wigley hull form. In their studies, the RANS method was coupled with the SPLASH free surface code of Rosen [10~.
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From page 343... ...
Since this technique eliminates the dispersion error and wave damping associated with the upstream differencing, SLAW's free surface solution is more suitable for the present zonal calculation than many other free surface potential flow methods. Since the free surface boundary condition is linearized about the double body (Fr=0.0)
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From page 344... ...
The LAMP code is generally used to compute the flow around a ship moving with forward speed in a seaway. In the LAMP approach, the exact body boundary condition is satisfied on the instantaneous wetted surface of the moving body while the free-surface boundary conditions 344
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From page 345... ...
has been em ployed for the solution of viscous boundary lay ers, wakes and nonlinear free surface waves in the near field. We shall briefly describe the general ized RANS method in the following: Consider the nondimensional Reynolds-Averaged Navier-Stokes equations for incompressible flow in a orthogonal curvilinear coordinate system (at, x2, x3, t)
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From page 346... ...
Any face can be divided into sub-sections that match different blocks, or that can be assigned different boundary conditions. Each block is allowed arbitrary dimension and orientation as long as the assembly of all blocks covers the entire solution domain.
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From page 347... ...
The iteration between the RANS and the SLAW solutions is done by constructing an imaginary SLAW solution boundary (inner matching boundary) which lies outside the viscous boundary layers and wakes, but still embedded in the RANS solution domain.
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From page 348... ...
In the initial phase of this study, the free surface boundary conditions in RANS domain were also linearized to simplify the coupling between the RANS and potential flow methods. Within the context of the linear wave theory, the dynamic and kinematic free surface boundary conditions were specified at the mean free surface of the RANS solution domain.
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From page 349... ...
For nonzero Froude number calculations, it was necessary to adjust the solution domain to conform with the exact free surface profiles. As noted earlier, this was achieved by stretching only the upper portion of the coordinate surfaces beneath the free surface once the new wave profile is obtained from the integration of kinematic free surface boundary conditions.
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From page 350... ...
The interactions between the viscous boundary layer and free surface flows completely altered the potential flow wave profiles in the stern and wake regions. In particular, the free surface waves decay very quickly along the wake centerline due to the convergence of low momentum fluid towards the ship stern and the centerplane of the wake.
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From page 351... ...
In potential flow calculations of low Froude number free surface flows, very fine panels and prolong simulation time are often required in order to resolve the short wavelength, small amplitude free surface waves observed at low speeds. Since the interaction between the far field free surface waves and the viscous boundary layers and wakes becomes quite weak at low Froude numbers, it is possible to neglect the free surface wave effects on the RANS outer boundary without significant ef fects on the viscous free surface flows in the near field.
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From page 352... ...
Double-Body Results In order to facilitate a direct comparison of free surface wave effects between low and high Froude numbers cases, we shall present both the Fr = 0.160 and 0.316 results in the same plots. Furthermore, comparisons will also be made with double body solutions for more detailed examinations of complex interactions between the turbulent boundary layers, ship wakes and nonlinear free surface waves.
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From page 353... ...
It is also seen from perspective views shown in Figures 15 and 16 that the nonlinear free surface waves induced very strong pressure gradients, both in the longitudinal and transverse directions. The presence of these wave-induced pressure gradients have led to significant modifications of the viscous boundary layer and wake flows shown in Figures 13 and 14.
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From page 354... ...
method and the free-surface potential flow calculations has been developed for the prediction of ship flows including both the viscous and nonlinear free-surface wave effects. In this zonal approach, the RANS method is employed to resolve the viscous boundary layer, wake and the nonlinear free-surface waves around the ship hull while the potential flow method is used to provide the wave information outside the viscous region.
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From page 355... ...
and Rosen, B., "An Interactive Approach for Calculating Ship Boundary Layers and Wakes for Nonzero Froude Number," Proc. 18th ONR Symposium on Naval Ship Hydrodynamics, 20-24 August, 1990, Ann Arbor, MI.
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From page 356... ...
[16] Hess, J., and Smith, A., "Calculation of Nonlifting Potential Flow about Arbitrary Three Dimensional Bodies", Journal of Ship Research, Vol 8, 1964, pp 20-24.
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From page 357... ...
interval Eta/length.21Froude.~2 = Hull ~urface Pressure; Double Body Q co o o _ J \ i -0.5 O.O SLAW, Bare-Hull RAXS/SLA\\ iter=0 .......................................... RAN'S/SLA\Y iter -- 1 RAN'S/SLAW iter=2 ~ f~' : 0.5 1.0 X 1.5 2.0 Fig.
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From page 358... ...
_ O i j ~1 1 I2.0 -0.5 0.0 0.5 1.0 1.5 2.0 X Fig. 7: Influence of SLAW Matching Boundary.
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From page 359... ...
RANS Axial Velocity Contours, (d) RANS/SLAW Pressure Contours.
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From page 360... ...
Etr = 0.316, x = 1.1 Fig. 12: Pressure Contours: (a)
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From page 361... ...
,, Fig. 13: Axial Velocity Contours: (a)
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From page 363... ...
in RANS Solution Domain.
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