Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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Unstructured Nonlinear Free Surface Simulations for the Fully Appended DTMB Model 5415 Series Hull Including Rotating Propulsors
Unstructured Nonlinear Free Surface Simulations for the Fully Appended DTMB Model 5415 Series Hull Including Rotating Propulsors
Pages 192-210
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From page 192... ...
Hyams, Brent Mitchell (Computational Simulation and Design Center, Mississippi State, MS) ABSTRACT Nonlinear free surface simulations around realistic geometries, such as the DTMB Model 5415 Series hull, are a necessary step to achieve the goal of simulation of maneuvering surface vessels.
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From page 193... ...
For the unpowered case, the propulsors are removed, so a steady-state simulation is obtained; for the powered case, the propulsor is rotating providing an unsteady simulation. Even though the nonlinear free surface implementation assumes a steady-state flow, it is assumed that the unsteadiness produced by the propulsor can be adequately In the following section, the free surface algonthm is presented, which includes the method for solving the kinematic free surface equation, the imposition of the hydrostatic pressure on the Navier-Stokes equations and the grid movement algorithm.
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From page 194... ...
NUMERICAL APPROACH FOR NAVIER-STOKES EQUATIONS The baseline flow solver is a node-centered, finite volume, implicit scheme applied to general unstructured grids with nonsimplical elements. The flow variables are stored at the vertices and surface integrals are evaluated on the median dual surrounding each of these vertices.
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From page 195... ...
This allows the evaluation of viscous fluxes on each face of the control volume without regard to the varying element types of the mesh. An algorithm in which no element information is used outside of metric computations is termed a "grid transparent" algorithm (Haselbacher, 1999~.
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From page 196... ...
rl,r~+1 I = Viscous conditions are enforced by modifying the linear system such that no change is allowed in the velocity, and the pressure is driven according to the imbalance in the continuity equation in the boundary control volume (Anderson, 1994~. Farfield conditions are handled via a characteristic variable reconstruction; all boundary conditions are handled in an implicit fashion.
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From page 197... ...
NONLINEAR FREE SURFACE ALGORITHM A nonlinear free surface is obtained for a steady-state simulation by solving the kinematic free surface boundary condition at each time level and imposing the hydrostatic pressure distribution based on the new free surface elevation onto the free surface boundary within the mean flow. After several time steps, typically on the order of 200, the grid is moved to match the free surface elevations while conforming to the surfaces that intersect the free surface, such as the hull of a ship or the sail of a submarine; and as the loosely coupled interaction between the free surface, the Navier-Stokes equations and the grid movement algorithm converges, the solution approaches the nonlinear free surface solution.
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From page 198... ...
R ~ + Q ~— Within the viscous boundary layer, special care is needed in solving the kinematic free surface equation. On viscous surfaces, the flow velocity plus the grid velocity (i.e., u + all is set to zero, which prevents the free surface from moving at the viscous surface.
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From page 199... ...
GRID MOVEMENT ALGORITHM After several time steps, the grid is moved to match the free surface while conforming to any solid surfaces intersecting the free surface, with displacements on the surface being propagated into the volume grid. Several methods are available for this grid movement, including the use of a Laplacian solver to propagate the surface perturbations inversely proportional to the length of the edge.
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From page 200... ...
The derivations of the three-dimensional torsional spring equations are beyond the scope of this paper and will be presented elsewhere. EXAMPLES The two examples given in this paper deal with the fullyappended DTMB Model 5415 series hull, one without propulsors and the other with propulsors rotating.
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From page 201... ...
and consist of prisms in the boundary layer generated from the triangles on the viscous surfaces, tetrahedra and pyramids in the transition region at the edge of the boundary layer grid and tetrahedra outside of the boundary layer. On the free surface grid, quadrilaterals exist within the boundary layer region and triangles exist outside of the boundary layer.
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From page 202... ...
This asymmetry in the grid produces an asymmetry in the discretization error within the code, but the free surface, even in the stern region, regains symmetry as the solution approaches steady-state. In Figures 8 and 9, contour plots of the free surface elevations around the unpowered 5415 are presented showing the Kelvin wake pattern originating from the bow and the "rooster tail" in the stern region.
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From page 203... ...
And for the powered case, the propulsors have accelerated the flow past the rudders, which sucks the free surface down. In Figure 12, the vertical velocity on the free surface and for a cutting plane just aft of the stern are presented from a view beneath the hull, showing that the velocity is relatively uniform between the rudders and the vertical velocity is nearly uni .
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From page 204... ...
The underlying unstructured solver has been developed to simulate turbulent boundary layer effects and is capable of performing rudder and propulsor induced maneuvering. The addition of nonlinear free surface capabilities is a necessary step towards the simulation of maneuvering surface vessels.
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From page 205... ...
This support is gratefully acknowledged. Special thanks to Toby Ratcliffe at Naval Surface Warfare Center Carderock Division for providing the data files for the experimental data and to Stephen Nichols at the Computational Simulation and Design Center for many hours of conversations about free surface issues, especially pertaining to the structured code UNCLE.
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From page 206... ...
L "An investigation of parallel implicit solution algorithms for incompressible flows on multielement unstructured topologies," Proceedings of the 38th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2000-0271, January 2000.
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From page 207... ...
D., and Lombard, C K., "Geometric conservation law and its application to flow computations on moving grids" AIAA Journal, Vol.
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From page 208... ...
The goal of the work that was presented was to develop efficient, robust and stable algorithms for the nonlinear free surface capabilities of our unstructured flow solver. In the future, we plan on analyzing the ability of our code to predict the forces on the hull form and the propulsors.
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From page 209... ...
Hence, we would suggest wrapping the grid around the transom for one element, so as to allow the viscous packing to terminate cleanly into the water surface, as shown in the diagram labeled Dry Transom Case. By doing this, no special considerations for either the free surface solver or the grid movement algorithm would be required, and the points in the free surface along the transom stern would still be allowed to move up and down to a small extent and would then be a better indication of whether the numerics suggest that the transom is truly dry.
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From page 210... ...
published it because improvements are under development in regards to computational efficiency.
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