The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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New Viscous and Inviscid CFD Techniques for Ship Flows
New Viscous and Inviscid CFD Techniques for Ship Flows
Pages 185-210
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From page 185... ...
Methods for potential flow calculations including first and higher order theories with linear or non-linear free surface boundary conditions are presented. The importance of higher order effects and nonlinearity is discussed.
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From page 186... ...
as r -- (3) The source density ~ is to be determined from the boundary conditions on the hull and free surface.
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From page 187... ...
= ah + g(~x~xz + ~Y.YZ + ~z~zz) 6h Therefore the linearized free surface boundary conditions are xhx + Why - fez + ~X5hx + Achy + (~Xzhx+~yzhy ~zz)
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From page 188... ...
The free surface sources are moved to the previous wavy surface in every step and the boundary condition is applied there. This means that the hull surface has to change as well, so a special panelization procedure has been introduced in the program.
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From page 189... ...
= ~° + ~~: + Ann (22) This is fitted in the least squares sense to the values of source density at the control points of the M adjacent panels.
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From page 190... ...
In the present work, the magnitude of the second derivative terms related to the curvature and linear variation of source density are assumed to be small and vanish rapidly during the iteration. Therefore the second order derivative terms are calculated from a source velocity which corresponds to the flat panel with constant source density.
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From page 191... ...
Interesting comparisons between all three methods may thus be made. 2.3.1 Grid Dependence Study Since one of the most important questions in connection with the present methods is the dependence of the solution on the panel distribution, particularly on the free surface, a systematic variation was carried out.
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From page 192... ...
From run No 7 to run No 8, part of the free surface region was moved from the bow to the stern. The wave resistance did not change at Fn = 0.266, whereas it was increased by 10% viva at Fn = 0 45 There were no systematic changes in the panel distribution on the hull, but two slightly different hull panel distributions were used in the successive tests.
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From page 193... ...
.1 ,~^ 0.2 En i l ,, 0.3 Predicted wave resistance compared with measured residual resistance. SSPA Ro-Ro ship, medium bulb A common problem in most evaluations of wave resistance calculations is that the wave pattern resistance is seldom measured.
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From page 194... ...
The absolute values of the wave resistance, Fig 9, are not as accurate in all cases, but the method is able to rank the cases in the right order. 3 VISCOUS FLOW METHODS Although r as indicated in the Introduction' a number of different methods for computing the viscous flow (boundary layer/wake)
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From page 195... ...
the components based on unit vectors parallel to the covariant base vectors go, whose magnitude igi~ is denoted h(i) , gij is tlhe contravariant metric tensor and r i j is a Christoffel symbol of the second kind.
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From page 196... ...
If wall functions are used as the inner boundary condition for the flow, the k-E model is used throughout. The transport equations for k and e are as follows auk + h(i)
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From page 197... ...
In most ship flows there is a predominant flow direction usually approximately aligned with the x1 direction of the grid. Under these circumstances the term a 1a 1¢ may be neglected and the elliptic equations (53)
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From page 198... ...
u3 = ue - Be(pE - pp) where the ui is the solution of the momentum equations using the pressure from the previous time level and B' is the coefficient for the orthogonal part of the pressure gradient in the i-th momentum equation.
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From page 199... ...
are solved using pressure and coefficients based on velocities from previous time level. The algebraic equation systems are solved using a fixed number of line by line sweeps with a tri-diagonal matrix algorithm.
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From page 200... ...
. The components serve as boundary conditions for the momentum equations.
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From page 201... ...
The systematic variations were made using four different grids to investigate the grid dependence in the three coordinate directions. For all four grids the calculation domain was the same, that is the inlet plane was placed at the midship, 2x/L = 0.0; the outlet plane at 2x/L = 10 in the far wake; the outer edge boundary on a circular cylinder located one ship length from the centre line; and the two innermost grid points were located within the logarithmic layer.
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From page 202... ...
Velocity profiles at 2x/L = 0.8 Fig 15 Grid dependence. Iso-wakes at Waterline, mid-girth and keel 2x/L = 0.9 202
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From page 203... ...
The pressure and friction velocity ° variations along the water line and the keel from the results of grid 2 and 3 are shown in Fig 16. Grids 1 and 4 are not shown in this figure, since their (xl, x2)
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From page 204... ...
For each calculation the boundary conditions at the outer edge and at the inflow (outside the boundary layer) were calculated from the potential flow solution.
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From page 205... ...
The normal component V and the transverse component W were assumed to be zero. Outside the boundary layer the distribution of U was calculated using Hess & Smith's potential flow calculation method.
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From page 206... ...
It can be seen from the figures that in the stern region the calculations overpredict the wall shear velocity along the water line, but underpredict it along the keel. This indicates that the calculated velocity profiles in these regions might differ somewhat from the measured profiles.
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From page 207... ...
Preliminary results from the latest version of NASPAR, where the wall law is removed, indicate that the prediciton of the flow near the keel can be much improved in this way. Measurements Colculotion Iso-wakes measurements x=O.R u/U=0.6, 0.7, 0.8, 0.9, 0.95 calculation x=0.81 q/U=0.6, 0.7, 0.8, 0.9, 0.95 Measurements Colculation :~ / Iso-wakes measurements x= 0.9, u/U=0.6, 0.7, 0.8, 0.9, 0,95, 1.0 calculation x=0.&9, q/U=0.6, 0.7, 0.8, 0.9, 0.95 Iso-wakes at two stations 4 FINAL COMMENTS Methods for computing free surface potential flows as well as complex viscous flows have been presented.
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From page 208... ...
Kim, K.-J. & Larsson, L., "Comparison Between First and Higher Order Methods for Computing the Boundary Layer and Viscous Resistance of Arbitrary Ship Hulls", International Symposium on Resistance and Powering Performance, Shanghai (1989)
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From page 209... ...
2 Ni, S.Y., Kim, K.-J., Xia, F & Larsson, L., "A Higher Order Panel Method for Calculating Free Surface Potential Flows with Linear Surface Boundary Conditions", International Symposium on Resistance and Powering Performance, Shanghai (1989)
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From page 210... ...
The experiments should include detailed velocity measurement, such as the ones by Fry and Kim, presented at the 15th Symposium on Naval Hydrodynamics using an LDV, and flow visualization to find the stagnation point. The numerical part should include free surface as well as viscous flow calculations.
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