Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Evaluation of Eddy Viscosity and Second-Moment Turbulence Closures for Steady Flows Around Ships
Evaluation of Eddy Viscosity and Second-Moment Turbulence Closures for Steady Flows Around Ships
Pages 453-469
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From page 453... ...
Despite the relative geometric simplicity of the body, the flowfield around this hull is the result of many complicated features in~rolving convergence and divergence of streamlines, a strong thickening of the boundary layer due to rapid changes in cross-sectional shape leading to the development of an intense longitudinal vortex which is slowly relaxed in the wake at large distances downstream from the ship. A more accurate understanding of the flow is provided by the analysis of the limiting streamlines (Figure 1 from t14~.
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From page 454... ...
Here again, their results clearly established the superiority of second-moment closures over simpler isotropic eddy viscosity models for this kind of applications, even if, on the contrary of the previous contributors, the longitudinal vorticity appeared to be slightly underestimated. The objectives of the present study are twofold: · The analysis in the first part will be conducted under the general context of isotropic eddy viscosity turbulence closures.
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From page 455... ...
to models requiring the solution of Reynolds Stress Transport Equations (Shima's model t7i, Craft & Launder's model presently in test (1643. To avoid any wall-function boundary conditions which turn out to be unacceptable when three-dimensional flows are considered, near-wall low-Reynolds number treatments are sytematically implemented in the aforementionned turbulence models.
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From page 456... ...
(14) 4 The Second Moment Closures Difficulties encountered by eddy-viscosity models in modelling complex flows are most often related to models' inability to account for the selective amplification or attenuation of different Reynolds stresses by curvature-related strain components.
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From page 457... ...
On complex three-dimensional flows, second-moment closures will be probably superior because of the exact representation of stress production which enables realistic interactions between normal stress anisotropy and shear-stress components. Here and there, very promising computational studies employing second-moment closures on highly complex three-dimensional flows are emerging (~5]
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From page 458... ...
In the momentum equations, the predominant role played by the source terms in absence of turbulent 458 viscosity makes it necessary deep modifications of the original numerical algorithm. When the Reynolds stress is treated implicitly in the momentum equations when using eddy-viscosity models, it appears explicitly when second-moment closures are used.
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From page 459... ...
~ ~ Ui = J~uj (44) With this special treatment of turbulent stresses gradients in the pressure equation source term, the discrete link between pressure and turbulence gradients is enforced, and a first source of numerical oscillations is avoided when pressure and turbulent correlations gradients compete in the momentum equations.
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From page 460... ...
(48) This joint under-relaxation of pressure and turbulent stresses will maintain the discrete equilibrium for which the pressure is designed in the modified Solve the second-moment transport equations: pressure equation.
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From page 461... ...
K-Epailon(Chen-Pstel) Figure 3: Chen & Patel k—~ model - Computed wall flow Figures 3, 4, 5 and 6 show the limiting streamlines on the hull with the various turbulence closures.
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From page 462... ...
It is important to notice that the iso-velocity contours are regular, which confirms the efficiency of the proposed modifications, except near the symmetry plane where computational grid is not fine and regular enough to capture rapid changes of flow field due to the longitudinal vortex. These conclusions are illustrated more convincingly by Figures 11, 12, 13, 14, 15 and 16 which show the axial and vertical velocity profiles at different longitudinal stations and depths.
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From page 463... ...
W 463 1.0 _ 0.5 _ 0.0 _ ~ ~ ~ I ~ .. I 0~00 0.02 0.04 I 0.06 0.08 0.10 0.12 y Figure 12: Half-body- Vertical velocity profiles at x/L = 0.941 as functions of y for several depths: symbols are from measurements
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From page 464... ...
0.00 0.02 0.04 0.06 0.08 0.10 0.12 Figure 14: Half-Body- Vertical velocity profiles at x/L = 0.978 as functions of y for several depths: symbols are from measurements 2.0 W ..
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From page 465... ...
. 0.00 0.02 0.04 0.06 0.08 0.10 0.12 y Figure 18: Full-body - Vertical velocity profiles at x/L = 0.941 as functions of y for several depths: symbols are from measurements ~ .s 1 ~ o.o' : ....
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From page 466... ...
Deep modifications of the original algorithm have been designed to maintain the discrete equilibrium between the various source terms involved in the momentum equations. These modifications made it possible to implement a second-moment closure into a Poisson pressure RANSE solver without introducing any apparent turbulent viscosity.
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From page 467... ...
Practical near-wall 21 turbulence models for complex flows including separation.
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From page 468... ...
AUTHORS' REPLY lathe modelization of Reynolds Stress Transport equations requires the development of closures for several complicated turbulent correlations (pressure-strain, diffusion, and dissipation correlations) mainly based on a local turbulence homogeneity hypothesis.
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From page 469... ...
and robust isotropic eddy-viscosity based turbulence models and the future Large Eddy Simulations, as long as high Reynolds number flows on complex geometries are considered. But, it is still difficult to evaluate their actual potentialities because of a lack of countervalidations on flows in realistic configurations.
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