Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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High-Incidence and Dynamic Pitch-Up Maneuvering Characteristics of a Prolate Spheroid-CFD Validation
High-Incidence and Dynamic Pitch-Up Maneuvering Characteristics of a Prolate Spheroid-CFD Validation
Pages 609-623
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From page 609... ...
INTRODUCTION Despite its simple geometry, flow around a prolate spheroid in maneuvering carries a rich gallery exhibiting a variety of complex three-dimensional turbulent shear flows, featuring stagnation flow, highly three-dimensional boundary layer under the influence of strong pressure gradients and streamline curvature, cross-flow separation, and formation of free-vortex sheet and ensuing stream-wise vortices. All these features of spheroid flows are the archetypes of flows around airborne and underwater bodies at incidence or in maneuvering, warranting an in-depth study.
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From page 610... ...
crossbow in the boundary layer, free vortex sheet, and stream-wise vortices. The whole phenomena depicted here are an embodiment of the so-called "crossflow" or"open" separation, the significance of which can be recognized from the fact that the structure of separation and its change with incidence angle greatly affect maneuvering characteristics of the body such as forces and moments acting on it.
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From page 611... ...
They found that the Reynolds stresses are largely aligned with the strain rates inside the boundary layer at a low incidence angle (a = 10°~. However, they become grossly misaligned almost everywhere else, especially along the free vortex sheet and near the vortices on the leeward side of the body and at high incidence angle.
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From page 612... ...
model, one directly solves the transport equation for an effective viscosity, v (Spalart and Allmaras, 19941. The SA model has become rapidly popular especially in the aerospace community due to its commendable performance for boundary layer flows subjected to adverse pressure gradient.
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From page 613... ...
The baseline model, which will be called RSTM-1 hereafter, was implemented in an unstructured mesh based finite-volume RANS solver, and has been been validated for a number of complex threedimensional internal and external flows (Kim, 2001; Kim, 2002~. The unique features of the implementation include: an isotropic turbulent diffusion models for Reynolds-stress and dissipation equations, a highorder dissipation term designed to prevent decoupling of Reynolds stresses, and mean velocity field arising from co-located, cell-centered finite volume discretization scheme.
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From page 614... ...
When fine meshes are used, the wall boundary conditions for the mean velocity and turbulent quantities essentially exploit no-slip condition at walls. For ce, we "fix" the asymptotic value of ce as y ~ O at wall-adjacent cells, using: 6v pyp2 where yp is the distance from the wall to the cell center, andp=0.075.
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From page 615... ...
The overall trends shown by the different turbulence models remain largely unchanged from what were seen earlier. Particularly noteworthy is that KO-2 and RSTM-2 models better predict the actual separation locations than the locations of minimum Cf.
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From page 616... ...
Furthermore, atx/L = 0.772, the KO-2 model appears to capture, far closer than other models, the small kink caused by a secondary vortex above the surface, which was found to occur at o = 140° secondary _ / y separation line reattachment line windward AL 0.600 x/L = 0.772 primary separation line Fig. 6 Wall limiting streamlines showing the pattern of the crossflow separation at a = 20° - based on the KO-2 prediction (a)
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From page 617... ...
The crossbow becomes progressively stronger in the order of SA, SST, KO-1, and KO-2 models. Thus far, we have looked at the surface quantities predicted with the fine mesh without using wall functions.
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From page 618... ...
distributions at a = 20° predicted using wall functions Comparisons of the coarse mesh results shown here and with the fine mesh results presented earlier indicate that, insofar as high-Reynolds number flows are concerned, CFD predictions based on wall functions are perhaps better than has been commonly believed. A similar conclusion was made by Kim (2002)
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From page 619... ...
Steady lift and pitching moment predictions The lift acting on slender bodies like prolate spheroids is characterized by a nonlinear increase of lift with incidence angle. The nonlinear lift is often called "vortex" lift because the augmented lift is due to the low pressure at the core of the vortices which x/~=n772 .;2 K0-2o 0 0.05 0.1 0.15 n 0.1 >0.08 non 0.04 0.02 I_ 0.1 0.15 Fig.
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From page 620... ...
The lift predictions are largely consistent with the behaviors of the surface quantities discussed before. Interestingly, the predicted pitching moment coefficients shows an opposite trend.
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From page 621... ...
SUMMARY AND CONCLUSION The turbulent shear flow around a 6:1 prolate spheroid at the Reynolds number of 4 x 106 was studied numerically using the Reynolds-averaged NavierStokes equations. The study covered the steady flow for a full range of incidence angle (a = 10° ~ 30°)
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From page 622... ...
Kim, S.-E., "Unstructured Mesh Based Reynolds Stress Transport Modeling of Complex Turbulent Shear Flows," AIAA Paper 2001-0728, 2001 Kim, S.-E., "Assessment of Eight Turbulence Models for a Three-Dimensional Boundary Layer Involving Crossflow and Streamwise Vortices," AIAA Paper 2002-0852, 2002 Luo, J and Lakshiminarayana, B., "Analysis of Streamline Curvature Effects on Wall-Bounded Turbulent Flows," AIAA Journal, Vol.
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From page 623... ...
and Simpson, R.L., and Chesnakas, C.J., "Unsteady Crossflow Separation Location Measurements on a Maneuvering 6:1 Prolate Spheroid," AIAA Journal.
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