Twenty-Second Symposium on Naval Hydrodynamics (1999) / Chapter Skim
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12 Bluff Body Hydrodynamics
12 Bluff Body Hydrodynamics
Pages 665-707
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From page 665... ...
ABSTRACT The present investigation discusses the resolution of the turbulent vertical motion behind two bluff bodies. The LES results of the cylinder wake at Reynolds number of 5,600 showed good comparisons to the published experimental data in terms of the global and local wake characteristics such as the drag and base pressure coefficients, shedding frequencies, near wake structure, and the Reynolds stresses.
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From page 666... ...
Using a curvilinear coordinate form of the basic LES formulation and dynamic SGS model, Jordan and Ragab (1998) showed excellent comparisons to the published experimental data in terms of both the global and local wake charactenstics; such as the drag and base pressure coefficients, shedding and detection frequencies, peak vortici~, and the downstream mean velocitydefect and Reynolds stresses.
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From page 667... ...
This model gives the correct asymptotic behavior of the turbulent stresses when approaching solid walls and can suitably distinguish between laminar and turbulent flow regimes. For the present application, the SGS model was transformed to the computational space.
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From page 668... ...
. This third operation gave two resolvable tensors; a modified Reynolds stress tensor ~,~ -=k q~,( = uj U -uiuk and a modified Leonard tensor ~ -k _ _ ~ = Ui U -Ui Uk (6)
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From page 669... ...
Before presenting the LES results of the near wake region, questions regarding significant contributions from SGS model must be addressed relative to the inherent artificial dissipation produced when using third-order upwind-biased differences. To appreciate the model's quality, the investigation should be local.
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From page 670... ...
5 of the near wake, in terms of the magnitude of vorticity Ail, clearly displays the formation region structure, Strouhal vortices, and the large-scale streamwise structures connecting the alternating shed vortices. The latter elongated filaments have been experimentally viewed and termed as "fingers" (Gerrard, 1978~.
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From page 671... ...
Downstream Location (referenced to cylinder centerline) of Peak Reynolds Stresses and Base Pressure Coefficient as a Function of Reynolds Number (refer to Table 1 for the reference source of the data points)
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From page 672... ...
Contours of Reynolds Stresses; (a) Streamuise, (b)
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From page 673... ...
Also, the Reynolds stress statistics share equivalent orders-of-magnitude and similar distributions over the entire range of subcntical Reynolds numbers. Finally, the location of the peak Reynolds stresses within the formation region scale according to the magnitude of the downstream base pressure coefficient.
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From page 674... ...
The spatial distributions shown in Figure 6 of the phase-averaged Reynolds stresses will be useful for understanding the momentum budget for the cylinder wake vortices in the formation region. The results reported in Table 1 and Figure 7 concerning the magnitude and location of maxima suggest that the spatial distribution plots are reasonably quantitatively accurate; comparison of cross-wake profiles of the stresses with observed data would strengthen this point.
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From page 675... ...
(1998) , "A LargeEddy Simulation of Me Near Wake of a Circular Cylinder," Journal of Fluids Engineering, V120, No.
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From page 676... ...
is the relative velocity, Xi is the velocity potential of the irrotational flow about the body, dS is the elemental surface area, and w is the vonicity. It is seen that Fi 676 9 +2 p~D3 6 is represented as the sum of its three constituent components: An inviscid inertial force, vector sum of the normal surface stresses induced by vortici~ in the fluid, and the shear force or slain friction Neither the above decomposition nor the interpretation of the resulting elements is unique.
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From page 677... ...
This was due to the complexity of the problem rather than due to the lack of imagination of the model makers. Even in a sinusoidally oscillating flow (a relatively more manageable unsteady flow)
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From page 678... ...
However, The experience of the past 50 years has also shown that the MOJS equation still represents the best twocoefficient fit to the measured force. In the so-called drag/inertia regime, it produces relatively poor results where the error (defined, e.g., as the RMS value of called "Morison equation.
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From page 679... ...
asserted that the viscous drag force and the inviscid inertia force operate independently and therefore it is possible to divide the measured time-dependent force into two distinct components: an inviscid inertial force, either corrected or uncorrected for a weakly non linear flow field (19) , and a viscous drag force.
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From page 680... ...
Figures 1 and 2 show representative measured forces for a sinusoidally oscillating flow about a circular cylinder. Also shown in these figures are the traces of force calculated using Eq.
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From page 681... ...
it reproduces the measured force with remarkable accuracy (the rms value of the residue, normalized by the rms value of the measured force remains less than 10 percent for all smooth and rough cylinder data within the range of Re, Kc, and k/D values encountered in Sarpkaya's experiments (17-18, 21-27)
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From page 682... ...
5 through 12 for four smooth and four rough cylinders. Each figure contains four curves representing the measured force, the prediction of the MOJS equation, the prediction of the modified MOJS equation (i.e., Eq.
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From page 683... ...
J Offshore Resistance In Harmonic Flow About Smooth and Rough Circular Cylinders at High Reynolds Numbers,.
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From page 684... ...
1. Nonnalized measured force, force calculated from Eq.
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From page 685... ...
and (16) with each other, with the measured force, and with the prediction of the MOJS equation The residue is the difference between the predictions of Eq.
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From page 686... ...
Fig. 10 Normalized force versus time for Kc = 12.7, Re = 62,380, k/D = 1/50.
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15 Nonnalized force versus lame for a bluff plate with Kc = 6.5 and Re = 192,000. New Mode ~ Measured Force A, MOJS L Fig.
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Normalized force versus time for Kc=15.4, Re=18,560, k/D=0.0 (data from (1~.
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From page 689... ...
The measured forces are all from the author's experiments (see Refs.
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From page 690... ...
(14) and it represents the ratio of the deviation of the maximum inertial force from its ideal value to the maximum drag force (for a circular cylinder)
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From page 691... ...
examined constant thickness wings with 6:1 elliptical nose, measured static pressure distribution and provided oil-film flow visualization. They carried out threedimensional hot-wire measurements of the mean velocity and Reynolds stresses in the constant thickness region along the appendage.
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From page 692... ...
ence of modeling errors by employing a near-wall Reynolds stress closure based on a combination of the near-wall Reynolds stress model of Shima [13] and the pressure-strain correlations of Speziale & al.
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From page 693... ...
Therefore, the essential inability of eddy viscosity closures to simulate anisotropic turbulence can explain their bad performances on flows contain ing recirculating regions or intense vortices, since the turbulence anisotropy strongly influences the magni tude of longitudinal vorticity [16~. With the need to resolve anisotropy taken for granted, the main choice for new statistical turbulence closures is between non linear eddy-viscosity models and second-moment clm surest The explicit non-linear eddy-viscosity mod els are very attractive because they can be seen as the most natural evolution from linear eddy-viscosity models.
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From page 694... ...
In the present model, the function ¢1 and ¢2 proposed by Shima are kept with only a small modification on ¢1 by limiting the ratio P over c. The coefficient as well as the kinematic viscosity ~ are altered near the wall in order to obtain a good prediction for the zero pressure gradient boundary layer flow.
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From page 695... ...
, t34~) to models requiring the solution of Reynolds Stress Transport Equations (Shima's model t18]
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From page 696... ...
. At the external boundary, 71 = T7MAX, velocity profiles and Reynolds stress components are specified by a previous infinite flat plate computation.
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From page 697... ...
Both models predict a primary line of separation located at the intersection between the three-dimensional surface and the flat plate. However, the low-shear stress line which was observed in the experiments between the wing and the primary line of separation is only visible in the second-moment solution, indicating that the secondary motion predicted by the anisotropic turbulence closure is far more intense.
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From page 698... ...
The most interesting feature is the dramatic difference between the two turbulence closures concerning the inner line of low streamwise shear stress. Whereas the k-~ solution does not reveal any second line of convergence, the anisotropic Rij-w solution Figure 8: Surface oil-flow visualization on the flat plate (from [35)
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From page 699... ...
A local maximum is located in the region where the distorsion of U/Uref contours occurs, indicating that this local peak of turbulence is probably due to the increased mixing of the boundary layer fluid by the horseshoe vortex. The k-~ solution exhibits a large zone of high normal stress located in the corner between the wing and the flat plate.
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From page 700... ...
All the velocity and Reynolds stress components are given in their respective local free-stream coordinate axes. In the computations, the free-stream coordi (b)
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From page 701... ...
Solid line: Reynolds-stress model; dashed line: k-~ model; symbols: experiment 701
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From page 702... ...
Solid line: Reynolds-stress model; dashed line: k-e model; symbols: experiment Figure 23: Normal stress components in free-stream coordinates at station 5. Solid line: Reynolds-stress model; dashed line: k-~ model; symbols: experiment ^~ ~ ~ ~ Yrr instance, at station 5 (Fig.
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From page 703... ...
This behaviour is well captured by the anisotropic model even if the computed normal stress is slightly underevaluated in the outer region of the boundary layer. 4.5.3 Turbulent shear stresses Figs.
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From page 704... ...
This new Reynolds-stress transport model accurately reproduced the anisotropic behaviour of the normal Reynolds stress components, which led to a clear amplification of the longitudinal vorticity. Moreover, the Reynolds stress anisotropy was also responsible for the strong augmentation of the shear stress uw close to the horizontal plane.
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From page 705... ...
Launder, "Improvments in near-wall Reynolds stress ~nodelling for complex flow geometries," Proceedings of the 10th Turbulent Shear Flows, 1995, pp.
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From page 706... ...
Sung and M.J. Griffin Naval Surface Warfare Center, Carderock Division, USA There is no doubt that of all He turbulence models, the Reynolds Stress model contains He most physics and should be pursued.
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From page 707... ...
Consequently, other important features such as the distinction of high shear stress and low shear stress regions, the position of the pigment accumulation line, etc., captured by the Reynolds stress transport model, are unable to be predicted with nonlinear models. Predictions with a Reynolds stress transport model given by A
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