only minor dispersion, the large scale motion remains strongly coherent for many characteristic lengths downstream of the cylinder. Closer to the cylinder, the upper and lower separated shear layers constitute the transverse outer regions of the formation regime. These layers define the transition activity between the point of laminar separation and the initial formation of the turbulent vortices. Besides these shear layers, the fluctuating base pressure near the downstream stagnant region, directly behind the cylinder, strongly influences the large-scale vortex characteristics.

The near wake remains fully turbulent over a many diameters downstream. Our experimental evidence suggests that the shed vorticies of the Karmon street display little variation in their cross-sectional area. Zhou and Antonia (1993) found for moderate Reynolds numbers (Re) that the convection velocity slowly increased downstream to over 90% of the freestream velocity after 50 diameters. While the peak vorticity as well as the magnitudes of the Reynolds stresses gradual decay downstream, the respective statistical distributions remain essentially unchanged. The peak horizontal stress components occur at the vortex center, but the circumferential intensities closely mimic that of an Oseen vortex.

Three LES investigations of the cylinder near wake flow have been formally published above the low-Re regime. The first was a study by Kato et al. (1993) who concentrated on predicting the aerodynamic noise in the near wake using the finite element method. Due to their highly dissipative subgrid-scale turbulence model and their relatively coarse mesh of the wake region, agreement with the experimental data in terms of the spectral physics was obtained only at the very low frequency levels. A study by Mittal and Moin (1997) focused on contrasting the predictive accuracy of second-order central and fifth-order upwind-biased schemes for the convective terms of the governing equations. Both schemes gave similar results provided a 20–30 percent finer grid was generated when selecting the lower order scheme. 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 characteristics; such as the drag and base pressure coefficients, shedding and detection frequencies, peak vorticity, and the downstream mean velocity-defect and Reynolds stresses.

Figure 1: Large-Scale Physics of the Cylinder Near Wake.

The present paper will also discuss LES results of the turbulent wake motion resulting from trailing edge separation of the boundary layer of a NACA 0018 hydrofoil. The US Navy began utilizing the symmetric NACA 0018 section in 1970 to serve as their submarine control surfaces. This particular section as well as other symmetric thick sections can deliver high lift and low drag while maintaining strong structural integrity during complicated maneuvers. Thus, understanding both the instantaneous and mean character of the associated flow at various upstream conditions is crucial for effective use of these sections.

This material is the first in-depth numerical investigation of the fine-scale physics of the NACA 0018 section. The results were generated for upstream velocities at zero angle-of-attack. Previous numerical studies, notably by Hodge et al. (1978) and Sugavanam and Wu, (1980) (among others), used various phenomenological models to represent all the turbulent scales, thus their results can not provide useful details of the fine-scale physics.

To adequately resolve the turbulent wake flow of the cylinder and hydrofoil geometries, nonorthogonal O-type and C-type grid topologies were generated to facilitate control over the spatial resolution. The corresponding LES governing equations were solved in a generalized curvilinear coordinate framework. The dynamic SGS model of Germano et al. (1991) was reformulated for application to the curvilinear space. Since nonorthogonal topologies are often necessary to properly resolve the flow characteristics in many complex domains like these wake flows, the present formulation has extensive applicability.



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement