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Twenty-First Symposium on NAVAL HYDRODYNAMICS
A viable alternative for numerical simulation of complex turbulent flows is the large-eddy simulation (LES). This approach is gaining popularity over the traditional RANS simulation. The LES success rests primarily on the rapid advancements in supercomputer technology as well as the recent developments in the methodology itself. Unlike the full-scale modeling inherent in a RANS technique, the LES method requires resolution of the dominate energy-bearing scales of the turbulent field while modeling only the remaining finer eddies which tend toward homogeneous and isotropic characteristics. Demarcation between the resolved and modeled scales is formally instituted by spatially filtering the basic governing equations of the fluid motion. In most computations however, this filter is actually treated implicitly through the spatial resolution of the implemented grid. Those physics lying beneath the grid resolution embody the subgrid scales (SGS) of the turbulent field and usually encompass most of the equilibrium range of the kinetic energy. Under this premise of an energy balance, today's SGS models are much simpler in form and better delineate the turbulent physics of their assigned scales as opposed to the typical full-turbulence models used in the RANS computations.
Studies of the turbulent vortical formation behind bluff bodies and the subsequent transport of the vorticity downstream has many important and practical Naval implications. Resolution of the turbulent vortical characteristics within the bluff body wake poses an excellent challenge for the large-eddy simulation. Except for only minor dispersion, the large scale motion usually remains strongly coherent for many characteristic lengths downstream of the bluff body. Since the impetus of LES is full resolution of the large scale motion, the results can provide specific information regarding the cyclic formation and downstream transport of the vortical motion including the local turbulent physics.
The formation and the downstream transport of the Strouhal vortices in the near wake of a circular cylinder is an excellent example of a difficult bluff body flow. The vortices themselves derive most of their large-scale vorticity from the separated shear layers and they organize downstream to form the well-known Karman vortex street. The upper and lower separated shear layers constitute the transverse outer regions of the formation regime. Both layers lie between the point of separation and the initial formation of the shed Strouhal vortices. Besides these shear layers, the fluctuating base pressure near the downstream stagnation location contributes to the Strouhal vortex formation as well. A sketch illustrating these features is depicted in Figure 1.
Figure 1: Sketch of the Primary Strouhal Vortex and Secondary Eddies in the Cylinder Wake Formation Region.
Our understanding of the cylinder shear layer physics improved significantly due to the experimental investigation by Bloor (1), Unal and Rockwell (2) and Wei and Smith (3). Bloor hypothesized that transition from laminar separation to turbulent vortex formation occurs within the separated boundary layer. This process occurs in two phases. Soon after separation, two-dimensional small-scale instabilities arise within the separated layer that amplify into Tollmien-Schlichting waves and eventually lead to turbulence. Due to the three-dimensional nature of the flow, these instabilities experience substantial spanwise distortion which also contribute to the transition mechanism. Unal and Rockwell also found high-frequency instabilities to exist, but for only Re≥1900 with pronounced amplification at specific Reynolds numbers of Re= 3400 and Re=5040. At the latter Re in particular, they showed the spectral amplitudes to vary significantly across the shear layer at the predominant frequencies of the small-scale instabilities as well as the frequencies of the much larger scale Strouhal vortex.
Through flow visualization testing, Wei and Smith proposed a different phenomena for the separated shear layer physics. They observed creation of small-scale secondary vortices between separation and the initial large-scale Strouhal vortex formation. These secondary structures evolve from the same two-dimensional instabilities described by Bloor. The Strouhal vortices receive the majority of their vorticity from the secondary structures which