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The oriented-eddy collision model
The physical and mathematical foundations of the Oriented-Eddy Collision turbulence model are provided through a discussion of the Reynolds averaged Navier-Stokes (RANS) equations, probability density functions (PDF), PDF collision models, Reynolds stress transport models (RSTM), and two-point correlations. Behavior of the Oriented-Eddy Collision turbulence model near solid boundaries is examined in depth. The Oriented-Eddy Collision turbulence model treats turbulence in a novel way: the average behavior of a turbulent flow can be modeled as a collection of interacting fluid particles, or eddies, which have inherent orientation. The model is cast in the form of a collection of Reynolds stress transport models. Underlying this approach is a unique PDF collision model that departs from more common PDF methods as it includes orientation information along with the usual position and velocity information. This adds important physics and differentiates it from other PDF collision treatments that return RANS-type models. To operate in physical space, the model is cast as a unique decomposition to the two-point velocity correlation transport equation. The Oriented-Eddy Collision turbulence model accurately captures fast pressure-strain in rapid distortion, which is a major shortcoming of nearly all Reynolds stress transport models. The Oriented-Eddy Collision turbulence model contains no special provisions to satisfy realizability, and maintains frame and coordinate invariance. Models to account for turbulent dissipation, diffusion, and system rotation are presented with canonical benchmark flows for validation. Inhomogeneous, anisotropic cases are also considered. Model to capture non-local pressure effects near solid boundaries are proposed in the form of turbulent eddy reorientation schemes with associated Reynolds stress treatments. These schemes aim to capture the asymptotic approach of the Reynolds stress components and basic turbulent, wall-bounded flows are investigated as a means of validation. Boundary conditions for solid and shear-free surfaces are discussed and several alternatives to the standard viscous diffusion model proposed.
Martell, Michael B., "The oriented-eddy collision model" (2012). Doctoral Dissertations Available from Proquest. AAI3518387.