A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation of incompressible flow

In large-eddy simulations of turbulence, the large scales of the flow are resolved by a numerical solution of the equations of motion for these scales, but the contribution of the fine-scale turbulence must be modeled. The stretched-vortex model estimates the influence of these unresolved subgrid-scale turbulence fluctuations on the resolved-scale velocities by using kinematic results for homogeneous, anisotropic turbulence consisting of locally straight, unidirectional vortex structures [D. I. Pullin and P. G. Saffman, Phys. Fluids 6 (5), 1994]. A new method is presented to dynamically determine the value of model constants related to the subgrid kinetic energy. For this purpose, a relation between the resolved-scale velocity structure function of second order and the energy spectrum is derived based on the kinematics of the model vortex structures, and therefore without the assumption of isotropy. Implementation of this relation using a local, circular average allows application of the model to wallbounded turbulent flows without special modifications. The resulting algebraic model is completely localized, i.e., no global flow quantities like the resolved-scale spectrum are required. This facilitates the application of the model in physical-space numerical methods using, for example, finite differences or Lagrangian-interpolation polynomials. The model includes an estimate of the subgrid kinetic energy, which is used to compute subgrid contributions to low-order turbulence statistics of the full flowfield. Results will be shown for the decay of kinetic energy and energy spectra of decaying, isotropic turbulence, for mean velocities, root-mean-square velocity fluctuations and turbulence-kinetic-energy budgets of channel flow up to a Reynolds number of approximately 23 000 (based on channel halfwidth and centerline velocity), and for mean velocities and turbulence kinetic energy of channel flow under spanwise rotation. The results are compared to unfiltered data from direct numerical simulations and experiment.

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