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Graduate Aeronautical Laboratories
Caltech
Abstract-
The stretched-vortex model estimates the influence of the 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. Saffmann, 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 wall-bounded 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 22800 (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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