On the Properties
of Similarity Subgrid-Scale Models as
Deduced from Measurements
in a Turbulent Jet
Shewen Liu, Charles Meneveau and Joseph Katz
Department of Mechanical Engineering
The Johns Hopkins University | Baltimore, MD 21218
ABSTRACT: The
properties of turbulence subgrid-scale stresses are studied using
experimental data in the far-field of a round jet, at a Reynolds
number of Rl ~ 310. Measurements are performed using two-dimensional
Particle Displacement Velocimetry. Three elements of the subgrid-scale
stress tensor are calculated using planar filtering of the data. Using a-priori
testing, eddy-viscosity closures are shown to
display very little correlation with the real stresses, in accord with earlier
findings based on direct numerical simulations at lower Reynolds numbers. Detailed
analysis of subgrid energy fluxes and of the velocity field decomposed into
logarithmic bands, leads to a new similarity subgrid-scale model. It is based
on the `resolved stress' tensor Lij, which is obtained by filtering products
of resolved velocities at a scale equal to twice the grid scale. The correlation
coefficient of this model with the real stress is shown to be substantially
higher than that of the eddy-viscosity closures. It is shown that mixed models
display similar levels of correlation. During the a-priori test, care is taken
to only employ resolved data in a fashion that is consistent with the information
that would be available during Large-Eddy-Simulation. The influence of the
filter shape on the correlation is documented in detail, and the model is compared
to the original similarity model of Bardina et al. (1980). A relationship between
Lij and a nonlinear subgrid-scale model is established. In order to control
the amount of kinetic energy backscatter, which could potentially lead to numerical
instability, an ad-hoc weighting function that depends on the alignement between
Lij and the strain-rate tensor, is introduced. A 'dynamic' version of the model
is shown, based on the data, to allow for a self-consistent determination of
the coefficient. In addition, all tensor elements of the model are shown to
display the correct scaling with normal distance near a solid boundary.
Journal of Fluid Mechanics, 275, pp. 83-119
DOI: 10.1017/S0022112094002296 | Full PDF
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