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TECHNICAL PAPERS

A Priori Assessments of Numerical Uncertainty in Large-Eddy Simulations

[+] Author and Article Information
Stephen A. Jordan

 Naval Undersea Warfare Center, Newport, RI 02841jordansa@npt.nuwc.navy.mil

J. Fluids Eng 127(6), 1171-1182 (Apr 26, 2005) (12 pages) doi:10.1115/1.2060735 History: Received December 15, 2004; Revised April 26, 2005

Current suggestions for estimating the numerical uncertainty in solutions by the Large-Eddy Simulation (LES) methodology require either a posteriori input or reflect global assessments. In most practical applications, this approach is rather costly for the user and especially time consuming due to the CPU effort needed to reach the statistical steady state. Herein, we demonstrate two alternate a priori graphical exercises. An evaluation of the numerical uncertainty uses the turbulent quantities given by the area under the wave number spectra profiles. These profiles are easily constructed along any grid line in the flow domain prior to the collection of the turbulent statistics. One exercise involves a completion of the spectrum profile beyond the cutoff wave number to the inverse of Kolmorgorov’s length scale by a model of isotropic turbulence. The other extends Richardson Extrapolation acting on multiple solutions. Sample test cases of both LES solutions and direct numerical simulations as well as published experimental data show excellent agreement between the integrated matched spectra and the respective turbulent statistics. Thus, the resultant uncertainties themselves provide a useful measure of accumulated statistical error in the resolved turbulent properties.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch showing the resolved (u′)r and total (u′) turbulence intensities under the energy spectrum curve

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Figure 2

Spectral energy of DHI turbulence (19) and example evaluation of the numerical uncertainty. (a) Dimensional energy spectra. (b) Percent numerical uncertainty.

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Figure 3

LES grid-convergence study of DHI turbulence (20) and evaluation of the numerical uncertainty. (a) Dimensional energy spectra. (b) Numerical uncertainty.

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Figure 4

SGS model study of DHI turbulence (20-21,23) and evaluation of the numerical uncertainty. (a) Dimensional energy spectra. (b) Numerical uncertainty.

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Figure 5

DK model of isotropic turbulence (19) and model evaluation of the numerical uncertainty. (a) Dimensionless energy spectra. (b) Numerical uncertainty.

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Figure 6

Profile of subrange coefficient (α3∕2ε) and DK model results using two definitions for the dimensionless energy wave number (k̂ε). (a) Coefficient α3∕2ε. (b) Dimensionless spectral energy.

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Figure 7

Spectral energy and Kolmorgorov coefficient for estimating numerical uncertainty of grid turbulence at low-wave number cutoff. (a) Dimensionless spectral energy. (b) Kolmorgorov coefficient.

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Figure 8

Resolved-model spectra of grid-turbulence at high-wave number cutoff

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Figure 9

Two ideal examples for estimating the numerical uncertainty of LES resolved grid turbulence. (a) Low wave number cutoff. (b) High wave number cutoff.

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Figure 10

Match and numerical uncertainty between measurement spectral energy data and DK model. (a) Energy spectrum. (b) Numerical uncertainty.

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Figure 11

Resolved-model match of energy spectrum and numerical uncertainty of the turbulent channel. (a) Energy spectrum. (b) Numerical uncertainty.

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Figure 12

Spectral energy and resolved-model match inside the formation region of the cylinder near wake; Re=3900. (a) Resolved energy spectrum. (b) Resolved-model match.

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Figure 13

Estimates of numerical uncertainty for DNS computation inside the formation region of the cylinder near wake (r∕D=1.5); Re=3900. (a) Streamwise intensity. (b) Dissipation.

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Figure 14

Example spectrum profile (26) showing match with the DK spectrum model

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Figure 15

Spectral energy for estimating numerical uncertainty of turbulent wake at low-wave number cutoff. (a) Spectral energy. (b) Resolved-model match.

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Figure 16

Improved resolved-model match of wake spectral energy through grid refinement. (a) Spectral energy. (b) Numerical uncertainties

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