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Realizable versus non-realizable dynamic subgrid-scale stress models
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10.1063/1.4767538
/content/aip/journal/pof2/24/11/10.1063/1.4767538
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/11/10.1063/1.4767538

Figures

Image of FIG. 1.
FIG. 1.

The domain considered: (L x * L y * L z ) = (2π * 2 * π) according to the DNS of Moser et al. 38

Image of FIG. 2.
FIG. 2.

OpenFOAM DNS and DNS data of Moser et al.:38 (a) Normalized mean streamwise velocity U + = U 1/u τ, (b) Reynolds shear stress normalized by .

Image of FIG. 3.
FIG. 3.

OpenFOAM DNS and DNS data of Moser et al.:38 Reynolds streamwise normal stress (a), wall-normal stress (b), spanwise normal stress (c), and turbulent kinetic energy K (d) normalized by .

Image of FIG. 4.
FIG. 4.

Illustration of filtering and test filtering over 2Δ (left-side) and Δ (right-side).

Image of FIG. 5.
FIG. 5.

The standardized error e = [|E|/|L d |]2 of the DSM and LDM is shown in (a) for r = Δ T /Δ = 1 and r = 2. The LDM error is compared to the errors of the nonlinear NDM and WBDM for r = 2 in (b).

Image of FIG. 6.
FIG. 6.

Correlation coefficients defined in Sec. IV A. Results for the DSM and LDM are shown for r = 1 and r = 2 in (a), (c), and (e). The other plots show results obtained for the NDM and WBDM for r = 2.

Image of FIG. 7.
FIG. 7.

Instantaneous values of the dynamic constant C s along (π, y, π/2) for the DSM and LDM obtained from a priori analysis, where r = Δ T /Δ = 2.

Image of FIG. 8.
FIG. 8.

Comparison of the PDF of C s obtained for the DSM and LDM: (a) PDF, (b) PDF logarithm, where r = Δ T /Δ = 2. The PDFs were calculated for the horizontal slice at y + = 40.

Image of FIG. 9.
FIG. 9.

Realizations of the dynamic constants along (π, y, π/2) obtained from a priori analysis for r = 2: (a) NDM, (b) WBDM.

Image of FIG. 10.
FIG. 10.

PDFs of the dynamic constants of nonlinear models for r = 2: (a) NDM, (b) WBDM. The PDFs were calculated for the horizontal slice at y + = 40.

Image of FIG. 11.
FIG. 11.

The DNS backscatter is compared in (a) with the backscatter of the DSM and LDM for r = 1 and r = 2. In (b), the DNS backscatter is compared with the backscatter of the LDM, NDM and WBDM for r = 2.

Image of FIG. 12.
FIG. 12.

A posteriori DSM, LDM, NDM, and WBDM results for r = 2 in comparison with DNS: (a) mean streamwise velocity, (b) resolved Reynolds shear stress.

Image of FIG. 13.
FIG. 13.

A posteriori DSM, LDM, NDM, and WBDM results for r = 2 in comparison with DNS: (a) resolved Reynolds streamwise normal stress, (b) resolved Reynolds wall-normal stress, (c) resolved Reynolds spanwise normal stress, and (d) resolved turbulent kinetic energy.

Image of FIG. 14.
FIG. 14.

A realization of the dynamic LDM constant for r = 2 at the location (π, y, π/2).

Image of FIG. 15.
FIG. 15.

Instantaneous streamwise velocity contours at y + = 5 (left-hand side pictures) and y + = 50 (right-hand side pictures) obtained for DNS (upper row) and DNS on the 81 * 64 * 81 grid used for performing LES (lower row).

Image of FIG. 16.
FIG. 16.

Instantaneous streamwise velocity contours at y + = 5 (left-hand side pictures) and y + = 50 (right-hand side pictures) obtained for the LDM (upper row) and DSM (lower row).

Image of FIG. 17.
FIG. 17.

CPU time (in s) for performing a single time step of numerical simulation using the dynamic models considered for various grid resolutions. The data points are represented by circles and the fits are represented by solid lines. The DSM, NDM, and WBDM curves are shifted upwards by (0.5, 1.0, 1.5), respectively, to improve the visibility of the comparison between measured and modeled cost data.

Tables

Generic image for table
Table I.

CPU time (in s) for performing a numerical simulation over a single time step with the dynamic models considered for the specified grid resolutions.

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/content/aip/journal/pof2/24/11/10.1063/1.4767538
2012-11-27
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Realizable versus non-realizable dynamic subgrid-scale stress models
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/11/10.1063/1.4767538
10.1063/1.4767538
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