No abstract

A new dynamic subgrid-scale (SGS) mixed model is proposed for large-eddy simulation of turbulent flows. This model is based on the decomposition of the SGS stress terms into the modified Leonard, modified cross and modified SGS Reynolds stress terms. In this model, the modified Leonard term is computed explicitly. The modified cross term and modified SGS Reynolds stress are assumed to be proportional to a new term, the form of which is comparable to the generalized central moment, derived as an extension of the filtered Bardina model proposed by Horiuti [J. Phys. Soc. Jpn. 66, 91 (1997)]. Using a linear combination of this new term with the Smagorinsky model for the modified SGS Reynolds stress, the proposed model contains two model parameters, which are computed dynamically. Two formulations for the test-filtered SGS stress reported by Zang et al. [Phys. Fluids A 5, 3186 (1993)] and Vreman et al. [Phys. Fluids 6, 4057 (1994)] are compared, and the compatibility of the SGS models with the standard dynamic SGS model procedure is discussed. The proposed model is assessed for incompressible channel and mixing layer flows, in comparison with the dynamic Smagorinsky model of Germano et al. [Phys. Fluids A 3, 1760 (1991)], the dynamic mixed model of Zang et al. and the dynamic two-parameter mixed model of Salvetti and Banerjee [Phys. Fluids 7, 2831 (1995)]. In the “a priori” test, the proposed model gave the closest agreement with the modified cross term as well as the modified SGS Reynolds stress term. It is shown that the proposed term represents a more general model of the SGS stress than the modified Leonard term and yields a more accurate approximation. These SGS models are tested further in actual LES of channel and mixing layer flows (“a posteriori” test). The results were consistent with those of the “a priori” tests; the proposed model yielded the most accurate results. In the proposed model, the SGS quantities were predominantly represented using the new term, and the contribution of the Smagorinsky model was minimal. The two parameters contained in the model were determined locally in space on a point-by-point basis.

A new identification method was proposed for an eduction of vortex sheet structures in turbulent flows. This method took advantage of a prominent feature of a sheet, i.e., comparable dominance of both strain rate and vorticity and their strong correlation. The effectiveness of the proposed method was presented in the assessment using direct numerical simulation data for homogeneous isotropic turbulence. Both strain rate and vorticity were indeed large and correlated in the region identified using the proposed method. As a result, intense dissipation took place in the educed region. The relationship between the eigenvalue solution used in the present method and the invariants of fourth-order moments of velocity gradients was discussed. It was shown that the proposed method performed better than other invariants and previous identification methods for educing the vortex sheets.

Alignment of the eigenvectors for strain-rate tensors and subgrid-scale (SGS) stress tensors in large-eddy simulation (LES) is studied in homogeneous isotropic turbulence. Non-alignment of these two eigenvectors was shown in Tao, Katz & Meneveau (2002). In the present study, the specific term in the decomposition of the SGS stress tensor, which is primarily responsible for causing this non-alignment, is identified using the nonlinear model. The bimodal behaviour of the alignment configuration reported in Tao et al. (2002) was eliminated by reordering the eigenvalues according to the degree of alignment of the corresponding eigenvectors with the vorticity vector. The preferred relative orientation of the eigenvectors was ${\approx}\,42^\circ$. The alignment trends were conditionally sampled based on the relative dominance of strain and vorticity. The effect of the identified term on the alignment was the largest in the region in which the magnitudes of strain and vorticity were comparable and large (flat sheet). The most probable alignment configuration in the flat-sheet region was different from those in the strain-dominated and vorticity-dominated regions. The relative orientation of the eigenvectors was dependent on the degree of resolution for the flat sheet region yielded on the LES mesh. When the alignment was conditionally sampled on the events with the backward scatter of the SGS energy into the grid scale, the interchange of the alignment of the eigenvectors took place. Relevance of the identified term for the generation of turbulence is investigated. It is shown that the identified term makes no contribution to the production of the total SGS energy, but contributes significantly to the generation of the SGS enstrophy. The identified term causes a time-lag in the evolution of the turbulent energy and enstrophy. It is shown that generation of vorticity is markedly attenuated when the magnitude of the identified term is modified, and the original nonlinear model yielded the results which are in the closest agreement with the direct numerical simulation data.