Using vortex identifiers to build eddy-viscosity subgrid-scale models for large-eddy simulation

In this paper, we present a generalized framework of incorporating vortex identifiers into subgrid-scale (SGS) models for large-eddy simulation. This research is inspired by the keystone principle of modern turbulence theory that kinetic energy is cascaded from large to small scales by the vortex stretching mechanism. We propose that regions without local vortex structures do not possess significant subgrid motions due to the lack of energy cascade and therefore do not need significant SGS stresses/dissipation, whereas strong local SGS dissipation should be applied in regions with strong small-scale (close to the cutoff length scale) vortices owing to the subgrid motions enhanced by the vortex stretching mechanism. Following this idea, four new SGS models are constructed based on four different vortex identifiers. The new models possess some important characteristics of the vortex identifiers, including sensitivity to small-scale vortices and Galilean invariance. The correct near-wall cubic asymptotic behavior for the SGS viscosity is also satisfied by the new models. The proposed models are validated using three test cases, including isotropic decaying turbulence, isotropic forced turbulence, and fully developed turbulent channel flow. The proposed models are robust without any local clipping/filtering or averaging along homogeneous direction(s). The results indicate that the proposed models automatically apply stronger SGS dissipation to small-scale motions, and predict satisfactory turbulence statistics with less computational expense compared with the conventional dynamical Smagorinsky model.

Figure 1

Comparison of predicted resolved TKE and energy spectra of the decaying isotropic turbulence against those of CBC [56] experiment, with the values of $C_m$ listed in Table 1. In panel (a), the resolved TKE is normalized using the initial TKE value $K_0$.

Figure 2

Comparison of energy spectra of the isotropic forced turbulence with different Reynolds numbers using different grid resolution against the DNS results by Kaneda et al. [49]. For clarity, every second resolved wave number in LES is plotted.

Figure 3

Comparison of compensated energy spectra predicted by LES using four different SGS models at different Reynolds numbers (for ${\text{Re}}_{\lambda }=257$–1201) against the DNS results of Kaneda et al. [49]. Energy spectra of ${\text{Re}}_{\lambda }=732$ and 1201 use the vertical scale on the left side of each panel, and energy spectraof ${\text{Re}}_{\lambda }=257$ and 471 use the vertical scale on the right side of each figure panel. Energy spectra predicted without a SGS model severely deviate from the DNS results and only those of the two lower Reynolds numbers (${\text{Re}}_{\lambda }=257$ and 471) are plotted for the purpose of illustrations. Dashed boxes mark the LES predictions of the flat region in the compensated energy spectra.

Figure 4

Spectra of SGS dissipation (${\varphi }_{\text{sgs}}$) predicted by different models for different Reynolds numbers. Compensated energy spectra are superimposed to visualize the inertial subrange.

Figure 5

Profiles of the mean streamwise velocity predicted based on different SGS models. For clarity, the inset figure zooms into the region of $y^{+}\in [100,300]$ to facilitate visualization.

Figure 6

Profiles of Reynolds stresses for different SGS models. All four subfigures share the same legend as subfigure (a). In subfigure (d), the inset figure zooms in for the mean SGS stress ${\langle {\tau }_{12}\rangle }^{+}$. The filtered DNS data are extracted from Nicoud et al. [1]. Following Nicoud et al. [1], to show the wall effect and to make the figure presentation clear, the range of $y^{+}$ is limited to $[0,200]$.

Figure 7

Contours of instantaneous nondimentionalized SGS dissipation rate (${\varepsilon }_{\text{sgs}}=-{\tau }_{ij}^{*}{\overline{S}}_{ij}$) superimposed with cross-stream velocity vectors in a typical $y\text{−}z$ plane predicted by the DSM and ${\lambda }_2$ model. Note that different contour levels are used in the figures due to the drastically different values of ${\varepsilon }_{\text{sgs}}$ predicted by these two SGS models. To emphasize the regions of strong SGS dissipation, contours of ${\varepsilon }_{\text{sgs}}/(u_{\tau }^3/\delta )<20$ and ${\varepsilon }_{\text{sgs}}/(u_{\tau }^3/\delta )<60$ are clipped in the first and second subfigures, respectively.

Figure 8

Premultiplied energy spectra ($k_z{E}_z$) in the spanwise direction at two different wall-normal locations from different SGS models. Subfigure (b) shares the same legend as subfigure (a).

Figure 9

Profiles of averaged SGS viscosity $\langle {\nu }_{\text{sgs}}\rangle$ predicted by different SGS models.