Investigations of the NS-alpha model using a lid-driven cavity flow

TL;DR

This study explores an anisotropic NS-alpha subgrid model in lid-driven cavity flow at Re=10,000, addressing numerical oscillations and improving flow feature predictions through a new alpha definition based on velocity gradients.

Contribution

Introduces an anisotropic NS-alpha subgrid model with a novel alpha definition based on velocity gradients, improving flow predictions in cavity simulations.

Findings

Significant improvement in flow feature predictions with the new alpha definition.

The model captures energy transfer directions consistent with DNS results.

Addressed numerical oscillations caused by discontinuities in alpha.

Abstract

In this paper we investigate a subgrid model based on an anisotropic version of the NS-$\alpha$ model using a lid-driven cavity flow at a Reynolds number of 10,000. Previously the NS-$\alpha$ model has only been used numerically in the isotropic form. The subgrid model is developed from the Eulerian-averaged anisotropic equations [Holm, \textit{Physica D}, v.133, pp 215-269, 1999]. It was found that when $\alpha^{2}$ was based on the mesh numerical oscillations developed which manifested themselves in the appearance of streamwise vortices and a `mixing out' of the velocity profile. This is analogous to the Craik-Leibovich mechanism, with the difference being that the oscillations here are not physical but numerical. The problem could be traced back to the discontinuity in $\alpha^{2}$ encountered when $\alpha^{2}=0$ on the endwalls. An alternative definition of $\alpha^{2}$ based on velocity gradients, rather than mesh spacing, is proposed and tested. Using this definition the results with the model shown a significant improvement. The splitting of the downstream wall jet, rms and shear stress profiles are correctly captured a coarse mesh. The model is shown to predict both positive and negative energy transfer in the jet impingement region, in qualitative agreement with DNS results.