A numerical study of the subgrid-scale fluid motion in turbulent flows

Hossen, Mohammed Khalid (2021) A numerical study of the subgrid-scale fluid motion in turbulent flows. Masters thesis, Memorial University of Newfoundland.

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Abstract

The numerical solution of the Navier–Stokes equations for different turbulence regimes has become more prevalent for many years. This thesis has investigated the large eddy simulation method for solving the Navier–Stokes equations. A primary goal is to design a subgrid-scale model for small-scale coherent vortices while statistically maintaining an accurate dissipation rate. Past investigations of turbulence indicate that the vortex stretching mechanism can transport the turbulence kinetic energy from large to small scales. Thus, a turbulence model can learn the energy dissipation rate from the statistics of the velocity gradient tensor. Following such a hypothesis, this thesis validates how vortex stretching can directly account for the subgrid-scale dissipation rate while solving the Navier–Stokes equations on a relatively coarse mesh. Current findings suggest a potential subgrid-scale model based on invariants of the square of the velocity gradient tensor. The turbulence statistics obtained from the proposed model agree well with the three commonly used dynamically adaptive large eddy simulation techniques. The results also suggest that statistics of the velocity gradient tensor dynamically adapt the dissipation rate to the local variation of turbulence. Furthermore, considering the square of the deformation tensor, this thesis suggests that the singular values of the snapshots of the velocity gradient may improve the model in future studies of more challenging turbulent flows.

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