ABSTRACT
For the evaluation of a broad range of in incompressible flows, particularly unsteady and transition regimes, the Vreman subgrid scale model is studied within the framework of a modified lattice Boltzmann equation. A unique multiple relaxation time form which recovers the fully incompressible unsteady Navier-Stokes equations is derived for the D3Q19 lattice. Solutions to the 3D-driven cavity are compared to a number of lattice Boltzmann and Navier-Stokes solutions. Initial simulations demonstrate the vanishing nature of eddy viscosity in the steady laminar regime. Onset of unsteadiness is found between 1900 and 1950, matching well with the wealth of literature. At 6000, velocity history and complex vortex structures show a transition to turbulence near the domain bottom and front walls while the centre of the domain retains laminar characteristics. By 8000 intermittent turbulence has progressed to the domain centre. This range of for transition and the flow characteristics are in agreement with the general ranges in literature, with further observations being added here. The Vreman model with an incompressible lattice Boltzmann method is found to be a promising tool for laminar-to-turbulent simulation.
Notation
CFD Computational fluid dynamics
DdQq d-dimension q-velocity lattice architecture
DNS Direct numerical simulation
FVM Finite volume method
LBE\LBE Lattice Boltzmann equation\incompressible form
LBM Lattice Boltzmann method
LDC Lid-driven cavity
LES Large eddy simulation
MRT Multiple relaxation time
NS Navier-Stokes
PSD Power spectral density
ReReynolds number
RMS Root mean square
SGS Subgrid scale model
SRS Scale resolving simulation
SRT Single relaxation time
TGL Taylor-Goertler-like
WALE Wall Adapting Local Eddy Viscosity model
Note
1.The solver was written in the C language, and parallelised using OpenMP. A MATLAB script for computing equilibrium distribution functions and components required for MRT implementation can be found at https://drive.google.com/file/d/1yLfCq7HBcuZglRGe2JWPV7GDJdHfSW64/view?usp=sharing.
Disclosure statement
No potential conflict of interest was reported by the authors.