Hydrodynamic stability and turbulent transition with the Vreman LES SGS and a modified lattice Boltzmann equation

ABSTRACT

For the evaluation of a broad range of $Re$ 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 $Re$ 1900 and 1950, matching well with the wealth of literature. At $Re$ 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 $Re$ 8000 intermittent turbulence has progressed to the domain centre. This range of $Re$ 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.

KEYWORDS:

• Transition
• lattice Boltzmann
• incompressible
• multiple relaxation time (MRT)
• large eddy simulation (LES)
• Vreman subgrid model
• hydrodynamic stability

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.