Velocity Vorticity-based Large Eddy Simulation
With The Boundary Element Method
Author(s)
J. Ravnik, L. ˇSkerget & M. Hriberˇsek
Abstract
A large eddy simulation using velocity-vorticity formulation of the incompressible
Navier-Stokes equations in combination with the turbulent heat transfer equation
is proposed for the solution of the turbulent natural convection drive flow in a 1:4
enclosure. The system of equations is closed by an enstrophy based subgrid scale
model. The Prandtl turbulent number is used to estimate turbulent diffusion in the
heat transfer equation. The boundary element method is used to solve the kinematics
equation and estimate the boundary vorticity values. The vorticity transport
equation is solved by the finite element method. The numerical example investigated
in the paper is the onset of a turbulent flow regime occurring at high Rayleigh
number values (Ra = 107−1010). The formation of vortices in the boundary layer
is observed, along with buoyancy driven diffusive convective transport. Quantitative
comparison with the laminar flow model and the work of other authors is also
presented in terms of Nusselt number value oscillations.
1 Introduction
Over the last few decades two-dimensional buoyancy driven flows have been investigated
thoroughly by several authors. Natural convection in a rectangular enclosure
is present in many industrial applications, such as the cooling of electronic
circuitry, nuclear reactor insulation and ventilation of rooms.
A benchmark solution for two-dimensional flow of Boussinesq fluid in a square
differentially heated enclosure was presented by De Vahl Davies [1]. They used
the stream function-vorticity formulation. 2D DNS was preformed by Xin and Le
Qu´er´e [2] for an enclosure with aspect ratio 4 up to Rayleigh number based on
the enclosure height 1010 using expansions in series of Chebyshev polynomials.
Keywords
Related Book
Other papers in this volume
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