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Two-dimensional velocity-vorticity based LES for the solution of natural convection in a differentially heated enclosure by wavelet transform based BEM and FEM
Jure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2006, original scientific article

Abstract: A wavelet transform based boundary element method (BEM) numerical scheme is proposed for the solution of the kinematics equation of the velocity-vorticityformulation of Navier-Stokes equations. FEM is used to solve the kinetics equations. The proposed numerical approach is used to perform two-dimensional vorticity transfer based large eddy simulation on grids with 105 nodes. Turbulent natural convection in a differentially heated enclosure of aspect ratio 4 for Rayleigh number values Ra=107-109 is simulated. Unstable boundary layer leads to the formation of eddies in the downstream parts of both vertical walls. At the lowest Rayleigh number value an oscillatory flow regime is observed, while the flow becomes increasingly irregular, non-repeating, unsymmetric and chaotic at higher Rayleigh number values. The transition to turbulence is studied with time series plots, temperature-vorticity phase diagrams and with power spectra. The enclosure is found to be only partially turbulent, what is qualitatively shown with second order statistics-Reynolds stresses, turbulent kinetic energy, turbulent heat fluxes and temperature variance. Heat transfer is studied via the average Nusselt number value, its time series and its relationship to the Rayleigh number value.
Keywords: numerical modelling, boundary element method, discrete wavelet transform, large eddy simulation, velocity-vertocity formulation, natural convection
Published: 31.05.2012; Views: 1515; Downloads: 52
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Velocity vorticity-based large eddy simulation with the bounadr element method
Jure Ravnik, Leopold Škerget, Matjaž Hriberšek, 2006, published scientific conference contribution (invited lecture)

Abstract: A large eddy simulation using the 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 enthropy-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 FEM. The numerical example studied in this paper is the onset of a turbulent flow regime occuring at high Rayleigh number values ▫$(Ra=10^7-10^10)$▫. 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 worh of other authors is also presented in terms of Nusselt number value oscillations.
Keywords: fluid mechanics, incompressible viscous fluid, turbulent flow, velocity vorticity formulation, finite element method, large eddy simulation
Published: 31.05.2012; Views: 1243; Downloads: 18
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