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Boundary element analysis of general laminar and turbulent fluid flow problems [Elektronski vir]
Škerget, Leopold ; Ravnik, Jure
A time-dependent accurate boundary-domain integral method for the prediction of two-dimensional unsteady fluid flows is presented in this article. The velocity-vorticity formulation of the time ...dependent set of equations is employed, where the kinematics is given with the false transient form of the Poisson velocity vector equation, while the kinetics is represented with the vorticity transport equation, and the pressure field function is governed by the Poisson pressure scalar equation. The method makes use of the domain decomposition strategy to increase the applicability of the BEM numerical model. The numerical algorithm is applied to the calculation of the time-dependent and chaotic flows at high Reynolds Re or Rayleigh Ra number values flows in cavities. The cases considered are the lid-driven cavity problem and the buoyant flow in differentially heated cavities. Accurate results are obtained for the lid-driven cavity ranging from Re = 1000 to Re = 20000, indicating that the steady flow bifurcates to a periodic regime for a Reynolds number value in the range Re = 7500 - 10000, and to chaotic for greater Re number values. The results for a differentially heated enclosures are presented for a Prandtl number value equal to Pr = 0.71, with values of the Rayleigh number values Ra =▫$1x10^8, 2x10^8, 4x10^8 and 1x10^9▫$, indicating again the flow development from the steady state, periodic, and toward the chaotic flow regime.
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