The present work investigates the role of different treatments of the lower boundary condition on the numerical prediction of flows over two-dimensional, smooth, steep hills. Four different law of the wall formulations are tested when a large recirculating region is formed on the lee side of the hill. Numerical implementation of the near-wall functions was made through a finite elements code. The standard κ-model was used to close the averaged Navier-Stokes equations. Results are validated through original data obtained in a water tank. Measurements resorted to laser Doppler anemometry. The experiment provide detailed data for the characterization of the reverse flow in the region between the separation and the reattachment points, with emphasis on the near wall region. The experimental wall shear stress distribution is compared with the results provided by the different laws of the wall showing good agreement. The numerical predictions are shown to vary markedly between different formulations.Keywords Hill · κ-model · Laser-Doppler anemometry · Law of the wall · Separation · Wall shear stress.

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The present work investigates the role of different treatments of the lower boundary condition on the numerical prediction of bubbly flows. Two different wall function formulations are tested against experimental data obtained for bubbly boundary layers: (i) a new analytical solution derived through asymptotic techniques and (ii) the previous formulation of Troshko and Hassan (IJHMT, 44, 871-875, 2001a). A modified k-e model is used to close the averaged Navier-Stokes equations together with the hypothesis that turbulence can be modelled by a linear superposition of bubble and shear induced eddy viscosities. The work shows, in particular, how four corrections must the implemented in the standard single-phase k-e model to account for the effects of bubbles. The numerical implementation of the near wall functions is made through a finite elements code.