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A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

The presence of low-frequency fluctuations in the wake of bluff bodies have been observed in several investigations. Even though the flow past a circular cylinder at Re = 3900 (Re = U ref D/ν) has been the object of several experimental and numerical investigations, there is a large scattering in the average statistics in the near wake. In the present work, the flow dynamics of the near wake region behind a circular cylinder has been investigated by means of direct numerical simulations and statistics have been computed for more than 858 shedding cycles. The analysis of instantaneous velocity signals of several probes located in the vortex formation region, point out the existence of a low-frequency fluctuation at the non-dimensional frequency of f m = 0.0064. This large-scale almost periodic motion seems to be related with the modulation of the recirculation bubble which causes its shrinking and enlargement over the time.

This paper presents a methodology for simulation of two-phase flows with surface tension in the framework of unstructured meshes, which combines volume-of-fluid with level-set methods. While the volume-of-fluid transport relies on a robust and accurate polyhedral library for interface advection, surface tension force is calculated by using a level-set function reconstructed by means of a geometrical procedure. Moreover the solution of the fluid flow equations is performed through the fractional step method, using a finite-volume discretization on a collocated grid arrangement. The numerical method is validated against two-and three-dimensional test cases well established in the literature. Conservation properties of this method are shown to be excellent, while geometrical accuracy remains satisfactory even for

The turbulent flow around a square cylinder at Reynolds number 22000 (based on the cylinder diameter and the inflow velocity) is studied by means of direct numerical simulation. An overview of the numerical methods and the methodology used to verify the simulation is presented with special emphasis to determine the proper domain size and time-integration period.