No abstract

No abstract

Numerical experiments are conducted to study high-Rayleigh-number convective turbulence ($Ra$ ranging from $2\times 10^6$ up to $2\times 10^{11}$) in a $\Gamma=1/2$ aspect-ratio cylindrical cell heated from below and cooled from above and filled with gaseous helium ($Pr=0.7$). The numerical approach allows three-dimensional velocity, vorticity and temperature fields to be analysed. Furthermore, several numerical probes are placed within the fluid volume, permitting point-wise velocity and temperature time series to be extracted. Taking advantage of the data accessibility provided by the direct numerical simulation the flow dynamics has been explored and separated into its mean large-scale and fluctuating components, both in the bulk and in the boundary layer regions. The existence of large-scale structures creating a mean flow sweeping the horizontal walls has been confirmed. However, the presence of a single recirculation cell filling the whole volume was observed only for $Ra < 10^9 - 10^{10}$ and with reduced intensity compared to axisymmetric toroidal vortices attached to the horizontal plates. At larger $Ra$ the single cell is no longer observed, and the bulk recirculation breaks up into two counter-rotating asymmetric unity-aspect-ratio rolls. This transition has an appreciable impact on the boundary layer structure and on the global heat transfer properties. The large-scale structure signature is reflected in the statistics of the bulk turbulence as well, which, taking advantage of the large number of numerical probes available, is examined both in terms of frequency spectra and of temperature structure functions. The present results are also discussed within the framework of recent theoretical developments showing that the effect of the aspect ratio on the global heat transfer properties at large $Ra$ still remains an open question.

Results from direct numerical simulations for three dimensional Rayleigh-Bénard convection in a cylindrical cell of aspect ratio 1/2 and P r = 0.7 are presented. They span five decades of Ra from 2 × 10 6 to 2 × 10 11 . Good numerical resolution with grid spacing ∼ Kolmogorov scale turns out to be crucial to accurately calculate the Nusselt number, which is in good agreement with the experimental data by Niemela et al., Nature, 404, 837 (2000). In underresolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the fully resolved case, because the thermal dissipation close to the sidewall (where the grid cells are largest) is insufficient. We compared the fully resolved thermal boundary layer profile with the Prandtl-Blasius profile. We find that the boundary layer profile is closer to the Prandtl Blasius profile at the cylinder axis than close to the sidewall, due to rising plumes in that region.

The application of the Immersed Boundary ͑IB͒ method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard Reynolds-Averaged Navier-Stokes models or the more sophisticated Large Eddy Simulation approach. The main features of the IB technique are described with emphasis on the treatment of boundary conditions at an immersed surface. Examples of flows around a cylinder, in a wavy channel, inside a stirred tank and a piston/cylinder assembly, and around a road vehicle are presented. Comparison with experimental data shows the accuracy of the present technique. This review article cites 70 references.The continuous growth of computer power strongly encourages engineers to rely on computational fluid dynamics ͑CFD͒ for the design and testing of new technological solutions. Numerical simulations allow the analysis of complex phenomena without resorting to expensive prototypes and difficult experimental measurements.The basic procedure to perform numerical simulation of fluid flows requires a discretization step in which the continuous governing equations and the domain of interest are transformed into a discrete set of algebraic relations valid in a finite number of locations ͑computational grid nodes͒ inside the domain. Afterwards, a numerical procedure is invoked to solve the obtained linear or nonlinear system to produce the local solution to the original equations. This process is simple and very accurate when the grid nodes are distributed uniformly ͑Cartesian mesh͒ in the domain, but becomes computationally intensive for disordered ͑unstruc-tured͒ point distributions.For simple computational domains ͑a box, for example͒ the generation of the computational grid is trivial; the simulation of a flow around a realistic configuration ͑a road vehicle in a wind tunnel, for example͒, on the other hand, is extremely complicated and time consuming since the shape of the domain must include the wetted surface of the geometry of interest. The first difficulty arises from the necessity to build a smooth surface mesh on the boundaries of the domain ͑body conforming grid͒. Usually industrially relevant geometries are defined in a CAD environment and must be translated and cleaned ͑small details are usually eliminated, overlapping surface patches are trimmed, etc͒ before a surface grid can be generated. This mesh serves as a starting point to generate the volume grid in the computational domain.In addition, in many industrial applications, geometrical complexity is combined with moving boundaries and high Reynolds numbers. This requires regeneration or deformation of the grid during the simulation and turbulence modeling, leading to a considerable increase of the computational difficulties. As a result, engineering flow simulations have large computational overhead and low accuracy owing to a lar...

No abstract

Direct numerical simulations of Taylor-Couette flow (TC), i.e. the flow between two coaxial and independently rotating cylinders were performed. Shear Reynolds numbers of up to 3 · 10 5 , corresponding to Taylor numbers of T a = 4.6 · 10 10 , were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect-and rotation-ratios, but depends significantly on the radius-ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius-ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15% of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner vs outer Reynolds number parameter space and in the Taylor vs inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech. 164, 155-183, 1986) phase diagram towards the ultimate regime.

No abstract