F.X. Trias

DIRECT NUMERICAL SIMULATION OF A THREE-DIMENSIONAL NATURAL-CONVECTION FLOW IN A DIFFERENTIALLY HEATED CAVITY OF ASPECT RATIO 4

The majority of the direct numerical simulations of turbulent and transition natural- convection flows in cavities assume two-dimensional behavior. To investigate the effect of the three-dimensional fluctuations, a complete direct numerical simulation has been carried out, in a cavity with aspect ratio 4, Raz = 6.4 × 108 , and Pr = 0.71, using a low-cost PC cluster. A description of the parallel algorithm and the methodology used to verify the code and the accuracy of the statistics obtained is presented. The main features of the two- and three-dimensional flows are described and compared. Several first- and second-order statistic distributions have been evaluated, including the Reynolds stress tensor. Significant differences are observed between the second-order statistics of the two- and three- dimensional simulations.

Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction

In the context of time-accurate numerical simulation of incompressible flows, a Poisson equation needs to be solved at least once per time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is one of the most time consuming and difficult to parallelise parts of the code. In this paper, a parallel direct Poisson solver restricted to problems with one uniform periodic direction is presented. It is a combination of a direct Schur-complement based decomposition (DSD) and a Fourier diagonalisation. The latter decomposes the original system into a set of mutually independent 2D systems which are solved by means of the DSD algorithm. Since no restrictions are imposed in the non-periodic directions, the overall algorithm is well-suited for solving problems discretised on extruded 2D unstructured meshes. The load balancing between parallel processes and the parallelisation strategy are also presented and discussed. The scalability of the solver is successfully tested using up to 8192 CPU cores for meshes with up to 10^9 grid points. Finally, the performance of the DSD algorithm as 2D solver is analysed by direct comparison with two preconditioned conjugate gradient methods. For this purpose, the turbulent flow around a circular cylinder at Reynolds numbers 3900 and 10,000 are used as problem models.

Parallel algorithms for Sn transport sweeps on unstructured meshes

The Boltzmann Transport Equation is solved on unstructured meshes using the Discrete Ordinates Method. The flux for each ordinate is swept across the computational grid, within a source iteration loop that accounts for the coupling between the different ordinates. In this paper, a spatial domain decomposition strategy is used to divide the work among the available CPUs. The sequential nature of the sweep process makes the parallelization of the overall algorithm the most challenging aspect. Several parallel sweep algorithms, which represent different options of interleaving communications and calculations in the solution process, are analysed. The option of grouping messages by means of buffering is also considered. One of the heuristics proposed consistently stands out as the best option in all the situations analyzed, which include different geometries and different sizes of the ordinate set. With this algorithm, good scalability results have been achieved regarding both weak and strong speedup tests with up to 2560 CPUs.

Building proper invariants for eddy-viscosity subgrid-scale models

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Turbulent natural convection in a differentially heated cavity of aspect ratio 5 filled with non-participating and participating grey media

In the present work, turbulent natural convection in a tall differentially heated cavity of aspect ratio 5:1, filled with air (Pr = 0.7) under a Rayleigh number based on the height of 4.5 · 1010, is studied numerically. Two different situations have been analysed. In the first one, the cavity is filled with a transparent medium. In the second one, the cavity contains a grey participating gas. The turbulent flow is described by means of Large Eddy Simulation (LES) using symmetry-preserving discretizations. Simulations are compared with experimental data available in the literature and with Direct Numerical Simulations (DNS). Surface and gas radiation have been simulated using the Discrete Ordinates Method (DOM). The influence of radiation on fluid flow behaviour has also been analysed.

A new subgrid characteristic length for turbulence simulations on anisotropic grids

Direct numerical simulations of the incompressible Navier-Stokes equations are not feasible yet for most practical turbulent flows. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are probably the most popular example thereof. This type of models requires the calculation of a subgrid characteristic length which is usually associated with the local grid size. For isotropic grids this is equal to the mesh step. However, for anisotropic or unstructured grids, such as the pancake-like meshes that are often used to resolve near-wall turbulence or shear layers, a consensus on defining the subgrid characteristic length has not been reached yet despite the fact that it can strongly affect the performance of LES models. In this context, a new definition of the subgrid characteristic length is presented in this work. This flow-dependent length scale is based on the turbulent, or subgrid stress, tensor and its representations on different grids. The simplicity and mathematical properties suggest that it can be a robust definition that minimizes the effects of mesh anisotropies on simulation results. The performance of the proposed subgrid characteristic length is successfully tested for decaying isotropic turbulence and a turbulent channel flow using artificially refined grids. Finally, a simple extension of the method for unstructured meshes is proposed and tested for a turbulent flow around a square cylinder. Comparisons with existing subgrid characteristic length scales show that the proposed definition is much more robust with respect to mesh anisotropies and has a great potential to be used in complex geometries where highly skewed (unstructured) meshes are present.

A priori study of subgrid-scale features in turbulent Rayleigh-Bénard convection

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Benard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and π spanwise open-ended distance are used at two Rayleigh numbers Ra∈{108,1010} [Dabbagh et al., “On the evolution of flow topology in turbulent Rayleigh-Benard convection,” Phys. Fluids 28, 115105 (2016)]. First, DNS at Ra = 108 is used to assess the performance of eddy-viscosity models such as QR, Wall-Adapting Local Eddy-viscosity (WALE), and the recent S3PQR-models proposed by Trias et al. [“Building proper invariants for eddy-viscosity subgrid-scale models,” Phys. Fluids 27, 065103 (2015)]. The outcomes imply that the eddy-...

On the evolution of flow topology in turbulent Rayleigh-Bénard convection

Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Benard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 108 and 1010, inside an air-filled rectangular cell of aspect ratio unity and π span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (QG, RG) has displayed the so-called “teardrop” spiraling shape through the bulk region. Therein, the mean trajectories are swirling inwards revealing a periodic spin around the converging origin of a constant period that is found to be proportional to the plumes lifetime. This suggests that the thermal plumes participate in the coherent large-scale circulation and the tu...

Building proper invariants for large eddy simulation

where u denotes the velocity field, p represents the kinematic pressure and ν is the kinematic viscosity. In the foreseeable future, numerical simulations of turbulent flows will have to resort to models of the small scales because the non-linear convective term produces too many scales of motion. Large-Eddy Simulation (LES) is probably the most popular example thereof. In short, LES equations result from applying a spatial filter, with filter length ∆ , to the NS Eqs.(1)

Building Proper Invariants for Eddy-Viscosity Models

Direct numerical simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Regularization and eddy-viscosity models for LES are examples thereof. They rely on differential operators that should capture well different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime ...). Most of them are based on the combination of invariants of a symmetric second-order tensor that is derived from the gradient of the resolved velocity field. In the present work, they are presented in a framework where the models are represented as a combination of elements of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space.