ENGINEERING AND CFD

Introduction

A tremendous variety of physical phenomena involve turbulence, such as bird and airplane flight, propulsion of fish and boats, sailing, and even galaxy formation. Computational fluid dynamics uses numerical methods and algorithms to analyze such turbulent flows. Turbulent flow is characterized by chaotic swirling movements that vary widely in size, from sub-millimeters, over the extent of storm clouds, to phenomena on a galactic scale. The interaction of the chaotic movements on different scales makes it very challenging to simulate and understand the underlying geometric structures within turbulent flows. At the same time understanding these fundamental patterns is crucial for industry to optimize a wide range of applications.

Turbulent thermal convection is a class of turbulent flows in which temperature differences drive the flow. Prime examples are convection in the atmosphere, the thermocline circulation in the oceans, heating and ventilation in buildings, or in industrial processes. The model system for turbulent thermal convection is Rayleigh-Bénard flow in which a layer of fluid is heated from below and cooled from above. The temperature difference between the two plates leads to the formation of a large-scale flow pattern in which hot fluid moves up on one side, while cold fluid moves down on the other side of the cell, see figure 1. The beauty of the Rayleigh-Bénard system is that it is mathematically very well defined. This feature allows direct comparison of simulation results with theory, and one-to-one comparison with state of the art laboratory experiments. As a result, for more than a century, Rayleigh-Bénard convection has been the perfect playground to develop novel experimental and simulation techniques in fluid dynamics that enable a better understanding of underlying turbulent flow structures [2,3].

Results and Methods

According to the classical view on turbulence, strong turbulent fluctuations should ensure that the effect of the system geometry on the turbulent flow structures is minimal in highly turbulent flows as the entire phase space is explored statistically This view justifies the use of small aspect ratio, i.e. small horizontal length compared to its height, domains when studying very turbulent flows. This massively reduces the experimental or simulation cost to reach the high Rayleigh number, which indicates the dimensionless temperature difference between the bottom and top plate, regime relevant for industrial applications and astrophysical and geophysical phenomena. Therefore, in a quest to study Rayleigh-Bénard convection at ever increasing Rayleigh, most experiments and simulations have focused on small aspect ratio cells in which the horizontal domain size is small compared to its height. This approach has resulted in major developments in our understanding of heat transfer in turbulent flows.

However, while heat transfer in industrial applications occurs in confined systems, many natural instances of convection take place in horizontally extended systems. Previous experiments and simulations at relatively low Rayleigh have shown that large scale horizontal flow patterns can emerge. Until now it was unclear what happens at very high Rayleigh when the flow in the bulk of the domain becomes fully turbulent. Motivated by major advances in computational capabilities of supercomputers like SuperMUC, we set out to perform unprecedented simulations for very large aspect ratio Rayleigh-Bénard convection at high Rayleigh.

In order to achieve this, we performed large-scale simulations of turbulent thermal convection using an in-house developed second order finite difference flow solver. Our code is written in Fortran 90 and large-scale parallelization is obtained using a two-dimensional domain decomposition, which is implemented using Message Passing Interface (MPI). On SuperMUC we performed simulations on grids with up to 60x10⁹ computational nodes using up to 16 thousand computational cores. A snapshot of the entire flow field requires up to 1.7 terabytes, while the entire database we generated is over 1 petabyte. The generated database allows us to perform advanced flow field analysis unlocking detailed flow characteristics. This has, for example, allowed us to analyze the analogies and differences in the energy-containing flow structures found in pressure and thermally driven wall-bounded flows. In order to achieve this, we had to perform many simulations for which long term averaging was required to obtain the required statistical convergence. As a result, the simulations in this project required over a hundred million computational hours. The developed code has been made available to the fluid dynamics community at www.afid.eu and can also be used to simulate other canonical flow problems such as channel, Taylor Couette, and plane Couette flow [4].