Rayleigh-Benard flow – the flow in a box heated from below and cooled from above – and Taylor-Couette flow – the flow between two counter-rotating cylinders – are the two paradigmatic systems in the physics of fluids, and many new concepts have been tested with them. Professor Detlef Lohse and his colleagues from the Physics of Fluids group at the University of Twente have been carrying out simulations of these systems to try and improve our understanding of turbulence.
Turbulent flow – the irregularly fluctuating flow of fluid seen everywhere from blood moving through arteries to air moving past aircraft wingtips – is abundant in nature and technology. A topic notorious for its complexity, it has proven frustratingly difficult to pin down and describe fully in mathematical terms. Understanding it is of great practical use in many fields, but getting meaningful experimental data is difficult. Numerical simulations on supercomputers have recently helped researchers move further than ever before towards unlocking the secrets of this elusive phenomenon.
Professor Detlef Lohse of the University of Twente has devoted much of his academic work to studying turbulence, specifically two systems – Rayleigh-Benard (RB) flow and Taylor-Couette (TC) flow. Much like the fruit fly Drosophila in biological research, RB and TC flow are the go-to experimental systems in the field of fluid dynamics.
RB convection systems involve the turbulent flow seen in a closed box that is heated from below and cooled from above. Investigations seek to understand how much heat transfer occurs depending on the difference in temperature between the top and bottom. RB systems are one of the classical problems of fluid dynamics, and various concepts of fluid dynamics have been tested using it.
In an RB system, an increasing temperature gradient at first causes some diffusive transport of heat. Then, the onset of convection rolls occurs. These convection rolls become more intense, after which pattern formation begins. Finally, spatio-temporal chaos turbulence begins. This final turbulent regime is the area that Lohse is interested in. “There is a particular transition from the point where there is turbulence in the bulk of the flow but it is still of laminar type in the boundary layers, to a new regime where there is also turbulence in the boundary layer,” says Lohse. “This is known as the ultimate regime, where heat transport is enhanced greatly. If you extrapolate this to real geophysical and astrophysical applications, this can become quite significant.”
Lohse has been studying the nature of this transition – when it happens, and what the flow organisation looks like. Experiments have been done on this, but Lohse’s work aims to complement experimental work with numerical simulations. “Experimental work is limited because it isn’t possible to get full flow information; you can only measure global or local quantities, but you cannot look at the whole temperature and velocity field and in particular not simultaneously. With numerical simulations, all of this is possible.”
Numerical simulations of turbulence are, unsurprisingly, computationally demanding. Access to 11.1m core-hours on Curie TN in and 7.5m core-hours on Hermit in Germany has allowed Lohse and colleagues to study this particular transition in greater detail than ever before.
Another well-studied convection system is (TC) Taylor-Couette flow – the flow between two counter-rotating cylinders. Although this involves the transport of angular momentum rather than heat, mathematically it can be shown to be analogous to RB flow. Numerical simulations of TC flow offer insight into the workings of RB flow. This is because mechanical driving is more efficient than thermal driving, so it is less computationally demanding to see TC flow reach the transition to ultimate turbulence. “Experimentally, RB flow reaches the transition at a Rayleigh number of 1014 (a higher Rayleigh number indicates a more strongly driven RB system),” says Lohse. “Unfortunately, we can only currently achieve 1013 in simulations, where we see indications that the transition is setting in but do not see it fully. But, in the analogous TC flow we can see and now understand the transition and the enhanced transport.”
Knowledge of turbulence can be applied almost everywhere, from astrophysical processes to the heating of buildings. The Gulf Stream – the warm Atlantic Ocean current originating at the tip of Florida that has a warming effect on the climate of Western and Northern Europe – illustrates the important role that turbulence plays in the real world. The current is affected by both salt concentration and temperature concentration – a so-called double diffusion system. Competing density gradients within such as system cause the organisation of the flow to be complex, and changing conditions within the Gulf Stream mean that this flow could potentially change, with far reaching consequences. Lohse explains: “At the equator you have hot water which is very saline due to evaporation from the surface, whereas at Greenland you have cold water which is less saline due to melting ice. Changes in these conditions have led to speculation that at some point the flow may turn around. Having a detailed understanding of turbulence allows people to test how robust the Gulf Stream system is and whether there really is a chance that this change in flow may occur.”
Knowledge and support
Lohse is keen to stress that the support that he has received from PRACE has not only come in the form of CPU hours. Staff from SURFsara were invaluable in helping Lohse and his colleagues with efficient parallelisation. “It is not only hardware that you need – you also need knowledge from the people who know how to use it. I am a fluid dynamics physicist, but I could not tell you a lot about the details of computer architecture. This is a crucial but overlooked service that PRACE provides. Take China, for example – they have the fastest computers, but the support given to use those computers is not nearly as good as what you receive here in the Netherlands by SURFsara.”
The code developed by Lohse’s Physics of Fluids team is currently the highest quality around, and it has now been made public domain so that others can use it. In the future he hopes to push simulations of RB flow to higher Rayleigh numbers in order to see the transition to the ultimate regime of turbulence. He is also planning to carry out simulations of turbulence that are both thermally and shear driven. “This is a much more realistic simulation of flow. What we work with now are idealised systems that help us understand fluid dynamics, but they do not look like flows that we see in the natural world. I expect that adding this extra element of driving will mean that the ultimate regime is reached at a lower Rayleigh number.”
This article was originally published in the PRACE annual report 2015