Modelling the heat flux: understanding of convection in geophysics and astrophysics.
Many different physical phenomena take part in a flow. The geostrophic regime is the part where the main force balance is between the Coriolis effect and the local pressure gradient, part of the Navier-Stokes equation.
Beneath our feet liquid metal flows around in the earth’s outer core in a spiral-like manner, which generates the earth’s magnetic field. Researchers in the Troconvex project are using experiments and numerical simulations to gain new insights into heat and energy transfer in this kind of turbulent flow, as Professor Rudie Kunnen explains. The earth’s outer
core is comprised of liquid, mainly iron, which flows in a highly turbulent manner. Researchers believe that the flow inside the earth’s outer core is organised in such a way that this liquid metal moves around in a spiral-like fashion, a topic of great interest to Rudie Kunnen, an Assistant Professor in Applied Physics at Eindhoven University of Technology. “This spiral-like flow then generates the earth’s magnetic field,” he outlines. As the Principal Investigator of the Troconvex project, Professor Kunnen aims to gain deeper insights into the nature of these kinds of turbulent flows, looking at the geostrophic regime. “Many different physical phenomena take part in a flow. The geostrophic regime is the part where the main force balance is between the Coriolis effect and the local pressure gradient, part of the NavierStokes equation, which expresses momentum conservation in fluids,” he says.
Geostrophic regime A number of simulations have been developed to represent flow behaviour in the earth’s outer core, yet they have some significant limitations. The results generated so far do not match up with ground-based measurements of the earth’s magnetic field, which would suggest that current simulations are not big enough to show the entire picture. “We cannot fully resolve all the active turbulent scales, so we need to do some simplifications,” explains Professor Kunnen. By using a simpler system, researchers hope to build a fuller picture of some of the underlying processes involved. “With those simplified systems, we can see some hints of processes that we may not see in full earth simulations,” continues Professor Kunnen. “For example, we can see the formation of big helical flows, big vortices. These may then grow, and we can investigate them in depth.” The experimental setup that researchers are using in the project is relatively simple. Researchers are using a standard plastic cylinder, which is filled with water, then sealed off above and below with cooled and heated plates, respectively. “We can then apply thermal forcing. This whole arrangement
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rotates around the vertical axis,” outlines Professor Kunnen. The plan is to take two kinds of measurements of flow behaviour in this cylinder. “The first is actually to look at the thermal properties of this kind of flow. We wrap the cylinder in insulation, to prevent any heat leaks and ensure that all of the heat put in from below will travel upwards through the water, to the top plate,” says Professor Kunnen. “This is an important property in terms of modelling large-scale systems, as it represents the amount of heat loss. At a given rotation rate, a specific amount of heat is lost.” A second measurement involves making part of the cylinder transparent, so that flow measurements can be taken. This can be done by adding tiny plastic particles to the water, which then passively follow the flow. “We use laser illumination to record the movement of these particles with cameras. From that, we can then look at what kinds of structures are developing in the flow,” says Professor Kunnen. This then directly reproduces the structures that may form inside large-scale natural flows; Professor Kunnen and his colleagues are breaking new ground in this area. “We are among the first to study these structures in the geostrophic regime. This is mainly because of the design of the experiment, as it’s pretty hard to get into this geostrophic regime. We are currently preparing the measurements,” he outlines.
Rayleigh number The wider objective in this research to investigate how much heat and energy is transferred in a flow. The Rayleigh number, a dimensionless number which essentially describes the strength of the thermal forcing, is a major consideration in this respect. “It’s related to temperature differences that occur. Typically we consider a system that’s heated from below – the fluid near the bottom plate will be heated, so it will become lighter and rise up. Then at the top the fluid is cooled, so it will become heavier and sink,” explains Professor Kunnen. The strength of this thermal forcing is denoted by the Rayleigh number; Professor Kunnen and his colleagues aim to probe
deeper in this area. “We hope to establish a relationship that, based on the value of the Rayleigh number and other parameters, enables us to predict the overall amount of heat that is transferred outwards,” he outlines. Researchers in the project are also using numerical simulations to complement the experimental work. While in the experimental setup researchers are essentially limited to investigating water, using numerical simulations opens up other possibilities. “We can look at different kinds of fluids in the simulations. We could put in a liquid metal, we could put in a gas, and see what happens,” says Professor Kunnen. Ideally, the results of the simulations will match up to those from the experiments, from which Professor Kunnen and his colleagues can then look to draw wider conclusions. “Our experiment will give us insights into certain trends. For example, we can predict the behaviour of the heat transfer as a function of this Rayleigh number,” he outlines. “We unfortunately can’t do experiments in the exact same conditions as in nature, but we can identify trends.” A further step could be to extrapolate from these trends to make predictions about natural flows, including not just in the earth’s outer core, but also other geophysical and astrophysical flows. Rotation is needed in order to reach the geostrophic regime, something which Professor Kunnen says occurs in many large-scale flows. “For example, the liquidmetal core of the earth, but also the giant gaseous planets like Jupiter and Saturn, and also our own Sun to some degree. These systems are all very large and are all rotating – and based on estimates of the flow conditions, we expect them to be in the geostrophic regime,” he explains. The project’s work could also lead to new insights in atmospheric dynamics, although Professor Kunnen is cautious in this area. “Things like phase transitions from liquid to vapour, and the significant interaction of the shallow atmosphere with earth’s surface topography, make the atmosphere more complicated than those areas that we can directly contribute to,” he continues.
EU Research
TROCONVEX Turbulent rotating convection to the extreme (TROCONVEX) Project Objectives
The geostrophic regime of turbulent rotating convection is relevant for geo- and astrophysical flows. The flow behaviour in this regime displays significant and unexpected differences with the traditionally studied regime, making extrapolations impossible. We study heat transfer and flow structure with a revolutionary experiment and high-end numerical simulations.
Project Funding
TROCONVEX is funded by the European Research Council - Starting Grant -2015, project no. 678634.
Contact Details
Project Coordinator, Professor Rudie Kunnen Department of Applied Physics P.O. Box 513 5600 MB Eindhoven Netherlands T: +31 40 247 3194 E: r.p.j.kunnen@tue.nl W: https://www.tue.nl/en/research/ researchers/rudie-kunnen/
Professor Rudie Kunnen
Rudie Kunnen is assistant professor at Eindhoven University of Technology (NL). His research focuses on the experimental investigation of turbulent flows, including rotating convection in the geophysical context in the ERC StG project TROCONVEX and the behavior of droplets in turbulence.
Temperature fluctuations from a simulation. Left: nonrotating convection displays very fine structures. Right: with rotation, the formation of a large vortex can be observed.
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