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Samples - Particles in a turbulent flow (Splendid Science 2008)


Modelling of turbulent flows is a challenging task. Things get even more complicated when these flows contain particles. Particles affect the flow, and vice versa. Scientists at the department of Multi-Scale Physics (MSP) are taking on this modelling challenge.

Nienke Beintema

“Most flows in nature are turbulent,” says dr. Luís Portela at the department of MSP. “Rivers, oceans, clouds… they all show turbulence, which is characterized by a wide range of scales.” These flows become even more interesting, as Portela points out, when they contain particles. These may either be solid particles, such as sand, or droplets or bubbles. Portela and his colleagues study the interactions between these particles and the surrounding flows. They make models that explain a system’s behaviour at all scales: from the tiniest vortices to very large eddies, from the movement of individual particles to large-scale distribution patterns.

“Let’s take a look at cloud formation, for instance,” says Portela. “This process is strongly influenced by turbulence. Rain droplets - which typically have a size of the order of onemillimeter- form around condensation nuclei that are perhaps one micrometer in diameter. For a single droplet, this process can take hours. But rain can begin much faster! How is this possible? The answer is that smaller droplets collide and merge to form larger droplets – a process which is accelerated by turbulence.”

A similar process is the transport of sediment in flowing water, as Portela indicates. Large-scale water systems such as rivers and oceans carry sand particles and deposit them elsewhere.Portela: “The patterns of sand deposition are strongly dependent on turbulence. If we understand that process, we are able to better predict processes like underwater ridge formation.”

A third example is presented by industrial flows. Flows inside reactor pipes, as well as in oil and gas pipes, often contain multiple phases – solid, gas and/or liquid. The MSP scientists aim to understand, for instance, droplet formation and deposition in gas flows, and clustering of catalytic particles in reactor flows. This understanding will help to design systems that ensure an optimal flow and optimal industrial reactions.


Turbulence determines the movement of particles. These particles, in turn, affect the turbulence. Portela makes a sketch on his whiteboard to illustrate this ‘two-way coupling’.

“In principle each particle moves with the flow: its trajectory is determined by the vortex in which it finds itself,” he shows. “Locally, each particle produces a tiny disturbance in the flow. In the case of small particles, the effect of one single particle is negligible, but the combined effect of millions of particles can exert a large change on the flow. In other words, the particles are changing the flow dynamics.”

Portela then draws a cross-section of a gasoline pipe. Gasoline, as he explains, can be produced by catalytic ‘cracking’ of heavy oil. Sand-like, catalytic particles are used to ‘crack’ the larger oil molecules. “Both the oil and the catalytic particles are injected into this pipe,” he indicates. “Ideally, you want a uniform distribution of the catalyst. But it turns out that the particles are pushed towards the wall, where they keep piling up. This affects the turbulence, and thus the mixing of the oil and the catalyst. If the pipe is short enough, there won’t be enough time for the particles to cluster. How long does it take for the clusters to form, and when does this become inhibitive for the chemical reaction?”

To answer this question, Portela and his colleagues are using a combination of experimental design and computer modelling. In their lab, they measure the movements of particles in flows using a combination of Laser-Doppler Anemometry (LDA) and Particle Tracking Velocimetry (PTV). LDA measures how the particles scatter laser light. This is based on the Doppler effect: particles moving faster scatter light with a higher frequency than particles moving more slowly. PTV uses successive pictures of the same particle to track its movement and measure its speed. The scientists use these data to develop and validate their computer models. These are based on solving equations that predict the flow of a single phase, combining these with equations describing the particles, and then integrating these with models for the interaction between the fluid and the particles. “If I can model the interaction between particles and small vortices,” says Portela, “I can extend this to the larger scale. This will result in a model that predicts the effect of small particles on the large vortices and on the entire flow.”

Specific challenges

The clustering of catalyst particles in an oil pipe is an example of so-called ‘near-wall behaviour’. This is a phenomenon that makes Portela’s models much more complicated. “There is currently no ‘first-principles theory’ for wall-bounded flows,” Portela highlights. “In fact we try to simplify this problem by representing it in a cartoon-like picture. We break it up into understandable parts, and then combine these later in an overarching model. People who are more mathematically inclined may find this a problem, but there is no alternative: there is simply no mathematics that completely describes this ‘zoo’ of behaviour.”

Atmospheric science also presents the MSP-experts with some specific challenges. So far, people have modelled cloud formation without an adequate consideration of the complex interactions between the different droplet sizes and the turbulence. “Cloud formation is characterised by the formation of different-sized droplets,” Portela says. “Different sizes result in different behaviours – which makes it hard to model the overall flows.” When looking at this flow, Portela distinguishes two phenomena: preferential concentration, and preferential sweeping. The first means that the droplets are not uniformly distributed. In a system of vortices, they experience a centrifugal force. They are thrown towards the edges of the vortices, where they form ring-like structures.

“This is where it becomes messy,” says Portela. “In these places they have a much higher chance to collide. This results in droplets of different sizes.” These droplets are subject to gravity. This is where the second phenomenon comes in: preferential sweeping. Smaller droplets take a longer time to reach the outside of a vortex. They ‘jump’ out of the vortex slightly later than their larger brothers, and they fall slightly slower. As a result, they follow a slightly different path when they are swept back and forth as they fall past successive vortices. As a result, different-sized droplets will collide less often than droplets of the same size – even at tiny size differences. “So far, scientists have generally overlooked the effect of these size differences,” says Portela. “We were the first to show that both mechanisms play a role – preferential concentration and preferential sweeping – and that their relative importance depends on the size of the droplets. This allows us to design models that take into account the right circumstances.” These improved models, as he points out, may help to make meteorological simulations more accurate.

Particle-laden flows, as Portela concludes, are more the norm than the exception. The work of the MSP scientists therefore finds a wide range of applications. “I am not an application guy,” Portela smiles, “but I find myself working together with people working on clouds, hydraulics, industrial reactions, and oil and gas. We are also becoming interested in dredging. Dutch people spend a lot of time moving sand from one place to another. The same principles work here too. Dredging companies generally inject a jet into the ground to make the sediment looser, which results in sharp particle-concentration gradients within the flow – just like, for example, at a cloud interface. Our models provide useful insights into what happens inside these jets. Things that appear different may be similar when you take a closer look.”

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