Dancing in the Pipe
Athanasia Kalpakli
Ramis Örlü
P. Henrik Alfredsson
Linné FLOW Centre & CCGEx
KTH Mechanics
Royal Institute of Technology
Osquars Backe 18
100 44 Stockholm
Sweden
Dean vortices in the cross-section of a curved pipe
Vortices created by the imbalance of a centrifugal force and a radial pressure gradient in a curved pipe move fluid from the inner wall (left side) towards the outer wall. These so called 'Dean vortices' (referring to the two symmetric structures in the rightmost figure) are common features of flows in curved geometries and occur in nature, such as in rivers, and technical applications, such as in heat exchangers and piping systems, where they are sometimes specifically generated for particle separation or filtration purposes.
By measuring the speed of tracer particles it is possible to obtain snapshots of the three dimensional velocity field in a cross plane and thereby capture the unsteady behavior of the vortices under turbulent flow conditions. Surrounded by an irregular and chaotic environment, the couple of 'undetermined' vortices appears to 'dance.' Sometimes they dance together while at other times one of them is taking the lead by swinging its partner (referring to the three snapshots to the left). Nonetheless, on average, they successfully manage to keep up an ordered, laminar-like, appearance as a harmonic couple.
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in the familiar equation 
. Going on to fluids, we’ll give the definition of the coefficient of viscosity for liquids and gases, give some values for different fluids and temperatures, and demonstrate how the microscopic picture can give at least a qualitative understanding of how these values vary: for example, on raising the temperature, the viscosity of liquids decreases, that of gases increases. Also, the viscosity of a gas doesn’t depend in its density! These mysteries can only be unraveled at the molecular level, but there the explanations turn out to be quite simple.
can be viewed in two rather different (but of course consistent) ways: it is a measure of how much heat is generated when faster fluid is flowing by slower fluid, but it is also a measure of the rate of transfer of momentum from the faster stream to the slower stream. Looked at in this second way, it is analogous to thermal conductivity, which is a measure of the rate of transfer of heat from a warm place to a cooler place.
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