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978-3-8439-1821-3, Reihe Strömungsmechanik

Christoph Siewert Numerical Analysis of Particle Collisions in Isotropic Turbulence

131 Seiten, Dissertation Rheinisch-Westfälische Technische Hochschule Aachen (2014), Softcover, A5

Motivated by applications primarily in meteorology but also in astrophysics, engineering, and biology, collisions of small particles settling in turbulence are investigated numerically. The result of this work is twofold: A new setup is introduced and the influence of the particle shape on the collision probability is investigated.

Since it is unclear whether and if so how the periodicity and the large scale forcing of typical direct numerical simulations influence the particle motion, an alternative setup is proposed. At the inflow synthetic turbulence is generated and is transported through the flow domain with a mean carrier flow. The resulting flow field shares similarities with the decaying isotropic turbulence in wind tunnel experiments.

First, the motions of 43 million spherical particles at 20 sizes are tracked using a Lagrangian point particle model. Turbulence can largely increase the gravitation induced collision probabilities. Particles at a specific size preferentially pass turbulent eddies on their downward motion side. Hence, the mean settling velocity as well as the local particle concentration increases. The collision statistics at different turbulence intensities are validated against other simulations and compared with an experimental study with a very similar setup using a fit of the results. The setup can be interpreted as water drops in turbulent clouds and the collision statistics can be used to study the impact of turbulence on the droplet growth.

However, particles are often non-spherical, e.g., ice crystals. Ellipsoids are the most general non-spherical shaped particles for which the drag and torque is known analytically. Hence, the motions and collisions of ellipsoids are investigated. Depending on the turbulence intensity the ellipsoids preferentially align with the direction of gravity. This is due to the complex coupling of the turbulence and the particle sedimentation which also increases the settling velocity. Collisions of ellipsoids are considerably more likely than collisions of spheres at the same mass and volume. Unequally orientated ellipsoids have different gravitation induced settling velocities and can come in contact with each other featuring these large relative velocities. It is expected that these effects apply to all kinds of non-spherical particles since the condition of orientation-dependent settling velocities is generally fulfilled.