Homogene Turbulenz versetzt mit Partikeln finiter Größe: eine numerische Studie
Zusammenfassung der Projektergebnisse
When a dense sphere settles due to gravity in a viscous fluid, its path is essentially determined by the wake flow which gives rise to the hydrodynamic forces. When increasing the non-dimensional gravity, the particle path undergoes a number of transitions from steady vertical motion to steady oblique to oscillating oblique, finally yielding to a chaotic state. Adding a multitude of particles to the picture (but still remaining in the so-called dilute regime with less than one percent solid volume fraction) can lead to interesting additional effects such as spontaneous particle clustering due to the mutual hydrodynamic interactions via the particles’ wakes. Any deviation from a random particle arrangement in turn can have significant consequences for various quantities associated with the disperse phase, such as the average settling velocity, the collision statistics, the particle dispersion, etc., all of which may be relevant in practical applications such as meteorology or chemical engineering. In the present project we have simulated the coupled dynamics of such fluid-particle systems by means of direct numerical simulation, resolving all the relevant length- and time-scales, including the phase interfaces, i.e. particles are fully resolved by the numerical grid. A number of parameter points has been computed using unprecedented system sizes with O(1010 ) grid points and O(104 ) spheres. The data has enabled us to determine a threshold for cluster formation in dilute systems in terms of the non-dimensional gravitational settling velocity (i.e. the Galileo number). It was found that the critical value roughly coincides with the transition from steady vertical to steady oblique motion for a single settling particle in ambient flow. As a consequence of clustering, particles settle on average some 12% faster than a corresponding single particle, and their velocity fluctuation amplitude is strongly increased due to their predominant residence in the cluster regions of the flow. When the carrier phase is in turbulent motion, the particle phase reacts selectively to a certain part of the energy spectrum. Here we have found for dense particles which are larger than the smallest flow feature that practically no clustering occurs in the absence of gravity, and still there exists an instantaneous correlation between the particle positions and the presence of coherent flow structures. It turns out that the particle motion is mostly affected by vortices of a size comparable to the particle diameter. This shows that effects due to the finite size of the particles should in principle be expected over the entire range of existing flow scales, provided that the time scales governing the fluid-particle interaction are matched. Finally, we have added background turbulence to the case with dense particles and finite gravity. It was found that even moderate turbulence intensity prevents the formation of strong particle clusters which was observed in the absence of turbulence as soon as the Galileo number was sufficiently high. As a consequence, no significant enhancement of the settling velocity is observed in this case. The most surprising fact which we have found during the course of the project was the clear relevance of the single particle’s wake regimes for the multi-particle collective motion. Part of the project is currently exhibited on the web-site of the GCS alliance.
Projektbezogene Publikationen (Auswahl)
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Finite size particles in homogeneous turbulence. In K. Binder, G. Münster, and M. Kremer, editors, NIC Symposium 2012, volume 45 of Publication series of the John von Neumann Institute for Computing, pages 377–384, Jülich (Germany), February 2012
M. Uhlmann and T. Doychev
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DNS of horizontal open channel flow with finite-size, heavy particles at low solid volume fraction. New J. Phys., 15(2):025031, 2013
A.G. Kidanemariam, C. Chan-Braun, T. Doychev, and M. Uhlmann
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Settling of finite-size particles in an ambient fluid: a numerical study. In M.H. Kim, editor, ICMF 2013, Proc. 8th Int. Conf. Multiphase Flow, Jeju, Korea, 2013. CDROM
T. Doychev and M. Uhlmann
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Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion. J. Fluid Mech., 752:310–348, 2014
M. Uhlmann and T. Doychev
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The dynamics of finite-size settling particles. PhD Thesis, Karlsruhe Institute of Technology, 2014
T. Doychev
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The motion of a single heavy sphere in ambient fluid: a benchmark for interface-resolved particulate flow simulations with significant relative velocities. Int. J. Multiphase Flow, 59:221–243, 2014
M. Uhlmann and J. Dušek
