Direct Numerical Simulation of the Gravitational Settling of Finite Size Particles in Homogeneous Flow

Principal Investigator:
Markus Uhlmann

Institute for Hydromechanics, Karlsruhe Institute of Technology/KIT (Germany)

Local Project ID:

HPC Platform used:
SuperMUC of LRZ

Date published:

The sedimentation of a large number of particles in a fluid medium is ubiquitous in our everyday live and is involved in a large number of engineering applications including aerospace, mechanical, chemical or civil engineering systems, as well as natural and environmental processes. Examples include a variety of energy generating systems, such as fluidized beds, the transport of sediment particles in the atmosphere as well as rain or hail formation. Thus, the ability to understand and predict the behaviour of the particulate phase and the fluid flow in such systems would be critical for assessing possible impacts on the environment or the effectiveness and efficiency in many engineering applications. For instance the understanding of the different physical processes encountered in dispersed phase flows could lead to the production of cleaner, more reliable and safer energy or assessing environmental hazards and taking adequate precaution steps.

A research project, carried out by scientists of the Computational Fluid Dynamics group of the Institute for Hydromechanics at the Karlsruhe Institute of Technology (KIT) addressed the fundamental mechanisms and processes involved in the dynamics of a large number of rigid particles settling under the influence of gravity in an initially quiescent fluid, as well the characteristics of the particle-induced flow field. Such flow systems are particularly challenging, since a wake flow forms downstream of each particle leading to number of hydromechanical coupling phenomena, such as wake-induced particle agglomerations. Thus, the correct description of the particle wakes by the numerical model is critical for the correct representation of the underlying physical mechanisms.

In order to tackle this objective, the scientists employ direct numerical simulation [1] by resolving all relevant scales of the motion of both, the particles and the fluid. In order to ensure that the flow field in the vicinity of the particle surface is correctly represented, special care was taken to chose the small-scale resolution, which is sufficient to resolve the boundary layer on the particle surface [3].

The resulting simulations are computationally extremely demanding involving up to approximately 17 billion grid nodes, running on up to 8,192 processor cores. This facilitated the generation of a high-fidelity data-set, which is anticipated to help verify and improve already existing empirical and industrial models for particulate flows. Thus, the present work greatly benefited from the utilization of the high-performance supercomputer SuperMUC at Leibniz Supercomputing Centre Garching/Munich.

The complete information about the flow field and the motion of the particles produced by the simulations allowed for the exploration of the complex processes involved in particulate flows. An instantaneous view of the flow field and the particle position showing the complex interaction between the particles and the flow field is depicted in figure 1.

The researchers performed a detailed statistical analysis of the flow field and the dynamics of the particles. It was observed that the collective effect of the particles led to significant attenuation of the individual particle wakes. Nevertheless, the wake flow induced by the settling particles was found to be responsible for the formation of particle agglomerations, figure 2, which induce large-scale fluid motion by entrainment. As a consequence, the average particle settling velocity was increased by 12%. These results, which were published in [2] fundamentally related the clustering mechanism to the regime of settling of a single particle.

The generated data-set is potentially of considerable interest for the multiphase flow community since it can be highly useful in model development and validation. It is anticipated that the main impact of the present results will be in providing new insight into the dynamical processes driving turbulent-particle interaction and laying the foundations for the improvement of engineering-purpose models, in particular the point-particle approach.


[1] Uhlmann, M. (2005). An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys., 209(2):448–476. doi:10.1016/

[2] Uhlmann, M. and Doychev, T. (2014). Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: particle motion and clustering. J. Fluid

[3] Uhlmann, M. and Dušek, J. (2014). The motion of a single heavy sphere in ambient fluid: A benchmark for interface-resolved particulate flow simulations with significant relative velocities. Int. J. Multiph. Flow,
59:221–243. doi:10.1016/j.ijmultiphaseflow.2013.10.010

Scientific Contact:

Todor Doychev and Markus Uhlmann
Computational Fluid Dynamics Group
Institute for Hydromechanics
Karlsruhe Institute of Technology (KIT)
Kaiserstraße 12, D-76131 Karlsruhe (Germany)