Fully-Resolved, Finite-Size Particles in Statistically Stationary, Homogeneous Turbulence

Principal Investigator:
Markus Uhlmann

Karlsruhe Institute of Technology (Germany)

Local Project ID:

HPC Platform used:
SuperMUC of LRZ

Date published:

Turbulent flow seeded with solid particles is encountered in a number of natural and man-made systems, as diverse as the earth’s atmosphere, rivers, the human respiratory tract, chemical engineering devices, etc. From a technological point of view it is often important to be able to understand and describe the dynamics of such particulate flow systems with sufficient accuracy and at reasonable cost. However, many physical effects occurring when the fluid and the solid phase interact strongly have so far obstinately resisted analytical and experimental approaches, sometimes with far reaching consequences in various practical applications. By way of example let us consider the field of meteorology: the collision rate of raindrops (which is believed to be of prime importance to their growth rate, and consequently a vital ingredient to precipitation models) is strongly and non-trivially affected by turbulence.

It has recently become possible to numerically simulate the motion of a considerable number of finite-size particles including interface resolution and an accurate description of the surrounding flow field on the particle scale (e.g. Uhlmann, 2005). In this project, researchers are simulating with unprecedented detail the turbulent flow in an unbounded domain in the presence of suspended, heavy, solid particles. The fluid is considered Newtonian and incompressible; the particles are rigid, spherical and mono dispersed (equal diameter); turbulence is maintained by large-scale random forcing. The large-scale grant of compute time on SuperMUC as well as generous allotment of storage on the LSDF system at KIT allowed to carry out the present project in an efficient manner.

The simulations involve different values of the Galileo number Ga (a measure for the relative importance of the gravitational force as compared to the viscous forces), ranging from zero-gravity to the value at which strong particle clustering is observed in the absence of background turbulence. The investigation has focused upon two particular problems: (a) which is the nature of the turbulence-particle interactions in the zero-gravity case? (b) how does background turbulence affect the tendency of particles to cluster at larger Galileo number? The present figure 1 shows a visualisation corresponding to problem (a), i.e. without mean particle settling. In this context, the scientists have analysed in detail the geometrical relation between the particle phase and the coherent flow structures. This study has revealed that particles (with Stokes number based upon Kolmogorov scales of approximately 2.5) do exhibit preferential concentration which is detectable via Vorono¨ı tesselation, and which corresponds to particles either sticking on the surfaces of strong worm-like vortices or being located relatively far away from these.

Figure 2 illustrates problem (b), where in the presence of gravity the statistical isotropy is obviously broken. In this case large-scale particle agglomerations do tend to form, but they are much less pronounced than what has been observed in quiescent surroundings (Uhlmann and Doychev, 2014).

The numerical approach to forced turbulence in the presence of suspended particles, the derivation of the energy budget as well as a discussion of results of medium-sized simulations can be found in Chouippe and Uhlmann (2015).


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

M. Uhlmann and T. Doychev. 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. doi:10.1017/jfm.2014.330.

A. Chouippe and M. Uhlmann. Forcing homogeneous turbulence in DNS of particulate flow with interface resolution and gravity. Phys. Fluids, 27(12):123301, 2015. doi:10.1063/1.4936274.

J.C.R. Hunt, A.A. Wray, and P. Moin. Eddies, streams, and convergence zones in turbulent flows. In Proceedings of the Summer Program,pages 193–208. (Center for Turbulence Research, Stanford), 1988.

Core Research Team:

Markus Uhlmann and Agathe Chouippe, Institute for Hydromechanics (IfH), Karlsruhe Institute of Technology (KIT)

Scientific Contact:

Markus Uhlmann
Computational Fluid Dynamics group
Institute for Hydromechanics
Karlsruhe Institute of Technology (KIT)
Kaiserstraße 12, D-76131 Karlsruhe (Germany)
e-mail: markus.uhlmann [@]