Christoph Siewert

On the Collision Detection for Ellipsoidal Particles in Turbulence

Collisions of small and heavy non-spherical particles settling in a turbulent environment are very important to various fields of physics and engineering. However, in contrast to spherical particles the collision probabilities are virtually unknown. In this study we focus on a very important condition for the numerical determination of collision probabilities: the collision detection. We discuss the need for efficient strategies to narrow down the number of possible collision pairs and compare three collision detection methods for ellipsoidal particles. We derive an analytical formula for the collision probability in the case of gravitational settling and validate the collision detection methods with this. Finally, we present statistics of the accuracy and efficiency of the methods. For the case of ellipsoidal particles in turbulence we find that the continuous collision detection with neglected rotation within a time step is the optimal trade-off between accuracy and efficiency.Copyright

Statistical steady state in turbulent droplet condensation

Motivated by systems in which droplets grow and shrink in a turbulence-driven supersaturation field, we investigate the problem of turbulent condensation in a general manner. Using direct numerical simulations we show that the turbulent fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. Based on that, we propose a Lagrangian stochastic model for condensation and evaporation of small droplets in turbulent flows. It consists of a set of stochastic integro-differential equations for the joint evolution of the squared radius and the supersaturation along the droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral timescale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterised by an exponential tail in the droplet mass distribution. These results reconcile those of earlier numerical studies, once these various regimes are considered.

Numerical Investigation of the Combined Effects of Gravity and Turbulence on the Motion of Small and Heavy Particles

Numerical studies [1, 2] show that the influence of gravity and turbulence on the motion of small and heavy particles is not a simple superposition. However, in [3] it is shown that these studies may be artificially influenced by the turbulence forcing scheme. In the present study, a new numerical setup to investigate the combined effects of gravity and turbulence on the motion of small and heavy particles is presented, where the turbulence is only forced at the inflow and is advected through the domain by a mean flow velocity. Within a transition region the turbulence develops to a physical state which shares similarities with grid-generated turbulence in wind tunnels. In this flow, trajectories of about 43 million small and heavy particles are advanced in time. It is found that for a specific particle inertia the particles fall faster in a turbulent flow compared with their fall velocity in quiescent flow. Additionally, specific regions within the turbulent vortices cannot be reached by the particles as a result of the particle vortex interaction. Therewith, the particles tend to cluster outside the vortices. These results are in agreement with the theory of Davilla and Hunt [4].

Influence of turbulence on the drop growth in warm clouds, Part I: comparison of numerically and experimentally determined collision kernels

This study deals with the comparison of numerically and experimentally determined collision kernels of water drops in air turbulence. The numerical and experimental setups are matched as closely as possible. However, due to the individual numerical and experimental restrictions, it could not be avoided that the turbulent kinetic energy dissipation rate of the measurement and the simulations differ. Direct numerical simulations (DNS) are performed resulting in a very large database concerning geometric collision kernels with 1470 individual entries. Based on this database a fit function for the turbulent enhancement of the collision kernel is developed. In the experiments, the collision rates of large drops (radius > 7.5μm

Efficient Coupling of an Eulerian Flow Solver with a Lagrangian Particle Solver for the Investigation of Particle Clustering in Turbulence

> 7.5\,\text{\textmu{}m}

Towards Large Multi-scale Particle Simulations with Conjugate Heat Transfer on Heterogeneous Super Computers

) are measured. These collision rates are compared with the developed fit, evaluated at the measurement conditions. Since the total collision rates match well for all occurring dissipation rates the distribution information of the fit could be used to enhance the statistical reliability and for the first time an experimental collision kernel could be constructed. In addition to the collision rates, the drop size distributions at three consecutive streamwise positions are measured. The drop size distributions contain mainly small drops (radius < 7.5μm

Orientation statistics and settling velocity of ellipsoids in decaying turbulence

< 7.5\,\text{\textmu{}m}

Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds

). The measured evolution of the drop size distribution is confronted with model calculations based on the newly derived fit of the collision kernel. It turns out that the observed fast evolution of the drop size distribution can only be modeled if the collision kernel for small drops is drastically increased. A physical argument for this amplification is missing since for such small drops, neither DNSs nor experiments have been performed. For large drops, for which a good agreement of the collision rates was found in the DNS and the experiment, the time for the evolution of the spectrum in the wind tunnel is too short to draw any conclusion. Hence, the long-time evolution of the drop size distribution is presented in a submitted paper by Riechelmann et al.

Collision rates of small ellipsoids settling in turbulence

Numerical studies show that particles suspended in a turbulent flow tend to cluster due to their inertia (Wang and Maxey, J. Fluid Mech. 256:27–68, 1993; Bec et al., Phys. Rev. Lett. 98:084502, 2007). It was shown by Woittiez et al. (J. Atmos. Sci. 66:1926–1943, 2009) and Onishi et al. (Phys. Fluids 21:125108, 2009) that gravity influences the clustering of small and heavy particles in turbulence. However, these results might be artificially influenced by the periodicity of the used computational domains and also by the turbulence forcing scheme (Rosa et al., J. Phys. Conf. Ser. 318:072016, 2011). In the present study, a new numerical setup to investigate the combined effects of gravity and turbulence on the motion of small and heavy particles is presented, where the turbulence is only forced at the inflow and is advected through the domain by a mean flow velocity. Within a transition region the turbulence develops to a physical state which shares similarities with grid-generated turbulence in wind tunnels. Since the turbulence is decaying in streamwise direction statistical averages can only be performed over small parts of the domain. Hence, a very large number of particles has to be considered to obtain converged statistics compared with the periodic setups of the other numerical studies where averaging can be performed over all particles in the whole domain. This results in the need of a very efficient parallelization strategy. In this study, trajectories of about 43 million small and heavy particles are advanced in time. It is found that specific regions within the turbulent vortices cannot be reached by the particles as a result of the particle vortex interaction. Therewith, the particles tend to cluster outside the vortices. These results are in agreement with the theory of Davila and Hunt (J. Fluid Mech. 440:117–145, 2001).

Comparison of scattering behaviour for spherical and non-spherical particles in pulverized coal combustion

We present numerical methods based on hierarchical Cartesian grids for the simulation of particle flows of different length scales. These include Eulerian-Lagrangian approaches for fully resolved moving particles with conjugate heat-transfer as well as one-way coupled Lagrangian particle models for large-scale particle simulations. The domain decomposition of all phases involved is performed on a joint hierarchical Cartesian grid where the individual cells can belong to one or more sub-grids discretizing different physics, such that numerical methods can operate independently on these sub-sets of the joint mesh to solve, e.g., the Navier-Stokes equations, the heat equation, or the particle motion. Due to the wide range of length scales involved, we first demonstrate the scalability of our automatic mesh generation approach. We then proceed to detail the method for fully-resolved particle simulation and the first steps towards its porting to heterogeneous supercomputers. Finally, we detail the parallelization strategy for the particle motion used by large scale one-way Lagrangian particle simulations.