Abstract
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 Dávila and Hunt (J. Fluid Mech. 440:117–145, 2001).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L.-P. Wang, M.R. Maxey, Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68 (1993)
J. Bec, L. Biferale, M. Cencini, A. Lanotte, S. Musacchio, F. Toschi, Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98, 084502 (2007)
E.J.P. Woittiez, H.J.J. Jonker, L.M. Portela, On the combined effects of turbulence and gravity on droplet collisions in clouds: a numerical study. J. Atmos. Sci. 66, 1926–1943 (2009)
R. Onishi, K. Takahashi, S. Komori, Influence of gravity on collisions of monodispersed droplets in homogeneous isotropic turbulence. Phys. Fluids 21, 125108 (2009)
B. Rosa, H. Parishani, O. Ayala, L.-P. Wang, W.W. Grabowski, Kinematic and dynamic pair collision statistics of sedimenting inertial particles relevant to warm rain initiation. J. Phys. Conf. Ser. 318, 072016 (2011)
J. Dávila, J.C.R. Hunt, Settling of small particles near vortices and in turbulence. J. Fluid Mech. 440, 117–145 (2001)
P.G. Saffman, J.S. Turner, On the collision of drops in turbulent clouds. J. Fluid Mech. 1, 16–30 (1956)
J. Bec, L. Biferale, M. Cencini, A.S. Lanotte, F. Toschi, Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536 (2010)
K.D. Squires, J.L. Eaton, Preferential concentration of particles by turbulence. Phys. Fluids 3A, 1169–1178 (1991)
W.W. Grabowski, P. Vaillancourt, Comments on “preferential concentration of cloud droplets by turbulence: effects on the early evolution of cumulus cloud droplet spectra”. J. Atmos. Sci. 56, 1433–1436 (1999)
D. Hartmann, M. Meinke, W. Schröder, An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods. Comput. Fluids 37, 1103–1125 (2008)
P. Batten, U. Goldberg, S. Chakravarthy, Interfacing statistical turbulence closures with large-eddy simulation. AIAA J. 42(3), 485–492 (2004)
S.B. Pope, Turbulent Flows (Cambrigde University Press, Cambrigde, 2000)
R.P.J. Kunnen, C. Siewert, M. Meinke, W. Schröder, K. Beheng, Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds. Atmos. Res. 127, 8–21 (2013)
M.R. Maxey, J.J. Riley, Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889 (1983)
S. Sundaram, L.R. Collins, Numerical considerations in simulating a turbulent suspension of finite-volume particles. J. Comput. Phys. 124, 337–350 (1996)
J. Li, W. keng Liao, A. Choudhary, R. Ross, R. Thakur, R. Latham, A. Siegel, B. Gallagher, M. Zingale, Parallel netcdf: a high-performance scientific i/o interface, in Proceedings of Supercomputing, 2003
D. Hilbert, Über die stetige Abbildung einer Linie auf ein Flächenstück. Math. Ann. 38, 459–460 (1891)
Message Passing Interface Forum, MPI: A Message-Passing Interface Standard, Version 2.2 (High Performance Computing Center Stuttgart (HLRS), Stuttgart, 2009)
O. Ayala, B. Rosa, L.-P. Wang, W.W. Grabowski, Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 1. Results from direct numerical simulation. New J. Phys. 10, 075015 (2008)
Acknowledgements
The funding of this project under grant number SCHR 309/39 by the Deut-sche Forschungsgemeinschaft is gratefully acknowledged. The authors thank HLR Stuttgart for the provided computational resources.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Siewert, C., Meinke, M., Schröder, W. (2013). Efficient Coupling of an Eulerian Flow Solver with a Lagrangian Particle Solver for the Investigation of Particle Clustering in Turbulence. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ‘13. Springer, Cham. https://doi.org/10.1007/978-3-319-02165-2_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-02165-2_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02164-5
Online ISBN: 978-3-319-02165-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)