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Micro-Mixing Modelling of Scalar Fluctuations for Plumes in Homogeneous Turbulence

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Abstract

We use the interaction by exchange with the mean (IEM) and interaction by exchange with the conditional mean (IECM) mixing models coupled to a Langevin model for particle trajectories to make detailed predictions of statistics of the concentration field downstream of line sources in grid turbulence and compare these predictions with suitable laboratory data. A critical part of the model is the prescription of a mixing time scale. We show that the IECM model gives a good representation of data for a single line source for a range of source conditions and also reproduces very well the variations with both travel time and source separation of the correlation between the concentrations from the two sources. We show that in the limit of zero mixing time scale the IECM model is equivalent to a meandering plume model and thus has a sound physical basis in the near-field where meandering dominates the concentration fluctuations. In contrast, the IEM model ignores the effect of plume meandering and underestimates the centreline intensity of fluctuations in the near and mid fields.

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References

  1. Anand, M.S. and Pope, S.B., Diffusion behind a line source in grid turbulence. In: Bradbury, L.J.S., Durst, F., Launder, B.E., Schmidt, F.W. and Whitelaw, J.H. (eds.), Turbulent Shear Flows 4. Springer-Verlag, Berlin (1985) pp. 46-52.

    Google Scholar 

  2. Borgas, M.S., Meandering plume models in turbulent flows. In: Proceedings of the 13th Australasian Fluid Mechanics Conference, Monash University, Melbourne (1998) pp. 139-142.

  3. Borgas, M.S. and Sawford, B.L., A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence. J. Fluid Mech. 279 (1994) 69-99.

    Google Scholar 

  4. Borgas, M.S. and Sawford, B.L., Molecular diffusion and viscous effects on concentration statistics in grid turbulence. J. Fluid Mech. 324 (1996) 25-54.

    Google Scholar 

  5. Borgas, M.S. and Yeung, P.K., Relative dispersion in isotropic turbulence: Part 2. Anewstochas-tic model with Reynolds number dependence. J. Fluid Mech. 503 (2004) 125-160.

    Google Scholar 

  6. Brethouwer, G. and Nieuwstadt, F.T.M., DNSof mixing and reaction of two species in a turbulent channel flow: A validation of the conditional moment closure. Flow Turb. Combust. 66 (2001) 209-239.

    Google Scholar 

  7. Cassiani, M. and Giostra, U., A simple and fast model to compute concentration moments in a convective boundary layer. Atmos. Environ. 36 (2002) 4717-4724.

    Google Scholar 

  8. Dopazo, C., Probability density function approach for a turbulent axisymmetric heated jet. Centreline evolution. Phys. Fluids 18 (1975) 397-410.

    Google Scholar 

  9. Du, S., Sawford, B.L., Wilson, J.D. and Wilson, D.J., Estimation of the Kolmogorov constant (C0) for the Lagrangian structure function, using a second-order Lagrangian model of grid turbulence. Phys. Fluids 7 (1995) 3083-3090.

    Google Scholar 

  10. Flesch, T.K., The footprint for flux measurements, from backward Lagrangian stochastic models. Bound. Layer Meteorol. 78 (1996) 399-404.

    Google Scholar 

  11. Flesch, T.K. and Wilson, J.D., Atwo-dimensional trajectory simulation model for non-Gaussian, inhomogeneous turbulence within plant canopies. Bound. Layer Meteorol. 61 (1992) 349-374.

    Google Scholar 

  12. Fox, R.O., On velocity conditioned scalar mixing in homogeneous turbulence. Phys. Fluids 8 (1996) 2678-2691.

    Google Scholar 

  13. Gardiner, C.W., Handbook of Stochastic Methods for Physics Chemistry and the Natural Sciences, Springer, Berlin (1983) pp. 442.

    Google Scholar 

  14. Gonzalez, M., Analysis of the effect of microscale turbulence on atmospheric chemical reactions by means of the pdf approach. Atmos. Environ. 31 (1997) 575-586.

    Google Scholar 

  15. de Haan, P. and Rotach, M.W., A novel approach to atmospheric dispersion modelling: The puff-particle model. Quart. J. Roy. Meteorol. Soc. 124 (1995) 2771-2792.

    Google Scholar 

  16. Haworth, D.C. and Pope, S.B., A generalized Langevin model for turbulent flows. Phys. Fluids 29 (1986) 387-405.

    Google Scholar 

  17. Lai, C.-T., Katul, G., Ellsworth, D. and Oren, R., Modelling vegetation-atmosphere CO2 ex-change by a coupled Eulerian-Lagrangian approach. Bound. Layer Meteorol. 95 (2000) 91-122.

    Google Scholar 

  18. Luhar, A.K. and Britter, R.E., Arandom walk model for dispersion in inhomogeneous turbulence in a convective boundary layer. Atmos. Environ. 23 (1989) 1911-1924.

    Google Scholar 

  19. Luhar, A.K., Hibberd, M.F. and Borgas, M.S., A skewed meandering plume model for concen-tration statistics in the convective boundary layer. Atmos. Environ. 34 (2000) 3599-3616.

    Google Scholar 

  20. Mole, N. and Clarke, E.D., Relationships between higher moments of concentration and of dose in turbulent dispersion. Bound. Layer Meteorol. 73 (1995) 35-53.

    Google Scholar 

  21. Monin A.S. and Yaglom, A.M. In: Lumley, J.L. (ed.), Statistical Fluid Mechanics. MIT Press, Cambridge, MA, Vol. II (1975) 874 pp.

    Google Scholar 

  22. Overholt, M.R. and Pope, S.B., Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence. Phys. Fluids 8 (1996) 3128-3148.

    Google Scholar 

  23. Pipino, M. and Fox, R.O., Reactive mixing in a tubular jet reactor: A comparison of pdf simu-lations with experimental data. Chem. Eng. Sci. 49 (1994) S229-S241.

    Google Scholar 

  24. Pope, S.B., Pdf methods for turbulent reactive flows, Prog. Energy Combust. Sci. 11 (1985) 119-192.

    Google Scholar 

  25. Pope, S.B., On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys. Fluids 6 (1994) 973-985.

    Google Scholar 

  26. Pope, S.B., The vanishing effect of molecular diffusivity on turbulent dispersion: Implications for turbulent mixing and the scalar flux. J. Fluid Mech. 359 (1998) 299-312.

    Google Scholar 

  27. Pope, S.B., Turbulent Flows. Cambridge University Press, Cambridge (2000) 806 pp.

    Google Scholar 

  28. Pumir, A., Shraiman, B.I. and Chertkov, V., Geometry of Lagrangian dispersion in turbulence, Phys. Rev. Lett. 85 (2000) 5324-5327.

    Google Scholar 

  29. Saffman, P.G., On the effect of molecular diffusivity in turbulent diffusion. J. Fluid Mech. 8 (1960) 273-283.

    Google Scholar 

  30. Sawford, B.L., The effect of Gaussian particle-pair distribution functions in the statistical theory of concentration fluctuations in homogeneous turbulence. Quart. J. Roy. Meteorol. Soc. 109 (1983) 339-354.

    Google Scholar 

  31. Sawford, B.L. and Borgas, M.S., On the continuity of stochastic models for Lagrangian velocity in turbulence. Physica D 76 (1994) 297-311.

    Google Scholar 

  32. Sawford, B.L., Frost, C.C. and Allan, T.C., Atmospheric boundary-layer measurements of con-centration statistics from isolated and multiple sources. Bound. Layer Meteorol. 31 (1985) 249-268.

    Google Scholar 

  33. Sawford, B.L. and Guest, F.M., Uniqueness and universality in Lagrangian stochastic models of turbulent dispersion. In: Preprints 8th Symposium on Turbulence and Diffusion. American Meteorological Society, Boston (1988) pp. 96-99.

  34. Sawford, B.L. and Sullivan, P.J., A simple representation of a developing contaminant concen-tration field. J. Fluid Mech. 289 (1995) 141-157.

    Google Scholar 

  35. Sawford, B.L. and Stapountzis, H., Concentration fluctuations according to fluctuating plume models in one and two dimensions. Bound. Layer Meteorol. 37 (1986) 89-106.

    Google Scholar 

  36. Sawford, B.L. and Tivendale, C.M., Measurement of concentration statistics downstream of a line source in grid turbulence. In: Proceedings of the 11th Australasian Fluid Mechanics Conference, University of Tasmania, Hobart (1992) pp. 945-948.

  37. van Slooten, P.R. and Pope, S.B., Application of PDF modeling to swirling and nonswirling turbulent jets. Flow Turb. Combust. 62 (1999) 295-333.

    Google Scholar 

  38. Stapountzis, H., Sawford, B.L., Hunt, J.C.R. and Britter, R.E., Structure of the tempera-ture field downwind of a line source in grid turbulence. J. Fluid Mech. 165 (1986) 401-424.

    Google Scholar 

  39. Sykes, R.I., Lewellen, W.S. and Parker, S.F., A turbulent transport model for concentration fluctuations and fluxes. J. Fluid Mech. 139 (1984) 193-218.

    Google Scholar 

  40. Thomson, D.J., Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech. 180 (1987) 529-556.

    Google Scholar 

  41. Thomson, D.J., Eulerian analysis of concentration fluctuations in dispersing plumes. Phys. Fluids 9 (1997) 2349-2354.

    Google Scholar 

  42. Townsend, A.A., The Structure of Turbulent Shear Flow. Cambridge University Press, Cambridge (1976) pp. 429.

    Google Scholar 

  43. Tsai, K. and Fox, R.O., Pdf simulation of a turbulent series-parallel reaction in an axisymmetric reactor. Chem. Eng. Sci. 49 (1994) 5141-5158.

    Google Scholar 

  44. Villermaux, J. and Devillon, J.C. In: Proceedings of the Second International Symposium on Chemical Reaction Engineering, Elsevier, New York (1972).

    Google Scholar 

  45. Warhaft, Z., The interference of line sources in grid turbulence. J. Fluid Mech. 144 (1984) 363-387.

    Google Scholar 

  46. Yeung, P.K., Xu, S., Borgas, M.S. and Sawford, B.L., Scaling of multi-particle Lagrangian statistics in Direct Numerical Simulations. In: Smits, A.J. (ed.), IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, Kluwer, Dordrecht (2002) pp. 163-168.

    Google Scholar 

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  1. CSIRO Atmospheric Research, PMB1 Aspendale, Victoria, Australia

    B.L. Sawford

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Sawford, B. Micro-Mixing Modelling of Scalar Fluctuations for Plumes in Homogeneous Turbulence. Flow, Turbulence and Combustion 72, 133–160 (2004). https://doi.org/10.1023/B:APPL.0000044409.74300.db

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