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Dispersion and deformation of molecular patterns written in turbulent air

Willem van de Water1,*, Nico Dam2,3, and Enrico Calzavarini4

  • 1Laboratory for Aero and Hydrodynamics, Delft University of Technology and J.M. Burgers Centre for Fluid Dynamics, 2628 CD Delft, The Netherlands
  • 2Institute for Molecules and Materials, Radboud University, 6500 GL Nijmegen, The Netherlands
  • 3Mechanical Engineering Department, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
  • 4Université de Lille, ULR 7512–Unité de Mécanique de Lille Joseph Boussinesq (UML), F-59000 Lille, France

  • *Corresponding author: w.vandewater@tudelft.nl

Phys. Rev. Fluids 9, 014502 – Published 12 January, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.014502

Abstract

Molecular tagging is used to study the dispersion and deformation of patterns written in turbulent air. The writing is done by fusing O2 and N2 molecules into NO in the focus of a strong ultraviolet laser beam. By crossing several of these laser beams, patterns that have both small and large scales can be painted. The patterns are visualized a while later by inducing fluorescence of the NO molecules with a second UV laser and registering the image. The width of the lines that make the pattern is approximately 50µm, a few times the Kolmogorov length η, the smallest length scale in turbulence, while the largest size of the patterns (4mm) is inside the inertial range of the used turbulent jet flow. At small scales molecular clouds disperse under the joint action of molecular diffusion and turbulence. The experiments reveal this highly nontrivial interaction. At inertial-range scales (200η) we verify the Batchelor dispersion of objects whose size is inside the inertial range. Patterns are compressible objects and spontaneously develop concentration fluctuations. We show for the first time the nontrivial statistical properties of these fluctuations. Finally, we use the information in written and deformed lines to quantify turbulent intermittency, obtaining results that agree with the established scaling anomaly of velocity structure functions.

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References (56)

  1. R. B. Miles and W. R. Lempert, Quantitative flow visualization in unseeded flows, Annu. Rev. Fluid Mech. 29, 285 (1997).
  2. M. M. Koochesfahani and D. G. Nocera, Molecular tagging velocimetry, in Handbook of Experimental Fluid Dynamics, edited by J. Foss, C. Tropea, and A. Yarin (Springer-Verlag, Berlin, 2007), Chap. 5.4.
  3. G. S. Diskin, W. R. Lempert, and R. B. Miles, Observation of vibrational relaxation dynamics in x3σg oxygen following stimulated Raman excitation to the v=1 level: Implications for the RELIEF flow tagging technique, Report No. AIAA Paper 96-0301, NASA, 1996.
  4. N. J. Dam, R. J. H. Klein-Douwel, N. M. Sijtsema, and J. J. ter Meulen, Nitric oxide flow tagging in unseeded air, Opt. Lett. 26, 36 (2001).
  5. N. J. DeLuca, R. B. Miles, N. Jiang, W. D. Kulatolaka, A. K. Patnaik, and J. R. Gord, FLEET velocimetry for combustion and flow diagnostics, Appl. Opt. 56, 8632 (2017).
  6. J. Bominaar, T. Elenbaas, M. Pashtrapanska, N. Dam, J. J. ter Meulen, and W. van de Water, Writing in turbulent air, Phys. Rev. E 77, 046312 (2008).
  7. F. Li, H. Zhang, and B. Bai, A review of molecular tagging technique, Measurement 171, 108790 (2021).
  8. R. W. Pitz, J. A. Wehrmeyer, L. A. Ribarov, D. A. Oguss, F. Batliwala, P. A. D. S. Deusch, and P. E. Dimotakis, Unseeded molecular flow tagging in cold and hot flows using ozone and hydroxyl tagging velocimetry, Meas. Sci. Technol. 11, 1259 (2000).
  9. R. Sánchez-González, R. Srinivasan, R. D. W. Bowersox, and S. W. North, Simultaneous velocity and temperature measurements in gaseous flow fields using the VENOM technique, Opt. Lett. 36, 196 (2011).
  10. E. M. Thurlow and J. C. Klewicki, Experimental study of turbulent Poiseuille–Couette flow, Phys. Fluids 12, 865 (2000).
  11. M. Mirzaei, N. J. Dam, and W. van de Water, Molecular tagging velocimetry in turbulence using biacetyl, Phys. Rev. E 86, 046318 (2012).
  12. A. Noullez, G. Wallace, W. Lempert, R. B. Miles, and U. Frisch, Transverse velocity increments in turbulent flow using the RELIEF technique, J. Fluid Mech. 339, 287 (1997).
  13. P. G. Saffman, On the effect of the molecular diffusivity in turbulent diffusion, J. Fluid Mech. 8, 273 (1960).
  14. A. A. Townsend, The diffusion of heat spots in isotropic turbulence, Proc. R. Soc. London A 209, 418 (1951).
  15. A. A. Townsend, The diffusion behind a line source in homogeneous turbulence, Proc. R. Soc. London A 224, 487 (1954).
  16. U. Frisch, Turbulence, The Legacy of A. N. Kolmogorov (Cambridge University Press, New York, 1995).
  17. W. R. Mickelsen, Measurements on the effect of molecular diffusivity in turbulent diffusion, J. Fluid Mech. 7, 397 (1960).
  18. A. Mazzino and M. Vergassola, Interference between turbulent and molecular diffusion, Europhys. Lett. 37, 535 (1997).
  19. K. Kontomaris and T. J. Hanratty, Effect of molecular diffusivity on point source diffusion in the center of a numerically simulated turbulent channel flow, Int. J. Heat Mass Transf. 37, 1817 (1994).
  20. P. C. Chatwin and P. J. Sullivan, The relative diffusion of a cloud of passive contaminant in incompressible turbulent flow, J. Fluid Mech. 91, 337 (1979).
  21. G. I. Taylor, Diffusion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London A 219, 186 (1953).
  22. P. B. Rhines and W. R. Young, How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech. 133, 133 (1983).
  23. G. I. Taylor, Diffusion by continuous movements, Proc. London Math. Soc. S2-20, 196 (1921).
  24. S. B. Pope, The vanishing effect of molecular diffusivity on turbulent dispersion: Implications for turbulent mixing and the scalar flux, J. Fluid Mech. 359, 299 (1998).
  25. W. van de Water, N. Dam, and E. Calzavarini, Dispersion of molecular patterns written in turbulent air, Phys. Rev. Lett. 129, 254501 (2022).
  26. B. L. Sawford and J. C. R. Hunt, Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence, J. Fluid Mech. 165, 373 (1986).
  27. D. Buaria, P. K. Yeung, and B. L. Sawford, A Lagrangian study of turbulent mixing: Forward and backward dispersion of molecular trajectories in isotropic turbulence, J. Fluid Mech. 799, 352 (2016).
  28. D. Buaria, B. L. Sawford, and P. K. Yeung, Characteristics of backward and forward two-particle relative dispersion in turbulence at different Reynolds numbers, Phys. Fluids 27, 105101 (2015).
  29. R. M. Kerr, Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence, J. Fluid Mech. 153, 31 (1985).
  30. G. K. Batchelor, Diffusion in a field of homogeneous turbulence: II. The relative motion of particles, Proc. Cambridge Philos. Soc. 48, 345 (1952).
  31. R. Dhariwal and A. D. Bragg, Fluid particles only separate exponentially in the dissipation range after extremely long times, Phys. Rev. Fluids 3, 034604 (2018).
  32. D. Buaria, E. Bodenschatz, and A. Pumir, Vortex stretching and enstrophy production in high Reynolds number turbulence, Phys. Rev. Fluids 5, 104602 (2020).
  33. G. K. Batchelor, The effect of homogeneous turbulence on material lines and surfaces, Proc. R. Soc. London A 213, 349 (1952).
  34. L. F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc. London A 110, 709 (1926).
  35. B. R. Pearson, P.-A. Krogstad, and W. van de Water, Measurements of the turbulent energy dissipation rate, Phys. Fluids 14, 1288 (2002).
  36. W. van de Water and N. Dam, How to find patterns written in turbulent air, Exp. Fluids 54, 1574 (2013).
  37. M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, Int. J. Comput. Vision 1, 321 (1988).
  38. C. Xu and J. L. Prince, Snakes, shapes and gradient vector flow, IEEE Trans. Image Process. 7, 359 (1998).
  39. W. J. Massman, A review of the molecular diffusivities of H2O, CO2, CH4, CO, O3, SO2, NH3, N2O, NO, in air, O2 and N2 near STP, Atmos. Environ. 32, 1111 (1998).
  40. P. K. Yeung and Y. Zhou, Universality of the Kolmogorov constant in numerical simulations of turbulence, Phys. Rev. E 56, 1746 (1997).
  41. M. Bourgoin, N. T. Ouelette, H. Xu, J. Berg, and E. Bodenschatz, The role of turbulent pair dispersion in turbulent flow, Science 311, 835 (2006).
  42. N. T. Ouellette, H. Xu, M. Bourgouin, and E. Bodenschatz, An experimental study of turbulent relative dispersion models, New J. Phys. 8, 109 (2006).
  43. B. Sawford, Turbulent relative dispersion, Annu. Rev. Fluid Mech. 33, 289 (2001).
  44. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975).
  45. A. Celani, A. Lanotte, A. Mazzino, and M. Vergassola, Fronts in passive scalar turbulence, Phys. Fluids 13, 1768 (2001).
  46. M. Holzer and E. D. Siggia, Turbulent mixing of a passive scalar, Phys. Fluids 6, 1820 (1994).
  47. C. Tong and Z. Warhaft, On passive derivative statistics in grid turbulence, Phys. Fluids 6, 2165 (1994).
  48. K. P. Iyer, J. Schumacher, K. R. Sreenivasan, and P. K. Yeung, Steep cliffs and saturated exponents in three-dimensional turbulence, Phys. Rev. Lett. 121, 264501 (2018).
  49. D. Buaria, M. P. Clay, K. R. Sreenivasan, and P. K. Yeung, Small-scale anisotropy and ramp-cliff structures in scalar turbulence, Phys. Rev. Lett. 126, 034504 (2021).
  50. E. Calzavarini, Y. X. Huang, F. G. Schmitt, and L. P. Wang, Popelled microprobes in turbulence, Phys. Rev. Fluids 3, 054604 (2018).
  51. J. Bec, H. Homann, and G. Krstulovic, Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles, Phys. Rev. Lett. 112, 234503 (2014).
  52. L. Bentkamp, T. D. Drivas, C. C. Lalescu, and M. Wilczek, The statistical geometry of material loops in turbulence, Nat. Commun. 13, 2088 (2022).
  53. H. E. Cekli and W. van de Water, Stirring anisotropic turbulence with an active grid, Phys. Fluids 32, 075119 (2020).
  54. Z.-S. She and E. Leveque, Universal scaling laws in fully developed turbulence, Phys. Rev. Lett. 72, 336 (1994).
  55. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48, R29(R) (1993).
  56. B. Stier and M. M. Koochesfahani, Molecular tagging velocimetry (MTV) measurements in gas phase flows, Exp. Fluids 26, 297 (1999).

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