Skip to main content
SpringerLink
Log in

Investigation of the Cross-beam Correlation Algorithm to Reconstruct Local Field Statistics from Line-of-sight Measurements in Turbulent Flows

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

Optical techniques such as speckle photography and rainbow schlieren deflectometry yield path integrated measurements of deflection angle instead of the local field variable such as density, temperature and/or species concentration. Thus, a reconstruction algorithm is employed to obtain the local properties from the path-integrated measurements. Cross-beam correlation (CBC) algorithm provides the link between path-integrated and local field statistics in time-averaged axisymmetric turbulent flows. Path-integrated statistics are obtained using orthogonal light rays crossing within the turbulent flow. The algorithm assumes local isotropy and negligible correlation between points on orthogonal beams, which is valid strictly in fully turbulent flows. In this study, noise-free synthetic scalar turbulence data are generated and used to determine how different assumptions in the CBC algorithm affect the reconstruction accuracy. Results show that the reconstruction accuracy is excellent for a narrow correlation function (or small integral length scale), while significant errors are incurred in case of a wide correlation function. A procedure to improve the reconstruction accuracy of the CBC algorithm is proposed in this study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Mathew, J., Basu, A.J.: Reacting, circular mixing layers in transition to turbulence. Flow Turbul. Combust. 64, 71–93 (2000)

    Article  MATH  Google Scholar 

  2. Jiang, X., Luo, K.H.: Spatial direct numerical solution of the large vortical structures in forced plumes. Flow Turbul. Combust. 64, 43–69 (2000)

    Article  MATH  Google Scholar 

  3. Zhou, X., Luo, K.H., Williams, J.J.R.: Dynamic behavior in reacting plumes. In: Proceedings of Combustion Institute, vol. 28, pp. 2859–2865 (2000)

  4. Asendrych, D., Drobniak, S.: Buoyancy-driven coherent structures in free round flame. Flow Turbul. Combust. 67, 325–353 (2001)

    Article  MATH  Google Scholar 

  5. Kolhe, P.S., Agrawal, A.K.: Role of buoyancy on instabilities and structure of transitional gas jet diffusion flames. Flow Turbul. Combust. 79, 343–360 (2007)

    Article  Google Scholar 

  6. Fisher, M.J., Krause, F.R.: The crossed-beam correlation technique. J. Fluid Mech. 28(4), 705–717 (1967)

    Article  ADS  Google Scholar 

  7. Wilson, L.N., Damkevala, R.J.: Statistical properties of turbulent density fluctuations. J. Fluid Mech. 43, 291–303 (1970)

    Article  ADS  Google Scholar 

  8. Winarto, H., Davis, M.R.: Fluctuations of density, pressure and temperature in a turbulent mixing region. Proc. R. Soc. Lond. Ser. A. 395, 203–228 (1984)

    Article  ADS  Google Scholar 

  9. Kalghatgi, G.T., Cousins, J.M., Bray, K.N.C.: Crossed-beam correlation measurements and model predictions in a rocket exhaust plume. Combust. Flame 43, 51–67 (1981)

    Article  Google Scholar 

  10. Davis, M.R.: Intensity, scale and convection of turbulent density fluctuations. J. Fluid Mech. 70, 463–479 (1975)

    Article  ADS  Google Scholar 

  11. Davis, M.R.: Turbulent refractive index fluctuations in a hydrogen diffusion flame. Combust. Sci. Technol. 64, 51–65 (1989)

    Article  Google Scholar 

  12. Davis, M.R., Rerkshanandana, P.: Influence of large eddies on thermal mixing. Int. J. Heat Mass Transfer 34(7), 1633–1647 (1991)

    Article  Google Scholar 

  13. Davis, M.R., Rerkshanandana, P.: Schlieren measurement of turbulent structure in diffusion flame. Exp. Therm. Fluid Sci. 6, 402–416 (1993)

    Article  Google Scholar 

  14. Davis, M.R., Rerkshanandana, P.: Integral scales and mixing lengths in turbulent mixing and combustion. Exp. Therm. Fluid Sci. 8, 239–244 (1994)

    Article  Google Scholar 

  15. Erbeck, R., Merzkirch, W.: Speckle photographic measurement of turbulence in an air stream with fluctuating temperature. Exp. Fluids 6, 89–93 (1998)

    Google Scholar 

  16. Sivathanu, Y.R., Lim, J., Joseph, R.: Statistical absorption tomography for turbulent flows. J. Quant. Spectrosc. Radiat. Transfer 68, 611–623 (2001)

    Article  ADS  Google Scholar 

  17. Fomin, N.A., Laviskaya, E., Takayama, K.: Limited projections laser speckle tomography of complex flows. Opt. Lasers Eng. 44, 335–349 (2006)

    Article  Google Scholar 

  18. Atta, C.V.: Local isotropy of the smallest scales of turbulent scalar and velocity fields. Proc. R. Soc. Lond. Ser. A. 434, 139–147 (1991)

    Article  MATH  ADS  Google Scholar 

  19. Cormack, A.M.: Computed tomography: some history and recent developments. In: Shepp, L.A. (ed.) Proc. Symp. Appl. Math., vol. 27, pp. 35–42 (1982)

  20. Dasch, C.J.: One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered back projection methods. Appl. Opt. 31, 1146–1152 (1992)

    Article  ADS  Google Scholar 

  21. Keating, A., Piomelli, U., Balaras, E., Kaltenbach, H.J.: A priori and a posteriori tests of inflow conditions for large eddy simulation. Phys. Fluids 16(12), 4696–4712 (2004)

    Article  ADS  Google Scholar 

  22. Kraichnan, R.H.: Diffusion by a random velocity field. Phys. Fluids 13(1), 22–31 (1970)

    Article  MATH  ADS  Google Scholar 

  23. Lund, T.S., Wu, X., Squires, K.D.: Generation of turbulent inflow data for spatially developing boundary layer simulations. J. Comput. Phys. 140, 233–258 (1998)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. Smirnov, A., Shi, S., Celik, I.: Random flow generation technique for large eddy simulations and particle-dynamics modeling. J. Fluids Eng. 123, 359–371 (2001)

    Article  Google Scholar 

  25. Bryner, N., Richards, C.D., Pitts, W.M.: A Rayleigh light scattering facility for investigation of free jets and plumes. Rev. Sci. Instrum. 63(7), 3629–3635 (1992)

    Article  ADS  Google Scholar 

  26. Panchapakesan, N.R., Lumley, J.L.: Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium jet. J. Fluid Mech. 246, 225–247 (1993)

    Article  ADS  Google Scholar 

  27. Richards, C.D., Pitts, W.M.: Global density effects on the self-preservation behaviour of turbulent free jets. J. Fluid Mech. 254, 417–435 (1993)

    Article  ADS  Google Scholar 

  28. Shabbir, A., George, W.K.: Experiments on a round turbulent buoyant plume. J. Fluid Mech. 275, 1–32 (1994)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Alabama, Tuscaloosa, AL, 35487, USA

    Pankaj S. Kolhe & Ajay K. Agrawal

Authors
  1. Pankaj S. Kolhe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ajay K. Agrawal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ajay K. Agrawal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolhe, P.S., Agrawal, A.K. Investigation of the Cross-beam Correlation Algorithm to Reconstruct Local Field Statistics from Line-of-sight Measurements in Turbulent Flows. Flow Turbulence Combust 84, 617–638 (2010). https://doi.org/10.1007/s10494-009-9244-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-009-9244-9

Keywords

Search

Navigation