volume | PIER Journals

Abstract

This paper is devoted to a laser --- based diagnostic technique described as a method for solving an applied inverse problem in turbulent media using laser beam propagation. This problem consists of extracting local information about temperature fluctuations inside a hot turbulent jet of air, from the luminous photodiode trace produced by a laser beam, after having traversed the jet. A genetic algorithm is implemented in order to calculate the optimized laser beam directions corresponding to the whole luminous trace. An approximated ray equation which is proved from the geometrical optics is solved numerically by using those directions and enables to determine the variance of temperature fluctuations along the whole path of the laser beam. A good agreement coming from the comparison between the results obtained and the published experimental data proves the validity of the method.

1. Kolmogorov, A. N., "The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers," Turbulence Classic Papers on Statistical Theory, S. K. Friedlander and L. Topper (eds.), 151-155, Wiley-Interscience, New-York, 1961.

2. Frish, U., Turbulence: The Legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge, 1995.

3. Tennekes, H. and J. L. Lumley, "A First Course in Turbulence," MIT Press, Cambridge, 1971.

4. Monin, S. A. and A. M. Yaglom, "Statistical Fluid Mechanics: Mechanics of Turbulence (1 & 2)," MIT Press, Cambridge, 1975.

5. O'Halloran, M., M. Glavin, and E. Jones, "Rotating antenna microwave imaging system for breast cancer detection," Progress In Electromagnetics Research, Vol. 107, 203-217, 2010.
doi:10.2528/PIER10071002

6. Alexopoulos, A., "Effect of atmospheric propagation in RCS predictions," Progress In Electromagnetics Research, Vol. 101, 277-290, 2010.
doi:10.2528/PIER09121509

7. Genc, O., M. Bayrak, and E. Yaldiz, "Analysis of the effects of GSM bands to the electromagnetic pollution in the RF spectrum," Progress In Electromagnetics Research, Vol. 101, 17-32, 2010.
doi:10.2528/PIER09111004

8. Bukhsh, W. A., B. L. G. Jonsson, and P. Persson, "Element position perturbation for a narrow spot beam with applications in satellite communications antennas," Progress In Electromagnetics Research, Vol. 104, 283-295, 2010.
doi:10.2528/PIER10040602

9. Wang, C. J., B. Y. Wen, Z. G. Ma, W. D. Yan, and X. J. Huang, "Measurement of river surface currents with UHF FMCM radar systems Measurement of river surface currents with UHF FMCM radar systems," Journal of Electromagnetics Waves and Applications, Vol. 21, No. 3, 375-386, 2007.
doi:10.1163/156939307779367350

10. Liang, D., P. Xu, L. Tsang, Z. Gui, and K.-S. Chen, "Electromagnetic scattering by rough surfaces with large heights and slopes with applications in microwave remote sensing of rough surface over layered media ," Progress In Electromagnetics Research, Vol. 95, 199-218, 2009.
doi:10.2528/PIER09071413

11. Titterton, D. H., "A review of optical countermeasures," Proceedings SPIE Conference on Technologies for Optical Countermeasures, Vol. 5615, 1-15, London, 2004.

12. Chernov, L. A., Wave Propagation in a Random Medium, McGraw-Hill, New-York, 1960.

13. Tatarskii, V. I., Wave Propagation in a Turbulent Medium, McGraw-Hill, New-York, 1961.

14. Martini, A., L. Marchi, M. Franceschitti, and A. Massa, "Stochastic ray propagation in stratified random lattices --- comparative assessment of two mathematical approaches," Progress In Electromagnetics Research, Vol. 71, 159-171, 2007.
doi:10.2528/PIER07022002

15. Ishimaru, A., Wave Propagation and Scattering in Random Media (1 & 2), Academic Press, New-York, 1978.

16. Clifford, S. F., "The classical theory of wave propagation in a turbulent medium," Laser Beam Propagation in the Atmosphere, J. W. Strohbehn (ed.), 9-43, Topics in Applied Physics (25), Springer-Verlag, 1978.

17. Li, Y. and H. Ling, "Numerical modelling and mechanism analysis of VHF wave propagation in forested environments using the equivalent slab model ," Progress In Electromagnetics Research, Vol. 91, 17-34, 2009.
doi:10.2528/PIER09012306

18. Tromeur, E., E. Garnier, P. Sagaut, and C. Basdevant, "Large eddy simulations of aero-optical effects in a turbulent boundary layer ," Journal of Turbulence, Vol. 4, No. 5, 1-22, 2003.

19. Hona, J., E. Ngo Nyobe, and E. Pemha, "Experimental technique using interference pattern for measuring directional fluctuations of a laser beam created by a strong thermal turbulence," Progress In Electromagnetics Research, Vol. 84, 289-306, 2008.
doi:10.2528/PIER08072803

20. Consortini, A. and K. A. O'Donnell, "Beam wandering of thin parallel beams through atmospheric turbulence," Waves in Random Media, Vol. 3, S11-S28, 1991.
doi:10.1088/0959-7174/1/3/002

21. Wei, H.-Y., Z.-S. Wu, and Q. Ma, "Log-amplitude variance of laser beam propagation on the slant path through the turbulent atmosphere," Progress In Electromagnetics Research, Vol. 108, 277-291, 2010.
doi:10.2528/PIER10072205

22. Hanada, T., K. Fujisaki, and M. Tateiba, "Theoretical analysis of a bit error rate for satellite communications in ka-band under atmospheric turbulence given by Kolmogorov model," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 11-12, 1515-1524, 2009.
doi:10.1163/156939309789476464

23. Ivanova, I. V., D. I. Dimitriev, and V. S. Sirazetdinov, "Probability density of intensity fluctuations for laser beams disturbed by turbulent aero-engine exhaust ," Proceedings of SPIE, 6594, 2007.

24. Innocenti, C. and A. Consortini, "Refractive index gradient of the atmosphere at near ground levels," Journal of Modern Optics, Vol. 52, No. 5, 671-689, 2005.
doi:10.1080/09500340512331313926

25. Gagnaire, A. and A. Tailland, "Interferometrical setup for the study of thermic turbulence in a plane airstream," Proceedings of SPIE, Vol. 138, 69-73, 1977.

26. Pemha, E., B. Gay, and A. Tailland, "Measurement of the diffusion coefficient in a heated plane airstream," Physics of Fluids, Vol. 5, No. 6, 1289-1295, 1993.
doi:10.1063/1.858565

27. Ngo Nyobe, E. and E. Pemha, "Shape optimization using genetic algorithms and laser beam propagation for the determination of the diffusion coefficient in a hot turbulent jet of air," Progress In Electromagnetics Research B, Vol. 4, 211-221, 2008.
doi:10.2528/PIERB08010605

28. Benzirar, M., E. Pemha, A. Tailland, and B. Gay, "About a new modelling of an optical technique for measuring local turbulent temperature fluctuations inside a hot free-plane jet of air ," Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, M. D. Kelleher, R. K. Shah, K. R. Sreenivasan, and Y. Joshi (eds.), 1615-1619, Elsevier Science Publishers B. V., New-York, 1993.

29. Ngo Nyobe, E. and E. Pemha, "Propagation of a laser beam through a plane and free turbulent heated air flow: Determination of the stochastic characteristics of the laser beam random direction and some experimental results," Progress In Electromagnetics Research, Vol. 53, 31-53, 2005.
doi:10.2528/PIER04073001

30. Alim, A., E. Ngo Nyobe, and E. Pemha, "Theoretical prediction and experimental validation of the angle-of-arrival probability density of a laser beam in a strong plane-flame turbulence ," Optics Communications, Vol. 283, No. 9, 1859-1964, 2010.
doi:10.1016/j.optcom.2009.12.033

31. Beck, J. V. and K. J. Arnold, "Parameter Estimation in Engineering and Science," John Wiley and Sons, New-York, 1977.

32. Holland, J. H., Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, 1975.

33. Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning , Addison-Wesley, Reading, MA, 1989.

34. Deb, K. and Multi-objective Optimization Using Evolutionary Algorithms, John Wiley and Sons, New-York, 2001.

35. Tokan, F. and F. Gunes, "The multi-objective optimization of non-uniform linear phased arrays using the genetic algorithm," Progress In Electromagnetics Research B, Vol. 17, 135-151, 2009.
doi:10.2528/PIERB09072309

36. Zhang, Y.-J., S.-X. Gong, and Y.-X. Xu, "Radiation pattern synthesis for arrays of conformal antennas mounted on an irregular curved surface using modified genetic algorithms," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 10, 1255-1264, 2009.
doi:10.1163/156939309789108589

37. Panduro, M. A., C. A. Brizuela, L. I. Balderas, and D. A. Acosta, "A comparison of genetic algorithms, particle swarm optimization and the di®erential evolution method for design of scannable circular antenna arrays," Progress In Electromagnetics Research B, Vol. 13, 171-186, 2009.
doi:10.2528/PIERB09011308

38. Siakavara, K., "Novel fractal antenna arrays of satellite networks: Circular ring Sierpinski carpet arrays optimized by genetic algorithms ," Progress In Electromagnetics Research, Vol. 103, 115-138, 2010.
doi:10.2528/PIER10020110

39. Obayashi, S. and S. Takanashi, "Genetic optimization of target pressure distributions for inverse design methods," AIAA Journal, Vol. 34, No. 5, 881-886, 1993.
doi:10.2514/3.13163

40. Foster, N. F. and G. S. Dulikravich, "Three-dimensional aerodynamic shape optimization using genetic and gradient search algorithms," Journal of Spacecraft Rockets, Vol. 34, No. 1, 36-42, 1997.
doi:10.2514/2.3189

41. Kumar, A., D. Sahoo, S. Chakraborty, and N. Chakraborty, "Gas injection in steelmaking vessels: Coupling a fluid dynamic analysis with a genetic algorithms-based pareto-optimality," Materials and Manufacturing Processes, Vol. 20, No. 3, 363-379, 2005.
doi:10.1081/AMP-200053434

42. Colaco, M. J. and G. S. Dulikravich, "Solidification of double-diffusive flows using thermo-magneto-hydrodynamics and optimization ," Materials and Manufacturing Processes, Vol. 22, No. 5, 594-606, 2007.
doi:10.1080/10426910701322583

43. Kumar, A., S. Chakraborty, and N. Chakraborty, "Fluid flow in a tundish optimized through Genetic Algorithms," Steel Research International, Vol. 78, No. 7, 517-521, 2007.

44. Davis, L., Handbook of Genetic Algorithms, Van Nostrand Reinhold, New-York, 1990.

45. Michalewicz, Z., Genetic Algorithms + Data Structures =Evolution Programs, Springer Verlag, 1992.

Prof. Elkana Pemha

Dr. Elisabeth Ngo Nyobe