ru
Back
DOI: 10.17586/1023-5086-2025-92-09-3-13
УДК: 535.4, 535.417
Application of the Gauss–Newton optimization algorithm in the phase function reconstruction from interferometry data in flame diagnostics
Full text on elibrary.ru
Арбузов Э.В., Дубнищев Ю.Н., Золотухина О.С. Применение алгоритма оптимизации Гаусса–Ньютона при реконструкции фазовой функции по данным интерферометрии в диагностике пламен // Оптический журнал. 2025. Т. 92. № 9. С. 3–13. http://doi.org/10.17586/1023-5086-2025-92-09-3-13
Arbuzov E.V., Dubnishchev Yu.N., Zolotukhina O.S. Application of the Gauss–Newton optimization algorithm in the phase function reconstruction from interferometry data in flame diagnostics [in Russian] // Opticheskii Zhurnal. 2025. V. 92. № 9. P. 3–13. http://doi.org/10.17586/1023-5086-2025-92-09-3-13
Aim of study. Development of a method based on the Gauss–Newton algorithm, which allows for phase profile automatic reconstruction of the studied reacting medium and ambiguity minimization in interference pattern complex areas, and also determine the temperature of the flame being diagnosed.Method. The phase structure detection of the probing radiation is based on the Gauss–Newton algorithm, which consists of selecting a phase profile specified by the sum of Bezier curves, then calculating the interferogram and comparing it with the experimental data. The structures coincidence of the experimental and reconstructed interferograms serves as a reliabi-lity criterion. The refractive index of the flame is calculated from the reconstructed phase function, which is converted into temperature. The Gauss–Newton algorithm use is justified by its efficiency and implementation ease. Main results. The reconstructing phase structures method of reacting media from interferometry data, based on the use of Gauss–Newton optimization, has been developed. The method was used to process the burner flame interferogram: the phase function and temperature distribution were calculated in the section. The practical significance of the results obtained lies in the method development that allows automatic diagnostics of phase and temperature fields using interferometry data. Further application will be extended to studies of the pre-mixed mixtures combustion of CH4 and CH4/H2 with air, which are promising fuels in the hydrogen energy field.
phase function reconstruction, interferometry, optimization, Gauss–Newton algo-rithm, flame diagnostics
Acknowledgements:the work was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation, agreement dated April 24, 2024 № 075-15-2024-543.
OCIS codes: 120.5050, 100.5070, 260.3160
References:1. Karaminejad S., Askari M.H, Ashjaee M. Temperature field investigation of hydrogen/air and syngas/air axisymmetric laminar flames using Mach–Zehnder interferometry // Appl. Opt. 2018. V. 57. № 18. P. 181122. https://doi.org/10.1364/AO.57.005057
2. Xun Yuan, Yuge Xue, Junwei Min, et al. High-precision gaseous flame temperature field measurement based on quadriwave-lateral shearing interferometry // Opt. Lasers Eng. 2023. V. 162. P. 107430. https://doi.org/10.1016/j.optlaseng.202107430
3. Chaobo Qi, Shu Zheng, Huaichun Zhou. Experimental investigation on gas-phase temperature of axisymmetric ethylene flames by large lateral shearing interferometry // Int. J. Therm. Sci. 2017. V. 115. P. 104–111. https://doi.org/10.1016/j.ijthermalsci.2017.01.026
4. Chehouani H., Said A.A., Mahfoud El Fagrich. Heat transfer study of free convection through a horizontal open ended axisymmetric cavity using holographic interferometry // Exp. Therm. Fluid Sci. 2015. V. 60. P. 308–316. https://doi.org/10.1016/J.EXPTHERMFLUSCI.20110.007
5. Irandoost M.S., Ashjaee M., Askari M.H., et al. Temperature measurement of axisymmetric partially premixed methane/air flame in a co-annular burner using Mach–Zehnder interferometry // Opt. Lasers Eng. 2015. V. 74. P. 94–102. https://doi.org/10.1016/j.optlaseng.20105.013
6. Beygi-Khosroshahi F., Houshfar E., Yousefi-Asli V., et al. Experimental investigation on heat transfer characteristics of partially premixed round methaneair impinging flame jet using Mach–Zehnder interferometry // Int. J. Therm. Sci. 2019. V. 137. P. 601–615. https://doi.org/10.1016/j.ijthermalsci.2018.12.032
7. Arbuzov E.V., Zolotukhina O.S. Gauss–Newton method application in the problem of phase function reconstructing from hilbertograms // Eurasian J. Math. Comput. Appl. 2023. V. 11. № 4. P. 4–13. https://doi.org/10.32523/2306-6172-2023-11-4-4-13
8. Арбузов Э.В., Арбузов В.А., Дубнищев Ю.Н. и др. Метод Гаусса–Ньютона в задаче оптимизации расчета осесимметричной фазовой функции по данным гильберт-диагностики // Научная визуализация. 2023. Т. 15. № 4. С. 56–67. https://doi.org/0.26583/sv.15.4.05
Arbuzov E.V., Arbuzov V.A., Dubnishchev Yu.N., et al. Gauss–Newton method in the problem of optimizing the axisymmetric phase function calculation based on the Hilbert diagnostic data // Scientific Visualization. 2023. V. 15. № 4. P. 56–67. https://doi.org/0.26583/sv.15.4.05
9. Khan K., Lobiyal D.K., Kilicman A. Bézier curves and surfaces based on modified Bernstein polynomials // Azerbaijan J. Math. 2019. V. 9. № 1. P. 3–21.
10. Дэннис Дж., Шнабель Р. Численные методы безусловной оптимизации и решения нелинейных уравнений / Пер. с англ. Бурдакова О.П. Под ред. Евтушенко Ю.Г. М.: Мир, 1988. 440 с.
Dennis J.E., Schnabel R.B. Numerical methods for unconstrained optimization and nonlinear equations. Englewood Cliffs, NJ.: Prentice-Hall, Inc., 1983. 395 p.
11. Lai W.H., Kek S.L., Tay K.G. Solving nonlinear least squares problem using Gauss–Newton method // Int. J. Innov. Sci. 2017. V. 4. № 1. P. 258–262.
12. Белозеров А.Ф. Оптические методы визуализации газовых потоков. Казань: изд. Казан. гос. техн. унта, 2007. 747 с.
Belozerov A.F. Optical methods for visualizing gas flows [in Russian]. Kazan: Kazan Publishing House. State Tech. Univ., 2007. 747 p.
13. Piecewise cubic Hermite interpolating polynomial (PCHIP). URL: https://www.mathworks.com/help/matlab/ref/pchip.html
14. Васильев Л.А. Теневые методы. М.: Наука, 1968. 400 с.
Vasiliev L.A. Shadow methods [in Russian]. Moscow: "Nauka" Publ., 1968. 400 p.
15. Najafian Ashrafi Z., Ashjaee M., Askari M.H. Twodimensional temperature field measurement of a premixed methane/air flame using Mach–Zehnder interferometry // Opt. Commun. 2015. V. 341 P. 55–63. https://doi.org/10.1016/j.optcom.2014.12.004
16. Chehouani H., Said A.A.H., Fagrich M.E. Heat transfer study of free convection through a horizontal open ended axisymmetric cavity using holographic interferometry // Exp. Therm. Fluid Sci. 2015. V. 60. P. 308–316. https://doi.org/10.1016/J.EXPTHERMFLUSCI.2014.10.007
17. Левин Г.Г., Вишняков Г.Н. Оптическая томография. М.: Радио и связь, 1989. 224 с.
Levin G.G., Vishnyakov G.N. Optical tomography [in Russian] / Moscow: "Radio and Svуaz" Publ., 1989. 224 p.