519.6, 621.4 Mathematical model of conditional pressure optimization in the crack detection system of gas turbine blades
Andrianov I. K. (Комсомольский-на-Амуре государственный технический университет), Chepurnova E. K. (Комсомольский-на-Амуре государственный технический университет)
NONLINEAR PROGRAMMING, CONDITIONAL OPTIMIZATION, CRACK DETECTION SYSTEM, TURBINE BLADE, SHELL, PRESSURE
doi: 10.18698/2309-3684-2024-2-316
The study considers the problem of optimizing the crack detection system of gas turbine blades. The shell of the capsule of the damage detection system, which is under the influence of internal pressure, is considered as an object of research. The task of the study was devoted to the mathematical modeling of optimal pressure in capsules of the damage detection system. As part of solving the research problem, a mathematical formulation of the problem of optimizing the nonlinear pressure function was carried out in the presence of restrictions on variable parameters: wall thickness and outer diameter of the cylindrical capsule shell. The construction of the optimization objective function was carried out on the basis of the equilibrium condition of the shell element in the area of crack opening of the turbine blade, the limit state criterion using the Tresk-Saint-Venant strength theory. The research methodology was based on the approximate decomposition of the function into a Taylor series, the Lagrange multiplier method, and the Kuhn-Tucker theorem. When solving the problem of conditional optimization, the cases of violation of the regularity conditions of the limiting functions are analyzed. According to the calculation results, the minimum value of the required pressure for the destruction of the capsule shell in case of opening of the crack banks of the turbine blade is achieved at the maximum value of the outer diameter of the shell and the minimum thickness of its wall. According to the test calculation data, the area of acceptable solutions to the optimization problem is graphically presented, and the lines of the level of the target function of pressure optimization are shown. The constructed mathematical model and calculation algorithm will automate the process of calculating the required pressure in the capsules of the turbine blade crack detection system and obtain an estimate of the minimum pressure value in the presence of restrictions on the absolute and relative values of the capsule shell wall thickness, the outer diameter of the capsule.
[1] Grinkrug M.S., Mohamad K. B., Novgorodov N. A. Sistema povysheniya bezopasnosti aviacionnyh gazoturbinnyh dvigatelej vo vremya ekspluatacii [System for increasing the safety of aviation gas turbine engines during operation]. Nauka, innovacii i tekhnologii: ot idej k vnedreniyu: Materialy II Mezhdunarodnoj nauchnoprakticheskoj konferencii molodyh uchenyh, Komsomol'sk-na-Amure. CHast' 2 [Science, innovation and technology: from ideas to implementation: materials of the II International Scientific and Practical Conference of Young Scientists, Komsomolsk-on-Amur. Part 2]. Komsomolsk-na-Amure, ФГБОУ ВО «КнАГУ», 2022, pp. 197-199.
[2] Mohamad, K.B., Grinkrug, M.S., Novgorodov, N.A., Tkacheva, J.I. Development of a system for detecting microcracks in turbine blades of aircraft engines. AIP Conference Proceedings, 2023, vol. 2700, art. 020027.
[3] Certificate no. № 2023610220 Programma vychisleniya neobhodimogo kolichestva veshchestva dlya razmeshcheniya v tonkostennyh kapsulah pri sozdanii sistemy obnaruzheniya treshchin v lopatkah rabotayushchih gazoturbinnyh dvigatelej [The program for calculating the required amount of substance for placement in thin-walled capsules when creating a system for detecting cracks in the shoulder blades of working gas turbine movements]: Certificate of state registration of a computer program / M. S. Grinkrih, B. M. Kara, N. A. Novgorodov, Yu. I. Tkachev; applicant Komsomolsk-na-Amure State Technical University ― no. 2023611350; application 10.01.2023; registered in the register of computer programs 19.01.2023 ― [1].
[4] Mohamad K.B., Grinkrug M.S. Tekhnologicheskoe issledovanie harakteristik sistemy rannego obnaruzheniya mikrotreshchin v lopatke turbiny dvigatelya [Technological study of the characteristics of the early detection system of microcracks in the engine of the engine turbine]. Proizvodstvennye tekhnologii budushchego: ot sozdaniya k vnedreniyu: Materialy V Mezhdunarodnoj nauchno-prakticheskoj konferencii [Production technologies of the future: from creation for implementation: Materials of V International Scientific and Practical Conference]. Komsomolsk-na-Amure, Komsomolsk-na-Amure State Technical University, 2022, pp. 290-293.
[5] Kara B.M., Grinkrug M.S., Tkacheva Yu.I. Sposob obnaruzheniya mikrotreshchin v lopatkah rabotayushchih gazoturbinnyh dvigatelej [Methods of detecting microcracks in the shoulder blades of operating gas turbine engines]. Molodezh' i nauka: aktual'nye problemy fundamental'nyh i prikladnyh issledovanij: Materialy II Vserossijskoj nacional'noj nauchnoj konferencii studentov, aspirantov i molodyh uchenyh. V 4-h chastyah. CHast' 3 [Youth and science: Actual problems of fundamental and applied research: Materials of the II All-Russian National Scientific Conference of Students, graduate students and young scientists. In 4 parts. Part 3]. Komsomolsk-na-Amure, Komsomolsk-na-Amure State Technical University, 2019, pp. 237-240.
[6] Andrianov I., Kara Balli M., Grinkrug M., Novgorodov N. Finite Element Calculation of the Limiting Pressure for Rupture of Capsules with an Active Substance in the Crack Detection System of Gas Turbine Blades. Lecture Notes in Networks and Systems, 2023, no. 722, pp. 757–768.
[7] Andrianov I., Chepurnova E. Optimization Model of the Shell Capsules Geometry for a System for Diagnosing Damage to Gas Turbine Blades in Nonstationary. International Journal of Mechanics, 2023, no. 17, pp. 38–44.
[8] Andrianov I.K., Chepurnova E.K. Optimizing Crack Detection in Gas Turbine Blades Using Implanted Capsules of Ionizing Gas in Nonsteady Operation at Nonuniform Temperature. Russian Engineering Research, 2023, vol. 43, pp. 1361–1366.
[9] Andrianov I.K., Гринкруг М.С. he parametric identification of the mathematical model of the heat-expanded process for thin-walled curvilineous membranes of turbines. Mathematical Modeling and Computational Methods, 2016, no. 2, pp. 24-38.
[10] Dornberger R., Stoll P., Bueche D., Neu A.. Multidisciplinary turbomachinery blade design optimization. 38th Aerospace Sciences Meeting and Exhibit, 2000. URL: https://arc.aiaa.org/doi/10.2514/6.2000-838. DOI: 10.2514/6.2000-838.
[11] Agromayor, Roberto, Anand, Nitish, Mueller, Jens-Dominik, Pini, Matteo, Nord, Lars. A Unified Geometry Parametrization Method for Turbomachinery Blades. Computer-Aided Design, 2021, vol. 133, no. 3, art. 102987.
[12] Chen, Naixing, Zhang, Hongwu, Huang, Weiguang, Xu, Yanji. Study on Aerodynamic Design Optimization of Turbomachinery Blades. Journal of Thermal Science, 2005, vol. 14, no. 4, pp. 298-304.
[13] Zhang Xiao, Zheng M. Numerical Simulation of Fluid-Structure Coupling for a Multi-Blade Vertical-Axis Wind Turbine. Applied Sciences, 2023, vol. 13, no. 15, art. 8612.
[14] Dimitrienko Yu.I., Gubareva E.A., Pichugina A.E. Thin composite cylindrical shells stress modeling based on the asymptotic theory. Mathematical Modeling and Computational Methods, 2018, no. 3, pp. 109-126.
[15] Mohammed, Mohammed, Sarraf, Ziad, Jamil, Sabah. Finite Element Simulation and Stress Analysis of Gas Turbine Blade Due to Centrifugal Force. International Journal of Advanced Natural Sciences and Engineering Researches, 2023, vol. 7, no. 6, pp. 250-255.
[16] Dimitrienko Yu.I., Yurin Yu.V., Koryakov M.N., Maremshaova A. A. Finite element modeling of temperature fields in thin-walled multilayer anisotropic shells. Mathematical Modeling and Computational Methods, 2023, no. 1, pp. 43-63.
[17] Stratula B. A. Mathematical modeling of fatigue failure during high frequency bending vibrations of titanium alloy specimens. Mathematical Modeling and Computational Methods, 2021, no. 4, pp. 45-57.
[18] Songyi P., Grigoryev V.G. Modeling of dynamic stability of thin-walled structures partially filled with liquid under hydrostatic action. Mathematical Modeling and Computational Methods, 2022, no. 3, pp. 3-17.
[19] Xiaodong Zhang, Yiwei Xiong, Xin Huang, Bochao Fan, Zhen Zhao, Jiahao Zhu. Dynamic Characteristics Analysis of 3D Blade Tip Clearance for Turbine Blades with Typical Cracks. International Journal of Aerospace Engineering, 2022, vol. 6, pp. 1-17.
[20] Jaeger B.E., Schmid S., Grosse C.U., Gögelein A., Elischberger F. Infrared Thermal Imaging-Based Turbine Blade Crack Classification Using Deep Learning. Journal of Nondestructive Evaluation, 2022, vol. 41, no. 4, art. 74.
[21] Ganicheva, Antonina, Ganichev, Alexey. (2022). Approximate method of optimization of nonlinear programming problems. Applied Mathematics and Control Sciences, 2022, vol. 4, pp. 9-25.
[22] Onuma, K., Sato, S. Existence results on Lagrange multiplier approach for gradient flows and application to optimization. 2023, Japan Journal of Industrial and Applied Mathematics, 2024, vol. 41, pp. 165-189.
Андрианов И.К., Чепурнова Е.К. Математическая модель условной оптимизации давления в системе обнаружения трещин лопаток газовых турбин. Математическое моделирование и численные методы, 2024, № 2, с. 3–16.
Научное исследование выполнено за счет гранта Российского научного фонда № 22-79-10114 «Разработка системы диагностирования повреждений турбинных лопаток и способа оптимизации теплоотвода в условиях термической усталости» (https://rscf.ru/project/22-79-10114/).
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