Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers
The stability problem solution of the manufacturing (drawing) of the quartz capillaries (pipes) for microstructured optical fibers (hole-assisted fiber) is important for determining the effective technological production modes. This importance is also caused by the high cost of fiber production and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/16/2/83 |
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| author | Vladimir Pervadchuk Daria Vladimirova Anna Derevyankina |
| author_facet | Vladimir Pervadchuk Daria Vladimirova Anna Derevyankina |
| author_sort | Vladimir Pervadchuk |
| collection | DOAJ |
| description | The stability problem solution of the manufacturing (drawing) of the quartz capillaries (pipes) for microstructured optical fibers (hole-assisted fiber) is important for determining the effective technological production modes. This importance is also caused by the high cost of fiber production and strict requirements for the accuracy of the fiber’s geometric characteristics. Therefore, a theoretical approach to this problem is relevant and necessary. A modified capillary drawing model that takes into account inertial, viscous, and surface tension forces, as well as all types of heat transfer is proposed in the research. Within the framework of the linear theory of stability, a mathematical model of isothermal and nonisothermal capillary drawing has been developed. The stability of the process is studied depending on the drawing ratio and the Reynolds number. The analysis of the sensitivity of the process to perturbations in the boundary conditions is carried out. The secondary flow that occurs upon transition to the region of instability is also studied. It has been found that at draw ratios above critical values (instability region), undamped oscillations arise. The existence of optimal parameters of the heating element is shown: temperature distribution over the furnace surface and furnace radius, at which the stability of the process of drawing quartz tubes increases significantly (several times). |
| first_indexed | 2024-03-11T09:15:46Z |
| format | Article |
| id | doaj.art-2c9061b6362847899dbcba50dc57c733 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-11T09:15:46Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-2c9061b6362847899dbcba50dc57c7332023-11-16T18:37:30ZengMDPI AGAlgorithms1999-48932023-02-011628310.3390/a16020083Mathematical Modeling of Capillary Drawing Stability for Hollow Optical FibersVladimir Pervadchuk0Daria Vladimirova1Anna Derevyankina2Department of Applied Mathematics, Perm National Research Polytechnic University, 614990 Perm, RussiaDepartment of Applied Mathematics, Perm National Research Polytechnic University, 614990 Perm, RussiaDepartment of Applied Mathematics, Perm National Research Polytechnic University, 614990 Perm, RussiaThe stability problem solution of the manufacturing (drawing) of the quartz capillaries (pipes) for microstructured optical fibers (hole-assisted fiber) is important for determining the effective technological production modes. This importance is also caused by the high cost of fiber production and strict requirements for the accuracy of the fiber’s geometric characteristics. Therefore, a theoretical approach to this problem is relevant and necessary. A modified capillary drawing model that takes into account inertial, viscous, and surface tension forces, as well as all types of heat transfer is proposed in the research. Within the framework of the linear theory of stability, a mathematical model of isothermal and nonisothermal capillary drawing has been developed. The stability of the process is studied depending on the drawing ratio and the Reynolds number. The analysis of the sensitivity of the process to perturbations in the boundary conditions is carried out. The secondary flow that occurs upon transition to the region of instability is also studied. It has been found that at draw ratios above critical values (instability region), undamped oscillations arise. The existence of optimal parameters of the heating element is shown: temperature distribution over the furnace surface and furnace radius, at which the stability of the process of drawing quartz tubes increases significantly (several times).https://www.mdpi.com/1999-4893/16/2/83photonic crystal fiberscapillary drawingmathematical modelstabilitycalculation algorithms |
| spellingShingle | Vladimir Pervadchuk Daria Vladimirova Anna Derevyankina Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers Algorithms photonic crystal fibers capillary drawing mathematical model stability calculation algorithms |
| title | Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers |
| title_full | Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers |
| title_fullStr | Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers |
| title_full_unstemmed | Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers |
| title_short | Mathematical Modeling of Capillary Drawing Stability for Hollow Optical Fibers |
| title_sort | mathematical modeling of capillary drawing stability for hollow optical fibers |
| topic | photonic crystal fibers capillary drawing mathematical model stability calculation algorithms |
| url | https://www.mdpi.com/1999-4893/16/2/83 |
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