Cruising speed of a cylindrical wing performing small translational-rotational oscillations
This work considers the propulsive motion of a flapping wing of a circular cross section. The problem of harmonic translational-rotational oscillations of the wing with an arbitrary phase shift in a viscous incompressible fluid, the motion of which is described by the non-stationary Navier–Stokes eq...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2022-09-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/uz-eng-phm-2022-2-3-2.html |
| _version_ | 1797857422231994368 |
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| author | A.N. Nuriev |
| author_facet | A.N. Nuriev |
| author_sort | A.N. Nuriev |
| collection | DOAJ |
| description | This work considers the propulsive motion of a flapping wing of a circular cross section. The problem of harmonic translational-rotational oscillations of the wing with an arbitrary phase shift in a viscous incompressible fluid, the motion of which is described by the non-stationary Navier–Stokes equation, is handled. An analytical solution of the problem is obtained in the first two terms by using the method of successive asymptotic expansions for the case of small oscillation amplitudes. It is shown that the nonlinear interaction of time harmonics of translational and rotational oscillations creates secondary flows that make the wing to move in the direction perpendicular to the axis of translational oscillations. For the cruising motion regime, when the average hydrodynamic force acting on the wing is equal to zero, the dependences of the average speed on the parameters of dimensionless oscillation are found. |
| first_indexed | 2024-04-09T20:56:27Z |
| format | Article |
| id | doaj.art-754e673ba27a42c7966ff0f09eec8259 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-09T20:56:27Z |
| publishDate | 2022-09-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-754e673ba27a42c7966ff0f09eec82592023-03-29T17:36:57ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982022-09-011642-317018010.26907/2541-7746.2022.2-3.170-180Cruising speed of a cylindrical wing performing small translational-rotational oscillationsA.N. Nuriev0Kazan Federal University, Kazan, 420008 RussiaThis work considers the propulsive motion of a flapping wing of a circular cross section. The problem of harmonic translational-rotational oscillations of the wing with an arbitrary phase shift in a viscous incompressible fluid, the motion of which is described by the non-stationary Navier–Stokes equation, is handled. An analytical solution of the problem is obtained in the first two terms by using the method of successive asymptotic expansions for the case of small oscillation amplitudes. It is shown that the nonlinear interaction of time harmonics of translational and rotational oscillations creates secondary flows that make the wing to move in the direction perpendicular to the axis of translational oscillations. For the cruising motion regime, when the average hydrodynamic force acting on the wing is equal to zero, the dependences of the average speed on the parameters of dimensionless oscillation are found.https://kpfu.ru/uz-eng-phm-2022-2-3-2.htmlflapping wingharmonic oscillationscruising speednavier–stokes equationasymptotic analysis |
| spellingShingle | A.N. Nuriev Cruising speed of a cylindrical wing performing small translational-rotational oscillations Учёные записки Казанского университета. Серия Физико-математические науки flapping wing harmonic oscillations cruising speed navier–stokes equation asymptotic analysis |
| title | Cruising speed of a cylindrical wing performing small translational-rotational oscillations |
| title_full | Cruising speed of a cylindrical wing performing small translational-rotational oscillations |
| title_fullStr | Cruising speed of a cylindrical wing performing small translational-rotational oscillations |
| title_full_unstemmed | Cruising speed of a cylindrical wing performing small translational-rotational oscillations |
| title_short | Cruising speed of a cylindrical wing performing small translational-rotational oscillations |
| title_sort | cruising speed of a cylindrical wing performing small translational rotational oscillations |
| topic | flapping wing harmonic oscillations cruising speed navier–stokes equation asymptotic analysis |
| url | https://kpfu.ru/uz-eng-phm-2022-2-3-2.html |
| work_keys_str_mv | AT annuriev cruisingspeedofacylindricalwingperformingsmalltranslationalrotationaloscillations |