Internal Shocks in Supersonic Flows past the Contours of Optimal Bodies and Nozzles.
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| Title: | Internal Shocks in Supersonic Flows past the Contours of Optimal Bodies and Nozzles. |
|---|---|
| Authors: | Kraiko, A. N.1,2 akraiko@ciam.ru, P'yankov, K. S.1 kspyankov@ciam.ru, Tillyaeva, N. I.1 ntill@ciam.ru, Shapovalov, V. A.1,2 vladimirs44@yandex.ru |
| Source: | Fluid Dynamics. Nov2020, Vol. 55 Issue 6, p840-857. 18p. |
| Subjects: | Supersonic flow, Streamlines (Fluids), Nozzles, Steady-state flow, Genetic algorithms |
| Abstract: | The problems of designing the contours of two-dimensional and axisymmetric bodies of minimum wave drag and maximum-thrust nozzles, such that flow past them can contain internal shocks, are considered within the ideal (inviscid and non-heat-conducting) gas model. These shocks may occur in flows past internal breaks in the optimal contours or on intersection of characteristics of the same family proceeding from these breaks. The submerged shocks occurring in the latter case are named internal, if their initial points lie within the domain of determinacy of the flowed-over optimal contour region. Further downstream the domain of determinacy is bounded by the characteristic coming to the end point of this contour. The internal submerged shocks can appear, when the optimal contour includes an interval of an isobaric streamline. The appearance of internal breaks in the optimal contours is possible due to the reflection of the pressure waves induced by them from the bow shock (for body noses) or, as might be expected, from tangential discontinuities (for afterbodies). In the case of supersonic freestreams having a tangential discontinuity the search for optimal two-dimensional afterbodies with an internal concave break flowed-over with an oblique shock is performed using the direct method with the representation of the required contours by the Bernstein—Bézier curves, a genetic algorithm, and a rapid and accurate marching scheme for calculating steady supersonic flows. While the optimal two-dimensional afterbodies with a convex internal break designed earlier using the general method of Lagrange multipliers could be reliably reproduced using the above-mentioned method, the expected optimal configurations with a concave break and an internal shock were not found. Instead, optimal contours with centered compression and expansion waves with the common focus on a tangential discontinuity and an "external" oblique shock proceeding from it were discovered. Then the new "discontinuous shock-free" solutions were constructed in the exact formulation, within the framework of the method of indefinite control contours and the method of characteristics. The solutions are generalized to include the contours of the afterbodies of revolution and supersonic parts of nozzles. In the case of a uniform freestream the flow past optimal afterbodies never includes internal shocks. [ABSTRACT FROM AUTHOR] |
| Copyright of Fluid Dynamics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Header | DbId: egs DbLabel: Engineering Source An: 146914535 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Internal Shocks in Supersonic Flows past the Contours of Optimal Bodies and Nozzles. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kraiko%2C+A%2E+N%2E%22">Kraiko, A. N.</searchLink><relatesTo>1,2</relatesTo><i> akraiko@ciam.ru</i><br /><searchLink fieldCode="AR" term="%22P'yankov%2C+K%2E+S%2E%22">P'yankov, K. S.</searchLink><relatesTo>1</relatesTo><i> kspyankov@ciam.ru</i><br /><searchLink fieldCode="AR" term="%22Tillyaeva%2C+N%2E+I%2E%22">Tillyaeva, N. I.</searchLink><relatesTo>1</relatesTo><i> ntill@ciam.ru</i><br /><searchLink fieldCode="AR" term="%22Shapovalov%2C+V%2E+A%2E%22">Shapovalov, V. A.</searchLink><relatesTo>1,2</relatesTo><i> vladimirs44@yandex.ru</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Fluid+Dynamics%22">Fluid Dynamics</searchLink>. Nov2020, Vol. 55 Issue 6, p840-857. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Supersonic+flow%22">Supersonic flow</searchLink><br /><searchLink fieldCode="DE" term="%22Streamlines+%28Fluids%29%22">Streamlines (Fluids)</searchLink><br /><searchLink fieldCode="DE" term="%22Nozzles%22">Nozzles</searchLink><br /><searchLink fieldCode="DE" term="%22Steady-state+flow%22">Steady-state flow</searchLink><br /><searchLink fieldCode="DE" term="%22Genetic+algorithms%22">Genetic algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The problems of designing the contours of two-dimensional and axisymmetric bodies of minimum wave drag and maximum-thrust nozzles, such that flow past them can contain internal shocks, are considered within the ideal (inviscid and non-heat-conducting) gas model. These shocks may occur in flows past internal breaks in the optimal contours or on intersection of characteristics of the same family proceeding from these breaks. The submerged shocks occurring in the latter case are named internal, if their initial points lie within the domain of determinacy of the flowed-over optimal contour region. Further downstream the domain of determinacy is bounded by the characteristic coming to the end point of this contour. The internal submerged shocks can appear, when the optimal contour includes an interval of an isobaric streamline. The appearance of internal breaks in the optimal contours is possible due to the reflection of the pressure waves induced by them from the bow shock (for body noses) or, as might be expected, from tangential discontinuities (for afterbodies). In the case of supersonic freestreams having a tangential discontinuity the search for optimal two-dimensional afterbodies with an internal concave break flowed-over with an oblique shock is performed using the direct method with the representation of the required contours by the Bernstein—Bézier curves, a genetic algorithm, and a rapid and accurate marching scheme for calculating steady supersonic flows. While the optimal two-dimensional afterbodies with a convex internal break designed earlier using the general method of Lagrange multipliers could be reliably reproduced using the above-mentioned method, the expected optimal configurations with a concave break and an internal shock were not found. Instead, optimal contours with centered compression and expansion waves with the common focus on a tangential discontinuity and an "external" oblique shock proceeding from it were discovered. Then the new "discontinuous shock-free" solutions were constructed in the exact formulation, within the framework of the method of indefinite control contours and the method of characteristics. The solutions are generalized to include the contours of the afterbodies of revolution and supersonic parts of nozzles. In the case of a uniform freestream the flow past optimal afterbodies never includes internal shocks. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Fluid Dynamics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1134/S0015462820060075 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 840 Subjects: – SubjectFull: Supersonic flow Type: general – SubjectFull: Streamlines (Fluids) Type: general – SubjectFull: Nozzles Type: general – SubjectFull: Steady-state flow Type: general – SubjectFull: Genetic algorithms Type: general Titles: – TitleFull: Internal Shocks in Supersonic Flows past the Contours of Optimal Bodies and Nozzles. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kraiko, A. N. – PersonEntity: Name: NameFull: P'yankov, K. S. – PersonEntity: Name: NameFull: Tillyaeva, N. I. – PersonEntity: Name: NameFull: Shapovalov, V. A. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 00154628 Numbering: – Type: volume Value: 55 – Type: issue Value: 6 Titles: – TitleFull: Fluid Dynamics Type: main |
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