Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids
In the process of turbomachinery development, it is of great importance to accurately design impellers and select their blade shape. One of the promising approaches to solving this problem is based on the theory of inverse boundary-value problems in aerodynamics. It helps to develop methods for prof...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2016-12-01
|
| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | http://kpfu.ru/portal/docs/F237092296/158_4_phys_mat_4.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846092633437372416 |
|---|---|
| author | A.M. Elizarov A.V. Potashev E.V. Potasheva |
| author_facet | A.M. Elizarov A.V. Potashev E.V. Potasheva |
| author_sort | A.M. Elizarov |
| collection | DOAJ |
| description | In the process of turbomachinery development, it is of great importance to accurately design impellers and select their blade shape. One of the promising approaches to solving this problem is based on the theory of inverse boundary-value problems in aerodynamics. It helps to develop methods for profiling airfoil grids with predetermined properties in the same way as it is done for isolated airfoils. In this paper, methods have been worked out to find quasisolutions of the inverse boundary-value problem in aerodynamics for a plane airfoil grid. Two methods of quasisolution have been described.
The first “`formal” method is similar, in its essence, to the method used for construction of quasisolution for an isolated airfoil. It has been shown that such quasisolutions provide satisfactory results for grids having a sufficiently large relative airfoil pitch. If pitch values are low, this method is unacceptable, because “modified” velocity distribution in some areas is significantly different from the original one in this case. For this reason, areas with significant changes in the angle of the tangent line appear in the airfoil contour and the flow region becomes multivalent.
To satisfy the conditions of solvability in the case of grids having a small airfoil pitch, a new quasisolution construction method taking into account the specifics of the problem has been suggested. The desired effect has been achieved due to changes in the weighting function of the minimized functional. The comparison of the results of construction of the new quasisolution with the results obtained by the “formal” method has demonstrated that the constructed airfoils are very similar when the pitch is large. In the case of dense grids, it is clear that preference should be given to the second method, as it brings less distortion to the initial velocity distribution and, thus, allows to physically find an actual airfoil contour. |
| format | Article |
| id | doaj-art-37c9f096c3f34e62b5ffbb6095a36c6e |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2016-12-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-37c9f096c3f34e62b5ffbb6095a36c6e2025-01-02T20:43:55ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982016-12-011584500510Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil GridsA.M. Elizarov0A.V. Potashev1E.V. Potasheva2Kazan Federal University, Kazan, 420008 RussiaKazan Cooperative Institute, Branch of Russian University of Cooperation, Kazan, 420081 RussiaKazan Cooperative Institute, Branch of Russian University of Cooperation, Kazan, 420081 RussiaIn the process of turbomachinery development, it is of great importance to accurately design impellers and select their blade shape. One of the promising approaches to solving this problem is based on the theory of inverse boundary-value problems in aerodynamics. It helps to develop methods for profiling airfoil grids with predetermined properties in the same way as it is done for isolated airfoils. In this paper, methods have been worked out to find quasisolutions of the inverse boundary-value problem in aerodynamics for a plane airfoil grid. Two methods of quasisolution have been described. The first “`formal” method is similar, in its essence, to the method used for construction of quasisolution for an isolated airfoil. It has been shown that such quasisolutions provide satisfactory results for grids having a sufficiently large relative airfoil pitch. If pitch values are low, this method is unacceptable, because “modified” velocity distribution in some areas is significantly different from the original one in this case. For this reason, areas with significant changes in the angle of the tangent line appear in the airfoil contour and the flow region becomes multivalent. To satisfy the conditions of solvability in the case of grids having a small airfoil pitch, a new quasisolution construction method taking into account the specifics of the problem has been suggested. The desired effect has been achieved due to changes in the weighting function of the minimized functional. The comparison of the results of construction of the new quasisolution with the results obtained by the “formal” method has demonstrated that the constructed airfoils are very similar when the pitch is large. In the case of dense grids, it is clear that preference should be given to the second method, as it brings less distortion to the initial velocity distribution and, thus, allows to physically find an actual airfoil contour.http://kpfu.ru/portal/docs/F237092296/158_4_phys_mat_4.pdfinverse boundary-value problem of aerohydrodynamicsairfoil gridsquasisolution |
| spellingShingle | A.M. Elizarov A.V. Potashev E.V. Potasheva Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids Учёные записки Казанского университета: Серия Физико-математические науки inverse boundary-value problem of aerohydrodynamics airfoil grids quasisolution |
| title | Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids |
| title_full | Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids |
| title_fullStr | Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids |
| title_full_unstemmed | Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids |
| title_short | Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids |
| title_sort | quasisolutions of inverse boundary value problem of aerodynamics for dense airfoil grids |
| topic | inverse boundary-value problem of aerohydrodynamics airfoil grids quasisolution |
| url | http://kpfu.ru/portal/docs/F237092296/158_4_phys_mat_4.pdf |
| work_keys_str_mv | AT amelizarov quasisolutionsofinverseboundaryvalueproblemofaerodynamicsfordenseairfoilgrids AT avpotashev quasisolutionsofinverseboundaryvalueproblemofaerodynamicsfordenseairfoilgrids AT evpotasheva quasisolutionsofinverseboundaryvalueproblemofaerodynamicsfordenseairfoilgrids |