Inverse Design of Airfoil using Elastic Surface Method in Viscous Subsonic and Transonic Flow
Authors
Abstract
In this research, a new method called elastic surface algorithm is presented for inverse design of 2-D airfoil in a viscous flow regime. In this method as an iterative one, airfoil walls are considered as flexible curved beams. The difference between the target and the current pressure distribution causes the flexible beams to deflect at each shape modification step. In modification shape algorithm, the finite element equations of two-node Timoshenko beam are solved to calculate the deflection of the beams. In order to validate the proposed method, various airfoils in subsonic and transonic regimes are studied, which show the robustness of the method in the viscous flow regime with separation and normal shock. Also, three design examples are presented here, which show the capability of the proposed method.
Keywords
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8. Malone, J., Vadyak, J., and Sankar, L., “Inverse Aerodynamic Design Method for Aircraft Components”, Journal of Aircraft, Vol. 24, No. 1,
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10. Petrucci, D. R., and Manzanares Filho, N., “A Fast Algorithm for Inverse Airfoil Design Using a Transpiration Model and an Improved Vortex Panel Method”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 29, No. 4, pp. 354-365, 2007.
11. Ghadak, F., Nili, M., and Dourali Mohammad, H. B. A., “A New Method in Inverse Design, Based on Ball-Spine for Axisymmetric Ducts with Application in Gas Turbines”, Mechanical Aerospace Engineering Journal, Vol. 7, No. 4, pp. 65-75, 2012.
12. Nili Ahmadabadi, M., Ghadak, F., and Mohammadi, M., “Subsonic and Transonic Airfoil Inverse Design via Ball-Spine Algorithm”, Computers & Fluids, Vol. 84, pp. 87-96, 2013.
13. Nili-Ahmadabadi, M., Durali, M., Hajilouy-Benisi, A., and Ghadak, F., “Inverse Design of 2-D Subsonic Ducts Using Flexible String Algorithm”, Inverse Problems in Science and Engineering, Vol. 17, No. 8, pp. 1037-1057, 2009.
14. Nili-Ahmadabadi, M., Hajilouy-Benisi, A., Ghadak, F., and Durali, M., “A Novel 2D Incompressible Viscous Inverse Design Method for Internal Flows Using Flexible String Algorithm”, Journal of Fluids Engineering, Vol. 132, No. 3, pp. 031401-1-9, 2010.
15. Felippa, C., “Nonlinear Finite Element Methods (ASEN 6107)”, DAES., University of Colorado at Boulder. Published Online (http://www. colorado. edu). DOI: CAS/courses. d/NFEM. d, 2012.
2. Dulikravich, G. S., and Baker, D. P., “Aerodynamic Shape Inverse Design Using a Fourier Series Method”, 37th AIAA Aerospace Sciences, pp. 99-185, 1999.
3. Nili-Ahmadabadi, M., Durali, M., Hajilouy-Benisi, A., and Ghadak, F., “Duct Design in Subsonic and Supersonic Flow Regimes with and without Normal Shock Waves Using Flexible String Algorithm”, Scientia Iranica Transaction B: Mechanical Engineering, Vol. 17, No. 3, pp. 179-193, 2010.
4. Garabedian, P., and McFadden, G., “Design of Supercritical Swept Wings”, AIAA Journal, Vol. 20, No. 3, pp. 289-291, 1982.
5. Garabedian, P., and McFadden, G., “Computational Fluid Dynamics of Airfoils and Wings”, Proceedings of Symposium on Transonic, Shock and Multidimensional Flows: Advances in Scientific Computing, Academic Press, New York, pp. 1-16, 1982.
6. Malone, J., Narramore, J., and Sankar, L., “An Efficient Airfoil Design Method Using the Navier–Stokes Equations”, Presented at the AGARD specialists Meeting on Computational Methods for Aerodynanic Design (Inverse) and Optimization, Loen, Norway, 1989.
7. Malone, J., Vadyak, J., and Sankar, L., “A Technique for the Inverse Aerodynamic Design of Nacelles and Wing Configurations”, AIAA Journal, AAIA-85-4096, 1985.
8. Malone, J., Vadyak, J., and Sankar, L., “Inverse Aerodynamic Design Method for Aircraft Components”, Journal of Aircraft, Vol. 24, No. 1,
pp. 8-9, 1987.
9. Dulikravich, G. S., and Baker, D. P., “Using Existing Flow-Field Analysis Codes for Inverse Design of Three-Dimentional Aerodynamic Shapes”, In: Recent Development of Aerodynamic Design Methodologies, Eds., pp. 89-112: Springer, 1999.
10. Petrucci, D. R., and Manzanares Filho, N., “A Fast Algorithm for Inverse Airfoil Design Using a Transpiration Model and an Improved Vortex Panel Method”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 29, No. 4, pp. 354-365, 2007.
11. Ghadak, F., Nili, M., and Dourali Mohammad, H. B. A., “A New Method in Inverse Design, Based on Ball-Spine for Axisymmetric Ducts with Application in Gas Turbines”, Mechanical Aerospace Engineering Journal, Vol. 7, No. 4, pp. 65-75, 2012.
12. Nili Ahmadabadi, M., Ghadak, F., and Mohammadi, M., “Subsonic and Transonic Airfoil Inverse Design via Ball-Spine Algorithm”, Computers & Fluids, Vol. 84, pp. 87-96, 2013.
13. Nili-Ahmadabadi, M., Durali, M., Hajilouy-Benisi, A., and Ghadak, F., “Inverse Design of 2-D Subsonic Ducts Using Flexible String Algorithm”, Inverse Problems in Science and Engineering, Vol. 17, No. 8, pp. 1037-1057, 2009.
14. Nili-Ahmadabadi, M., Hajilouy-Benisi, A., Ghadak, F., and Durali, M., “A Novel 2D Incompressible Viscous Inverse Design Method for Internal Flows Using Flexible String Algorithm”, Journal of Fluids Engineering, Vol. 132, No. 3, pp. 031401-1-9, 2010.
15. Felippa, C., “Nonlinear Finite Element Methods (ASEN 6107)”, DAES., University of Colorado at Boulder. Published Online (http://www. colorado. edu). DOI: CAS/courses. d/NFEM. d, 2012.
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