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Abstract
Numerical simulation of unsteady motion of wing through undisturbed fluid is formulated using Unsteady Vortex Lattice Method. A free-wake algorithm is developed using a fourth order Adam-Bashforth technique. Rankine vortex model is used to avoid numerical singularities and wake decay algorithm is used to model the viscous dissipation of the shed wake. The resulting MN x MN equations are solved for unknown Γwing using LU decomposition, where M and N are number of divisions of the wing along chord and span respectively. The aerodynamic coefficient of lift, CL, induced drag, CDi , distribution of circulation, Γ and wake geometry are calculated for unsteady plunging motion. Effect of cross-flow is studied. The results are found to be in good agreement with available literature.
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References
- Theodore Von Karman., "Aerodynamics: Selected Topics in the Light of Their Historical Development", Dover Publications, New York, 2004, pp.50-56.
- Robinson Abraham., "Wing Theory", Cambridge University Press, 1956, pp.242-245.
- John DeYoung., "Historical Evolution of Vortex-Lattice Methods", NASA Langley Research Center, N76-28164, 1976.
- Asfar, K. R., Mook, D. T. and Nayfeh, A. H., "Application of the Vortex-Lattice Technique to Arbitrary Bodies", Journal of Aircraft, Vol.16, No.7, 1979, pp.421-424.
- Vernon J Rossow., "Validation of Vortex Lattice Method for Loads on Wings in Lift-generated Wakes", Journal of Aircraft, Vol.32, No.6, 1995, pp.1254-1262.
- Dovgi, S. A. and Shekhovtsov, A. V., "An Improved Vortex Lattice Method for Non-stationary Problems", Journal of Mathematical Sciences, Vol.104, No.6, 2001, pp.1615-1627.
- Tracy E. Fritz and Lyle N. Long., "Object-Oriented Unsteady Vortex Lattice Method for Flapping Flight", Journal of Aircraft, Vol.41, No.6, 2004, pp.1275-1290.
- Seong Yong Wie., Seongkyu Lee and Duck Joo Lee., "Potential Panel and Time-Marching Free-Wake Coupling Analysis for Helicopter Rotor", Journal of Aircraft, Vol.46, No.3, 2009, pp.1030-1041.
- Elsa M Cardenasand., Pedro J. Boschetti and Andrea Amerio., "Stability and Flying Qualities of an Unmanned Airplane Using the Vortex-Lattice Method", Journal of Aircraft, Vol.46, No.4, 2009, pp.1461-1464.
- Melin, T., Isikveren, A. T. and Friswell, M. I., "Induced-Drag Compressibility Correction for Three-Dimensional Vortex-Lattice Methods", Journal of Aircraft, Vol.47, No.4, 2010, pp.1458-1460.
- Joseba Murua., Rafael Palacios and Michael R Graham, J., "Applications of the Unsteady Vortex-lattice Method in Aircraft Aeroelasticity and Flight Dynamics", Progress in Aerospace Sciences, Vol.55, 2012, pp.46-72.
- Christopher C Chabalko., Timothy Fitzgerald and Balakumar Balachandran., "GPGPU Implementation and Benchmarking of the Unsteady Vortex Lattice Method", Progress in Aerospace Sciences, AIAA Paper, 2013-0288.
- Bruno A Roccia., Julio C Massa and Dean T Mook., "Modified Unsteady Vortex-Lattice Method to Study Flapping Wings in Hover Flight", AIAA Journal, Vol.51, No.11, pp.2628-2642.
- Greengard, L. and Rokhlin, V., "A Fast Algorithm for Particle Simulations", Journal of Computational Physics, Vol.73, 1987, pp.325-348.
- Prabhu Ramachandran Rajan, S. C. and Ramakrishna, M., "A Fast Multipole Method for Two-dimensional Panel Methods", Society for Industrial and Applied Mathematics, Vol.24, No.6, 2004, pp.1864-1878.
- Sverre J Aarseth., "Gravitational N-body Problem", Cambridge University Press, 1-49, 2003.
- Ira Herbert Abbott and Albert E Von Doenhoff., "Theory of Wing Section", Dover Publication, New York, USA, 1959, pp.321-322.
References
Theodore Von Karman., "Aerodynamics: Selected Topics in the Light of Their Historical Development", Dover Publications, New York, 2004, pp.50-56.
Robinson Abraham., "Wing Theory", Cambridge University Press, 1956, pp.242-245.
John DeYoung., "Historical Evolution of Vortex-Lattice Methods", NASA Langley Research Center, N76-28164, 1976.
Asfar, K. R., Mook, D. T. and Nayfeh, A. H., "Application of the Vortex-Lattice Technique to Arbitrary Bodies", Journal of Aircraft, Vol.16, No.7, 1979, pp.421-424.
Vernon J Rossow., "Validation of Vortex Lattice Method for Loads on Wings in Lift-generated Wakes", Journal of Aircraft, Vol.32, No.6, 1995, pp.1254-1262.
Dovgi, S. A. and Shekhovtsov, A. V., "An Improved Vortex Lattice Method for Non-stationary Problems", Journal of Mathematical Sciences, Vol.104, No.6, 2001, pp.1615-1627.
Tracy E. Fritz and Lyle N. Long., "Object-Oriented Unsteady Vortex Lattice Method for Flapping Flight", Journal of Aircraft, Vol.41, No.6, 2004, pp.1275-1290.
Seong Yong Wie., Seongkyu Lee and Duck Joo Lee., "Potential Panel and Time-Marching Free-Wake Coupling Analysis for Helicopter Rotor", Journal of Aircraft, Vol.46, No.3, 2009, pp.1030-1041.
Elsa M Cardenasand., Pedro J. Boschetti and Andrea Amerio., "Stability and Flying Qualities of an Unmanned Airplane Using the Vortex-Lattice Method", Journal of Aircraft, Vol.46, No.4, 2009, pp.1461-1464.
Melin, T., Isikveren, A. T. and Friswell, M. I., "Induced-Drag Compressibility Correction for Three-Dimensional Vortex-Lattice Methods", Journal of Aircraft, Vol.47, No.4, 2010, pp.1458-1460.
Joseba Murua., Rafael Palacios and Michael R Graham, J., "Applications of the Unsteady Vortex-lattice Method in Aircraft Aeroelasticity and Flight Dynamics", Progress in Aerospace Sciences, Vol.55, 2012, pp.46-72.
Christopher C Chabalko., Timothy Fitzgerald and Balakumar Balachandran., "GPGPU Implementation and Benchmarking of the Unsteady Vortex Lattice Method", Progress in Aerospace Sciences, AIAA Paper, 2013-0288.
Bruno A Roccia., Julio C Massa and Dean T Mook., "Modified Unsteady Vortex-Lattice Method to Study Flapping Wings in Hover Flight", AIAA Journal, Vol.51, No.11, pp.2628-2642.
Greengard, L. and Rokhlin, V., "A Fast Algorithm for Particle Simulations", Journal of Computational Physics, Vol.73, 1987, pp.325-348.
Prabhu Ramachandran Rajan, S. C. and Ramakrishna, M., "A Fast Multipole Method for Two-dimensional Panel Methods", Society for Industrial and Applied Mathematics, Vol.24, No.6, 2004, pp.1864-1878.
Sverre J Aarseth., "Gravitational N-body Problem", Cambridge University Press, 1-49, 2003.
Ira Herbert Abbott and Albert E Von Doenhoff., "Theory of Wing Section", Dover Publication, New York, USA, 1959, pp.321-322.