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Abstract
Comparison of theoretical and experimental data (flight test data) reveals that still there is a gap between theory and experiment. Some of the observed phenomenon in flight test may be due to the nonlinearities associated with the aeroelastic problems and this paper attempts to develop a theoretical formulation including the geometrical nonlinearities associated with structural modeling and the aerodynamic nonlinearities associated with dynamic stall. In this paper, the consolidated set of equations representing blade dynamics, rotor inflow and sectional aerodynamics are presented. The iterative computational solution technique developed for trim and response analysis is described and a systematic study is undertaken to analyse the influence of various aerodynamic models, representing rotor inflow and sectional loads, on the helicopter trim and aeroelastic response of the rotor blades. It is also shown that the structural coupling due to blade pretwist significantly influences the rotor blade response and loads compared to an untwisted rotor blade.
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References
- Friedmann, P. P., "Renaissance of Aeroelasticity and Its Future", Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 105-121.
- Friedmann, P. P and Hodges, D. H., "Rotary Wing Aeroelasticity - A Historical Perspective", Journal of Aircraft, Vol. 40, No. 6, 2003, pp. 1019-1046.
- Friedmann, P. P., "Rotary Wing Aeroelasticity: Current Status and Future Trends", AIAA Journal, Vol. 42, No. 10, 2004, pp. 1953-1972.
- Hodges, D. H., "Review of Composite Rotor Blade Modeling", AIAA Journal, Vol. 28, No. 3, 1990, pp. 561-564.
- Johnson, W., "Rotorcraft Dynamics Models for a Comprehensive Analysis", Proceedings of the 54th Annual Forum of the American Helicopter Society, Washington, D.C., 1998.
- Hodges, D. H., Saberi, H and Ormiston, R. A., "Development of Nonlinear Beam Elements for Rotorcraft Comprehensive Analyses", Journal of the American Helicopter Society, Vol. 52, No. 1, 2007, pp. 36-48.
- Gaonkar, G. H and Peters, D. A., "Flap-Lag Stability with Dynamic Inflow by the Method of Multiblade Coordinates", Presented at the 20th AIAA /ASME /ASCE / AHS Structures, Structural Dynamics, and Materials Conference, St. Louis, Missouri, April 4-6, 1979.
- Gaonkar, G. H and Peters, D. A., "Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow", Journal of Aircraft, Vol. 17, No.2, 1980, pp.112-118.
- Gaonkar, G. H and Peters, D. A., "Effectiveness of Current Dynamic-Inflow Models in Hover and Forward Flight", Journal of the American Helicopter Society, Vol. 31, No. 2, 1986, pp. 47-57.
- Peters, D. A and HaQuang, N., "Dynamic Inflow for Practical Application", Journal of the American Helicopter Society, Vol. 33, No. 4, 1988, pp. 64-68.
- Su, A., Yoo, K. M and Peters, D. A., "Extension and Validation of an Unsteady Wake Model for Rotors", Journal of Aircraft, Vol. 29, No. 3, 1992, pp. 374- 383.
- Peters, D. A and Su, A., "Effect of an Unsteady Three-Dimensional Wake on Elastic Blade-Flapping Eigenvalues in Hover", Journal of the American Helicopter Society, Vol. 38, No. 1, 1993, pp. 45-54.
- Manjunath, A. R., Nagabhushanam, J., Gaonkar, G. H., Peters, D. A and Su, A., "Flap-Lag Damping in Hover and Forward Flight With a Three-Dimensional Wake", Journal of the American Helicopter Society, Vol. 38, No. 4, 1993, pp. 37-49.
- Manjunath, A. R., Chunduru, S. J., Nagabhushanam, J and Gaonkar, G. H., "Flap-Lag-Torsion Stability in Hover and Forward Flight With a Three-Dimensional Wake", AIAA Journal, Vol. 34, No. 1, 1996, pp. 18-28.
- Nagabushanam, J and Gaonkar, G. H., "Hingeless Rotor Aeromechanical Stability in Axial and Forward Flight With Wake Dynamics", Journal of the American Helicopter Society, Vol. 44, No. 3, 1999, pp. 222-233.
- Tran, C. T and Falchero, D., "Application of the ONERA Dynamic Stall Model to a Helicopter Blade in Forward Flight", 7th European Rotorcraft and Power Lift Aircraft Forum, Garmisch-Partenkirchen, F.R.G., Sept. 8-11, 1981.
- Rogers, J. P., "Application of an Analytic Stall Model to Time-History and Eigenvalue Analysis of Rotor Blades", 8th European Rotorcraft Forum, Aix-en- Provence, France, Sept. 1982.
- Bergh, H and Van der Wekken, J. P., "Comparison Between Measured and Calculated Stall-Flutter Behaviour of a One-Bladed Model Rotor", Vertica, Vol. 11, No. 3, 1987, pp. 447-456.
- Dunn, P and Dugundji, J., "Nonlinear Stall Flutter and Divergence Analysis of Cantilevered Graphite/ Epoxy Wings", AIAA Journal, Vol. 30, No. 1, 1992, pp. 153-162.
- Tang, D and Dowell, E. H., "Comparison of Theory and Experiment For Non-linear Flutter and Stall Response of a Helicopter Blade", Journal of Sound and Vibration, Vol. 165, No. 2, 1993, pp. 251-276.
- Barwey, D., Gaonkar, G. H and Ormiston, R. A., "Investigation of Dynamic Stall Effects on Isolated Rotor Flap-Lag Stability with Experimental Correlation", Journal of the American Helicopter Society, Vol. 36 No. 4, 1991, pp. 12-24.
- Barwey, D and Gaonkar, G. H., "Investigation of Dynamic Stall Effects on Isolated Rotor Flap-Lag Stability with Experimental Correlation", AIAA Journal, Vol. 32, No. 4, 1994, pp. 811-819.
- Tang, D and Dowell, E. H., "Damping Prediction for a Stalled Rotor in Flap-Lag with Experimental Correlation", Journal of the American Helicopter Society, Vol. 40 No. 4, 1995, pp. 79-89.
- Peters, D. A., Barwey, D and Su, A., "An Integrated Airloads - Inflow Model for Use in Rotor Aeroelasticity and Control Analysis", Mathematical and Computer Modelling, Vol.19, No. 3/4, 1994, pp.109- 123.
- Chunduru, S. J., Subramanian, S and Gaonkar, G. H., "Dynamic Stall and Wake Effects on Trim and Stability of Hingeless Rotors with Experimental Correlation", Journal of the American Helicopter Society, Vol. 42, No. 4, 1997, pp. 370-382.
- Subramanian, S., Ma, G., Gaonkar, G. H and Maier, T. M., "Correlation of Several Aerodynamic Models and Measurements of Hingeless - Rotor Trim and Stability", Journal of the American Helicopter Society, Vol. 45, No. 2, 2000, pp. 312-318.
- Postsdam, M., Yeo, H and Johnson, W., "Rotor Airloads Prediction Using Loose Aerodynamic/ Structural Coupling", Journal of Aircraft, Vol. 43, No. 3, 2006, pp. 732-742.
- Datta, A and Chopra, I., "Prediction of UH-60A Dynamic Stall Loads in High Altitute Level Flight Using CFD/CSD Coupling", Proceedings of the 61st Annual Forum of the American Helicopter Society, Washington D.C., 2005.
- Bhagwat, M. J., Ormiston, R. A., Saberi, H. A and Xin, H., "Application of CFD/CSD Coupling for Analysis of Rotorcraft Airloads and Blade Loads in Maneuvering Flight", Proceedings of the 63rd Annual Forum of the American Helicopter Society, Washington D.C., 2007.
- Lytwyn, R. T., "An Analysis of the Divergent Vertical Helicopter Oscillations Resulting from the Physical Presence of the Pilot in the Collective Control Loop", Proceedings of the 22nd Annual Forum of the American Helicopter Society, Washington, D.C., 1966.
- Bousman, W. G., "Putting the Aero Back Into Aeroelasticity", Proceedings of the 8th Annual Workshop on Aeroelasticity of Rotorcraft Systems, University Park, PA, USA, 1999.
- Prasad, C. G. N., Dwivedi, V and Dutta, R., "Vibration Monitoring in Helicopter Structure Using Rotor Noise: Flight Test Results and Discussions", Proceedings of the 15th National Seminar on Aerospace Structure, Shree Maruthi Publishers, Coimbatore, India, 2007, pp. 161-165.
- Yuan, K. A and Friedmann, P. P., "Aeroelasticity and Structural Optimization of Composite Helicopter Rotor Blades with Swept Tips", NASA Report 4665, May 1995.
- He, Cheng Jian., "Development and Application of a Generalized Dynamic Wake Theory for Lifting Rotors", Ph.D. Thesis, Georgia Institute of Technology, July 1989.
- Greenberg, M. J., "Airfoil in Sinusoidal Motion in a Pulsating Stream", NASA Technical Report 1326, 1947.
- Laxman, V and Venkatesan, C., "Chaotic Response of an Airfoil due to Aeroelastic Coupling and Dynamic Stall", AIAA Journal, Vol. 45, No. 1, 2007, pp. 271-280.
- Venkatesan, C., "Lecture Notes on Helicopter Technology", Department of Aerospace Engineering, Indian Institute of Technology Kanpur, India.
- Padfield, G. D., "Helicopter Flight Dynamics", Blackwell Science Ltd, 1996.
References
Friedmann, P. P., "Renaissance of Aeroelasticity and Its Future", Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 105-121.
Friedmann, P. P and Hodges, D. H., "Rotary Wing Aeroelasticity - A Historical Perspective", Journal of Aircraft, Vol. 40, No. 6, 2003, pp. 1019-1046.
Friedmann, P. P., "Rotary Wing Aeroelasticity: Current Status and Future Trends", AIAA Journal, Vol. 42, No. 10, 2004, pp. 1953-1972.
Hodges, D. H., "Review of Composite Rotor Blade Modeling", AIAA Journal, Vol. 28, No. 3, 1990, pp. 561-564.
Johnson, W., "Rotorcraft Dynamics Models for a Comprehensive Analysis", Proceedings of the 54th Annual Forum of the American Helicopter Society, Washington, D.C., 1998.
Hodges, D. H., Saberi, H and Ormiston, R. A., "Development of Nonlinear Beam Elements for Rotorcraft Comprehensive Analyses", Journal of the American Helicopter Society, Vol. 52, No. 1, 2007, pp. 36-48.
Gaonkar, G. H and Peters, D. A., "Flap-Lag Stability with Dynamic Inflow by the Method of Multiblade Coordinates", Presented at the 20th AIAA /ASME /ASCE / AHS Structures, Structural Dynamics, and Materials Conference, St. Louis, Missouri, April 4-6, 1979.
Gaonkar, G. H and Peters, D. A., "Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow", Journal of Aircraft, Vol. 17, No.2, 1980, pp.112-118.
Gaonkar, G. H and Peters, D. A., "Effectiveness of Current Dynamic-Inflow Models in Hover and Forward Flight", Journal of the American Helicopter Society, Vol. 31, No. 2, 1986, pp. 47-57.
Peters, D. A and HaQuang, N., "Dynamic Inflow for Practical Application", Journal of the American Helicopter Society, Vol. 33, No. 4, 1988, pp. 64-68.
Su, A., Yoo, K. M and Peters, D. A., "Extension and Validation of an Unsteady Wake Model for Rotors", Journal of Aircraft, Vol. 29, No. 3, 1992, pp. 374- 383.
Peters, D. A and Su, A., "Effect of an Unsteady Three-Dimensional Wake on Elastic Blade-Flapping Eigenvalues in Hover", Journal of the American Helicopter Society, Vol. 38, No. 1, 1993, pp. 45-54.
Manjunath, A. R., Nagabhushanam, J., Gaonkar, G. H., Peters, D. A and Su, A., "Flap-Lag Damping in Hover and Forward Flight With a Three-Dimensional Wake", Journal of the American Helicopter Society, Vol. 38, No. 4, 1993, pp. 37-49.
Manjunath, A. R., Chunduru, S. J., Nagabhushanam, J and Gaonkar, G. H., "Flap-Lag-Torsion Stability in Hover and Forward Flight With a Three-Dimensional Wake", AIAA Journal, Vol. 34, No. 1, 1996, pp. 18-28.
Nagabushanam, J and Gaonkar, G. H., "Hingeless Rotor Aeromechanical Stability in Axial and Forward Flight With Wake Dynamics", Journal of the American Helicopter Society, Vol. 44, No. 3, 1999, pp. 222-233.
Tran, C. T and Falchero, D., "Application of the ONERA Dynamic Stall Model to a Helicopter Blade in Forward Flight", 7th European Rotorcraft and Power Lift Aircraft Forum, Garmisch-Partenkirchen, F.R.G., Sept. 8-11, 1981.
Rogers, J. P., "Application of an Analytic Stall Model to Time-History and Eigenvalue Analysis of Rotor Blades", 8th European Rotorcraft Forum, Aix-en- Provence, France, Sept. 1982.
Bergh, H and Van der Wekken, J. P., "Comparison Between Measured and Calculated Stall-Flutter Behaviour of a One-Bladed Model Rotor", Vertica, Vol. 11, No. 3, 1987, pp. 447-456.
Dunn, P and Dugundji, J., "Nonlinear Stall Flutter and Divergence Analysis of Cantilevered Graphite/ Epoxy Wings", AIAA Journal, Vol. 30, No. 1, 1992, pp. 153-162.
Tang, D and Dowell, E. H., "Comparison of Theory and Experiment For Non-linear Flutter and Stall Response of a Helicopter Blade", Journal of Sound and Vibration, Vol. 165, No. 2, 1993, pp. 251-276.
Barwey, D., Gaonkar, G. H and Ormiston, R. A., "Investigation of Dynamic Stall Effects on Isolated Rotor Flap-Lag Stability with Experimental Correlation", Journal of the American Helicopter Society, Vol. 36 No. 4, 1991, pp. 12-24.
Barwey, D and Gaonkar, G. H., "Investigation of Dynamic Stall Effects on Isolated Rotor Flap-Lag Stability with Experimental Correlation", AIAA Journal, Vol. 32, No. 4, 1994, pp. 811-819.
Tang, D and Dowell, E. H., "Damping Prediction for a Stalled Rotor in Flap-Lag with Experimental Correlation", Journal of the American Helicopter Society, Vol. 40 No. 4, 1995, pp. 79-89.
Peters, D. A., Barwey, D and Su, A., "An Integrated Airloads - Inflow Model for Use in Rotor Aeroelasticity and Control Analysis", Mathematical and Computer Modelling, Vol.19, No. 3/4, 1994, pp.109- 123.
Chunduru, S. J., Subramanian, S and Gaonkar, G. H., "Dynamic Stall and Wake Effects on Trim and Stability of Hingeless Rotors with Experimental Correlation", Journal of the American Helicopter Society, Vol. 42, No. 4, 1997, pp. 370-382.
Subramanian, S., Ma, G., Gaonkar, G. H and Maier, T. M., "Correlation of Several Aerodynamic Models and Measurements of Hingeless - Rotor Trim and Stability", Journal of the American Helicopter Society, Vol. 45, No. 2, 2000, pp. 312-318.
Postsdam, M., Yeo, H and Johnson, W., "Rotor Airloads Prediction Using Loose Aerodynamic/ Structural Coupling", Journal of Aircraft, Vol. 43, No. 3, 2006, pp. 732-742.
Datta, A and Chopra, I., "Prediction of UH-60A Dynamic Stall Loads in High Altitute Level Flight Using CFD/CSD Coupling", Proceedings of the 61st Annual Forum of the American Helicopter Society, Washington D.C., 2005.
Bhagwat, M. J., Ormiston, R. A., Saberi, H. A and Xin, H., "Application of CFD/CSD Coupling for Analysis of Rotorcraft Airloads and Blade Loads in Maneuvering Flight", Proceedings of the 63rd Annual Forum of the American Helicopter Society, Washington D.C., 2007.
Lytwyn, R. T., "An Analysis of the Divergent Vertical Helicopter Oscillations Resulting from the Physical Presence of the Pilot in the Collective Control Loop", Proceedings of the 22nd Annual Forum of the American Helicopter Society, Washington, D.C., 1966.
Bousman, W. G., "Putting the Aero Back Into Aeroelasticity", Proceedings of the 8th Annual Workshop on Aeroelasticity of Rotorcraft Systems, University Park, PA, USA, 1999.
Prasad, C. G. N., Dwivedi, V and Dutta, R., "Vibration Monitoring in Helicopter Structure Using Rotor Noise: Flight Test Results and Discussions", Proceedings of the 15th National Seminar on Aerospace Structure, Shree Maruthi Publishers, Coimbatore, India, 2007, pp. 161-165.
Yuan, K. A and Friedmann, P. P., "Aeroelasticity and Structural Optimization of Composite Helicopter Rotor Blades with Swept Tips", NASA Report 4665, May 1995.
He, Cheng Jian., "Development and Application of a Generalized Dynamic Wake Theory for Lifting Rotors", Ph.D. Thesis, Georgia Institute of Technology, July 1989.
Greenberg, M. J., "Airfoil in Sinusoidal Motion in a Pulsating Stream", NASA Technical Report 1326, 1947.
Laxman, V and Venkatesan, C., "Chaotic Response of an Airfoil due to Aeroelastic Coupling and Dynamic Stall", AIAA Journal, Vol. 45, No. 1, 2007, pp. 271-280.
Venkatesan, C., "Lecture Notes on Helicopter Technology", Department of Aerospace Engineering, Indian Institute of Technology Kanpur, India.
Padfield, G. D., "Helicopter Flight Dynamics", Blackwell Science Ltd, 1996.