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Abstract
At very high speeds, bubbles form on the body of underwater vehicles because of sharp trailing edges or at places where the local pressure is lower than the vapor pressure. These bubbles are called cavities and the size of the cavities grows as the velocity increases. A properly designed cavitator can induce the formation of a single big cavity all over the vehicle. Such a vehicle travelling in the vaporous cavity is called a supercavitating vehicle and the present research work mainly focuses on the dynamic modeling of such vehicles. Cavitation of the fins is also accounted and the effect of the same on trajectory is well explained. The entire dynamics has been developed using the state space approach and emphasis is given on the effect of size and angle of attack of the cavitator. Control law has been established for the motion of the vehicle using Non-linear Dynamic Inverse (NDI) method with cavitator as the control surface.
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References
- Lee Qi-tao., Xue Lei-ping and He You-sheng., "Experimental Study of Ventilated Supercavities with a Dynamic Pitching Model", Journal of Hydrodynamics, 20(4), pp.456-460, 2008.
- Bàlint Vanek., "Control Methods for High Speed Supercavitating Vehicles", Ph.D Thesis, University of Minnesota, 2008.
- Daijin Li., Yuwen Zhang., Kai Luo and Jianjun Dang., "Motion Control of Underwater Supercavitating Projectiles", Modern Applied Science, Vol.3, No.2, pp.60-65, 2009.
- Garabedian, P.R., "Calculation of Axially Symmetric Cavities and Jets", Pac. J. Math., 6, No.4, pp.611-684, 1956.
- Vladimir N., "Semenenko - Artificial Supercavitation", Physics and Calculations, DTIC, ADP012080.
- Travis Jon Schauer., "An Experimental Study of Ventilated Supercavitating Vehicle", M.S. Thesis, University of Minnesota, 2003.
- Zhang Xue-wei., Wei Ying-jie, Zhang Jia-zhong, Wang Cong and Yu Kai-ping., "Experimental Research on the Shape Characteristics of Natural and Ventilated Supercavitation", Journal of Hydrodynamics, Ser.B, 19 (5), pp.564-571, 2007.
- Birkhoff, G. and Zarantonello, E.H., "Jets, Wakes and Cavities", Academic Press Inc Publishers, New York, 1957.
- Kurdila, A.J., Lind, R., Dzielski, J., Jammulamadaka, A. and Goel, A., "Dynamics and Control of Supercavitating Vehicles," Office of Naval Research - Supercavitating High Speed Bodies, Technical Report, 2003.
- Ivan N. Kirschner., David C. Kring., Ann W. Stokes., Neal E. Fine and James S. Uhlman, Jr., "Control Strategies for Supercavitating Vehicles", Journal of Vibration and Control, Vol.8, No.2, pp.219-242, 2002.
- Lane, S.H. and Stengel, R.F., "Flight Control Design using Nonlinear Inverse Dynamics", Automatica, Vol.24, pp.471-483, 1988.
- Seong Sik Ahn., "An Integrated Approach to the Design of Supercavitating Underwater Vehicles", Ph. D. Thesis, Georgia Institute of Technology, 2007.
- Knapp, R.T., Daily, J.W. and Hammitt, F.G., "Cavitation", McGraw-Hill, New York, 1970
- Franc, J.P. and Michel, J.M., "Fundamentals of Cavitation", Kluwer Academic Publishers, Dordrecht, 2004.
- Nelson., "Flight Stability and Automatic Control", Tata McGraw Hill, New Delhi, 2007.
- Tewari, A., "Modern Control Design with Matlab and Simulink", John Wiley and Sons Ltd, Kundli, 2003.
- Logvinovich, G.V., "Hydrodynamics of Free Boundary Flows", IPST Press, Jerusalem, 1972.
- Vladimir N. Semenenko., "Fundamentals of Calculation and Designing the Underwater Supercavitating Vehicles", Special Lecture Course, Institute of Hydromechanics, National Academy of Sciences of Ukraine.
- Davies, T.V., "Steady Two Dimensional Cavity Flow Past an Aerofoil Using Linearized Theory", Quarterly Journal of Mechanics and Applied Mathematics,Vol.23, Part-1, 1970.
- David R. Stinebring., Michael L. Billet., Jules W. Lindau and Robert F. Kunz., "Developed Cavitation-Cavity Dynamics", DTIC, ADP012075.
- Santosh Kumar Burnwal., "Modeling and Simulation of High Speed Supercavitating Vehicle", M.Tech Thesis, Indian Institute of Technology Kanpur, Kanpur, 2011.
- " Supercavitating Flows", RTO EN-010/AVT-058, January, 2002.
- Selected Lecture Notes on "Ship Hydrodynamics", Course, Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University.
- Selected Lecture Notes on "Performance of Marine Vehicles at sea", Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur.
References
Lee Qi-tao., Xue Lei-ping and He You-sheng., "Experimental Study of Ventilated Supercavities with a Dynamic Pitching Model", Journal of Hydrodynamics, 20(4), pp.456-460, 2008.
Bàlint Vanek., "Control Methods for High Speed Supercavitating Vehicles", Ph.D Thesis, University of Minnesota, 2008.
Daijin Li., Yuwen Zhang., Kai Luo and Jianjun Dang., "Motion Control of Underwater Supercavitating Projectiles", Modern Applied Science, Vol.3, No.2, pp.60-65, 2009.
Garabedian, P.R., "Calculation of Axially Symmetric Cavities and Jets", Pac. J. Math., 6, No.4, pp.611-684, 1956.
Vladimir N., "Semenenko - Artificial Supercavitation", Physics and Calculations, DTIC, ADP012080.
Travis Jon Schauer., "An Experimental Study of Ventilated Supercavitating Vehicle", M.S. Thesis, University of Minnesota, 2003.
Zhang Xue-wei., Wei Ying-jie, Zhang Jia-zhong, Wang Cong and Yu Kai-ping., "Experimental Research on the Shape Characteristics of Natural and Ventilated Supercavitation", Journal of Hydrodynamics, Ser.B, 19 (5), pp.564-571, 2007.
Birkhoff, G. and Zarantonello, E.H., "Jets, Wakes and Cavities", Academic Press Inc Publishers, New York, 1957.
Kurdila, A.J., Lind, R., Dzielski, J., Jammulamadaka, A. and Goel, A., "Dynamics and Control of Supercavitating Vehicles," Office of Naval Research - Supercavitating High Speed Bodies, Technical Report, 2003.
Ivan N. Kirschner., David C. Kring., Ann W. Stokes., Neal E. Fine and James S. Uhlman, Jr., "Control Strategies for Supercavitating Vehicles", Journal of Vibration and Control, Vol.8, No.2, pp.219-242, 2002.
Lane, S.H. and Stengel, R.F., "Flight Control Design using Nonlinear Inverse Dynamics", Automatica, Vol.24, pp.471-483, 1988.
Seong Sik Ahn., "An Integrated Approach to the Design of Supercavitating Underwater Vehicles", Ph. D. Thesis, Georgia Institute of Technology, 2007.
Knapp, R.T., Daily, J.W. and Hammitt, F.G., "Cavitation", McGraw-Hill, New York, 1970
Franc, J.P. and Michel, J.M., "Fundamentals of Cavitation", Kluwer Academic Publishers, Dordrecht, 2004.
Nelson., "Flight Stability and Automatic Control", Tata McGraw Hill, New Delhi, 2007.
Tewari, A., "Modern Control Design with Matlab and Simulink", John Wiley and Sons Ltd, Kundli, 2003.
Logvinovich, G.V., "Hydrodynamics of Free Boundary Flows", IPST Press, Jerusalem, 1972.
Vladimir N. Semenenko., "Fundamentals of Calculation and Designing the Underwater Supercavitating Vehicles", Special Lecture Course, Institute of Hydromechanics, National Academy of Sciences of Ukraine.
Davies, T.V., "Steady Two Dimensional Cavity Flow Past an Aerofoil Using Linearized Theory", Quarterly Journal of Mechanics and Applied Mathematics,Vol.23, Part-1, 1970.
David R. Stinebring., Michael L. Billet., Jules W. Lindau and Robert F. Kunz., "Developed Cavitation-Cavity Dynamics", DTIC, ADP012075.
Santosh Kumar Burnwal., "Modeling and Simulation of High Speed Supercavitating Vehicle", M.Tech Thesis, Indian Institute of Technology Kanpur, Kanpur, 2011.
" Supercavitating Flows", RTO EN-010/AVT-058, January, 2002.
Selected Lecture Notes on "Ship Hydrodynamics", Course, Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University.
Selected Lecture Notes on "Performance of Marine Vehicles at sea", Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur.