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Revisiting Froude’s Theory for Hovering Shrouded Rotor

Published Online:https://doi.org/10.2514/1.J053507

This paper extends Froude’s momentum theory for free propellers to the analysis of shrouded rotors. A one-dimensional analytical approach is provided, and a homokinetic normal inlet surface model is proposed. Formulations of thrusts and power for each system component are derived, leading to the definition of optimum design criteria and providing insight into the global aerodynamics of shrouded rotors. In the context of micro-air vehicles applications, assessment of the model is conducted with respect to numerical data. Overall, comparison between numerical and analytical results shows good agreement and highlights the sensitivity of the model to viscous effects.

References

  • [1] Mueller T. J. and DeLaurier J. D., “Aerodynamics of Small Vehicles,” Annual Review of Fluid Mechanics, Vol. 35, No. 1, 2003, pp. 89–111. doi:https://doi.org/10.1146/annurev.fluid.35.101101.161102 CrossrefGoogle Scholar

  • [2] Torres G. E. and Mueller T. J., “Low Aspect Ratio Aerodynamics at Low Reynolds Numbers,” AIAA Journal, Vol. 42, No. 5, 2004, pp. 865–873. doi:https://doi.org/10.2514/1.439 LinkGoogle Scholar

  • [3] Pines D. J. and Bohorquez F., “Challenges Facing Future Micro-Air-Vehicle Development,” Journal of Aircraft, Vol. 43, No. 2, 2006, pp. 290–305. doi:https://doi.org/10.2514/1.4922 LinkGoogle Scholar

  • [4] Dickinson M. H., Lehmann F. O. and Sane S. P., “Wing Rotation and the Aerodynamic Basis of Insect Flight,” Science, Vol. 284, No. 5422, 1999, pp. 1954–1960. doi:https://doi.org/10.1126/science.284.5422.1954 CrossrefGoogle Scholar

  • [5] Platzer M. F., Jones K. D., Young J. and Lai J. C. S., “Flapping Wing Aerodynamics: Progress and Challenges,” AIAA Journal, Vol. 46, No. 9, 2008, pp. 2136–2149. doi:https://doi.org/10.2514/1.29263 LinkGoogle Scholar

  • [6] Shyy W., Aono H., Chimakurthi S. K., Trizila P., Kang C. K., Cesnik C. E. S. and Liu H., “Recent Progress in Flapping Wing Aerodynamics and Aeroelasticity,” Progress in Aerospace Sciences, Vol. 46, No. 7, 2010, pp. 284–327. doi:https://doi.org/10.1016/j.paerosci.2010.01.001 CrossrefGoogle Scholar

  • [7] Jardin T., Farcy A. and David L., “Three Dimensional Effects in Hovering Flapping Flight,” Journal of Fluid Mechanics, Vol. 702, July 2012, pp. 102–125. doi:https://doi.org/10.1017/jfm.2012.163 CrossrefGoogle Scholar

  • [8] Lipera L., Colbourne J. D., Tischler M. B., Mansur M. H., Rotkowitz M. C. and Patangui P., “The Micro Craft iSTAR Micro Air Vehicle: Control System Design and Testing,” Annual Forum Proceedings–American Helicopter Society, Vol. 57, AHS International, Alexandria, VA, 2001, pp. 1998–2008. Google Scholar

  • [9] Pereira J. L. and Chopra I., “Hover Tests of Micro Aerial Vehicle Scale Shrouded Rotors, Part I: Performance Characteristics,” Journal of the American Helicopter Society, Vol. 54, No. 1, 2009, p. 12001. doi:https://doi.org/10.4050/JAHS.54.012001 CrossrefGoogle Scholar

  • [10] Pereira J. L. and Chopra I., “Hover Tests of Micro Aerial Vehicle Scale Shrouded Rotors, Part II: Flow Field Measurements,” Journal of the American Helicopter Society, Vol. 54, No. 1, 2009, Paper 12002. doi:https://doi.org/10.4050/JAHS.54.012002 Google Scholar

  • [11] Lakshminarayan V. K. and Baeder J. D., “Computational Investigation of Microscale Shrouded Rotor Aerodynamics in Hover,” Journal of the American Helicopter Society, Vol. 56, No. 4, 2011, Paper 042002. doi:https://doi.org/10.4050/JAHS.56.042002 CrossrefGoogle Scholar

  • [12] Lee T. E., Leishman J. G. and Rand O., “Design and Testing of a Ducted Coaxial Rotor System for Application to a Micro Aerial Vehicle,” Annual Forum Proceedings–American Helicopter Society, Vol. 66, AHS International, Alexandria, VA, 2010, pp. 1404–1425. Google Scholar

  • [13] Hrishikeshavan V. and Chopra I., “Performance, Flight Testing of Shrouded Rotor Micro Air Vehicle in Edgewise Gusts,” Journal of the American Helicopter Society, Vol. 49, No. 1, 2012, pp. 193–205. doi:https://doi.org/10.2514/1.C031477 Google Scholar

  • [14] Horlock J. H., Actuator Disk Theory, McGraw Hill, New York, 1978. Google Scholar

  • [15] Rosen A. and Gur O., “Novel Approach to Axisymmetric Actuator Disk Modelling,” AIAA Journal, Vol. 46, No. 11, 2008, pp. 2914–2925. doi:https://doi.org/10.2514/1.37383 LinkGoogle Scholar

  • [16] Huo C., Barènes R., Gressier J. and Grondin G., “Numerical Study on Parametrical Design of Long Shrouded Contra-Rotating Propulsion System in Hovering,” World Academy of Science, Engineering and Technology, Vol. 5, 2011, pp. 1963–1972. Google Scholar

  • [17] Huo C., “Experimental and Numerical Analysis of a Shrouded Contrarotating Coaxial Rotor in Hover,” Ph.D. Dissertation, Aerodynamics, Energetics and Propulsion Dept., Univ. of Toulouse, Toulouse, France, 2012. Google Scholar

  • [18] Quartapelle L. and Napolitano M., “Force and Moments in Incompressible Flows,” AIAA Journal, Vol. 21, No. 6, 1983, pp. 911–913. doi:https://doi.org/10.2514/3.8171 LinkGoogle Scholar

  • [19] Noca F., Shiels D. and Jeon D., “A Comparison of Methods for Evaluating Time-Dependent Fluid Dynamic Forces on Bodies, Using Only Velocity Fields and Their Derivatives,” Journal of Fluids and Structures, Vol. 13, No. 5, 1999, pp. 551–578. doi:https://doi.org/10.1006/jfls.1999.0219 CrossrefGoogle Scholar

  • [20] David L., Jardin T. and Farcy A., “On the Non-Intrusive Evaluation of Fluid Forces with the Momentum Equation Approach,” Measurement Science and Technology, Vol. 20, No. 9, 2009, Paper 095401. doi:https://doi.org/10.1088/0957-0233/20/9/095401 CrossrefGoogle Scholar

  • [21] Moschetta J. M., “Explo-Drone: Autonomous Exploration of Confined Environments by Compact Micro Air Vehicles,” Actions Thématiques Stratégiques de l’Université de Toulouse, Toulouse, France, 2013. Google Scholar

  • [22] Dyer K., “Aerodynamic Study of a Small, Ducted VTOL Aerial Vehicle,” M.Sc. Dissertation, Aeronautics and Astronautics Dept., Massachusetts Institute of Technology, Cambridge, MA, 2002. Google Scholar

  • [23] Pereira J. L. and Chopra I., “Effects of Shroud Design Variables on Hover Performance of a Shrouded-Rotor for Micro Air Vehicle Applications,” Specialists’ Meeting Proceedings–American Helicopter Society, AHS International, Alexandria, VA, 2005. Google Scholar