Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-18T18:15:41.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical solutions for the actuator disk with variable radial distribution of load

Published online by Cambridge University Press:  26 April 2006

John T. Conway
John T. Conway
Affiliation:
Agder College, Grimstad, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

An analytical method somewhat analogous to finite wing theory has been developed which enables the flow induced by a linearized propeller actuator disk with variable radial distribution of load to be solved in closed form for the first time. Analytical solutions are given for various load distributions including the case of an arbitrary polynomial loading. As in finite wing theory, the case of elliptic loading is exceptionally simple and the induced velocities and stream function are simple expressions of elementary functions. Results are also given for a practical propeller load distribution with finite hub. The method can also be used to solve a wide range of analogous electromagnetic problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 327 - 355
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun I. S. 1972 Handbook of Mathematical Functions. Dover.
Basset, A. B. 1888 A Treatise on Hydrodynamics, Vol. II. Deighton Bell.
Betz, A. 1919 Schraubenpropeller mit geringstem Energieverlust. Göttinger Nachr., pp. 193–217Google Scholar
Breslin, J. P. & Andersen, P. 1994 Hydrodynamics of Ship Propellers. Cambridge University Press.
Byrd, P. F. & Friedman, M. D. 1971 Handbook of Elliptic Integrals for Engineers and Scientists, 2nd edn. Springer.
Clark, R. J. & Valarezo, W. O. 1990 AIAA-90-0031, 28th Aerospace Sciences Meeting, Reno, Nevada.
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series, and Products. Academic Press.
Greenberg, M. D. & Powers, S. R. 1970 NASA Rep. CR-1672.
Goldstein, S. 1929 Proc. R. Soc. Lond. A 123, 440–465.
Hobson, E. W. 1896 Phil. Trans. R. Soc. Lond. A 187, 522.
Hough, G. R. & Ordway, D. E. 1965 Developments in Theoretical and Applied Mechanics, Vol. 2, pp. 317–336. Pergamon.
Johnsson, C. A. 1983 Propellers with reduced tip loading and unconventional blade form and blade sections. Eighth School Lecture Series, Ship Design for Fuel Economy, WEGEMT, Göteborg.
Koning, C. 1935 Aerodynamic Theory, Vol. 4 (ed. W.F. Durand). Guggenheim Fund for the Promotion of Aeronautics.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lerbs, H. W. 1952 Soc. Naval Archit. Marine Engrs 60, 73–123.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in FORTRAN. Cambridge University Press.
Prudnikov, A. P., Brychkov, Y. A. & Marichev, O. I. 1992 Integrals and Series, Vol. 4: Direct Laplace Transforms. Gordon & Breach.
Sonine, N. J. 1880 Math. Ann. 16, 1–80.
Spiegel, M. R. 1965 Theory and Problems of Laplace Transforms. Schaum.
Stern, F., Kim, H. T., Patel, V. C. & Chen, H. C. 1988 J. Ship Res. 32, 246–262.
Strash, D. J., Nathman, J. K., Maskew, B. & Dvorak, F. A. 1984 AIAA-84-2178, AIAA 2nd Applied Aerodynamics Conference, Seattle.
Theodorsen, T. 1944 NACA Rep. 775.
Von Mises, R. 1945 Theory of Flight. McGraw-Hill.
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions. Cambridge University Press.
Wu, T. Y. 1962 Schiffstechnik. 9, No. 47, 134–138.
Supplementary material: PDF

Conway supplementary material

Supplementary Material

Download Conway supplementary material(PDF)
PDF 882.8 KB