Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-18T04:27:47.808Z Has data issue: false hasContentIssue false
  • English
  • Français

The effects of trailing vorticity on the flow through highly loaded cascades

Published online by Cambridge University Press:  29 March 2006

James E. Mccune  and
William R. Hawthorne
James E. Mccune
Affiliation:
Gas Turbine Laboratory, Massachusetts Institute of Technology, Cambridge
William R. Hawthorne
Affiliation:
Engineering Department, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a procedure whereby three-dimensional inviscid flow through a highly loaded turbomachinery cascade of lifting lines can be treated by methods corresponding to classical aerodynamic theory. In contrast to earlier linearized (thin airfoil) three-dimensional theory, the present study allows analysis of the flow corresponding to the large turning and/or large pressure ratios induced by practical rotors or stators. For the sake of simplicity, the present paper is limited to incompressible flow through a highly loaded rectilinear cascade and to the design problem, i.e. given blade loading. Formulae are derived for both the mean and the three-dimensional components of the flow; in particular, the velocities at the blades induced by the trailing vorticity associated with nonuniform blade circulation are determined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 74 , Issue 4 , 22 April 1976 , pp. 721 - 740
Copyright
© 1976 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

Bragg, S. L. & Hawthorne, W. R. 1950 Some exact solutions of the flow through annular cascade actuator discs J. Aero. Sci. 17, 243.Google Scholar
Cheng, W. K. 1975 A three dimensional theory for the velocity induced by a heavily loaded annular cascade of blades. S.M. thesis, Department of Aeronautics and Astronautics, M.I.T.
Falcáto, A. F. De O. 1970 Three-dimensional flow analysis in axial turbomachines. Ph.D. thesis, Engineering Department, Cambridge University.
Hawthorne, W. R. 1967 The applicability of secondary flow analyses to the solution of lateral flow problems. Fluid Mechanics of Internal Flow, pp. 238–265. Elsevier.
Lighthill, M. J. 1958 An Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press.
Mccune, J. E. 1958a A three-dimensional theory of axial compressor blade rows — subsonic, supersonic and transonic. Ph.D. thesis, Cornell University. (See also US AFOSR TN-58-72.)
Mccune, J. E. 1958b A three-dimensional theory of axial compressor blade rows — application in subsonic and supersonic flows J. Aero. Space Sci. 25, 544.Google Scholar
Mccune, J. E. 1958c The transonic flow field of an axial compressor blade row J. Aero. Space Sci. 25, 616.Google Scholar
Mccune, J. E. & Dharwadkar, S. P. 1972 Lifting line theory for subsonic axial compressor rotors. M.I.T. Gas Turbine Lab. Rep. no. 110.Google Scholar
Mccune, J. E. & Okurounmu, O. 1974 Three-dimensional flow in transonic axial compressor blade rows. Proc. Int. Symp. Fluid Mech., Acoustics & Design of Turbo-machinery, Pennsylvania State University, 1970 (ed. B. Lakshminarayana, W. R. Britisch & W. S. Gearhart), N.A.S.A. Special Publ. SP-304-Pt-1 (N75-11174), p. 155.
Morton, K. B. 1974 Three-dimensional, compressible flow through highly-loaded, rectilinear cascade. S.M. thesis, Department of Aeronautics and Astronautics, M.I.T.
Namba, M. 1974 Lifting surface theory for a rotating subsonic or transonic blade row. Aero. Res. Counc. R. & M. no. 3740.Google Scholar
Oates, G. C. 1971 Actuator disc theory for incompressible highly rotating flows. A.S.M.E. Paper, 71-WA/FE-18.Google Scholar
Okurounmu, O. 1967 Wave drag in transonic axial compressors. Sc.D. thesis, Mechanical Engineering Department, M.I.T.
Okurounmu, O. & Mccune, J. E. 1970 Three-dimensional vortex theory of axial compressor blade rows at subsonic and transonic speeds A.I.A.A. J. 8, 1275.Google Scholar
Okurounmu, O. & Mccune, J. E. 1971 Transonic lifting surface theory for axial flow compressors. United Aircraft Res. Labs., E. Hartford, Ct, Rep. K 213580-1.Google Scholar
Okurounmu, O. & Mccune, J. E. 1974a The lifting surface theory of axial compressor blade rows. Part I: the subsonic compressor. A.I.A.A. J. 12, 1363.Google Scholar
Okurounmu, O. & Mccune, J. E. 1974b The lifting surface theory of axial compressor blade rows. Part II. The transonic compressor A.I.A.A. J. 12, 1372.Google Scholar
Reissner, H. 1937 On the vortex theory of the screw propeller J. Aero. Sci. 5, 1.Google Scholar
Thwaites, B. (ed.) 1960 Incompressible Aerodynamics. Oxford: Clarendon Press.