Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-20T00:19:24.578Z Has data issue: false hasContentIssue false
  • English
  • Français

A linearized unsteady aerodynamic analysis for transonic cascades

Published online by Cambridge University Press:  20 April 2006

Joseph M. Verdon  and
Joseph R. Caspar
Joseph M. Verdon
Affiliation:
United Technologies Research Center, East Hartford, Connecticut 06108
Joseph R. Caspar
Affiliation:
United Technologies Research Center, East Hartford, Connecticut 06108
Get access Rights & Permissions [Opens in a new window]

Abstract

A linearized potential-flow analysis is presented for predicting the unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers. The unsteady aerodynamic model includes the effects of blade geometry, non-zero mean-pressure variation across the blade row, high-frequency blade motion, and shock motion within the framework of a linearized frequency-domain formulation. The unsteady equations are solved using an implicit least-squares finite-difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady flow field is determined by matching a solution determined on a rectilinear-type cascade mesh, which covers an extended blade-passage region, to a solution determined on a detailed polar-type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Results are presented for cascades of double-circular-arc and flat-plate blades to demonstrate the unsteady analysis and to partially illustrate the effects of blade geometry, inlet Mach number, blade-vibration frequency and shock motion on unsteady response.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 149 , December 1984 , pp. 403 - 429
Copyright
© 1984 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

Aris, A. 1962 Vectors, Tensors and the Basic Equations of Fluid Mechanics. Prentice-Hall.
Atassi, H. & Akai, T. J. 1978 Effect of blade loading and thickness on the aerodynamics of oscillating cascades. AIAA 16th Aerospace Sciences Meeting; Paper 78–227.Google Scholar
Carta, F. O. 1983 Unsteady aerodynamics and gapwise periodicity of oscillating cascaded airfoils. Trans. ASME A: J. Engng for Power 105, 565.Google Scholar
Caruthers, J. E. 1981 Aerodynamic analysis of cascaded airfoils in unsteady rotational flow. In Proc. 2nd Intl Symp. on Aeroelasticity in Turbomachines (ed. P. Suter), pp. 31–64. Juris, Zurich.
Caspar, J. R. 1983 Unconditionally stable calculation of transonic potential flow through cacades using an adaptive mesh for shock capture. Trans. ASME A: J. Engng for Power 105, 504.Google Scholar
Caspar, J. R. & Verdon, J. M. 1981 Numerical treatment of unsteady subsonic flow past an oscillating cascade. AIAA J. 19, 1531.Google Scholar
Ehlers, F. E. & Weatherill, W. H. 1982 A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils. NASA CR 3537.Google Scholar
Fung, K. Y., Yu, N. J. & Seebass, R. 1978 Small unsteady perturbations in transonic flows. AIAA J. 16, 815.Google Scholar
Goldstein, M. E. 1979 Turbulence generated by the interaction of entropy fluctuations with non-uniform mean flows. J. Fluid Mech. 93, 209.Google Scholar
Goldstein, M. E., Braun, W. Adamczyk, J. J. 1977 Unsteady flow in a supersonic cascade with strong in-passage shocks. J. Fluid Mech. 83, 569.Google Scholar
Hounjet, M. H. L. 1981 Transonic panel method to determine loads on oscillating airfoils with shocks. AIAA J. 19, 559.Google Scholar
Hunt, J. C. R. 1973 A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61, 225.Google Scholar
Jameson, A. 1974 Iterative solution of transonic flows over airfoils and wings including flows at Mach 1. Commun. Pure Appl. Maths 27, 283.Google Scholar
McNally, W. D. & Sockol, P. M. 1981 Computational methods for internal flows with emphasis on turbomachinery. NASA Tech. Memo. 82764.Google Scholar
Murman, E. H. & Cole, J. D. 1971 Calculation of plane steady transonic flows. AIAA J. 9, 114.Google Scholar
Tijdeman, H. 1977 Investigations of the transonic flow around oscillating airfoils. Natl Aerosp. Lab. Rep. NLR TR 77090-U.Google Scholar
Tijdeman, H. & Seebass, R. 1980 Transonic flow past oscillating airfoils. Ann. Rev. Fluid Mech. 12, 181.Google Scholar
Verdon, J. M. & Caspar, J. R. 1980 Subsonic flow past an oscillating cascade with finite mean flow deflection. AIAA J. 18, 540.Google Scholar
Verdon, J. M. & Caspar, J. R. 1982 Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades. AIAA J. 20, 1259.Google Scholar
Whitehead, D. S. 1980 Unsteady aerodynamics in turbomachinery. Special Course on Unsteady Aerodynamics; AGARD Rep. 679.Google Scholar
Whitehead, D. S. & Grant, R. J. 1981 Force and moment coefficients for high deflection cascades. In Proc. 2nd Intl Symp. on Aeroelasticity in Turbomachines (ed. P. Suter), pp. 85–127. Juris, Zurich.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Williams, M. H. 1979 Linearization of unsteady transonic flows containing shocks. AIAA J. 17, 394.Google Scholar