Calculation of unsteady flows in turbomachinery using the linearizedEuler equations

AIAA Journal

Volumn 27, Issue 6, 1989, Pages 777-787

  Hall, Kenneth C ^a   Crawley, Edward F ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW OF FLUIDS--UNSTEADY FLOW; MATHEMATICAL MODELS; SHOCK WAVES;

BLADE LOADING; FLUTTER; GUST RESPONSE; SHOCK FITTING; SHOCK MOTION; WAKE MOTION;

TURBOMACHINERY;

EID: 0024673636     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/3.10178     Document Type: Article

References (38)

1. Whitehead, D. S., “Force and Moment Coefficients for Vibrating Aerofoils in Cascade,” Aeronautical Research Council, London, Reports and Memoranda 3254, Feb. 1960.
2. Whitehead, D. S., “Bending Flutter of Unstalled Cascade Blades at Finite Deflection,” Aeronautical Research Council, London, Reports and Memoranda 3386, Oct. 1962.
3. Atassi, H. and Akai, T. J., “Aerodynamic Force and Moment on Oscillating Airfoils in Cascade,” American Society of Mechanical Engineers, New York, Paper 78-GT-181, April 1978.
4. Atassi, H. and Akai, T. J., “Aerodynamic and Aeroelastic Characteristics of Oscillating Loaded Cascades at Low Mach Number. Part I: Pressure Distribution, Forces, and Moments,” Transactions of the ASME: Journal of Engineering for Power, Vol. 102, No. 2, April 1980, pp. 344-351.
5. Lane, F. and Friedman, M., “Theoretical Investigation of Subsonic Oscillatory Blade-Row Aerodynamics,” NACA TN 4136, Feb. 1958.
6. Whitehead, D. S., “Vibration and Sound Generation in a Cascade of Fiat Plates in Subsonic Flow,” Aeronautical Research Council, London, Reports and Memoranda 3685, Feb. 1970.
7. Smith, S. N., “Discrete Frequency Sound Generation in Axial Flow Turbomachines,” Aeronautical Research Council, London, Reports and Memoranda 3709, March 1972.
8. Verdon, J. M., “The Unsteady Aerodynamics of a Finite Supersonic Cascade with Subsonic Axial Flow,” Transactions of the ASME: Journal of Applied Mechanics, Vol. 40, No. 3, Sept. 1973, pp. 667-671.
9. Verdon, J. M. and McCune, J. E., “Unsteady Supersonic Cascade in Subsonic Axial Flow,” AIAA Journal, Vol. 13, Feb. 1975, pp. 193-201.
10. Nagashima, T. and Whitehead, D. S., “Linearized Supersonic Unsteady Flow in Cascades,” Aeronautical Research Council, London, Reports and Memoranda 3811, Feb. 1977.
11. Adamczyk, J. J. and Goldstein, M. E., “Unsteady Flow in a Supersonic Cascade with Subsonic Leading-Edge Locus,” AIAA Journal, Vol. 16, Dec. 1978, pp. 1248-1254.
12. Bendiksen, O. O., “Bending-Torsion Flutter in Supersonic Cascades,” AIAA Journal, Vol. 19, June 1981, pp. 774-781.
13. Bendiksen, O. O., “Role of Shocks in Transonic/Supersonic Compressor Flutter,” AIAA Journal, Vol. 24, July 1986, pp. 1179-1186.
14. Goldstein, M. E., Braun, W., and Adamczyk, J. J., “Unsteady Flow in a Supersonic Cascade with Strong In-Passage Shocks,” Journal of Fluid Mechanics, Vol. 83, Pt. 3, 1977, pp. 569-604.
15. Verdon, J. M. and Caspar, J. R., “Subsonic Flow Past an Oscillating Cascade with Finite Mean Flow Deflection,” AIAA Journal, Vol. 18, May 1980, pp. 540-548.
16. Carta, F. O., “Unsteady Gapwise Periodicity of Oscillating Cascaded Airfoils,” American Society of Mechanical Engineers, New York, Paper 82-GT-286, April 1982.
17. Whitehead, D. S., “Force and Moment Coefficients for High Deflection Cascades,” Univ. of Cambridge, Dept, of Engineering, Cambridge, England, CUED/A-Turbo/TR 98, May 1980.
18. Verdon, J. M. and Caspar, J. R., “A Linearized Unsteady Aerodynamic Analysis for Transonic Flows,” Journal of Fluid Mechanics, Vol. 149, Dec. 1984, pp. 403-429.
19. Whitehead, D. S., “The Calculation of Steady and Unsteady Transonic Flow in Cascades,” Univ. of Cambridge, Dept, of Engineering, Cambridge, England, CUED/A-Turbo/TR 118, 1982.
20. Ni, R. H. and Sisto, F., “Numerical Computation of Nonstation-ary Aerodynamics of Flat Plate Cascades in Compressible Flow,” Transactions of the ASME: Journal of Engineering for Power, Vol. 98, April 1976, pp. 165-170.
21. Giles, M. B., “UNSFLO: A Numerical Method for Unsteady Inviscid Flow in Turbomachinery,” Massachusetts Inst, of Technology, Cambridge, MA, TR CFDL-TR-86-6, Dec. 1986.
22. Giles, M. B., “Calculation of Unsteady Wake/Rotor Interactions,” AIAA Paper 87-0006, Jan. 1987.
23. Ni, R. H., “A Multiple-Grid Scheme for Solving the Euler Equations,” AIAA Journal, Vol. 20, 1982, pp. 1565-1571.
24. Giles, M. B., “Newton Solution of Steady Two-Dimensional Transonic Flows,” Ph.D. Thesis, Massachusetts Inst, of Technology, Cambridge, MA, June 1985.
25. Drela, M., “Two-Dimensional Transonic Aerodynamic Design and Analysis Using the Euler Equations,” Massachusetts Inst, of Technology, Cambridge, MA, Gas Turbine Lab. Rept. 187, Feb. 1986.
26. Hall, K. C., “A Linearized Euler Analysis of Unsteady Flows in Turbomachinery,” Sc.D. Thesis, Massachusetts Inst, of Technology, Cambridge, MA, May 1987.
27. Moretti, G., “Floating Shock Fitting Technique for Imbedded Shocks in Unsteady Multidimensional Flows,” Proceedings of the 1974 Heat Transfer and Fluid Mechanics Institute, Stanford Univ. Press, Stanford, CA, 1974, pp. 184-201.
28. Moretti, G., “Circumspect Exploration of Multidimensional Imbedded Shocks,” AIAA Journal, Vol. 14, July 1976, pp. 894-899.
29. Verdon, J. M., Adamczyk, J. J., and Caspar, J. R., “Subsonic Flow Past an Oscillating Cascade with Steady Blade Loading—Basic Formulation,” Unsteady Aerodynamics, edited by R. B. Kinney, Univ. of Arizona, Tucson, AZ, July 1975, pp. 827-851.
30. Verdon, J.M., “Linearized Unsteady Aerodynamic Theory,” United Technologies Research Center, East Hartford, CT, UTRC Rept. R85-151774-1, Nov. 1985.
31. Giles, M. B., “Non-Reflecting Boundary Conditions for the Euler Equations,” Massachusetts Inst, of Technology, Cambridge, MA, TR CFDL-TR-87-1, Feb. 1987.
32. Berry, P. E., “Computation of Unsteady Flow in a Blade Passage,” Unsteady Aerodynamics of Turbomachines and Propellers, Cambridge Univ., Dept, of Engineering, Cambridge, England, Sept. 1984, pp. 191-203.
33. Engquist, B. and Majda, A., “Absorbing Boundary Conditions for the Numerical Simulation of Waves,” Mathematics of Computation, Vol. 31, No. 139, July 1977, pp. 629-651.
34. Emmons, H. W., “The Numerical Solution of Compressible Fluid Flow Problems,” NACA TN 932, May 1944.
35. Emmons, H. W., “The Theoretical Flow of a Frictionless, Adiabatic, Perfect Gas Inside of a Two-Dimensional Hyperbolic Nozzle,” NACA TN 1003, May 1946.
36. Park, M. and Caughey, D. A., “Transonic Potential Flow in Hyperbolic Nozzles,” AIAA Journal, Vol. 24, June 1986, pp. 1037-1039.
37. Gostelow, J. P., Cascade Aerodynamics, Pergamon Press, New York, 1984, Chap. 5.
38. Thompson, J. F., Thames, F. C., and Mastin, W., “A Code for Numerical Generation of Boundary-Fitted Curvilinear Coordinate Systems on Fields Containing any Number of Arbitrary Two-Dimensional Bodies,” Journal of Computational Physics, Vol. 24, No. 3, 1977, pp. 274-302.