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The forced response of choked nozzles and supersonic diffusers

Published online by Cambridge University Press:  07 August 2007

WILLIAM H. MOASE ,
MICHAEL J. BREAR  and
CHRIS MANZIE
WILLIAM H. MOASE
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Melbourne, VIC, 3010, Australia
MICHAEL J. BREAR
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Melbourne, VIC, 3010, Australia
CHRIS MANZIE
Affiliation:
Department of Mechanical and Manufacturing Engineering, University of Melbourne, VIC, 3010, Australia
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Abstract

The response of choked nozzles and supersonic diffusers to one-dimensional flow perturbations is investigated. Following previous arguments in the literature, small flow perturbations in a duct of spatially linear steady velocity distribution are determined by solution of a hyper-geometric differential equation. A set of boundary conditions is then developed that extends the existing work to a nozzle of arbitrary geometry. This analysis accommodates the motion of a plane shock wave and makes no assumption about the nozzle compactness. Numerical simulations of the unsteady, quasi-one-dimensional Euler equations are performed to validate this analysis and also to indicate the conditions under which the perturbations remain approximately linear.

The nonlinear response of compact choked nozzles and supersonic diffusers is also investigated. Simple analyses are performed to determine the reflected and transmitted waveforms, as well as conditions for unchoke, ‘over-choke’ and unstart. This analysis is also supported with results from numerical simulations of the Euler equations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 281 - 304
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Culick, F. E. C. & Rogers, T. 1983 The response of normal shocks in diffusers. AIAA J. 21, 1382–1390.CrossRefGoogle Scholar
Dowling, A. P. & Hubbard, S. 2000 Instablity in lean premixed combusters. Proc. Inst. Mech. Engrs A 214, 317–332.Google Scholar
Kim, J. W. & Lee, D. J. 2001 Adaptive nonlinear artificial dissipation model for computational aeroacoustics. AIAA J. 39, 810–818.Google Scholar
Marble, F. E. & Candel, S. M. 1977 Acoustic disturbance from gas non-uniformities convected through a nozzle. J. Sound Vib. 55, 225–243.Google Scholar
Mayer, D. W. & Paynter, G. C. 1995 Prediction of supersonic inlet unstart caused by freestream disturbances. AIAA J. 33, 266–275.Google Scholar
Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct simulation of compressible viscous flows. J. Comput. Phys. 101, 104–129.Google Scholar
Rein, M., Grabitz, G. & Meier, G. E. A. 1988 Non-linear wave propagation in transonic nozzle flows. J. Sound Vib. 122, 331–346.Google Scholar
Stow, S. R., Dowling, A. P. & Hynes, T. P. 2002 Reflection of circumferential modes in a choked nozzle. J. Fluid Mech. 467, 215–239.Google Scholar
Tam, C. K. W. & Webb, J. C. 1993 Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107, 262–281.Google Scholar
Tsien, H. S. 1952 The transfer functions of rocket nozzles. Am. Rocket Soc. J. 22, 139–143.Google Scholar