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Thrust nozzle optimization including boundary-layer effects

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Abstract

An optimization analysis employing the calculus of variations and a numerical relaxation scheme for applying the results are presented for the design of axisymmetric, maximumthrust nozzle contours including boundary-layer effects. The method is illustrated by comparison with a known solution without boundary-layer effects. A parametric study of boundary-layer effects for a range of parameters typical of scramjet thrust nozzles is presented.

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References

  1. 1.

    Guderley, G., andHantsch, E.,Beste Formen für Achsensymmetrische Überschallschubdüsen, Zeitschrift für Flugwissenschaften, Vol. 3, No. 9, 1955.

  2. 2.

    Rao, G. V. R.,Exhaust Nozzle Contour for Optimum Thrust, Jet Propulsion, Vol. 28, No. 6, 1958.

  3. 3.

    Rao, G. V. R.,Spike Nozzle Contour for Optimum Thrust, Ballistic Missile and Space Technology, Vol. 2, Edited by C. W. Morrow, Pergamon Press, New York, 1961.

  4. 4.

    Guderley, G.,On Rao's Method for the Computation of Exhaust Nozzles, Zeitschrift für Flugwissenschaften, Vol. 7, No. 12, 1959.

  5. 5.

    Guderley, K. G., andArmitage, J. V.,General Approach to Optimum Rocket Nozzles, Chapter 11, Theory of Optimum Aerodynamic Shapes, Edited by A. Miele, Academic Press, New York, 1965.

  6. 6.

    Hoffman, J. D., andThompson, H. D.,A General Method for Determining Optimum Thrust Nozzle Contours for Gas-Particle Flows, Journal of the American Institute of Aeronautics and Astronautics, Vol. 5, No. 10, 1967.

  7. 7.

    Hoffman, J. D.,A General Method for Determining Optimum Thrust Nozzle Contours for Chemically Reacting Gas Flows, Journal of the American Institute of Aeronautics and Astronautics, Vol. 5, No. 4, 1967.

  8. 8.

    Shmyglevskii, Yu. D.,Some Variational Problems in Gas Dynamics, Moscow, 1963.

  9. 9.

    Thompson, H. D., andMurthy, S. N. B.,Design of Optimized Three-Dimensional Nozzles, Journal of Spacecraft and Rockets, Vol. 3, No. 9, 1966.

  10. 10.

    Borisov, V. M.,Variational Problem on Three-Dimensional Supersonic Flows, Prikladnaya Matematica i Mechanika, Vol. 29, No. 1, 1965.

  11. 11.

    Kraiko, A. N.,Variational Problems of Gas Dynamics of Nonequilibrium and Equilibrium Flows, Prikladnaya Matematica i Mechanika, Vol. 28, No. 2, 1964.

  12. 12.

    Kraiko, A. N., Naumova, I. N., andShmyglevskii, Iu. D.,On the Construction of Bodies of Optimum Shape in a Supersonic Stream, Prikladnaya Matematica i Mechanika, Vol. 28, No. 1, 1964.

  13. 13.

    Galyun, N. S., andKraiko, A. N.,A Variational Problem in One-Dimensional Nonequilibrium Gas Dynamics, Izvestiya, Mekhanika Zhidkosti i Gaza, Vol. 1, No. 2, 1966.

  14. 14.

    Scofield, M. P., Thompson, H. D., andHoffman, J. D.,Thrust Nozzle Optimization including Boundary Layer Effects, Air Force Aero-Propulsion Laboratory, TR No. AFAPL-TR-67-158, 1967.

  15. 15.

    Huang, H. U.,Optimization of Supersonic Rocket Nozzles with Viscous Flow, University of Massachusetts, Ph.D. Thesis, 1970.

  16. 16.

    Miele, A.,Generalized Approach to the Calculus of Variations in Two Independent Variables, Chapter 4, Theory of Optimum Aerodynamic Shapes, Edited by A. Miele, Academic Press, New York, 1965.

  17. 17.

    Elliott, D. G., Bartz, D. R., andSilver, S.,Calculation of Turbulent Boundary-Layer Growth and Heat Transfer in Axisymmetric Nozzles, Jet Propulsion Laboratory, Report No. 32-387, 1963.

  18. 18.

    Bartz, D. R.,Turbulent Boundary-Layer Heat Transfer from Rapidly Accelerating Flow of Rocket Combustion Gases and of Hot Air, Advances in Heat Transfer, Vol. 2, Edited by J. P. Hartnett and T. F. Levine, Academic Press, New York, 1965.

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This work was sponsored by the Air Force Aero-Propulsion Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract No. F33615-67-C-1068.

Communicated by K. G. Guderley

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Hoffman, J.D., Scofield, M.P. & Thompson, H.D. Thrust nozzle optimization including boundary-layer effects. J Optim Theory Appl 10, 133–159 (1972). https://doi.org/10.1007/BF00934730

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Keywords

  • Parametric Study
  • Optimization Analysis
  • Relaxation Scheme
  • Nozzle Contour
  • Thrust Nozzle