International Journal of Aeronautical and Space Sciences

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
권호 표지
DOI QR코드

DOI QR Code

Numerical Quadrature for the Prandtl Meyer Function at High Temperature with Application for Air

  • Zebbiche, Toufik (Department of Aeronautics, Faculty of Engineering, University SAAD Dahleb of Blida)
  • Published : 2008.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function, having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented in this context. The classical form of the Prandtl Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air.

Keywords

References

  1. Zebbiche, T., "Stagnation Temperature Effect on the Prandtl Meyer Function", AIAA Journal, Vol. 45, No. 4, pp. 952-954, 2007 https://doi.org/10.2514/1.24868
  2. Zebbiche, T. and Youbi, Z., "Supersonic Flow Parameters at High Temperature. Application for Air in Nozzles", The Aeronautical Journal, Vol., 111, $N^{\circ}$ 1115, Janvier 2007, pp. 31-40, 2007 https://doi.org/10.1017/S0001924000001731
  3. Raltson, A. and Rabinowitz, A., "A First Course in Numerical Analysis", McGraw Hill Book Company, 1985
  4. Zebbiche, T. and Youbi, Z., " Supersonic Two-Dimernsional Minimum Length Nozzle Design at High Temperature. Application for Air", AIAA Paper 2006-4599, July 2006
  5. Zebbiche, T. and Youbi, Z., "Supersonic Plug Nozzle Design at High Temperature. Application for Air", 2006, AIAA Paper 2006-0592, Janvier 2006
  6. Fletcher, C. A. J. " Computational Techniques for Fluid Dynamics: Specific Techniques for Different Flow Categories," Vol. II, Springer-Verlag, Berlin, 1988
  7. Anderson, J. D. Jr., "Modern Compressible Flow: With Historical Perspective, Mc Graw-Hill Book Company, New York, 1982.
  8. Stroud, A. H. and Secrest, D. H., "Gaussian Quadrature Formulas", Prentice-Hall, Inc., Engiewood Cliffs, N.J., 1966
  9. Raltson, A., "A Family of Quadrature Formulas Which Achieve High Accurary in Composite Rules", J. Ass. Comput. Mach.", Vol. 6, pp. 384-394, 1959 https://doi.org/10.1145/320986.320993
  10. Demidovtch B. et I. Maron I., "Elements de calcul numerique", 1987, Edition MIR, Moscou
  11. Zebbiche, T., "Supersonic Axisymmetric Minimum Length Nozzle Conception at High Temperature", AIAA paper AIAA-2008-4110, 40th AIAA Thermophysics Conference, 23-26 June 2008, Washington, USA, 2008