Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-23T02:28:31.242Z Has data issue: false hasContentIssue false
  • English
  • Français

Stagnation pressure effect on the supersonic flow parameters with application for air in nozzles

Published online by Cambridge University Press:  29 February 2016

Merouane Salhi ,
Toufik Zebbiche  and
Abderrahmane Mehalem
Merouane Salhi*
Affiliation:
Aeronautical Sciences Laboratory, Institute of Aeronautics and Space Studies, University of Blida, BlidaAlgeria
Toufik Zebbiche
Affiliation:
Aeronautical Sciences Laboratory, Institute of Aeronautics and Space Studies, University of Blida, BlidaAlgeria
Abderrahmane Mehalem
Affiliation:
Aeronautical Sciences Laboratory, Institute of Aeronautics and Space Studies, University of Blida, BlidaAlgeria
*
salhimerouane@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

When the stagnation pressure of a perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas doesn't stay perfect. Its state equation changes and it becomes a real gas. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation. The aim of this work is to determine the effect of stagnation pressure on the thermodynamic, physical and geometrical supersonic flow parameters in order to find a general form for real gas. With the assumptions that Berthelot's state equation accounts for molecular size and intermolecular force effects, expressions are developed for analysing the supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The design parameters of the supersonic nozzle-like thrust coefficient depend directly on the stagnation parameters of the combustion chamber. The application made for air. A computation of error was made in this case to give a limit of the perfect gas model compared to the real gas model.

Keywords

Supersonic flowperfect gas modelreal gas modelhigh temperature modelBerthelot's state equationnumerical derivationSimpson's methodstretching functionrelative errorstagnation pressurestagnation temperature
Type
Research Article
Information
The Aeronautical Journal , Volume 120 , Issue 1224 , February 2016 , pp. 313 - 354
Copyright
Copyright © Royal Aeronautical Society 2016 

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

1.Anderson, J.D. Jr., Fundamentals of Aerodynamics, 2nd ed, 1998, McGraw-Hill, New York, US.Google Scholar
2.Anderson, J.D., Modern Compressible Flow With Historical Perspective, 2nd ed, 1992, McGraw-Hill, New York, US.Google Scholar
3.Rhyming, I. L., Dynamique Des Fluides, 1984, Press Polytechnique Romandes, Lausanne, Suisse.Google Scholar
4.Tsien, H.-S.One-dimensional flow of a gas characterized by van der waal's equation of state, J Math Phy, January 1947, XSV, (6), pp 301–324.Google Scholar
5.Zebbiche, T. and Youbi, Z.Effect of stagnation temperature on supersonic flow parameters. Application for air in nozzles, Aeronaut J, January 2007, 111, (1115), pp 31–40.CrossRefGoogle Scholar
6.Zebbiche, T. and Youbi, Z. Supersonic flow parameters at high temperature. Application for air in nozzles, DGLR 2005–256, German Aerospace Congress 2005, 26–29 September 2005, Friendrichshafen, Germany, 26–29 September 2005.Google Scholar
7.Picard, Ch. Thermochimie, 2ème ed, 1996, Bruxelles, Belgium.Google Scholar
8.Annamalai, K., Ishwar, K.P. and Milind, A.J.Advanced Thermodynamics Engineering, 2nd ed, 2011, CRC press, Taylor and Francis Group, Florida, US.CrossRefGoogle Scholar
9.Shapiro, A.H.The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1, 1953, John Wiley and Sons, Inc., New York, US.Google Scholar
10.Singh, O.Applied Thermodynamics, 2003, New Age International Limited Publishers, New Delhi, India.Google Scholar
11.Oosthuisen, P.H. and Carscallen, W.E., Compressible Fluid Flow, 1997, McGraw-Hill, New York, US.Google Scholar
12.Fletcher, C.A.J.Computational Techniques for Fluid Dynamics: Specific Techniques for Different Flow Categories, Vol. II, 1988, Springer-Verlag, Berlin, Heidelberg.Google Scholar
13.Nag, P.K.Engineering Thermodynamics, 4th ed, 2008, McGraw-Hill, New Delhi, India.Google Scholar
14.Comolet, R.Mécanique Expérimentale des Fluides. Statique et Dynamique des Fluides Non Visqueux,” Tome 1, 3ème ed, 1979, Masson.Google Scholar
15.Demidovitch, B. et Maron, I.I. Eléments De Calcul Numérique, 1987, Edition MIR, Moscou, Russia.Google Scholar
16.Raltson, A. and Rabinowitz, A.A First Course in Numerical Analysis, 1985, McGraw-Hill, New York, US.Google Scholar
17.Peterson, C.R. and Hill, P.G.Mechanics and Thermodynamics of Propulsion, 1965, Addition-Wesley, New York, US.Google Scholar
18.Zebbiche, T., Salhi, M. and Boun-jad, M.Numerical computational of supersonic flow around a pointed airfoil, J Comput Methods Sci Eng, 2012, 12, pp 213–233.Google Scholar
19.Haynes, W.M.CRC Handbook of Chemistry and Physics, 75th ed, 1995, Oxford University, Florida, US.Google Scholar
20.Hilsenrath, J.W., Beckett, C., Benedict, W.S., Fano, L.J., Hoge, H.F., Masi, J.L., Nuttall, R.S., Touloukian, Y.W. and Woolley, H. Tables of Thermal Properties of Gases, National Bureau of Standard, 1955.CrossRefGoogle Scholar