Advertisement

Gas Dynamics

  • Kolumban HutterEmail author
  • Yongqi Wang
Chapter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)

Abstract

This chapter on gas dynamics illustrates a technically important example of a fluid field theory, where the information deduced by the second law of thermodynamics delivers important properties, expressed e.g. by the thermal and caloric equations of state of, say, ideal and real gases. Problems of acoustics, steady isentropic flow processes and their stream filament theory are briefly touched. The description of the propagation of small perturbations in a gas serves in its one-dimensional form ideally as a model for the propagation of sound e.g. in a flute or organ pipe, and it can be used to explain the Doppler shift occurring when the sound source is moving relative to the receiver. Moreover, with the stream filament theory, the sub- and supersonic flow through a nozzle can be explained. In a final section the three dimensional theory of shocks is derived as the set of jump conditions on surfaces for the balance laws of mass, momentum, energy and entropy. Their exploitation is illustrated for steady surfaces for simple fluids under adiabatic flow conditions. This leads to the well-known RankineHugoniot relations. These problems are classics; gas dynamics, indeed forms an important advanced technical field that was developed in the 20th century as a subject of aerodynamics and astronautics and important specialties of mechanical engineering.

Keywords

Acoustic waves Generation of sounds D’Alembert’s and Bernoulli’s solution Acoustic Doppler effect Isentropic stream filament theory Laval nozzle Theory of shocks Stationary shocks RankineHugoniot relations 

References

  1. 1.
    Becker, E.: Gasdynamik. Teubner, Stuttgart (1965) Engl. Translation (1988)Google Scholar
  2. 2.
    Chéret, R.: The life and work of Pierre Henri Hugoniot. In: Johnson J.N., Chéret R. (eds.) Classic Papers in Shock Compression Science, pp. 149–160. New York: Springer. (1998)Google Scholar
  3. 3.
    Courant, R., Friedrichs, K.O.: Supersonic Flow and Shock Waves. Applied Mathematical Sciences, vol. 21, Springer, Berlin, fifth printing (1999)Google Scholar
  4. 4.
    d’Alembert, le Rond J.-B.: Traité de dynamique. Paris (1743)Google Scholar
  5. 5.
    d’Alembert, le Rond J.-B.: Réflexions sur la cause générale des vents (Reflections on the general causes of winds) (Paris, David l’ainé) (1747)Google Scholar
  6. 6.
    d’Alembert, le Rond J.-B.: Essai d’ une nouvelle théorie de la résistance des fluids (Essay on a new theory of resistance of fluids) (1752)Google Scholar
  7. 7.
    Eden, A.L.: Christian Doppler: Leben und Werk. Salzburg: Landespressebureau, ISBN 3-85015-069-0 (1988)Google Scholar
  8. 8.
    Hutter, K., Jöhnk, K.: Continuum Methods of Physical Modeling. Springer, Berlin, 635 pp. (2004)Google Scholar
  9. 9.
    Hugoniot, P.-H.: Mémoire sur la propagation du mouvement dans un fluide indéfini. Journal de Mathématiques pures et appliquées (4th series), 3, 477–492 and 4, 153–168 (1887)Google Scholar
  10. 10.
    Hugoniot, P.-H.: Sur la propagation du mouvement dans les corps et spécialement dans les gaz parfaits (première partie). Journal de l’école Polytechnique, 57, 3–97 (1887)Google Scholar
  11. 11.
    Hugoniot, P.-H.: Sur la propagation du mouvement dans les corps et spécialement dans les gaz parfaits (deuxième partie). Journal de l’école Polytechnique (in French), 58, 1–125 (1889)Google Scholar
  12. 12.
    Oswatitsch, K.: Grundlegende Gasdynamik. Springer, Wien (1976)Google Scholar
  13. 13.
    Oswatitsch, K.: Contributions to the development of Gasdynamics: Selected Papers. Translated on the occasion of K. Oswatitsch’s 70th Birthday, Vieweg, Paperback (2013)Google Scholar
  14. 14.
    Zierep, J.: Vorlesungen über Gasdynamik. Verklag G. Braun, Karlsruhe, 298 pp. (1963)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.c/o Versuchsanstalt für Wasserbau, Hydrologie und GlaziologieETH ZürichZürichSwitzerland
  2. 2.Department of Mechanical EngineeringTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations