Summary
In real gas flow several effects are inverted if the fundamental gasdynamic derivative Γ becomes negative. Here we investigate stationary flows with multiple sonic points. In a nozzle with two throats three sonic points occur where the first or the last is related with the absolute maximum of the mass flux density; the location of this absolute maximum depends on the reservoir state. Then we calculate 2-D flows in a circular arc nozzle by solving the Euler equation with a time dependent finite volume method (FVM) of Jameson. For a high exit pressure (p e /p 01 = 0.94) two sonic shocks occur whereas the flow remains entirely subsonic in between. In order to demonstrate nonclassical effects in strongly bended channels we present results of potential vortex flow of dense gases. Here we observe the formation of separated circular ring shaped supersonic and subsonic regions in the interior of the vortex.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Duhem, P.: Sur la propagation des ondes de choc au sein des fluides. Z. Phys. Chem. 69, 169–186 (1909).
Thompson, P. A.: A fundamental derivative in gasdynamics. Phys. Fluids 14, 1843–1849 (1971).
Cramer, M. S., Kluwick, A.: On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142, 9–37 (1984).
Cramer, M. S.: Nonclassical dynamics of classical gases. In: Nonlinear waves in real fluids (Kluwick, A., ed.), pp. 91–145. Wien New York: Springer 1991.
Bethe, H.: The theory of shock waves for an arbitrary equation of state. Off. Sci. Res. Dey. Rep. 545 (1942).
Zel’dovich, Y.: On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz. 4, 363–364 (1946).
Thompson, P., Lambrakis, K.: Negative shock waves. J. Fluid Mech. 60, 187–208 (1973).
Cramer, M. S., Best, L.: Steady, isentropic flows of dense gases. Phys. Fluids A3, 219–226 (1991).
Kluwick, A.: Transonic nozzle flow of dense gases. J. Fluid Mech. 247, 661–688 (1993).
Cramer, M. S., Fry, R.: Nozzle flows of dense gases. Phys. Fluids A5, 1246–1259 (1993).
Schnerr, G. H., Leidner, P.: Two-dimensional nozzle flow of dense gases. ASME Paper 93-FE-8, ASME Fluids Engineering Conference, Washington, DC, June 20–24, 1993.
Cramer, M. S., Crickenberger, A. B.: Prandtl-Meyer function for dense gases. AIAA J. 30, 561–564 (1992).
Reid, R., Prausnitz, J., Poling, B.: The properties of gases and liquids, 4th edn. New York: Mc Graw-Hill 1987.
Jameson, A., Schmidt, W, Turkel, E.: Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes. AIAA Paper 81–1259 (1981).
Schnerr, G. H., Leidner, P.: Realgaseinflüsse auf einen senkrechten Stoß an einer gekrümmten Wand. Z. Angew. Math. Mech. 73, T548 - T551 (1993).
Schnerr, G. H., Leidner, P.: Real gas effects on the normal shock behavior near curved walls. Phys. Fluids A5, 2996–3003 (1993).
Zierep, J.: Der senkrechte Verdichtungsstoß am gekrümmten Profil. Z. Angew. Math. Phys. XIb, 764–776 (1958) (Festschrift Jakob Ackeret).
Oswatitsch, K.: Grundlagen der Gasdynamik. Wien New York: Springer 1976.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag
About this chapter
Cite this chapter
Schnerr, G.H., Leidner, P. (1994). Internal flows with multiple sonic points. In: Schnerr, G.H., Bohning, R., Frank, W., Bühler, K. (eds) Fluid- and Gasdynamics. Acta Mechanica, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-9310-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-7091-9310-5_17
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82495-5
Online ISBN: 978-3-7091-9310-5
eBook Packages: Springer Book Archive