On the Noble-Abel stiffened-gas equation of state

The inviscid hydrodynamics of inert compressible media governed by the Euler equations of motion only require knowledge of a caloric equation of state e(p, v) for the material relating the internal energy e to the fluid pressure p and specific volume v (or density). For departures from the ideal gas...

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Bibliographic Details
Published in:Physics of fluids (1994) 2019-11, Vol.31 (11)
Main Author: Radulescu, M. I.
Format: Article
Language:English
Subjects:
Compressible flow
Computational fluid dynamics
Density
Equations of motion
Equations of state
Euler equations of motion
Fluid dynamics
Fluid flow
Fluid pressure
Gases
Hydrodynamics
Ideal gas
Internal energy
Mathematical models
Physics
Specific volume
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Summary:The inviscid hydrodynamics of inert compressible media governed by the Euler equations of motion only require knowledge of a caloric equation of state e(p, v) for the material relating the internal energy e to the fluid pressure p and specific volume v (or density). For departures from the ideal gas behavior, simple equations of state such as the stiffened gas, Noble-Abel, or a hybrid recently generalized by Le Métayer and Saurel [“The Noble-Abel stiffened-gas equation of state,” Phys. Fluids 28, 046102 (2016)] can correctly model compressible flows in gases, liquids, and solids. However, reactive and multicomponent descriptions require a formal definition of temperature. In the present note, we formulate a general thermodynamically based method to determine the thermal equation of state T(p, v) compatible with a generic e(p, v) relation. We apply our method to the Noble-Abel Stiffened Gas equation of state and recover the closed form solution of Le Métayer and Saurel. We also show that variations of the model taking its exponent different from the ratio of specific heats do not permit to define a thermodynamic temperature.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.5129139