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Real gas normal shock waves with the redlich-kwong equation of state

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Summary

The calculation of the normal shock wave of real gases poses serious difficulties either because of the complexity of the exact thermal and caloric equations of state of the real gas considered, or because of the total lack of these equations. The present work describes a method for the prediction of the normal shock wave of real gases, which is based on the Redlich-Kwong generalized equation of state. The method involves iterative solution of the energy conservation equation for one of the state variables, while all the other variables are calculated explicitly. The method is applicable to real gases for which no detailed thermodynamic data are available, as the only gas-dependent information required is the values of pressure and temperature at the critical point and the heat capacity in the ideal gas state (pressure approaching zero). Because of the short computational time, the method is recommended even in the case of real gases for which the exact thermal and caloric equations of state are available. Applications have been made in the case of real air, for which exact shock wave values are available for comparison with the present method. The agreement is very good in a wide range of conditions.

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Abbreviations

A, B, C :

Constants in Eq. (10)

a, b :

Coefficients in the Redlich-Kwong equation of state

c :

Velocity

c p :

Constant pressure heat capacity

c p′ :

Constant pressure heat capacity in the ideal gas state

c v :

Constant volume heat capacity

c v′ :

Constant volume heat capacity in the ideal gas state

h :

Specific enthalpy

h′:

Specific enthalpy in the ideal gas state

k pv :

Real gas isentropic exponent corresponding to the pair of variablesp, v

M :

Mach number

p :

Pressure

R :

Gas constant

s :

Specific entropy

T :

Temperature

v :

Specific volume

α:

Sound velocity

ϱ:

Density

Δh′:

Residual enthalpy

c :

Denotes values at the critical point

id:

Denotes ideal gas

ref:

Denotes reference value

0:

Denotes stagnation conditions

1:

Denotes values upstream the shock wave

2:

Denotes values downstream the shock wave

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Authors and Affiliations

  1. Mechanical Engineering Department, National Technical University of Athens, 42 Patission Street, 106 82, Athens, Greece

    D. A. Kouremenos &  K. A. Antonopoulos

Authors
  1. D. A. Kouremenos
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  2. K. A. Antonopoulos
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Kouremenos, D.A., Antonopoulos, K.A. Real gas normal shock waves with the redlich-kwong equation of state. Acta Mechanica 76, 223–233 (1989). https://doi.org/10.1007/BF01253581

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  • DOI: https://doi.org/10.1007/BF01253581

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