Summary
Using the best available relations describing the thermodynamic behaviour of H2O (steam), numerous shock wave states realized on isentropic expansions starting at various initial points, were computed. The results obtained were approximated by explicit relations having mathematical forms similar to those of the ideal gas shock wave but with different coefficients and exponents such as to describe the real gas steam. The numerous values of these new coefficients and exponents corresponding to the stagnation points were fitted by appropriate curves and are illustrated in diagrams with respect to the stagnation temperature and the stagnation density as a parameter.
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Abbreviations
- A :
-
cross sectional area of the nozzle, m2
- A :
-
specific free internal energy, J/kg
- A base :
-
base function of H2O, J/kg
- A ideal gas :
-
ideal gas function of H2O, J/kg
- A residual :
-
residual function of H2O, J/kg
- \(\bar B\) b :
-
parameters in base function of H2O, m3/kg
- B j,b j :
-
coefficients of parameters in base function of H2O, m3/kg
- c :
-
velocity of flow, m/s
- C ij :
-
coefficients in ideal gas function of H2O
- c p :
-
specific heat capacity at constant pressure, J/kg K
- c v :
-
specific heat capacity at constant volume, J/kg K
- g i :
-
coefficients in residual function of H2O, J/kg
- h :
-
specific enthalpy, J/kg
- J :
-
momentum flux, N/m2
- k :
-
isentropic exponent
- k(i), l(i) :
-
coefficients in residual function of H2O
- M :
-
Mach number
- \(\dot m\) :
-
mass flow rate, kg/s
- p :
-
pressure, N/m2
- p o :
-
constant in base function of H2O, N/m2
- Q :
-
exchanged heat, J
- R :
-
ideal gas constant for H2O, J/kg K
- s :
-
specific entropy, J/kg K
- T :
-
absolute temperature, K
- t :
-
temperature, °C
- T i :
-
coefficients in residual function of H2O, K
- T o :
-
constant in base and residual functions of H2O, K
- T R :
-
reduced temperature in residual function of H2O
- u :
-
specific internal energy, J/kg
- v :
-
specific volume, m3/kg
- x ij :
-
coefficients and exponents in shock wave relations
- Y :
-
parameter in base function of H2O
- α:
-
sound velocity, m/s
- \(\bar \alpha ,{\text{ }}\bar \beta ,{\text{ }}\bar \gamma\) :
-
constants in base function of H2O
- δ i , τi :
-
parameters in residual function of H2O
- ϱ:
-
density, kg/m3
- ϱ i :
-
coefficients in residual function of H2O, kg/m3
- 0:
-
stagnation state
- 1:
-
upstream from the shock wave
- 2:
-
downstream from the shock wave
- id :
-
ideal gas
References
Kouremenos, D. A., Kakatsios, X. K.: Ideal gas relations for the description of real gas isentropic changes. Forsch. Ing.-Wesen51, 169–174 (1985).
Kouremenos, D. A., Kakatsios, X. K.: Isentrope Expansion des Wasserdampfes. BWK37, 263–265 (1985).
Haar, L., Gallagher, J. S., Kell, G. S.: Steam tables. New York: McGraw-Hill 1983.
Houzouris, G.: Determination of thermodynamic properties and phase of H2O from its primary properties (in Greek). Dipl. Thesis, NTUA, Athens 1989.
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Kakatsios, X.K. Numerical evaluation of steam normal shock waves. Acta Mechanica 110, 183–197 (1995). https://doi.org/10.1007/BF01215424
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DOI: https://doi.org/10.1007/BF01215424