THERMODYNAMIC MODELING AT HIGH PRESSURE AND TEMPERATURE
Glushko Thermocenter, IVTAN Association of Russian
Academy of Sciences
At the time being high pressures are often used in various branches
of chemical engineering. In some cases high pressure allows to accelerate
reactions velocity, in others, it helps to increase the product output.
High pressures permit to enhance performance characteristics of power units,
when the fuel chemical energy serves as energy source.
Experimental examination of the known processes or development of the
new ones is expensive and time consuming, so accomplishing thorough computer
modeling before the experiment is reasonable. Chemical reactions in the
processes mentioned can involve various chemical elements, that is why
the tools for modeling must be supplied with an extensive database on thermodynamic
properties of substances.
The equilibrium model is successfully used for the analysis of high
temperature processes. This model allows to apply methods of thermodynamics
for the theoretical examination of complex chemically reacting systems.
So the task is reduced to the determination of phase and chemical composition
of the thermodynamic system.
If the gas density is low (pressure is less than 20 MPa and temperature
is more than 1000 K) the gas phase behavior can be adequately described
by the ideal gas equation of state (EOS). However in high-pressure area
influence of the intermolecular forces becomes significant, and real gas
EOS should be used. Detailed review of the problem and methods for its
solution are given in
Baibuz V.F., Zitserman V.Yu., Golubushkin L.M., et al., ed. Yungman
V.S. Chemical equilibrium in nonideal systems. Moscow, IVTAN, 1986. (In
Russian).
The reference mentioned above contains some useful source codes in FORTRAN.
Freedman E., “Thermodynamic properties of military gun propellants”,
in: L. Stiefel (ed), Gun propulsion technology, Washington, 1988, pp.103-132.
Smith W.R., and R.W. Missen, Chemical reaction equilibrium analysis.
John Wiley, New York (1982).
To enable the researchers to accomplish the computer modeling of thermodynamic
equilibrium in complex chemically reacting systems at high pressure (up
to 600 - 800 MPa) and temperature (up to 6000 K) a new algorithm has been
developed. The algorithm allows to take into account the intermolecular
forces of the gas substances, significant at high pressure. Due to this
ability the values of such parameters of the energetic materials as specific
impulse, powder force and chemical composition of the combustion products
may be computed more reliably than in ideal gas assumption. The developed
algorithm, which is described in
Belov G.V. REAL - thermodynamic examination of combustion products
under high pressure. Proceedings of 28th International ICT-Conference,
Karlsruhe, Germany, -27 June, 1997, pp.70-1 - 70-12,
was derived from an older version of well known in Russia ASTRA algorithm,
see
Siniarev, G.B., Vatolin, N.A., and B.G. Trusov, Computer modeling
of the metallurgical processes. Nauka, Moscow, 1982. (In Russian).
On the basis of the algorithm a computer code REAL has been created.
The software allows to determine the following characteristics of the energetic
materials
To calculate equilibrium characteristics of the system assigning of
the equilibrium conditions of the system and environment is necessary.
As a rule these conditions are set by values of two thermodynamic parameters,
for example (P, H). Besides, the setting of the source composition of the
system is necessary. REAL determines phase and chemical composition of
the system and its thermodynamic properties if equilibrium conditions are
specified by values of any pair of parameters from the following list:
P, T, V, S, H, U.
To facilitate the apprehension of the results of calculations REAL allows
to draw the charts on the screen. Possible kinds of the charts are
Now, there exists hundreds of real gas equations of state. Unfortunately
the most part of them is valid for the small groups of gases only, and
the parameters of these equations of state for many gases are unavailable.
So, very few of them may be used for the investigation of variuos classes
of the gaseous combustion products. REAL allows to accomplish computer
modeling using of one of three equations of state:
- ideal gas EOS: P = D*R0*T,
- virial EOS: P = D*R0*T*(1 + B*D + C*D2);
- Nedostup EOS: P = D*R0*T*[1 + B*(T0)/(1-D/D0)],
Nedostup V.I., and E.P. Gal'kevich, “New real gas equation of state”,
Dokl. Akad. Nauk SSSR, No.2A, pp.179-182 (1978).
D - density, B, C - virial coefficients, T0= T/(1-D/D0),
D0 - conventional density at 0 K. The last two equations of
state have strong theoretical background. Their coefficients may be obtained
using Lennard-Jones 6-12 potential, the parameters of which are known or
may be evaluated for many gases. Both of these equations adequately describe
the gas phase behavior up to pressure values 600 - 800 MPa. This limit
is rather conditional one, because sometimes calculations may be carried
out at higher pressure values. Indeed, for Nedostup EOS the upper limit
is defined by the relation D/D0, which must be less than 0.9.
Virial EOS has not an exact upper boundary, and evaluating its reliability
at pressures higher than 600 MPa or at low temperatures is difficult. From
theory it follows, that virial EOS is valid if density value is lower than
critical one. However, the latter is usually unknown for complex mixtures
of combustion products. Being compared, these two EOS display approximately
the same P(D) dependence up to pressure 300 MPa (D = 0.2 g/cm3).
We consider it very useful for the researcher to have at disposal two real
gas EOS for study of the high pressure systems.
No serious computer modeling is possible without reliable and extensive
information about thermodynamic properties of compounds, so REAL is supplied
with a database on thermodynamic properties of individual substances. The
database contains information about thermodynamic and thermochemical properties
of 2500 compounds made up by 79 chemical elements. Main body of the database
(about 70%) consists of the information from
The database welcomes improvement and expansion. There is a special
service software (ASTD) for the interactive access to database information:
contents review, extraction of properties of the species given, detailed
reaction analysis, new data insertion or verification.
Lennard-Jones potential parameters s and e/k for the gas substances
in the database were collected from various data sources. Many values of
these parameters were calculated by the author from the critical point
parameters (Tcr, Pcr, Vcr).
Feedback:gbelov@iname.com.
Last modified December, 14 1998
© 1998 Gleb V. Belov
e-mail: gbelov@iname.com.
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Introduction
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REAL Algorithm
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Computer Code
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The calculation of thermodynamic and other parameters is based on the following
assumptions: one-dimensional form of the continuity, energy and momentum
equations; complete combustion; adiabatic combustion; zero velocity in
the combustion chamber; homogeneous mixing. For equilibrium expansion,
composition is assumed to attain equilibrium instantaneously during expansion.
For frozen expansion, composition is assumed to remain fixed at the combustion
composition starting from predefined freezing temperature.
There are two versions of REAL - DOS-version and for Windows-version.
Real Gas Equation of State
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Database on Thermodynamic Properties
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