[Doc] Describe NASA9 parameterization in CTI guide
Also note availability of data in the NASA9 form using the ThermoBuild web tool and explain how to convert it to the CTI format.
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Ray Speth
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1 changed files with 111 additions and 13 deletions
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@ -122,18 +122,15 @@ no requirement that all species in a phase use the same parameterization; each
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species can use the one most appropriate to represent how the heat capacity
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depends on temperature.
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Currently, three entry types are implemented, all of which provide species
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properties appropriate for models of ideal gas mixtures, ideal solutions, and
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pure compounds. Non-ideal phase models are not yet implemented, but may be in
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future releases. When they are, additional entry types may also be added that
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provide species-specific coefficients required by specific non-ideal equations
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of state.
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Currently, several types are implemented which provide species properties
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appropriate for models of ideal gas mixtures, ideal solutions, and pure
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compounds.
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The NASA Polynomial Parameterization
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------------------------------------
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The NASA 7-Coefficient Polynomial Parameterization
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--------------------------------------------------
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The NASA polynomial parameterization is used to compute the species
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reference-state thermodynamic properties :math:`\hat{c}^0_p(T)`,
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The NASA 7-coefficient polynomial parameterization is used to compute the
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species reference-state thermodynamic properties :math:`\hat{c}^0_p(T)`,
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:math:`\hat{h}^0(T)` and :math:`\hat{s}^0(T)`.
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The NASA parameterization represents :math:`\hat{c}^0_p(T)` with a fourth-order
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@ -150,9 +147,10 @@ polynomial:
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\frac{a_4}{4} T^4 + a_6
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Note that this is the "old" NASA polynomial form, used in the original NASA
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equilibrium program and in Chemkin. It is not compatible with the form used in
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the most recent version of the NASA equilibrium program, which uses 9
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coefficients, not 7.
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equilibrium program and in Chemkin, which uses 7 coefficients in each of two
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temperature regions. It is not compatible with the form used in the most recent
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version of the NASA equilibrium program, which uses 9 coefficients for each
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temperature region.
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A NASA parameterization is defined by an embedded :class:`NASA` entry. Very
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often, two NASA parameterizations are used for two contiguous temperature
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@ -170,6 +168,102 @@ ranges. This can be specified by assigning the ``thermo`` field of the
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-7.579666690E-07, 2.094705550E-10, -2.167177940E-14,
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-1.088457720E+03, 5.453231290E+00] ) ) )
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The NASA 9-Coefficient Polynomial Parameterization
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--------------------------------------------------
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The NASA 9-coefficient polynomial parameterization [#McBride2002]_ ("NASA9" for
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short) is an extension of the NASA 7-coefficient polynomial parameterization
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which includes two additional terms in each temperature region, as well as
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supporting an arbitrary number of temperature regions.
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The NASA9 parameterization represents the species thermodynamic properties with
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the following equations:
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.. math::
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\frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T
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+ a_4 T^2 + a_5 T^3 + a_6 T^4
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\frac{H^0(T)}{RT} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2
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+ \frac{a_3}{2} T + \frac{a_4}{3} T^2 + \frac{a_5}{4} T^3 +
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\frac{a_6}{5} T^4 + \frac{a_7}{T}
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\frac{s^0(T)}{R} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T
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+ a_3 T + \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8
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The following is an example of a species defined using the NASA9
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parameterization in three different temperature regions::
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species(name=u'CO2',
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atoms='C:1 O:2',
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thermo=(NASA9([200.00, 1000.00],
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[ 4.943650540E+04, -6.264116010E+02, 5.301725240E+00,
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2.503813816E-03, -2.127308728E-07, -7.689988780E-10,
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2.849677801E-13, -4.528198460E+04, -7.048279440E+00]),
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NASA9([1000.00, 6000.00],
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[ 1.176962419E+05, -1.788791477E+03, 8.291523190E+00,
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-9.223156780E-05, 4.863676880E-09, -1.891053312E-12,
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6.330036590E-16, -3.908350590E+04, -2.652669281E+01]),
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NASA9([6000.00, 20000.00],
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[-1.544423287E+09, 1.016847056E+06, -2.561405230E+02,
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3.369401080E-02, -2.181184337E-06, 6.991420840E-11,
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-8.842351500E-16, -8.043214510E+06, 2.254177493E+03])),
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note='Gurvich,1991 pt1 p27 pt2 p24. [g 9/99]')
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Thermodynamic data for a range of species can be obtained from the `NASA
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ThermoBuild <http://cearun.grc.nasa.gov/cea/index_ds.html>`_ tool. Using the web
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interface, an input file can be obtained for a set of species. This input file
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should then be modified so that the first line reads "`thermo nasa9`", as in the
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following example::
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thermo nasa9
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200.000 1000.000 6000.000 20000.000 9/09/04
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CO Gurvich,1979 pt1 p25 pt2 p29.
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3 tpis79 C 1.00O 1.00 0.00 0.00 0.00 0 28.0101000 -110535.196
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200.000 1000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 8671.104
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1.489045326D+04-2.922285939D+02 5.724527170D+00-8.176235030D-03 1.456903469D-05
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-1.087746302D-08 3.027941827D-12 -1.303131878D+04-7.859241350D+00
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1000.000 6000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 8671.104
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4.619197250D+05-1.944704863D+03 5.916714180D+00-5.664282830D-04 1.398814540D-07
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-1.787680361D-11 9.620935570D-16 -2.466261084D+03-1.387413108D+01
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6000.000 20000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 8671.104
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8.868662960D+08-7.500377840D+05 2.495474979D+02-3.956351100D-02 3.297772080D-06
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-1.318409933D-10 1.998937948D-15 5.701421130D+06-2.060704786D+03
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CO2 Gurvich,1991 pt1 p27 pt2 p24.
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3 g 9/99 C 1.00O 2.00 0.00 0.00 0.00 0 44.0095000 -393510.000
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200.000 1000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 9365.469
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4.943650540D+04-6.264116010D+02 5.301725240D+00 2.503813816D-03-2.127308728D-07
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-7.689988780D-10 2.849677801D-13 -4.528198460D+04-7.048279440D+00
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1000.000 6000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 9365.469
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1.176962419D+05-1.788791477D+03 8.291523190D+00-9.223156780D-05 4.863676880D-09
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-1.891053312D-12 6.330036590D-16 -3.908350590D+04-2.652669281D+01
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6000.000 20000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 9365.469
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-1.544423287D+09 1.016847056D+06-2.561405230D+02 3.369401080D-02-2.181184337D-06
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6.991420840D-11-8.842351500D-16 -8.043214510D+06 2.254177493D+03
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END PRODUCTS
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END REACTANTS
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This file (saved for example as `nasathermo.dat`) can then be converted to the
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CTI format using the `ck2cti` script::
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ck2cti --thermo=nasathermo.dat
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To generate a full phase definition, create an input file defining the phase as
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well, saved for example as `nasa.inp`::
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elements
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C O
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end
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species
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CO CO2
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end
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The two input files can then be converted together by calling::
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ck2cti --input=nasa.inp --thermo=nasathermo.dat
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The Shomate Parameterization
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----------------------------
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@ -240,3 +334,7 @@ written as::
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.. [#Kee1986] R. J. Kee, G. Dixon-Lewis, J. Warnatz, M. E. Coltrin, and J. A. Miller.
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A FORTRAN Computer Code Package for the Evaluation of Gas-Phase, Multicomponent
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Transport Properties. Technical Report SAND86-8246, Sandia National Laboratories, 1986.
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.. [#Mcbride2002] B. J. McBride, M. J. Zehe, S. Gordon. "NASA Glenn Coefficients
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for Calculating Thermodynamic Properties of Individual Species,"
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NASA/TP-2002-211556, Sept. 2002.
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