From 9fdf7c0c590e73ba19d401dd2fa5aa51607a805e Mon Sep 17 00:00:00 2001 From: Ray Speth Date: Tue, 21 Apr 2015 16:05:59 -0400 Subject: [PATCH] [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. --- doc/sphinx/cti/species.rst | 124 +++++++++++++++++++++++++++++++++---- 1 file changed, 111 insertions(+), 13 deletions(-) diff --git a/doc/sphinx/cti/species.rst b/doc/sphinx/cti/species.rst index c16ade6f0..a02b0efe0 100644 --- a/doc/sphinx/cti/species.rst +++ b/doc/sphinx/cti/species.rst @@ -122,18 +122,15 @@ no requirement that all species in a phase use the same parameterization; each species can use the one most appropriate to represent how the heat capacity depends on temperature. -Currently, three entry types are implemented, all of which provide species -properties appropriate for models of ideal gas mixtures, ideal solutions, and -pure compounds. Non-ideal phase models are not yet implemented, but may be in -future releases. When they are, additional entry types may also be added that -provide species-specific coefficients required by specific non-ideal equations -of state. +Currently, several types are implemented which provide species properties +appropriate for models of ideal gas mixtures, ideal solutions, and pure +compounds. -The NASA Polynomial Parameterization ------------------------------------- +The NASA 7-Coefficient Polynomial Parameterization +-------------------------------------------------- -The NASA polynomial parameterization is used to compute the species -reference-state thermodynamic properties :math:`\hat{c}^0_p(T)`, +The NASA 7-coefficient polynomial parameterization is used to compute the +species reference-state thermodynamic properties :math:`\hat{c}^0_p(T)`, :math:`\hat{h}^0(T)` and :math:`\hat{s}^0(T)`. The NASA parameterization represents :math:`\hat{c}^0_p(T)` with a fourth-order @@ -150,9 +147,10 @@ polynomial: \frac{a_4}{4} T^4 + a_6 Note that this is the "old" NASA polynomial form, used in the original NASA -equilibrium program and in Chemkin. It is not compatible with the form used in -the most recent version of the NASA equilibrium program, which uses 9 -coefficients, not 7. +equilibrium program and in Chemkin, which uses 7 coefficients in each of two +temperature regions. It is not compatible with the form used in the most recent +version of the NASA equilibrium program, which uses 9 coefficients for each +temperature region. A NASA parameterization is defined by an embedded :class:`NASA` entry. Very often, two NASA parameterizations are used for two contiguous temperature @@ -170,6 +168,102 @@ ranges. This can be specified by assigning the ``thermo`` field of the -7.579666690E-07, 2.094705550E-10, -2.167177940E-14, -1.088457720E+03, 5.453231290E+00] ) ) ) +The NASA 9-Coefficient Polynomial Parameterization +-------------------------------------------------- + +The NASA 9-coefficient polynomial parameterization [#McBride2002]_ ("NASA9" for +short) is an extension of the NASA 7-coefficient polynomial parameterization +which includes two additional terms in each temperature region, as well as +supporting an arbitrary number of temperature regions. + +The NASA9 parameterization represents the species thermodynamic properties with +the following equations: + +.. math:: + + \frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T + + a_4 T^2 + a_5 T^3 + a_6 T^4 + + \frac{H^0(T)}{RT} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2 + + \frac{a_3}{2} T + \frac{a_4}{3} T^2 + \frac{a_5}{4} T^3 + + \frac{a_6}{5} T^4 + \frac{a_7}{T} + + \frac{s^0(T)}{R} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T + + a_3 T + \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8 + +The following is an example of a species defined using the NASA9 +parameterization in three different temperature regions:: + + species(name=u'CO2', + atoms='C:1 O:2', + thermo=(NASA9([200.00, 1000.00], + [ 4.943650540E+04, -6.264116010E+02, 5.301725240E+00, + 2.503813816E-03, -2.127308728E-07, -7.689988780E-10, + 2.849677801E-13, -4.528198460E+04, -7.048279440E+00]), + NASA9([1000.00, 6000.00], + [ 1.176962419E+05, -1.788791477E+03, 8.291523190E+00, + -9.223156780E-05, 4.863676880E-09, -1.891053312E-12, + 6.330036590E-16, -3.908350590E+04, -2.652669281E+01]), + NASA9([6000.00, 20000.00], + [-1.544423287E+09, 1.016847056E+06, -2.561405230E+02, + 3.369401080E-02, -2.181184337E-06, 6.991420840E-11, + -8.842351500E-16, -8.043214510E+06, 2.254177493E+03])), + note='Gurvich,1991 pt1 p27 pt2 p24. [g 9/99]') + +Thermodynamic data for a range of species can be obtained from the `NASA +ThermoBuild `_ tool. Using the web +interface, an input file can be obtained for a set of species. This input file +should then be modified so that the first line reads "`thermo nasa9`", as in the +following example:: + + thermo nasa9 + 200.000 1000.000 6000.000 20000.000 9/09/04 + CO Gurvich,1979 pt1 p25 pt2 p29. + 3 tpis79 C 1.00O 1.00 0.00 0.00 0.00 0 28.0101000 -110535.196 + 200.000 1000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 8671.104 + 1.489045326D+04-2.922285939D+02 5.724527170D+00-8.176235030D-03 1.456903469D-05 + -1.087746302D-08 3.027941827D-12 -1.303131878D+04-7.859241350D+00 + 1000.000 6000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 8671.104 + 4.619197250D+05-1.944704863D+03 5.916714180D+00-5.664282830D-04 1.398814540D-07 + -1.787680361D-11 9.620935570D-16 -2.466261084D+03-1.387413108D+01 + 6000.000 20000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 8671.104 + 8.868662960D+08-7.500377840D+05 2.495474979D+02-3.956351100D-02 3.297772080D-06 + -1.318409933D-10 1.998937948D-15 5.701421130D+06-2.060704786D+03 + CO2 Gurvich,1991 pt1 p27 pt2 p24. + 3 g 9/99 C 1.00O 2.00 0.00 0.00 0.00 0 44.0095000 -393510.000 + 200.000 1000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 9365.469 + 4.943650540D+04-6.264116010D+02 5.301725240D+00 2.503813816D-03-2.127308728D-07 + -7.689988780D-10 2.849677801D-13 -4.528198460D+04-7.048279440D+00 + 1000.000 6000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 9365.469 + 1.176962419D+05-1.788791477D+03 8.291523190D+00-9.223156780D-05 4.863676880D-09 + -1.891053312D-12 6.330036590D-16 -3.908350590D+04-2.652669281D+01 + 6000.000 20000.0007 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 0.0 9365.469 + -1.544423287D+09 1.016847056D+06-2.561405230D+02 3.369401080D-02-2.181184337D-06 + 6.991420840D-11-8.842351500D-16 -8.043214510D+06 2.254177493D+03 + END PRODUCTS + END REACTANTS + +This file (saved for example as `nasathermo.dat`) can then be converted to the +CTI format using the `ck2cti` script:: + + ck2cti --thermo=nasathermo.dat + +To generate a full phase definition, create an input file defining the phase as +well, saved for example as `nasa.inp`:: + + elements + C O + end + + species + CO CO2 + end + +The two input files can then be converted together by calling:: + + ck2cti --input=nasa.inp --thermo=nasathermo.dat + + The Shomate Parameterization ---------------------------- @@ -240,3 +334,7 @@ written as:: .. [#Kee1986] R. J. Kee, G. Dixon-Lewis, J. Warnatz, M. E. Coltrin, and J. A. Miller. A FORTRAN Computer Code Package for the Evaluation of Gas-Phase, Multicomponent Transport Properties. Technical Report SAND86-8246, Sandia National Laboratories, 1986. + +.. [#Mcbride2002] B. J. McBride, M. J. Zehe, S. Gordon. "NASA Glenn Coefficients + for Calculating Thermodynamic Properties of Individual Species," + NASA/TP-2002-211556, Sept. 2002.