NASA Polynomials

The calculation of the heat functions [eqns 5 and 6] is not easy from the tabulated values of 0° as a function of T. It is therefore desirable to have an analytical expression available. The NASA representation used in the CHEMKIN computer program is a polynomial of degree 4 in T  

Expressions for the apparent standard enthalpy of formation Afgl (T) and for the Standard entropy Sj (T) can be deduced using equations (2) and (7), which are written in the following form  

The five coefficients a j, a2j. .. are calculated from the tabulated values of Cpjas a function of T. In general, two sets of coefficients are used, one which is valid from 300 to 1000 K, and the other from 1000 to 5000 K. 

The CHEMKIN recording of the NASA polynomials of ethylene is given in the following form  

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MECHMOD A utility program written by Turanyi, T. (Eotvos University, Budapest, Hungary) that manipulates reaction mechanisms to convert rate parameters from one unit to another, to calculate reverse rate parameters from the forward rate constant parameters and thermodynamic data, or to systematically eliminate select species from the mechanism. Thermodynamic data can be printed at the beginning of the mechanism, and the room-temperature heat of formation and entropy data may be modified in the NASA polynomials. MECHMOD requires the usage of either CHEMK1N-TT or CHEMKIN-III software. Details of the software may be obtained at either of two websites http //www.chem.leeds.ac.uk/Combustion/Combustion.html or http //garfield. chem.elte.hu/Combustion/Combustion. html. 

Currently, the most popular way to document a chemical kinetic model is to list the reactions and corresponding rate parameters (typically in a CHEMKIN format (Kee et al., 1989)), and separately to list the molecular parameters including enthalpies and heat capacities (typically in a NASA polynomial format). 

An output file format can be easily converted to the NASA polynomial data format, which is used in other computational packages, using THERM (see section 2.2.4). Scaling factors are optional for vibrational frequencies. 

The modified Arrhenius parameters are determined from regression analysis with application of the principle of least squares. CTST describes the forward rate constant from reactant to the transition state (TS) s a function of the equilibrium between reactant and TS. ThermKin requires thermodynamic properties in the NASA polynomial format, needs to know whether the reaction is uni- or bimolecular, and either a two-parameter fit or a three-parameter fit is desired. Finally, the reaction to be calculated has to be given in the form ... 

The ThermKin code described in chapter 2 is used to determine the elementary reaction rate coefficients and express the rate coefficients in several Arrhenius forms. It utilizes canonical transition state theory to determine the rate parameters. Thermodynamic properties of reactants and transition states are required and can be obtained from either literature sources or computational calculations. ThermKin requires the thermodynamic property to be in the NASA polynomial format. ThermKin determines the forward rate constants, k(T), based on the canonical transition state theory (CTST). 

Relationship (26) is handy when tabulated values are available, and relationship (27) when NASA polynomials are being used ( 1.5). 

Expressions (30) and (34) are particularly handy to use with NASA polynomials ( 1.5). Example 4... 

Formula (48) allows the values of to be calculated at several temperatures between 1000 and 5000 K for example, and the corresponding NASA polynomials to be deduced. 

This computer program calculates the coefficients of the NASA polynomials from thermodynamic data supplied by the user. 

THERMDAT is a base of thermodynamic data of the CHEMKIN system, in the form of NASA polynomials. 

The Gurvich polynomial [19] for the partition function is seldom used in the western part of the world. Various series of negative powers of the temperature were also proposed in the past. However, none of them got the wide acceptance and extensive use of the seven-term NASA polynomials, mainly due to the existence of big free databases of these polynomials. 

The seven-coefficient NASA polynomials can be used to calculate the following functions ... 

How to Change A, HzgsK Without Recalculating NASA Polynomials Sometimes better enthalpies of formation values are available for a substance and the polynomials need to be adapted. This can be done in the polynomial form without changing the remaining of the thermodynamic data of the species, if the other molecular properties of the substance need no update. In this case, we shall refer to Eq. (1.35) for NASA seven-term polynomials. The term that includes the information on the enthalpy of formation is a. To change, write... 

The database is reviewed and available reference literatore values (calculated and measured ones) and own calculation results are provided. Today this database is the biggest collection of ATcT and G3B3 calculated values that were provided for about half of the included species. In addition, the accuracy of the data and the used values are shown in detail to make the calculation results traceable and or correctable, if better data are available (e.g., quantum chemical results such as spectroscopic properties like vibrations and rotational constants, additional data used to calculate the partition functions, and finally the deviations of the fits to obtain NASA polynomial data from the temperature-dependent thermochemical properties). 

A CHEMKIN input file containing the thermochemical data and rate expressions in the NASA polynomial form is included in the CD that accompanies this text. For details of this format, see the CHEMKIN documentation [44,45] and http //www.reactiondesign.com... 

The heat capacity is a quantity that characterizes the ability of a body to store heat as it changes its temperature. It is common to employ NASA polynomials [23] for the temperature dependence on cp for many different species. These polynomials have the following general form ... 

In combustion systems, thermodynamic properties are often calculated from 14 fitted polynomial coefficients called the NASA polynomials for each species (Burcat 1984). Seven are used for the low-temperature range Tiow to and seven... 

As well as rate coefficient information, thermodynamic data are required for the description of many chemical systems. A number of software packages are available to calculate thermodynamic data such as THERM (Ritter and Bozzelli 1991) or THERGAS (Muller et al. 1995). NASA polynomials are often used as a starting point for the calculation of thermod3niamic properties (see Sect. 2.2.3) and have been made available for many years via the data base of Alexander Burcat (Burcat 1984 Burcat and Ruscic 2005 Burcat) as well as in recent evaluations (Ruscic et al. 2003). 

In the study, the reactions were treated as reversible, with reverse rates calculated from the appropriate equilibrium constants based on enthalpies of formatiOTi calculated using NASA polynomials (see Sect. 2.2.3). Because so many of the input parameters were estimated, derived from a low number of measurements or from single theoretical studies, the input distributions were cmisidered to be uniform between predefined minimum and maximum values (Tomlin 2006). Uncertainties in the rate coefficients were expressed using A-factors only, since for most reactions, there was insufficient information to determine the joint of the Arrhenius parameters. 

The NASA polynomials are usually fitted in the temperature range 300 to 5000 K. The reason for choosing this range is practical. Combustion calculations require thermodynamic and thermochemical properties between room temperature and 3000 or (for special fuels or detonations) 4000 K. In the course of automatic calculations, as well as in some exotic conditions such as spaceship reentry, knowledge of properties to 6000 K is required. Thus, the polynomials discussed here follow the bulk of existing tables (such as JANAF and TSIV as discussed later) by being fit in the range 300-5000 K. Extrapolation to 6000 K is easily done with little error. Extrapolation below 300 K, seldom needed in combustion research, is less accurate. In some cases the polynomials were fit up to 3000 K only. 

First, the literature should be searched for spectroscopic data, and if these are sufficient, the thermodynamic properties can be calculated by statistical mechanics formulas. McBride and Gordon s program (1967) is recommended for this purpose. The latest verson, PAC3, includes, among many possible calculation methods, an accurate calculation method for internal rotation contributions, which are important when organic species are involved, and a subroutine which automatically calculates the coefficients of the NASA polynomials. Wilhoit s extrapolation method was recently included in the code. 

PRINT OUT THE NASA POLYNOMIAL COEFFICIENTS AGAIN IN A COUPLE OF USEFUL FORMATS. YOU WILL NEED THESE FORMATS TO CONSTRUCT NASA-TYPE DATA CARDS HOLDING TWO SETS OF COEFFICIENTS, I.E. ONE SET FOR 300 TO 1000 K AND ONE SET FOR ABOVE 1000 K. 

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