Approximations for the thermodynamic and transport properties of high-temperature air Page: 4 of 69
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NACA TN 4150
high temperatures that the molecules not only vibrate but may dissociate
into atoms and even ionize. Under these conditions, the behavior of air
deviates widely from that of an ideal gas and the thermodynamic and trans-
port properties all become functions of pressure as well as of tempera-
ture. It is, of course, essential to evaluate these functions in order
to calculate the pattern of air flow about high-speed vehicles, the vis-
cous and pressure forces which result, and the heat flux which occurs
between the air and the vehicle.
The equilibrium thermodynamic properties of a gas can be calculated
with great confidence, provided the energy levels of the gas particles
and the degeneracy of these levels are known. For monatomic and diatomic
gases this information can generally be deduced from spectroscopic data
with such accuracy that the calculated thermodynamic properties can be
trusted to very high temperatures, even where experimental confirmation
is lacking. In the case of air, however, one of the important energy
terms was not known with confidence until recently, namely, the dissocia-
tion energy of molecular nitrogen. This uncertainty arose because the
available spectroscopic data were consistent with two different models
for nitrogen dissociation, one leading to a dissociation energy of 7.37
electron volts per molecule and the other to 9.76 electron volts per
molecule. At first, the lower value was widely accepted as the most
probable one (Herzberg, ref. 3). Krieger and White (ref. 4) and
Hirschfelder and Curtiss (ref. 5) have published tables of thermodynamic
properties of high-temperature air based on this value. Gaydon (ref. 6)
was perhaps one of the first advocates of the view that the higher value
was the correct one. Subsequently a number of experiments were performed
which confirmed Gaydon's opinion, among them the measurements of strong
shock waves in nitrogen made by Christian, Duff, and Yarger (ref. 7) and
the detonation studies made by Kistiakowsky, Knight, and Malin (ref. 8).
This rendered the work of references 4 and 5 obsolete, but shortly there-
after Gilmore (ref. 9) computed the chemical composition, energy, entropy,
compressibility, and pressure of air as functions of temperature and den-
sity based on the higher value for the dissociation of nitrogen. Later,
Hilsenrath and Beckett (ref. 10) published a similar table of these prop-
erties, but in much smaller increments of temperature and density. The
calculations in both of these references (9 and 10) are highly refined
in the sense that they not only account for the major components of air
and their most significant energy states, but they also take into account
a large number of the higher energy states which are infrequently excited,
even at high temperatures, and most of the very minor chemical components
of air are included. Therefore these works are among the most detailed
estimates for the thermodynamic properties of air which have been made.
Also it is not likely that these works will become obsolete, since the
values of all the important energy levels used in these calculations are
now quite secure. However, it is desirable to have approximate expres-
sions for these properties in closed form which can be solved without
iteration. Such solutions would be particularly valuable, for example,
in preparing tables to be used with the method of characteristics for
calculating the flow of real air.
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Hansen, C. Frederick. Approximations for the thermodynamic and transport properties of high-temperature air, report, March 1958; (digital.library.unt.edu/ark:/67531/metadc56742/m1/4/: accessed January 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.