Approximations for the thermodynamic and transport properties of high-temperature air Page: 3 of 69
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL NOTE 4150
APPROXIMATIONS FOR THE THERMODYNAMIC AND TRANSPORT
PROPERTIES OF HIGH-TEMPERATURE AIR
By C. Frederick Hansen
The thermodynamic and transport properties of high-temperature air
are found in closed form starting from approximate partition functions
for the major components in air and neglecting all minor components.
The compressibility, energy, entropy, the specific heats, the speed of
sound, the coefficients of viscosity and of thermal conductivity, and
the Prandtl numbers for air are tabulated from 5000 to 15,0000 K over a
range of pressure from 0.0001 to 100 atmospheres. The enthalpy of air
and the mol fractions of the major components of air can easily be found
from the tabulated values for compressibility and energy. It is predicted
that the Prandtl number for fully ionized air will become small compared
to unity, the order of 0.01, and this implies that boundary layers in
such flow will be very transparent to heat flux.
It is axiomatic that the science of aerodynamics must be based on
a good understanding of the atmospheric medium through which vehicles
are to fly. Under subsonic flight conditions, air may be treated as an
ideal gas composed of rigid, rotating diatomic molecules. The thermody-
namic properties of such a gas are well known and they are accounted for
in the gas flow equations by the familiar ratio of specific heats, which
in this case is a constant. Under supersonic flight conditions, air may
be raised to temperatures where the molecules can no longer be treated
as simple, rigid rotators. At relatively low supersonic speeds, vibra-
tional energy is excited and then the specific heats become functions of
temperature. However, both the thermodynamic and transport properties
of air in vibrational excitation can be predicted with fair accuracy by
the methods of quantum statistics and kinetic theory (ref. 1), and the
air-flow relations can be modified accordingly. Eggers (ref. 2) has
calculated the effects of vibrational energy on the one-dimensional,
inviscid flow of diatomic gases, for example.
Further changes in air properties may occur at still higher flight
velocity. Flight velocities of practical interest have now increased
from low supersonic speeds to the escape velocity, 37,000 feet per second.
Vehicles which travel at these hypervelocities excite the air to such
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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/m1/3/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.