A.4.2.2.5 Chemical Equilibrium with Applications Code
1
A.4.2.2.5.1 Chemical Equilibrium with Applications Code
The NASA Chemical Equilibrium with Applications (CEA) code is widely used by
students and in industry to calculate the thermochemical properties of a combustion
process.1 In our case, we used the CEA code to calculate engine performance parameters
for our launch vehicle.
In our case, CEA was run to calculate specific impulse, c*, exit pressure, exit Mach
number, exit speed of sound, and coefficient of thrust. All performance information can
is used to calculate thrust, mass of propellant, and mass flow rate. CEA requires some
inputs by the user as listed; chamber pressure, area ratio, propellant, oxidizer to fuel ratio,
and temperature of propellants entering combustion chamber. In order for us to work the
code, we use historical data to find a reasonable chamber pressure, area ratio, and
temperature of propellants entering the combustion chamber.
Chamber pressure is the first calculated because area ratio calculations are dependent on
knowing the chamber pressure. We know we are using a pressure fed system requiring a
chamber pressure between one and three megapascals for liquid propellant systems.2
Due to our need to minimize inert mass, we decided to choose chamber pressures not
exceeding 2.5 megapascals.
Solid propellant systems are known to have chamber
pressures of around five to eight megapascals.2 For the purposes of minimizing mass, we
chose six megapascals. Designers generally choose chamber pressures as we did, by
using historical data and guessing what would work best for their design. While not a
very efficient method, there is no way to predict the ideal chamber pressure until more is
known about the engine performance and weight.
Calculation requires an iterative
process between propulsion, structures, and trajectory.
Now that chamber pressure is known, area ratio may be found. In vacuum conditions, the
ideal engine would have an infinitely expanding nozzle.2 However, that is not possible
and so we must balance the mass of the nozzle with the performance. The nozzle must be
Author: Nicole Wilcox
A.4.2.2.5 Chemical Equilibrium with Applications Code
2
expanded enough to minimize detriment caused by the nozzle weight. For vacuum
conditions, area ratio was chosen as 60.
During ground launch, area ratio must be found so that separation is prevented.
Separation causes a loss in engine performance by significantly reducing the area ratio
and pressure thrust. By using the Kalt-Bendall equation, we can find the separation
pressure.
Psep
 P 
 0.667 Pamb  c 
 Pamb 
0.2
(A.4.2.2.5.1)
where Pc is the chamber pressure, Pamb is the ambient pressure, and Psep is the separation pressure.
In order to find an area ratio that is applicable, exit pressure of the nozzle selected must
be greater than the separation pressure calculated. In our case, ambient pressure will be
atmospheric pressure at sea level. In our case, we find the following first stage area and
pressure ratios:
Table A.4.2.2.5 First Stage Area and Pressure Ratios
Propellant
LOX / LH2
H2O2 / RP-1
H2O2 / HTPB
AP / HTPB / Al
Aexit/Athroat
6.497
8.244
8.150
20.00
Pc/Pexit
54.54
63.64
54.12
200.6
Footnotes:
The above area ratios were used only in first stage ground launch. For aircraft and
balloon it was assumed that the launch vehicle was already high enough to prevent
separation.
Lastly, the CEA code needs the temperature in which the propellants enter the
combustion chamber. For all but cryogenic fuels, the temperature was assumed ambient
temperature (298.15 K). Cryogenic fuels are kept much cooler and therefore, the boiling
temperatures of the cryogenic fuels were used. In our case, liquid oxygen enters the
Author: Nicole Wilcox
A.4.2.2.5 Chemical Equilibrium with Applications Code
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chamber at 20.27 K and liquid hydrogen at 90.20 K.3 These boiling points are imbedded
in the CEA code and did not need a separate source.
All other information that would have been needed had we written a code ourselves,
heats of formation, gibbs free energy, etc. are found in the CEA code. The built in
parameters and functions make the code very convenient and relevant to our engine
computations. Also, the code has the option of calculating performance parameters based
on frozen or equilibrium flow. During frozen flow, the constituent products are assumed
to remain in that form throughout the nozzle.3 During equilibrium flow, the constituent
products are assumed reform during all possible recombination reactions.3 Neither of
these methods allows for an accurate measure of engine performance parameters, but a
mean value is usually used. Therefore, we used the CEA code twice and calculated all
engine performance parameters with both methods.
The CEA code proves useful as a tool for us and industry. If CEA were not available to
us our engine performance parameters would have been based off frozen flow. The
frozen flow assumption would make our launch vehicle heavier and more costly due to
lower performance of the fuels we are using.
References
1
Chao, M., “NASA Chemical Equilibrium with Applications,” Marshall Space Flight Center, Alabama,
February, 2008. [www.grc.nasa.gov/WWW/CEAWeb. Accessed 1-25-08.]
2
Humble, R. W., Henry, G. N., Larson, W. J., Space Propulsion Analysis and Design, McGraw-Hill, New
York, NY, 1995.
3
Heister, Stephen D., AAE 539 class., Purdue University, West Lafayette, IN, 1/14/08.
Author: Nicole Wilcox