NASA Technical Reports Server (NTRS) 19910015028: Determination of alloy content from plume spectral measurements

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by  NASA Technical Reports Server (NTRS)

NASA Technical Memorandum 104442
AIAA - 91- 2531
Determination of Alloy Content From
Plume Spectral Measurements
George C. Madzsar
Lewis Research Center
Cleveland, Ohio
Prepared for the
27th Joint Propulsion Conference
cosponsored by the AIAA, SAE, ASME, and ASEE
Sacramento, California, June 24-27, 1991
NASA
DETERMINATION OF ALLOY CONTENT FROM PLUME SPECTRAL MEASUREMENTS
George C. Madzsar
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
Abstract W weight percentage
Z(t) partition function
The mathematical derivation for a
method to determine the identities and
Background
amounts of alloys present in a flame
where numerous alloys may be present is
When a single alloy is present in a
described. This method is applicable if
flame, the identity of its elemental con-
the total number of elemental species
stituents, and therefore the alloy
from all alloys that may be in the flame
itself, can readily be determined using
is greater than or equal to the total
spectroscopic techniques. If multiple
number of alloys. Arranging the atomic
alloys are present in the flame, the
spectral line emission equations for the
identification process is again rela-
elemental species as a series of simulta-
tively simple if the alloys are composed
neous equations enables solution for
of different elements. However, many
identity and amount of the alloy present
alloys contain some of the same elemental
in a flame. This technique is intended
species, their differences being various
for identification and quantification of
weight fractions of the elements. If
alloy content in the plume of a rocket
numerous alloys are present in a flame,
engine. Spectroscopic measurements
and these alloys contain some of the same
reveal the atomic species entrained in
elemental constituents, the spectra of
the plume. Identification of eroding
the individual elements are summed, and a
alloys may lead to the identification of
direct determination of identity and
the eroding component.
amount of the alloy cannot be made solely
with spectroscopic techniques.
Nomenclature
The emission spectrum of an alloy is
A transition probability
the sum of the line emissions from its
Av Avogadro's number elemental constituents. Identifying key
spectral lines from the various atomic
energy
species enables identification of the
statistical weight elements. Since the radiance of a spec-
tral line is related to the number of
Planck's constant
atoms in the emitting system, atomic con-
Boltzmann's constant centration can also be determined. If
numerous alloys contain some of the same
MW molecular weight
elements, the atom population for the
radiant power various elements may be due to contribu-
tions of the element from numerous
T temperature
alloys. The resulting spectral radiance
V frequency that is measured from an atomic species
may be due to contributions of the ele- constituents, weight fraction of their
ment from numerous alloys. elemental constituents, spectral charac-
teristics of these elements, and the tem-
Emission spectroscopy of a rocket perature at the location of the emitting
engine exhaust plume is being investigat- system, a series of simultaneous equa-
ed to determine if engine degradation can tions may be developed and solved. The
be monitored from measurements of mate- solution to these equations yields the
rial erosion. 1-4 Knowledge of material amount and identity of the alloy in the
erosion from internal components may pro- flame. Current state of the art in
vide insight into the engine's current rocket engine diagnostics using plume
health and remaining life. In the space spectral measurements enables identifica-
shuttle main engines (SSME), it has been tion and quantification of the atomic
determined that material does in fact species. Application of the technique
erode from internal engine components. presented in this paper to a rocket
Eroded particles are carried along with engine enables identification and quant-
the hydrogen and oxygen propellants into ification of eroding alloys, which pro-
the combustion chamber, where they are vides information that can lead to the
burned (dissociated to atomic species), identification of the eroding engine com-
thermally excited, and emit their charac- ponent. Note that this technique is not
teristic spectrum. Figure 1 displays the specific to rocket engine diagnostics;
propellant flow path within the SSME. it may be used in other applications
Note that the propellants travel through- requiring alloy identification and
out the entire engine, with the ultimate quantification.
destination being the combustion chamber.
Figure 2 displays a typical SSME emission
spectrum. Atomic lines can readily be Theory
identified in this figure. Alloys from
which the SSME is fabricated are listed Radiance from atomic line emissions
in Table 1. This table lists the alloys, is a function of several variables. In
their elemental constituents, and the this paper, the general expression for
weight fraction of these elemental con- line radiance as a function of atomic
stituents. 5 As can be seen from this population densities shall be considered.
table, there are numerous alloys in the It is assumed that the collection of
engine, many of which contain some of the atoms in the emitting system are in ther-
same elements. Table 2 is a list of the mal equilibrium, and that there is a low
SSME components in the propellant flow population density of the emitting atoms.
path and the alloy from which they are It is also assumed that the radiance of
fabricated. Note that the propellants the line is sufficient to enable spectro-
and impurities in the propellants are not scopic measurements. The radiant power
included in the above tables. of an atomic line is given by the equa-
tion:5
This paper presents a technique that
-Ei/kT
enables determination of the identities
Ajihi/jigjne
( I )
and amounts of alloys that are present in
a flame. The mathematical derivation,
and errors associated with this technique
are discussed. Note that the primary where ji represents one of the allowed
purpose of this paper is to document the transitions for an atomic species from an
mathematics describing this technique, upper energy state j to a lower energy
with minimal consideration given to state i and n is the total number of
implementation, calibration, and opera- free atoms in the emitting system.
tion of this capability. Selection of a particular transition
defines the frequency v and therefore
From knowledge of which alloys may the wavelength of the emitted photons.
be present in the flame, their elemental
Numerical values for the transition prob- molecular weight and multiplying by
ability, statistical weight and upper Avogadro's number . Therefore, Eq. (5)
energy state for the selected transition can be rewritten as:
can be found in reference tables. ? The

partition function can either be found in
Na = xaAv w1 + w2 + ... + wQ (6)
reference tables$ or calculated from the mw 11 mw2 mw Q
following equation:
Z(t) = Ej-0 gje-Ej/kT (2)
where Na is the total number of atoms
in the amount x of alloy a. Writing
The solution to Eq. (1) yields the similar equations for m different
radiation at a given wavelength from a alloys yields:
collection of atoms at a particular tem-
perature. Utilizing emission spectro- wll + 12 lP (7-1)
N1 = xlAv + ... +
scopy techniques, this radiance can be mWl mw2
MW
measured. Therefore, at a known tempera-
ture for an allowed transition, Eq. (1)
can be solved for the total number of
free atoms in the emitting system. The
N2 = x2Av w21 + w22 + ... + w2P (7-2)
number of atoms for the various elemental mWl mW2 mWp
species can be used to determine the
amount of the alloy that is present in
the flame. To simplify the writing of
Eq. (1), the following definition will be
made:
/kT
R = Ajihvjigje- Ej (3) N,n xlnAv wm1 + wm2 + ... + wmP (7—m)
mwl mW2 MW
where R represents the radiant power where N through N are the number of
i
from a single atom. Substituting Eq. (3) atoms in alloys 1 A rough m; x
into Eq. (1) yields: through xm are the amounts of alloys 1
through m; mw through mw are the
0 = Rn (4) molecular weig^ts of elemental species 1
through p, and wll through w are
Consider an unknown amount x, of the weight percentages of the e Mmental
alloy a. The alloy consists of Q ele- species in the alloys. Note that the
mental constituents, with the weight number of elemental species in Eqs. (7-1)
fractions of these elements equal to wl, to (7-m) has changed from Q to p.
W2 , w It is assumed that the While Q represents the total number of
exact composition and weight fractions elemental species found in a single
are known. The total weight w of alloy alloy, p represents the total number of
a can be expressed as: different elemental species that can be
found in all alloys 1 through m. With
Wa = xa(W1 + W2 + ... + WQ ) (5) this type of notation, the weight per-
centage of an element in the alloy is set
This equation can be expanded to equal to zero if the particular element
calculate the total number of atoms in is not present in an alloy.
the alloy based on the total number of
atoms of each elemental species by divid- By summing vertically down the col-
ing the weight of an element by its umns of the above equations, the total
3
number of atoms of each elemental species ages of the elemental species in the var-
can be calculated: ious alloys are obtained from metallurgi-
cal handbooks, while the elemental molec-
nl = Avl (XIW11 + X2W21 + + XmWml) (8-1) ular weights and Avogadro's number are
rrlw known. The unknowns are the amounts of
the alloys x throughx Therefore,
examination of Eqs. (9-1) ^o (9-p) indi-
cates that there are p equations with
n2 = A Z (X1W12 + X2W22 + + Xmwm2) (8-2) m unknowns. If p is greater than or
equal to m, a sufficient number of equa-
tions are available to solve for all
unknowns. If m is greater than p, the
equations cannot be solved.
np mAwvP (XlWlP + X2W2p + ... + XmWmP) (8-P) Mathematical Implementation
Assuming that there are a sufficient
number of equations to solve for the
where n through n are the total
unknowns, (the total number of different
number of atoms of the each elemental
elemental species is equal to or greater
species contributed from alloys 1
than the number of alloys) the following
through m. Substituting these values
matrix expression of Eqs. (9-1) to (9-p)
into Eq. (4) and calculating a value for
can be written:
R from Eq. (3) enables radiance calcula-
tions of the p elemental species as a
function of the amount x of the alloy. RlWll RIW21 R1Wmll [X1 01
With this substitution, the following mWl mWl f N2
series of equations can be written:
R2W12 R2W22 R2Wm2 X2 02
R1Av
^l MW (XIWll + X2W21 + ... + XmWml) (9-1) mW2 M2 mW2
(10)
A
R2Av
^2 = 2 ("12 + X2W22 + ... + Xmwm2) (9-2)
MW R1w1pP R1W2PP RIwmP
ffrw MW mWp Xm ^p
The above matrices can be expressed
as [R][X] = [^], where the R matrix
R Av
contains the R1+Pw1} Av/mwli terms, the
0P = P p(XlWlp + X2W2p + ... + XmW (9-p)
m w mP) X matrix contains t4 xl Through x,n
terms, and the 0 matrix contains the
^1 through ^P terms. Values for the
At this point, consideration must be R matrix are derived by simple calcula-
given to the known and unknown variables tions, values for the ^ matrix are
in Eqs. (9-1) to (9-p). The radiant measured spectroscopically from the
power 0 is measured spectroscopically flame, and the X matrix contains the
from the flame, and therefore is known. unknown mass and by definition the iden-
It is assumed that the temperature of the tity of a particular alloy. If the
emitting system is known, resulting in total number of elemental species is
known values for R1 through RP as greater than the number of alloys, (p-m)
defined by Eq. (3). The weight percent- equations can be eliminated. After
4
elimination of the excess equations, the alloy content, and the assumption that
R matrix is square and can be inverted. all constituents of the alloy wear at a
The solution to the X matrix is constant rate. Spectroscopically, the
[X] = [R] -1 [^]. The matrix inversion and assumptions that may lead to error
subsequent matrix multiplication can be include: (1) the temperature is known
performed on a computer. Given that the and uniform throughout the emitting sys-
[R] matrix can be inverted, a solution tem, (2) the radiance can be accurately
will be produced. The accuracy of the measured regardless of the number of
solution is limited by the accuracy of atoms and radiance from the emitting sys-
the values in the [R] and [^] tem, and (3) that exact values for the
matrices. transition probabilities are known. Met-
allurgically, the assumption that the
Examination of Table 1 reveals that exact composition and weight percentages
there are 17 alloys consisting of 20 ele- of the elements in the alloys are known
mental species in the SSME. Therefore, may lead to error. The assumptions that
three elemental species do not need to be the various elemental species in the
spectroscopically monitored for alloy alloy erode evenly and at the same rate
identification and quantification. The is also a potential source of error.
selection of which elements to eliminate Following is a discussion of the various
is based on the relative abundance and errors that may be caused by the
emission intensity of the species. Since assumptions.
zirconium, lanthanum, and nitrogen appear
in trace quantities in a very limited Temperature dependence of the radi-
number of alloys and are relatively weak ance from atomic emissions can be seen in
emitters,9 they should be the species Eq. (1). For the SSME, temperatures in
that are eliminated. the combustion chamber and Mach disk
regions are well established from analyt-
10,11
ical calculations. The assumption
Discussion that the emitting atoms are in thermal
equilibrium is valid since the tempera-
Although the mathematics described tures in the chamber or the Mach disk are
above are relatively straightforward, reasonably uniform. Temperature varia-
implementation of this technique requires tions occur near the walls of the cham-
additional considerations. These consid- ber, and near the edges of the Mach
erations include the errors that are structure. If spectral emissions from
inherently associated with the technique, the center of the combustion chamber or
and the sensitivity, dynamic range, and center of the Mach structure are measured
calibration of the instrumentation used and used in the Eq. (9), thermal equilib-
to measure the emission spectrum. Fol- rium and uniform temperature is assured.
lowing is a discussion of the errors and Note that using a limited field of view
instrumentation issues. While there may introduces the assumption that metallic
be numerous sources of error, the errors species entrained in the plume are homo-
do not appear to be insurmountable indi- geneously mixed within it; and that
vidually or collectively. observation of a known percentage of the
plume accurately reflects the overall
The derivation of this technique is composition of the entire plume. Meas-
based on spectroscopic, metallurgical, urements from a limited field of view
and mathematical considerations. Errors requires that a scaling factor be incor-
associated with the implementation of porated into Eq. (9) to account for the
this technique to the analysis of a rock- hot gases and therefore spectral emis-
et engine exhaust plume are the result of sions that are not being observed.
the limitations and assumptions in spec-
troscopic theory and spectroscopic meas- To gain insight into the temperature
urement techniques, uncertainties in effects with respect to the SSME, the
5
Boltzmann distribution (temperature the transition probability of the speci-
dependent terms in Eq. (1)) were evalu- fic transition that is being monitored.
ated at 3000 and 3149 K for chromium and Low transition probability could lead to
titanium. Numerical values for the error due to the low overall radiance
energy levels, statistical weights, and from the atoms in the emitting system.
partition functions were obtained from The uncertainty associated with the vari-
Refs. 7 and 8 respectively. It was cal- ous transition probabilities may also
culated that for the 5 percent tempera- cause errors. Typically, values for the
ture change, the radiant power increased transition probabilities are listed with
46.0 percent for chromium, and an associated uncertainty band. These
83.6 percent for titanium. As seen from uncertainties range from 1 percent up to
Eq. (1), the temperature term appears in 50 percent for the various transitions as
an exponential, and the significance of seen in Ref. 7. Selection of a transi-
this term depends on the slope of the tion with a low uncertainty will minimize
exponential at the temperature regime of error; however this may be difficult,
the emitting system. For the SSME tem- since not all species have been ade-
perature regime, temperature is critical quately studied to generate high accuracy
for accurate measurements, and a transition probabilities.
5 percent temperature deviation would
yield unusable results for this Sensitivity, signal to noise ratio,
technique. dynamic range, and resolution of the
spectrometer may limit the accuracy of
It is assumed that an adequate num- this technique. The sensitivity and sig-
ber of free atoms of the species being nal to noise ratio dictate the minimum
spectrally monitored are available within radiance level that can be measured. The
the observed region to enable measure- dynamic range limits the maximum radiance
ment. A single or very few emitting level that can be measured, assuming the
atoms of a particular species will not be spectrometer is optimized for low radi-
seen in an environment consisting of many ance levels. Spectrometer resolution
free atoms from numerous species due to must be adequate to separate closely
either the low radiance from the few spaced spectral lines. It was assumed
atoms, poor sensitivity of the detector, that spectral emissions from all elemen-
or low transition probability of the tal species that may be in the plume can
transition that is being monitored. If be measured. This assumption is correct
an extremely large number of atoms of a if the detector is sensitive enough to
particular species are present in the measure potentially low radiance levels.
flame, the flame is optically thick From Table 1 it can be seen that some
rather than optically thin, requiring alloys contain trace amounts of certain
that the self absorption terms be elements. It may be extremely difficult
included in Eq. (1). 6 Therefore, the to measure spectral emissions from these
population of the metallic species must trace amounts unless a large quantity of
be sufficient to provide radiance in the alloy is eroding, or the transition
excess of that of the background chemi- that is being monitored has a large tran-
luminescence from the combustion process, sition probability. Past work has indi-
yet not great enough to cause self cated that large amounts of some elements
absorption. In the SSME, the population must be present in the plume for observa-
of the eroded metallic species from the tion due to low transition probabilities.
alloys is much less than the population The worst case scenario is the low weight
of the oxygen and hydrogen propellants percentage species that has low transi-
(unless_a major failure is occurring). tion probabilities. The lack of sensi-
tivity may be overcome with higher
Error may result from the transition sensitivity detectors, or by using atomic
probabilities and their associated uncer- absorption rather than atomic emission
tainties. Radiance emitted from an spectroscopy.
excited atom is directly proportional to
6
Spectrometer calibration must also of eroding material from internal compo-
be considered since absolute, rather than nents of a rocket engine based on its
relative spectral emissions are being plume spectral emissions. Identification
measured. Calibration must take into of the eroding alloy may lead to identi-
account spectrometer throughput, effi- fication of the eroding component, and
ciency of the detector at all observed quantification of erosion may lead to
wavelengths, and view angle of the plume. determination of the remaining life of a
It may be possible to calibrate the spec- component.
trometer at a few spectral lines using
calibrated lamps and use these measure- Requirements for implementation of
ments as the basis for calibration of the this technique include knowledge of which
spectrometer. alloys may be present in the flame, their
elemental constituents, weight fraction
The assumptions that the composition of the elemental constituents, spectral
of the alloy is known exactly and that characteristics of these elements, tem-
the elemental constituents of the alloy perature at the location of the emitting
are homogeneously mixed may lead to system, and measured radiance values from
error.Typically, the composition of an the atomic emissions in the emitting sys-
alloy is expressed as the nominal, rather tem. Arranging the atomic emission equa-
than exact, weight percentages of its tions for all the elemental species in
elemental constituents. The exact per- the alloys as a series of simultaneous
centages of the elements are not known equations enables solution for the iden-
unless a thorough analysis of the alloy tity and amount of the alloy in the
is made. Also, the alloys may contain flame. To enable a mathematical solu-
trace impurities. If an element is a tion, the total number of elemental spe-
trace impurity in one alloy but a consti- cies from all alloys must be greater than
tuent in another alloy, errors may or equal to the number of alloys that are
result. For critical applications such found in the engine. An appropriate set
as the SSME, it is presumed that the of equations must be generated for the
exact composition of the alloys are temperature of the emitting system, and
known. that if the temperature changes, a new
set of equations must be generated. Note
To enable a mathematical solution, that an "alloy" may consist of a single
the number of elemental species must be element.
greater than or equal to the number of
alloys that are found in the engine. The viability of this technique is
Examination of Table 1 will verify that limited by the inherent errors and
this is the case for the SSME. Note that assumptions that went into its deriva-
an appropriate set of equations must be tion. Although there are numerous
generated for the temperature of the sources of errors, they do not appear to
emitting system. be insurmountable. Critical sources that
may lead to the most significant error
are the uncertainty and likely
Concluding Remarks fluctuation of the temperature in the
emitting region, and the uncertainty
The mathematical derivation of a associated with the transition
technique that enables determination of probabilities.
the identities and amounts of alloys
present in a flame where numerous alloys It is assumed that an adequate num-
may be present has been described. This ber of free atoms of the species being
technique is particularly useful when the spectrally monitored are available within
same elemental species are found in many the observed region to enable measure-
of the different alloys. The intended ment, and that spectral emissions from
application of this technique is to all elemental species that may be in the
enable identification and quantification plume can be measured. The population of
the metallic species must be sufficient 4. Bickford, R.L., Duncan, D.B., and
to provide radiance in excess of that of Madzsar, G.C., "Development of a
the background chemiluminescence from the Fabry-Perot Interferometer for
combustion process, yet not great enough Rocket Engine Plume Monitoring", 2nd
to cause self absorption. The sensitiv- Annual Health Monitoring Conference
ity, signal to noise ratio, dynamic for Space Propulsion Systems, Uni-
range, and resolution of the spectrometer versity of Cincinnati, 1990,
that is measuring the spectral emissions pp. 160-168.
must be adequate for the widths and peak
intensities of the spectral lines being Tejwani, G.D. and Gardner, D.G., Pre-
measured. liminary Report: "Engine Diagnostics
Database Development and DTF Seeding
The composition of the alloys must Experiment Test Matrix", NASA-SSC
be known, and the elemental constituents Report No. TWR J9-A901, July 14,
of the alloy must be homogeneously mixed. 1989.
The assumption that the exact composition
of the alloy is known may lead to error, 6. Ingle, J.D. and Crouch, S.R., Spec-
since alloy composition is typically trochemical Analysis, Prentice Hall,
expressed as the nominal weight percent- Englewood Cliffs, NJ, 1988.
ages of its elemental constituents.
Also, the alloys may contain trace impu- Reader, J., et al., "Wavelengths and
rities. If an element is a trace impuri- Transition Probabilities for Atoms
ty in one alloy but a constituent in and Atomic Ions," NSRDS-NBS-68,
another alloy, errors may result. The National Standard Reference Data
elemental constituents of the alloy must System, National Bureau of Stand-
be homogeneously mixed, or the erosion ards, 1980 (avail. NTIS,
rate of the elementals will not be PB81-206120).
constant.
8. Drawin, H.W. and Felenbok, P., Data
for Plasmas in Local Thermodynamic
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1. Cikanek, H.A., et al., "Space Shuttle
Main Engine Plume Spectral Monitor- 9. Meggers, W.F., et al., Tables of
ing Preliminary Results," AIAA Paper Spectral-Line Intensities, National
87-1792, July 1987. Bureau of Standards Monogram 32 -
Part I, 1961.
2. McCoy, R.C., et al., "Analysis of

UV-Visible Spectral Radiation from 10. Nickerson, G.R. and Dang, L.D.,

SSME Plume," 1987 JANNAF Propulsion "Improved Two-Dimensional Kinetics

Meeting, Vol. 5, D.S. Eggelston and (TDK) Computer Program," NASA

K.L. Strange, eds., CPIA-PUBL-480- CR-170922, 1983.
VOL-5, Chemical Propulsion Informa-

tion Agency, Laurel, MD, 1987, 11. Dash, S.M. and Pergament, H.S., "The

pp. 205-213. JANNAF Standard Plume Flowfield
Model (SPF)," DRSMI/RD-CR-82-9, U.S.

3. Powers, W.T. and Cikanek, H.A., Army Missile Command, Redstone Arse-

"Analysis of UV-VIS Spectral Radia- nal, AL, April 1981. (Avail. NTIS,

tion from SSME Plume", Advanced AD-B064536L).
Earth to Orbit Propulsion Technology
1988, Vol. 2, R.J. Richmond and
S.T. Wu, eds., NASA CP-3012-VOL-2,
1988, pp. 595-611.
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