selection of spectral lines for combustion diagnostics

Selection of spectral lines for combustion diagnostics

Xiang Ouyang and Philip L. Varghese

This paper reports part of our effort to develop practical systematic techniques for measurements in hightemperature gases using laser absorption spectroscopy. We present a brief summary of the analysis tech-niques we have developed for line-of-sight measurements. We show that the accuracy of the absorptionmeasurement in a given experiment is largely determined by the spectral lines used for the measurement.Thus the selection of spectral lines is critical for the success of a diagnostic measurement. In this paper, wepropose a set of criteria for selecting spectral transitions for temperature and concentration measurements atvarious experimental conditions. They include the requirements for spectral line resolution, absorptionstrength, sensitivity, and insensitivity to systematic errors. These rules could be implemented in an expertsystem. A simplified version of the selection criteria was implemented in a PASCAL program. The capabili-ties of the program are demonstrated by the selection of absorption transitions of CO for simultaneoustemperature and species concentration measurements at several experimental conditions. The criteria andprogram may be readily extended to other spectroscopic techniques such as laser-induced fluorescence.

1. Introduction

With the advancement of laser technology, lasersources are becoming more compact and affordable.Because it is simple and easy to use, laser absorptionspectroscopy is attractive in many remote sensing ap-plications, especially for combustion measurements.In previous publications,1-3 we described techniquesfor the analysis of line-of-sight experimental data. Inthis paper, the optimal selection of spectral lines for anabsorption measurement is discussed.

A laser absorption measurement includes threesteps:

(1) Select a proper laser operating frequency rangein which there exists one or more spectral lines whichmeet prescribed criteria.

(2) Record the transmissivity in some frequencyrange and fit the data to the mathematical model4'5:

-lnr(v) = n 10W = A aV( -vYij)Li)..

coefficient defined by a = Spx, where S is the integrat-ed intensity and px is the partial pressure of an ab-sorbing species. We have denoted the line shapefunction by V for the Voigt function. This function isgenerally adequate for calculating the integrated in-tensity at atmospheric pressure and combustion tem-peratures.4 More complex line shape functions areneeded if the details of the line shape are to be de-scribed accurately.6 7 Only the integrated absorptionis needed for the analysis presented here, so the Voigtline shape is used. The parameter Yij is related to thenormalized collision width -yij (HWHM) by Yij =2yijpo/B, where po is the total pressure of the gas. Ifthere is a possible base line shift in the experimentaldata, a shift parameter A is introduced and the curve-fit model is written as

r(V) = (v) =exp[-A E aijv( B LJ +, . (lb)(la)

where i and j are indices for absorption line and spe-cies, respectively. Constants A and B are related toeach other by A = L/(BC/). Equation (la) is valid forany constant B. The absorption path length of thelaser beam is L, and a is the integrated absorption

Both authors are with University of Texas at Austin, Austin,Texas 78712; X. Ouyang is in the Department of Mechanical Engi-neering and P. L. Varghese is in the Department of AerospaceEngineering & Engineering Mechanics.

Received 22 March 1990.0003-6935/90/334884-07$02.00/0.

© 1990 Optical Society of America.

Reliable and efficient programs have been developedfor the two models.1 245 It should be noted that thefrequency in the models is scaled by a constant Brather than the conventional l/e Doppler halfwidth.Proper choice of B is crucial for the success of a curvefit of the experimental data, especially for data withmultiple overlapping lines. Optimizing constant Bcan minimize the residual error of the curve fit for agiven set of experimental data. The fit programs wedeveloped have a built-in feature for optimizing B.

(3) The temperature of a quasiuniform gas is ex-tracted from the ratio of the integrated absorptioncoefficients of two lines of the same species:

a SM(T)=9S9 T F(T) (2a)

4884 APPLIED OPTICS / Vol. 29, No. 33 / 20 November 1990

with

,Vll~exp (h-vo2Q(T) T hcEms i 1 1-ex kT)

S(T=S(To) Q(T) -,,ex " _ _ hcvQ(TO) TO k To T - exP(_ kT 0o)

(3)

where S is the integrated line intensity, which is afunction of temperature T of the sample gas, To is areference temperature, Q is the internal partition func-tion, E" is the energy of the lower level of the absorp-tion transition, v is the transition frequency, h isPlanck's constant, c is the velocity of light, and k isBoltzmann's constant. (Energies and frequencies areassumed to be expressed in cm-'.) The ratio of thesums of two groups (I and II) of lines of the samespecies may be used:

t, = I -, = F(T). (2b)Za,' ZSP'(T)

The absolute pressure of the absorbing species maybe calculated from

ai , (4a)

or, using a group of lines of the same species,

a Ei (4b)

The success of a particular measurement is closelyrelated to the spectral line or lines chosen.3 The prop-er choice of lines results in a more accurate determina-tion of the desired physical parameters and less ma-nipulation of the experimental data. A practicalmethod for implementing these criteria is proposed.The line selection process is demonstrated by the dis-cussion of a computer program and the selection of COabsorption line for high temperature gas diagnostics.

This work deals with direct absorption measure-ments, which is suitable for relatively strong absorp-tions. It can be used to monitor major combustionspecies such as C02, CO, and H20. For weak absorp-tions (<2% typically), modulation spectroscopy mustbe employed. The current data reduction proceduremay be extended to the modulation technique. Abrief discussion of this proposed work was given in Ref.4.

II. Selection Criteria

The general requirements for selecting spectral linesin an absorption measurement are listed below.

A. Resolution Requirement

In a high temperature measurement the spectral lineor group of lines of interest may not be free frominterference from other lines. Whether a line or linegroup can be reasonably well resolved in a fit proceduredepends on the experimental conditions, the relativeintegrated intensities of the spectral lines in the re-corded spectrum, the SNR, the number of experimen-tal data points, and the separation distance between

spectral lines.1 Temperature and concentration mea-surements described are only based on the absorptioncoefficients extracted from the fitting procedure.Thus resolution of the details of the spectral line shapeis not as important here, and the requirements forresolving the line shape discussed in Ref. 1 may berelaxed. The two primary parameters affecting theresolution are the separation distance of line centersbetween spectral lines (or centers of line groups) andthe linewidth of these lines (or groups). The resolu-tion criterion for a particular group may be expressedas

1Io - P'l < c(r + r), (5)

where vo is the line center position of the candidategroup, v0 is the line center position of the closest adja-cent group, r and r' are linewidths of the candidateand adjacent groups, respectively, and C is a scalingconstant. The effect of other parameters (relativeintegrated intensity, SNR, etc.) on resolution can beconsidered when choosing C. For generality, no for-mal definition of the linewidth is given here, and Cdepends on the definition of r as well as other variableslisted above. The linewidth P may be defined as thefull linewidth at half-magnitude for an isolated line.In this case, a line is considered reasonably resolvedwhen C is around unity.'

B. Absorption Strength Requirement

The absorption strength for a particular measure-ment may be represented by the maximum absorptioncoefficient defined by

Amax = ( ) o )mIx)IO ma.

If Amax is too close to unity the laser beam entering thesample gas is totally absorbed by the gas. If Amax is tooclose to zero the SNR is small. The requirement forthe absorption strength may be expressed as

Al < Amax < A2,

where 0 < Al < A2 < 1. The choice of Al and A2

depends on the experimental conditions, the noise lev-el of the experimental data, and the requirements forthe precision of the measurement. Typical limits forthe selection process are Al 0.1 and A2 0.95. Foran isolated line the above equation can be written as

SLp~-lnA9 < x <-lnA,

-yp0

(6)

where y is the normalized linewidth, px is the partialpressure of the absorbing species, and po is the totalpressure.

If the absorption is too weak for isolated lines, onemay consider using multiple overlapping lines. Theuse of multiple lines may provide a larger SNR, al-though the curve fit process is a little more complicat-ed. As discussed in Ref. 1, the overlapping of spectrallines presents no difficulty in experimental data analy-sis as long as the line group of interest is adequatelyresolved.

20 November 1990 / Vol. 29, No. 33 / APPLIED OPTICS 4885

C. Sensitivity Requirement

The sensitivity of temperature measurement XT canbe defined as the normalized partial derivative of thefunction F of Eq. (2) with respect to temperature:

TOEXT = (7)

If XT > 1, the uncertainty in the temperature deducedfrom Eq. (2) will be less than the uncertainty in theratio of the absorption coefficients F; the converse istrue if XT < 1. The uncertainty in F is determinedprimarily by the degree of resolution of the spectrallines in the ratio. High sensitivity helps to reduce theerror of a measurement. Thus the temperature sensi-tivity requirement can be expressed as

XT > Xmin (8)

For the two-line case, a simple expression can be de-rived using Eqs. (2a) and (3):

hc(E; - E;)XT= kT(9)

Note that vol v02 was assumed in deriving Eq. (9). Itis clear from this equation that the larger the differ-ence in the energy of the lower states of the two transi-tions, the higher the sensitivity. For a given pair oflines, the sensitivity decreases monotonically as thetemperature increases.

The sensitivity of concentration measurement Xpmay be defined as the normalized derivative of theintegrated absorption coefficient with respect to par-tial pressure Px For the single line case

Px o a'P a a 1 (10)

For the multiple line case

XP p a mi1

Because a is linearly dependent on p the concentrationsensitivity is always unity. The uncertainty of p. in anabsorption measurement equals that of a or a in themeasurement.

D. Insensitivity to Systematic Error Requirement

In a line-of-sight measurement, the basic assump-tion is that the gas condition along the absorption pathis uniform. In a real experiment, absolutely uniformconditions are rarely obtained, especially in combus-tion applications. Whether a given sample gas can beregarded uniform depends on the physical parameterbeing measured and the absorption line used in theexperiment. Because of the linear dependence of inte-grated absorption on pressure, fluctuations in pressureor concentration are simply averaged out in the line-of-sight measurement and do not cause systematic errors.However, variations in temperature do cause system-atic errors in both concentration and temperaturemeasurements because of the nonlinear dependence ofthe integrated absorption on temperature. Thus the

discussion below focuses on the errors arising fromtemperature variations.

Two kinds of nonuniformity are commonly seen inhigh temperature measurements: (1) thermal or con-centration boundary layers at the ends of the absorp-tion path; (2) temperature fluctuations of the samplegas along the absorption path. For a good candidateabsorption line or lines, the physical parameter beingmeasured should not be very sensitive to the nonuni-formities. The two kinds of nonuniformity are dis-cussed separately. The energy-temperature curveand the effective absorption length concept are used toassist the analysis.3

(1) Boundary layer case. If one assumes a uniformcore region with boundary layers, the temperature dif-ference between the inferred temperature and the realcore temperature T = - T is given by

6T = T l al _ 6C2IaF a2\ 62 / (12)

where a = ai - , and the prime denotes the experi-mentally measured values.

Using the effective absorption length,L

fJ Sjp.dt

effi (SiPx)core'

the local absorption coefficient a at the core conditionand experimentally deduced a' can be related by

Leffiai = - a1.

Substituting this relationship into Eq. (12),OT a, Leff - LeM

aF 2 L

(13)

(14)

Without losing generality one can assume El < E;.Then for cool thermal boundary layers, Leffm - Leff2 > 0and aT/F < 0 for all combinations of El and E2.8Thus T is always less than zero, or the two-line tech-nique tends to underestimate the core temperature.The measurement error can be reduced by selectinglines with approximately the same effective absorptionlength at the experimental conditions. If the energiesof the lower states of both transitions are well abovethe E(7) curve at the estimated core temperature,absorption in the boundary layers will be negligible.3The effective absorption lengths of both lines are ap-proximately equal to the length of the core region.Thus accurate measurement of temperature can beobtained if the boundary layers are not too large.

For concentration measurements, the error causedby the boundary can be expressed as

6Px = a Leff L

Px a L(15)

It is clear that if one can choose an absorption transi-tion so that Leff L, the error caused by boundarylayers may be neglected. Since px may be a function ofposition, it is very difficult to determine the effectiveabsorption length in general. Additionally, if the ab-


sorption in the boundary layers is significant, the rela-tively simple fitting procedure which works for homo-geneous experimental conditions may fail. Both theseproblems are resolved if the E" of the candidate line iswell above the E(T) curve. In this case there is rela-tively weak absorption in the cooler boundary layers sothat the effective absorption length method may beused to account approximately for them even if theabsorber concentration is somewhat different from thevalue in the core flow. In many cases, the absorptionin the boundary layers may be neglected, and the effec-tive absorption length is approximately equal to thelength of the core region. Additionally, the fittingprocedure for the uniform temperature case can beused because the line shape is not distorted significant-ly. Thus absorption transitions with high lower stateenergy E should be chosen for either temperature orconcentration measurements in systems with coolthermal boundary layers. This simplifies the datareduction and provides more accurate measurements.

(2) Temperature fluctuation case. In this case, weassume that there are no boundary layers and only thetemperature fluctuates along the absorption path. IfT is the average temperature of the sample gas alongthe absorption path and a is the absorption coefficientat T, the errors in the inferred temperature and con-centration may be estimated from Eqs. (12) and (13),respectively. If E; > El then

Leffl- Leff > 0 and < 0.

Conversely, if E; < El,

Leffl - LeIl < 0 and T > 0.

Thus T is always less than zero, or the absorptionmeasurement will consistently underestimate the av-erage temperature of the sample gas. The greater thedifference in energy of the lower energy states of theline pair, the greater the error in the measured tem-perature.

If AE- E- E(T) > 0, the absorption measure-ment will underestimate the average concentration.The converse is true if AE" < 0. The error is mini-mized if E" is near the E(T) curve at the estimatedaverage temperature. This conflicts with the tem-perature sensitivity requirement as might be expected.(If there are both large temperature fluctuations andsignificant boundary layers in the gas, a line-of-sightmeasurement is probably inappropriate anyway.) Itshould be noted that for the same iAE,"I, the choice ofE" so that AE" > 0 is better because the absorptiondeviation from the average temperature case is lesswhen E" is above the E(T) curve.3

In summary, there are three important parametersin selecting candidate absorption lines. One is thestrength of the absorption lines at the estimated tem-perature, which determines the SNR achievable. Thesecond is the frequency separation of each selected lineor line group from adjacent lines or line groups, whichdetermines the resolution of the line or line group.Finally, the energies of the lower level of the transi-

tions must be considered. They determine the sensi-tivity of the measurement and the robustness of themeasurement to systematic error caused by the non-uniformity of the sample gas. The task of selecting alaser operating frequency is to select a frequency rangein which some of the absorption lines or groups of lineshave proper S, E", and separation from adjacent linesto meet the four selection criteria. Generally speak-ing, once the operation frequency is determined for agiven case, there is a limit on the maximum precisionachievable, and the limit can be predicted by the SNRof the data, the resolution of the absorption lines, andthe sensitivity of the absorption data to the desiredquantities.

Ill. Example: Selection of CO Absorption Lines forSimultaneous Temperature and ConcentrationMeasurements

We developed a PASCAL program to handle the sim-plest situation: selecting adjacent spectral lines fortwo-line temperature measurement and single line forconcentration measurement. A more detailed de-scription of the program is provided in Ref. 4.

The computer program was used to select CO linesfor temperature and concentration measurements us-ing a tunable diode laser system. The search of ab-sorption lines was performed in the 2000-2200-cm'1frequency range. In this frequency range, there arestrong vibration-rotational absorption lines, and theinterference from other major combustion species(CO2,H 2 0) is weak. The required CO spectral data forthe program were calculated from a separate computerprogram based on the work of Varghese.9 The E(T)curve of CO was given in a previous publication. 3 Theselection of spectral lines for concentration measure-ments of CO is relatively simple since at a given condi-tion many lines can be found satisfying the selectioncriteria. In the rest of this section, selection of linepairs for simultaneous temperature and concentrationmeasurements is discussed.

The selection criteria for line pairs for simultaneoustemperature and concentration measurement aremore strict. To meet the sensitivity criterion, thedifference in lower state energies of the two transitionsmust be greater than a certain value at a given tem-perature. In particular, the lines must correspond todifferent vibrational bands since the energy differencefor two adjacent rotational lines of the same band isquite small. In addition to the four criteria described,the separation between the lines must be small enoughto be scanned with a single sweep of the laser. Typi-cally, the maximum frequency range that the tunablediode laser can be scanned continuously is 0.3-0.5cm-'. This restriction was applied to the searchingprocess by adding two additional restrictions to a can-didate line pair. First, the candidate line pair had tobe relatively isolated from other absorption lines. Theseparation between either line of the candidate pairwith other lines was required to be at least twice thesum of the linewidths of the two lines. Additionally,the separation of the line centers of the line pair had to


Table 1. Summary of Criteria for Selection of CO Spectral Line Pairs forSimultaneous Temperature and Concentration Measurement with Cool

Boundary Layers

Resolution requirement: a b C3 > (02 - sa1 > Cl (l + r2 ).

01 -cOO >C2 (r +r2)

and 03 - e02 > C2 (r1 + 2),

where Ci and C2 are dimensionless constants; C1 = 1.2,

C2 = 2, and C3 = 0.15 cn-.

Absorption strength requirements -In A2 < SLp < -In Ai,YPO

with A1 = 0.2, A2 = 0.95

Sensitivity requirement XT | EkT > 1.0

Insensitivity to systematic E'1 > E(T) and E2 > EM; EM is read from the curve

ereor requirement: for CO (see Ref. 3) at the estimated temperature of the

sample gas

a. Subscripts are used to denote absorption lines. Line I and Line 2 are candidate line pairs, Line

0 and Line 3 the adjacent lines. Assume sa0<t0I<u2<mo3.

b. r is defined as the full linewidth at half magnitude.

Table II. Candidate CO Line Pairs for Temperature Measurements

Case Exp. E,, Line pair El' E2'

Conditions [cm-t] ID (v3') 1 (v".J")2 t [Ccm']' o)2 (cm-]' [cm-] [cn-

1] XT

A T-2000 K 3000 Al 2, P20 3, P14 2008.421 2008.552 6233.3 7824.5 1.2

p,=0.l atm A2 2, P19 3, P13 2012.834 2012.734 6058.0 7772.2 1.2

L=lOcm A3 1, P4 2, R2 2101.491 2101.342 3263.0 5353.0 1.5

p0=l atm A4 1, P3 2, R3 2105.257 2105.125 3247.7 5364.3 1.5

A5 1, R7 2, R15 2145.999 2145.912 3331.5 5794.3 1.5

A6 2, R21 3, R31 2164.312 2164.432 6212.4 9281.1 2.2

B T=1500 K 2400 I1 1, P4 2, R2 2101.491 2101.342 3263.0 5353.0 2.0

px=0.1 atm. B2 1, P3 2, R3 2105.257 2105.125 3247.7 5364.3 2.0

L-10cm

Pbo I atml

C T=1000 K 1500 Cl 1, P3 2, R3 2105.256 2105.125 3247.7 5364.3 3.0

p5 =O.l atm C2 1, P2 2, R4 2109.136 2108.724 3236.3 5379.4 3.1

-30 cm

p. 5 1 atm

The subroutine COBSL written by Varghese9 was modified to calculate these data.

be <0.15 cm-'. The selection criteria used to selectCO lines are summarized in Table I.

Table II gives the results of three sample runs of theprogram. For each case, the expected experimentalconditions are listed in the second column. A thermalboundary layer is assumed in all three cases. Thus therequired minimum lower state energy is chosen ap-proximately equal to the E(T) value at the estimatedtemperature. (If no thermal boundary layer were ex-pected, the required minimum E" would have beenzero.) For every selected candidate line pair, the tran-sition frequencies, the energy of the lower states of thetransitions, and the sensitivity at the estimated coretemperature are also listed in Table II.

The experimental conditions assumed in case A aresimilar to those of Hanson and Falcone,10 who mea-sured the temperature of the postflame gases of a flat-flame burner. In their experiments, significantboundary layers existed. They measured the tem-perature of the postflame gas using the absorption linepairs A3 (v:2 - 1, P4 and v:3 - 2, R2) and A4 (v:2- 1,P3 and v:3 - 2, R3). Their experimental results areconsistent with our calculations. However, line pairA6 is even more insensitive to the thermal boundarylayers because the transitions have higher lower stateenergies and temperature sensitivity. It should benoted that many of the candidate line pairs suggestedby Hanson and Falcone only meet some of the selectioncriteria and thus are not suitable for flame tempera-ture measurement.

The significance for selecting optimum spectrallines can be demonstrated by simulated temperatureand concentration absorption measurements of twoCO line pairs:

line pair I: (4 3, R31) and (3 - 2, R21), one ofthe candidate line pairs (A6) chosen bythe line selection program;

line pair II: (2 - 1, R2) and (1 - 0, P4), one of theline pairs recommended by Hansonand Falcone. 1 0

In the simulation, the partial pressure of CO alongthe absorption path was assumed to be 0.1 atm (con-stant) in postflame gases at atmospheric pressure. Atrapezoidal temperature profile was assumed:

o < < 1 cm T[K] = 500 + 1500f;

1 < < 9 cm TK] = 2000;

9 < < 10 cm T[K] = 2000-1500(Q - 9).

Figures 1(a) and (b) show the transmissivity thatwould be recorded for the two line pairs in a line-of-sight absorption measurement. The correspondingspatially integrated line shapes (see below) calculatedfor this temperature profile are shown in Fig. 2. Thetransmissivity and integrated line shape that would berecorded for uniform temperature are also shown inthe figures for comparison. If one ignores the bound-ary layers when analyzing the data, one has the follow-ing comparisons for the two line pairs.

A. Spatially Integrated Line Shape3

The spatially integrated line shape is defined byIL

SpX0O(v)dt

N() = °LfJ Sp,,dt

When conditions are uniform along the line of sight,q1(v) = (v). If not, the line shape is distorted. Theline shapes are not distorted very much for either linein pair I [Fig. 2(a)]. Because distortion is negligiblethe standardized line shape profiles and the fittingprocedure for the uniform temperature case may beused for analysis of the experimental data. The inte-grated line shapes are distorted considerably for pair II


(16)

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Relative Frequency (cm')

C0

.

.0--o

E0z

0.8 0.9

(b)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Relative Frequency (cm-')

Fig. 1. (a) Simulation of CO absorption of line pair (3-2, R21) and

(4 - 3, R31) in the postflame gases of a flat-flame burner: po = 1

atm and Pco = 0.1 atm. (b) Simulation of CO absorption of line pair(1 f- 0, P4) and (2 - 1, R2) in the postflame gases of a flat-flame

burner: po = 1 atm and Pco = 0.1 atm.

[Fig. 2(b)], and the relatively simple fit procedure isnot suitable for the experimental data analysis.3

B. Temperature Measurement by the Two-LineTechnique

When the integrated absorption coefficients a' areused to determine the core temperature, the calculatedvalue would be 1970 K for line pair I, which is in errorby only 1.5% even though the boundary layers werecompletely neglected in the calculation. The corre-sponding calculation for line pair II gives a tempera-ture of 1530 K, an error of more than 20%.

C. Concentration Measurement

If one calculates the concentration from the sum ofintegrated absorption coefficients of the line pair withno boundary layer correction and uses the temperaturefrom the two-line technique, there would be a 12%error using line pair I and 68% error using line pair II.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Relativc Frequency (cm-')

(b)

0.0

aE117]

0Z

0.0 0.1 0.2 0.3 0.4 0.5 0.6, 0.7 0.8 0.9 1.0 1.1

Relative Frequency (cmt')

Fig. 2. (a) Spatially integrated line shape for the simulated COabsorption of line pair (3 - 2, R21) and (4 - 3, R31) in the postflamegases of a flat-flame burner [Fig. 1(a)]. (b) Spatially integrated lineshape for the simulated CO absorption of line pair (1 - 0, P4) and (2

4 1, R2) in the postflame gases of a flat-flame burner [Fig. 1(b)].

IV. Discussion

It should be emphasized that no simple figure ofmerit can be constructed that can be used to select asingle optimum pair of lines. Several factors affect theselection process as described in Sec. II, and the rela-tive weight that is given to these factors depends on theparticular experimental situation. For example, someof the candidate line pairs in Table II will not satisfythe selection criteria when the expected experimentalconditions are changed, while other line pairs continueto be suitable. Table II shows that the line pair (2 - 1,P4; 3 - 2, R2) meets the selection criteria at 2000 and1500 K (cases A and B), while the pair (2 - 1, P3; 3 - 2,R3) satisfies the selection criteria for the 1000-2000 Krange (all three test cases). This pair is clearly mostsuitable if one needs to monitor the CO concentrationand temperature in a sample gas over a very widetemperature range although one trades off tempera-


(a)

ture sensitivity at high temperatures. The pair (3 -2,R21; 4 - 3, R31) is most sensitive to temperature at2000 K but not suitable for measurements at lowertemperatures because the absorption of these hot-band lines is too small resulting in poor SNR.

Of all the candidate line pairs listed in Table I ateach condition, the optimum line pair for an experi-ment will be determined by other factors that affectthe experimental data reduction, e.g., variation in ex-perimental conditions, available spectral resolution,relative line intensity of the two lines in the pair, andthe SNR level of the signal. The uncertainties in thetemperature and concentration values are reduced ifthe two lines in the candidate pair are relatively wellseparated and have approximately equal intensities.The experimental data reduction procedure will bediscussed in more detail in a future publication.5 Theobjective here is to demonstrate the various aspectsone needs to consider in choosing spectral lines for adiagnostic measurement in a combustion environ-ment.

The program described helps the selection processby automatically selecting line pairs that meet certainminimum criteria for acceptability. The other factorsmentioned could be included in an expert system thatcan handle criteria that cannot be expressed in simplequantitative fashion. In conjunction with a spectraldata base and knowledge of data acquisition and re-duction, the expert system could be used to examinethe feasibility of absorption diagnostics and to selectthe optimal spectral lines for a particular absorptionspecies and for a particular experimental condition.The development of a general expert system for selec-tion of spectral lines for laser diagnostics was outsidethe scope of this work.

V. Summary and Conclusions

We have developed a systematic and practical tech-nique for measuring both temperature and speciesconcentrations using line-of-sight absorption spec-troscopy only. In this paper, the technique was sum-marized, and a method for selecting near-optimal ab-sorption transitions for diagnostics was discussed indetail. The precision limit can be predicted from theSNR of the data, the resolution of the absorption lines,and the sensitivity of the absorption data to the de-sired quantities. A strategy for selecting optimal ab-sorption transitions for diagnostics was proposed. Aset of selection rules is first developed to select spectrallines for diagnostic measurements. The rules are thenimplemented in an expert system. In conjunctionwith a spectral database, the expert system could beused to examine absorption spectra in any specifiedfrequency range, and optimum absorption lines could

be chosen for a particular measurement. The feasibil-ity of the method was demonstrated by the selection ofCO line pairs for simultaneous temperature and spe-cies concentration determinations.

In future work, the current techniques will be ex-tended to resolve spatial distributions of temperatureand species concentrations. The work will includereconstructing the laser absorption as a function offrequency from a limited number of line-of-sight mea-surements using tunable absorption spectroscopy.The temperature or species concentration of eachpoint is then retrieved by the line-of-sight data reduc-tion procedure. A detailed procedure for this work hasbeen proposed.4

This work was supported by the National ScienceFoundation under grant ECS-8604411, the Texas Ad-vanced Research Program, and by The Center for En-ergy Studies, The University of Texas at Austin.

References

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6. P. L. Varghese and R. K. Hanson, "Collisional Narrowing Ef-fects on Spectral Line Shapes Measured at High Resolution,"Appl. Opt. 23, 2376-2385 (1984).

7. E. C. Rea, A. Y. Chang, and R. K. Hanson, "Motional Narrowingin Spectral Line Profiles of OH," presented at Western StatesSection/The Combustion Institute, Livermore, CA (Oct. 1989),paper 89-45.

8. The lower state energies E' and E; of the two transitions may beclassified according to the E(T) curve value of CO at the averagetemperature of the sample gas. TheE(T) curve was defined anddiscussed in detail in Ref. 3. The possible combinations of E;and E' are E' < E < E(T); E' < E(T), E;(T) > E(T); and E; >E; > E(T).

9. P. L. Varghese, "Tunable Infrared Diode Laser Measurementsof Spectral Parameters of Carbon Monoxide and HydrogenCyanide," Report 6-83-T, High Temperature GasdynamicsLaboratory, Stanford U., Stanford, CA (1983).

10. R. K. Hanson and P. K. Falcone, "Temperature MeasurementTechnique for High-Temperature Gases Using a Tunable DiodeLaser," Appl. Opt. 17, 2477-2480 (1978).


selection of spectral lines for combustion diagnostics

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