JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Photographic Technique for Measuring Temperatures in LuminousRocket Exhaust Flames

FREDERICK S. SIMMONS AND ARTHUR G. DEBELLRocketdyne, a Division of North American Aviation, Inc., Canoga Park, California

(Received January 6, 1958)

The theory of the two path-length method for optically determining flame temperature is reviewed, and

the requirements for quantitative photographic measurement are presented. Apparatus which includes a

camera with the necessary combination of film and filters to accept light in a narrow wavelength interval,

and several adjustable lamps to serve as standard sources, is described. The film record contains an image

of the rocket exhaust jet adjacent to the images of the lamp filaments whose temperatures are known from

a previous calibration with an optical pyrometer. Comparison of measured intensities with and without a

reflector behind the flame yields the emittance and flame temperature. Some results of measurements at

the exit regions of rocket nozzles affording nearly optimum expanison are presented. The utility of the

method in rocket performance studies is discussed.

INTRODUCTION

KNOWLEDGE of the temperature in the exhaustjet would be of considerable value in an analysis

of the performance of a rocket engine. Optical tech-niques appear to be the only feasible means of produc-ing, with any degree of reliability, experimentalmeasurements of these temperatures.

The radiant emission from the products of liquidoxygen and hydrocarbon fuel combustion consists oflines, bands, and continua from any optically activemolecular and atomic species present superimposedon a continuum emitted by solid carbon suspended inthe gases. A number of unpublished spectroscopic dataindicates that the continuum is quite predominant inthe exhaust jets of rocket engines utilizing this pro-pellant combination.

The measurement of radiant intensities by photo-graphic means is attractive primarily for the reasonthat the radiation from the entire flame may besimultaneously recorded; however, accurate correlationof image densities on the processed film with absoluteobject intensities usually requires a very close controlof the many variables in the photographic process.The present apparatus essentially duplicates thatdeveloped for measuring apparent surface tempera-tures.' It was designed to eliminate most of the un-certainties in the quantitative analysis of photographicrecords by including several standard lamps in thefield of view, and to provide for a valid determinationof temperature from intensity measurements byaccepting light only in a narrow wavelength band.

The two path-length method of determining tem-peratures from spectral intensity measurements inflames of emittance less than unity is but one of several

well-known techniques2 ; its principal advantage is thata comparison source behind the flame is not required.The present application of the two path-length method

is novel in that the spectral intensities are measured by

1 D. W. Male, Rev. Sci. Instr. 22,769 (1951).2 P. J. Dyne and S. S. Penner, J. Am. Rocket Soc. 23,174 (1953).

photographic means, and a corner-cube prism placedbehind the flame provides the double light path with-out the rigid structures usually required to maintainoptical alignment between the reflector and the detector.

THEORY

The intensity of radiation from a homogeneousflame may be stated as

(1)JX= eXJX, b( T)-JX,b(Tbr))

where Ax is the observed spectral intensity in powerper steradian per unit wavelength interval per unitarea of emitter, ex the spectral Remittance" (in prefer-ence to "emissivity," according to the recommendationsof the American Standards Association'), and JX,b thecorresponding blackbody intensity for flame tempera-ture T and for flame brightness temperature Tbr.

The intensity of radiation observed when a reflectoris placed behind the flame is given by

(2)AX'= [l1+Rx(1 -ax)]exJxb,

where Rx is the reflectance for wavelength X of thereflector and ax the absorptance of the flame.

For systems in thermal equilibrium Kirchhoff'sradiation law states the equivalence of the emittanceand the absorptance. At wavelengths where Wien'slaw for blackbody radiation is sufficiently accurate,Eqs. (1) and (2), solved for the flame temperature,yield the relation

1/T= 1/Tbr+ (X/C2) log[1-(1/Rx) (JX'/Jx-1)], (3)

where C2 is the second radiation constant. From thedefinitions of emittance and brightness temperature,it follows that

ex= 1-(/Rh) (A'/Jx 1). (4)

Equation (3) is generally valid only for a differentialwavelength interval; in practice its use requires the

3ASA Z10.4, Trans. Am. Soc. Mech. Engrs., p. 17, 1943.

717

OCTOBER, 1958VOLUME 48, NUMBER 10

F. S. SIMMONS AND A. G. DEBELL Vol. 48

invariance of the emittance throughout the finiteinterval in which radiation for the intensity measure-ment is accepted. This requirement will be discussedpresently.

Should the emittance be known or determined for aflame of given size, the emittance of flames of othersizes may be calculated from Beer's law

ax= 1-exp(-kxpL), (5)

where kx is the specific absorption coefficient at wave-length X, p the density of the emitting and absorbingparticles, and L the depth of the flame.

The preceding equations apply only to homogeneousflames i.e., flames of constant temperature and particledensity in cross section. For heterogeneous flames,relations corresponding to Eqs. (1), (2), and (4) mustbe written in integral form.

To evaluate the sensitivity of the two path-lengthmethod under various conditions of flame temperatureand emittance, error equations may be derived in theusual manner. Differentiation of Eq. (4) yields aftersome manipulation

ZA~ ex-1-1/RX (Jx'Jx)_=. ~~~~~~~~~~(6)

'ex \ e;< (Jx /Jx)

Similarly, from Eq. (1)

(C2/XT) (T/T) =-(Aex/ex)

+ (C2/X Tb,) (A Tbr/Tbr). (7)

If it may be assumed that the single path brightnesstemperature may be measured with negligible in-accuracy, i.e., ATb,=O, Eqs. (6) and (7) then yield

AT I/1-ex+1/Rx\ /XT\1A(Jx'/Jx)

T Lt ex )'C2J (Jx'/Jx)

The preceding equations illustrate the fact that largeerrors in the experimental determination of emittanceand hence temperature may result from small errorsin the ratio of single and double path intensities whenthe emittance is small, as in the case of thin andtransparent flames. Indeed, the method becomescompletely insensitive as the optical depth of the flameapproaches zero and, conversely, the sensitivity in-creases to the maximum when the optical depth be-comes very large, i.e., the flame radiates as a blackbody.The condition for equal errors in temperature andmeasured intensity ratio is obtained by setting thequantity in the bracket in Eq. (8) equal to unity. ForRx=0.8, X=0.65 microns, and T=200 0 'K, the resultantvalue of emittance is 0.2. Below this value, errors inintensity ratio measurements are magnified in deter-mining temperatures; above, errors are reduced.

INTENSITY MEASUREMENTS

In order to apply Eq. (3) with validity, the intensity-measuring instrument must accommodate but a narrowband of wavelengths. In photographic detection, thiscan be accomplished by a selection of suitable filmsand filters. Super Panchro-Press type B film with aWratten No. 29 filter, or with both Wratten numbers29 and 34 were found to be useful combinations fornarrow bands in the red. The same film filtered by acombination of Wratten numbers 35 and 45 was usedfor measurements involving narrow bands in the blue.

Since image densities on film vary markedly withapertures, shutter speeds, film characteristics, and themany variables of the development process, in orderto relate accurately image density to source intensity,all variables must either be very well monitored, oreffects due to their uncertainties obviated in somemanner. The latter can be achieved by photographing,along with the object of interest, several standardsources set at known brightnesses which span those ofthe object. This procedure yields, in effect, an in-dividually calibrated record for each measurement; theknown temperatures of the sources, previously deter-mined with an optical pyrometer, thus establish abrightness temperature vs film density scale for eachnegative. For optimum sensitivity, these densitiesshould lie on the straight line portion of the familiardensity vs log exposure curve for the film. Therefore,the many variables in exposure and processing need becontrolled only to the extent of producing a negativewith a satisfactory range of densities.

A valid procedure for reducing the data would be adirect plotting of brightness temperature vs filmdensity for the comparison source images, therebyproducing a curve from which the unknown brightnesstemperatures of the object could be read. However, aplot of film density vs reciprocal temperature is ad-vantageous for the following reason. By definition, theexposure is proportional to the intensity of the lightfrom the object. From Eq. (1) and Wien's law, thisintensity is proportional to the exponential of thereciprocal temperature. Hence the density vs logexposure curve is equivalent, except for the sign of theslope, to a curve of density vs reciprocal temperature.By remaining well within the linear region of this curve,accuracy in interpolation (and extrapolation if neces-sary) is gained.

A measurement of brightness temperature with anoptical pyrometer yields a value for the wavelengthband utilized by that instrument. Most commonly,this band is defined by the cutoff of a filter and of theeye, and is usually centered about 0.65 microns. Inorder to determine brightness temperatures of thestandard sources at other wavelengths from such ameasurement, knowledge of the source emittance as afunction of wavelength is required. This information

718

October1958 MEASURING TEMPERATURE

is available for tungsten ribbon4 which, as a lampfilament, is the usual comparison source for opticalflame temperature determinations. The brightness tem-perature correction follows immediately from thedefinition given in Eq. (1) and is most convenientlyexpressed by

1ITb,, 2= 1ITb,, 1+ (X/C2)[lgEX, 1-(X2/X1) 10geX, 2]- (9)

Additional corrections would be required to accountfor any variations with wavelength in transmittanceor reflectance of optical components included in thesystem during calibration.

APPARATUS AND PROCEDURES

The photographic pyrometer with a side plate re-moved is shown in Fig. 1. It consists of a commercial4X5 camera mounted upon a chassis which containsfour tungsten ribbon filament lamps installed behindadjustable range correction lenses, and a pair of firstsurface mirrors to reflect the light into the camera.The range lenses were so adjusted that the images ofthe lamps, and that of the object, i.e., the rocket flame,were brought to a common focus by the camera, forthe particular object distance. The camera was equippedwith a 208-mm lens and a between-the-lens shutterwith a solenoid for remote operation. The focal lengthof the range lenses was chosen to yield images ofapproximately full size; the diameter was selected tomake the limiting aperture of the system that of thecamera objective. The mirrors were located so thatslightly more than half of the field of view was used forthe rocket flame, the remainder for the comparisonlamps; their sizes were chosen to avoid vignetting.Field stops were placed in front of the lamps to definethe portion of the filament used as a standard.

The electrical circuit for the instrument consists of awell-regulated ac power supply and the necessary com-ponents to provide for individual setting of the lampcurents prior to use of the instrument, and for a re-motely controlled return to these same currents foroperation. Since an appreciable length of time wasrequired for the attainment of lamp current equilibrium,

FIG. 1. The photographic instrument in detailed view.

4 J. C. DeVos, Physica 20, 690 (1954).

FIG. 2. The photographic instrument set up for ameasurement on a rocket exhaust jet.

equal warmup periods were employed for calibrationand use of the instrument.

The photographic pyrometer, set up for operation inthe field, is shown in Fig. 2.

An optical pyrometer, temporarily located in thecamera position where its aperture was filled, was usedto calibrate the comparison lamps in place. This calibra-tion method avoided the necessity of making correctionsfor the lens transmittance and mirror reflectances. Theoptical pyrometer, when checked against a NationalBureau of Standards certified lamp, showed an averagedeviation of 6C in the range from 1200 to 1800C.

In order to provide a source of reflected flameradiation for application of the two path-length methodwithout the necessity of maintaining optical alignmentunder severe vibration, a corner-cube reflecting prismwas employed. This type of prism has the property ofreflecting light in the direction from which it came,regardless of the incident angle, to within narrow limitsdepending on the tolerances of manufacture. With sucha reflector located behind a flame whose emittance isless than unity, the photographic records contained adenser spot, within the image of the flame, of a size

corresponding to the effective area of the prism. Theratios of intensities in Eq. (3) were then obtained fromthe measured densities of this spot and the adjacentareas in the flame image.

The films were processed in accordance with themanufacturer's published recommendations in orderto insure repeatability in obtaining the desired rangeof densities. Film densities were measured with a

IN ROCKET EXHAUST FLAMES 719

F. S. SIMMONS AND A. G. DEBELL

TABLE I. Summary of experimental data taken in the exhaustjet near the nozzle exit of a small rocket engine,

XA cxb Tba Tbr'd Te,' Tihcf Tgu..g

0.65 0.82 1667 1685 1692 1770 21800.65 0.85 1644 1658 1664 1740 21100.65 0.86 1682 1696 1701 1775 22100.65 0.83 1643 1659 1666 1700 20000.65 0.83 1639 1655 1662 1740 21100.45 0.90 1792 1800 1803 1790 22100.65 0.90 1645 1655 1658 1710 20100.65 0.80 1647 1666 1675 1740 20700.65 0.80 1671 1690 1699 1750 21200.65 0.78 1635 1655 1665 1760 2140

a X =Wavelength, microns.b x =Spectral emittance at .wavelength X.o Tb, =Brightness Temperature, single path, K.d T =Brightness temperature, double path, K.o Tx =Experimental nozzle exit temperature, K.Tih,, =Theoretical nozzle exit temperature, constant composition, K.

e Th,, =Theoretical nozzle exit temperature, variable composition, K.

recording microphotometer. Some preliminary tests, inwhich an additional tungsten strip lamp was calibratedand photographed in the part of the camera fieldintended for the flame, indicate the precision of thecomplete process to be of the order of 10TC for lamptemperatures between 10000C and 2000 C with awarmup period of 3-1 min.

EXPERIMENTAL RESULTS

The results of a number of two path-length measure-ments made at the nozzle exit regions of a small researchrocket engine are given in Table I. The experimentallydetermined temperatures are shown along with theoret-ical values'6 calculated for constant and for variablechemical composition expansions. Figure 3 is a positivemade from a negative record of the jet from a small

FIG, 3. A positive reproduction made from a negative recordshowing the image of a rocket exhaust jet with the images of thestandard lamp filaments.

I V. N. Huff and A. Fortini, "Theoretical performance of JP-4fuel and liquid oxygen as a rocket propellant. I-Frozen composi-tion," Natl. Advisory Comm. Aeron. RME 56 A27 (1956).

6 Huff, Fortini, and Gordon, "Theoretical performance of JP4fuel and liquid oxygen as a rocket propellant. II-EquilibriumComposition," Natl. Advisory Comm. Aeron. RME 56 D23 (1956).

Vol. 48

engine; the bright spot due to the prism is faintlyvisible near the nozzle exit. Figure 4 is a typical curveof the film density vs reciprocal temperature obtainedfrom such a record.

A number of other data were obtained from measure-ments made in the red and in the blue at the nozzleexit region of a large rocket engine. These measurementswere made without a reflector behind the flame; theemittances were estimated from the data for the smallengine using Eq. (5) with the assumption that thecombustion products were identical. The results werequite similar to those obtained for the small engine.

DISCUSSION

Equation (3) is strictly valid only for the case wherethe emittance of the flame is constant throughout thewavelength interval accepted by the detector. Nowalthough it is known that the emittance of flames

I--znwC

C.b .8 6.0 6.2 6.4RECIPROCAL TEMPERATURE (K)-

6.6 x o

FIG. 4. A typical curve of film density vs reciprocaltemperature obtained from a film record.

containing incandescent particles does vary with wave-length,7 the variation is slight throughout the intervalutilized by the present instrument, and the assumptionof invariance can be justified. Such an assumptionwould not be reasonable, however, for measurementsin nonluminous flames, where the radiation is emitteddiscontinuously, e.g., in molecular bands, unless aninstrument with sufficient resolving power to isolatethe center of a line were used.

The two path-length method for determining flametemperature seems to be quite workable in the presentapplication; the error analysis does suggest, however,that some difficulty might be experienced in flames ofless than 0.2 emittance. The photographic pyrometerappears to be well behaved and sufficiently precise as atransfer device for an optical pyrometer; however, the

7 H. G. Wolfhard and W. G. Parker, Proc. Phys. Soc. (London)62, 523, (1949).

Io c __ _ __

0.8

0.6

0 LAMPS0.4 9 FLAME, SINGLE PATH - _ .

a FLAME, DOUBLE PATH

0.2 - -- - --

720

October1958 MEASURING TEMPERATURE IN ROCKET EXHAUST FLAMES 721

absolute accuracy and validity of the temperaturedeterminations depend on the structure of the flameand the interpretation of the film record. It may there-fore be useful at this point to consider some of thefeatures of the supersonic exhaust jets of rocket engines.

The most salient feature of such jets is the formationof standing shock waves which result from the inter-action of the supersonic exhaust gases with the ambientatmosphere. The variations in pressure, density, andtemperature associated with these shock patterns canbe predicted from aerodynamic theory only to withincertain limits set by the uncertainties in the exhaustgas composition and properties. In addition to theheterogeneity resulting from these aerodynamic effects,there is usually a mantle of high luminosity surroundingthe exhaust jet of a rocket engine using liquid oxygenand hydrocarbon fuel as propellants. Optimum per-formance of such engines is attained at fuel-richmixture ratios; the luminous mantle, or "afterburning,"is the result of the combustion of partially oxidizedfuel with air in the mixing region of the jet.

In general, therefore, rocket exhaust jets present aheterogeneous field of view for an optical instrument;a particular exception of interest is the region at theexit plane of a nozzle affording an optimum expansion.Here the stream is virtually free from the shockstructure created from the exit pressure adjusting tothe ambient'level, and from the gradual loss of momen-tum along its length; here also the luminous mantle is

of minimum depth, and in some cases does not appearfor a significant distance downstream, cf. Fig. 3. It isin this region that valid temperature determinationscan most likely be made using Eq. (3) as derived for ahomogeneous flame.

Experimental data presented in Table I were obtainedfor nozzles yielding expansions close to optimum; theexit regions in all cases appeared to be sensibly homo-geneous, and in the calculations such was assumed tobe the case. Although the results indicate conditionsclose to those produced by a constant compositionexpansion, some caution must be exercised in theirinterpretation, since the physical areas of the nozzlewere slightly different from those theoretically requiredfor optimum expansion; moreover, the assumption ofa completed reaction was made. These data arepresented primarily to show that the technique doesappear capable of providing an additional fundamentalmeasurement in the static testing of rocket engines. Itis reasonable to expect that the technique would be ofvalue for measurement of temperature and emittancein luminous flames of other origin.

ACKNOWLEDGMENTS

The authors are grateful to Mr. John E. Witherspoonof Rocketdyne for his interest and support of the work,and to Mr. Donald Buchele of the NACA LewisLaboratory for his helpful comments and suggestions.