resistance-thermometer measurements in'a low-pressure flame

RESISTANCE-THERMOMETER MEASUREMENTS IN LOW-PRESSURE FLAME 285

matical Theory of Non-Uniform Gases, Cam- bridge (1939).

18. RICE, O. K.: Electronic Structure and Chemical Binding. McGraw-Hill (1940).

19. SMITH, W. V.: J. Chem. Phys., 11, 110 (1943). 20. HERZFELD, K. F.: Z. Phys., 8, 132 (1922). 21. RICHARDSON, L. F.: Proc. Roy. Soc., A. 186, 422

(1946). 22. JosT, W.: Explosion and Combustion Processes in

Gases, McGraw-Hill (1946).

23. LEWIS, B. AND VON ELBE, G.: Combustion Flames and Explosions of Gases, Cambridge (1938).

24. GAYDON, A. G.: Spectroscopy and Combustion Theory, 2nd Edition, Chapman and Hall (1948).

25. GRIFFITHS, E. AND AWBERY, J. H.: Proc. Roy. Soc., 129, 401 (1929).

26. Looms, A. G., AND PERROTT, G. ST. J.: Ind. Eng. Chem., 20, 1004 (1928).

27. GAYDON, A. G., AND WOLFHARD, H. G.: Proc. Roy. Soc., 194, 169 (1948).

33

R E S I S T A N C E - T H E R M O M E T E R M E A S U R E M E N T S

IN'A L O W - P R E S S U R E FLAME 1

By MITCHELL GILBERT AND JOHN H. LOBDELL

1. INTRODUCTION"

This paper describes some research in a low- pressure flame on measurements of translational tcmperature. A measurement technique using a platinum resistance thermometer was developed and found successful, subject to certain limitations. The pertinent background leading to this research is of interest because of the serious problems encountered in any attempts at definitive study of combustion.

Previous work (1) with low-pressure flames in a two-dimensional laminar jet at total pressures less than 10 mm Hg abs indicates that detailed explorations of the reaction zones could be made with great resolution of the flame phenomena. Spatial extension and the extraordinary steadiness of the flame make this precision possible. Lowering the total pressure under the proper conditions preserves the Bunsen-like character and isolation of the flame and acts through effects of molecular mean free paths to increase the physical scale of the flame inversely with the pressure. Flames thus extended preserve also the average number of molecular collisions per reaction zone, and the visual luminous character remains unchanged except for greater diffuseness.

1 This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology under Contract No. W 33-038-ac-4320 sponsored by the Air Materiel Com- mand and Contract No. DA-04-495-Ord 18 sponsored by the Department cf the Army, Ordnance Corps.

So long as the gas density is appreciable, the collision rate per unit volume remains large, and statistical considerations are unaltered relative to atmospheric conditions. The local temperatures and temperature structure in the flame zones continue to be of major interest as basic parameters governing the flame process. The problem includes the kind as well as the level of temperature: internal as well as translational temperature. Nontranslational temperatures are not the subject of this paper, but pertinent references are given.

Some earlier measurements were made by Klaukens and Wolfhard (2) and Gilbert (1) with thermocouples. Certain evaluations of Klaukens' measurements were doubtful because of an as- sumption that treated a spherical shape as a cylindrical one in determining heat transfer to the thermocouple. This treatment was investigated and clarified (1), but the interpretation of the measurements was disputable even after removing Klaukens' difficulties. Estimates of the thermal conductivity of the gas film surrounding a wire were necessary and yet subject to unavoidable uncertainty. The uncertainty depends on the nature of thermal transport in a gas containing atomic hydrogen, atomic oxygen, and hydroxyl radical in appreciable quantity. The thermal-

conductivity coefficients were estimated from very

simplified considerations (3), and their contri-

butions to total transport were evaluated according to trends observed in theoretical calculations by

286 LAMINAR COMBUSTION AND DETONATION WAVES

Hirschfelder et al. (4) on multicomponent mixtures. The result of this treatment, however qualified, made it evident that transport considerations without including the heterogeneous gas-surface behavior cannot sufficiently clarify the situation. Data for emissivities of the thermocouple surface were not measured in the earlier work but were obtained from the literature; thus another uncertainty was introduced.

2. BASIS AND DESCRIPTION OF PRESENT RESEARCH

The work described in the present paper is based on the addition of electrical energy to a resistance-wire thermometer in the flame. Schmidt (5) used such a technique in a null form for measuring flame temperatures. The null form is the most effective use of the resistance thermometer and consists of obtaining, experimentally, the heat loss or temperature vs current behavior of the wire both in the flame and in vacuum. The temperature which satisfies a single value of the current is the flame temperature. This value is determined at the intersection of the heat-loss curves in vacuum and in the flame. Ordinarily temperature levels in flames exceed the melting point even of platinum, and the null method is limited. The course adopted by the present authors was to extrapolate in order to find the null point representing the flame temperature. Because this procedure involves additional possible errors, it becomes necessary to use wires of different diameters to provide further verification of the

data. As is shown in Section 3A, the heat-balance

equations for an electrically heated wire make it possible to obtain data on the local gas temperature, the thermal conductivity of the gas under conditions of heat transfer to the wire surface, and the emissivity-temperature relationship for the surface. Ambiguities of earlier work appear to be removed, but the modified Schmidt technique has limitations with regard to extensive use in temperature-mapping the reaction zone whenever catalytic effects occur at the wire surface. Extension of the method to the most active regions of combustion 2 depends on finding materials not subject, as platinum was found to be, to surface catalysis in these regions.

Temperature was measured for a lean acetylene- oxygen flame at 4.3 mm Hg abs. Platinum wires

2 In these regions spectroscopic measurements (6 through ll) reveal temperatures for the rotational levels of excited OH and other species, deviating markedly from equilibrium.

of different purities and diameters were used as resistance thermometers. Vacuum data were obtained in a bell-jar apparatus evacuated to as low as t0 -G mm Hg abs. The combustion chamber and its associated equipment for maintaining and controlling the low-pressure flame were described in detail by Gilbert (1). The apparatus described herein is the additional equipment required to make these measurements.

The method used appears to be successful, under the discussed limitations. The flame temperature found is strikingly close to the calculated equilibrium value. A somewhat unexpected value is found for the thermal conductivity. Analysis raises interesting questions concerning the nature of the thermal transport from a flame-gas film to the wire or to any surface in a reacting gas mixture.

3. MEASUREMENT TECHNIQUE AND THEORY

The heat-transfer relations governing the experimental technique are developed in the first part of this section. In the second part attention is given to the energy-transfer term that can exist because of chemical processes not included in normal heat transfer. I t is shown that in some cases the experimental technique may permit evaluation of the existence and magnitude of such energy transfer. The discussion is pertinent to the general investigation of gas-surface interactions.

A. Development of heat-transfer relations

The effectively complete heat-balance equation for a homogeneous, cylindrical wire element dx in a flame, with current flowing in the wire, is given by

I t ~r/~t4 x dx hd(Tg -- T,o) + a ~ g a ~ o

- ~o d(T~ - T:) ~d~ ~ 1 4 Ox ~ + qd

+ cI~Rdx -- 0 (1) t

where

h ~ heat-transfer coefficient for forced convection (Btu/hr sq ft ~

d ~ wire diameter (ft) T~ ~ gas temperature (~ Tw -- wire temperature (~

~ radiation constant (0.173 X 10 -~ Btu/hr sq ft ~ 4)


e,, = emissivity of wire surface assumed to be graybody

e~' = effective gas emissivity corresponding to Tg p

Tg t = effective average gas temperature for radiation (~

T, = temperature of surroundings (chamber walls, etc.) assumed to be blackbody (~

K = wire conductivity (Btu/hr ft ~ q = extraneous thermal transfer to surface

(Btu/hr sq ft) I = current (amperes) R = resistance of length of wire included

between potential leads (ohms) l = length of wire (of resistance R) acting as

resistance thermometer (ft) c = conversion factor (for watts to Btu/hr)

This equation is simplified by experimental conditions which justify the neglect of terms for radiative exchange between the flame and the walls and between the flame and the wire and for the conduction-loss term in the central portion of a length of wire positioned along an isotherm perpendicular to the axes of the two-dimensional jet (1). In the center of the two-dimensional flame, gas-conduction losses vanish wherever the temperature gradient in the flow direction is zero, and the local temperature T,~ can then be assumed adiabatic.

Dividing by r dx d, equation (1) becomes

4 cI'2R h (T~ - - T,,,) - - r Tw q- ~ + q = 0 (2)

Since I a n d d are measured at room temperature, the factor f2 is introduced to account for thermal expansion in the flame and for the subsequent change in surface area of the wire. This expansion is significant in the present experiments. The use of plat inum also makes possible the measurement of T~ through the accurately known resistance vs temperature behavior.

The emissivity ew of the wire sample l used in flame is determined in a vacuum. At very low pressures the convective term in equation (2) is zero. The term q is then obviously zero, and the emissivity is

c F R

~ - rrcrf21 d T ~ (3)

Equation (3) provides a relationship between e,, and T~ to be obtained in vacuum measurements

since all the other quantities are measured, and since T~ is a function of R. The valtms of ew were checked after each specimen was used in the flame, and it was found thaf the values were unchanged. Consideration was given to the possibility that the plat inum wire might experience a transient behavior leading to emissivity properties in the flame different from those measured. No reasonable physical-chemical basis for such transience is conjecturable for plat inum under the conditions of these experiments.

The quantities left to be determined are h and T , . Designating the algebraic sum of the electrical and radiative energy terms as S, we ,write, from equation (2),

S = h(Tg - T,,,) + q (4)

In equation (4), S is a linear function of T , with a slope equal to h if it is assumed that q is zero and that h is independent of T~. At the intercept S = 0, and Tg = T~. Because the data which are the principal results of this work show an excellent agreement between the intercepts obtained and the equilibrium flame temperature there is no concern as to the existence of catalytic processes or other extraneous thermal effects in the flame region represented by the data. Thus q is actually zero in this case.

The determination of the heat-transfer coefficient requires special comment. King's equation (12), stated in terms of the Nusselt number h d /k l when applied, for example, to two wires of different diameters, gives the relation for the thermal conductivity ki of the gas film surrounding the wire in the flame that can be expressed as

k,,_ h,d (o.a2 + o.43R~176 kh h2 d2 \ 0 . 3 2 if- 0 . 4 3 R ~ 2 /

where R,, is the Reynolds number for the wire. A term for the effect of Prandt l number is neglected in equation (5) as insignificant. Equation (5) should have the value uni ty at a fixed point in the flame for a given Tw (i.e. ks = ks1 = k]2) and thus represents a test of the data obtained with wires of different diameters. The use of equation (5) implies that the wires are of such size that effects of molecular mean free paths are of no importance in the heat transfer from low-density flames. Investigation (1) of this factor showed that, despite the low density, King's equation is obeyed when the wire diameter is not less than four times the mean free path. Care was taken to use plat inum wires of sufficiently large diameter.


B. The nature and effect of q

The quant i ty q was introduced into the heat- balance equation to account for an anomalous heat-transfer rate per unit surface area originating directly on the surface or arising from gas-to- surface phenomena not included in ordinary convection. The latter phenomena can arise as a result of homogeneous exothermic recombination of dissociated species and/or of thermal diffusion. Thermal-diffusion contributions are quite small. Low pressure decreases the probability of homogeneous recombination dependent on three-body gas collisions as also does the restriction that the gas region involved is limited to an extent of a few mean free paths. Atomic species (e.g. H atoms) would not be expected to recombine appreciably, therefore, in the gas phase. Any other recombination where heat release is, except under unusual conditions, sufficient to cause the particles to fly apart immediately would also not occur. The q term can thus be assumed to represent only thermal effects of direct surface origin. Equation (4) may be re-examined with this origin in view.

Consider the case of two wires of different diameters used in the measurement. There are then two equations to be satisfied,

$1 = hl(Tg - T,,I) + ql and S~

= h~(Tg - T,~2) + q 2 (6)

and for the condition S = 0

To = T'~, - - q! = T : , - - q2 (7) hi h2

Primes indicate intercepts on the temperature axis.

The question arises as to the meaning of the intercept on the temperature axis [of. equation (7)]. Three interpretations are of concern. First, no catalysis is present, and q is zero. Thus both wires will give the same intercept, and T o' = T~rl = T~t~ from equation (7). Second, catalysis is present, and q is not zero; moreover q,/h~ # q2/h2. Here it is seen that the intercepts are un- equal. The intercept for the data of each wire at S = 0 would exceed Ta by the amounts q,/hl and q2/h2. The third interpretation is similar to the second; that is, catalysis is present, q is not zero, bu t q,/h, = q2/h,2. This last interpretation can be confused with the first because here also the same intercept occurs for both wires.

Unless the last interpretation can be ruled out as an unlikely possibility, the problem of deter-

mining To from the intercept at S = 0 becomes exceedingly complicated. The first two interpretations clearly distinguish between the no-catalysis condition and catalysis through the examination of the intercepts for different wires and, as is shown later in this section, permit the determination of To and q when the latter exists. In this paper the results themselves are evidence that q is indeed zero and that only the first interpretation applies. Generally the results offer no such clear indication; thus consideration must be given to these interpretations from the viewpoint of actual validity.

For the third interpretation to be true the rate of heat release per unit surface area q would have to vary with wire diameter in precisely the same way as the convective coefficient h depends upon diameter. This dependence is approximately q(x d -1 since this is the behavior exhibited by h in equation (5) at R, ~ 1.

The analogies between heat, mass, and mo- mentum transfer suggest a basis for q and h varying similarly with diameter, bu t the physical-chemical criteria implied as governing such a situation are not likely to be satisfied for q. These criteria are (a) that the concentration of surface-active species at the surface must be determined and controlled by the diffusion rate in the gas around the wire and (b) that, even if the first criterion is obeyed, the concentration gradient upon which the diffusion rate depends must vary inversely with the diameter of the wire if q is to vary inversely with diameter. The present view of gas-surface heterogeneous processes (13) suggests that adsorption and desorption phenomena rather than diffusion would generally be the rate-controlliiag processes in a mixture such as surrounds a wire in a flame. Furthermore, the concentration gradient would not be expected to behave as required; this is seen from consideration of the nature of the effective gradient-layer thickness. As a consequence of the failure of both of these criteria to apply to the behavior of q, it follows that no inverse dependence of q on d exists. When q is considered as a direct energy release on the surface, inappreciably af- fected by gas phase phenomena, one is led to the conclusion that q is independent of wire diameter; in other words ql = q2.

The foregoing discussion essentially rules out the third interpretation of the meaning of the temperature-axis intercept. A clean distinction remains between the cases where catalysis is or is not present on the wire surface, based on the test


of equality of the intercepts at S = 0 through the application of the first and second interpretations.

I t may now be shown that the magnitude of q can be roughly determined in principle. A simple temperature dependence of q is also considered. There are two cases: (1) when q is independent of both d and T~, and (2) when q is independent of d but a linear function of T~ over a restricted range of wire temperature. More complicated dependence of q on T~ may be investigated perhaps by suitable analysis of the experimental data for several wires.

For case 1: qt = q2 = q, and equation (6) re- duces to a set with the unknowns hL, h2, T~, and q. The slopes measure hi and h2 ; S] and $2 are obtained from the experimental data. Al- ternative solutions are, at 5"1 = $2 = 0 (by extrapolation if necessary),

h l h ~ ( T ' , -- T ' 2 ) (10) q "~ h2 - hi

and also at fixed T,~,

h~. Si -- haS2 (11) q ~ h2 - hi

For ease 2:q~ = q2 = q0 + ~ T ~ . I f q0ando~ (the temperature coefficient of surface energy release) are assumed independent of T~, there may be obtained from equations (5) and (6) and from the derivatives of equation (6) with respect to T~ the five necessary relations for determining Ta, h i , h2, q0, and a.

4. DESCRIPTION OF APPARATUS

A. Electrical heating circuit

The electrical heating circuit for the resistance thermometer consists of a regulated ac power source, a current-measuring and current-calibrating circuit, a Kelvin bridge, and a dc supply to operate the bridge (fig. 1). A rectifier and inverter change 60 cyc ac to 400 cyc ac. A step-down transformer is used for obtaining the heating current. Instrumentation troubles caused by 60-cyc hum are thus eliminated by use of 400 cyc.

The standard resistor consists of a coil of No. 10 gage Advance wire, air-cooled. Potential leads in the bridge circuit are immersed in oil at junc- tion points to minimize thermal electromotive forces. The technique of polarity reversal is used to eliminate effects of stray electromotive forces from measurements in the bridge.

The current-measuring and current-calibrating

circuit employs a vacuum thermocouple, a ten- turn Duodial mounted on a helipot rheostat, and fixed-series resistors in a network paralleling the standard resistor. The combined rms alternating and superimposed direct current is measured.

VACUUM 7Hs

1~+13a 2 ~ a IS ~

. . . .

FLIP-FLOP I

O Z ~ I . . . . . .

8=TTERIE$ I . . . . . . I , ~ _ ~ _ " _ _ _

4,l I

VOLTA~ -C~OL L . . . . . . . . . . . . RHEOSTAT C ~ CALIBRATION ~

in 0

Fia. 1. Circuit diagram of temperature-measuring system using resistance thermometers.

-- POTENTIA L LEAD CONOUIT

COMBUSTION CHAMBER WALL

~ ~ i ~ CICEM[NTED . . . . . . . . . . . . . . . . . . CERAMIC BRACE CURRENT LEADS

DUCT (3#I 5 l

PL AT~NUM WIR E

FIG. 2, Resistance-thermometer mounting fork in combustion chamber.

B. Platinum wire mounting

Figure 2 shows the resistance thermometer mounted in the combustion chamber in a mechanism capable of vertical and horizontal position- ing by means of external controls. Buckling effects which arise from thermal expansion are minimized by shaping the specimen into a U configuration. Remaining sag which arises during heating is taken into account by using a cathetometer as a position monitor.


In the bell jar (fig. 3) a fixed mounting is used. Provision is made to facilitate outgassing; external connections permit the heating and bridg- ing of the wire for the emissivity measurement.

but monitoring of the ambient resistance provided a sensitive means of following the change in diameter. From the ambient resistance R , a(p~ l~/d~) and from mass conservation for the wire l~d~ ~ = constant, the following expressions are obtained:

AR,,_ 4hd~,_ 2al~ (14) R~ d, l~

I t is seen from equation (14) that the relative change in ambient resistance R~ is four times the relative change in ambient diameter d, and twice the change in ambient length I , . For example, an increase in l~ of 0.1 per cent with a concomitant decrease in d~ of 0.05 per cent is not easily de- tectable, but the resulting increase of 0.2 per cent in R~ is readily detected. Dimensional corrections of this nature were made throughout by observ- ing Ro.

FIG. 3. Diagram of bell-jar apparatus for emissivity measurements.

5. DESCRIPTION OF MEASUREMENTS

A. Resistance-thermometer calibration

The purest platinum-wire specimens used were �9 thermocouple wire, grade I. Their resistance-

calibration equation, with the 0~ resistivity experimentally obtained at the Je t Propulsion Laboratory, was [(14) and p. 162 of (15)]

pt = 9.86(1 + 3.9788 )< 10 -3 t - 5.88 X 10- 7 t 2)

#ohm cm (12)

where pt is the specific resistivity at t~ One specimen of somewhat uncertain purity was used. I t was calibrated over a range of temperatures (0 to 700~ immersed in an aluminum oxide bath in a special furnace. The equation fitted to the furnace calibration was

pt = 9.918(1 + 3.9512 X 10- 3 t - 5.36 X 10 -7 t 2)

~ohm cm (13)

Figure 4 shows the resistance-temperature calibrations.

A special correction was found necessary to account for a slow, continuous increase in the ambient resistance of the wire specimen caused by elonga- tion arising from prolonged heating. The change in diameter was too slow to be readily measured,

6r

ZO

/ io~ 2co

/ /

REREF~NED GRADE I ~

/ / /

y I GRA0g I

I

TEMPs163 ('C)

Fro. 4. Resistivity of platinum wire

B. Emissivity measurements

Emissivity measurements were made in the bell jar at pressures down to 10 -6 mm Hg abs. Meas- urements at a particular temperature were begun at pressures of about 10 microns. As the pressure decreased, the dependence of the apparent ew with pressure was noted through the variation of the heating current. The true value of ew at a given wire temperature was obtained from a semi- log plot of apparent ew vs pressure. A lower asymp- totic behavior toward zero pressure was observed which defines the true ew. Extrapolation permits refinement of the emissivity value of 1 to 2 per cent.

Emissivity data for three experimental specimens are shown in figure 5. The data in figure 5 are in very poor agreement with data reported in the literature [p. 1164 of (15)]. The crucial nature of the experimental emissivity values lies in the fact that values for the particular specimen, other than those of figure 5, cause complete disorienta-


tion of the results calculated by equations (2) or (4). Emissivity calibrations before and after heating in the flame showed no appreciable differences, and it has been mentioned that no transient emissivity effects were considered likely.

C. Length and diameter measurements

A traveling microscope measured the wire length between the potential leads to the nearest I).002 inch (i.e. approximately to 0.1 to 0.2 per cent) in a length of 1.500 inches. Diameter was measured to the nearest 0.0001 inch with a calibrated micrometer.

To reduce the error in diameter measurement a radial and lengthwise survey was made, and the results were averaged. After corrections were included for thermal creep described in Section V-A, the diameter measurement had a probable error of about ~ per cent.

~ 1 l REREFINED GRADE ~ \

GRADE I , ---- ~ ~ "

I I , z o o ,400 ,600

TEMPERATURE {~

FIG. 5. Emissivity of platinum-wire specimens

o , r

:

O'6

o , s - - - -

o ,4oo ~

D. Measurements in the flame

The platinum resistance thermometer was mounted on the fork and positioned in the flame at the point of maximum temperature and mini- mum axial gradient [this point is 20.2 mm above the duct lip according to Fig. 42 of (1)]. The current was raised gradually to produce wire temperatures up to about 1750~ (3642~ and the resistance and current were measured. The test was repeated many times to provide agood check. The data in figure 6, however, are those taken from a few representative tests. During each test, time to reach equilibrium was allowed on heating or cooling. At equilibrium the wire position was checked and adjusted with the cathetometer. Data were obtained in an acetylene-oxygen flame of 1 to 6.18 mol ratio, more than twice stoichio- metric. The pressure was 4.3 mm Hg abs. Da ta were reduced by equation (4), using figure 5 for e~.

6. RESULTS

A. Flame temperature

From the data in figure 6 the slopes seem fairly constant. When the data are extrapolated to S = 0, the curves are found almost to intersect. This result indicates that q is indeed zero for reasons indicated in Section 3. The value itself of the intersection is probably more convincing on this score, as is indicated later in this section. A

1300 F600 t?O0 1 9 0 0 2 ~ 0 0 2 } 0 0 ZSO0 "r E M P E R A r U R [ ( ' e l

Fro. 6. Determination of maximum flame temperature.

few data points lying conspicuously above the straight line for the 0.045-inch wires can be ac- counted for on the basis of emissivity-measurement errors that involve relatively larger conduction errors for larger wires at lower temperatures. The resultant errors in ew are on the high side and would account for the deviations observed. Evaluation of the errors in all the measured quantities indicates that the data are even more

reliable at higher temperatures. The extrapolation

is thus made with some confidence.

The average value of the extrapolation point Tg = T'w found from the three curves is 2223 -4-

18~ (4461~ The calculated adiabatic equi-

librium temperature for the flame is 2210~

(4438~ The agreement is striking and well

within the region of maximum experimental error


estimated herein. Table 1 shows the estimated uncertainty in the experimental quantities.

TABLE 1

Magnitude of errors

Measurement

Ew

I R l d Tw

Maximum Error

p ~ e n t

4-1 4-0.5 4-0.1 • ~0.3 4-0.3

Error Caused in T a

~ -4-15 -4-15 4-3 -4-9 -4--9 4-25*

* Including uncertainty in T, due to error in measuring R and in the calibration of R vs Tw.

The maximum probable error is about 4-45~ in Tg. The agreement between the experimental value of Tg and the calculated equilibrium temperature lies well within the range of maximum experimental error. In fact it appears as if the estimate of error is conservative by at least a factor of 2. Support is lent to the idea of q = 0 for these experiments. It should be noted that, besides obliterating the trends in the data, the use of literature values of ew would easily result in errors in T~ of 400~ Values in the literature differ by as much as 40 per cent from those reported in this paper. In equations (2) and (4) it is seen that such variations in ew can cause up to 20 per cent variation in S with large effects on the intercepts.

The equilibrium temperature which was obtained contrasts greatly with the spectroscopic values reported (6 through 11). Values exceeding 5000~ are often mentioned for rotational temperatures of excited OH. Several aspects of the latter research must be examined. Energy equi- partition can be assumed not to exist in the reaction zone where temperature and concentration gradients may be large. The data are indecisive on the degree of departure from equilibrium since they represent emitted radiation and hence excited levels. The concentration of species in excited energy states may be negligibly small, and their radiation misleading as to the indication of general departure from equilibrium in the flame and as to their role in the flame kinetics. Furthermore, much of the data represents the flame including together both the active gradient regions and the completed reaction region beyond. In the latter region the reported spectroscopic temperatures

may be entirely misleading as to the extent of equilibrium departure. One of the advantages of the low-pressure flame research has been that col- limation is possible in order to obtain sufficient space resolution of the flame radiation for resolving the behavior of species in different reaction zones. Still another important approach is to observe OH, for example, in absorption, obtaining thereby the ground-state temperature behavior which would be more crucial with regard to equilibria and kinetics. The close agreement of the temperature reported herein with the equilibrium value makes further check necessary.

B. Thermal conductivity

The slopes of the data in figure 6 represent It, the heat-transfer coefficient. The gas property upon which h depends primarily is the thermal conductivity kl. The platinum wire represents a heat-transfer situation with the gas temperature To as the "film" boundary condition and the wire temperature Tw approximately as the surface- boundary condition. As Tw is increased, k~ would necessarily increase, depending as it does on the temperature regions between the two bounds; using average values, one may estimate the increase [Fig. 30 of (1)] to be about 10 per cent. The data in figure 6 would thus show a trend concave downward. This is clearly not the case. At the longer mean free paths of lower pressures it is conceivable that the high-temperature boundary may be controlling (in slip-flow region the temperature of the gas does not extrapolate to the surface temperature because of mean-free-path effects), and this situation would tend to keep h constant.

The unexpected aspect of the data lies in the values obtained for kl , using equation (5). The values thus obtained from the curves in figure 6 spread within 10 per cent, and the average obtained for kl is 0.069 Btu/hr ft ~ • 4 per cent.

If the gas temperature is accepted, the gas composition is necessarily the equilibrium value; then the mol-fraction composition of the mixture is calculated (1) as CO2,0.161; CO, 0.0953; H20, 0.081; H~, 0.00743; O2, 0.455; O, 0.129; OH, 0.0505; H, 0.0254. The atomic and free-radical species contribute about 20 per cent of the total composition. Yet the value of kl obtained experimentally is actually within 5 per cent of the value estimated (1), based on complete neglect of the possible contributions of H, OH, and O. I t may be speculated that the surface collisions of these species are particularly ineffective in energy trans-


fer; in other words, they may have exceedingly low accommodation coefficients for temperatures about that of the flame and wire, whereas all of the other species accommodate well.

In any case the thermal-conductivity value reported herein suggests two possibilities, one of which is that all the species accommodate par- tially, with a coefficient less than unity. This partial accommodation would produce the observed decrease in kl through the lowering of h but is to be doubted since the order of the mean free path and the thermocouple data of reference 1 indicated that, for wires as small as 0.015 inch in diameter, h obeyed the high-pressure, heat- transfer equation, extrapolated to low Reynolds numbers. Such behavior requires an accommodation of unity for all species actually contributing to the convective transfer. The second possibility is the aforementioned speculation that the gas behaves, in so far as surface transfer of heat is concerned, as if the atomic species are relatively not present. Collisions of these species with the surface under the described conditions are to be considered as essentially resulting in specular re- flections.

Wise and Altman (17) in developing an expres- sion for the accommodation coefficient based on absolute-reaction-rate theory make an interpretation that is not inconsistent with the view which the present data suggest as the second possibility. These authors offer a mechanism that accommodation effectively takes place by separating incident homogeneous particles into two groups, one which collides and rebounds specularly, without energy exchange, and the other which, by virtue of pos- sessing the necessary energy to overcome the adsorption barrier, adsorbs on the surface and comes to complete equilibrium with the surface. The situation in regard to a multicomponent mixture is certainly more complex than that of a single-component gas, as any attempt to consider the process will show. It must be emphasized that the speculation concerning the accommodation of the atomic species is made without precise knowl- edge of the actual thermal transport coefficients at high temperatures. The magnitude of their potential thermal transport is, however, not felt to be overestimated and thus the speculation has reasonable basis.

C. Gradient region of reaction zone

The technique of this research was tried in the region of the reaction zone below the maximum

temperature in order to obtain information concerning To, h, and kl, as well as indication of chemical equilibrium. However, catalytic effects on the platinum surface were noted. For example, a platinum wire introduced from the cold upstream region would, after a brief time lag, suddenly show an almost discontinuous jump to a temperature corresponding to the maximum even though at a position well below the maximum temperature region. The earlier experiments (1) had observed this effect and also the fact that other materials, such as chromel and alumel, did not exhibit this behavior except under special circumstances.

Some preliminary tests were made with pure rhodium wire (melting point, 1966~ and indi- cations were obtained that rhodium may not exhibit catalysis in some instances where platinum does so in the gradient region. The course of some future experiments is to investigate rhodium as a resistance thermometer. A possible allotropy may be the stumbling block to its high-temperature resistance behavior. If rhodium should prove a reliable material for a resistance thermometer, it can, in addition, be investigated for emissivity, and flame studies can be carried out as high as 1900~ Extrapolations could then be made with greater confidence.

7. CONCLUSION

By means of platinum resistance thermometers the maximum temperature of an acetylene-oxygen flame at 4.3 mm Hg abs was found, by extrapolation, to be very close to the calculated equilibrium value of 2208~ The thermometric technique required a careful auxiliary measurement of the emissivity of the platinUm-wire surface.

The method, at present, can be used with precision only when catalysis on the wire surface is absent. Exploration of the gradient region of the reaction zone with platinum as a material is not recommended. However, theoretical considerations indicate that a semiquantitative investigation of surface catalytic effects can be made experimentally, and possibly some understanding can be obtained of the nature of surface-gas interactions in flame mixtures or other reacting mixtures in which the thermal transfer to the surface can be accurately studied.

The special form of the heat-balance equation deduced for the resistance thermometer under the conditions of these experiments is found to contan the local heat-transfer coefficient h from the flame to the wire surface as the slope of the equation.


A value was obtained for h from the data for several wires, and an average was derived for the thermal conductivity ks in the flame film around the wire. A value of 0.069 Btu/hr ft ~ + 4 per cent was deduced for kf. This value of kf, representing the thermal-conductivity coefficient to a surface from a dissociated flame mixture, suggest unexpected but not unreasonable behavior possibilities for the components of the flame mixture. A possibility is a small accomodation coefficient for H, O, and OH at the platinum surface, whereas the other species accommodate more or less fully.

When carefully used, the method is promising for further study of the gradient region of the reaction zone of the flame if materials suitable in regard to their emissive, catalytic, and temperature-resistance properties are used.

ACKNOWLEDGMENT

The authors are happy to acknowledge some provocative discussion with Professor H. S. Tsien, of the California Institute of Technology, in stimulating this research. Valuable discussions with Dr. David Altman, Dr. S. S. Penner, and Mr. Leo Davis, all of the Jet Propulsion Labora- tory, contributed to the theoretical and experimental aspects of the research.

REFERENCES

1. GILBERT, M.: Report No. 4-54. Pasadena: Jet Propulsion Laboratory, August 30, 1949.

2. KLAUKENS, H., AND WOLI~'fIARD, H. G.: Proc. Roy. Soc. (London), A193, 512-524 (1948).

3. GILBERT, M.: Memorandum No. 4-51. Pasadena: Jet Propulsion Laboratory, July 6, 1949.

4. HIRSCRFELDER, J. 0., BIRD, R. B., AND SPOTZ, E. L.: Chem. Rev., 44, 205-231 (1949).

5. SCH~IDT, H.: Annal. Phys., 29, 971-1028 (1909). 6. GAYDON, A. G., AND WOLFHAm), H. G. : Proc. Roy.

Soc. (London), A194, 169-184 (1948). 7. GAYDON, A. G., AND WOLrHAm), H. G.: Proc. Roy.

Soc. (London), A199, 89-104 (1949). 8. GAYnON, A. G., AND WoLFnARD, H. G.: Proc. Roy.

Soc. (London), A201, 561-569, 570-586 (1950). 9. GAYDON, A. G., AND WOLFHARD, H. G.: Proc. Roy.

Soc. (London), A208, 63-75 (1951). t0. PENNER, S. S., GILBERT, M., AND WEBER, D.:

J. Chem. Phys., 20, 522 March (1952). 1l. BROIDA, H. P.: J. Chem. Phys., 19, 1383-1391

(1951). 12. MCADAMS, W. H.: Heat Transmission, 2nd ed.

New York, McGraw-Hill Book Company (1942). 13. GLASSTO~q~, S., LA1DLER, R. J., AND EYING, H.:

The Theory of Rate Processes, 1st ed. New York, McGraw-Hill Book Company (1941).

14. Vim~s, R. F.: The Platinum Metals and Their Alloys. New York, International Nickel Com- pany (194l).

15. American Institute of Physics: Temperature, Its Measurement and Control in Science and In- dustry. New York, Reinhold Publishing Com- pany (1941).

16. KENIqARD, E. H.: Kinetic Theory of Gases, 1st ed. New York, McGraw-Hill Book Company (1938).

17. WisE, H., AND ALTMAN, D.: The Interaction of Gases with Solid Surfaces, a Theoretical Analysis of the Thermal Accommodation Coefficient, Memorandum No. 9-18. Pasadena: Jet Pro- pulsion Laboratory, June 2, 1950.

18. DEVONSItlRE, A. F.: Proc. Roy.. Soc. (London), A158, 269-279 (1937).

34

A METHOD OF ANALYSIS OF A PLANE COMBUSTION WAVE

By .l .H. BURGOYNE AND F. WEINBERG

The question of the mechanism of flame propa- gation in gases has received a great deal of theoretical consideration, which has resulted in equations, or systems of equations, aiming to represent the processes causing the gases to react under the influence of the adjacent combustion zone.

Various factors have been thought of as being

the most important in this process of initiation; thus, while the earlier theories postulated a purely thermal mechanism, subsequent workers thought that the initiation by diffusing active radicals or even by quanta of radiation (1) might be of major importance. Some attempts have also been made at forming general theories including all possible

resistance-thermometer measurements in'a low-pressure flame

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