1024
D. L. HILDENBRAND AND A. GREENVILLE WHITTAKER
the C;c clny-amine salt reaction shows negative heat i d t i e , (- 1.22 cnl.) indicating that coiisidernble energy is used up in replacing the Ca ion on the c h y by an amine ion. When the amine hydrochloride reacts with a clay it is concei\*able that the process is primarily ai1 eschange. Ho\ve-\.er, t,he interaction of an amine with a clay iiitroduces the possibility of adsorption of the amine to the CILZJ~without appreciable eschange. The resulting differelices in the energy chaiiges of these two processes are reflec,ted in the data obser\.ed nbo\.e. The 4.82 cnl. per g. of H-clay, relensed when immersed in butylamine, are equivalent to 7300 c d . per mole of hydrogen ion on the H111 contrast
:L
Vol. 59
clay. This arnouiit of heat is esseiitially the heat of neutralization between the amine ant1 the H-clay. I n an earlier study8 an entirely differeiit method gave 0,400 cal. for the heat of neutralization of a similar H-clay by NaOH. In addition to exchange aiid ntlsorpt'ioii, there are other factow which undoubtedly contribute to the heats of reaction-the dissocintioii of the exchangeable ion from the clay, the desol\ration of the amiiie and amiiie ion upoii reacting \vit,h the clay surfsces, niid the orientation of the hydrocnrboii cliaiu of the amine 011 the clay surface. ( 8 ) W. 1%. Slabaugli, J . A m . Chem. SOC.,74, 4402 (1082).
BUILNIN G RATE STUDIES. 11. VAKIXTION OF TERrIPElIA'L'UKE DISTRIBUTION WITH CONSUMPTION RATE FOE BURNING LIQUID SYSTEMS BY D. L. HILDENBRAND A N D A. GREENVILLE WHITTAKER C'hemist,y Division, U.8. Naval Ordnance Test Slation, In yokern, China Lake, Califomia Received April 6, 1066
Tlie thermocouple method has been used on several burning liquid systems to study variations in the teitipernture distribution brought about by changing the consumption rate. Data are presented showing the effect on surface and mauiinuiii gas temperatures and the results are discussed with respect to their possible significance. A thermal model for the coinbustion process appears to be compatible with the data and, in particular, a radiation and conduction tnotlel cnn be used to describe all or part of the temperature distribution in the condensed phase. funiiiig nitric acid atid conccnt,rnt,rcl sulfuric acid at, n pressuw of less than 2 millimeters of inei'cury. The rwultirig acid was analyzed and t,hen diluted to D5mo with distilled water. This ncid contained less than 0.1% nitrogen dioside. Enstinan Kotlak Go. white-lalwl ethyl n i t r a k \vas used without fwthei. purification. The purity of the metriol triiiitrate-t,i,incetiii mixture was nhout the s:me as that of the ethyl nitrate. Apparatus.-The nppnrstup used i n this study has hecn descrihed previously .I In nddi tion, several ot,her types of yecording instruments were used for t,eniperature mertsureniciit where possiljlr. A Snnlmm recording oscillograph WILS used at, low and iiiternietliate hurning i,:ttes, and a Leeds nud Nortjhrul:, Hpeedomiix tmortler wns used a t estreincly low rates in order to c,tiecli the cathode r;ty osc,il!osc,ope nieasui,ements. These two nddi tional i i i n t runient8s did not, have sufficient frequency response t o reproduce faithfully the clet8niled shape of t#hetemperature-time curve in most Experimental cases, but a compnrisbn of some of the teniprmture lcvels was possible. A comparison of the results from the t,hree Materials.-Two types of conihustihle liquids were in- different instruinent,s gave excellent agreement with respect vestigated. One consisted of the homogeneous binary sys- t o surface tempernture. .I11 of these nieasurement9 were tem 2-nitropropane-05% nitric ncid in which the oxidizer made with 7.5 p diameter platinum, platinum-lO% i,hoand fuel were in different molecules. T h e other type con- diuin t,hermocouples niounted in 3.7 min. inside-dinnieter sisted of ethyl nitrnt,e, and an 82y0 metria1 trinitrate (i.. ., closed-end Pyres tubes from which a temperature profilc methyltrimetliylolmct,haiie trinit,rate)- I 8 06 triacet,iii (i.e., \vas o1)tainetl as t,hc mnibustioii wave passed over tho glycerol triacet)ate)mixture in which the fuel itnd all the availThe iiiitinl teinperature of the liquid W:LS able oxygen wei'e in the same niolccule. These compounds 2thermocouple 5 " . The tcsult,iiig tempernture record is called the forwere of varying degrees of purity. The 2-nitropropane wtlrtl profile. A nioditied liquid holder was built 1rtt.w was prepared by disti1lat)ion of comnlercinl grade material, so that nfter the fot,\vai,d profile hntl heen recorded as aiid only the center fraction W ~ used. P This fraction had ail described above, the opening of a liquid filled reservoir index of refract,ion of 13950 at 20" using the sodium-D lines. conitected to the combustion t,ube nllovrd the burniug T h e literature value is given as 1.3041.3 Nitric acid was liquid to flow back u p the tube, again p:tssing over the prepared by distillation of a 50-50 mixture of C.P. white t,hermocouple, t,o give what is called a I'everse profile. This reverse profile gives the temperature record corre(1) D. L. Hildenhrand, A . 0.Whittnkev and C. B. Euntott, T I I I R sponding t,o stjartiny the theimocouple in t81ie ga.s phttse J O U R N A L .68, 1130 (1Y51). atJOVe t,lir: liquid nnd ending in the liquid phase tit) rooni (2) "Consumption rate" denotes tlie uhual itieaaured riuantity, teinlwnlure.
Introduction Previously a method was developed for obtaiiiiiig a reproducible arid reasonably accurate measurement of the temperature distribution i i i the coiideused phase of a liquid system burning in ai1 inert atm0sphere.l The method has beeii used to study the variation in temperature distribution as the result of changing consumpt,ion rate.2 Of principal interest were variations iii liquid surface temperature and maximum gas phase temperature, results for which w e reported liereiii. I t is hoped tjhat work of this type will help lead to an elucidation of the pi'ocesses involved in liquid combustion.
L e . . the linear rate of regression of the surface uncorrected f o r deviation of t h e shape of t h e liquid-gas interface from a plane surface. (3) "Handbook of Chemistry a n d Physics," Cliernical Rubber PuIIlisliinrr Co., 33rd Edition, p. 1077.
Results and Discussion At tlie outset it may lie well to make a statement
Oct., 1065
CONSUMPTION
RATEFOR BURNING LIQUIDSYSTEMS
regarding .the validity of thermocouple measurements in the condensed phase since several investigators have challenged the usefulness of thermocouples on the basis of very steep calculated temperature gradients. I n the cases of which the authors are aware, e.g., the work of Olds and Shook,4 the gradients were calculated for substances burning a t rates some 5 to 20 times higher than those investigated in this research and since the depth of the heated zone in the condensed phase decreases with increasing burning rate for a thermal model, it is not unreasonable to expect these steeper gradients a t the higher rates. It is not intended to imply that all problems related t o frequency response of thermocouples are necessarily eliminated by obtaining profiles a t these lower rates, but rather that, because of the strong dependence of temperature gradient 011 rate and because of the physical dimensions of tho smallest available thermocouple wire, the thermocouple method is mainly useful a t relatively low rates of burning. Actually the experimental records showed that the temperature differences across the thermocouple was usually about 3 or 4 degrees in the steepest portion of the liquid phase rise and never exceeded 15 degrees a t the highest rates studied. As will be pointed out, the experimental liquid phase profiles obtained are in good agreement with those calculated for a simple radiation arid conduction model. A representative forward and rei'erse temperature-time record obtained with the modified liquid holder is shown in Fig. 1. The reverse record does not show the plateau observed in the forward profile but does show the same smoot'h expoiieiitinl variation of temperature with distance in the liquid phase, thus serving to show that the plateau is indeed caused by surface tension effects. Illoreover, it is evident that because of these surface tension effects, the forward record misses a most iiiterest,iiig part of the profile, i.e., the very rapid temperature rise in the gas phase adjacent to the surface shonw in the reverse record a i d iidicated by the arrow in Fig. 1. Because of the extremely large t,empernture gradieiit there (approximately 70,000 degrees per centimeter for the record in Fig. 1) a study of that part of the profile is esceediiigly difficult. Indications are that important rapid gtts phase reactions are taking place in this very narrow regioii close to the wrface. Variation of Surface Temperature with Pressure. -The variation of surface temperature with bomb pressure for the system metriol trinitrate (82%)triacetin waa determined over the pressure range 34.9 to 100.3 atm. Results obtained from the experimental profiles are shown in Table I. It is clear that surface temperature was constant a t 290 h 10". A similar set of data was obtained for the system 2-nitropropane-85~~ nitric acid over the pressure range 14.5 to 62.2 atm. Surface temperature appeared to remain constaiit a t about 180 f 15" and showed n o consistent trend. Because of a great deal of sub-surfnce rnndom motmion01' turbulence, profiles olitained on this *\.stern \mime somewhat erratic, resiiltiiig in a 1:trger spread of the, (4) R. H. Oldti a n d G . B. Sliook, Presented at tile 1!139 Sutiiiiier RIecting of t h e .4merican Pliysical Society, Denvcr Colo. Sce also Phus. Reu., 88, llj0 (1082).
1025
Q
0
0 5
I 5
TIME
2 5
SEC
Fig. 1.-Forward nnd reverse profile for material trillitrate (82%)-triacetin, 54.4 atin.
data. For ethyl nitrate the variation of surface temperature with pressure was studied over the range from 1 to (32.2 atm. with the results shown in Table 11. The uncertainty of the temperature measurements was less than *5" in the low pressure range atid increased to about = t l O " a t the higher pressures. The data show that surface temperature increases fairly rapidly with pressure up to about 14.5 atm. Above this pressure surface temperature increases much more slowly. It was of interest in this connection to compare surface temperature and boiling point as a function of pressure. Since no vapor pressure data on ethyl nitrate covering this pressure range were available in the literature, these measurements were carried out as a part of the study. The vapor pressure measurements were made in a special apparatus, with conditions similar to those under which the liquid was burned and were made rapidly enough t o minimize the effects of thermal decomposition. Details of the measurements mill be described in a separate article. TABLE I CONSUMPTION RATE,SURFACE TEMPERATURE AND MAXIMUM GASTEMPERATURE FOR THE SYSTEM METRIOLTRINITRATE (82 . %)-TRIACETIN . Bomb pressure
Consumption rate, cin./sec.
Surface temp.,
M a x . gas
atm.
OC.
teiiip., QC.
34.9 48.6 62.2 75.8 89.4 100.3
0.146 .198 .244 ,305 .350 ,398
290 280 290 280 290 300
1G30 1610 1620 1630 1GlO 1610
TABLE I1 CONSUMPTION RATE,SURFACE TEMPERATURE A N D RS~x~firunr GASTEMPERATURE FOR ETHYLNITRATE Bomb pressure atm.
Consumption rate on,./seo.
0.92 2.0 3.0 4.3 7.7 14.5 21.3 34.9 48.6 62.2
... ... 0.020 ,028 .052 .I22 .I78 .279 ,378 ,429
Surface tolnp.,
OC.
70
83 94 105 120 140 145 149 155 1 G5
M a x . gas t e;n p , C.
.
... ... 940 980 I050 1090 1230 1590 1G10 1G-10
The vapor preisure mid surfnco temperature data are plotted in Fig. 2 as log absolute pressure us. reciprocal absolute temperature. It caii be
GHEENVILLE WHITTA4KEll
VOl. 59
teiid to hold the surface temperature constant in spite of the fact that heat transfer t o the liquid may increase as pressure rises. I n order that this interpretatioir be valid, reaction (1) must occur in the liquid, and the reaction products must be immediately evaporated into the vapor phase where they can continue to react exothermically in accordance with mechanisms proposed by other investigators.5 Thus reaction ( I ) could be the primary factor controlling surface temperature ill this region. Accepting the value of -8.0 kcal. per mole for the standard heat of formamtionof the ethoxy radical,6 8.1 and -3B.G kcal. per mole as heats of formation of nitrogen dioxide7 and ethyl nit,rate,* respect'ively, reaction (1) is endothermic by 36.7 kcal. in the vapor phase. To convert this to liquid phase lieat of reaction, values for the heat of vaporization of 9.1 and 8.2 kcnl. were used for nitrogen dioxide9 and ethyl nitrate3 and 9.0 kcal. was assumed for the ethoxy radical. This gives a heat of reaction of 27.7 kcal. for reaction (1) in the liquid phase. From kinetic measurements, Levysc has obtained a lieat 0.6 of reaction of 41.2 kcal. for reaction (1) in the gas phase which leads to a liquid phase AH of 32.3 kcal. 0.4 using the heats of vaporization given above. Since the reverse of reaction (1) is a remtion between radicals it is probalile that its activation energy is small, 0.2 hence the heat of reaction for equation 1 is approximately equal to the activation energy of this reaction. Consequently, the agreement of this energy value and the 30 kcal. obtained from the surface 2.0 2.2 2.4 2.6 2.8 2 temperature data in the upper region of consumpW T ) x 103. tion rates may not be purely accidental. From the Fig. 2.--Cloinpn~i~isoi~of burning surface temperature with boiling point of ethyl iiit,rate: 0, boiling point; a, surface slope of the profile near the surface and surface temperature data it can be shown that reaction ( I ) temperature; 0 , boiling point a t 1 ntm., literature value. would occur in a region about 20 p below the liquid seen that in the region helow 14.5 atm. tthe two surface. This estimate was based on the assumpcurves are iiearly parallel. Since the slope of the tion that reaction (1) was not tippreciable below surface t,emperative curve iii this region corre- 140°. sponds to a heat effect, of approsimately 10.5 kcal. I f the above hypotheses are cori)ect it appears per mole, it appears that surface temperature may that ethyl nitrate can undergo sustsined combusbe controlled hy an evaporation process. However, tion with a simple evaporation type mechanism, and from t.he data shoivn in Fig. 2, it is evident that it is unlikely that the suggested liquid phase reacthe surface temperatuie is well below the thermo- tioii is essential. This does not mean that the evapdynamic boiling point a t any given pressure as oration process ~ o u l dbe a slo-w step in the commight be expected in a non-equilibrium type proc- bustion mechanism. A simple kinetic theory caless in which the mat,erial is consumed as soon as it culation iudicat,es that evaporatioii itself is sevei'al eiiters the gas phase. I n the region above 14.5 orders of magnitude more rapid than observed rates atm. the situation appears to be different,. At) of burning, so that the speed of vapo~izat~ion is most least up to 48.G atjm.surface temperature increased likely dependent on the rate of heat transfer to the much more slowly with pressure than it did below liquid. I n the case of the other two liquid systems 14.5 atm. If log consumption rate (data in Table it \vas not possible to produce sustained IT) is plotted against log of the reciprocal of the studied, combustion a t pressures corresponding to the evapabsolute surface temperature, a curve similar to the oration region of ethyl nitrate. Sustained comhusone shown in Fig. 2 results. The slope of this curve tioii was obtained only in the region of constant or in the region covering the 14.5 to 48.6 atm. range nea,rly constant surface temperntiire. Heiice it W R S was fouiid to give an endothermic lieat effect of tentatively concluded that for these systems liqnid about 30 kcal. per mole. It was observed during phase reactlions tire essentid to tJhe combustioil initial attempts to measure the vapor pressure of process. I n addition to ally changes in surface ethyl nitrate that thermal decomposition became ( 5 ) (a) G. K. Adains a n d C. E. H. B a w ~ i ,T,,ans. Faradnu S o c . . 4 6 , easily detectable a t ahout 140", and since surface (1049); (b) L. Phillips, Nature, 166, 564 (19,501; ( 0 ) J. B. Levy, temperature just, begins to exceed t,liis value a t 4R4 J. Am. Chem. S o c . , 76, 3254 (1954): 76, 37110 (1054). pressures ab0r.e 14.Fi n,tm. it was possilde that, the (G) P. Gray, Fifth Symposium (Internntionnl) o n Coiiibustion, reaction Paper No. 39.
CeHSONO? +CnHjO
+ NO2
(1)
came into play a t this point. Because this mode of decomposition is endothermic reaction (1) would
(7) N a t . Bur. Standards Circular No. J O O , "Clieinicnl Tlierinodynamic Properties." 1950. (8) P. Gray a n d P. L. Siriitli, J . Chcin. S u c . . 7lXJ (I!l64), (9) W, F. Giauque and J. L). Iiciii]), J . C ' l i c m . Phgs., 6 , 10 (1938).
the maximum flame temperature of the metriol trinitrate system are greater than the corresponding values for ethyl nitrate when compared a t 34.0 at,m. Yet the coiisuniption rate of ethyl nitrate is greater by a factor of two. There are other instances of such behavior. The reason for this may be that surface temperature and maximum flame temperature are only two points on the profile a ' i d they alone do not uniquely define the temperature distribution. Consequently no ralid general statenieiit can be made concerning the effect of flamc temperature on the consumption rate. A similar conclusion relating to solid powders has been reached by Crawford and co-workers. I1 The relatii-ely weak influence of maximum ga,s temperature upon consumption ratje niay be further sho\vii on esamining the data of Table I1 giving t'he variation of these quantities with boml) pressure n8s measured for ethyl nitrate. The wide variations i i i gas temperature, especially near the point a t which a luminous flame appears, are in 110 way reflected on consumption rate since the latter is a smooth 1.80 x 103 = -function of pressure over this regioii with no inflecP1.81 tion points. This rela,tive indifference of consumpwhere X is the distance in millimeters and P is the tion rate to the behavior of the final gas temperature absolute pressure in at.mospheres. It thus appears is further eridence that the rate of burning is inthat the gas pha,se temperature gradients are fluenced much more strongly by reactions occurriiig strongly pressure dependent. This behavior is com- very close to the liquid surface, particularly those patible with the observed increases in coiisumpt'ioii responsible for the rapid initial gas phase temperarate a t essentially constaiit maximum gas tempera- ture rise. ture, since the rate of heat transfer to the conTheoretical Considerations.-Quite a number of densed phase is regulated by these changing gradi- tlieoretical treatments have been proposed to ents. describe the combustion of solids or liquids and all For ethyl nitrate, the measured maximum gas could be examined in detail with respect to their phase temperature (Table 11) increa,ses almost lin- compatibility with the results obtained in this early from about 040" a t 3.0 atm. to about 1280" a t study. By way of illust'ration only two sucli 24.7 atm., :followed by a sharp rise l)o about 1G00" treat8nientswill lie considered briefly. Rice and a t 35 atm. There is no further significant rise in Ginel112 proposed that inass lourning rate is conmasimum temperature above 35 ntin. The meas- trolled by tlie surface temperature acc,ording to the ured gas temperatures are in good agreement with following Arrhenius type re1at'ion calculated temperatures based on the distribut,ion AI = A (exp) - AE/RT. (2) of products observed in ethyl iiitrate deconiposit'ion flames. lo Combustion in the low pressure region, where is the mass burning rate, A a frequency where the nitrate ester buriis without a luminous factor, AE the actil*atioiienergy of the rate controllflame is characterized by t#lie formation of rela- ing step a t the surface, Ts surface temperature and tively large amounts of nitric oside and methane. R the gas constant. For the systems that show no The sharp rise t'o a masimum tempemture of 1600" change in surface temperature with consumption is accompanied 1)s' the appearance of a 1irightJy rate, equation 2 is obviously of no value. In the luminous flame and tjhe disappenraiice of CH, ant1 case of ethyl nitrate, equation 2 can be applied, but, NO in favor of CO and Nz. In this case the dis- it must be carried out separately for the two regions tance from ;surface to maximum t'emperat'ure can be of different activation energy, if it is assumed that expressed :is the activation energies given above are the ones to 9.30 x 103 be used in equation 2 . In the region below 14.5 s = p2.12 atm. the frequency factor A turns out to be of the, No gas phase temperatures were ol)taiiied for tlie order l O I 3 per see. when the dimensions of conceiinitropropane-nitric acid syst'em siiice t'lie flanie tratioii are removed. This value is riot unreasontemperature far esceedetl the meltiiig poiiit of the able but seems to indicate that each time a surface platilium thermocouples. molecule imdergoes collisioii it leaves the surface The concept that consumption ra,te is approxi- and enters the vapor phase. However, in the region mately linearly related to heat of esplosion or mmi- above 14.5 atm. the frequency factor has a value mum flame temperature is often encountered. This of about l o g 2which seenis unreasonably high. As relation is probably true if a sufficientJly narrow n result, equation 2 does not appear t o be compatifield of related substances is considered. However, ble with the data of any of the systems studied. 011 itJ is iiot generallj. true, as is shown by the data in the other hand, the simple radintioii-conductioti Tables I and 11. Both the surface teinperature aiicl (11) B. L. Crawford, Jr., C. Huggett a n d J. J. AIcBmda, THIS temperature, all three systems showed a progressive decrease in the liquid preheat zone thickness with increasing pressure. For example, in the ethyl nitrate case the thickness varied from rouglily 350 p a t the lower pressures to about 200 p a t the highest pressures studied. Although the data point out some interesting possibilities, tlie mtliors are reluctant to attach too much significance to surfa,ce temperatures per se and feel that in any comprehensive treatment of the combustlion process, the entire temperature distribution must be esamined in detail. Variation of Maximum Gas Temperature with Pressure.--Table I gives the measured maximum gas temperatures for the metriol trinitrate system. Over the range studied, there is no apparent trend and the temperature is constant a t about 1620 =t 10". An analysis of the data lins shown, however, that the distance from liquid surfnce tfo maximum temperature varies smoothly and can be accurately represented by the relation
(10) C . K. Aclains. W. 0 . P a r k e r a n d I l . G. Wolfhard. Discs. F a m No. 14, 97 (1983).
dav Soc.,
,JOI'RNAL, 6 4 , 854 (1450). (12) 0. I
