DietrichR,ossT,'ienandShu CandlFelames Page1 CANDLE FLAMES IN NON-BUOYANT ATMOSPHERES (Shortened Title: CANDLE FLAMES) D. L. Dietrich* and H. D. Ross NASA Lewis Research Center, Cleveland, Ohio Y. Shu _ and J. S. T'ien Case Westem Reserve University, Cleveland, Ohio # Currently with Diesel Cummings, Columbus, Indiana. * Please address all correspondence to: Daniel L. Dietrich Mail Stop 110-3 NASA Lewis Research Center 21000 Brookpark Road Cleveland, Ohio 44135 Phone: (216) 433-8759 FAX: (216) 433-3793 e-mail: [email protected] Dietrich, Ross, T'ien and Shu Candle Flames Page 2 This paper addresses the behavior of a candle flame in a long-duration, quiescent microgravity environment both on the space Shuttle and the Mir Orbiting Station (OS). On the Shuttle, the flames became dim blue after an initial transient where there was significant yellow (presumably soot) in the flame. The flame lifetimes were typically less than 60 seconds. The safety-mandated candlebox that contained the candle flame inhibited oxygen transport to the flame and thus limited the flame lifetime. The flames on the Mir OS were similar, except that the yellow luminosity persisted longer into the flame lifetime because of a higher initial oxygen concentration. The Mir flames burned for as long as 45 minutes. The difference in the flame lifetime between the Shuttle and Mir flames was primarily the re- designed candlebox that did not inhibit oxygen transport to the flame. In both environments, the flame intensity and the height-to-width ratio gradually decreased as the ambient oxygen content in the sealed chamber slowly decreased. Both sets of experiments showed spontaneous, axisymmetric flame oscillations just prior to extinction. The paper also presents a numerical model of candle flame. The model is detailed in the gas-phase, but uses a simplified liquid/wick phase. The model predicts a steady flame with a shape and size quantitatively similar to the Shuttle and Mir flames. The model also predicts pre-extinction flame oscillations if the decrease in ambient oxygen is small enough. INTRODUCTION The behavior of a candle flame is the most common public inquiry about combustion in the absence of gravity. This is primarily because the candle flame is so familiar to everyone. From a fundamental perspective the candle flame is a complex combustion system. The fuel is a mixture of long chain- hydrocarbon molecules with complicated oxidation chemistry. The flame interacts with a porous wick, with intricate heat and mass transfer. Despite these complexities, candles offer such simplicity in experimental setup that they are used often to study a wide range of combustion phenomena such as flame flicker Dietrich, Ross, T'ien and Shu Candle Flames Page 3 (Buckmaster and Peters, 1986), spontaneous, near-extinction flame oscillations (Chan and T'ien, 1978), low-gravity smoke production (Urban et al., 1996), effects of electric fields (Carleton and Weinberg, 1989), elevated gravity (Villermaux and Durox, 1992), and magnetic fields (Lawton and Weinberg, 1969 ). The candle flame in microgravity is uniquely stationary where, excepting Stefan flow, diffusion is the only trasport mechanism for fuel and oxygen to the flame and combustion products away from the flame. Both Carleton and Weinberg (1989) and Ross and co- workers (Ross et al., 1991a,b; Dietrich et al., 1994) studied the effects of reduced gravity on candle flames in both aircraft and drop tower facilities. The reduced gravity airplane tests typically produce fluctuating flames due to g-jitter, but on occasion show, consistent with drop tower studies, a nearly hemi-spherical flame. These tests, however, could not study the characteristics of the candle flame in a long-duration microgravity environment. We were interested in how long the candle flame could exist in the absence of gravity. We were also interested in the extinction behavior of the candle flame burning in a large sealed chamber in microgravity. We used the candle flame as the model diffusion flame and present the results of two sets of long-duration, quiescent, microgravity experiments. The first experiment flew aboard the Shuttle on the STS-50 (USML-1) mission in 1992. The second flight was on the Mir Orbiting Station (Mir OS) in 1995. This paper presents the results of the experiments and compares the results of the experiments to the predictions of a numerical model of the candle flame. EXPERIMENTAL HARDWARE Figures 1 and 2 show the hardware for the Shuttle and Mir experiments, respectively. The Shuttle hardware consisted of a perforated candlebox (11.5 cm on a side) made of a 0.95 cm thick polycarbonate, and a Separate, manually operated igniter. The box, required by safety engineers, permitted fresh oxidizer to reach the candle but preempted the possibility of a crew-worn glove or other surrounding material from accidentally igniting. The ignition system was a loop of 250 gm aluminum alloy wire heated with a current of approximately 3 Dietrich, Ross, T'ien and Shu Candle Flames Page 4 amperes. The crew manually ignited the candle and removed the hot-wire after ignition. The Shuttle's pressure and oxygen mole fraction were 1 atm and 0.217 at the time of each experiment. The hardware was different for the second set of experiments on the Mir OS. The container was a 20 cm cube-shaped wire mesh screen as opposed to the perforated polycarbonate. The screen provided more than 50% free area (as opposed to less than 15% on the Shuttle experiment) yielding significantly less resistance for oxygen to diffuse to the flame and combustion products to diffuse away from the flame I. The ignition system was the same for the Mir experiments except that the igniter was automatically retracted after a preset ignition time (4-5 seconds for almost all tests), rendering the ignition a more repeatable process. The Mir operated at atmospheric pressure with an ambient oxygen mole fraction between 0.22 and 0.25. The crew operated the experiments inside a glovebox facility. This facility provided a working volume (25 1on the Shuttle and 44 1on the Mir OS), video cameras and recording capabilities. The data from the Shuttle experiments were primarily video recordings from orthogonally located black and white video cameras and a few still color photographs. The primary data in the Mir experiments were audio recordings of crew observations and color photographs of the flame from a 35 mm SLR camera. The color video cameras in the Mir glovebox facility lacked the low-light sensitivity necessary to image the flames. In some of the Mir tests, the crew turned on the lights in the glovebox at various times to allow video observation of the liquefied wax. The composition of the candle for both experiments was 80 percent (by weight) of an n-parrafin wax (typically C19-C35 hydrocarbon) with 20 percent stearic acid (C18H3602) to impart toughness. The Shuttle experiments used 7 identical candies (approximately 2 mm wick diameter, 5 mm candle diameter, 12 mm candle length, and 3 1 The changes in the design were possible because the safety of the experiment was demonstrated on the Shuttle experiment. Dietrich, Ross, T'ien and Shu Candle Flames Page 5 mm initial exposed wick length). There were 79 total candles supplied with the hardware in the Mir experiments with three different wick diameters (approximately 1, 2 and 3 mm), two different candle diameters (5 and 10 mm) and two different lengths of initially exposed wick (3 and 6 mm) in the Mir experiments. All candles in the Mir tests were 2 cm in length (from the base of the solid wax to the tip of the wick). A 3-axis accelerometer sampling at 125 Hz for the Shuttle experiments and 25 Hz for the Mir experiments was mounted underneath the floor of the glovebox working volume. Measured accelerations in both spacecraft were below 10.5go (go being the accleration due to gravity at sea level) at frequencies below a few Hz, rendering effects of residual gravity and g-jitter unimportant in these tests. EXPERIMENTAL OBSERVATIONS Immediately after ignition, the candle flame in the Shuttle tests was spherical and bright yellow. After 8-10 seconds, the yellow, presumably from soot, disappeared, and the flame became blue and hemispherical with a diameter of approximately 1.5 cm (Figure 3(a)). These behaviors are consistent with the earlier, short-duration microgravity studies in aircraft (Carleton and Weinberg, 1989) and the NASA Lewis Research Center 5.2 second drop tower experiments (Ross et al., 1991a). After the ignition transient, the flame luminosity decreased continuously until extinction. For the Mir experiments the flames were luminous and spherical immediately after ignition, resembling the Shuttle flames. Unlike on the Shuttle, however, the yellow luminosity often lasted for minutes into the flame lifetime. This was due to the increased oxygen concentration in the Mir OS. The entire mass of wax melted (but did not drip) within two minutes of ignition for the 5 mm diameter candles and within five minutes of ignition for the 10 mm diameter candles. The candle flame then looked as in Figure 3(b). Small bubbles, presumably from air that had been trapped inside the wick, circulated inside the liquid wax. This motion was the result of surface tension gradients (temperature gradients) along the surface of the liquid. At some point, this molten ball of wax suddenly DietrichR,ossT,'ienandShu CandlFelames Page6 becameunstablec,ollapsedandmovedbackalongthecandleholderasinFigure3(c).The flamechangedonlyslowlythenuntilextinction. FortheShuttletests,extinctiontypicallyoccurredbetween40and60seconds, exceptoneflamethathadalifetimeof 105seconds.All ofthecandlesintheMir tests burnedlongerthantheShuttlecandlesT.heflamelifetimesvariedfromover100seconds toover45minutes.FortheMir tests,thecandleswiththelargestwickdiameterstypically hadtheshortesftlamelifetimesandthecandleswiththesmalleswt ickdiameterstypically hadthelargest. IntheMir experimentst,hecrewswitchedthelightsinthegloveboxonafterflame extinction,andawhite,sphericaclloudwithadiameter2-3timesthatofthecandleflame waspresent(Figure3(d)). Thiscloudisprobablyamistofcondensedwaxdroplets(and possiblywaterdroplets)thatformedwhilewaxcontinuedtovaporizeaftertheflame extinguished. EachcandleflameontheShuttleoscillatedspontaneousliynthefinal5seconds. Theflametracedsymmetricallybackandforthalongthecandleaxisineachcycle(Figure 4). Thetopoftheflamedidnotmoveduringtheoscillation.Thebaseoftheflame retreatedandflashedbackwithafrequencyofabout1Hzwithanamplitudethatstarted smallandgrewuntilextinction. NooscillationsoccurredinanyMir testswiththesmallest wickdiameter,whichwassmallerthanthewicksusedintheShuttleexperiments.The flamesintheMir testswiththetwolargerwickdiametersh,owever,didoscillatebefore extinction.TheoscillationfrequencywassimilartothatintheShuttleexperimentso,nly foramuchlongerperiodoftime,upto90seconds. AnalysisofthevideorecordingsfortheShuttleexperimentsandthe35mm photographsfortheMir experimentsyieldedboththeflamediameter,D(maximumvisible flamedimensionperpendiculatrothecandleaxis),andheight,H (maximumvisibleflame dimensionparalleltothewick),asfunctionsoftime(seedefinitionofHandD inFig.7). FortheShuttleexperimentst,herewasnoconsistentbehavioroftheflameswithrespectto DietrichR,ossT,'ienandShu CandlFelames Page7 HandD. Theflamediameterandheightsometimesincreasedwithtimeandsometimes decreasewdithtime.Thiswasduetovariationsin theignitionprocedureandintheinitial ambientenvironmentinthecandlebox.Figure5showsDandH asafunctionoftimefor thethreedifferentwicksizesintheMir experimentsT. heflamediameterandheightinthe Mir experimentsalwaysstartedsmallandincreasedwithtime.Thisconsistencywasthe resultofamorerepeatableignitionmethod.Theflamegrowthforthefirst50-75seconds forallofthecandlesinFigure5correspondtsothetimeforthesolidwaxtomelt.Around this time, the liquid wax collapsed (Figures 3c and 3d), and afterward the flame size changed only slowly, if at all, with time. Additionally, Figure 5 shows that the larger the wick size, the larger the quasi-steady flame size, as expected. For both the Shuttle and Mir experiments, the ratio IadD always decreased slightly with time (over the flame lifetime) and was quite repeatable from test to test. Figure 6 shows H/D as a function of time for a Shuttle test and two Mir tests. The candle diameter for each test in Figure 6 was 5 mm. One of the Mir tests in Figure 6 had the same wick (approximately 2 mm diameter) as the Shuttle test, and the other had the smaller wick size (approximately 1 mm diameter). While the values of the flame size of the Mir experiments were consistent with the Shuttle, the value of H/D is somewhat higher for the Mir tests. This latter observation is probably be due to the increased ambient oxygen concentration in the Mir tests. For the Mir experiment with the larger wick diameter in Figure 6, H/D increased slightly for the first 75 seconds, then decreased until extinction. The change in behavior at 75 seconds corresponds to the collapse of the liquid wax. NUMERICAL MO1)I_L The numerical model of the candle flame is two-dimensional and axisymmetric in the gas-phase. While the model is relatively detailed in the gas-phase by considering finite- rate chemistry and radiative loss, the detailed heat and mass transfer processes occuring in the porous wick and solid wax are neglected. Specifically, we assume that the fuel Dietrich, Ross, T'ien and Shu Candle Flames Page 8 evaporates from a small porous sphere with constant radius, R, that is coated with a pure liquid fuel at its boiling temperature. This sphere is connected to an inert cone with a prescribed temperature distribution. The cone, which has a half angle of 23", acts as a heat sink to simulate the flame quenching aspect of the candle wick and wax 2. Figure 7 shows a schematic of the problem. The mathematical formulation utilizes a two-dimensional spherical coordinate system. The gas-phase model assumes: one-step, second-order overall Arrhenius reaction, constant specific heats and thermal conductivity, constant Lewis number for each species (although different species can have different, constant Lewis numbers), ideal gas behavior and no buoyant force. The last assumption allows a simplified treatment of the momentum equation (Baum, 1994). This includes the assumption of potential flow and the product (,_T) to be constant. Flame radiative losses from CO 2and H20 are accounted for by a gray gas treatment. The following non-dimensional variables are defined as (bars indicate dimensional quantities): Da ="p2 _-pxR-2 _ ; qr = cp-._---_. The non-dimensional equations are: 1 ,9 , 2 3_. 1 o_ sin0 o_ ¢aF-qr r2 _rr tr -'a-r-r)-_ rsin0 00 ('--7-- ("_ -)) = Too paY__p u aYi_puooYi 1 a (r2,aYi,, 1 a (si__(oY. ¢_t r dr ' r O0 Leir2c_ r t"_'r ))-LeirsinO00 r o._t)) = Vi_F aT OT P u0 aT 1 o3 (r2O_T) 1 O sinO(OT P'ff-i'+PUr a"_r 4 r O0 r2 Or Or rsin0 _'( -'7-- -'_-))= °JF -qr 2 A cone rather than a rod is easier to prescribe in the spherical coordinate system used. Also, examination of the photos shows that the liquid ball of wax may more closely resemble a cone than a rod. Dietrich, Ross, T'ien and Shu Candle Flames Page9 =o p2rorr • is a coupling variable. The gas-phase radiative loss term, qr, is qr -- -_o (T4 - 'I".4). The mean aborption coefficient, A, is ._ -- 0.4[Pco 2.,_,(CO2) + PH2o.,_,(H20)], where P_is the partial pressure of species i and _(i) is the Planck-mean absorption coefficient of species i. The Planck- mean absorption coefficients are from Abu-Romia and Tien (1967). The multiplication factor of 0.4 reflects the non-optically thin nature of the flame and the possible overestimate of the Planck-mean absorption data (Liu, et al., 1981; Bedir, et al. 1997). The radiative loss from liquid surface is neglected. The one-step reaction for the candle wax is C_H52 + 0.31 C,8H3602 + 4602 ---> 30.58CO 2 + 31.58H20. The physical properties of the candle wax are in the nomenclature. The activation energy, E, of the reaction is 30 kcal/mole. The pre-exponential factor, A, is selected such that the limiting oxygen index for a candle with a 0.6 mm radius is 0.19 (mole fraction). The resulting value for ,_ is 1.0 (10") cm3/(g s) which is quite reasonable. The boundary conditions in non-dimensional form are: atr= 1: T=T b -/)YF/Or =p Ur(1"YF) /)Y/0r =p u,Y_ (i - 02, CO2, H20) /)O/_ = (1/oL - 1/T.o)*/)T//)r at 0 -- 157°: T(r) = Tc + (r¢-r)/(r¢-l)* ( Tb - To) at (1< r< rc) T(r)=T_ at (r¢<r < oo) /)Y//)0 = 0 ( i- F, 02, CO2, H20) /)O//)0 = - (I/T.o)*/)T//)0 at r = co: T=T Y_=0 (i - F, CO2, H20) Dietrich, Ross, T'ien and Shu Candle Flames Page 10 o-_/o-h"= - (1/T.,)*c3T/_ at 0 = 0: /)T/_0 = 3_/00 = OY,/O0 =0 ( i- F,02, CO2, H20) The computations below are for a porous sphere radius, R -- 0.6 mm, r¢ = 3.2 cm, and Tb= 620 K. The temperature distribution boundary condition at 0 = 157 ° and r > 1 simulates the temperature distribution of the wick and the molten wax. Solution Procedure The reduced momentum equation is solved using an efficient Poisson solver. The equations for temperature and species are solved numerically based on finite difference and time marching techniques. The explicit scheme is used for the unsteady terms, the central difference for the diffusion terms and the upwind difference for the convective terms. The computation typically starts with a 'hot' profile or a previously converged flame solution (not the same condition as the case to be computed) as the initial condition. A steady flame solution (or extinction) evolves from the time marching procedure. The computation is carried out on a two-dimensional spherical non-uniform grid system. The number of grid points is 36 in the r-direction and 26 in the 0 direction. The variable grid distribution satisfies different requirements. The highest concentration of grid points is placed near the spherical wick, the cone surface, and the reaction zone. Along the r-direction, the minimum cell size is 0.1 times the porous sphere radius close to the sphere surface and expands with increasing r. The far-field boundary conditions are sufficiently far from the flame at a non-dimensional radius, r = 206. A complete description of the model, boundary conditions and solution procedures is available in Shu (1998). Numerical Results The model predicts that the candle flame will reach a steady-state in an infinite ambient. The inner portion of the flame reaches steady-state within 10 seconds, but_the outer portion takes tens of seconds to reach steady state (similar to King, 1996). The time