The behavior of flames spreading over thin solids in microgravity

The Behavior of Flames Spreading over Thin Solids in Microgravity PRASHANT A. RAMACHANDRA, ROBERT A. ALTENKIRCH,* SUBRATA BHATTACHARJEE, LIN TANG, KURT SACKSTEDER, and M. KATHERINE WOLVERTON Department of Mechanical Engineering and the National Science Foundation, Engineering Research Center for Computational Field Simulation, Mississippi State UniL,ersity, Mississippi State, MS 39762 (P.A.R.; R.A~A.; L. T.; M.K. FE), Department of Mechanical Engineering, San Diego State Unicersi~, San Diego, CA 92182 (S.B.), NASA Lewis Research Center, Cleceland, OH 44135 (K.S.) Experiments were conducted aboard Space Shuttle Orbiters during five different flights to study flame spread over a thin cellulosic fuel in a quiescent, microgravity environment. Data, which include spread rate and temperature measurements in the gas and solid phases, and also recordings of the flame from ignition to extinction using two 16-ram cameras, were gathered for two different oxygen levels and three different pressures. Detailed observation of the flame evolution is described along with theoretical support from steady and unsteady models that include radiation from CO2 and H20. Experimental results indicate that the spread rate increases with ambient oxygen level and pressure. The brightness of the flame and the visible soot radiation increases monotonically from the slowest to the fastest spreading flame. Steady-state t h e o ~ compares well with experiments in the vicinity of the flame leading edge. Trends in temperature, spread rate, and structure of the flame are qualitatively reproduced in this region, but the feature of a flame trailing edge curving back to the fuel surface and flame evolution over time is only captured through an unsteady model.

INTRODUCTION Flame spreading over solid combustibles is a phenomenon of fundamental, scientific interest as well as one that has direct application to fire safety issues. A unique environment in which flame spreading has importance to fire safety issues is that of spacecraft in which the gravitational acceleration is low compared with that of the Earth, here referred to as microgravity. Development of an understanding of the flame spread process in this environment is hampered by the difficulty of conducting experiments in which buoyancy is absent. Here we describe the results of five experiments for flame spread over thermally thin fuels in the microgravity environment of the Space Shuttle. Some results from the first three experiments, conducted for different environ-

* Corresponding author. Presented at the Twenty-Fifth Symposium (International) on Combustion, Irvine, California, 3l July-5 August 1994.

mental pressures in an oxidizer of 50% oxygen, and limited comparison to a model for zerogravity, steady flame spread, in which the focus of the model is prediction of the rate of spread of the flame leading edge, are presented elsewhere [1-3]. Here we include the results from two additional experiments, for 35% oxygen and two different pressures and focus on an unsteady model that describes flame evolution and behavior that is evident when results from the complete set of experiments is reviewed.

HARDWARE DESCRIPTION The experiments described here were conducted aboard Space Shuttle Orbiters using the Solid Surface Combustion Experiment (SSCE) payload specifically designed for these tests [4]. The experiments were conducted during five missions from October 1990 to September 1992. The SSCE hardware consists of two modules: a chamber module and a camera module. The 0.039-m 3 chamber comprises two orthogonal windows and a centrally located sample

COMBUSTION AND FLAME 100:71-84 (1995) Copyright © 1995 by The Combustion Institute Published by Elsevier Science Inc.

0010-2180/95/$9.50 SSDI 0010-2180(94)00046-U

72 holder. The sample holder supports the fuel, three thermocouples, and a pressure transducer and was designed to withstand the stresses of a Shuttle launch. The camera module includes two 16-mm motion picture cameras, an electronics box, and a battery box. The cameras are positioned so spreading flames cross the fields of view, one axis normal to the sample surface (top view), the other parallel (side view). Tests conducted at 50% oxygen were photographed using Kodak VNF film, ASA rated 400; the 35% oxygen tests used Kodak 7296 color negative film, ASA rated 500. The cameras exposed a timing light strobe on the margin of the film to measure the framing rate. All experiments were filmed using lens apertures of f/1.4. A 1-Hz strobe light was used to illuminate the fuel surface for both 35% oxygen tests to ensure that at least the propagation of the pyrolysis front could be recorded. The test samples were made from ashless filter paper, Whatman #1, 7 × 10 -2 K g / m 2, 0.00825 cm half-thickness, with the area exposed on both sides to the atmosphere being 3.0 × 11.0 cm. The sample was clamped between two thin metal sheets. A nichrome ignitor wire with a webbed pattern, 1.0 cm long, was clipped over one end of the sample. A solution of nitrocellulose in acetone was applied to the sample over the ignitor wire and allowed to dry. Three Type R thermocouples of 0.13 mm wire diameter were installed: 7.0 mm above the center of the sample, embedded in the center of the sample, and 2.3 mm below the sample 2.54 cm farther from the ignitor than the first two. The experiment sequence is automated beginning with a 5-s camera acceleration to 24 frames per second. The ignitor is then energized with 2 A of current for 5 s. The camera operation and data acquisition continue for 68 s after the ignitor is energized. The film was forced processed two stops. A color frame grabber was used to digitize the flame images, frame by frame. An edge detection scheme based on the brightness of the blue component of the image was used to measure the flame position and calculate the flame spread rate. Five experiments were conducted, three at 50% oxygen/50% nitrogen by

P . A . RAMACHANDRA ET AL. volume, at 1.0, 1.5, and 2.0 atm pressure, and two at 35% oxygen/65% nitrogen, at 1.0 and 1.5 atm pressure.

MODELING Because details of the steady model have been described before [1, 5], the discussion here is limited [6]. The model consists of the unsteady, two-dimensional continuity, momentum (u, v) species (fuel, oxygen, nitrogen), and energy (T) equations in the gas and the continuity and energy (T) equations in the solid. Viscosity and thermal conductivity at 700 K are 0.0515 W m -1 K -1 and 2.46 x 10 -s kg m -1 s -1, respectively, for 50% oxygen, and 0.0508 W m -a K -1 and 2.63 x 10 -5 kg m -1 s -1, respectively, for 35% oxygen and vary with the square root of temperature for a fixed Prandtl number of 0.7 and unit Lewis number. Chemical reaction is a one-step, second-order Arrhenius process with a pre-exponential factor of 1.58 x 1011 m 3 kg-~ s-1 [1], activation energy of 1.167 × 105 kJ kmol-~ [1], and heat of combustion of 1.674 x 10 4 kJ kg- 1 [7]. The specific heat of the gas is 1.465 kJ kg- 1 K- 1 [8] for 50% oxygen and 1.352 kJ kg -1 K -1 for 35% oxygen. The source term in the gas-phase energy equation contains, in addition to the heat release term, a transient ignition energy input term, and a gas radiation loss term, which is modeled using an overall Planck absorption coefficient obtained from the detailed radiation model built into the steady-state model that accounts for radiation from CO 2 and H 2 0 [5]. Soot, present only in the higher pressure, 50% oxygen flames, is not accounted for here. Its inclusion here is beyond the scope of this initial model for investigating the overall effects of radiation on the flame spread process. First-order Arrhenius kinetics, with preexponential factor of 7.8 × 1016 S-1 [1], and activation energy of 2.494 × 105 kJ kmol-1 [1], describe fuel pyrolysis. The specific heat of the solid fuel and heat of vaporization are 1.256 kJ kg -1 K-1 [7] and 368.45 kJ kg-1 [7], respectively, and surface reradiation and gas-tosurface radiative feedback, as in one version of the steady model, are taken to balance for purposes here [3].

FLAME SPREAD OVER THIN SOLIDS The solid and gas phase are solved simultaneously and numerically, using the SIMPLER algorithm [9], in a domain 15 cm long by 10 cm above one side of the fuel with a 92 × 40 uniform grid and a time step on the order of 0.01 s, except during the ignition transient when the time step is made smaller. The fuel sample is 10 cm long. The domain is extended 2.3 cm behind the ignition end of the fuel sample, which allows oxygen to diffuse into this region to give rise to a trailing-edge flame. The other end of the fuel sample is extended by 2.7 cm and is inert with the properties of the metal holder. Computationally the flame spreads left to right across the domain atop the fuel surface. Boundary conditions on the left, right, and top of the domain are ambient pressure and zero gradients for all field variables. The fuel is within the computational domain such that the boundary condition at the bottom is that the fuel is insulated at its half-thickness; behind the fuel burnout is a slip plane. At the fuel gas interface, there is a no slip condition and diffusion-convection balances normal to the fuel for energy and species. The 1-cm-long ignition source, 2 × 108 W/m 2, is at the left end of the fuel sample and is turned on at the beginning of the simulation. The source is turned off once the flame develops, which is just over 1.0 s into the computation. The mean Planck absorption coefficient is increased linearly with time from zero until it reaches the values determined from the detailed, steady-state radiation model, which are used as input information here. Steady spread of the leading edge, which obtains following the increase of the Planck mean absorption coefficient, occurs from between 2 to 4 s.

DESCRIPTION OF FLAMES Filmed images of the flame were recorded for each of the tests with the exception of the side view of the flame at 50% oxygen and 2 atm, which was observed in real-time with a video camera. Top-view images show a relatively flat pyrolysis front across a central portion of the sample width such that a two-dimensional spread process appears to be a reasonable ap-

73 proximation for modeling purposes. The apparent brightness of the flames ranged from nearly undetectable in the 35% oxygen cases to near saturation, indicating enhanced soot production both with increasing atmospheric oxygen content and pressure (particularly at 50% oxygen). For the 35% oxygen cases the flame images from the top are not detectable on film, but the 1-Hz strobe light in the chamber allows the progress of the apparent pyrolysis front across the sample to be seen. In the 50% oxygen tests the brightest part of the flame is always at or near the leading edge of the flame, where the flame is closest to the fuel surface. At 1.0 atm, the flame is entirely blue from which an absence of significant soot production is inferred. At 1.5 atm a faint yellow glow of soot is visible near, but behind, the flame leading edge. At 2.0 atm the flame is apparently almost entirely yellow, with a blue leading edge visible in the top view. Behind the leading edge of the 50% oxygen flames the visible flame curves away from the surface to a maximum distance (height) from the surface and then curves back toward the surface near the trailing edge. In the top views of these tests there is evidence that the fuel is not entirely consumed as the flame passes, as it would be for the same conditions at normal gravity or a forced flow environment, and what appear to be cracks in the charred fuel are visible. These observations suggest that pyrolysis products may be available far behind the flame leading edge. In the 50% oxygen, 1.0-atm test, the flame, appearing as a thin blue sheet, extends over nearly one half of the sample length (5 cm) at one point in time momentarily, then varies in length as the spreading concludes. The maximum height of the flame, on one side of the sample, reaches 0.8 cm within 1 cm of the leading edge, and the lengthening flame tapers very slightly toward the trailing edge. The shape of the trailing edge of this flame is similar to the leading edge, but the trailing edge is dimmer. For 50% oxygen, 1.5 atm, the maximum height and length of the flame reach 0.95 and 1.9 cm, respectively, and do not appear to vary appreciably once developed. The visible outer boundary of the flame curves back toward the

74 surface, toward both the leading and trailing edges, starting at the point of maximum height, about 1.3 cm behind the leading edge. The visible inner boundary diverges away from the outer boundary near the flame leading edge, resulting in a somewhat blunt, rounded leading edge as compared to a rather pointed trailing edge. The side view of the 50%-oxygen 2.0-atm flame comes only from the monochromatic video, and the color and internal structure are not as readily discernible as the others recorded on film. The external boundary of the flame reaches a maximum height of 1.25 cm within 1.2 cm of the leading edge and appears, eventually, to achieve a steady length of 2.9 cm. The shapes of the visible flames in 35% oxygen are symmetrical about the midpoint of their length, and are ultimately steady. In 1.0 atm, the 35% oxygen flame has a maximum visible height of 0.5 cm at half of its length of 1.4 cm. Unlike the flames at 50% oxygen, the flame is nearly flat in the side view, curving very slightly back toward the fuel surface near the leading and trailing edges, resulting in almost a constant distance between the flame and fuel over its length. The leading edge and trailing edge are nearly of the same brightness. For the 35%-oxygen, 1.5-atm flame, the leading edge is somewhat brighter than the trailing edge, but the flame shape retained the front to back symmetry of the 1.0-atm case. The flame achieves a maximum height of 0.6 cm midway along its length of 1.8 cm, and the visible inner boundary of the flame has more curvature than the 1-atm case. SPREAD RATE AND TEMPERATURE MEASUREMENTS

The leading edge of the flame reaches a steady spread rate almost immediately following ignition, while the trailing edge develops more slowly. Nominal leading-edge spread rates determined from the film for 50% oxygen at 1.0, 1.5, and 2.0 atm are 0.36, 0.45, and 0.55 cm/s, respectively, and for 35% oxygen at 1.0 and 1.5 atm they are 0.092 and 0.15 cm/s, respectively. The spread rates are useful in interpreting the measured temperatures, which are shown as a function of time for all five experiments in

P. A. RAMACHANDRA ET AL. Figs. 1 and 2. Following an earlier error analysis of the thermocouple measurements [2], the reported temperatures are uncorrected. The temperature history of the gas-phase thermocouple 2.3 mm from the surface is shifted in time compared with the other two because it is farther from the ignitor. For 50% oxygen, the temperature-time histories for the three pressures show similar behavior. The solid-phase temperature increases as the leading edge of the flame approaches the thermocouple, a plateau in temperature is reached as the fuel pyrolyzes, the plateau being longer in time as the spread rate increases, and the temperature increases sharply as the trailing edge of the flame passes. Following passage of the trailing edge, the temperature falls until surface reaction of remaining char occurs, as observed on the film, and the temperature rises again. As noted above, the visible extent of the 50% oxygen flames was at least 0.8 cm from the surface, increasing with increasing pressure. The two gas-phase thermocouples being closer to the surface than this, coupled with the fact that the leading and trailing edges of the flame curve back to the surface, show an initial peak in temperature as the leading edge of the flame passes and a second peak as the trailing edge passes, which is followed by a decline in temperature and then an increase due to the surface reactions following passage of the gas-phase flame. For 35% oxygen, the surface temperature shows behavior similar to the 50% result, although the increase in temperature as the traling edge of the flames passes is not nearly as pronounced, particularly for 1.0 atm. The gasphase temperature histories are somewhat different from those at 50% because the maximum extent of the visible flame away from the surface is approximately equal to or less than the distance of the thermocouple farthest from the surface, and the flames do not curve back toward the surface nearly as much as those at 50%. Consequently, the thermocouple 7.0 mm from the surface shows only a single peak in temperature. The one 2.3 mm from the surface for 1.5 atm does show an increase in temperature, followed by a decrease, then followed by an increase, indicating a slight curvature of the

FLAME SPREAD OVER THIN SOLIDS

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flame, but for 1.0 atm only the leading edge is sensed prior to the time at which data taking ceases. MODEL COMPARISONS The steady-state model developed in detail elsewhere [1, 3, 5] describes well the overall characteristics of the leading edge of the flame. Predicted surface temperatures there match well with experiment [3], the model predicts an increase in spread rate with pressure [3] and

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Fig. 1. Measured surface and gas-phase temperatures for 35% oxygen.

with increasing oxygen concentration, and a slight increase of pyrolysis temperature with increasing pressure [3]. Measured pyrolysis temperature increases with pressure for 35% oxygen, although that behavior is not quite as clear for 50% oxygen. In comparison, the expression for spread rate given by de Ris not including radiation [10] predicts a decrease in spread rate with increasing pressure due to the prediction from the steady model of an increase in vaporization temperature with pressure.

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FLAME SPREAD OVER THIN SOLIDS

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The predicted increase in spread rate with pressure, consistent with experiment and opposite of the thermal theory of de Ris, can be explained from gas-phase radiation effects. An increase in pressure results in an increase in Planck mean absorption coefficient computed as described in Ref. 5 and taking into account the distribution of temperature, CO2, and H20, but neglecting the presence of soot. Predicted absorption coefficients, used in the radiative source term in the gas-phase energy equation, increase from 2.9 m-~ at 1.0 atm, to 3.1m i at 1.5atm, t o 3 . 2 m -~ at 2 . 0 a t m a n d 50% oxygen, but a thinning of the reaction zone occurs with an increase in pressure such that the optical thickness of the flame decreases [3]. As a result, flame cooling due to

radiation decreases with increasing pressure causing an increase in spread rate. Although this result was obtained neglecting radiative feedback to the surface, which is equivalent to taking the gas radiation fed back to the surface to be balanced by the surface reradiation such that the surface emittance and absorption are set equal to zero, inclusion of radiative feedback as described in Ref. 5 was found not to change this conclusion. The steady model additionally predicts qualitatively the overall size of the flame adequately as shown in Fig. 3, in which temperature contours, normalized by the ambient temperature of 298 K, for flames spreading from left to right are shown superimposed on a velocity vector field for the 50%/2.0-atm flame

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78 and the 35%/1.0-atm flame. The velocities shown, in which the scale is given in the units of computed spread rate, are absolute, rather than relative to the flame as the computations are carried out, so that the environment appears quiescent. From the flame description above, the 50%/2.0-atm flame extends away from the surface the farthest, and the 35%/1.0-atm flame the least. Additionally, the 35%/1.0-atm flame is nearly symmetrical about the midpoint of its length, which is nearly the case in Fig. 3. The asymmetry evident for the 50%/2.0-atm case is due to the higher spread rate, which results in a higher relative velocity coming into the flame much like downward spread in normal gravity. While the steady model describes the character of the leading edge of the flame properly, it is unable to describe the trailing edge structure and the evolution of the trailing edge and the elongation of some of the 50% oxygen flames over time. The tendency of the flame to curve back toward the surface near the trailing edge is never adequately captured by the steady model, as indicated by the model's inability to predict the substantial increases in gas and surface temperature found experimentally as the trailing edge of the flame passes over the thermocouples and the behavior of the higher temperature contours in Fig. 3. Predicted surface and gas temperatures rarely show a second peak behind the leading edge, never one even remotely as pronounced as that measured. Development of the trailing edge appears to be an inherently unsteady process, and requires some detail of the ignition event to be retained as the leading edge spreads. Predicted surface temperatures from the unsteady model outlined above for both oxygen concentrations are shown in Fig. 4. For 50% oxygen, the leading edge structure is described well, as is the pyrolysis plateau. The increase in temperature as the trailing edge passes is predicted, although the peak temperatures reached for 50% oxygen are not as high as in the experiment. As with the steady model, the unsteady model currently describes only the gas-phase spread process, so following passage of the gas-phase flame, observed surface reaction for some of the experiments is not accounted for. Gas-phase temperatures for one

P . A . RAMACHANDRA ET AL. condition compared to measurement are shown in Fig. 5, and the structure of the profiles is captured by the unsteady model. For predicted results of Figs. 4 and 5, radiation feedback to the surface was neglected, and the Planck mean absorption coefficients determined at 50% from the steady model were used directly in the gas-phase energy equation such that no detailed radiation computation is contained within the unsteady computation due to computational time limitations. For 35% oxygen, the absorption coefficients were estimated from the values at 50%, taking into account the differences in the amount of CO 2 and H 2 0 produced from stoichiometric reaction, to be 2.2 m -1 and 2.4 m -1 at 1.0 and 1.5 arm, respectively. Built into the one-step, Arrhenius, pyrolysis model is a need to provide a fuel density at burnout. Study of the films shows that, unlike the situation in normal gravity, a substantial amount of solid fuel remains following passage of the gas-phase flame, indicating that the fuel density at burnout is quite high. At present, the dimensionless fuel density at burnout, that is the ratio of the density at burnout to that of the virgin fuel, is a parameter in the models, chosen to be 0.7 for 35% oxygen, i.e., only 30% of the potentially pyrolyzable fuel is converted to gas-phase fuel, and for 50%, 0.5, 0.6, and 0.7 for 2.0, 1.5, and 1.0 atm, respectively. These values of burnout density are much higher than the value of 0.27 that the pyrolysis experiments of Kushida et al. suggest [11], but lower burnout densities do not allow the structure of the trailing edge to evolve. For a burnout density of 0.27 the trailing edge is predicted not to move from the point of ignition for the entire experimental time, which is contrary to observation. In Fig. 6, a set of computed temperature contours for different times in the spread process for 1.5 atm is shown for the flame spreading left to right in the 15-cm-long by 10-cm-high domain. The maximum temperature, i.e., the brightest contour, which occurs just after ignition, is 1677 K. Qualitatively, the general characteristics of the observed flames are predicted with leading and trailing edges propagating initially at different rates. At 16.2 s the flame has already reached the end of the sample and

FLAME SPREAD OVER THIN SOLIDS

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encountered the sample holder. The gas-phase flame continues to burn without propagating at this point as remaining available fuel in the solid is pyrolyzed. At 20.32 s, the flame has moved closer to the surface as it goes through the transient prior to extinction. Stationary flames at the end of the sample holder were observed experimentally consistent with this prediction. No attempt here was made to adjust model parameters at this time to obtain a best fit

Fig. 4. Comparison of measured and 60.0 predicted surface temperatures from the unsteady model formulation.

between measured and predicted spread rates. While it is clear that the unsteady model appears to capture more of the essential character of the observed flame structure than the steady model, as with the steady model, further refinement of the various submodels that make up the overall model, which are essentially the same within the two models, is needed before quantitative agreement between predicted and measured spread rate may be obtained. For the property selections here, predicted spread

80

P . A . RAMACHANDRA ET AL. Gas-phase

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rates, determined following the ignition transient by tracking the peak of the heat flux to the surface near the leading edge of the flame, are, for 50%, 0.387, 0.554, and 0.630 c m / s for 1.0, 1.5, and 2.0 atm, respectively, while the measured values are 0.36, 0.45, and 0.55 c m / s for the same pressures. For 35% oxygen, the predicted values are 0.290 and 0.476 c m / s for 1.0 and 1.5 atm, respectively, and the comparable measured values are 0.092 and 0.15 cm/s. While the proper trends are predicted, the effect of oxygen concentration on spread rate is underpredicted more than that of pressure on spread rate. Part of this discrepancy may be due to the fact that the 35% oxygen flames are very near extinction and are rather sensitive to the details of the submodels, particularly the radiative one. CONCLUSIONS Flame spread over a thin solid fuel in a quiescent, microgravity environment for different oxygen concentrations and pressures has been studied. Experimental results, reported along with results from the steady and unsteady models, show that the flame elongates after ignition, curving back to the surface to form a trailing edge that follows the leading edge ini-

tially at a slower speed. However, the spread rate, measured with respect to the leading edge, becomes steady almost immediately after ignition and increases with increasing pressure and oxygen level. The brightness of the flame increases with the spread rate along with a transition of the color of the flame from blue to orange, indicating increased soot production. The faster spreading flames are elongated and asymmetric as compared to the slower spreading flames, which exhibit symmetry about the midpoint of their length. Trends in flame size, temperature, and spread rate are reproduced by the steady and unsteady models when radiation loss from the flame is included in the model. However, trailing-edge phenomena, which appear to be inherently unsteady, as compared with the leading-edge phenomena, are only captured by the unsteady model. The presence of surface reactions in the experiments suggests that the fuel is not completely pyrolyzed after the flame passes. Accordingly, the fuel density at burnout, treated as a parameter, must be relatively high in order to obtain qualitative agreement between model and experiment. With basic flame structure and evolution predictable, submodel refinement will allow for quantitative agree-

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Fig. 6. Temperature contours for 50% oxygen/1.5 atm for times increasing from the upper left down to the lower left and then from the upper right down to the lower right. The temperature of the brightest contour is 1677 K with the temperature of the darker contours decreasing down to ambient. The six times are 2,30, 4.60, 7.32, 11.62, 16.20, and 20.32 s.

ment between model and experiment to be pursued.

This work was supported by NASA through Contract NAS3-23901. We thank Sandra Olson for serving as a contract monitor during one period of the project and Prof. S. V. Patankar for providing to us an initial version of the gas-phase software. We gratefully acknowledge the contributions of Ralph Zavesky, John Koudelka, and the

SSCE flight hardware team at the NASA-Lewis Research Center and the program support of NASA Headquarters, Microgravity Division, Office of Space Science and Applications. REFERENCES Bhattacharjee, S., and Altenkirch, R. A., TwentyFourthSymposium(International)on Combustion,The Combustion 1669-1676.

Institute,

Pittsburgh,

1992,

pp.

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2. Bhattacharjee, S., Altenkirch, R. A., and Sacksteder, K., Combust. Sci. Technol. 91:225-242 (1993). 3. Bhattacharjee, S., Altenkirch, R. A., and Sacksteder, K., ASME Winter Annual Meeting, 1993. 4. Vento, D., Zavesky, R., Sacksteder, K., and AItenkirch, R. A., The Solid Surface Combustion Space Shuttle Experiment Hardware Description and Ground-Based Test Results, NASA TM 101963, 1989. 5. Bhattacharjee, S., and Altenkirch, R, A., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 1627-1633. 6. Bullard, D. B., Tang, L., Altenkirch, R. A., and Bhattacharjee, S., Adv. Space Res. 13:(7)171-(7)184 (1993).

7, Altenkirch, R. A., Eichhorn, R., and Shang, P. C., Combust. Flame 37:71-83 (1980). 8. West, J., Bhattacharjee, S., and Altenkirch, R. A., Combust. Sci. Technol. 83:233-244 (1992). 9. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980. 10. de Ris J. N., Twelfth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1969, pp. 241-252. 11. Kushida, G., Baum, H. R., Kashiwagi, T., and di Blasi, C., Z Heat Trans. 114:494-502 (1992). Received 1 December 1993; revised 20 April 1994

Comments M. Suzuki, University of Tokyo, Japan. In Fig. 4, solid phase temperature profiles obtained by the experiments show that the preheating rate and decreasing at the plateau is rather small compared to that obtained by the theory (especially in the case of 35% 02). Is the diameter of the thermocouple small enough so that heat conduction through it can be neglected? Was the thermocouple wire parallel to the pyrolysing front on the sheet so as not to cross isotherm lines?

Authors' Reply. With respect to the preheating rate, the experimental and predicted rates for 50% oxygen are quite comparable in Fig. 4, while for 35%, the predicted rate is higher than the experimental rate. The temperature gradient in the streamwise direction is directly linked with the spread rate. Had Fig. 4 been presented as surface temperature as a function of streamwise location along the surface with respect to the flame leading edge, x, using the transformation that x = Vft, where t is time and ~ is either the experimental or predicted spread rate as appropriate, agreement between experimental and predicted temperatures in the preheat zone would be much better, indicating that the structure of the flame leading edge is relatively well-predicted, but the effect of oxygen concentration on spread rate is underpredicted. The gas-phase thermocouple projects into the flame from the side edges of the sample, and so the leads of these thermocouples are positioned along isotherms. The solid-phase

thermocouple, however, enters into the sample from the sides but then is turned such that the leads are parallel to the long edges, or sides, of the sample. The thermocouple then approaches the flame from upstream, i.e., the flame encounters the thermocouple bead first, and then the leads of the thermocouple. A limited discussion of thermocouple error can be found in Ref. 2. In the pyrolysis region in Fig. 4, particularly for 35%, the experimental solid temperature decreases more slowly than, and is above, the predicted temperature. It would seem that conduction losses through the thermocouple leads would cause the measured temperature to be depressed below the predicted, or actual, temperature and cause an apparent increase in the rate of temperature decrease over what is actually the case or predicted. Consequently, it seems unlikely that the fact that the predicted temperature in the pyrolysis region decreases more rapidly than what is measured is due to thermocouple conduction losses, rather the behavior is more likely due to the fact that the predicted flames in the pyrolysis region are much farther away from the surface than what is observed thus resulting in a heat flux in the pyrolysis region that is smaller than is actually the case.

D. N. Schiller, University of California'Irvine, USA. I have two questions. First, should the chemical kinetic parameters (activation energy, pre-exponential constant) used in the numeri-

FLAME SPREAD OVER THIN SOLIDS cal model depend on gravity level? Second, how does the inclusion of gas-phase radiation affect the total heat flux of the fuel surface? l would expect the flame temperature and therefore the conductive heat flux to decrease, but the radiative flux to the fuel surface will compensate for this to some extent.

Authors' Reply. Chemical kinetic parameters per se do not depend on gravity; however, gravity affects the diffusional processes that occur in the flame, through its effect on the velocity and length scales, and hence the structure of the flame, and so the flame chemistry may be affected, indirectly, by gravity. With a one-step reaction, changes in the chemistry may be accounted for by changes in the kinetic parameters, but there is no real functional dependence of the parameters on gravity. The comment with respect to radiation and heat flux is basically correct. A depressed flame temperature depresses the conduction heat transfer, but radiation may compensate for this. In the preheat zone, gas-to-surface radiation provides an additional flux larger than the reradiation because the surface temperature there is small compared to the pyrolysis temperature while in the pyrolysis region the surface reradiation dominates. So whether or not the inclusion of gas-phase radiation increases or decreases the heat flux to the surface depends on the environmental conditions. It would appear no general statements can be made.

M. D. Delichatsios, Factory Mutual Research Corp., USA. Chemical reactions would not be affected by high straining rates at low (oxg) velocities. However, you should seriously consider soot formation and radiation losses from soot in your model. What soot formation model would you use for an arbitrary material? My recommendation is to use a soot formation model based on smoke-point heights. Smokepoint (laminar) heights can characterize the "sootiness" of any given material, without knowing the detailed soot chemistry, or the detailed chemical composition of the material.

Authors' Reply. We agree with the comment that soot formation and radiative losses from

83 soot should be included in the model, and we have plans to do just that. We are currently exploring a soot model developed by Grosshandler and Vantelon [1] that directly predicts the contribution of soot to the local absorption coefficient from the local temperature, pressure, and fuel and oxygen concentration. We might point out that the level of sophistication of any soot model should not be substantially different from the level of sophistication, and detail, of the various other submodels. Consequently, the suggestion of using soot models that derive from smoke-point heights is a good one, and we will explore the suggestion. REFERENCE 1. Grosshandler, W. L. and Vantelon, J.-P., Combust. Sci. Tech. 44:143 160 (1985).

J. Siluer, Southwest Sciences, Inc., USA. Are the thermocouple measurements corrected? The possibility of extinction would be lessened if the actual temperatures are much higher than the raw measurements indicate.

Authors' Reply. The thermocouple measurements reported have not been corrected. A limited discussion of thermocouple corrections for the solid surface combustion experiment is contained in Ref. 2 of the paper, in which it was found that the corrections are not likely to be of substantial importance with respect to major findings and are difficult to determine accurately. From visual observation and drop tower experiments at oxygen concentrations lower than those used here, the flames at 35% oxygen are near extinction, but those at 50% are not.

C. F e r n a n d e z - P e l l o , University of California-Berkeley, USA. Due to the weakness of the flame and its low temperature in microgravity, the corresponding chemical kinetics would be different from those in normal gravity. Have you considered this in your analysis, and if so how? If not, how would the use of proper chemical kinetics change the nature of your predictions concerning the role of gas and solid phase radiation?

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Authors' Reply. We agree that there is a strong possibility that the chemistry in these flames is likely to be different than their normal gravity counterparts, which are further from extinction for the same environmental conditions than these microgravity flames, although as mentioned in the reply to an earlier comment, the kinetic parameters do not depend on gravity per se. Any shifting in the chemical mechanism is due to the temperature level being different than temperatures in normal gravity because of radiative losses and the effect of gravity on the length and velocity scales and hence the diffusional processes. At present, we do not take into account any shifting in flame chemistry as we move from normal gravity to microgravity. With a single step reaction, this is difficult to accomplish unless the kinetic parameters are written as a function, albeit empirical, of environmental conditions. We are currently investigating using multiple step, reduced reaction mechanisms to address this concern so that the kinetics adjust naturally to environmental conditions. It is unlikely that the overall, qualitative conclusions concerning the importance of the various heat transfer processes will change substantially with the inclusion of more accurate models for the chemistry, but detailed prediction capability, especially near extinction, would be enhanced.

A. Sobiesiak, Queen's University, Canada. Predicted surface temperatures in Fig. 4 and predicted gas-phase temperatures in Fig. 5 show a substantial decrease after the first peak (about 100°C in the surface temperature and 500°C in the gas temperature). Measured temperatures show much lower decreases in the gas-phase (about 200°C) and none in the solid surface temperature. Can you comment on what the source of this disagreement is?

P. A. RAMACHANDRA ET AL. In the video shown the extent of the predicted flame in the vertical direction was much greater than the vertical extent of the visible (blue) flame from the experiment (with the horizontal spread recovered accurately). Can you comment, please, on this difference?

Authors' Reply. The disagreement to which the commentor refers in the first portion of his comment is a result of his observation and question in the second portion of his comment. The computed flames in the pyrolysis region are farther away from the surface of the fuel than the experimental flames. Consequently, the computed heat fluxes to the surface are smaller than the actual fluxes, and the predicted flame has more curvature from the leading to the trailing edge than what is observed. This results in lower predicted temperatures in the pyrolysis zone than what is measured. The distance of the computed flame away from the surface is a function of the kinetics. By increasing the rate of the gas-phase chemistry, the flames can be brought closer to the surface. However, no parametric variations to obtain a "best fit" with experiment were carried out here, rather our interests were in qualitative description of the physics of the flame spread process. One additional point is that the reason that in the video the predicted horizontal spread matched the experiment was that for the video, the computed spread rates were adjusted to match the experimental spread so that the shape of the flames could be compared visually. The predicted spread rates are listed in the paper, and agreement for 50% oxygen is good whereas the dependence of spread rate on oxygen concentration is underpredicted. Again, no parametric variations were carried out to obtain a best fit.