Gravitational Effects On Sooting Diffusion Flames

Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 1301–1309

GRAVITATIONAL EFFECTS ON SOOTING DIFFUSION FLAMES C. R. KAPLAN, E. S. ORAN and K. KAILASANATH Laboratory for Computational Physics and Fluid Dynamics Naval Research Laboratory Washington, D.C. 20375, USA H. D. ROSS Microgravity Combustion Branch NASA Lewis Research Center Cleveland, OH 44135, USA

Simulations of a laminar ethylene-air diffusion flame burning in quiescent air are conducted to gain a better understanding of the effects of buoyancy on the dynamics and behavior of heavily sooting flames under normal-, partial-, micro-, zero-, and negative-gravity conditions and under conditions of gravitational jitter. The simulations solve the time-dependent reactive-flow Navier–Stokes equations coupled with submodels for soot formation and multidimensional radiation transport. Results from the computations follow many of the trends that have been experimentally observed in nonbuoyant diffusion flames. Due to the significant reduction in buoyancy-induced convection, diffusion becomes the dominant mechanism of transport. Microgravity flames are much longer and wider than their earth gravity counterparts due to the reduction in axial velocity and the thicker diffusion layers. In microgravity, flame flicker disappears due to the lack of a buoyancy-induced instability, and the entire sooting region is much larger. The reduction in the axial velocity results in significantly longer residence times, allowing more time for soot particle surface growth, and resulting in greatly enhanced soot volume fraction. The enhanced soot production results in increased radiative heat losses, resulting in reduced flame temperatures. By tracing the path lines along which a soot parcel travels, the simulations show significant differences in the local environments through which soot passes between earth-gravity and microgravity flames.

Introduction There has been a significant amount of work done over the past decade to try to gain a better fundamental understanding of the effects of gravity on the behavior of sooting gaseous jet diffusion flames. Experimental and theoretical studies of Bahadori et al. [1–3] have provided unique and new information on the effects of buoyancy in laminar, and more recently, transitional and turbulent jet diffusion flames. Although this work has not focused on sooting properties of such flames, it provides information on the flame height and shape, effects of pressure and oxygen concentration, onset of hydrodynamic instabilities, and stand-off and blow-off behavior of lifted flames. This work also showed that microgravity flames take longer to reach their near–steady state compared to flames in normal gravity, due to the lack of entrainment caused by buoyancy. The characteristic time scale for buoyant flames is approximately 100 ms, while that for nonbuoyant flames is approximately 1000 ms. Recent experimental and theoretical studies conducted by Faeth and co-workers [4–7] have provided

further insight on the effects of buoyancy on the structure and soot properties of jet diffusion flames. They have indicated that the laminar-flamelet approach, which states that temperature and major species concentrations are universal functions of mixture fraction, appears to successfully predict the structure of soot-containing laminar diffusion flames. This work also showed that streamwise diffusion, which is commonly neglected in theoretical studies of buoyant diffusion flames, is important in microgravity and that the residence times of soot in nonbuoyant flames were an order of magnitude larger than that for normal gravity flames. These studies demonstrated that nonbuoyant diffusion flames exhibit much broader soot-containing regions and larger soot oxidation regions in comparison to buoyant flames, which implies very different soot reaction conditions. Other numerical investigations of soot formation and radiation transport in turbulent microgravity flames have been made by Ku et al. [8,9], who have tested various phenomenological soot formation models coupled with Favre-averaged equations for conservation of mass, momentum, and mixture

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fraction. The importance of radiation heat transfer in microgravity flames, due to enhanced soot production and longer residence times, is addressed by experimental and theoretical studies on radiation-induced extinction of weak microgravity diffusion flames by Atreya et al. [10,11]. The computations for these studies have been done for counterflow and spherical (1D) diffusion flame geometries. Greenberg [12] conducted the first experimental measurements of soot volume fraction in a microgravity environment and showed a factor of 2 enhancement in peak soot volume fraction for a laminar 50:50 acetylene-nitrogen diffusion flame compared to that in earth gravity. For an undiluted acetylene diffusion flame, Ku et al. [9] showed no enhancement in peak soot volume fraction but still showed an enhancement in overall integrated soot volume fraction. In this paper, simulations of a laminar ethylene diffusion flame burning in quiescent air are used to gain a better understanding of the effects of buoyancy on the dynamics and behavior of heavily sooting flames under normal-, partial-, micro-, zero-, and negative-gravity conditions and under conditions of gravitational jitter (g-jitter). The partial-gravity, negative-gravity, and g-jitter conditions were selected to resemble the acceleration environments seen by experiments flown on NASA’s low-gravity aircraft; the microgravity condition was selected to resemble the environment on the shuttle. The simulations are conducted to study the interactions between the physical and chemical processes under various gravitational conditions and to gain further insight into the differences in sooting characteristics between buoyant and nonbuoyant flames. This work presents the first numerical study of sooting diffusion flames under conditions of negative gravity and transient gravitational jitter. Some of the techniques used in the numerical method and in the data analysis follow those developed in Kaplan et al. [15].

to solve for the convective, diffusive, and radiation transport processes have already been described [13] and are not discussed here in detail. The convection algorithm is Barely Implicit Correction to Flux-Corrected Transport (BIC-FCT), which was developed by Patnaik et al. [18] to solve convection equations for low-velocity flows. Thermal conduction, molecular diffusion, and viscosity are solved with explicit finite differencing [13–16]. We include all of the viscous terms in the compressible Navier–Stokes equations. All transport coefficients are functions of temperature and species concentrations and are calculated from kinetic theory (Lewis number is not restricted to unity). The radiative heat flux is found by solving the radiative transfer equation using the Discrete Ordinates Method [13] and includes radiative effects from soot, CO2, and H2O. The algorithms for chemical reaction and soot formation are different than those used previously [13–16] and, therefore, are described below. Due to the very large number of species and elementary reactions involved in a detailed ethylene-air chemical reaction mechanism, it is cost-prohibitive to include such a reaction set in this multidimensional model. Instead, we describe the chemical reaction and energy-release process phenomenologically, using a fuel consumption rate based on Bilger’s [19] formulation for chemical reaction in diffusion flames: xC2H4 4 1qD(¹n)2

The numerical model solves the time-dependent, two-dimensional equations for conservation of mass density, momentum, energy, individual species number densities, soot number density, and soot volume fraction [13–16]. The solution to the conservation equations includes both radial and axial components of molecular diffusion, thermal conduction, viscosity, radiation transport, and convection (no boundarylayer assumptions). These equations are rewritten in terms of finite-volume approximations on an Eulerian mesh and solved numerically for specified boundary and initial conditions. The model consists of separate algorithms for each of the individual processes, which are then coupled together by the method of time-step splitting [17]. The different algorithms and how they are applied

(1)

where q is the fluid density, n is the mixture fraction, Y is the mass fraction, and D is an overall diffusion coefficient [20], D 4 1.786 2 1015T1.662

(2)

Mixture fraction is expressed in the form n4

Numerical Method

d2YC2H4 dn2

b 1 b2 b1 1 b 2

(3)

where b is a weighted summation of atomic fractions [21] and the subscripts 1 and 2 refer to the fuel and oxidizer streams, respectively. The species tracked include C2H4, O2, CO2, H2O, and N2 (assumed to be chemically inert). After the C2H4 consumption rate is calculated from Eq. (1), the consumption rate of O2 and the production rates of CO2 and H2O are then evaluated from their respective stoichiometric coefficients. The amount of heat released is then calculated from d[C2H4] Q 4 1DHc dt

(4)

where DHc is the heat of combustion for ethylene. Since the focus of this paper concerns the differences in residence time and soot particle trajectory

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Fig. 1. Normal earth-gravity case. Contours are shown at one time step after 0.16 s. Due to buoyancy-induced instabilities, this flame flickers with a frequency of 14 Hz. The early stage of the flicker cycle is shown at this time step (the roll up of the structure on the outer part of the flame continues with time).

between normal and microgravity flames (not the differences in soot chemistry), the use of a phenomenological chemical reaction model is justified. The evolution of soot number density, n, and soot volume fraction, fm, is represented by two coupled ordinary differential equations derived by Moss et al. [22] based on their experimental measurements in ethylene-air diffusion flames and includes terms for soot nucleation, surface growth, coagulation, and oxidation: xn 4 CaNoq2T1/2Xfuele1Ta /T 1 xfm 4

Cb 1/2 2 T n No

(5)

Cd Caq2T1/2Xfuele1Ta /T qsoot

`

Cc (36p)1/3Woxn1/3f 2/3 m qT1/2Xfuele1Tc /Tn 1 qsoot qsoot

(6) where the soot particle density qsoot is assumed to be 1.8 g/cm3, No is Avogadro’s number, Wox is the Nagle–Strickland–Constable [23] oxidation rate by O2, and the coefficients and activation temperatures are defined in Ref. 22. The terms on the right-hand side of Eq. (5) correspond to nucleation and coagulation, while the terms on the right-hand side of Eq. (6) represent nucleation, surface growth, and oxidation, respectively. The thermophoretic term, which appears in the conservation equations [13–16] for soot number density and soot volume fraction, is solved with explicit finite differencing. Results Simulations were conducted for an axisymmetric ethylene-air diffusion flame in which undiluted ethylene flows at 7.9 cm/s through a 1-cm-diameter tube into a quiescent air background (cold flow Re 4 22). Computational cells of approximately 0.02

2 0.02 cm are concentrated around the jet exit; the grid spacing is then gradually stretched in both the radial and axial directions [13–16]. The full computational grid extends to 1 m in the radial direction and 1.3 m in the axial direction. Such an extended, stretched grid minimizes reflections of the boundary condition into the computational domain. There is an axis of symmetry on the left-hand side, a free slip wall on the right-hand side (at r 4 1 m), inflow at the bottom, and an outflow boundary at the top. The outflow boundary has a zero-gradient condition; however, at this boundary, a pressure control is used to control the outflow velocity and so maintain atmospheric pressure in the computational domain. Simulations were conducted for cases in which the gravitational field was held constant at 1.0, 0.01, 1 2 1015, 0, and 10.01 G. Figures 1, 2, and 3 show images of fuel and oxygen mole fraction, temperature, soot volume fraction, and velocity vectors for the cases of 1.0, 1 2 1015, and 10.01 G, respectively. Results for the 0 and 1 2 1015 G cases are virtually identical. The simulations are axisymmetric, and hence, only the right-hand side of the flame is shown. Figure 1 shows instantaneous images at one time step (0.16 s) for this earth-gravity flame and shows that the flame is close-tipped, the maximum soot volume fraction is 2.6 2 1016, and the maximum flame temperature is 2050 K. The velocity vectors show the strong effects of buoyant acceleration, as the maximum vector is 120 cm/s, which is significantly faster than the inflow jet velocity of 7.9 cm/s. Earth-gravity diffusion flames that are formed from a fuel jet flowing into a quiescent air background flicker with a frequency of approximately 10–20 Hz (depending on the fuel jet diameter), due to the instability resulting from the density gradients between the hot combustion products and the cooler surrounding air. The images shown in Fig. 1 correspond to the early stage of the roll-up of an outer structure. As time progresses (not shown due to space limitations), this structure rolls up along the outer surface of the flame [13].

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Fig. 2. Results for 1 2 1015 G case. There is practically no buoyant acceleration, and flame flicker disappears.

Fig. 3. Negative gravity (10.01 G) case. In this flame, the fuel jet stream propagates upward. The cool fuel jet is below the hot combustion products, which are below the cooler ambient gases. The negative direction of buoyancy pushes the flame toward the burner. The maximum velocity vector is 32 cm/s in the downward direction.

Figure 2 presents results for the 1 2 1015 G case after 5 s of microgravity conditions and shows an open-tipped flame with a maximum axial velocity of only 7 cm/s. Due to the significant reduction in buoyancy-induced convection, diffusion becomes the dominant mechanism of transport. The microgravity flame is larger (both taller and wider) than the earth-gravity flame due to the reduction in axial velocity and the thicker diffusion layers. Due to the slow axial velocities, the residence time in the microgravity flame is much longer. This contributes to an enhancement in soot volume fraction, as more time is available for soot surface growth. As shown in Fig. 2, the peak soot volume fraction is 30 2 1016, compared to 2.6 2 1016 for the earth-gravity flame. Because of the increase in soot volume fraction and the longer residence time, the soot particles emit and absorb larger quantities of thermal radiation in microgravity. These radiative heat losses result in a decrease in temperature in the reduced-gravity flame, as compared to an earth-gravity flame. This microgravity flame does not flicker, as the buoyancyinduced instability that causes flicker in the earth-

gravity flame disappears in the microgravity environment. Figure 3 shows the resulting flame for the negative gravity (10.01 G) case. The fuel and oxidizer flow configuration for this case is the same as for those flames presented in Figs. 1 and 2; however, the resulting flow patterns are considerably different. For such a flame in which the fuel jet flows upward, the cool fuel jet is below the hot combustion products, which are below the cooler surrounding air. The downward direction of buoyancy (under negative gravity conditions) pushes the hot combustion products toward the burner. The maximum downward (toward the burner) velocity is 32 cm/s, which is significantly greater than the 7.9 cm/s upward (away from the burner) fuel jet velocity. Figures 4 and 5 show radial profiles of normalized axial velocity and oxygen mole fraction, respectively, at one height in the flame (4 cm), for all gravitational levels considered. The radial profiles show the significant reduction in axial velocity due to the loss of buoyancy-induced convection for the reduced-gravity cases and shows the downward direction of

GRAVITATIONAL EFFECTS ON DIFFUSION FLAMES

Fig. 4. Axial velocity normalized by the inflow velocity (7.9 cm/s) at 4-cm axial height shows the buoyant acceleration associated with earth gravity. The velocity profiles for the 1 2 1015 G and 0-G cases are practically identical.

Fig. 5. Oxygen mole fraction as a function of radial distance at 4-cm height shows much steeper oxygen gradients in buoyant flames.

velocity for the negative gravity case. As gravitational levels are reduced from 1.0 to 0.01 to 1 2 1015 G, the maximum axial velocities decrease from 120 to 22 to 7 cm/s. The radial profile for the 1.0-G case goes through the buoyancy-induced rotating outer vortical structure and, hence, shows some slightly negative axial velocities at r 4 1.5 cm. Figure 5 shows that the oxygen gradients in reduced gravity flames are considerably less steep compared to those in normal gravity. This also indicates that air entrainment in nonbuoyant flames is considerably reduced.

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Fig. 6. Area-integrated soot volume fraction as a function of height above the burner indicates enhanced soot volume fraction in reduced gravity and microgravity flames. The enhanced soot volume fraction is most likely due to the increase in residence time (due to reduced velocities), allowing more time for surface growth. For the reduced gravity cases, soot formation begins at lower heights in the flame and covers a much wider region.

This results in a larger region for soot oxidation in reduced gravity flames. As discussed above, the reduction in the buoyant force results in decreased axial velocities in reduced gravity flames. Due to the slow axial velocities, the residence time in the reduced-gravity flame is much longer, allowing more time for soot particle surface growth, resulting in enhanced soot volume fraction. Figure 6 shows the area-integrated soot volume fraction as a function of height above the burner for the various gravitational conditions considered and shows the significant increase in soot volume fraction in the reduced gravity cases. The soot forms at lower axial heights in the flame, and the soot-containing region is much broader under reduced gravity conditions. The area-integrated soot volume fraction is smaller for the negative gravity case, as the flame itself (and hence the sooting region) is much smaller. Figures 7a, 7b, and 7c show soot volume fraction, temperature, and equivalence ratio, respectively, as a function of residence time along the path lines followed by a soot parcel as it travels through an earthand microgravity flame. As soot particles are too large (mean soot particle diameter for this ethylene flame is ;120 nm) to diffuse with the gas molecules, it is assumed that the particles are transported with the gas along the convective streamlines, with relatively minor diffusive transport effects from thermophoresis (the thermophoretic velocity is much smaller than the fluid convective velocity). The path lines shown are the convective streamlines that pass

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Fig. 7. Soot volume fraction (a), temperature (b), and equivalence ratio (c) as a function of residence time along the convective streamline of maximum soot volume fraction for earth- and microgravity cases. Results show the differences in the local environments through which a soot parcel passes as it travels through buoyant and nonbuoyant flames.

through the maximum sooting region of each of the flames. For buoyant flames, these path lines (see velocity vectors in Fig. 1) first originate in the fuel-lean region (low temperatures), then are pulled through the stoichiometric region (high temperatures) into the fuel-rich region (lower temperature) of the flame due to the effects of buoyant acceleration, and then are convected straight upward through the stoichiometric region (high temperatures) and out of the flame. However, the path lines for the nonbuoyant flames are very different (see velocity vectors in Fig. 2). These path lines originate in the fuel-rich region (low temperatures) and go through a region of continuously decreasing equivalence ratio into the stoichiometric region (high temperatures) and then out of the flame. Hence, these figures illustrate not only

the very large differences in residence time (order of magnitude) but also the differences in the soot path lines between buoyant and nonbuoyant flames. Figure 7a also shows that the soot oxidation time is much longer in microgravity flames compared to earth-gravity flames. Simulations of gravitational jitter (g-jitter) were conducted to try to obtain a better understanding of the effects of gravitational fluctuations on these flames, as these fluctuations are inherent in NASA aircraft experiments. The g-jitter simulations were conducted by varying the gravitational field from 0.01 G through 0 G to 10.01 G and back through 0 G to 0.01 G, with a 1-Hz sine-wave frequency. Simulations were followed through four sinusoidal cycles. These g-jitter simulation results showed that

GRAVITATIONAL EFFECTS ON DIFFUSION FLAMES

the flame height oscillated at the 1-Hz frequency, with a 30% phase lag.

Discussion The constant gravity simulations presented above follow many of the trends that have been observed experimentally in nonbuoyant flames. That is, microgravity flames are much longer and wider than their earth-gravity counterparts due to the reduction in axial velocity and the thicker diffusion layers. Diffusion becomes the dominant mechanism of transport, and flame flicker disappears due to the lack of a buoyancy-induced instability. The reduction in the buoyant force causes a significant decrease in axial velocity, resulting in significantly longer residence times, allowing more time for soot particle surface growth, and resulting in greatly enhanced soot volume fraction. The enhanced soot production results in increased radiative heat losses, resulting in reduced flame temperatures. By tracing the path lines along which a soot parcel travels, the simulations show significant differences in the local environments through which soot passes between earthgravity and microgravity flames. It should be noted that our predicted enhancement in peak soot volume fraction (factor of 10) for this ethylene-air flame is much greater than the enhancement in peak soot volume fraction experimentally measured by Greenberg [12] for nitrogen-diluted acetylene flames (factor of 2) and by Ku et al. [9] for undiluted acetylene flames (no enhancement). Although Ku et al. [9] and Greenberg [12] showed less enhancement in peak soot volume fraction, their studies did show significant enhancement in overall integrated soot volume fraction under microgravity conditions. Our simulation results are shown after 5 s of microgravity, while the experimental measurements discussed above are after 2 s of microgravity conditions. Simulation results after 2 s of microgravity (not shown) showed a smaller (factor of 4) peak soot volume fraction enhancement; however, the simulations did not reach steady-state conditions until approximately 3 s of microgravity. The differences between the computations and the experimental results are attributed to the differences in fuel type and flow rate, dilution, and the length of time under microgravity conditions. Acknowledgments These computations were supported by the Office of Naval Research and the Naval Research Laboratory (NRL). This work was supported in part by a grant of High Performance Computing (HPC) time from the DoD HPC Shared Resource Center, CEWES Cray-YMP, and the LANL Cray-YMP.

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REFERENCES 1. Bahadori, M. Y., Stocker, D. P., Vaughan, D. F., Zhou, L., and Edelman, R. B., Proc. of the 2nd International Microgravity Combustion Workshop, Cleveland, OH, September 15–17, 1992. 2. Bahadori, M. Y., Small, J. F., Hedge, U. G., Zhou, L., and Stocker, D. P., Proc. of the 3rd International Microgravity Combustion Workshop, Cleveland, OH, April 11–13, 1995. 3. Bahadori, M. Y., Hedge, U., Zhou, L., and Stocker, D. P., AIAA Paper No. 93-0710, American Institute of Aeronautics and Astronautics, Washington, D.C., 1993. 4. Mortazavi, S., Sunderland, P. B., Jurng, J., and Faeth, G. M., Proc. of the 2nd International Microgravity Combustion Workshop, Cleveland, OH, September 15–17, 1992. 5. Sunderland, P. B., Lin, K.-C., and Faeth, G. M., Proc. of the 3rd International Microgravity Combustion Workshop, Cleveland, OH, April 11–13, 1995. 6. Koylu, U. O., Sunderland, P. B., Mortazavi, S., and Faeth, G. M., AIAA Paper 94-0428, American Institute of Aeronautics and Astronautics, Washington, D.C., 1994. 7. Sunderland, P. B. and Faeth, G. M., AIAA Paper 950149, American Institute of Aeronautics and Astronautics, Washington, D.C., 1995. 8. Ku, J. C., Tong, L., Sun, J., Greenberg, P. S., and Griffin, D. W., Proc. of the 2nd International Microgravity Combustion Workshop, Cleveland, OH, September 15–17, 1992. 9. Ku, J. C., Tong, L., and Greenberg, P. S., Proc. of the 3rd International Microgravity Combustion Workshop, Cleveland, OH, April 11–13, 1995. 10. Atreya, A., Wichman, I., Guenther, M., Ray, A., and Agrawal, S., Proc. of the 2nd International Microgravity Combustion Workshop, Cleveland, OH, September 15–17, 1992. 11. Atreya, A., Agrawal, S., Shamim, T. Pickett, K., Sacksteder, K. R., and Baum, H. R, Proc. of the 3rd International Microgravity Combustion Workshop, Cleveland, OH, April 11–13, 1995. 12. Greenberg, P. S., Proc. of the 3rd International Microgravity Combustion Workshop, Cleveland, OH, April 11–13, 1995. 13. Kaplan, C. R., Baek, S. W., Oran, E. S., and Ellzey, J. L., Combust. Flame 96:1–21 (1994). 14. Kaplan, C. R., Oran, E. S., and Baek, S. W., TwentyFifth (International) Symposium on Combustion, The Combustion Institute, Pittsburgh, 1994, pp. 1183– 1189. 15. Kaplan, C. R., Shaddix, C. R., and Smyth, K. C., Combust. Flame 106:392–405 (1996). 16. Kaplan, C. R., Patnaik, G., and Kailasanath, K., Universal Relationships in Sooting Methane-Air Diffusion Flames, Combust. Sci. Technol. (submitted). 17. Oran, E. S. and Boris, J. P., Numerical Simulation of

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18. 19. 20. 21.

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Reactive Flow, Elsevier, New York, 1987, pp. 279–285, 325–327. Patnaik, G., Guirguis, R. H., Boris, J. P., and Oran, E. S., J. Comput. Phys. 71:1–20 (1987). Bilger, R. W., Combust. Sci. Technol., 13:155–170 (1976). Bilger, R. W., Combust. Flame 30:277–284 (1977). Bilger, R. W., Twenty-Second Symposium (Interna-

tional) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 475–488. 22. Moss, J. B., Stewart, C. D., and Young, K. J., Combust. Flame 101:491 (1995). 23. Nagle, J. and Strickland-Constable, R. F., Proc. of the 5th Carbon Conference, Pergamon, New York, 1962, Vol. 1, p. 154.

COMMENTS Ofodike A. Ezekoye, University of Texas—Austin, USA. In heavily sooting flames such as those that you predict in low and negative gravitational acceleration cases, I am interested in your assumptions of not using a finite rate fuel decomposition step to gaseous products. The fuel can decompose two ways (to gaseous and to solid products). The path to solid products may be biased due to its finite rate while the gas product path is assumed to occur independent of the amount of cooling that may have occurred. Could you comment on the applicability of your model assumptions on fuel and soot distributions? Author’s Reply. The path to solid products (the integrated soot model of Moss et al. [22]) is a phenomenological model, in which soot volume fraction and number density are calculated as a function of the local gas properties (gas density, gas temperature, and fuel mole fraction). The path to gaseous products, based on Bilger’s [19] formulation for chemical reaction in diffusion flames, has been shown to accurately predict the scalar properties (temperature and species concentrations) which are used in the integrated soot model. Both of these models (the chemical reaction model and the integrated soot model) are phenomenological. That is, they have been empirically developed to match experimental data, without realistically capturing the details of reaction rates, etc. As long as the local gas properties are being accurately predicted by the chemical reaction model (and the Bilger formulation [19] has been widely accepted for calculating these scalars in diffusion flames), it is certainly reasonable to pass these local scalars into a phenomenological soot model. In fact, when developing the constants for their integrated soot model, Moss et al. [22] calculate the gas phase temperature and species concentrations from the computed mixture fraction. ● Viswanath R. Katta, Innovative Scientific Solutions Inc., USA. You concluded that when the gravitational force is 0.01g, then the flame does not oscillate. I think, this conclusion is strongly influenced by the time-accuracy of the numerical scheme you are using. Our calculations and linear-instability analyses indicate that the fluctuation frequency and amplitude decrease with square root of g. They go to zero only when g is zero. For 0.01g, the oscillations

will be very weak and your numerical scheme may not be able to capture the phenomenon. Indeed, every numerical scheme will fail in predicting the oscillations at certain microgravity conditions. However, we should not mask the physics with our CFD limitations. Author’s Reply. The drop tower experiments at NASA Lewis Research Center, in which the gravitational environment is 1014 g, show no flicker. Additionally, flicker has not been observed in any of the experiments on the NASA low gravity aircraft, in which the gravitational environment is approximately 1012 g. It is possible that the effects of gravitational jitter in the low gravity aircraft could mask any oscillations, as the direction of the g-vector may change too often to allow flicker in any preferred direction. However, the effects of g-jitter, if any, on the low gravity aircraft experiments have not yet been quantified. Hence, although your calculations and linear-instability analyses indicate such oscillations at 0.01 g, these have not been observed experimentally. ● Kermit C. Smyth, NIST, USA. For the conditions of your calculation at normal gravity (fuel flow velocity of 7.9 cm/s; 1 cm diameter fuel tube), a flickering ethylene diffusion flame should emit smoke and should emit considerably higher soot concentrations within the flame than you find. These expectations are based upon the measurements of Santoro et al. [1]* and Shaddix and Smyth [2]* in both steady and flickering ethylene/air diffusion flames (fuel velocities of 4,0–4,1 cm/s), where maximum soot volume fractions are 1–2 2 1015. Can you comment on the accuracy of various terms (inception, growth and oxidation) of the Moss model for soot production in an ethylene flame? Author’s Reply. The 1-g flickering flame studied in this paper is formed by a fuel stream flowing into quiescent air; this flame flickers due to a buoyancy-induced instability. We chose a flame with no coflow as it would show greater differences under normal and microgravity conditions compared to a coflowing flame. The steady flames in [1–3] do have an air coflow stream, and the flickering flames in *See references in author’s reply.

GRAVITATIONAL EFFECTS ON DIFFUSION FLAMES [2] are acoustically forced on the fuel stream, which results in vigorous tip clipping. I can make some general comparisons between the flame studied here and those experimentally studied in [1–3], but direct comparisons are not warranted as the flow conditions (coflow, acoustic forcing of fuel stream) are quite different. The measured peak soot volume fraction for the steady flames [1–3] are ;1–1.3 2 1015, and for a strongly-flickering acoustically-forced flame is 1.8 2 1015 [2]. Reference [3] (p. 106) shows that at the location of peak soot volume fraction for the steady flame (fv,max ' 1 2 1015), the number density is ;4 2 1010 particles/cm3, and the mean particle size is ;100 nm. In [2], the peak number densities vary from ;2 2 1010 particles/cm3 (steady flame) to ;4 2 1010 particles/cm3 (flickering flame), and the peak mean particle diameter is 100–110 nm for both the steady and flickering flames. In these computations, at the location of peak soot volume fraction (fv,max ' 2.5 2 1016), the soot number density is 1.2 2 1010 particles/cm3, which corresponds to a mean particle diameter of 74 nm. Hence, the computations predict smaller peak quantities compared to the experimental measurements. However, on a more global basis, the area-integrated soot volume fraction from the computations compares more favorably with that measured experimentally, as the computations predict wider soot volume fraction radial profiles with a smaller peak value.

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2. Shaddix, C. R. and Smyth, K. C., Combust. Flame, in press. 3. Santoro, R. J., Yeh, T. T., Horvath, J. J., and Semerjian, H. G., Combust. Sci. Technol. 53:89–115 (1987). ● Jean Hertzberg, University of Colorado, USA. Have you considered negative 1-g flames? Such a condition is easy to reproduce in a laboratory. Author’s Reply. We have not done any simulations of negative 1 g flames. The results would probably show that the flame is even more strongly compressed down towards the burner (compared to the negative 0.01 g case) and may even penetrate below the burner lip, which could potentially create some boundary condition problems. ● C. Megaridis, University of Illinois of Chicago, USA. The time-dependent character of your 1-g flames makes the interpretation of the results a difficult task. Experimental work at the NASA- Lewis 2.2 second drop tower (see paper no. 511 in this symposium) has shown that burner diameters of the order of 1 mm and fuel exit velocities of the order of 1 m/s give steady flames even in normal gravity. You may wish to consider such conditions in your future simulations.

REFERENCES 1. Santoro, R. J., Semarjian, H. G., and Dobbins, R. A., Combust. Flame 51:203–218 (1983).

Author’s Reply. We are currently considering doing simulations with smaller diameter burners and higher fuel exit velocities to produce steady flames even in normal gravity.