Experimental simulation of premixed turbulent combustion using aqueous autocatalytic reactions

Twenty-Fourth Symposium (International) on Combustion/The Combustion Institute, 1992/pp. ,543-551

OF PREMIXED TURBULENT

EXPERIMENTAL SIMULATION COMBUSTION USING AQUEOUS

AUTOCATALYTIC

REACTIONS

S. S. SHY,* P. D. RONNEY, S. G. BUCKLEY AI~DV. YAKI1OT Department of Mechanical and Aerospace Engineering Princeton University, Princeton NJ 08544, USA

Aqueous autocatalytic reactions which produce propagating chemical fronts, analogous to premixed flame-fronts, are used to simulate premixed turbulent combustion in "'laminar-flamelet" and "distributed-combustion" regimes. The characteristics of these chemical fronts more nearly match those assumed by current theories of turbulent combustion than do gaseous flames. In this work, proper chemical solutions for this simulation are identified and applied using a Taylor-Couette flow. The effect of the velocity disturbance intensity (u') normalized by the laminar burning velocity (St) on the front propagation velocity (St) are obtained at values of U -~ u'/SL at least 200 times higher than those attainable in gas combustion experiments. At modest U, Ur =- Sr/SL data collapse onto a single curve, regardless of St., indicating stretch-free conditions; these data agree with an approximate theoretical model. Effects of the velocity spectrum are described. At higher U, Ur deviates away from this curve, indicating stretch effects which are characterized by a turbulent Karlovitz number (Ka). At high Ka, behavior suggesting distributed-combustion is observed; in this regime Ur data are fairly consistent with Damk6hler's hypothesis. No quenching is observed, even at Ka ~ 900, suggesting that the commonly-held view that the quenching of flames in intense turbulence results from mass extinction of flamelets may require reconsideration. It is proposed that instead, heat-loss could be an important factor in extinction.

Introduction Motivation: The study of turbulence effects on premixed flames has great practical importance because turbulence may increase the propagation rate (ST) in a given mixture to a value well above its laminar burning velocity (SL).1 This increases heat release rates and hence power available from combustors or internal combustion engines of fixed size. Turbulent premixed combustion studies are relevant to automotive engine performance and lean-burn, lowNOx turbine applications. Probably the simplest model of turbulent premixed combustion is the Huygen's propagation or "thin-flame" model proposed by Damk6hler: 2 the flame-front propagates normal to itself with velocity SL, independent of local front curvature and strain rate. The increase in Sr above SL results solely from front area increase caused by turbulence-induced front wrinkling. Sr depends only on SL and turbulence properties including the (one-component) *Present address: Department of Mechanical Engineering, National Central University, Chung-li TAIWAN 32054, ROC.

rms velocity disturbance intensity (u') and turbulent Reynolds number (ReT -~ u'LJv; Ll denotes integral length scale and ~ the kinematic viscosity). Figure 1 shows some predictions of theories 3-7 employing this simple framework. There is no consensus on any feature except Ur =-- Sr/SL increases as U =- u'/SL increases. (Ironically, in experiments l sometimes Ur decreases with increasing U at constant Rer). Theories do not agree whether Rer affects Ur at fixed U, whether heat release increases or decreases U~, or whether Ur is linear in U. Also, experiments compare unfavorably with these theories. Computational difficulties have limited direct numerical simulations8 to U < 5, providing little insight into these discrepancies. The discrepancies undoubtedly result partially from the theoretical assumptions usually invoked. In experimentally-accessible turbulent combustion regimes, at least four such assumptions are frequently violated: (I) Huygen's propagation (SL = constant); (II) constant density; (III) constant thermodynamic and transport properties; and (IV) turbulence which is homogeneous in the direction of front propagation and statistically time-invariant. This study introduces chemically reacting, propagating fronts in liquids for experimental simulation of premixed turbulent combustion. We shall show that such fronts obey assumptions (I)-(IV) better than

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TURBULENT COMBUSTION--PREMIXED

mally Sc effects are ignored since Sc ~ 1 in gases. For I - in water, 13 D ~ 2.0 • 10-5 cm2/s and u 0.01 cm2/s hence Sc ~ 500. Thus, at fixed ReT, the thin-flame assumption may hold at perhaps 20 times greater U in our system than in gases. At Ka ~> 0.3, flame-fronts are fragmented, 14 lopropagating fronts analogous to premixed-gas flames. cally quenched, 14 and there is significant probability of compositions intermediate between reactants and products 15 ("distributed-combustion"). Thin-flame Autocatalytic Systems: models are probably invalid here; DamkShler2 sugPropagating fronts occur in substances exhibiting gested that for distributed-combustion, turbulence autocatalytic reactions with generic form A + n B increases propagation rates by increasing diffusive (n + 1) B (n = constant). Propagation starts when transport without affecting RR. By analogy with localized B diffuses into A, catalyzing reaction, gen- laminar flames4, where SL ~ N/DL 9RR, DamkShler erating additional B, thereby sustaining autocata- proposed Ur ~ N/-DT/DL (subscripts L and T delysis. In gas combustion, A corresponds to fuel and note laminar and turbulent conditions, respecoxidant and B corresponds to heat and radicals; this tively). Unfortunately, this hypothesis is difficult to description of premixed flame propagation is well- test because complete flame extinction is observed16 established, lo when Ka is moderately large (~1.5), Some authors 16 Liquid chemical solutions exhibiting autocatalysis thereby conclude that global extinction results from and propagating fronts have been known since mass quenching of individual flamelets. However, 1906.12 After evaluating several candidate systems, this view does not consider that flame propagation we focussed on aqueous iodate--arsenous acid might occur in modes other than "thin" fronts. We systems I3 consisting of the Dushman reaction (5 Iwill employ aqueous chemical fronts, where the re+ 103- + 6 H § --~ 3 H20 + 3 I2) followed by sponse to heat-loss is different from premixed-gas the Roebuck reaction (I2 + H3AsO3 + H20 ----> flames, to examine distributed-combustion and flameH3AsO4 + 2 H + + 2 I-). If [H3AsO3]o > 3 [IO3-]o quenching hypotheses. (subscript o denotes initial values) the net reaction With the noted exceptions, theories assume conis (Dushman + 3"Roebuck) or 3 H3AsO3 q- 103stant density (II). This eliminates baroclinic pro---> 3 H3AsO4 + I-, which is autocatalytic in iodide duction of turbulent kinetic energy across the flame(I-) product since it catalyses the Dushman reac- front, thus u' is constant. This is nearly satisfied by tion. 13 aqueous chemical fronts; the fractional density change Our preliminary experiments revealed only one is typically13 0.03%, compared with ~600% is gases. qualitative feature of these chemical fronts notably The cited theories assume constant transport different from premixed-gas flames. From measure- properties (III). This is nearly satisfied by aqueous ments of temperature effects on SL (not shown) it chemical fronts because the relevant chemical sowas found that the Zeldovich number 1~ (Ze -= 2(AT~ lutions are weak (typically 0.01-0.15 M) and AT is Te)[O(ln SL)/0(ln Tp)]; AT =-- Te - TR; subscripts small. This was confirmed by viscosity measureP and R, denote products and reactants, respec- ments in reactants and products; both were identively) is about 0.05, whereas typically Ze ~ 10 tical, within experimental uncertainty, to pure water. 20 in gas combustion. Ze measures the sensitivity By comparison, v typically increases by 25 times of mean chemical reaction rate (RR =- SL2/D; D across gaseous flames. denotes characteristic reactant diffusivity) to T for Assumption (IV) is difficult to satisfy experimenTn < T < Te. The most important consequence 1~ tally because turbulent kinetic energy naturally deof low Ze is that these chemical fronts cannot be cays away from its source unless restored by some extinguished by heat-loss since T affects RR less than external process. Decay occurs on the integral time T affects heat-loss. In contrast, gaseous flames are and length scales, 1~ thus, producing turbulent clearly susceptible to heat-loss extinguishment, lO Low flows which are homogeneous over several integral Ze also indicates that heat diffusion plays little role scales is fundamentally difficult. The turbulent in these fronts. burning velocity is ill-defined in inhomogeneous flows because statistical stationarity of fronts cannot be assured. We shall show that utilizing aqueous Advantages of Aqueous Autocatalytic Fronts: chemical fronts facilitates forcing methods which are The thin-flame assumption (I) requires 1'1~ that RR homogeneous in the propagation direction. be much greater than the characteristic turbulent strain rate (--- u'/~t; A denotes the Taylor microObjectives: scale). Since h - LIReT- 1/2 this criterion may be 1 1/2 2 1 Our goal is to explore the utility of aqueous written using Karlovitz (Ka ~ 0.157Rer- U Sc- ) and Schmidt (Sc --= J,/D) numbers as Ka ~ i. Nor- chemical fronts for experimental simulation of pregaseous flames. Analogous experiments on turbulent non-premixed "combustion" in liquids are routinely conducted9 but these experiments are much simpler because non-premixed combustion is largely mixing-dominated1~ and most fluids exhibit mixing properties. In contrast, few fluids exhibit self-

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Experimental Approach Chemical Considerations: All solutions were prepared using reagent-grade chemicals and deionized water. Initiation of propagating fronts was accomplished by applying potential differences between Pt electrodes; initiation occurs at the negatively-biased electrode. The effects of [H3As03]o, [IO3-]o, and [H+]o on SL were measured in vertical glass tubes. Downward propagation was employed to eliminate slight buoyancy influences; essentially fiat fronts were observed and SL was independent of tube diameter.

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Consistent with previous results) 3 SL is proportional to [103-]o (Fig. 2a), nearly independent of [H+]o (Fig. 2b) and nearly independent of stoichiometrically-abundant [H3AsO3]o. Solutions of 0.15 M [H3As03]o and 0.008-0.03 M [IO3-]o at pH = 6.6 were chosen for all further experiments because stronger solutions reacted spontaneously when mixed. Previously17 the Huygen's propagation model was verified for the 0.02 M [IO3 ]o solution. Hydrodynamic Considerations: We abandoned fully three-dimensional forms of turbulence for a surrogate flow which exhibits our most-desired characteristics (see Objectives): Taylor-Couette (TC) flow in the annulus between two rotating concentric cylinders, here with the outer cylinder stationary. This flow exhibits several regimes depending on Reynolds number (ReTc -= O d / v;/2 denotes the inner-cylinder peripheral velocity and d the annulus width). The first regime transition occurs at Rerc = ReTc.c (~-80 in our apparatus) from axially-invariant Couette flow to "Taylor vortex" flow is where time-independent counter-rotating toroidal vortex pairs fill the annulus. At higher ReTc, these vortices exhibit azimuthally-progressing waves ("wavy vortex" flow). At yet higher ReTc = ReTC.T (~2500 in our apparatus), more random non-wavy flow appears ("turbulent Taylor vortex" flow); velocity spectra contain a major component

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corresponding to Taylor vortices and a background continuum. Is TC flows could be but have not been used in gas combustion studies. Flame-quenching by heat-loss to cylinder walls may be problematic. As discussed earlier, this is unimportant in our chemical fronts.

Experimental Apparatus and Procedures: Figure 3 illustrates our experimental arrangement. Chemical solutions of typical depth 22 cm were confined between two concentric cylinders. The outer cylinder was transparent with inside diameter 4.445 --- 0.003 cm. A DC motor coupled to a variable-voltage power supply rotated the inner cylinder, of diameter 3.10 + 0.01 cm, providing 0 < Rerc < 5000. The cylinders were immersed in a transparent rectangular box filled with water to minimize optical distortions induced by cylinder curvature. Flow velocities were measured using a Dantec fiber-optic Laser-Doppler Velocimeter (LDV) and Burst Spectrum Analyzer. The probe volume was

0.015 cm in diameter and 0.06 cm long. LDV measurements confirmed that at the values of Rerc employed herein, the Taylor vortices contain most of the undirected kinetic energy of the flow, even in the turbulent Taylor vortex regime 19. These vorrices exhibited nearly rigid-body rotation; from their size and rotation rate the kinetic energy per unit mass (KE) could be inferred. This rotation rate could also be inferred from video. The effective velocity disturbance for Taylor vortices (U'rv) is then in both axial and radial directions with no contribution from circumferential motions (Fig. 4). The (smaller) fluctuating component of velocity disturbance (u'f) was found to be nearly homogeneous and isotropic throughout the Taylor vortex (but lower near the walls) with a broad frequency spectrum similar to that reported previously,t8 Figure 4 shows the spatially- and directionally-averaged u'f. Henceforth u' -= "~,/u'rv2 + u'fz, i.e. the energyweighted sum of U'rv and u'f. Chemical front visualization was implemented using planar laser-induced fluorescence (LIF) of disodium fluorescein, which fluoresces above pH

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3.8-4.2. (Such techniques are inapplicable to gaseous flames; this e.xemplifies yet another advantage of aqueous chemical fronts.) Since the reactant/ product pH is about 6.6/2.3 for our mixtures, the reactants/products do/do not fluoresce when illuminated by Ar-ion laser light (514.5 nm). SL was unaffected by the small concentrations of fluorescein (typically 10-5 M) employed. The planar laser sheet cuts perpendicularly through the transparent rectangular box and passes through the two cylinder axes. The laser sheet thickness was ~0.3 ram. ST was defined as the axial propagation rate of product, which is consistent with conventional definitions1 because ST multiplied by the front area projected in the mean propagation direction (the annulus cross-section area in this case) provides the volumetric rate of product creation. ST was nearly constant along the entire cylinder length* after a development length of several gap widths. Chemical fronts were initiated at the top surface of solution with the inner cylinder stationary. The fronts were allowed to spread uniformly in the annulus and develop stable downward propagation before rotating the inner cylinder. Front topology *This observation emphasizes an important difference between propagating reaction fronts and passive scalars in nonuniform flows. In the latter, contours of constant mean composition generally advance with Sr ~ 1/V't (t = elapsed time); this has been demonstrated z~ for TC flows at high ReTc. This is characteristic of most random-walk (diffusion) processes because as the scalar advances, its mean gradient continually decreases due to dilution. In contrast, propagating fronts continually replenish their gradient by creating new product immediately behind the front, enabling constant SL arbitrarily far from external sources.

FIG. 5. Instantaneous (0.001 sec exposure) crosssectional LIF photographs of propagating fronts in Taylor-Couette flows at different SL and Rerc. a) SL = 0.0023 cm/sec, Rerc = 630; b) SL = 0.0023 cm/ sec, ReTc = 4500; c) SL = 0.0071 cm/sec, Rerc = 630; d) SL = 0.0071 cm/sec, Re~c = 4500. was then recorded using video and 35 mm still cameras.

Results

Front Appearance: Below ReTr fronts remained fiat and propagated with velocity SL. Above ReTc,c, in "Taylor vortex" and "wavy vortex" flow regimes, thin fronts wrapped around each vortex and propagated stepwise through the vortex array. Fronts were simultaneously visible in several vortices with successively less product in vortices closer to reactants. Figures 5a and 5c show front topology in "wavy vortex" arrays at different U. As U increases, more cells contain active fronts. Pockets of reactants 21 are probably present but uncertainty about the third dimension precludes definite conclusions. At ReTr --< ReTC,T, fronts are much more contorted (Figs. 5b and 5d); at high Ka (low SL), sharp interfaces between reactants and products disappear and fragmented reaction zones, suggesting distributed-combustion, are observed (Fig. 5b).

548

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Since disodium fluoreseein exhibits a sharp, nonlinear pH response, it is uncertain whether observed "thin" LIF interfaces imply thin reaction zones. UT data (below) provide alternate assessment of thin-flame thresholds. However, where broad interfaces are observed, chemical reaction is likely to be occurring in the distributed-combustion mode. Changing exposure time and laser-sheet thickness confirmed that the broad interfaces were not imaging artifacts.

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To clearly distinguish this result from the analogous multiple-scale result5 U~ = exp(U~/U~) requires high U (~100), which is inaccessible to gaseous flames (see Introduction). For lower SL and higher U, agreement is less satisfactory, indicating Ka effects. Fig. 6b, where data are correlated with Ka, illustrates this effect. Note ReT =-- u'L1/v, not ReTr is needed for Ka estimates; Lt is taken as the cylinder gap. For Ka ~< 5, all data nearly collapse onto a single curve, indicating a thin-flame regime. By comparison, the thin-flame regime ends at Ka 0.15 in gas combustion) 5 The reason for this difference is not obvious, though the high Ze of gaseous flames may be a factor. For Ka ~> 5, at fixed U, Ur is lower for higher Ka. This indicates that

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Front Propagation Velocities: Figure 6a shows the effect of U on UT for different SL- Data at each SL show a slight jump in UT at U corresponding to ReTr ~ 2500, where the turbulent Taylor vortex regime begins: Thus, increasing the velocity scale diversity at fixed U increases UT, consistent with gas combustion data. 1 For all SL, UT is lower than multiple-scale predictions3-7 (Fig: 1). At low ReTr (thus low U) this is probably because TC flows are essentially single scale, ts At sufficiently high U, the rate of area increase of a propagating front interacting with a one-scale flow-field could partially "saturate" due to collisions between front elements. This causes "pocket" formation which annihilates flame-front area and reduces St. 2] In multiple-scale flow-fields, fronts may avoid saturation by wrinkling on many separate scales. As Rexc increases, the amount of smallscale, broad-spectrum disturbance (u'f) increases, thus increasing ST (Fig. 6a). However, since Ka also increases, the fronts partially quench, lessening the increase in UT (see below). For high SL and low U, all data nearly collapse onto a single curve. These data follow a proposed relation (see Appendix) for the interaction of propagating fronts with steady, uniform 2-D vortex arrays:

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F1G. 6. Measured effect of velocity disturbance intensity (u'/S~,) on the front propagation velocity (S~/SI,) a) Data correlated with SL and compared with theoretical predictions for Hugyen's propagation in a single-scale 2-D vortex array (Eq. (i)). Inset: small u'/S~+ only. b) Same as a) but correlated with Karlovitz number (Ka) and compared with theoretical predictions for distributed-combustion (Eq. (2)) at Ka = 25. straining of laminar flamelets by flow disturbances decreases their mean reaction rate, consistent with gas combustion data 1 and theory. 3 At high Ka, distributed-combustion is expected and is consistent with the LIF images (Fig. 5c). Using Damk6hler's2 hypothesis for distributed-combustion (see Introduction) UT ~ DV~~T/DL, along with empirical data2~ in turbulent TC flow from which DT ~ 0.14 v ReTc 3/4 can be inferred and the relation between Rewc and ReT inferred from the data in Fig. 4, we obtain 0. t9U 3/2 UT ~ Ka3/4Scl/4 for ReTc >> 1, Ka -> 1 (2) At the highest Ka range for which several experi-

EXPERIMENTAL SIMULATION OF PREMIXED TURBULENT COMBUSTION mental data are available, predictions of Eq. (2) are shown in Fig. 6b. The agreement with experiment is only fair but encouraging considering the simplicity of the model employed.

Flame-Quenching:

One point not shown in Fig. 6 is with SL = 0.0019 cm/sec, U = 10,200 (corresponding to Ka = 900), for which UT ~ 870. Even at this large Ka, no global front-quenching was observed; instead t h e ~ fragmented front exhibited a quasisteady propagation rate and front thickness. If the reaction had quenched, progressive front slowing and broadening would be expected. By comparison, gaseous flames globally quench 16 at Ka ~> 1.5. This suggests that extinction of gaseous turbulent flames may not result primarily from mass extinction of flamelets. As discussed elsewhere, z2 since distributed turbulent flames are much thicker than laminar flames, they suffer much more severe heatlosses; in gaseous flames extinction could result from these losses, lo Another possibility is that since thicker flames require greater ignition energy, sparks adequate to ignite "thin" flames may be insufficient for distributed flames.

549

Appendix Consider two points on a line in a nonuniform, zero mean velocity 2-D flow which are initially infinitesimally separated. Separation distance (L) increases exponentially with time in the early (linear) evolution stage according toz3 L(t) = L(O)et/~ where zf denotes the flow time scale. In a steady, uniform array of 2-D vortices of size Lt and rotation frequency - u'/Lt, "rf -~ L t / u ' is the only relevant scale. In the thin-flame regime, only front length (or area in 3-D) affects ST(t), hence ST(t)/SL = L(t)/ L(O) = et/~L ST(t) is averaged over the time required for the front to consume the entire eddy ('rc), given by LI/(Sv), where ( ) denotes average. Thus U T ~- (ST)IS L = etc/rY or U T = e U/Ur. This relation is valid at high U but does not reproduce the ClavinWilliams result 1~ Uv = 1 + U2 for small U. A simple interpolation formula {Eq. (1)} satisfies both asymptotic limits; the low-U correction is significant (>10%) only for U < 10. Acknowledgements

This work was supported by the National Science Foundation Presidential Young Investigator Prograin, Grant No. CBT-86-57228 and NASA-Lewis under Grant No, NAG3-1242. We thank' Dr. Alan Kerstein and Prof. Andrew Bocarsly for helpful discussions.

Conclusions REFERENCES Propagating fronts in aqueous autocatalytic chemical reactions show significant potential for experimental simulation of turbulent premixed combustion because (1) many common modelling assumptions are more nearly matched by these fronts than premixed-gas flames and (2) regimes inaccessible to gaseous flames and numerical modelling (high U, distributed combustion, . . .) can be studied. For one-scale (Taylor vortex) flows at low Ka, "thin-flame" behavior is exhibited and the measured effect of U on UT compares favorably with predictions of a simple model. Increased diversity of flow scales is shown to increase UT~ The mean chemical reaction rate per unit of flame surface decreases as Ka increases, consistent with gas combustion experiments. At very high Ka, modes similar to distributed combustion are observed; Damkfhler's 2 original hypothesis provides fair estimates of ST. No global quenching of fronts by flow disturbances was observed even at Ka ~ 900, which is 600 times greater than that which extinguishes gaseous flames. This suggests that current models of flame-quenching by turbulence may require some re-evaluation, perhaps in connection with conductive or radiative heat-losses or ignition effects.

1. ABDEL-GAYED,a., BRADLEY, D. AND LAWES, M.: Proc. Roy. Soc. (London) A414, 389 (1987). 2. DAMKOHLEILG.: Z. Elektrochem. angew, phys. Chem 46, 601 (1940). 3. BRAY, K.: Proc. Roy, Soc. (London) A431, 315 (1990). 4. ANAND, M. AND POPE, S.: Combust. Flame 67, 127 (1987). 5. YA~HOT, V.: Combust. Sci. Tech. 60, 191 (1988). 6. SIVASHINSKY, G., in: Dissipative Structures in Transport Processes and Combustion, Springer Series in Synergetics, Vol. 48, Springer-Verlag, 1990, p. 30. 7. GOULDIN, F.: Combnst. Flame 68, 249 (1987). 8. RUTLAND, C., FERZIGER, J. AND El TAHRY, S.: Twenty-Third Symposium (International) on Combustion, p. 621. The Combustion Institute, 1991. 9. DAHM, W. AND DIMOTAKIS,P.: J. Fluid Mech. 217, 299 (1990). 10. WILLIAMS, F. (1985): Combustion Theory, 2nd ed., Benjamin-Cummins. 11. PETERS, N.: Twenty-First Symposium (International) on Combustion, p. 1231. The Combustion Institute, 1986.

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TURBULENT C O M B U S T I O N - - P R E M I X E D

12. LUTHEI~, R.: Z. Elektrochem. 12, 596 (1906). 13. HANNA, A., SAUL, A. AND SHOWALTER, K.: J. Am. Chem. Soc. 104, 3838 (1982). 14. ABDEL-GAYED, R., BRADLEY, D. AND LUNG, F.: Combust. Flame 76, 213 (1989). 15. YOSttlD^, A.: Twenty-Second Symposium (International) on Combustion, p. 1471. The Combustion Institute, 1989. 16. ABDEL-GAYED, R. AND BILttl)LEY, D.: Combust. Flame 62, 61 (1985). 17. BUCKLEY, S., SriY, S. AND RO.~NEY, P.: Paper no. 91-13, Spring Technical Meeting, Western States Section, Combustion Institute, Boulder, CO, March 1991.

18. FENSTERMACttER, P., SWINN~',Y, H. AND GOLUB, J.: j. Fluid Mech. 94, 103 (1979). 19. SMITtt, G. AND TOWNSEND, A.: J. Fluid Mech. 123, 187 (1982). 20. TAM, W. AND SWINNEY, H.: Phys. Rev. A 36, 1374 (1987). 21. JOULIN, G. ^ND SIVASmr~SKY, G.: Combust. Set. Tech. 77, 329 (1991). 22. ROr~NEY, P. AND YAKnOT, V.: Flame Broadening Effects on Premixed Turbulent Flame Speed. To appear in Combust. Sci. Tech. (1992). 23. BATCItELOR, G.: Proc. Roy. Soc. (London) A213, 349 (1952).

COMMENTS John Grifftths, University of Leeds, U.K. This is an interesting and novel approach to the experimental simulation of complex combustion phenomena. However, in order to maximise the potential for application of such analogues to turbulent combustion and flame propagation, readers might benefit from an awareness of the very extensive background related to the understanding of spatio-temporal phenomena in chemical systems, and especially that which is closely connected to this paper. Perhaps the most distinguished work on spatio-temporal patterns in the Couette reactor is that of Swinney et al., concerned mainly with the Belousov-Zhabotinsky reaction (e.g., W. Y. Tam and H. L. Swinney, Physica D, 46 (1990) 10). Recently this group has also reported experimental results for the spatial variation of species concentrations in the iodate-arsenite reaction (R. D. Vigil, Q. Quyang and H. L. Swinney, J. Chem Phys, 96 (1992) 6126). The mathematical analysis of propagating reaction-diffusion fronts in the iodate-arsenite reaction is discussed by A. Saul and K. Showalter in Chapter 11 of "'Oscillations and Traveling Waves in Chemical Systems" (R.J. Field and M. Burger, Eds., Wiley lnterscience, New York, 1985, p. 415). Finally, in order to discover the remarkably rich spatial and temporal behaviour, including chemical chaos, that can be exhibited by autocatalytic reactions formalised as A + mB ~ nB, readers should turn to "Chemical Oscillations and Instabilities", by Peter Gray and Stephen Scott, International Series of Monographs on Chemistry, 21, Oxford Science Publications, 1990. Author's Reply. As Prof. Grifl~ths points out, there is a vast body of literature on the subject of autocatalytic reactions. There are many potentially interesting applications of these reactions to the experimental simulation of premixed combustion

processes. We appear to be the first group to have done so, and we have explored only one such application. We note that Swinney's studies of autocatalytic reactions in Taylor-Couette flows considered the case where one reactant was fed in from one end of the apparatus and the other reactant from the opposite end. In other words, Swinney developed a "turbulent flow reactor" and operated it in a nonpremixed mode (in his case at very high Karlovitz numbers). One can imagine other interesting nonpremixed "'combustion" experiments using autocatalytie reactions. It is also interesting to note that the mathematical an',dysis of the iodate-arsenous acid system (which is also given in Ref. 13 of our paper) yields an exact solution for the propagation rate in a buffered solution (pll = constant) with large excess of arsenous acid. This may facilitate subsequent mathematical analyses (e.g., of stretch effects, stability properties) which are intractable (without approximations) for systems having reactions dominated by Arrhenius kinetics. We look forward to such developments.

j. Chomiak, Chalmers University of Technology, Sweden. The autocatalitic reaction fronts have no unique solution for front speeds and so it is difficult to speak here on equivalent laminar flame speed. Have you checked the stability of flame speeds? The Taylor vortices in your apparatus hardly resemble turbulence as it is very difficult for the front to pass from one vortex to another which changes totally the flame propagation picture especially in the case of the very slow fronts of your experiment. Obviously this effect determines the overall slow front propagation not the stretching which in the non-Arrhenius chemistry systems can only increase

EXPERIMENTAL SIMULATION OF PREMIXED TURBULENT COMBUSTION front speeds and not decrease them as no quenching is possible in this case. The quenching of flames both local and global always occurs due to heat losses.

Author's Reply. While the KPP criterion does not ensure that a unique stable front propagation rate will exist, we have found the propagation rates to be very stable, repeatable, consistent between experiments performed in tubes and petri dishes, and consistent with previous work by others. On the other hand, when iodate is in stoichiometric excess, there is no unique propagation rate for the reasons discussed in Ref. 13. In a similar context, it should be nnted that the "cold boundary difficulty" causes gaseous flames with Arrhenius-like kinetics to exhibit nouunique propagation rates, since the incoming mixture is reacting. (There is no corresponding problem in the arsenous acid-iodate system because there is no reaction without the product iodide, which is not present in the reactants.) Furthermore, the existence and uniqueness of the turbulent burning velocity has not been established theoretically. So it is the rule rather than the exception to discuss steady propagation rates of laminar and turbulent fronts in gaseous or aqueous systems even though the validity of these concepts is not theoretically assured. As discussed in the written paper, at the Reynolds numbers employed in this study, Taylor vortices are the dominant flow structure but not the only one. There is a turbulent content superimposed on the mean (Taylor vortex) flow, just as jets, pipe flows, etc. have both mean and fluctuating components. Consequently, there is random, smallscale motion which can conveet the front from the

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domain of one Taylor vortex to another. The correspondence of our simple model (which does not consider the time for a front to jump from one vortex to another) with the experimental results suggests that it is not so difficult for the front to jump across vortices. Your statement that stretching increases the propagation rate is not consistent with our experim e n t s - t h e measured effect of stretch was to decrease the mean SL as in gaseous turbulent flames. We disagree with your statement that no local quenching of fronts is t)ossible in non-Arrhenius systems. Even when heat release is absent, we expect local disruption of the front when the local strain rate is higher than the chemical rate because the residence time is less than the time required for reaction. This expectation is consistent with our experimental results.

Derek Bradley, University of Leeds, U.K. This is very stimulating research. Questions of the degree to which the results are analogous to those from turbulent gaseous flames might best be answered after theoretical analysis of stretched laminar liquid flames. Author's Reply. We agree with your comment, and have begun both theoretical and experimental investigations on this topic. However, the results do suggest that behavior similar to that expected of gaseous flames is indeed present--namely, thin fronts with constant St. when the characteristic strain rates are much lower than the characteristic chemical rates (i.e., low Ka), and fragmented reaction zones at high Ka.