a 16 It involves a change of laminar burning velocity, widening or narrowing combustion limits for

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1 Peculiarities of filtration combustion of hydrogen-, propane- and methane-air mixtures in inert porous media. Kakutkina N.A., Korzhavin A.A., Mbarawa M. * Institute of chemical kinetics and combustion SB RAS, , Novosibirsk, kktk@kinetics.nsc.ru * Tshwane University of Technology, X860, Pretoria 000, South Africa It is well recognized that effects of Lewis number which is the ratio of diffusivity of gas mixture component to gas thermal conductivity, can change essentially a gas combustion characteristics. We will recognize as Lewis number effects both proper Lewis number effects and effects of flame front curvature be related with Markstein number, Ma, which depends on Lewis number. At filtration gas combustion (FGC) in inert porous media conditions for Lewis number effects manifestation realize automatically. Indeed, at FGC in porous medium a bending of flame front is inevitably due to the proper porous medium structure. Therefore at FGC in porous media these effects must be inhere in the system itself. A set of phenomena attributed commonly to Lewis number effects in laminar flames is wide enough. 0 It involves a change of laminar 8 burning velocity, widening or a 6 narrowing combustion limits for 4 curved flame front, flame stretch effects, diffusion-thermal instability, cellular flames. Lewis number effects are more apparently for lean hydrogenand rich propane-air mixtures, that is when Lewis number of deficient component of gas mixture is more than. Taking into account this fact the attempt to reveal Lewis number effects at FGC is done in this paper by the way of comparative experimental study of FGC characteristics of hydrogen-, propane- and methane-air mixtures. T, K Coordinate, cm Time, s Fig.. Typical dependencies of wave front coordinate (a) and increment of porous medium temperature (b) on time. 70% H +air. Experimental setup. Setup for FGC study consists of burner and a system for registration of characteristics of FGC waves. The burner is a vertical quartz tube with wall thickness mm, length 500 mm and outer diameter 40 mm for experiments with b

2 hydrogen, and 50 mm for experiments with propane and methane. The tube was filled with porous medium. A filling of granular carborundum was used as porous medium. The filling with grain size from to mm was used in experiments with hydrogen, from to 3 mm for propane and two filling, i.e. to 3 and 5 to 6 mm for methane. The combustible mixtures were prepared on the base of flow rates of fuel and air. The separate gas flows were mixed outside of the burner and entered a burner through inlet port. Combustible gas mixture was ignited at the upper part of the tube by pilot flame. The flame heated up the upper layer of porous medium, forming combustion wave. Visually the combustion wave was observed as brightly luminous zone, which moved through the porous medium. The combustion wave was introduced into a given segment of the burner by changing the parameters of the gas mixture. Next, the given parameters of the gas flow were set and the recording system was started. Combustion wave propagation was recorded by a digital Web-camera connected to a personal computer. The combustion wave was photographed automatically at regular intervals (from 0 to 00 seconds) and stored into the computer memory. The dependencies of flame coordinate on time were obtained as a result of snaps treatment. The temperature in the combustion wave measured by Chromel-Alumel thermocouple inserted in porous medium on the tube axis. The thermocouple reading was recorded with a digital voltmeter at regular intervals and stored by the PC-data based acquisition system for further processing. Experimental results. Fig. shows typical recording of coordinate of FGC wave front (a) and porous medium temperature in combustion wave with time. The steady-state velocity of FGC wave propagation (u) was determined on combustion wave trajectory. The temperature recording was used for determination of maximum porous medium temperature in combustion wave (T m,exp ). Moreover, the temperature distribution in combustion wave T(x) was obtained on the base of the temperature recording and measured value of FGC wave. Fig. shows dependencies of FGC wave velocity on gas mixture composition (which is characterized by equivalence ratio φ) for mixtures of air with hydrogen (a), propane (b) and methane (c). Positive velocity values correspond to coflow and negative to counterflow wave propagation. All dependencies have V-form. It makes oneself conspicuous that the minimum of u(φ) dependence is for hydrogen mixtures in rich area at φ,5, and for propaneand methane mixtures is at lean areas. Dark symbols in Fig. 3 show experimentally measured values of maximum heating up of porous medium in combustion wave depending on mixture composition. The value of heating up T m,exp was determined as Tm, exp = Tm,exp T0, where T m,exp is maximum value on the measured temperature profile in porous

3 medium, and T 0 is the room temperature. Note, that for hydrogen both and for hydrocarbon mixtures the porous medium heating up depends weakly on gas mixture composition. From hydrocarbon mixtures data the weak dependence of heating up on filtration wave velocity can be noticed. Combustion wave velocity, cm/s 0,06 0,04 0,0 0,00-0,0-0,04-0,06-0, ,05 b 0,00 0,005 0,000-0,005-0,00 0,00 0,05 0,00 0,005 0,000-0, ,4 0,6 0,8,0,,4,6,8-0,00 0,4 0,6 0,8,0,,4,6,8,0,,4 φ Fig.. Dependencies of combustion wave velocity on equivalence ratio. a H +air, filtration velocity v=,45 m/s; b C 3 H 8 +air: v=0.5 m/s (), 0.66 m/s (), 0.79 m/s (3); c CH 4 +air: -4 grain size of porous medium 3 mm, mm, v=0.4 m/s (), 0.3 m/s (, 5), 0.45 m/s (3), 0.6 m/s (4) a c 3

4 Analysis and discussion. Analysis of data obtained has been carried out in the frame of simplified one-temperature model of FGC, corresponding to fast heat exchange between gas and porous medium. The expression for velocity of propagation of an adiabatic FGC wave u has been obtained in [] dependent on gas mixture composition R( T ) ( ) b T0 GuthZe R Tb T0 T0 GuthZe u uth + ln ln. () E κ sk0ρ gb E κ sk0ρ gb c g ρ gvm Here uth = is the thermal velocity, where c is heat conductivity, ρ is cs ρ s ( m) density, m is porosity of porous medium, v is gas filtration velocity, λ is heat conductivity, subscripts g and s relate to gas and porous medium respectively, λs G=ρ g v is mass flow rate of the gas, κ s = is thermal diffusivity of porous cs ρ s medium. Mixture composition is characterized by the value of adiabatic heating up T b T = 0 Q / c, where Q is heat release of gas mixture combustion. E( Tb T0 ) g Ze = RTb is Zeldovich number, k 0 is preexponent and, E is activation energy of one-step chemical reation, ρ gb is the density of gas mixture at temperature T b. The second term in () under typical values of experimental parameters is always negative. The third term in the brackets is also negative. Then it can be seen from Eq. () that at a constant filtration velocity, the minimum value of combustion wave velocity is reached at the maximum value of adiabatic heating up i.e. for stoichiometric gas mixture. However, according to experimental data in Fig. the minimum of u(φ) dependence is shifted to rich region for hydrogen-air mixtures and in the lean region for methane- and propane-air mixtures. The shifting of the minimum of u(φ) dependence increases as filtration velocity decreases for both propane air mixtures and methane-air mixtures. At a very low filtration velocity of 0.4 m/s for methane-air mixtures, a sharp decreasing of minimum shift almost to zero is observed. Furthermore, the minimum shifting decreases as mean size of porous medium grain increases. The maximum porous medium heating up value in FGC wave T m is related unambiguously with combustion wave velocity. For adiabatic combustion wave this relation is [] Q Tm =. () u c g uth For real nonadiabatic combustion wave this relation involves the term accounting for heat losses: 4

5 T m = c u u, (3) g Ku ( u u) th th th where α e is the heat transfer coefficient from the outside of tube with porous ( m) λs medium, K =. Empty symbols in Fig. 3 show T m values calculated by Eq κ s + Q α e a T m, T m,exp, K b 0,4 0,6 0,8,0,,4,6,8,0 600 c ,5,0,5,0,5 φ Fig. 3. Dependencies of calculated (empty symbols) and measured (dark symbols) values of maximum increment of porous medium temperature on equivalence ratio. a H +air, v=,45 m/s; b C 3 H 8 +air: v=0.5 m/s (), 0.66 m/s (), 0.79 m/s (3); c CH 4 +air: v= m/s (), m/s (), m/s (3). 5

6 (3), using the measured u values. The following parameters values were used for estimations: λ s =4 W/(m K), ρ s =300 kg/m 3, c s =800 J/(kg K), m=0.5. ρ g for every gas mixture were calculated on the base of partial pressures and densities of gas mixture components. The values of heat release of gas mixtures were calculated at initial temperature 300 K using the code ChemKin [3]. Mean values of heat capacities of gas mixtures were determined as the ratio of enthalpy change of the gas under its heating from the initial temperature T 0 to maximum temperature T m, exp to the value of temperature change (T m,exp -T 0 ). The corresponding enthalpy change were calculated also with help of ChemKin. The u values were obtained from the same experiments in which the temperature values T m, exp were measured. The α e values were estimated on the base of the experimental temperature profiles in combustion wave for the same experiments. As it can be seen in Fig. 3 that for hydrogen-air mixtures the measured temperature values are almost fit experimental one s at φ>3. In the lean region the measured T m values are lower considerably than the calculated ones. Opposite for propane-air mixtures, the good agreement is in the lean region at φ<0,9 and in the rich region the measured T m values are lower than the calculated ones. For methane-air mixtures the measured temperatures are lower than the calculated ones at both lean and rich mixture regions. The dark symbols in Fig. 4 show the divergence between calculated and measured T m values. For hydrogen-air mixtures noticeable divergence arises at φ 3 and rise monotonically as φ increases. At φ 0, the temperature difference reaches about 40 К. For propane-air mixtures the divergence value increases as φ increases and the maximum difference reaches also about 400 К. For methane-air mixtures the minimum divergence value of about 00 К occurs at the lean region of about φ 0,5. At φ increasing the divergence rises weakly, until it reaches the maximum value of about 300 К. Note, that the filtration velocity changes do not lead to noticeable changing of divergence between measured and calculated temperatures: the experimental points for different filtration velocities are grouped near the same curves both for propane and methane-air mixtures. Thus the experimental study carried out has revealed two anomalous peculiarities of FGC namely: the shifting of the minimum of u(φ) dependence relative to φ= and the reduction of temperature in combustion wave relative to thermodynamically calculated one. Effected values, at least on the combustion wave temperature, are very large and observed in a wide φ ranges. These two types of anomalies are undoubtedly interrelated. It is evidently from the relationship between combustion wave velocity and maximum temperature in combustion wave obtained in [] for the one-temperature adiabatic model: ( ) ( ) m RT λsρ m g E / RTm u = uth k e 0. m E Tm T0 mcgg 6

7 It is clear from this expression that the low T m corresponds to the high velocity of combustion wave if all other things are being constant. Therefore in φ region, where deterioration of combustion wave temperature is observed, u values must be a ( T m - T m,exp ), К ,4 0,6 0,8,0,,4,6,8,0 0,5,0,5,0,5 φ Fig. 4. Dependencies of difference between calculated and measured temperature of porous medium on equivalence ratio. a H +air, v=.45 m/s; b C 3 H 8 +m/s: v=0.5 m/s (), 0.66 m/s (), 0.79 m/s (3); c CH 4 +air: v= m/s (), m/s (), m/s (3). excessive. The increasing of u values in the region of anomalous temperature deterioration leads to deformation of u(v) curve, which theoretically must have the minimum at φ=, and as a consequence there is shifting of the minimum of this 3 b c 3 7

8 curve to the region of φ values opposite to the temperature deterioration region. Therefore, for hydrogen mixtures, the minimum of u(v) dependence is shifted to rich mixtures region and for propane mixtures is at the lean mixtures region as it is observed experimentally (see Fig. ). For methane-air mixtures temperature deterioration is observed at both lean and rich mixtures regions. Correspondingly, combustion wave velocity must increase in a whole range of φ values. However more high values of temperature deterioration are observed at the rich mixture region. Therefore minimum of u(v) dependence is shifted to the opposite - lean mixture region. From aforesaid it follows that two revealed anomalies are most probably two consequence of the same reason. 0,5 0,4 a 0,3 0, ( T m - T m,exp )/ T m 0, 0,0 0,3 0, 0,5,0,5,0,5 3,0 b 0, 0,0-0, 0,5 0,6 0,7 0,8 0,9,0 Anomalous temperature and velocity characteristics of FGC waves were observed for lean hydrogen and rich propane-air mixtures at the same regions where as a rule Lewis number effects on laminar flames manifests. This circumstance allows to assume that the revealed anomalies have the same nature as Lewis number effects on laminar flames. The change of laminar burning velocity at the curved flame front [4], and as a consequence development of flame instability relative to flame front curving [5], the cellular flame appearance [6] Le ef Fig. 5. Dependencies of relative difference between calculated and measured porous medium temperatures on effective Lewis number. a H +air, b C 3 H 8 +air 8

9 relate to such effects. Diffusion demixing is one of the phenomena underlied the Lewis number effects. At FGC in porous medium the conditions favorable for appearance of diffusion demixing are due to difference in diffusivity of different gas mixture components. In a filling porous media the nearest pores are not in the same plane. Therefore, flamelets in the nearest-neighbor pores are at different levels along the gas filtration direction. Flamelets prominently in the fresh mixture such as laminar flame convexity, are supplied with additional flux of gas mixture components, extracted diffusionally from the ambient gas mixture. Correspondingly, in the flamelets of the following layer of pores gas mixture depleted with reacting components burns. Such diffusion demixing effects produce higher heat release in the first flamelets layer than in the normal case of flat flame for the given gas mixture and less in the second layer. Moreover, if diffusion demixing is strong the gas mixture enters in the second layer could be out of the flammability limits. Then, the averaged heat release in two layers can be less than heat release from initial (nondemixing) gas mixture. This could lead to temperature deterioration in FGC wave and increasing of combustion wave velocity. Otherwise depleted gas mixture will ignite nevertheless, but not in the following layer and only when the residence time in the warmed up porous medium becomes more than the induction time for ignition of a given depleted gas mixture, i.e. far from the first flamelets layer. As a result the reaction zone is widened. In a wide reaction zone in nonadiabatic system heat losses from this zone compete with heat release of chemical reaction and this leads to deterioration of maximum temperature in combustion wave. Effects of diffusion demixing on laminar flames, for example, a change of laminar burning velocity in a curved flames, increases gradually with the change of the gas mixture composition. At the same time Lewis number of deficit component of gas mixture changes by threshold at φ=. This contradiction has been overcame in [7], where the effective Lewis number (Le ef ) has been introduced, which changes continuously as φ changes. In [7], calculated Le ef values dependent on φ for hydrogen- and propane-air mixtures are given and it is shown that Le ef increase leads to increasing of laminar burning velocity due to diffusion demixing phenomena. Fig. 5 shows the values of the relative temperature deterioration in FGC wave for hydrogen- and propane-air mixtures as a function of effective Lewis number. It can be seen that relative value of ( T m - T m,exp )/ T m for both hydrogen and propane-air mixtures increases monotonically with increase of Le ef in the same way as the burning velocity for ordinary laminar flame. This fact is indicative for the hypothesis of diffusion demixing in FGC processes. Conclusion. The experimental studies carried out reveal deviations of FGC wave characteristics from theoretically determined. These anomalies manifest for the 9

10 same gas mixtures as Lewis number effects in laminar flames. This circumstance allows to assume the similarity of phenomena underlined Lewis number effects in laminar flames and the revealed anomalies in FGC wave characteristics, that is corroborated by the correlation between relative temperature deterioration in FGC wave and effective Lewis number. Assuming these evidences as the base to relate the revealed anomalies to Lewis number effects, one can ascertain that Lewis number effects at FGC is manifested by decreasing of temperature in combustion wave and increasing of velocity of combustion wave propagation. Note that the flexing of FGC wave front doesn t required for Lewis number effects manifestation. The effect is released at the level of flamelets, burning in porous of the filling, where flame front curving exists always in a varying degree. The revealed effects can be used in practical application of the FGC processes. One of the most attractive properties of FGC is superadiabatic effect, which allows to burn gas mixtures with low enthalpy, which beyond the combustion limit conditions of ordinary flames []. The revealed effect of temperature deterioration in FGC wave will limit the superadiabatic effect and narrowed combustion limits in porous medium. This will negatively affects the operation of practical devices operated on the base of FGC. Further study to establish the mechanism of Lewis number effects and the relationship of revealed effects with the system characteristics is required. Acknowledgements The work is supported partly by the Russian Foundation for Basic Researches (Grant No ). The financial support of National Research Foundation of South Africa for Dr. M. Mbarawa is gratefully acknowledged. References.. Kakutkina N.A. Some aspects of instability of gas combustion in porous media. //Combustion, explosion and shock waves V. 4, No. 4.. Laevskii Ju. M., Babkin V.S. Filtration combustion of gases // Propagation of thermal waves in heterogeneous media. Ed. Matros Yu. Sh. Novosibirsk, Nauka, Kee R.J., Rupley F.M., Miller J.A. CHEMKIN-II: A FORTRAN chemical kinetics package for the analysis of gas phase chemical kinetics // Sandia National Laboratories SAND B. 4. Nonsteady-state flame propagation. /Ed. Markstein J.G M., Mir 5. Zeldovich Ya.B., Barenblatt G.I., Librovich V.B., Mahviladze G.M. Mathematical theory of combustion and explosion. M.: Nauka, Lewis B., Elbe G. Combustion, flame and explosion in gases.m: Mir, Sun C.J., Sung C.J., He L., Law C.K. Dynamics of weakly stretched flames: quantitative description and extraction of global flame parameters // Combustion and Flame V. 8. P