ISSN 0018�151X, High Temperature, 2010, Vol. 48, No. 3, pp. 436–440. © Pleiades Publishing, Ltd., 2010.Original Russian Text © B.E. Gel’fand, S.P. Medvedev, S.V. Khomik, G.L. Agafonov, 2010, published in Teplofizika Vysokikh Temperatur, 2010, Vol. 48, No. 3, pp. 458–462.

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INTRODUCTION

The significant difference (by a factor of ten andmore) between the measured and calculated values ofdelay of self�ignition of hydrogen�oxygen gas mixturesat a relatively low temperature (900–1100 K) andmoderately elevated pressure (0.5–1 MPa) was firstobserved by Voevodsky and Soloukhin [1]. Therevealed feature was further reproduced in hydrogen�air mixtures behind reflected shock waves [2]. Thesame inferences were later made as a result of experi�ments [3–5] in shock tubes of a diameter other thanthat in [2] with simultaneous recording of self�ignitionby optical and baric instruments. In view of doubtswhich arose in the reliability of kinetic schemes ofexplosive phenomena in the pressure and temperatureranges of practical importance from the standpoint ofexplosion safety and operating modes of numerousenergy devices, activities were under way in recentyears aimed at obtaining experimental data and atimproving the kinetic models. A comprehensive pic�ture of present�day understanding of special featuresof self�ignition of hydrogen�containing mixtures isgiven in [6–8]. As was the case in the pioneering pub�lication [1], the values of delay of self�ignition τign attemperature T < 1000 K measured by various authorsturned out to be much lower than the values predictedby all models in the pressure range P = 0.1–2 MPa. Anumber of unsuccessful attempts were made atexplaining the revealed differences [4, 6–8]. Referredto as the reasons for reduction of delays of self�ignitionin shock tube experiments were the local hot spots dueto extraneous solid particles and the chemical impuri�ties in the reacting medium. References were furthermade to structural features of shock tube such as the

wall roughness of the measuring section and the emer�gence of secondary disturbances due to rupture ofmembrane. Structural changes were made in the shocktube for the purpose of extending the allowed time ofobservation to 20 ms [7]. Attempts at estimating theimportance of temperature inhomogeneity due to for�mation of boundary layer on the walls may likewise beregarded as unsuccessful. The theoretical and experi�mental data on the values of τign at Т < 960 K still dif�fered from one another by a factor of ten and more.

An appreciable difference between the calculatedand measured values of delay of self�ignition uponinjection of pre�stirred hydrogen�air mixture into apreheated volume was revealed in the experiments ofCiccarelli et al. [9] who studied the effect of initialtemperature on the initiation of gas detonation. It wasnoted that conventional calculations by standardschemes produce a many times longer time of safestorage of hydrogen�air mixture in a preheated closedvolume.

Our observations were performed with the objectiveof comparing the delays of self�ignition in reflectedshock and explosive waves. The latter waves are char�acterized by continuous decrease in pressure and tem�perature behind the front. In addition, it is necessaryto expand the data base on delays of self�ignition ofhydrogen�air mixtures at moderately high tempera�ture Т < 1200 K, i.e., in the neighborhood of the lim�iting value of T ≈ 800 K previously given in [9].

EXPERIMENTAL PROCEDURE

In order to eliminate the doubts [7] concerning theparameters of flow both behind and in front of the

Self�Ignition of Hydrogen�Air Mixtures behind Reflected Explosive Waves

B. E. Gel’fand, S. P. Medvedev, S. V. Khomik, and G. L. AgafonovSemenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 119991 Russia

Received June 30, 2009

Abstract—Experimental results are given, which reveal the special features of self�ignition of hydrogen�airgas mixtures behind reflected explosive pressure waves at moderate (below 1200 K) temperature and elevatedpressure. The experiments are performed in a modified shock tube which provides for generation of explosivepressure waves. The explosive waves are characterized by a jump of parameters of shock�compressed gas(pressure, temperature) at the front with their subsequent continuous decrease. This is how undesirable gas�dynamic effects are attenuated, which are due to hypothetical pre�explosion preheating of combustible mix�ture by compression waves. As previously, the experiments involving standard shock waves (with constantpressure/temperature levels) revealed a significant (by a factor of ten and more) deviation of measured valuesof delay of self�ignition from the calculated values towards decreasing.

DOI: 10.1134/S0018151X1003020X

HEAT AND MASS TRANSFER AND PHYSICAL GASDYNAMICS

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SELF�IGNITION OF HYDROGEN�AIR MIXTURES 437

reflected pressure wave, we used a modified shock tubewith different (including ultrashort) high�pressurechambers (HPC) instead of the classical scheme ofshock tube with a long HPC as was the case in [7]. Alow�pressure chamber (LPC) 1 m long with cross sec�tion of 35 × 50 mm2 contained the mixture underinvestigation. An HPC 50 mm in diameter was filledwith helium or a helium�air mixture. In our experi�ments, the length of HPC (LHPC) was in the range from0.03 to 0.5 m. At LHPC = 0.5 m, a step�like shock wavewith constant pressure behind the front was obtainedin the LPC. With two shorter HPCs (LHPC = 0.03 mand LHPC = 0.07 m), a typical explosive wave with con�tinuous decrease in pressure behind the leading frontwas produced in the LPC. The initial pressure of gasmixture in the LPC was varied in the range from 0.03to 0.2 MPa.

Hydrogen�air and hydrogen�nitrogen mixtureswith hydrogen concentration of 15% by volume wereprepared using a fan in a pre�evacuated mixer at tem�perature Т1 = 293 K. Each experiment with combusti�ble mixture was reproduced with its noncombustibleanalog. This enabled one, where possible, to eliminatethe distortion of signal caused by the structure of thesetup.

The pressure�time p(t) diagrams in transmitted andreflected waves were registered by piezoelectric pres�sure cells flush�mounted along the axis on the LPCwalls. Two cells were located in the vicinity of theclosed flat end at distances L1 = 4 mm and L2 =24 mm, respectively. Additional cells were mounted atdistances L3 = 242 mm and L4 = 542 mm from theend.

The total duration of the compression phasebehind the explosive wave traveling in the LPC towardits end ranges from 1 to 3 ms. At a distance of up to200 mm from the end, the velocity of incident wavewas almost constant and could decrease depending onthe wave intensity by not more than 10%. In the regionof observation (at a distance of up to 30 mm from theend), the velocities of incident and reflected waveswere assumed to be constant.

The delay of self ignition of gas mixtures was deter�mined by the p(t) diagrams behind reflected shock(LHPC = 0.5m) and explosive (LHPC = 0.03 m and0.07 m) waves.

Calculated time dependences of pressure and tem�perature are given in Fig. 1 for illustrating the dynam�ics of variation of pressure and temperature of com�pressed gas in the vicinity of the reflecting surface. Thecalculations were performed in a one�dimensionalformulation using the GasDynamicsTool softwarepackage [10] for realizing the procedure of solution ofNavier–Stokes equations by the modified method oflarge particles. In the calculations, similar to experi�ments, the pressure (temperature) profiles were com�pared when shock and explosive waves of the same

intensity (Mach number M) were approaching thetube end. One can see in Fig. 1 (inert gas) that, withthe HPC length LHPC = 0.5 m, a reflected shock waveis generated with a “shelf” of constant parameters atleast 300 µs in duration. When the HPC length isreduced to 0.07 m, the reflected wave (as well as theincident one) is characterized by a triangular profilewith decreasing pressure and temperature. Therefore,one can expect an increase in the delay of ignition inthe case of explosive waves. Calculations with modelreacting gas were performed for illustrating this effectof the pressure wave profile (Fig. 2). The gas wasassumed to be nonviscous and heat�conducting. Therate of chemical reaction (single�stage mechanism)was described by the Arrhenius dependence on tem�perature. The kinetic parameters of the adopted modelwere verified by way of comparison with delays of igni�tion of a mixture of 15% hydrogen in air, which werecalculated by a detailed mechanism including 42 reac�tions [2]. One can see in Fig. 2 that the delay of self�ignition in the case of transition from the shock toexplosive wave increases by a factor of 3.5.

0

0.5

1.0

1.5

2.0

2.5

Pressure, MPa(a)

1

2

(b)

50 μs/div

400

600

800

1000

1200

Temperature, K

12

50 μs/div

Fig. 1. Calculated profiles of (a) pressure and (b) tempera�ture at a distance of 1 mm from the end of shock tube uponreflection of shock and explosive waves. Inert gas. The HPClength is (1) 0.5 m, (2) 0.07 m; P1 = 0.05 MPa, M = 2.9.

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RESULTS AND DISCUSSION

Results of typical experiments are given in Fig. 3 ingraphic form. The p(t) diagrams in Fig. 3 demonstratethe dynamics of variation of pressure behind transmit�ted and reflected explosive waves in combustible(Fig. 3a) and inert (Fig. 3b) media. The distance of therespective pressure cell from the end is given for eachcurve. The gas pressure behind reflected wave at a dis�tance of 4 mm from the end is, in the case at hand, P5 ≈

2.55 MPa. The first pressure shock in all records cor�responds to the transmitted wave front. The secondaryovershoot of pressure corresponds to the time of trans�mission of reflected wave.

A method based on comparison of pressure profilesregistered in combustible and inert mixtures wasdeveloped for determining τign. In Fig. 4 this compari�son is made for the experiments of Fig. 3. Taken as thedelay of ignition is the time of reaching a maximum oncurve 3 reflecting the difference between the values ofpressure level on curves 1 (combustible mixture) and 2(inert mixture). According to the example in Fig. 4,τign ≈ 190 µs. Analysis of the presently employed meth�ods [2–4, 7] reveals that the suggested method givesthe upper estimate of τign.

Comparison of calculated (curves) and measured(points) values of τign behind reflected shock andexplosive waves is made in Fig. 5 depending on thequantity 1000/Т5, where T5 is the calculated tempera�ture behind a reflected wave whose velocity is deter�mined by pressure cells located at distances of 4 and24 mm from the end. Given as the shaded region arethe experimental data of Blumenthal et al. [3] for asimilar mixture with 15% hydrogen in air behindreflected shock waves in a tube (54 × 54) mm2 in crosssection, which were obtained using high�speed pho�tography, recording of UV radiation, and p(t) dia�grams.

All experiments revealed that, given the same tem�perature and pressure, the delays of self�ignition at thefront of shock and explosive waves are close in magni�tude. The disagreement between theory and experi�ment disappears at temperature T5 ≥ 1100 K. At alower temperature, the difference between theory andexperiment progressively increases and becomes unex�plainably large at Т5 ≤ 950 K. The decrease in theparameters of combustible mixture behind explosivewave has no effect on special features of self�ignition ofgas mixture. It will be recalled that in model calcula�tions, as well as in the case of systems with atomizedhydrocarbon fuel [11], the replacement of shock waveby explosive caused an increase in τign.

0

1

2

3

4

5

Pressure, MPa

(a)

1

2

(b)

50 μs/div.

500

1000

1500

2000

2500

Temperature, K

1 2

50 μs/div.

3000

Fig. 2. Calculated profiles of (a) pressure and (b) tempera�ture at a distance of 1 mm from the end of shock tube uponreflection of shock and explosive waves. Reacting gas. TheHPC length is (1) 0.5 m, (2) 0.07 m; P1 = 0.05 MPa, M = 2.9.

Time, 100 μs/div.

(a)

(b)

4 mm

24 mm

242 mm

542

4 mm

24 mm

242 mm

542P

ress

ure,

1 M

Pa/

div.

Fig. 3. The p(t) pressure profiles in explosive wave for amixture containing 15% by volume hydrogen in (a) air and(b) nitrogen.

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SELF�IGNITION OF HYDROGEN�AIR MIXTURES 439

Therefore, in experiments with explosive waves,the previously identified feature was retained forhydrogen�air mixtures, namely, the measured valuesof time of delay of ignition still turned out to be muchsmaller than the calculated values.

CONCLUSIONS

The significant difference between the calculatedand measured values of times of delay of self�ignitionin hydrogen�air mixtures at moderately high tempera�ture is not associated with the dynamics of variation ofgas temperature behind the front of reflected explosivewave in the case where measures are taken for forcedreduction of gas temperature and the sources of itsincrease are eliminated. With transition to measure�ments behind pressure waves with continuouslydecreasing thermogasdynamic parameters, the instru�mental effect [4, 7] on the final results becomes weakeror is eliminated. Most likely, the reasons for reductionof delays of ignition at Т < 1100 K are to be associatedwith the emergence of excited particles, as is indicatedin [12]. An approximate combination of probable par�ticipants of promoted self�ignition may be outlinedaccording to the review of Popov [13]. In so doing, theways of delivery or emergence of excited particles andmolecules in pulse�compressed gas at T < 1000 K stillremain obscure.

ACKNOWLEDGMENTS

This study was supported by the Russian Founda�tion for Basic Research (project no. 09�03�00487). Weare grateful to Prof. F.L. Dryer of Princeton Universityfor letting us familiarize with the data base on self�ignition of hydrogen�containing mixtures.

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1

2

3

Pre

ssur

e, 1

MP

a/di

v.

Time, 200 μs/div.

τign

Fig. 4. Illustration of the method of determining the delayof self�ignition: (1) combustible mixture, (2) inert mixture,(3) difference between the values of pressure level of pro�files 1 and 2 multiplied by coefficient >1.

1.251.201.151.101.051.000.950.900.850.801000/T5

101

100

10−1

10−2

10−3

10−4

τign, s

12345

Fig. 5. Comparison of measured (points) and calculated(curves) delays of self�ignition for a mixture of 15% hydro�gen+85% air; dashed curve indicates calculation at a pres�sure of 1 MPa, and continuous curve—at a pressure of2.5 MPa; shaded region indicates delays of self�ignition mea�sured in [3] at a pressure of 1.1–4.7 MPa: (1) P5 > 2.5 MPa,LHPC = 0.5 m; (2) P5 = 1–1.5 MPa, LHPC = 0.5 m; (3) P5 >2.5 MPa, LHPC = 0.07 m; (4) P5 = 1–1.5 MPa, LHPC =0.07 m; (5) P5 = 1–1.5 MPa, LHPC = 0.03 m.

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