Autoignition of hydrogen at high pressure

Autoignition of Hydrogen at High Pressure T. M. CAIN Defence ResearchAgency, Farnborough, Hampshire GU14 6TD, England The spontaneous ignition of hydrogen at pressures between 3.5 and 7 MPa has been investigated. A free piston compressor was used to rapidly increase the temperature and pressure of a mixture of hydrogen, oxygen, and helium. Explosion occurred during the stroke, and was detected by a piezoelectric pressure transducer. The temperature at ignition is found to be independent of pressure, and is calculated to be approximately 1150 K. A chemical kinetic analysis was conducted, and the results are in good agreement with the experiments. The analysis indicates that the ignition is initiated by the breakdown of H202 to the highly reactive radical OH via the reaction H202 + M ~ 20H + M. A new analytical expression for the "third limit" is derived from the reaction mechanism by introducing the concept of a critical OH concentration; it is shown to be in agreement with the experimental data. © 1997 by The Combustion Institute

NOMENCLATURE Cp CI

E kj Lo J'j R /7 i

P F

t T Y E

[ SPi ] u(i, T) A

specific heat at constant pressure, J mol 1 K 1 specific heat at constant volume, J m o l i K-1 activation energy, J mol-t rate constant of reaction j, in Eq. 4 length of compression tube, m rate of reaction j, mol m -3 s -~ universal gas constant, J mol-1 K-1 data point at bottom of step in pressure pressure, Pa spatial coordinate, m time, s temperature, K mole fraction third-body efficiency concentration of species i, mol m-3 internal energy of species i at temperature T, J molpiston's velocity, m s-1 volumetric compression ratio

INTRODUCTION

Application Hydrogen is burnt at high pressure in rocket, scramjet, and experimental automobile engines. In these engines, ignition may be influenced by the finite rate of the chemical reactions, in addition to other rate-limiting processes, such as heat and mass transfer. In this study of the spontaneous ignition of hydrogen at pressures in the range 3.5-7 MPa, ignition is

solely determined by the finite chemical kinetics, and the reaction was studied independently of these other processes.

History The nonexplosive peninsula between the second and third explosion limits of hydrogen and oxygen is a region of metastable equilibrium in which H 2 0 is produced at a constant rate and the intermediate species H, O, OH, HO 2, and H202 temporarily exist at stable concentrations. The explosion limits were defined by Lewis and Von Elbe [1] as a locus of singularities in the solution of the set of equations (the species balance equations), which determine the values of stable concentrations. Kordylewski and Scott [2] examined the stability of an updated set of species balance equations using bifurcation theory; with this method, they' endeavoured to account for the influence of the heat released by exothermic reactions on the limits. However, their numerical solutions do not differ significantly from those of Lewis and Von Elbe [1], and it will be demonstrated below that both approaches gave a misleading representation of the reaction's behaviour at high pressures. Exact solutions (for a given mechanism) are obtained by direct integration of equations which express the rate of change of a species' concentration with time. Gontkovskaya et al. [3], adopting this approach, found the system to be nonexplosive at pressures well above the traditional location of the third limit. More COMBUSTIONAND FLAME 111:124-132 (1997)

0010-2180/97/$17.00 PII S0010-2180(97)00005 -9

© 1997 by The Combustion Institute

Published by Elsevier ScienceInc.

IGNITION OF H 2 + 0 2 recently, Mass and Warnatz [4] investigated ignition of hydrogen in spherical vessels by integrating the rate equations coupled with transport equations. Their two-dimensional (r, t) model of the reaction did exhibit a third limit, but they found that if the volume was treated as one-dimensional and isothermal (no self-heating), no third limit existed. While there is a wealth of experimental evidence to support the second limit, the position/existence of a third limit is yet to be experimentally confirmed (see Section 2.1).

Present Aim The time scale of the compression in the free piston compressor is short compared to the induction times below the third limit, but long compared to the ignition delay times above the limit (as will be demonstrated). Thus, the facility can be used to determine the explosion limit directly. It is also possible to numerically simulate the compression, enabling a more exact comparison to be made. The ignition experiments revealed the existence of a high-temperature explosion limit, and this phenomenon is investigated both analytically and by integration of the rate equations using an established reaction mechanism.

E~E~ME~S Previous Experiments The traditional technique for determining the third limit is to introduce a measured quantity of oxygen into a vessel containing the hydrogen at the temperature of interest. The resulting pressure in the vessel is deemed to be below the explosion limit if no explosion is detected within an arbitrarily specified time (e.g. 5s, [6]). The results of this technique are notoriously erratic [1], sufficiently so that it was thought necessary to reject many experimental results (generally on the basis of suspected water contamination) when making comparisons with theoretical predictions [1]. Diamy and Ben-Aim [5] tried a variation on the technique, in which the reactants were premixed before admission to the vessel. They found that the position of the explosion limit

125 depended on how fast they opened the stopcock, and understood, with the help of a thermocouple, that the heat produced in the compression of gas admitted early by the gas following was having a significant effect. A second method was tried in which the mixture was introduced into the vessel at a low temperature, and then the furnace's temperature was slowly increased. With this technique, they were able to confirm the position of the second limit, but at pressures thought to be above the third limit, no explosion was detected; only a slow reaction was observed. Diamy and BenAim [5] concluded with the question: "Is the complicated three-limit explosion domain more expressive of the chemical reaction (as is thought usually) or of the experimental and physical conditions?" Barnard and Platts [6] noted that the temperature registered by a thermocouple at the centre of their reaction vessel fell during expansion of the gas to find the second limit. They suggested that this may be connected to the expansion process (the residual gas has done work on the expelled gas). They did not consider this effect when interpreting the increase in temperature, which they observed when admitting oxygen to the vessel to find the third limit. They attributed the temperature increase to heat released by reaction. From these observations, they drew the bold conclusion that the work "provided convincing proof of the very different origins of explosions below the second limit and above the third." Perhaps a conclusion similar to Diamy and Ben Aim's [5] would have been more appropriate. Early shock/detonation tube experiments give a different picture of the hydrogen-oxygen system. Gordon et al. [7] found that above a certain pressure in various mixtures of hydrogen + oxygen + diluent (typically at 1-2 atm), a minimum shock front temperature of 1100 K was required to establish a detonation wave. Lewis and Von Elbe, summarising the work, state that the limit is "definitely linked to chemical kinetic factors" [1], but chose to use experimental results from a reaction vessel when developing their model of the third limit. Voevodsky and Soloukhin [8] noted a "new effect" during experiments on the ignition of

126

T . M . CAIN

hydrogen + oxygen using a shock tube operated in reflected mode. They observed a change in character at postshock conditions, which appeared to lie on an extension of the second limit. At a constant pressure, there was a sharp increase in the ignition delay, with a decreased temperature at the extension of the second limit. Ignition at lower temperatures occurred in isolated localised regions, and is called "weak" ignition due to this characteristic. The temperature can be locally high downstream of a reflected shock, due to the shock's interaction with the boundary layer (formed behind the incident shock) on the wall of the tube. Meyer and Oppenheim [9] present a very clear high-speed Schlieren film, which shows the different nature of ignition in the "weak" and "strong" regimes. Weak ignition is seen to be initiated in the corners of the end plate of the shock tube, and then combustion propagates from these centres in the form of flames. Despite evidence that the position of the third limit is at best uncertain, Lewis and Von Elbe's diagram [1] of the explosion limits for H 2 + 0 2 remains the classic textbook example of branched-chain behaviour. Present Apparatus The free piston compressor consists of a steel compression tube (length 2.3 m; diameter 102 Pressure.

mm). A piston (mass 3.9 kg) is driven down the tube by air expanded from a reservoir at 3.5 MPa. The piston reaches its maximum velocity ( ~ 90 m s -1) close to the time when the gas ignites in front of the piston. The piston continues to compress the combustion products until it runs out of momentum and reverses. Stoichiometric mixtures of hydrogen and oxygen, diluted with helium, were prepared by simultaneously injecting the constituent gases through calibrated choked orifices into the previously evacuated compression tube via a long thin mixing pipe. Pressure Measurement Pressure was measured with a piezoelectric pressure transducer, and recorded on an 8 bit A-to-D converter sampling every 50 /zs. Ignition produced a step in pressure, as shown in Fig. 1. The subsequent pressure rise in Fig. 1 is due to the momentum of the heavy piston, which continues to compress the combustion products. The eventual reversal of the piston, in fact, limited the amount of chemical energy which could be added to the compression tube without driving the piston back through its starting position. It is inferred from the large pressure fluctuations following ignition (see Fig. 1) that not all of the gas was ignited spontaneously, due to ~

HPa

3O

2O

lO

2

4

6

8

10

12

t i m e , mS Fig. 1. Pressure measured during compression ofa stoichiometric 70%-weight-helium H2/O 2 mixture.

IGNITION OF

127

H 2 + 02

a nonuniformity in the pre-ignition temperature of the gas. It is assumed that a central core of gas was compressed isentropically, while heat transfer to the walls of the compression tube is confined to an adjacent thermal boundary layer. This two-part model has been verified indirectly by Knoos [10], who employed it in a successful calculation of heat transfer from free piston compressors.

COMPUTATION Reaction Mechanism

Calculation of Temperature

The reaction mechanism and rate constants used by Jachimowski and Mclain [12] were adopted for this study. The reactions are referred to with the prefix J, and the rates of the reactions are written with the notation J'. Thus, for example, following Table 1, J8' = [H][O2][M] ks, where [M] is the total concentration and

The temperature of the central core at ignition was calculated with the isentropic relation

k8 = EATne

fr0ri,TCp - d T = R l n ~ - - - ~[eni-l~ o )

(1)

where Cp was calculated by summing the contributions of H2, 02, and He. In the numerical simulation, the specific heat of each diatomic species was expressed as a polynomial in temperature, as obtained from Van Wylan and Sonntag [11]. To improve the accuracy of the calculation of the ignition temperature from the measured pressure ratio, the integral in Eq. 1 was determined from tabulated values at 0.1 MPa [11]. TABLE

E

RT.

(2)

For the mixture, E = F, Yiei where e i is the third-body efficiency of species i. The reverse reactions are written with the suffix R, and their rate constants are calculated from their equilibrium constant and forward rate constant. An additional reaction from the scheme of Baldwin et al. [13], H

+ H202

--~ H 2 0

(J17)

+ OH

is included with the rate constant of Foo and Yang [14]. 1

The Reaction Mechanism

No.

Reaction

A (m 3 m o l - 1 K - " /xs -1)

J1 J2 J3 J4 J5 J6 a J7 b J8 c J9 J10 Jll J12 J13 J14 J15 J16 J17

H 2 + 02 ~ 2OH O x + H ~ OH + O H 2 + O --* O H + H H 2 + OH ~ H + H20 2OH --* O + H 2 0 OH + H + M ~ H20 + M 2H+M--o H 2 + M 0 2+H+M~HO 2+M O H + H O 2 --) 0 2 + H 2 0 H + H O 2 --* H 2 + 0 2 H+HO 2~2OH O+HO 2~O 2+OH 2HO 2 --'~ O 2 + H 2 0 2 H 2 + H O E --¢ H + H 2 0 2 O H + H 2 0 2 --* H 2 0 + H O 2 H 2 0 2 + M ~ 2OH + M H + H 2 0 2 ---* H 2 0 + O H

17 1.2 × 105 210 3.2 x 10 -5 55 2.2 × 104 0.65 3.2 50 25 200 50 2 0.3 10 1.2 × 105 416

" F o r H 2 0 , • = 6.36. b For H 2 0 , • = 6 × 10-6; for H 2 , • = 4 × 10 - 6 . c For H 2 0 , • ~ 13.8; for H2, • = 2.19.

E/R (K) 0 - 0.91

0 1.8 0 -2 -1 -1 0 0 0 0 0 0 0 0 0

24220 8360 6930 1530 100 0 0 0 500 350 96O 500 0 9420 910 22910 4350

128

T . M . CAIN

Mathematical Model

Comparison with Experiment

The rate of change of the concentration of each species is written as

The computed results were produced for discrete time steps of 2 /xs, and exhibited a step rise in pressure at ignition (/ig). It was noted that the rate of pressure rise was equal to the rate for an isentropic compression 100 /xs before the step, and thereafter, due to heat release, it varied inversely with the time to the step. That is, the rate doubled at (% - 50) /xs and quadrupled at (tig - 25) /zs, etc. In order to synchronise the calculation with the measured pressure, which was sampled every 50 /zs, it is noted that the pressure measured for one sample before the sample at the bottom of the step rise (n i - 1) must correspond to the calculated pressure in the time interval (tig 100)-(% - 50). This procedure results in uncertainty in the comparison, due to the finite time steps being = 0.2 MPa. The results are presented in Table 2, and demonstrate good agreement between the experiment and the computations.

d[ Spi ]

dt

~_auijJj' + [SPi]h~o.

J

(3)

The first term is a summation over all the reactions, and the second term is due to compression. Temperature is calculated from the energy balance:

dT RT dt C~ (~i (U(i,T)~j viJJJ')/P (4)

Vp/Lo

The compression rate is approximately constant at 40 s -1 for this compression tube during the induction period. A number of computations were performed at compression rates of 8 and 80 s - l , and the temperature at ignition was found to be insensitive to the compression rate [15].

Integration A stiff differential equation integrator ~o l__qT) [16] was used to integrate the differential equations 3 and 4 for the temperature and concentration of every species. The equations were solved for the natural logarithm of each species to accommodate the large range of concentrations. Initial nonzero concentrations were obtained for the products by integrating the equations in nonlogarithmic form for a simulated time period of = 10 /xs. The differential equations for temperature and reactant concentrations were not integrated during this initial period, so that a relatively balanced set of product concentrations could be calculated with sufficient precision (product concentrations are less than seven orders of magnitude lower than the reactant concentrations). The temperature at which the integration was commenced was normally 900 K, but it was varied from 700 to 1450 K to investigate its effect [15]. Starting at temperatures in the range 700-900 K produced equivalent results.

The Nature of Ignition The calculations showed that HO 2 and H202 accumulated during the compression process, with HO 2 being produced in reaction J8 and approximately half of it reacting to form H202 (J13). The net effect is that the production of H in the chain-branching reactions J2 and J3 is kept in check by the depletion of H (in J8) and its subsequent storage in the form of HO 2 and H202. The chain-breaking reaction J8 is effective because HO2 and H202 are relatively unreactive: However, this process is clearly time-dependent, and does not lead to the traditional branched-chain explosion limit in which these species are consumed in surface and gas phase reactions which do not create additional chain centres (H, O, or OH). Although ignition was delayed by a time-dependent process, it was still insensitive to the compression rate, due to the overriding influence of the high activation energy of the reaction

M + H202 -+ 2OH + M.

(J16)

The strong temperature dependence of the rate of this reaction results in a rapid breakdown of H202 at temperatures above 1150 K

129

IGNITION OF H 2 + 0 2 TABLE 2 Comparison of Calculated and Measured Ignition Pressures % Weight Water

P0 (atm +_0.05)

Pressure Immediately Before and At Ignition Measured (MPa + 0.25 a) n i -

20 30 40

1.0 1.6 1.0 1.6 1.0 1.6

n i

(rig - 100)/xs

(tlg - 50)/./.s

tig

3.9 6.0 3.9 5.7 4.3 6.2

3.39 5.45 3.48 5.52 3.70 5.74

3.55 5.67 3.64 5.74 3.84 5.98

4.16 7.28 4.36 7.07 5.05 7.04

1

3.6 5.8 3.6 5.5 3.7 5.7

Calculated (MPa)

a Since eni/Po is independent of P0, the % error in P h i due to uncertainty in P0 is equivalent to the % error in P0. For example, for the 20%, 1 atm case, the measured and calculated ignition pressures should agree for 95% of the tests to

within V/(0.05 × 3.6) 2 + 0.252 = 0.31 MPa.

and an increase in [OH]. Subsequently, [H] increases via J4, and HO 2 becomes a direct source of OH in J l l . The high OH and H concentrations drive the exothermic reactions J8 and J4 at rates which result in significant self-heating, and a thermal explosion occurs. The explosive nature of the ignition was demonstrated by calculating the ignition delay times for a mixture of helium and 30% weight (H 2 + 0.5 0 2) initially at a temperature of 300 K and a pressure of 1.6 atm after instantaneous compression to temperatures of 1100, 1200, and 1300 K, respectively. The ignition delay times were found to be 770, 150, and 38 /xs, respectively. To be consistent with the experiment, ignition delay was defined as the time (from the start) at which the rate of pressure rise reached 1 MPa ~s -1. A QUASI-STEADY DERIVATION OF THE THIRD LIMIT

Previous Explosion Limit Definitions Lewis and Von Elbe [1] describe a branchedchain reaction with the equation dn/dt

= no -

(b - a)n

where n is the chain carrier's concentration, n o is the rate of the chain-initiating reaction, and b and a are the coefficients of the chain-breaking and chain-branching reactions, respectively. The explosion limit is defined by b = a. Note that it is the initiation reaction (J1 in the present scheme) which is responsible for pro-

ducing excess chains at the limit. In the nonexplosive region, the initiation reaction J1 is typically two orders of magnitude slower than the chain-branching reactions, and therefore b -~ a w h e r e v e r t h e s y s t e m is n o n e x p l o s i v e . This makes the explosive limit criterion b = a sensitive to otherwise negligibly slow reactions. Kordylewski and Scott's [2] chain-thermal theory is a mathematical extension of the above approach. Their method of solution is also sensitive to the nonlinear nature of the equations and the inclusion of reactions which, in practice, have little effect on the overall concentrations, but do have a strong effect on the very fine balance required for strict enforcement of the steady state condition. While it may be argued that this, in fact, is precisely the nature of chain-branching and should therefore be modelled by the mathematics, it should be remembered that the depletion of reactants and production of water are necessarily neglected. The approximation of steady state is only as good as the finite rates of change that result from ~these processes. Therefore, it is unreasonable to base explosion limits on an e x a c t balance of the species. Chain-thermal theory endeavours to account for the effect of heat release on the explosion limits. The mixture is assumed isothermal at a temperature somewhat higher than that of the reaction vessel (which absorbs the heat). In the energy balance equation, Kordylewski and Scott [2] assume diffusive heat transfer, but at high pressure, the vessel is more likely to contain nonuniform, convective, buoyancy-driven

130 flow. It is impossible to incorporate nonuniform temperatures into chain-thermal theory, and thus the theory is not applicable to predicting explosion limits at high pressures. The explosion limit predictions of Lewis and Von Elbe [1] and Kordylewski and Scott [2] were supported by favourable comparison with experimental results from reaction vessels. As discussed in Section 2.1, the reaction vessel technique is notoriously unreliable and completely unsuited to determining the third limit.

New Definition of Explosion Limit Integration of the rate equations at a temperature of 830 K and pressures of 0.5 atm, 2 atm, and 2 MPa under isothermal conditions (no self-heating) confirmed previous analyses [3, 4] that there was no explosion at pressures well above the "third limit," but simply an increase in the rate of formation of H 2 0 [15]. To redefine the boundary of the region in the pressure-temperature plane, in which no explosion occurs, the ignition limit was defined as the locus of states (P, T) at which [OH] = 5 × 10-3 mol m -3 in the solution of the species balance equations. The rate of J4 is so high at this concentration that self-heating rapidly brings the reaction to completion. This represents a significant departure from previous definitions of an explosion limit in that the derivation of the limit is not based on an exact balance of the steady-state equations. Instead, the equations are used to estimate [OH], and when its value is such that heat release will accelerate the reaction to completion, an explosion is to be expected. The use of such a critical OH concentration to define the explosion limit incorporates both the chain-branching and the thermal nature of the explosion into the limit's definition. The magnitude of the critical [OH] was assumed equal to that in common usage to define the end of the induction period in ignition delay calculations (e.g., [17]).

Species Balance Equations The reactions with significant rates at low temperature and high pressure were identified by integrating the rate equations as described

T . M . CAIN above. As an example, the rates determined at various times during the isothermal reaction of a stoichiometric H 2 / O 2 mixture at 0.5 atm and 830 K are given in Table 3. The adiabatic reaction with these initial conditions explodes after 2.12 s when the temperature has reached 872 K. The effect of the accumulated H 2 0 was investigated by setting the third-body efficiency, for H 2 0 in J8 to 1 (instead of 13.8; see Table 1). It can be seen from the lower J4' at the higher third-body efficiency (Table 3) that the rate of water formation was decreased by about 30% by the presence of water. Quasi-steady methods of determining reaction rates in the nonexplosive region do not account for the accumulated H20, and are therefore limited in accuracy. This inherent inaccuracy should not affect the calculation of the explosion limits since induction times are very short and water concentration must be negligible at ignition. In the nonexplosive region, the rate of change of the concentration of each of the intermediate species is small compared with the reaction rates, and the rate equations reduce to a set of nonlinear algebraic equations. At any temperature and pressure, there are five equations and five unknowns ([HI, [O], [OH], [HO2], and [H202]). In this analysis, [OH] was fixed at a critical value, and an approximate solution for the pressure as a function of temperature was sought. Neglecting J10, J l l , and J14 from the subset of the reaction scheme in Table 3 (for reasons dis-

TABLE 3 Net Reaction Rates at 0.5 atm, 830 K for a Stoichiometric H 2 / O 2 Mixture

No. J2 J3 J4 J8 JlO Jll J13 J14 J15 J16 J17

Net Reaction Rates (tool m - 3 s - 1 x 103) J8 e ( H 2 0 ) = 13.8 J8 e ( H 2 0 ) = 1 5s 10s 15s 5s 10s 15s

8.3 8.2 51 43 0.51 2.0 20 1.4 0.47 12 6.6

7.0 6.9 53 44 0.47 2.8 21 1.3 0.62 14 7.1

5.4 5.3 46 46 0.37 7.4 19 1.2 0.56 14 5.7

10 10 58 47 0.65 2.5 22 1.4 0.54 12 8.2

12 12 67 53 0.87 3.4 24 1.2 0.75 13 11

11 11 63 49 0.89 3.4 22 1.0 0.70 12 11

IGNITION OF H 2

+

02

131

cussed later), the species balance equations are

Eq. 11 by J2' and combining with Eq. 12 yields

O: J2'

2a

J3' = 0

-

(5)

H: - J 2 ' .+ J3' + J4' - J8' - J17' = 0 = 0

HO2: J15' + J8' - 2J13' = 0

(8)

H 2 0 2 : J13' - J15' - J16' - J17' = 0

(9)

From Eqs. 5 and 6: J4' = J8' + J17'

(10)

From Eqs. 8 and 9: J8' = J15' + 2J16' + 2J17'

(11)

From Eqs. 5, 7, 10, and 11: J2' = J15' + J17'.

(12)

Defining a = J 8 ' / 2 J 2 ' = ks[M]/(2k 2) (a = 1 on the well-established second limit [1]) and /3 = J 1 5 ' / J 1 7 ' = k15[OH]/(k17[H]) , Eqs. 10 and 12 combine to give

where

C

=

+

2a

(13)

k4k17[H2]/(k2k]5[02]).

(14)

1+/3

where B = 4k16k2/(kskls[OH]). Substitution for /3 from Eq. 14 into Eq. 13 results in a third-order polynomial in or. Only the positive real roots which are associated with positive real values of /3 are meaningful. These are plotted in Fig. 2 as a function of pressure and temperature for three orders of magnitude of [OH] centred on the critical value. Figure 2 demonstrates that the criterion for an explosion limit is not overly sensitive to the magnitude of the critical [OH]. At a high pressure, the explosion limit asymptotes to a temperature defined by B = 2 as J15 becomes the dominant chain breaker (/3 >> 1). At low temperatures, only one permissible root exists, and it is very close to the second limit at a = 1 where J17 is the dominant chain breaker (/3 << 1). J10 and J l l were neglected in the derivation, although their rates were higher than J15' at the example state described in Table 3. At that pressure, /3 << 1, but as pressure increases, the ratio [H]/[OH] decreases primarily due to the three-body reaction J8.

(7)

1 - 1+/3

1 +/3Ba +

(6)

O H : J2' + J3' - J4' - J15' + 2J16' + J17'

C/3

1

=

Dividing

10s

Une [O.],mo,m'

\

A B

\A \

5x10 ~ 5x10"~

\

\ \B

~C

~

a.

0 [] z~

~ 10o [_

10-'=1

\

.

700

I . / .

I

. . . .

800

~

t

.

900

,

,

I

. . . .

i

. . . .

1000 1100 Temperature, K

=

90 wt% He 80 w1% He 70 wW. He

. . . .

1200

i

. . . .

1300

J

1400

Fig. 2. Comparison of the measured ignition points with the calculated ignition limit, e was taken as 1 for J8. The prediction of Lewis and Von Elbe's [1] explosion limit was obtained from their Eq. 39 with variables calculated from Eqs. 4 2 - 4 4 [1] for a stoichiometric 20%-weight-helium mixture. It was assumed that He and N 2 are equivalent third-body molecules, and that the effective vessel diameter was 10 cm.

132 Since J10 and J l l both vary with [H], they remain insignificant, but J15, which varies with [OH], dominates the destruction of H 2 0 2 at high pressure and must be included.

Comparison with Experiment Experimental results for compression ignition are plotted in Fig. 2. Ignition is seen to occur close to the analytical explosion limit and far removed from the traditional third limit [1]. T h e r e is a fundamental difference between the mechanism by which ignition is delayed in the dynamic simulation and the chain-breaking mechanism of the quasi-steady model. H 2 0 2 accumulates in the dynamic model (see Section 3.5), but in the quasi-steady model, it acts as a sink for chain centres by reacting to form H 2 0 in J15 and J17. This difference is not as significant as the p h e n o m e n o n the models have in common, which is that the high activation energy of J16 means that a t e m p e r a t u r e is reached at which the reaction suddenly "turns on" and H 2 0 2 becomes a ready source of the chain centre OH. CONCLUSIONS 1. Spontaneous ignition of mixtures of helium, oxygen, and hydrogen was found to occur during compression at a t e m p e r a t u r e well above that at which the third limit is normally placed. The results were shown to be consistent with an established reaction mechanism, and the pressure-insensitive ignition t e m p e r a t u r e of = 1150 K is close to the minimum shock front t e m p e r a t u r e required to sustain a detonation wave (1100 K) at high pressure [7, 1]. 2. At high compression rates ( V e / L o = 40 s - l ) , the long induction periods of H O 2 and H 2 0 2 retard the ignition until the t e m p e r a ture exceeds 1150 K, after which the rate of breakdown of H 2 0 2 into O H is sufficient to initiate the explosion. At low compression rates, it is expected that ignition will be retarded by J15 until the t e m p e r a t u r e approaches a similar value. 3. The concept of a critical O H concentration in the equations for species' concentrations appears to be a satisfactory way to delineate the nonexplosive from the explosive states

T.M.

CAIN

of the H z / O 2 system at high pressure. The critical O H contour is an extension of the second limit, but asymptotes to constant t e m p e r a t u r e at high pressure. The contour corresponds closely to the boundary between "strong" and " w e a k " ignition in shock tube experiments [8, 9]. The research f o r this paper was essentially completed while the author was a postgraduate student o f P r o f R. J. Stalker at the Department o f Mechanical Engineering, University o f Queensland, Australia, Prof. Stalker's guidance was m u c h apprecia ted.

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