DISCHARGE
N. A. Popov
Skobel’tsyn Research Institute of Nuclear Physics, Moscow State University, Moscow, 119992 Russia
e-mail: NPopov@mics.msu.su
Abstract. The effect of various radicals and excited particles on the induction delay time reduction is discussed when analyzing the ignition of combustible mixtures under nonequilibrium conditions. A review is made of experimental and theoretical investigations of the effect of hydrogen and oxygen atoms, electronically excited O2(a1Δg) molecules on the induction times and on shift of the ignition temperature limits of hydrogen-oxygen mixtures. The addition of oxygen and hydrogen atoms to a combustible mixture may cause a significant reduction of the induction times and the lowering of the ignition temperature limit of combustible mixtures. However, the latter effect is observed only in the vicinity of the ignition limit. In the region of relatively low initial temperatures, the shift of the ignition limit is largely associated with the heating of mixture owing to recombination of atomic particles being added. In so doing, the nonequilibrium pattern of the impact hardly shows up.
Molecules of singlet delta oxygen (SDO) O2(a1Δg) may be involved in both chain initiation reactions and chain branching reactions. A kinetic model describing the impact of the admixture of SDO molecules O2(a1Δg) on the evolution of the composition of hydrogen-oxygen mixtures was worked out. There was shown in the framework of this model the possibility of describing all the main experimental data on the dynamics of quenching of singlet oxygen in H2 : O2 gas mixtures in the temperature range of T0 = 300 - 1050 K. Most of the acts of interaction between singlet oxygen molecules and atomic hydrogen O2(a1Δg) + H lead to quenching of O2(a1Δg). Efficiency of this interaction channel is more than 80%
and fraction of the reaction H + O2(a1Δg) → OH + O(3P) was only in 10-20%. The impact of the admixture of SDO molecules on the ignition of H2 : O2 mixtures was investigated. The dominant process determining the degree of impact of O2(a1Δg) is its deactivation by molecules of HO2. As a result, in H2 : O2 mixtures of high pressure, where the density of produced HO2 molecules can be high enough, the effect of singlet oxygen on the ignition time of these mixtures turns out to be relatively weak. This effect becomes even less noticeable if admixtures of atomic oxygen are present in the mixture. The last case is typical when the electric discharge systems are used for production of singlet oxygen. Presence of even small (10-
4) initial concentration of atomic oxygen reduces the effect of O2(a1Δg) admixtures on the processes of ignition only to additional heating of the mixture in the process of SDO deactivation
Introduction
Considerable recent attention has been given to the problem of fast ignition of combustible gas mixtures, which is motivated by a possibility of applying the obtained results in the design of engines and various plasmachemical systems. It is common knowledge that, in most cases of practical importance, the ignition of combustible mixtures is achieved by increasing their temperature to values exceeding the ignition temperature. The effect of an additional nonequilibrium excitation can be twofold: (i) a shorter induction period of a combustible mixture; (ii) a lower ignition temperature Tg*, i.e., the ignition of a mixture at initial temperatures below Tg*. In this case, the effect of the nonequilibrium excitation might be reckoned as substantial if the ignition temperature of the mixture is reduced by the value that considerably exceeds its heating due to relaxation of the excitation energy.
In recent years, several methods have been proposed for nonequilibrium initiation of the combustion in gas flows. Takita et al. [1] reported a significant increase in the velocity of combustion
wave as a result of direct injection of arc DC discharge plasma into a gas mixture. Besides, the feasibility of initiating the combustion by pulsed high-current DC discharges [2-8], by RF and microwave discharges [9-13], and by electron beams [14, 15] is being investigated. A review of some recent works on the ignition of combustible gas mixtures by means of electric discharges and on the stabilization of the combustion is given by Starikovskaia [3].
An analysis of kinetic processes which are initiated by electric discharges and affect the ignition of combustible gas mixtures is rather complicated, because the discharge is accompanied by excitation of various degrees of freedom of the mixture molecules. The same problems complicate a comparative analysis of different types of electric- discharge systems. Depending on a value of the reduced electric field E/N in a particular discharge, different species of chemically active particles dominate the mixture. At large values of E/N in the discharge, most of the discharge energy goes into ionization and dissociation of molecules in the mixture [16, 17]. At relatively low values of E/N, there take place an effective excitation of the
electronic states O2(a1Δg), O2(b1Σ+g) [18, 19] and vibrational degrees of freedom of molecules [16, 17].
Apparently, we must first analyze the effect of different chemically active particles on the characteristics of the ignition process. It is only after this that it will be possible to identify a set of particles and their ratios which have an optimal effect on ignition. It is only then that it will be possible to formulate the problem of determining the characteristics of electric discharges which enable one to produce the desired chemically active particles in optimal ratios.
1. The Effect of Hydrogen and Oxygen Atoms on the Ignition of H2 : O2 Mixtures
A number of papers are available at present, which deal with the investigation of additions of chemically active radicals on the shift of temperature ignition limits [20 - 26] and on the times of induction [14, 15, 27–29] in hydrogen- containing and hydrocarbon mixtures. These investigations involved the use of UV radiation, electric discharge, electron beam etc. for obtaining the initial concentration of chemically active particles.
Nalbandyan [21] investigated the effect of UV photolysis on the ignition temperature of a stoichiometric hydrogen-oxygen mixture at pressure P = 2 to 30 torr. The experiments were performed in a quartz tube 2.7 cm in diameter, whose walls were treated with hydrofluoric acid.
The radiation source was provided by a DC discharge in hydrogen, and the intensity of radiation was adjusted by varying the discharge current I = 0.1 - 1 A. A quartz membrane was used to identify a spectral region λ ≤ 175 nm corresponding to Schumann–Runge continuum of absorption of oxygen.
The possibility was demonstrated of some lowering of the temperature ignition limit ΔTg* of H2 : O2 mixtures. For example, at P = 20 torr, the maximal value of ΔTg* was 27 K at the radiating discharge current of 1 A. The intensity of the UV radiation source in the range of λ ≤ 175 nm was determined by the number of water molecules formed as a result of photolysis of H2 : O2 mixtures at room temperature. It was assumed that two atoms of oxygen are formed upon absorption of each radiation quantum and, with time, are converted to H2O.
Nalbandyan [21] further investigated the effectiveness of chain chemical reactions depending on the initial gas temperature. This effectiveness is characterized by the chain length φ which was determined as the ratio of the rate of
production of water molecules at a given gas temperature to the rate of production at T0 = 300 K,
φ= ⎛
⎝⎜ ⎞
⎠⎟ = dH O
dt
dH O dt T
2 2
300
As was already noted, the latter rate is defined by the intensity of the source of UV radiation. The experimental data of [21], as well as the results of calculation of the dependence of chain length φon the gas temperature under the effect of radiation of discharge with current I = 150 mA, are given in Fig.1. One can see in the figure that the chain pattern of the process starts showing up only in the region of temperatures close to the ignition limit. At low temperatures, the production of radicals as a result of UV photolysis leads only to heating of the mixture.
Fig. 1. The chain length in a mixture of H2 : O2 = 2 : 1 at P = 20 torr and discharge current I = 150 mA as a function of the initial temperature of gas: the points indicate the experiment of [21], the curve - calculation, and the dashed curve - the temperature limit of autoignition for the conditions of [21].
The absorption of radiation by oxygen in the region of Schumann-Runge continuum is accompanied by dissociation of O2, with one of the atoms being formed in the excited O(1D) state [30], O2(X3Σ−g) + h
ω
→ O(3P) + O(1D).This results in a rapid production of H and OH radicals during the quenching of O(1D) atoms by hydrogen [31],
O(1D) + H2 → H + OH k = 1.1⋅10-10 см3/c.
The results of the impact of UV radiation were simulated by introducing a source of atomic oxygen (O(3P) + O(1D)) of intensity νO2⋅[O2]. The calculation results given in Fig. 1 correspond to the value νO2 = 4.5⋅10-5 s-1 and, as one can see, agree with the experimental data. The existing differences
may be associated with the fact that, under conditions being considered (P = 20 torr), an important part is played by heterogeneous reactions on the discharge tube surface [32]. These processes are not known well enough at present. In order to increase the importance of the part played by the volumetric reactions, it is necessary to make a transition to higher pressures. However, problems arise in this case, which are associated with the nonuniformity of absorption of radiation by oxygen in the Schumann- Runge continuum.
Many experiments on the initiation of ignition of combustible mixtures by means of UV photolysis were conducted by using the focused laser radiation [22-24]. Most frequently in these experiments, a breakdown a fast gas heating occur on the focus of the laser beam with the resulting formation of a high-temperature region, where the combustion is then initiated. In this case, the probability for the ignition depends substantially on characteristic dimensions of this high- temperature region, since a critical question is of whether the mixture has time to ignite during its cooling by heat conduction. Such experiments with laser radiation have much in common with the combustion initiation by spark electric discharges [33].
Lavid et al. [24] used the focused radiation of an ArF laser (λ = 193 nm) for igniting atmospheric-pressure H2 : O2 mixtures. During the pulse, most of the energy of absorbed photons is spent for dissociation of oxygen molecules rather than for gas heating,
O2(X3Σ−g)+ hω → O(3P) + O(3P).
In this case, the temperature of mixture turns out to be below the limit of ignition, and reactions involving O(3P) and H atoms, OH radicals, and other play an important part in the initiation of combustion. The transverse dimension of the excitation zone in the focused laser beam was relatively small (R ≈0.4 mm [24]). Therefore, similar to [22, 23], the probability of ignition was affected both by the diffusion “departure” of radicals from the excitation zone and by the rate of cooling down of this region due to heat conduction.
Figure 2 gives the minimal values of the initial concentration of O(3P) atoms, required for the ignition of a stoichiometric H2 : O2 mixture at P = 1 atm, as a function of the initial gas temperature.
Note that both the calculation (curves) and experimental (symbols) results [24] indicate that very significant (in excess of 1016 cm-3) concentrations of oxygen atoms are required for the ignition of this mixture at temperatures below the ignition limit. In view of the small size of the excitation zone, the temperature limit of ignition of the mixture under consideration is higher than 880
K [33]. The results of calculations performed within a uniform 0-D model [47] (curve 1) lie markedly below the experimental data. As was already mentioned, this is indicative of the important part played by diffusion and heat conduction processes in determining the ignition temperature.
Fig. 2. The minimal initial concentration of O(3P) atoms required for the ignition of a stoichiometric H2 : O2
mixture at P = 1 atm as a function of gas temperature:
the symbols indicate the experiment of [24], and the curve indicates the calculation by the 0-D model (curve 1) and by the 1-D model (curve 2).
To analyse the effect of diffusive and thermal conductivity processes on determination of ignition temperature in H2 : O2 mixtures the comparison of calculation results executed in the frame of uniform (0-D) model and one dimensional (1-D) axisymmetric model has been performed. In the latter the corresponding diffusive terms for all considered components have been inserted in the balance equation. The values of diffusive coefficients Dk and their dependences on temperature were estimated using the data [36].
Apart from the thermal conductivity term was included in the equation for temperature. In the calculation of thermal conductivity coefficient λef of multicomponent mixture the following expression has been used:
λ λ
λ
ef k k
k k k k
X X
= ⋅ +⎛
⎝⎜ ⎞
⎠⎟
⎛
⎝⎜
⎜
⎞
⎠⎟
∑
⎟∑
−0 5
1
. , [36]
where the Xk is the mole fraction of main components, and λk are the corresponding values of thermal conductivity coefficients.
In calculations in the frame of one dimensional (1-D) model the initial distribution of O(3P) atom density and gas temperature were assumed as Gaussian with R0 = 0.4 mm [24]. Then,
under consideration of this simulation the values of temperature and atom concentrations at laser channel axis are given.
Figure 3. Temporal dynamics of the temperature and the density of atoms O(3P) at the axis for a stoichiometric H2
: O2 mixture at Р = 1 atm, T0 = 740 K and initial concentrations: [O]0 = 5.6⋅1016 cm-3 (solid lines) и [O]0
= 5.5⋅1016 cm-3 (dashed lines).
As example, in Figure 3 the simulation results (in frame of 1-D model) of the time dependence of O atom concentration and temperature at laser channel axis in mixture of H2 : O2 = 2 : 1 at P =1 atm and Т0 = 740 К with two different initial O(3P) concentrations ([O]0 = 5.6⋅1016 cm-3 and [O]0 = 5.5⋅1016cm-3) are demonstrated. As one can see in spite of very small change of [O]0, in first case the ignition of mixture occurs, but in the second one does not take place.
This example is evidence that in calculations described above the accuracy of determination of O(3P) concentration needed for mixture ignition is rather high.
The minimal atom concentrations [O(3P)]min, needed for ignition of H2 : O2 mixture in the range of T0 = 690 - 790 K are presented in Figure 2. Apparently, the 0-D model (curve 1) and 1-D model (curve 2) obtained results differ from each other in 3-5 times. That difference increases with gas temperature. The 1-D model results (curve 2) agree with experimental data [24]. The shown calculation results were executed in conditions of stoichiometric mixture of H2 : O2 = 2 : 1. Similar results were obtained for other [H2]/[O2] values as well (in the work [24] that ratio was varied from 0.4 to 4).
The experimental investigation of kinetic mechanisms of the effect of radical’s initial density on the ignition time requires the development of a rather uniform and extended excitation region.
Such experiments were described by Chou and Zukowski [25], who investigated the pulsed UV photolysis of stoichiometric H2 : O2, H2 : air, and CH4 : O2 mixtures with additions of molecules of ammonia NH3. The initial temperature of mixture
was 300 K, with pressure P = 1 atm. The radiation of ArF laser on wavelength λ = 193 nm, which is effectively absorbed by NH3 molecules, was used for production of radicals [30],
NH3 + hω → NH2 + H.
The power of laser radiation was sufficient for decomposition of all available molecules of ammonia. This provided for spatially uniform production of radicals of preassigned initial concentration equal to the concentration of NH3. Chou and Zukowski [25] assumed that the reactivity of the NH2 radicals being formed is relatively low; therefore, the main result of the impact of UV radiation on the characteristics of ignition is the production of atomic hydrogen with concentration [H]0 = [NH3].
Fig. 4. The induction period for stoichiometric mixtures of H2 : O2 and H2 : air excited by a pulsed source of UV radiation as a function of the initial fraction of NH3 molecules in the mixture: P0 = 1 atm, T0 = 300 K; the symbols indicate the experiment of [25].
Figure 4 gives the ignition times of stoichiometric mixtures of H2 : O2 and H2 : air at P
= 1 atm and T0 = 300 K as a function of the fraction of NH3 in the mixture [25]. The ignition of a 2⋅H2 : O2 mixture could be experimentally accomplished for a fraction of ammonia molecules of 0.6 - 0.7%.
The calculation results indicate that initial concentrations of hydrogen atoms [H]0/M = [NH3]/M ≥ 2%, are required for the ignition of the mixture under consideration. This is three times higher than the experimentally obtained values. The reason for discrepancy between the calculation and experimental data may be as follows. Indeed, NH2
radicals formed as a result of UV photolysis of ammonia hardly react with O2 and H2 molecules.
However, a fairly fast reaction of NH2 with O(3P) atoms may occur, which causes the emergence of additional channels of production of hydrogen radicals H and OH, as well as nitrogen oxides [34],
NH2 + O → NH + OH;