6.4. FAST DEFLAGRATION WAVES AND DDT-PROCESSES
ACCOMPANYING THE IGNITION OF CH
4:O
2MIXTURES IN THE
temperature distribution along the length of the chamber, the entire gas volume along the axis was divided into 10-mm thick layers, and the energy absorbed by each layer was computed. Thus, by analogy to [8], we calculated the gas temperature in the layer. Data on the temperature dependence of heat capacity were borrowed from [10]; heat- exchange processes between gas layers and chambers walls were ignored because the laser pulse action is short enough (τlas ≈3µs).
To analyze the dynamics of ignition and combustion of combustible mixtures, we used an FD-25k photodiode and FER-7 streak camera which provided the streak images of the reactor radiation; its slit was oriented along the axis of the cylindrical chamber (Z axis).To analyze the gas glow and the time evolution of glow intensity in different cross sections along the quartz, we used an AVANTES AvaSpec-2048 spectrographs and an FEU-106 photomultiplier. The gas radiation from the quartz tube was transmitted into the spectrograph and photomultiplier through fibers.
Fig. 2. Streak images of radiation recorded by the FER-7 streak camera. The horizontal axis is temporal, the vertical axis is spatial (axial). The energy density of incident laser radiation: (a) W1≅ 1.6 J/cm2; b) W1≅
2.5J/cm2.
Figure 2 shows typical streak images of radiation from the reactor recorded by the FER-7 streak camera for the case where ignition is not accompanied by detonation and for the case where ignition is accompanied by detonation and explosion of the chamber. A mixture CH4:O2:SF6 = 45:90:15 torr was ignited on its heating by the CO2- laser. The horizontal axis in the photographs is temporal, whereas the vertical axis is spatial.
Characteristic temporal and spatial scales are indicated in the figures.
Figure 3 shows typical oscillograms of the photomultiplier signals for these two cases, respectively.
Figure 4a illustrates a typical radiation spectrum (integrated over the burning time) measured in the wavelength range 400 ≤ λ ≤ 800.
The spectrum has a quasi-continuous component and emission lines. Most bright in the spectrum are the radiation lines identified with a sodium doublet and atomic potassium. The spectral interval does not include the radiation band of electronically excited molecule OH
(
A2Σ+)
(the edge is near λ≅ 306 nm) which contributes substantially into integral over spectrum measured by the FER-7 (Fig.2) and photomultiplier (Fig. 3) (see [7]). Radiation sources that form the quasi-continuous component of the spectrum are not identified. However, an analysis shows that the spectrum on its certain regions is very close to Planckian and can be used to determine the gas temperature by the method described in [11]. In this method, we treat the measured spectrum in the coordinates
( )
4ln I λ
x →
andy → 1 , 4388 ⋅ 10
8/ λ
as Fig. 3. Oscillograms of photomultiplier signals: (a) W1≅ 1.6J/cm2; b) W1≅ 2.5 J/cm2.
shown in Fig. 4b. The dependence obtained allows us to identify continuum in the spectrum with Planckian and infer the average temperature over the gas combustion time: Tg ≈ 4000K.
Figure 5 shows the gas temperature distribution along the axis of the cylindrical chamber, which is formed immediately after the end of the CO2-laser pulse, at the stage preceding the ignition of the three-component working gas mixture. The temperature distribution is calculated for two values of the energy density of the incident laser radiation which ensured reproducible initiation of combustion at Win = 1.6 J/cm2 or detonation of the combustible mixture at Win = 2.5 J/cm2 (the diameter of the diaphragm placed in front of the input window was 29 mm). It can be seen from Fig. 5 that the laser radiation provides heating of the gas at a considerable distance from the input window of the chamber. It is particularly remarkable that the induction time in our experiment (tind ≈ 600 µs) is rather short (its value is substantially smaller that the literature data on induction times of stoichiometric methane-oxygen mixtures where the initial gas temperatures during CO2-laser-heating correspond to the maximal values in distributions in Fig. 5).
It has been found experimentally that, depending on the diameter of a diaphragm limiting the cross-sectional dimension of the inherent laser beam, there exist always two threshold values of the laser-heating energy density (W1thr and W2thr) such that exceeding these thresholds leads to either
“nonexplosive” ignition of the combustible mixture or ignition followed by explosion of the chamber (detonation regime). As in [12], the threshold for initiation of combustion of a combustible mixture depends on the initiation energy, i.e., when the diaphragm diameter was increased, the value of Fig. 4. Spectral characteristics of the flame.
(а) Typical radiation spectrum of a burning methane-oxygen mixture (integrated over the burning time).
(b) Quasi-continuous spectrum plotted in coordinates
( )
4lnIλλ
x→ andy→1,4388⋅108/λ. Tg ≅4000K
Fig. 5. Gas temperature distribution along the axis of the cylindrical chamber, which is formed immediately after the end of the laser pulse, for two values of the energy density of the incident CO2-laser beam:
(1) W1≅ 1.6 J/cm2; (2) W1≅ 2.5 J/cm2.
W1thr decreased approximately in inversed proportion to the diaphragm area.
Discussion of Experimental Results
Our experiment have shown that the initiation of combustion of a CH4+O2+SF6 mixture inside a closed volume by CO2-laser due to local gas heating demonstrates features peculiar to previous experiments with different types of initiators, such as high-current gliding surface discharges [1,2], microwave discharges [3,4], surface laser sparks and laser sparks in the reactor space [5-7]. Fast heating of a small volume (which is much less than the chamber volume) near the focal spot of the laser beam to 1200 – 1400 K is followed by a radiation wave with a relatively low intensity (the “primary wave”) propagating inward from the initiator. The wave velocity is on the order of 105 cm/s, which far exceeds deflagration wave velocities in a stoichiometric CH4 + O2 mixture excited by low- power sparks (it is easy to show that the visible velocity of a combustion wave in a methane- oxygen mixture, where its propagation is determined by the heat-conduction and diffusion mechanisms, may not exceed values of order 4 × 103 cm/s).
In a time sufficient for the primary wave to run though the length of the reactor chamber, a bright burst is observed almost simultaneously throughout the reactor volume. Such a burst is characteristic of the processes of fast (“explosive”) combustion and is indicative of branching chain reactions coming to play.
A time interval τ1during which we observe the primary wave preceding the volume combustion in the reactor is indicated in Figs. 2, 3. The axial propagation velocity of this wave in the present experiment was determined from the slope of its bright front in high-speed photographs like these in Fig. 2.
In [13], numerical work was made of combustion initiation of a methane-oxygen mixture (φ = 1.5) at Р0 = 1.65 atm in a tube 32 mm in length and 5 mm in radius. Formulation of the problem was closely related to conditions of our experiment, and the results of calculations agree qualitatively with data of measurements. In particular, the calculations predict the formation of a fast combustion wave (its velocity approaching V = 2 × 104 cm/s) which is associated with active gas- dynamic processes initiated by heat release in the closed volume. It should be noted that in the calculations [13], the initial gas temperature in the combustion region was taken to be equal to 4000 K.
As mentioned above, however, the temperature value in the present experiments was T0 ≤ 1400 K.
Induction times observed in our experiments, τind≤ 500-600 µs are rather short for methane-oxygen mixtures (for a stoichiometric CH4 : O2 mixture at
T0 ≤ 1400 K and Р = 200 Torr, the ignition time is more than 6 ms). However, at given conditions of the present experiment one should take into account the presence of SF6 in the combustible mixture and possible dissociation of these molecules by CO2- laser radiation. In [14], the induction time was measured for a CH4 : O2 : SF6 = 7 : 14 : 1 mixture at Р = 100 Torr, excited by two successive pulses of a CO2 laser. The first pulse provided heating of the mixture, whereas the second provided its combustion. It was shown that, at initial temperature T0 = 1400 - 1430 K, the induction time of this mixture was 200 – 600 µs (depending on the temperature to which the gas was heated by the first pulse). These results compare well with the results of our measurements. The induction time was defined as a time interval between the end of the second pulse and a burst of radiation detected by a photomuliplier from the region the second pulse initiated combustion. Furthermore, from comparison of the induction times for second pulses in which the radiation energy density was the same but the action time was different, the author has made the inference that the combustion of this mixture may be affected by chemically active particles produced by laser radiation.
One is the most interesting results, which was first obtained in the present experiment and did not made itself so evident in previous studies [1-7] with various systems of electric-discharge initiation, is transition to the detonation regime at a maximum energy of laser radiation. This transition is evidenced by a substantially shorter duration and higher intensity of radiation from the reactor (see Figs. 2b, 3b), and by breakage of the reactor chamber (a quartz cylinder). Detonation occurring at moderate energy release in the initiation region (< 60 J) and at such a short axial length of the cylindrical chamber (L = 20 – 30 cm), in which combustion is initiated near one of its ends, seems a rather unusual and not readily achievable phenomenon. There is reason to interpret it as an effect of transformation of a deflagration wave into a detonation wave (Deflagration-to-Detonation Transition, DDT). Investigations of this phenomenon are of interest to the combustion physics, in particular, to the problem of shortening the length of the pre-detonation zone which is all- important in the development of pulse detonation propulsion [15,16].
The physics of the phenomenon of transition of combustion to the detonation mode is the subject of a considerable literature, including theoretical investigations (see, e.g., [17-22]) and experiments (see, e.g., [23,24]). Models presented in [17-22] are based on the assumption of definite mechanisms responsible for the acceleration of a combustion wave to velocities higher than the velocity of sound and for the transition of the combustion wave to detonation.
A number of mechanisms of acceleration of deflagration waves whose initial velocities are much less than the velocity of sound velocities were considered in the literature. Of these mechanisms, noteworthy are the following: first, the mechanism of the formation of a fast combustion wave in a gas with nonuniform temperature. This model proposed by Ya.B. Zel’dovich et al. [17] and then used as the basis for numerical calculations [18] predicts the formation of combustion waves with properties peculiar to “phase” waves, which at a certain distribution of the gas temperature, can accelerate to supersonic velocities. In [20, 21], where acceleration of deflagration waves a cylindrical chamber was dealt with, the authors considered the acceleration mechanism related to the processes occurring in the wall layer, which involve an increase of the frontal zone of the combustion wave and its resulting acceleration. And, lastly, in [19,22], the authors have pointed to the important role of shock waves formed in the region of combustion initiation, because their reflection from the walls and multiple interaction with the region of initiation will result in acceleration of a deflagration wave even to velocities higher than the velocity of sound.
So far as we know, experiments for studying the DDT process based on the Zel’dovich model [17] have never been conducted. It is possible that such experiments are absent because they pose a serious problem: it is essential that a gas- temperature profile with prescribed parameters should be formed in a combustible gas mixture.
From this point of view, the scheme described in the present work may be regarded as one of few feasible solutions of the difficult experimental problem. The axial gradient of the initial temperature here may be varied over rather wide limits by varying the content of SF6 absorbing CO2- laser radiation. However, in the present experiment, we used only the one composition of the working gas with its associated initial temperature distribution shown in Fig.5. Based on this distribution, the phase velocity of a deflagration wave, which can be estimated as
def indZ
v ∂τ
≈ ∂
(where Z is the axial coordinate, and
τ
ind is the induction time at a given T(Z)), is on the order of vdef ≈ 102 cm/s, which value is considerably smaller than the experimental value.It should be noted that, in the Zel’dovich model [17], we are dealing with the temperature gradient, but strictly speaking, the gradient of the induction time of combustible mixtures should be considered.
This gradient can be formed by not only the gas temperature profile but also by the density profile of chemically active particles. It is just this case which has been realized in our experiments, because the action of high-power CO2-laser
radiation on methane-oxygen mixtures with SF6
additions produces not only heating of theses mixtures but also the effective dissociation of SF6
molecules, thereby increasing the concentration of chemically active radicals CH3, CH2.
The most closely corresponding to the experiments described in this paper (and also in [1- 7]) is the mechanism of deflagration wave acceleration considered in [19,22] and related to strong gas-dynamic perturbations accompanying the electric-discharge initiation of combustion of gas mixtures. Understanding the obvious necessity of obtaining the experimental data to refine the acceleration mechanism for deflagration waves, we emphasize that the fact is certain that high velocities of combustion waves were obtained at rather short (a few centimeters to ten centimeters) distances from the region of electric-discharge initiation of combustion in both the present and previous experiments [1-7]. When these experiments are compared, it becomes clear that the combustion initiation with the use of the CO2-laser allowed maximal deflagration-wave velocities (~
105 cm/) to be obtained at minimal distances (~ 1 – 2 cm) from the region of local energy release provided the combustion. The result of the present experiment, i.e., the reliably achieved excitation of detonation waves, is consistent with the effect underlying the DDT model, specifically, the acceleration of an initially slow deflagration wave up to supersonic velocities.
In conclusion, we note that low-intensity glow wave preceding the volume combustion may only tentatively be defined as deflagration waves. It is our opinion that a more adequate definition for these waves was given in [1-7], namely,
“incomplete combustion” waves – that is the waves propagating along the reactor chamber at the initial stage, when chain branching reactions processes have not yet come into play (the first stage of the two-stage combustion). Even at this stage, however, the temperature behind the front of the incomplete combustion wave is as high as 1500 – 2000 K [25].
This temperature is considerably smaller than the burnout temperature of a stoichiometric methane- oxygen mixture but appears to be sufficient to initiate the DDP process.
Conclusion
The ignition of a three-component gas mixture (CH4:O2:SF6) by CO2-laser radiation was realized in the experiment under conditions excluding spark generation. As in the previous experiments with high-power electric-discharge initiation, a fast
“incomplete combustion” wave was observed, which propagated inward from the region initiation, thereby promoting combustion of the gas mixture throughout the reactor volume. This wave is
“deflagration” in character and possesses velocities
exceeding the velocity of sound. At a maximum energy density in the laser beam in our experiments, the fast incomplete combustion wave was transformed into a detonation wave (DDT process), which is evidenced particularly by explosion and breakage of the reactor. Thus the experiment has demonstrated the feasibility of DDT process at energy release in the initiation region as small 60 J and at distances from the region of initiation as small as ≤ 20 cm.
This work was supported in part by the Russian Foundation for Basic Research (project no. 11-02- 00465) and the Presidium of the RAS (program 09P
“Fundamental Problems of the Mechanics of Interaction in Technological and Natural Systems).
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