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Ignition and detonation in N2O-CO-H2-He mixtures
Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 2999–3005
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES ANDREI YU STARIKOVSKII Moscow Institute of Physics and Technology Dolgoprudny, Russia
Ignition and deflagration-to-detonation transition in the N2O-CO-H2 system behind the reflected shock wave in initial temperatures ranging between 1200 and 1800 K and pressures of 3–9 atm are studied. It is established that the chemical reactions are described adequately by the assumption of equilibrium between the translation-rotational and internal degrees of freedom of the molecules for shock-heated gas conditions. It is found that both the total heat release Q by the chemical reactions and the ratio of the induction period sind of the mixture to the characteristic energy release time H are the parameters governing the flow pattern. Two different modes of interaction between the exothermic reaction and the gas flow are distinguished. The single-front mode, with a single discontinuity, arises when sind # H, and twofront mode, in which a strong discontinuity formed behind the reflected shock front caused by interaction between the gasdynamic and chemical processes, arises when sind k H.
Introduction High-temperature kinetic processes in gases are often studied in shock tubes behind reflected shock waves [1]. Researchers [2,3,4] have attempted to model numerically the unsteady gasdynamic processes arising in shock tubes because of self-ignition of gaseous mixtures; they noticed a strong coupling between the chemical reaction and flow dynamics leading to detonation under certain conditions. N2O ` CO ` H2 mixtures are interesting because of the peculiarities of the global N2O ` CO reaction, which, according to the data of Ref. 5, may provide superequilibrium population of the CO2 levels due to energy release in the reactions and interactions of the vibrationally excited reaction products with reagents. For obtaining such reaction regimes, very high concentrations of the reactive gas must be used and gasdynamic phenomena must be taken into consideration. It has been shown [6,7] that burning of N2O-COH2-He mixtures behind reflected shock waves may also produce appreciable gasdynamic perturbations, sometimes leading to detonation onset. Bearing this in mind, one should take into account the mutual influence of the chemical reaction in the system and the flow dynamic parameters when interpreting the kinetic measurements in mixtures with high energy release. The objective of this work is to study experimentally the self-ignition of N2O-CO-H2 mixtures within a wide range of initial conditions and to analyze the reaction kinetics, vibrationally excited products formation, and transition from deflagration to detonation. Experimental Studies Experiments were conducted in a shock tube 50 mm i.d. with 3.5-m-long low-pressure and 1.2-m-
long high-pressure sections. A residual vacuum of p . 1016 torr in the low-pressure section of the shock tube at a (1–2) 2 1014 torr/min leakage rate was provided by a vacuum system that included a steamoil pump with a nitrogen trap. Experiments were performed after pumping the operating channel down to p , 1015 torr. The time interval between the end of pumping and the start of experiment was no longer than 2 min. The velocity of the incident waves was measured between station 1 (318 mm from the end plate of the shock tube) and station 3 (13 mm from the end plate). Reflected wave velocity was measured between the end plate and station 2 (113 mm from the end plate in all runs, except those with mixture 4, 85 mm). At station 3, we monitored IR emission of N2O at k 4 3.7 lm and of CO2 at k 4 4.31 lm (see Fig. 1). We studied ignition of five N2O-CO-H2-He mixtures of different compositions (see Table 1) behind reflected shock waves at temperatures and pressures ranging from 1200 to 1800 K and from 3.1 to 9.2 atm, respectively. In the regimes corresponding to runs with mixture 1 (T50 4 1502 K, p50 4 3.4 atm, mode I) and with mixture 5 (T50 4 1203 K, p50 4 9.2 atm, mode II), the IR emission profile of N2O, whose concentration decreases monotonically in the reaction, displays a prominent peak in both mixtures. The peak in mixture 5 is almost twice as high as the initial level of the signal. The IR emission profile of CO2 formed by the reaction shows a specific shape. Mixture 5 indicates a relatively slow increase in the emission intensity during the induction period, followed by a rapid acceleration to the quasi-steady level. Mixture 1 shows
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Fig. 1. Shock tube test section. 1, pressure gauges; 2, CaF2 optical windows; 3, glass optical windows; 4, CaF2 lenses; 5, IR-sensor Ge-Au, 77 K; 6, IR-monochromator; 7, solar-blend photomultiplier R-1657; 8, UV-monochromator; 9, He-Ne laser LG-52-3; 10, differential photodiod; 11, shock tube channel; 12, shock tube wall; and 13, shock tube end plate. I, II, III—test stations at 318, 113, and 13 mm from the shock tube end plate, respectively.
a smoother profile; no correlation was noticed between the emission intensity variation and the steep drop of the intensity of N2O IR emission. The pressure profiles at the end plate are somewhat similar to those of CO2 IR emission. Whereas in mixture 5 the pressure rises steeply to the new quasi-steady level after a long plateau corresponding to the induction period, the pressure profile recorded in mixture 1 exhibits a gradual monotonic rise behind the reflected shock wave throughout the observation time. The mixture in state 5 (state behind the reflected shock wave) ignites after the induction period is over. This produces a compression wave that propagates with a rapidly rising velocity and eventually
Fig. 2. The temperature dependence of the half-decay time of the N2O IR radiation intensity at k 4 3.7 lm. Symbols, experiment; curves, numerical modeling by the detailed kinetic scheme [15]; 1, mixture 1; 2, mixture 2; 3, mixture 3; 4, mixture 5; dotted line, the threshold of transition from the single-front combustion mode to two front.
transforms into the C-J detonation [8]. When the detonation front catches up with the reflected shock wave, a contact surface, overdriven detonation, and expansion wave arise. The contact surface keeps moving away from the end plate of the tube, the overdriven detonation propagates through state 2 (state 2 corresponds to the gas, heated by the incident shock wave only), and the expansion wave spreads toward the end plate. In mixture 1, containing no hydrogen, a rather smooth compression wave without a pronounced leading front follows the reflected shock wave. These differences in the behavior of the flow parameters provide evidence of significant differences in the energy-release kinetics in the “dry” mixture 1 compared with mixture 5 containing 0.11% hydrogen. These differences are clearly shown in Fig. 2 by comparing the measured half-decay time of the
TABLE 1 The mixtures studied
Mixture
N2O, %
CO, %
H2, %
CH4, %a
1 2 3 4 5 6
9.4 9.4 9.4 10.0 9.4 —
20 20 20 20 20 —
0 0.0066 0.0300 0.0850 0.1140 —
0.0020 0.0020 0.0020 0.0020 0.0020 —
aUncontrollable
hydrocarbon impurities are taken into account.
CO2, %
He, %
0 0 0 0 0 10.3
70.6 70.6 70.6 69.9 70.5 89.7
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES
Fig. 3. The average velocity of the reflected shock wave, U˜R, as a function of the incident shock wave velocity. Symbols, experiment; curves, numerical modeling by the reaction scheme [15]; 5, calculations assuming instantaneous attainment of the equilibrium composition at p1 4 150torr [13]; 6, calculations by the theory of ideal shock tube with frozen chemical reactions [11]; 1, mixture 1; 2, mixture 3; 3, mixture 4; 4, mixture 5.
intensity of N2O IR emission as a function of the initial temperature T50 behind the reflected shock wave. The initial temperature T50 was calculated from the velocity of the incident shock wave assuming equilibrium of the translational, rotational, and internal degrees of freedom of the molecules and frozen chemical reactions. It is seen that at identical pressures and temperatures, the half-decay time of the N2O IR radiation intensity s1/2 (called below the induction time) in mixture 1 is four times longer than that in mixture 5. Note that addition of only 66 ppm H2 (mixture 2) reduces s1/2 by a factor of 1.5. Comparing values of s1/2 in mixture 2 with mixture 1 can be considered an additional experimental proof of a rather low level of uncontrolled impurities in the mixtures studied and demonstrates the extremely high sensitivity of the reaction kinetics in the N2O-CO mixture to hydrogen-containing impurities. The reflected shock wave velocity is sensitive both to the rate of the reaction and the overall exothermicity. It is well-known that the compression waves generated in the reaction zone interact with and accelerate the reflected shock wave front [9]. Obviously, the time it takes for the reflected shock wave front to travel a certain distance from the end plate depends on (1) the induction period in the mixture during which the heat release is insignificant; (2) the heat-release rate after the induction period; and (3) the overall heat-release due to the chemical reactions. If the reflected shock wave passes through the measurement base before the induction period is over, its velocity corresponds to calculations with the frozen chemical reactions.
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In the other limiting case, when the induction period is very small, the time during which the reflected wave passes through the measurement base depends on the initial flow parameters and on the energy evolved during the measurement time. Figure 3 presents the results of treating the measured times during which the reflected shock wave travels between the pressure gauges at the shock tube end plate and station 2. It is seen that transition from the flow patterns, in which the heat-release effect on quantity U˜R 4 DX/Dt (where DX is the distance between the measurement stations and Dt is the travel time; generally, U˜R is not equal to the instantaneous reflected shock wave velocity UR) is insignificant, to those in which interaction between the chemical reaction and the gas flow is governing corresponds to various Us (and, hence, to different T50 ) values depending on the type of mixture studied. This follows, obviously, from the difference between the induction periods in various mixtures. Thus, a characteristic transition Us value for mixture 5 is 1.45 km/s (T50 4 1320 K) and for mixture 1 is 1.6 km/s. In Fig. 2, these values are observed to occur at nearly identical induction times (ps1/2 4 620 ls • atm). The U˜R values are also different in the other end of the range, at large Us. Whereas the data measured in the mixtures with a high hydrogen content (mixtures 4 and 5) are nearly equal to calculations performed assuming complete chemical equilibrium [10], the appropriate parameters for mixture 1 are closer to calculations with frozen chemical reactions. This is explained by changes in the composition of the reaction products in mixtures containing different amounts of hydrogen; in mixtures 4 and 5, the product composition approaches equilibrium within the measurement time, whereas in mixture 1, attainment of equilibrium requires a much longer time. It should be noted that the measured U˜R and s1/2 values depend significantly on the total pressure and the position of the measurement station with respect to the shock tube end plate, because the gas flow modes studied are essentially unsteady. The smooth dependence of these parameters on T and U˜S (Figs. 2 and 3, respectively) stems from the monotonic changes in the initial parameters (pressure, in particular) within each series of runs. To describe adequately the experimental results in numerical modeling, one should take into account explicitly the unsteady flow behavior caused by heat release in the chemical reactions and by purely gasdynamic phenomena associated with development of the dynamic boundary layers behind the incident shock wave [11].
Ignition Mode Analysis We consider reflection of a shock wave from the tube end plate. The gas in state 5 acquires
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parameters T5 and p5 after the wave reflection. We denote the induction time of the mixture in state 5 by sind, defining it as a time elapsed after the shock wave reflection from the shock tube end plate until onset of intense heat release. We analyze two conceivable versions of gas flow development that generalize the classification of the patterns of interaction between the combustion wave and reflected shock wave suggested in Refs. 8, 9, and 12: 1. Acceleration of the shock wave caused by its interaction with the compression waves generated by the combustion front without formation of strong discontinuities in state 5. 2. Transformation into the secondary shock discontinuity of the compression waves arising behind the reflected shock wave due to fast energy release by the chemical reactions. We introduce the following assumptions: • The gas pressure in the reaction zone varies only slightly until the secondary discontinuity is formed at instant tdisc, so that these changes can be neglected. • The gas velocity in this region is small compared to the reflected shock wave velocity UR. • Changes in the state of the gas caused by the compression waves do not affect the heat-release rate due to the chemical reactions, at least up to t 4 tdisc. • Specific heat ratio of the gas c is constant within the same time interval. We prescribe the heat release as a function of time s elapsed starting with the shock wave reflection at the tube end plate as follows:
5
dQ(s) 0 at s , sind 4 A(s 1 sind) exp[1(s 1 sind)/H] at s . sind dt
(1) These equations describe quite adequately the real-time history of the dQ/dt rate [13]. Parameters A and H characterize the total heat release and its rate, respectively. Assuming the gas to be polytropic and taking into account the p 4 const condition yields for the expansion rate of an elementary volume dV0,
5 6
d dV 1 dQ(t) At exp(1t/H) 4 4 dt dV0 CpT0 dt CpT0 where Cp is the specific heat at a constant pressure and t 4 s 1 sind. We use the piston analogy and approximation for the velocity of the chemical reactions front UF equal to the reflected shock wave velocity UR. From this relation, bearing in mind the one—dimensional nature of the problem in question, we derive the expression V 4 URt, and using Eq. (3), arrive at
dV AUR 4 dt CpT0 [H2
t
AUR
0
p 0
# s exp(1sH) ds 4 C T
1 H(H ` t) exp(1t/H)]
The rate of variation of the burning gas volume near the end plate can be interpreted in the one— dimensional formulation as a velocity, Up, of an effective piston moving away from the shock tube end plate and compressing the gas in state 5: Up 4
AUR [H2 1 H(H ` t) exp(1t/H)] CpT0
The velocity of this piston is limited and, when t → `, it tends to U`p 4 AUR/CpT0 (H2). The instantaneous piston position is defined by the relation Xp(t) 4
t
# U (s)ds 4 U [t ` (2H ` t) `
p
0
p
exp(1t/H) 1 2H]
(2)
As shown in Ref. 14, the position and time of discontinuity formation ahead of the piston moving in the channel are found by solving jointly two equations that define the steepening point of the compression wave front:
1]j]x 2 4 0, 1]j] x 2 4 0 2
t
(3)
2 t
where x is the coordinate and j is a parameter defining the coordinate of discontinuity formation. The x(j) dependence is found for a polytropic gas using the relation [14] v 4 x˙(j),
3
x 4 X(j) ` (t 1 j) C0 `
c`1 ˙ X(j) 2
4
(4)
Here, v is the gas velocity, X(j) is the instantaneous piston position, C0 is the acoustic velocity in unperturbed gas (in this case, C0 4 C(T50)), and the dot signifies differentiation with respect to j. We substitute the X(j) and X˙(j) values found earlier into Eq. (4): x 4 U`pH {(2 ` j/H) exp(1j/H) 1 (2 1 j/H)}
5
` U`p(t 1 j) C0/U`p `
6
c`1 [1 1 (1 ` j/H) 2
exp(1j/H)]
(5)
Solving Eqs. (3) and (4) with due regard for the expression derived for x, we obtain for the time of discontinuity formation (the time is measured from the mixture ignition instant): tdisc 4
(c ` 1) j (3H 1 j) 1 2Hj (c ` 1)(H 1 j)
(6)
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES
where parameter j is found from the following equation: c`1 (1 ` j2/H2) 1 1 exp(1j/H) 2
3
4
4 (1 1 j/H)
3c 12 1 ` C /U 4 0
`
p
(7)
It is seen from Eqs. (5) through (7) that the time to discontinuity formation depends on the specific heat ratio of the gas, characteristic heat release time H, and dimensionless parameter C0/U`p , specifying the ratio of the energy released by the chemical reactions to the internal energy of the gas with frozen chemical reactions: xdisc 4 U`pHU(C0/U`p, c), tdisc 4 HF(C0/U`p, c) where U and F are analytic functions. Obviously, the compression waves arising from the chemical reactions may be converted into a strong discontinuity only when UR(tdisc ` sind) . xdisc or, after the appropriate substitution, when sind . H
5U
U`p R
6
U(C0/U`p, c) 1 F(C0/U`p, c)
(8)
Thus, the two-front reflection mode with formation of a secondary discontinuity that follows the shock wave reflected from the shock tube end plate, behind which heat is released intensely in the flow, arises if under the selected initial conditions and mixture composition, the induction period is long and the heat-release rate, inversely proportional to parameter H, is high. When the ratio between the characteristic times of induction and heat release is reversed, the compression waves have no time to produce the secondary shock wave before they overtake the primary reflected shock wave. The reflected shock wave is accelerated, but the flow behind it (state 5) remains continuous. Figure 2 shows the boundaries between the single-front and two-front flow modes calculated using Eqs. (5) through (7) for all the mixtures studied. According to our calculations, the two-front mode is observed under the initial conditions, corresponding to the region to the right of the transition curve (for example, for regime II). At higher temperatures, the ratio sind/H between the characteristic times is such that no secondary discontinuity is formed (regime I). The reflected shock wave is accelerated gradually because of its interaction with the compression waves produced by the combustion front, and, eventually, the deflagration wave is converted into an overdriven detonation wave. This behavior of the system results from a substantial decrease in the rate of heat release by the dominating chain reactions N2O ` H → N2 ` OH and CO ` OH →
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CO2 ` H as compared to the rate of the triggering reaction of unimolecular N2O decomposition, whose rate constant is much more sensitive to the temperature than the rate constants of chain reactions. In mixtures containing about 10% N2O, 20% CO, and 70% He, the criterion of the two-front flow pattern formation can be approximated by relation sind/H . 7.5. Numerical Modeling As in Ref. 3, in our calculations, we employed the method of solution separation according to the physical processes. After each step in calculating the gas flow, we introduced corrections for the energy exchange between the internal and translation-rotational degrees of freedom and integrated the chemical kinetics equations involving more than 100 reactions. A total of 23 reactants were included in the kinetic scheme, N2O, NO, NO2, NO3, N2, N, H2O, OH, HO2, H2, H, O2, O, HNO, NH, CH4, CH3, CH2O, CHO, CH2, CO, CO2, CH, and the inert components Ar and He were involved in the reactions as collision partners [15]. In this work, we used the random choice method (RCM) [16] for gasdynamics equation solution. The method described in Ref. 13 employs the exact solution of the Riemann problem at the interface between adjacent computation cells for constructing the full solution [16]. The grids used in this work comprised 200 cells, on average, along the x axis, and calculations took into account flow inhomogeneity in the gas behind the incident shock wave. Because of the large number of computational cells, we were able to calculate accurately the position of the reflected shock front (the error of its determination in the RC method equals about one step along the x axis [17]) and to resolve confidently the chemical reaction zone. Simulation Results The pressure profiles calculated using the previously discussed model are displayed in Figs. 4a and 4b. Profiles (a) pertain to the flow mode I profiles and (b) are the results of modeling for mode II. As mentioned earlier, this pair of experiments corresponds to the same half-decay time of IR emission of N2O; however, in mode I, the unimolecular N2O decomposition is fast but the major fraction of the heat is released slowly by the CO ` O ` M → CO2 ` M reaction. In mode II, N2O is consumed and CO2 builds up synchronously by the fast chain reactions N2O ` H → N2 ` OH and CO ` OH → CO2 ` H. The identical sind times in these two cases are explained by appreciable differences in the temperatures: for mode I, T50 4 1502 K and for II, T50 4 1203 K; the initial rate of the unimolecular
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Fig. 4. The pressure profiles at various times. (a) Mixture 1, mode I; (b) mixture 5, mode II.
N2O decomposition reaction triggering the subsequent secondary reactions for mode II is 150 times as low as that for mode I. In mode I, all the flow parameters change gradually: slow heat release in the reaction zone generates weak compression waves that catch up with the reflected shock front and accelerate it smoothly. In mode II, the reflected shock wave velocity and pressure during initial 200 ls are nearly identical, with their values calculated disregarding the chemical reactions. The thermal explosion taking place 270 ls after shock wave reflection from the end plate produces an intense compression wave that is converted into a shock discontinuity at t . 320 ls. Its further propagation through state 5 in the form of a C-J detonation wave terminates at t 4 370 ls; at this instant, the detonation front catches up with the reflected shock wave, and the merged waves give rise to an overdriven detonation wave that keeps spreading through state 2. This produces a contact surface and rarefaction wave at the site where the two waves
Fig. 5. IR emission profile of N2O (k 4 3.7 lm). The solid line is experiment; the dashed line represents our numerical modeling. (a) Mixture 1, mode I; (b) mixture 5, mode II.
merge. The rarefaction wave propagates toward the shock tube end plate. The gas temperature behind the primary shock wave rises steeply, and the peak pressure and density fall off. Infrared Emission of the Gas The IR emission profiles of N2O and CO2 enable us to estimate the difference between the vibrational temperature in the reaction zone and the translation-rotational temperature. The emission profiles are complicated; therefore, a systematic analysis of the measurements presents difficulties. Consequently, in this work, we compared directly the emission profiles obtained in experiment with those calculated by the equilibrium model. The results of the comparison are displayed in Fig. 5. The results of the equilibrium calculations (Ttr 4 Trot 4 Tvib) reproduce the experimental profiles with a high accuracy in all cases. The insignificant
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES
deviations (not exceeding 5%) of the calculations profile from measurements of the maximum profile amplitude in all experiments can be explained by interference of a weak signal from light scattered by the polished shock tube walls. Thus, an analysis of the IR emission profiles carried out in this section with due regard for the results of the analysis of the kinetic and gasdynamics models (see earlier) leads us to conclude that thermal explosion in N2O-CO-H2-He mixtures proceeds in the equilibrium regime (i.e., at Ttr 4 Trot 4 Tvib) within a very wide range of the parameters. We failed to observe noticeable deviations from the equilibrium model at the temperature rise rates in the system up to dT/dt 4 40K/ls. Conclusions We studied ignition and deflagration-to-detonation transition in initial temperatures ranging between 1200 and 1800 K and pressures from 3 to 9 atm. It is inferred from the measured profiles and results of numerical modeling that the chemical reactions in the N2O-CO-H2 system are described adequately by the mechanism suggested in Ref. 15. It is based on reactions involving free radicals and assumes equilibrium between the translation-rotational and internal degrees of freedom of the molecules within a wide range of the initial parameters of the gas flow and under different conditions in the reacting shock heated mixture. Two different modes of interaction between the exothermic reaction and the gas flow are distinguished. The single-front mode with a single discontinuity, the reflected shock front, and two-front mode, in which the reflected shock front and a strong discontinuity formed due to interaction between the compression waves generated in the intense energy-release zone are present simultaneously in the gas flow. From the experimental data and analytical and numerical modeling results, we infer that both the total heat release by the chemical reactions and the ratio of the induction period of the mixture to the characteristic energy-release time are the parameters governing the flow pattern. We have derived a universal quantitative criterion that relates the gas flow
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pattern behind the reflected shock wave to the ratio between the induction period of the system and the characteristic heat-release time, the acoustic velocity in the gas, and the overall exothermicity of the reactions. Acknowledgment This work was supported in part by grant 96-03-32746 from the Russian Fundamental Research Foundation.
REFERENCES 1. Fujii, N., Kakuda, T., Takeishi, N., and Miyama, H., J. Chem. Phys. 91:2144–2148 (1987). 2. Elchert, H., Int. J. Hydrogen Energy 12:171–182 (1987). 3. Takano, V., J. Comput. Phys. 67:173–194 (1986). 4. Oran, E. S., Young, T. R., and Boris, J. P., Combust. Flame 48:135–153 (1982). 5. Zaslonko, I. S. and Mukoseev, Y. K., Kinetika Kataliz 34:408–421 (1993). 6. Britan, A. B., Zuev, A. P., and Starikovskii, A. Y., “Fundamental Problems of Shock Wave Physics,” International School-Seminar Chernogolovka, 1987, pp. 202– 204. 7. Britan, A. B., Zuev, A. P., and Starlkovskii, A. Y., Fiz. Goreniya Vzryva 25:89–96 (1989). 8. Strehlow, R. A. and Dynes, H. B., AIAA J. 1:591–603 (1963). 9. Gilbert, R. B. and Strehlow, R. A., AIAA J. 4:1777– 1791 (1966). 10. Starikovskii, A. Y., “Physics and Gasdynamics of Shock Waves,” International School-Seminar The Heat and Mass Transfer Institute, Minsk, 1992, pp. 641–644. 11. Starikovskii, A. Y., Sov. J. Chem. Phys. 10:1234–1251 (1991). 12. Strehlow, R. A. and Cohen, A., Phys. Fluids 5:97 (1962). 13. Starikovskii, A. Y., Chem. Phys. Reports 13:1422–1474 (1995). 14. Landau, L. D. and Lifshits, E. M., Hydrodynamics, Nauka, Moscow, 1986. 15. Starikovskii, A. Y. Chem. Phys. Reports 13:151–190 (1994). 16. Chorin, A. J., J. Comput. Phys. 25:517–538 (1977). 17. Collela, P., SIAM J. Stat. Comput. 3:76–91 (1982).
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES ANDREI YU STARIKOVSKII Moscow Institute of Physics and Technology Dolgoprudny, Russia
Ignition and deflagration-to-detonation transition in the N2O-CO-H2 system behind the reflected shock wave in initial temperatures ranging between 1200 and 1800 K and pressures of 3–9 atm are studied. It is established that the chemical reactions are described adequately by the assumption of equilibrium between the translation-rotational and internal degrees of freedom of the molecules for shock-heated gas conditions. It is found that both the total heat release Q by the chemical reactions and the ratio of the induction period sind of the mixture to the characteristic energy release time H are the parameters governing the flow pattern. Two different modes of interaction between the exothermic reaction and the gas flow are distinguished. The single-front mode, with a single discontinuity, arises when sind # H, and twofront mode, in which a strong discontinuity formed behind the reflected shock front caused by interaction between the gasdynamic and chemical processes, arises when sind k H.
Introduction High-temperature kinetic processes in gases are often studied in shock tubes behind reflected shock waves [1]. Researchers [2,3,4] have attempted to model numerically the unsteady gasdynamic processes arising in shock tubes because of self-ignition of gaseous mixtures; they noticed a strong coupling between the chemical reaction and flow dynamics leading to detonation under certain conditions. N2O ` CO ` H2 mixtures are interesting because of the peculiarities of the global N2O ` CO reaction, which, according to the data of Ref. 5, may provide superequilibrium population of the CO2 levels due to energy release in the reactions and interactions of the vibrationally excited reaction products with reagents. For obtaining such reaction regimes, very high concentrations of the reactive gas must be used and gasdynamic phenomena must be taken into consideration. It has been shown [6,7] that burning of N2O-COH2-He mixtures behind reflected shock waves may also produce appreciable gasdynamic perturbations, sometimes leading to detonation onset. Bearing this in mind, one should take into account the mutual influence of the chemical reaction in the system and the flow dynamic parameters when interpreting the kinetic measurements in mixtures with high energy release. The objective of this work is to study experimentally the self-ignition of N2O-CO-H2 mixtures within a wide range of initial conditions and to analyze the reaction kinetics, vibrationally excited products formation, and transition from deflagration to detonation. Experimental Studies Experiments were conducted in a shock tube 50 mm i.d. with 3.5-m-long low-pressure and 1.2-m-
long high-pressure sections. A residual vacuum of p . 1016 torr in the low-pressure section of the shock tube at a (1–2) 2 1014 torr/min leakage rate was provided by a vacuum system that included a steamoil pump with a nitrogen trap. Experiments were performed after pumping the operating channel down to p , 1015 torr. The time interval between the end of pumping and the start of experiment was no longer than 2 min. The velocity of the incident waves was measured between station 1 (318 mm from the end plate of the shock tube) and station 3 (13 mm from the end plate). Reflected wave velocity was measured between the end plate and station 2 (113 mm from the end plate in all runs, except those with mixture 4, 85 mm). At station 3, we monitored IR emission of N2O at k 4 3.7 lm and of CO2 at k 4 4.31 lm (see Fig. 1). We studied ignition of five N2O-CO-H2-He mixtures of different compositions (see Table 1) behind reflected shock waves at temperatures and pressures ranging from 1200 to 1800 K and from 3.1 to 9.2 atm, respectively. In the regimes corresponding to runs with mixture 1 (T50 4 1502 K, p50 4 3.4 atm, mode I) and with mixture 5 (T50 4 1203 K, p50 4 9.2 atm, mode II), the IR emission profile of N2O, whose concentration decreases monotonically in the reaction, displays a prominent peak in both mixtures. The peak in mixture 5 is almost twice as high as the initial level of the signal. The IR emission profile of CO2 formed by the reaction shows a specific shape. Mixture 5 indicates a relatively slow increase in the emission intensity during the induction period, followed by a rapid acceleration to the quasi-steady level. Mixture 1 shows
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Fig. 1. Shock tube test section. 1, pressure gauges; 2, CaF2 optical windows; 3, glass optical windows; 4, CaF2 lenses; 5, IR-sensor Ge-Au, 77 K; 6, IR-monochromator; 7, solar-blend photomultiplier R-1657; 8, UV-monochromator; 9, He-Ne laser LG-52-3; 10, differential photodiod; 11, shock tube channel; 12, shock tube wall; and 13, shock tube end plate. I, II, III—test stations at 318, 113, and 13 mm from the shock tube end plate, respectively.
a smoother profile; no correlation was noticed between the emission intensity variation and the steep drop of the intensity of N2O IR emission. The pressure profiles at the end plate are somewhat similar to those of CO2 IR emission. Whereas in mixture 5 the pressure rises steeply to the new quasi-steady level after a long plateau corresponding to the induction period, the pressure profile recorded in mixture 1 exhibits a gradual monotonic rise behind the reflected shock wave throughout the observation time. The mixture in state 5 (state behind the reflected shock wave) ignites after the induction period is over. This produces a compression wave that propagates with a rapidly rising velocity and eventually
Fig. 2. The temperature dependence of the half-decay time of the N2O IR radiation intensity at k 4 3.7 lm. Symbols, experiment; curves, numerical modeling by the detailed kinetic scheme [15]; 1, mixture 1; 2, mixture 2; 3, mixture 3; 4, mixture 5; dotted line, the threshold of transition from the single-front combustion mode to two front.
transforms into the C-J detonation [8]. When the detonation front catches up with the reflected shock wave, a contact surface, overdriven detonation, and expansion wave arise. The contact surface keeps moving away from the end plate of the tube, the overdriven detonation propagates through state 2 (state 2 corresponds to the gas, heated by the incident shock wave only), and the expansion wave spreads toward the end plate. In mixture 1, containing no hydrogen, a rather smooth compression wave without a pronounced leading front follows the reflected shock wave. These differences in the behavior of the flow parameters provide evidence of significant differences in the energy-release kinetics in the “dry” mixture 1 compared with mixture 5 containing 0.11% hydrogen. These differences are clearly shown in Fig. 2 by comparing the measured half-decay time of the
TABLE 1 The mixtures studied
Mixture
N2O, %
CO, %
H2, %
CH4, %a
1 2 3 4 5 6
9.4 9.4 9.4 10.0 9.4 —
20 20 20 20 20 —
0 0.0066 0.0300 0.0850 0.1140 —
0.0020 0.0020 0.0020 0.0020 0.0020 —
aUncontrollable
hydrocarbon impurities are taken into account.
CO2, %
He, %
0 0 0 0 0 10.3
70.6 70.6 70.6 69.9 70.5 89.7
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES
Fig. 3. The average velocity of the reflected shock wave, U˜R, as a function of the incident shock wave velocity. Symbols, experiment; curves, numerical modeling by the reaction scheme [15]; 5, calculations assuming instantaneous attainment of the equilibrium composition at p1 4 150torr [13]; 6, calculations by the theory of ideal shock tube with frozen chemical reactions [11]; 1, mixture 1; 2, mixture 3; 3, mixture 4; 4, mixture 5.
intensity of N2O IR emission as a function of the initial temperature T50 behind the reflected shock wave. The initial temperature T50 was calculated from the velocity of the incident shock wave assuming equilibrium of the translational, rotational, and internal degrees of freedom of the molecules and frozen chemical reactions. It is seen that at identical pressures and temperatures, the half-decay time of the N2O IR radiation intensity s1/2 (called below the induction time) in mixture 1 is four times longer than that in mixture 5. Note that addition of only 66 ppm H2 (mixture 2) reduces s1/2 by a factor of 1.5. Comparing values of s1/2 in mixture 2 with mixture 1 can be considered an additional experimental proof of a rather low level of uncontrolled impurities in the mixtures studied and demonstrates the extremely high sensitivity of the reaction kinetics in the N2O-CO mixture to hydrogen-containing impurities. The reflected shock wave velocity is sensitive both to the rate of the reaction and the overall exothermicity. It is well-known that the compression waves generated in the reaction zone interact with and accelerate the reflected shock wave front [9]. Obviously, the time it takes for the reflected shock wave front to travel a certain distance from the end plate depends on (1) the induction period in the mixture during which the heat release is insignificant; (2) the heat-release rate after the induction period; and (3) the overall heat-release due to the chemical reactions. If the reflected shock wave passes through the measurement base before the induction period is over, its velocity corresponds to calculations with the frozen chemical reactions.
3001
In the other limiting case, when the induction period is very small, the time during which the reflected wave passes through the measurement base depends on the initial flow parameters and on the energy evolved during the measurement time. Figure 3 presents the results of treating the measured times during which the reflected shock wave travels between the pressure gauges at the shock tube end plate and station 2. It is seen that transition from the flow patterns, in which the heat-release effect on quantity U˜R 4 DX/Dt (where DX is the distance between the measurement stations and Dt is the travel time; generally, U˜R is not equal to the instantaneous reflected shock wave velocity UR) is insignificant, to those in which interaction between the chemical reaction and the gas flow is governing corresponds to various Us (and, hence, to different T50 ) values depending on the type of mixture studied. This follows, obviously, from the difference between the induction periods in various mixtures. Thus, a characteristic transition Us value for mixture 5 is 1.45 km/s (T50 4 1320 K) and for mixture 1 is 1.6 km/s. In Fig. 2, these values are observed to occur at nearly identical induction times (ps1/2 4 620 ls • atm). The U˜R values are also different in the other end of the range, at large Us. Whereas the data measured in the mixtures with a high hydrogen content (mixtures 4 and 5) are nearly equal to calculations performed assuming complete chemical equilibrium [10], the appropriate parameters for mixture 1 are closer to calculations with frozen chemical reactions. This is explained by changes in the composition of the reaction products in mixtures containing different amounts of hydrogen; in mixtures 4 and 5, the product composition approaches equilibrium within the measurement time, whereas in mixture 1, attainment of equilibrium requires a much longer time. It should be noted that the measured U˜R and s1/2 values depend significantly on the total pressure and the position of the measurement station with respect to the shock tube end plate, because the gas flow modes studied are essentially unsteady. The smooth dependence of these parameters on T and U˜S (Figs. 2 and 3, respectively) stems from the monotonic changes in the initial parameters (pressure, in particular) within each series of runs. To describe adequately the experimental results in numerical modeling, one should take into account explicitly the unsteady flow behavior caused by heat release in the chemical reactions and by purely gasdynamic phenomena associated with development of the dynamic boundary layers behind the incident shock wave [11].
Ignition Mode Analysis We consider reflection of a shock wave from the tube end plate. The gas in state 5 acquires
3002
DETONATIONS
parameters T5 and p5 after the wave reflection. We denote the induction time of the mixture in state 5 by sind, defining it as a time elapsed after the shock wave reflection from the shock tube end plate until onset of intense heat release. We analyze two conceivable versions of gas flow development that generalize the classification of the patterns of interaction between the combustion wave and reflected shock wave suggested in Refs. 8, 9, and 12: 1. Acceleration of the shock wave caused by its interaction with the compression waves generated by the combustion front without formation of strong discontinuities in state 5. 2. Transformation into the secondary shock discontinuity of the compression waves arising behind the reflected shock wave due to fast energy release by the chemical reactions. We introduce the following assumptions: • The gas pressure in the reaction zone varies only slightly until the secondary discontinuity is formed at instant tdisc, so that these changes can be neglected. • The gas velocity in this region is small compared to the reflected shock wave velocity UR. • Changes in the state of the gas caused by the compression waves do not affect the heat-release rate due to the chemical reactions, at least up to t 4 tdisc. • Specific heat ratio of the gas c is constant within the same time interval. We prescribe the heat release as a function of time s elapsed starting with the shock wave reflection at the tube end plate as follows:
5
dQ(s) 0 at s , sind 4 A(s 1 sind) exp[1(s 1 sind)/H] at s . sind dt
(1) These equations describe quite adequately the real-time history of the dQ/dt rate [13]. Parameters A and H characterize the total heat release and its rate, respectively. Assuming the gas to be polytropic and taking into account the p 4 const condition yields for the expansion rate of an elementary volume dV0,
5 6
d dV 1 dQ(t) At exp(1t/H) 4 4 dt dV0 CpT0 dt CpT0 where Cp is the specific heat at a constant pressure and t 4 s 1 sind. We use the piston analogy and approximation for the velocity of the chemical reactions front UF equal to the reflected shock wave velocity UR. From this relation, bearing in mind the one—dimensional nature of the problem in question, we derive the expression V 4 URt, and using Eq. (3), arrive at
dV AUR 4 dt CpT0 [H2
t
AUR
0
p 0
# s exp(1sH) ds 4 C T
1 H(H ` t) exp(1t/H)]
The rate of variation of the burning gas volume near the end plate can be interpreted in the one— dimensional formulation as a velocity, Up, of an effective piston moving away from the shock tube end plate and compressing the gas in state 5: Up 4
AUR [H2 1 H(H ` t) exp(1t/H)] CpT0
The velocity of this piston is limited and, when t → `, it tends to U`p 4 AUR/CpT0 (H2). The instantaneous piston position is defined by the relation Xp(t) 4
t
# U (s)ds 4 U [t ` (2H ` t) `
p
0
p
exp(1t/H) 1 2H]
(2)
As shown in Ref. 14, the position and time of discontinuity formation ahead of the piston moving in the channel are found by solving jointly two equations that define the steepening point of the compression wave front:
1]j]x 2 4 0, 1]j] x 2 4 0 2
t
(3)
2 t
where x is the coordinate and j is a parameter defining the coordinate of discontinuity formation. The x(j) dependence is found for a polytropic gas using the relation [14] v 4 x˙(j),
3
x 4 X(j) ` (t 1 j) C0 `
c`1 ˙ X(j) 2
4
(4)
Here, v is the gas velocity, X(j) is the instantaneous piston position, C0 is the acoustic velocity in unperturbed gas (in this case, C0 4 C(T50)), and the dot signifies differentiation with respect to j. We substitute the X(j) and X˙(j) values found earlier into Eq. (4): x 4 U`pH {(2 ` j/H) exp(1j/H) 1 (2 1 j/H)}
5
` U`p(t 1 j) C0/U`p `
6
c`1 [1 1 (1 ` j/H) 2
exp(1j/H)]
(5)
Solving Eqs. (3) and (4) with due regard for the expression derived for x, we obtain for the time of discontinuity formation (the time is measured from the mixture ignition instant): tdisc 4
(c ` 1) j (3H 1 j) 1 2Hj (c ` 1)(H 1 j)
(6)
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES
where parameter j is found from the following equation: c`1 (1 ` j2/H2) 1 1 exp(1j/H) 2
3
4
4 (1 1 j/H)
3c 12 1 ` C /U 4 0
`
p
(7)
It is seen from Eqs. (5) through (7) that the time to discontinuity formation depends on the specific heat ratio of the gas, characteristic heat release time H, and dimensionless parameter C0/U`p , specifying the ratio of the energy released by the chemical reactions to the internal energy of the gas with frozen chemical reactions: xdisc 4 U`pHU(C0/U`p, c), tdisc 4 HF(C0/U`p, c) where U and F are analytic functions. Obviously, the compression waves arising from the chemical reactions may be converted into a strong discontinuity only when UR(tdisc ` sind) . xdisc or, after the appropriate substitution, when sind . H
5U
U`p R
6
U(C0/U`p, c) 1 F(C0/U`p, c)
(8)
Thus, the two-front reflection mode with formation of a secondary discontinuity that follows the shock wave reflected from the shock tube end plate, behind which heat is released intensely in the flow, arises if under the selected initial conditions and mixture composition, the induction period is long and the heat-release rate, inversely proportional to parameter H, is high. When the ratio between the characteristic times of induction and heat release is reversed, the compression waves have no time to produce the secondary shock wave before they overtake the primary reflected shock wave. The reflected shock wave is accelerated, but the flow behind it (state 5) remains continuous. Figure 2 shows the boundaries between the single-front and two-front flow modes calculated using Eqs. (5) through (7) for all the mixtures studied. According to our calculations, the two-front mode is observed under the initial conditions, corresponding to the region to the right of the transition curve (for example, for regime II). At higher temperatures, the ratio sind/H between the characteristic times is such that no secondary discontinuity is formed (regime I). The reflected shock wave is accelerated gradually because of its interaction with the compression waves produced by the combustion front, and, eventually, the deflagration wave is converted into an overdriven detonation wave. This behavior of the system results from a substantial decrease in the rate of heat release by the dominating chain reactions N2O ` H → N2 ` OH and CO ` OH →
3003
CO2 ` H as compared to the rate of the triggering reaction of unimolecular N2O decomposition, whose rate constant is much more sensitive to the temperature than the rate constants of chain reactions. In mixtures containing about 10% N2O, 20% CO, and 70% He, the criterion of the two-front flow pattern formation can be approximated by relation sind/H . 7.5. Numerical Modeling As in Ref. 3, in our calculations, we employed the method of solution separation according to the physical processes. After each step in calculating the gas flow, we introduced corrections for the energy exchange between the internal and translation-rotational degrees of freedom and integrated the chemical kinetics equations involving more than 100 reactions. A total of 23 reactants were included in the kinetic scheme, N2O, NO, NO2, NO3, N2, N, H2O, OH, HO2, H2, H, O2, O, HNO, NH, CH4, CH3, CH2O, CHO, CH2, CO, CO2, CH, and the inert components Ar and He were involved in the reactions as collision partners [15]. In this work, we used the random choice method (RCM) [16] for gasdynamics equation solution. The method described in Ref. 13 employs the exact solution of the Riemann problem at the interface between adjacent computation cells for constructing the full solution [16]. The grids used in this work comprised 200 cells, on average, along the x axis, and calculations took into account flow inhomogeneity in the gas behind the incident shock wave. Because of the large number of computational cells, we were able to calculate accurately the position of the reflected shock front (the error of its determination in the RC method equals about one step along the x axis [17]) and to resolve confidently the chemical reaction zone. Simulation Results The pressure profiles calculated using the previously discussed model are displayed in Figs. 4a and 4b. Profiles (a) pertain to the flow mode I profiles and (b) are the results of modeling for mode II. As mentioned earlier, this pair of experiments corresponds to the same half-decay time of IR emission of N2O; however, in mode I, the unimolecular N2O decomposition is fast but the major fraction of the heat is released slowly by the CO ` O ` M → CO2 ` M reaction. In mode II, N2O is consumed and CO2 builds up synchronously by the fast chain reactions N2O ` H → N2 ` OH and CO ` OH → CO2 ` H. The identical sind times in these two cases are explained by appreciable differences in the temperatures: for mode I, T50 4 1502 K and for II, T50 4 1203 K; the initial rate of the unimolecular
3004
DETONATIONS
Fig. 4. The pressure profiles at various times. (a) Mixture 1, mode I; (b) mixture 5, mode II.
N2O decomposition reaction triggering the subsequent secondary reactions for mode II is 150 times as low as that for mode I. In mode I, all the flow parameters change gradually: slow heat release in the reaction zone generates weak compression waves that catch up with the reflected shock front and accelerate it smoothly. In mode II, the reflected shock wave velocity and pressure during initial 200 ls are nearly identical, with their values calculated disregarding the chemical reactions. The thermal explosion taking place 270 ls after shock wave reflection from the end plate produces an intense compression wave that is converted into a shock discontinuity at t . 320 ls. Its further propagation through state 5 in the form of a C-J detonation wave terminates at t 4 370 ls; at this instant, the detonation front catches up with the reflected shock wave, and the merged waves give rise to an overdriven detonation wave that keeps spreading through state 2. This produces a contact surface and rarefaction wave at the site where the two waves
Fig. 5. IR emission profile of N2O (k 4 3.7 lm). The solid line is experiment; the dashed line represents our numerical modeling. (a) Mixture 1, mode I; (b) mixture 5, mode II.
merge. The rarefaction wave propagates toward the shock tube end plate. The gas temperature behind the primary shock wave rises steeply, and the peak pressure and density fall off. Infrared Emission of the Gas The IR emission profiles of N2O and CO2 enable us to estimate the difference between the vibrational temperature in the reaction zone and the translation-rotational temperature. The emission profiles are complicated; therefore, a systematic analysis of the measurements presents difficulties. Consequently, in this work, we compared directly the emission profiles obtained in experiment with those calculated by the equilibrium model. The results of the comparison are displayed in Fig. 5. The results of the equilibrium calculations (Ttr 4 Trot 4 Tvib) reproduce the experimental profiles with a high accuracy in all cases. The insignificant
IGNITION AND DETONATION IN N2O-CO-H2-He MIXTURES
deviations (not exceeding 5%) of the calculations profile from measurements of the maximum profile amplitude in all experiments can be explained by interference of a weak signal from light scattered by the polished shock tube walls. Thus, an analysis of the IR emission profiles carried out in this section with due regard for the results of the analysis of the kinetic and gasdynamics models (see earlier) leads us to conclude that thermal explosion in N2O-CO-H2-He mixtures proceeds in the equilibrium regime (i.e., at Ttr 4 Trot 4 Tvib) within a very wide range of the parameters. We failed to observe noticeable deviations from the equilibrium model at the temperature rise rates in the system up to dT/dt 4 40K/ls. Conclusions We studied ignition and deflagration-to-detonation transition in initial temperatures ranging between 1200 and 1800 K and pressures from 3 to 9 atm. It is inferred from the measured profiles and results of numerical modeling that the chemical reactions in the N2O-CO-H2 system are described adequately by the mechanism suggested in Ref. 15. It is based on reactions involving free radicals and assumes equilibrium between the translation-rotational and internal degrees of freedom of the molecules within a wide range of the initial parameters of the gas flow and under different conditions in the reacting shock heated mixture. Two different modes of interaction between the exothermic reaction and the gas flow are distinguished. The single-front mode with a single discontinuity, the reflected shock front, and two-front mode, in which the reflected shock front and a strong discontinuity formed due to interaction between the compression waves generated in the intense energy-release zone are present simultaneously in the gas flow. From the experimental data and analytical and numerical modeling results, we infer that both the total heat release by the chemical reactions and the ratio of the induction period of the mixture to the characteristic energy-release time are the parameters governing the flow pattern. We have derived a universal quantitative criterion that relates the gas flow
3005
pattern behind the reflected shock wave to the ratio between the induction period of the system and the characteristic heat-release time, the acoustic velocity in the gas, and the overall exothermicity of the reactions. Acknowledgment This work was supported in part by grant 96-03-32746 from the Russian Fundamental Research Foundation.
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