560 G.D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 test fuel in the allowable cor ratio. Since the definite reasons for considering engine 'knock'to be tical to the detonation phenomenon [116 the oN concept is sometimes attractive for at least qualitative The most important parameter defining detonability of various mixtures irrespective of the detonation wave geometry are ranges of the initial conditions under which detonation can be self-sustaining. These conditions com- °9 prise: concentrations at the fuel-lean and rich limits, the 444m9今 limiting initial pressure and size of the duct or unconfined cloud, critical diameters for detonation transition between 700800 volumes of various geometry, and permissible concentration variations in an inhomogeneous initial mixture. Fig. 12. Measured induction zone length ys. velocities of the Most of the detonation studies are performed in tubes nock front of decaying acetylene-oxygen-diluent(Ar) detona since detonation can be most easily initiated in ducts tions [123 ]: 1-induction time and 2-smoked foil measurements. Therefore, it is reasonable to start the analysis with Normal initial temperature. The detonation limits consideration of limiting parameters for detonations in terms of initial pressure tubes Analysis of the experimental observations pertaining to length Lind vS. velocities of the lead shock front D of marginal detonations reveals that a decrease in the decaying acetylene-oxygen-diluent(Ar) detonations. In ncentration of one of the mixture components, mixture the experiments [123). most of the data falls in the region dilution by an inert gas, or pressure reduction results in where the induction zone length(Lind=lind ncrease of the characteristic reaction time or detonation cell reaction induction time behind the shock wave) is less than size. As an example, Fig. II shows the comparison of the tube diameter d and slightly larger than the tube radius r [120] for hydrogen-oxygen mixtures with different dilution As the shock velocity approaches the limiting velocity of pinning detonation, Dc, the induction length tends to the with argon at different initial pressure value of 0.8r. The extrapolation of this data gives the In a tube of fixed diameter, it means that the number of criterion for detonation propagation in round tubes cells on the detonation front tends to one. when detonation propagates in the spinning mode. All the available ndD≤0.8r experimental data suggest that this is the last quasi-steady Although this correlation is stated to be a detonation limit state mode of detonation propagation. Hence, one may state the conditions under which the experiments have been that detonation decay always passes through the spinning conducted can hardly qualify to substantiate that this statement applies for detonation propagation in long ducts t is commonly recognized that the realistic relation between the induction zone length and the tube diameter is. Lind=tnd≈d where u is the particle velocity in the front-fixed frame of 2.0 reference and d is the tube diameter, rather than Eq.(1).It should be e because depending on the mixture composition and fuel type the ratio between the induction zone length and tube diameter may vary. Moreover, it depends on the accuracy of induction periods used in the comparison(experimental spread of ignition delays of nondilute detonable mixtures measured in shock tubes is at least off by a factor of 2)and the temperature behind the lead shock wave, which varies in 0.1 LLLLL LLLL a wide range behind the nonplanar front inherent in spinning waves. According to geometrical considerations, the findu/d p/ atm ratio should be close to 3 because the spin pitch nearly 1,2→X=0% 4 3.19) for H2 +O2+XAr mixtures(,A th equals to d and certainly the maximum induction zone length should be less that the spin pitch, otherwise 4-50%Ar, 5, 6--60% Ar,7,89-70% Ar, detonation would not propagate in a quasi-steady mode. 2,4,5,8-c in Ret.[120,6-107,and9-{121,122l. However, as observations of soot prints left by marginal
the test fuel in the allowable compression ratio. Since there are definite reasons for considering engine ‘knock’ to be identical to the detonation phenomenon [116], the ON concept is sometimes attractive for at least qualitative analyses [117,118]. The most important parameter defining detonability of various mixtures irrespective of the detonation wave geometry are ranges of the initial conditions under which detonation can be self-sustaining. These conditions comprise: concentrations at the fuel-lean and rich limits, the limiting initial pressure and size of the duct or unconfined cloud, critical diameters for detonation transition between volumes of various geometry, and permissible concentration variations in an inhomogeneous initial mixture. Most of the detonation studies are performed in tubes since detonation can be most easily initiated in ducts. Therefore, it is reasonable to start the analysis with consideration of limiting parameters for detonations in tubes. Analysis of the experimental observations pertaining to marginal detonations reveals that a decrease in the concentration of one of the mixture components, mixture dilution by an inert gas, or pressure reduction results in an increase of the characteristic reaction time or detonation cell size. As an example, Fig. 11 shows the comparison of predicted and measured transverse detonation cell size a [120] for hydrogen–oxygen mixtures with different dilution with argon at different initial pressure. In a tube of fixed diameter, it means that the number of cells on the detonation front tends to one, when detonation propagates in the spinning mode. All the available experimental data suggest that this is the last quasi-steadystate mode of detonation propagation. Hence, one may state that detonation decay always passes through the spinning mode. Fig. 12 [123] presents the measured induction zone length Lind vs. velocities of the lead shock front D of decaying acetylene–oxygen–diluent (Ar) detonations. In the experiments [123], most of the data falls in the region where the induction zone length (Lind ¼ tindD; tind is the reaction induction time behind the shock wave) is less than the tube diameter d and slightly larger than the tube radius r: As the shock velocity approaches the limiting velocity of spinning detonation, DCJ; the induction length tends to the value of 0:8r: The extrapolation of this data gives the criterion for detonation propagation in round tubes: tindD # 0:8r ð1Þ Although this correlation is stated to be a detonation limit, the conditions under which the experiments have been conducted can hardly qualify to substantiate that this statement applies for detonation propagation in long ducts. It is commonly recognized that the realistic relation between the induction zone length and the tube diameter is: Lind ¼ tindu < d where u is the particle velocity in the front-fixed frame of reference and d is the tube diameter, rather than Eq. (1). It should be emphasized that this relation is only approximate because depending on the mixture composition and fuel type the ratio between the induction zone length and tube diameter may vary. Moreover, it depends on the accuracy of induction periods used in the comparison (experimental spread of ignition delays of nondilute detonable mixtures measured in shock tubes is at least off by a factor of 2) and the temperature behind the lead shock wave, which varies in a wide range behind the nonplanar front inherent in spinning waves. According to geometrical considerations, the tindu=d ratio should be close to 3 because the spin pitch nearly equals to pd and certainly the maximum induction zone length should be less that the spin pitch, otherwise detonation would not propagate in a quasi-steady mode. However, as observations of soot prints left by marginal Fig. 11. Comparison of the calculated detonation cell size a with experimental data [63,119] for H2 þ O2 þ XAr mixtures (1, 3, 7). 1, 2—X ¼ 0% Ar, 3, 4—50% Ar, 5, 6—60% Ar, 7, 8, 9—70% Ar, 2, 4, 5, 8—calculated in Ref. [120], 6—[107], and 9—[121,122]. Fig. 12. Measured induction zone length vs. velocities of the lead shock front of decaying acetylene–oxygen–diluent (Ar) detonations [123]: 1—induction time and 2—smoked foil measurements. Normal initial temperature. The detonation limits were found in terms of initial pressure. 560 G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672
G D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 spinning detonation show [124 the maximum induction the following major factors: the initiation energy (too zone length intensely and irregularly fluctuates due to the small energies will lead to underestimation of the limits, hot spot nature of ignition, which naturally drastically whereas an excessively strong initiator in a tube of a limited reduces the aforesaid ratio and renders it fairly uncertain length will overdrive the wave and thus overestimate the What would happen if the conditions for detonation are mixture detonability ) the tube diameter and length worsened still further? The irregular fluctuations of the The distance required to reach steady-state detonation at induction zone increase local heat and momentum losses the limits increases as compared to that far from the limits, from this zone, which may eventually result in complete therefore quite long tubes are needed when measuring the decoupling of the reaction front from the lead shock front limiting concentrations. For example, Pawel et al. [1251 found out that a 7 m long tube 16 or 26 mm in diameter was convective or conductive energy transfer. Such local insufficient for the marginal fuel-lean hydrogen-air detona- separation of the two fronts was recorded quite clearly on tion to establish. It was possible to obtain the lean limit of smoked foils [124]. A local separation can be followed by detonation in tubes 14 m long with 17.3%(vol )H2 in a complete decoupling of the flame front and shock wave 16 mm diameter tube and 15.3%(vol )H, in a 26 mm throughout the tube cross-section diameter tube There is still a possibility for the mixture between the Another factor that may affect the results of measure- two fronts to self-ignite in a hot spot(or multiple hot spots) ments is the quality of the mixture: imperfect mixing and develop a secondary detonation wave(or strong reactive narrows the limits markedly wave)that then catches up with the lead shock front and Experiments show that the lean limits for hydrocarbo gives rise to an overdriven detonation. This overdriven nd both limits for hydrogen are independent of the tube detonation will certainly decay and, thus, the process enters iameter after it reaches a certain value which is close to the next cycle of detonation wave decay. Hence, the 70-100 mm [124]. However, the rich limits for hydro- pinning mode should be adjacent to the region of so-called carbons increase continuously with the diameter. The galloping propagation mode. This latter mode exhibits limiting diameters for FAMs range from about 6mm for sometimes rather regular velocity jumps and for this reason hydrogen-air and 20-30 mm for hydrocarbon-air mix may be thought of as being quasi-steady, but it is much more tures. For methane-air mixtures, the limiting diameter is sensitive to even minor changes in the initial conditions than estimated at 100 mm (in a 70 mm inner diameter tube the spinning mode is, therefore it would be proper to refer it detonation propagated only in a stoichiometric mixture and to unsteady propagation modes of supersonic reactive only in an unstable mode). Fuel-oxygen mixtures have aves. The larger the tube diameter and the sensitive smaller limiting diameters (for hydrogen-oxygen and is the reaction rate to temperature variations, the greater is methane-oxygen mixtures it is about 2 mm, while for a the scale of the pulsations. Usually, as the conditions depart ore detonable acetylene-oxygen mixture it is even less rom those required for the stable spinning mode, the than 1 mm) velocity pulsations become greater and of a larger scale. Initial temperature To affects the detonability limits as until the detonation wave degenerates completely into a clearly shown by Pawel et al. [125] who investigated the flame and a shock wave. Normally the galloping regime is fluence of initial temperature (To= 135, 195, and 295 K) observed within a very narrow concentration range [ 124]. on the detonability of CH4-O2, H2-O2, and H2-air For unstable, near-limit phenomena in some particular mixtures. Fig. 13 shows the results of their measurements. mixtures, like galloping detonations, the existence criterion For all the systems under investigation in Ref. [125, the [123]is( see Fig.12): concentration limits of stable detonation were found to 0.8r≤tmdD≤d become narrower for lower initial temperatures. This is artly confirmed by detonation cell measurements of Thus, one can define the detonation limit in a tube as a Tieszen et al. [ 126] shown in Table 1. As follows from boundary between the regions of Istence and failure of he table, stoichiometric propane-air mixture shows the spinning detonation mode. Although very approximate and pposite trend: detonation cell size tends to increase with To pplicable to mixtures studied, the criteria of types(1)and d detonability limits should be narrower at higher To (2)incorporate chemical properties of the mixture, particle Note, that based on the classical theory of detonation, one velocity, and characteristic dimensions of the channel, and could expect the effect of initial temperature To similar to can be very useful in analysis of near-limit and failure that shown by propane. The temperature behind the shock modes of detonation propagation. It is worthy to note that wave front leading detonation is nearly independent of To the Zel'dovich theory of detonability limits predicts a but the chemical kinetics behind the shock is affected by similar relationship between the induction zone lengt density. Because the reaction time is inversely proportional near-limit detonation and the tube diameter [1151 to the gas density to power n(where n is the reaction order) Of course, the procedure of measuring detonation the detonation limits should become narrower at higher To should be standardized somehow (like that for flammabili Here, however, it is worth noting that the effects associated limits), since the detonation limits should depend on with initial temperature (in its range studied) are to
spinning detonation show [124], the maximum induction zone length intensely and irregularly fluctuates due to the hot spot nature of ignition, which naturally drastically reduces the aforesaid ratio and renders it fairly uncertain. What would happen if the conditions for detonation are worsened still further? The irregular fluctuations of the induction zone increase local heat and momentum losses from this zone, which may eventually result in complete decoupling of the reaction front from the lead shock front and its conversion into the flame front governed by the convective or conductive energy transfer. Such local separation of the two fronts was recorded quite clearly on smoked foils [124]. A local separation can be followed by complete decoupling of the flame front and shock wave throughout the tube cross-section. There is still a possibility for the mixture between the two fronts to self-ignite in a hot spot (or multiple hot spots) and develop a secondary detonation wave (or strong reactive wave) that then catches up with the lead shock front and gives rise to an overdriven detonation. This overdriven detonation will certainly decay and, thus, the process enters the next cycle of detonation wave decay. Hence, the spinning mode should be adjacent to the region of so-called galloping propagation mode. This latter mode exhibits sometimes rather regular velocity jumps and for this reason may be thought of as being quasi-steady, but it is much more sensitive to even minor changes in the initial conditions than the spinning mode is, therefore it would be proper to refer it to unsteady propagation modes of supersonic reactive waves. The larger the tube diameter and the more sensitive is the reaction rate to temperature variations, the greater is the scale of the pulsations. Usually, as the conditions depart from those required for the stable spinning mode, the velocity pulsations become greater and of a larger scale, until the detonation wave degenerates completely into a flame and a shock wave. Normally the galloping regime is observed within a very narrow concentration range [124]. For unstable, near-limit phenomena in some particular mixtures, like galloping detonations, the existence criterion [123] is (see Fig. 12): 0:8r # tindD # d ð2Þ Thus, one can define the detonation limit in a tube as a boundary between the regions of existence and failure of the spinning detonation mode. Although very approximate and applicable to mixtures studied, the criteria of types (1) and (2) incorporate chemical properties of the mixture, particle velocity, and characteristic dimensions of the channel, and can be very useful in analysis of near-limit and failure modes of detonation propagation. It is worthy to note that the Zel’dovich theory of detonability limits predicts a similar relationship between the induction zone length of the near-limit detonation and the tube diameter [115]. Of course, the procedure of measuring detonation limits should be standardized somehow (like that for flammability limits), since the detonation limits should depend on the following major factors: the initiation energy (too small energies will lead to underestimation of the limits, whereas an excessively strong initiator in a tube of a limited length will overdrive the wave and thus overestimate the mixture detonability), the tube diameter and length. The distance required to reach steady-state detonation at the limits increases as compared to that far from the limits, therefore quite long tubes are needed when measuring the limiting concentrations. For example, Pawel et al. [125] found out that a 7 m long tube 16 or 26 mm in diameter was insufficient for the marginal fuel-lean hydrogen–air detonation to establish. It was possible to obtain the lean limit of detonation in tubes 14 m long with 17.3% (vol.) H2 in a 16 mm diameter tube and 15.3% (vol.) H2 in a 26 mm diameter tube. Another factor that may affect the results of measurements is the quality of the mixture: imperfect mixing narrows the limits markedly. Experiments show that the lean limits for hydrocarbons and both limits for hydrogen are independent of the tube diameter after it reaches a certain value, which is close to 70–100 mm [124]. However, the rich limits for hydrocarbons increase continuously with the diameter. The limiting diameters for FAMs range from about 6 mm for hydrogen–air and 20–30 mm for hydrocarbon–air mixtures. For methane–air mixtures, the limiting diameter is estimated at 100 mm (in a 70 mm inner diameter tube detonation propagated only in a stoichiometric mixture and only in an unstable mode). Fuel–oxygen mixtures have smaller limiting diameters (for hydrogen–oxygen and methane–oxygen mixtures it is about 2 mm, while for a more detonable acetylene–oxygen mixture it is even less than 1 mm). Initial temperature T0 affects the detonability limits as clearly shown by Pawel et al. [125] who investigated the influence of initial temperature (T0 ¼ 135; 195, and 295 K) on the detonability of CH4 –O2, H2 –O2, and H2 –air mixtures. Fig. 13 shows the results of their measurements. For all the systems under investigation in Ref. [125], the concentration limits of stable detonation were found to become narrower for lower initial temperatures. This is partly confirmed by detonation cell measurements of Tieszen et al. [126] shown in Table 1. As follows from the table, stoichiometric propane–air mixture shows the opposite trend: detonation cell size tends to increase with T0 and detonability limits should be narrower at higher T0: Note, that based on the classical theory of detonation, one could expect the effect of initial temperature T0 similar to that shown by propane. The temperature behind the shock wave front leading detonation is nearly independent of T0 but the chemical kinetics behind the shock is affected by density. Because the reaction time is inversely proportional to the gas density to power n (where n is the reaction order), the detonation limits should become narrower at higher T0: Here, however, it is worth noting that the effects associated with initial temperature (in its range studied) are too G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672 561
G.D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 26 8 01020304050607080901000102030405060708090100 Vol %o ch Vol %o h ies of the limiting tube diameter on the molar fraction of fuel in CH4-O2(a)and H2-O2(b)mixtures at pressure mperatures [125:(a)l-70=195k,2-295K;(b)l-70=135K.2-295K insignificant and can be concealed by the uncertainty in the concentraion limits of CH4-O2-N, detonations in measured cell size to make any definite conclusions Based tube 16 mm in diameter[128]. Clearly, the limiting pressure on general reasoning one can expect extension of the depends on mixture sensitivity: it is 200 Torr for pure detonation limits when the temperature approaches self- CHa-Oz mixture and about 360 Torr for CH4-O2-N2 gnition temperature mixture with 33% N2. It is interesting that at pressure Auffret et al. [127. based on their experimental studies, exceeding 600 Torr the fuel-rich limits were found to be have proposed the following correlation of the detonation wider for less sensitive mixtures size a for crh2-0, mixtures. The state of the tube walls also affects the limiting conditions for detonation propagation In rough tubes, the detonation limits(for detonation waves spreading at high Within the initial temperature range To=293-500 K, and velocity close to the ideal CJ value)are usually narrower than in smooth ones [124 This is because the loss of the m=0.9 for the stoichiometric mixtures tending to m =0 for momentum at the roughness reduces the detona- el-lean mixtures. Contrary to Ref. [125], the findings of tion velocity, and thereby in significantly the bulk Ref. [127] indicate that the detonability of near-stoichio. reaction zone (although vave reflections metric mixtures is deteriorated by increasing the initial temperature. Thus, the effect of initial temperature on detonability limits is still a controversial issue No detonation Reduction of the initial pressure affects significantly both he limiting diameter and concentration limits of detonation increasing the former and making narrower the latter. For example [124], propane-air mixtures are detonable within 0.7 atm, and only from 3.5 to e range of C3Hs molar concentration from 3 to 6%at detonation does not propagate in the 70 mm inner diameter ube Fig. 14 shows the measured pressure dependencies of 0 Table 1 parison between measured transverse cell size a at 25 and 00C for stoichiometric fuel-air mixtures of some gaseous hydrocarbons (initial pressure I bar)[126] a(100°Ca(25℃C) °C 00°C 4.0 Po/Torr ChS of CH4-O2-N2 detonations in a 16 mm in diameter(norma CHe initial temperature)[128 ]: I-molar fractions of N2 and O2 equal to 0and100%,210and90%,3-l8and82%,and4-33and67%
insignificant and can be concealed by the uncertainty in measured cell size to make any definite conclusions. Based on general reasoning one can expect extension of the detonation limits when the temperature approaches selfignition temperature. Auffret et al. [127], based on their experimental studies, have proposed the following correlation of the detonation cell size a for C2H2 –O2 mixtures: a , p2n 0 Tm 0 Within the initial temperature range T0 ¼ 293–500 K, and initial pressure range p0 ¼0.05–1 bar, n <1.1–1.3, and m <0.9 for the stoichiometric mixtures tending to m <0 for fuel-lean mixtures. Contrary to Ref. [125], the findings of Ref. [127] indicate that the detonability of near-stoichiometric mixtures is deteriorated by increasing the initial temperature. Thus, the effect of initial temperature on detonability limits is still a controversial issue. Reduction of the initial pressure affects significantly both the limiting diameter and concentration limits of detonation increasing the former and making narrower the latter. For example [124], propane–air mixtures are detonable within the range of C3H8 molar concentration from 3 to 6% at 0.7 atm, and only from 3.5 to 5.7% at 0.2 atm; at 0.15 atm detonation does not propagate in the 70 mm inner diameter tube. Fig. 14 shows the measured pressure dependencies of the concentraion limits of CH4 –O2 –N2 detonations in a tube 16 mm in diameter [128]. Clearly, the limiting pressure depends on mixture sensitivity: it is 200 Torr for pure CH4 –O2 mixture and about 360 Torr for CH4 –O2 –N2 mixture with 33% N2. It is interesting that at pressure exceeding 600 Torr the fuel-rich limits were found to be wider for less sensitive mixtures. The state of the tube walls also affects the limiting conditions for detonation propagation. In rough tubes, the detonation limits (for detonation waves spreading at high velocity close to the ideal CJ value) are usually narrower than in smooth ones [124]. This is because the loss of the momentum at the roughness elements reduces the detonation velocity, and thereby increases significantly the bulk reaction zone (although shock wave reflections at Table 1 Comparison between measured transverse cell size a at 25 and 100 8C for stoichiometric fuel–air mixtures of some gaseous hydrocarbons (initial pressure 1 bar) [126] Fuel a (mm) a (100 8C)/a (25 8C) 25 8C 100 8C C2H2 5.3 4.0 0.75 C2H4 19.5 16 0.82 C2H6 50 48 0.96 C3H8 50 52 1.04 CH4 305 260 0.85 Fig. 14. Measured pressure dependencies of the concentration limits of CH4 –O2 –N2 detonations in a tube 16 mm in diameter (normal initial temperature) [128]: 1—molar fractions of N2 and O2 equal to 0 and 100%, 2—10 and 90%, 3—18 and 82%, and 4—33 and 67%. Fig. 13. Measured dependencies of the limiting tube diameter on the molar fraction of fuel in CH4 –O2 (a) and H2 –O2 (b) mixtures at pressure 1 atm and different initial temperatures [125]: (a) 1—T0 ¼195 K, 2—295 K; (b) 1—T0 ¼135 K, 2—295 K. 562 G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672
G D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 38mm 20mm 13mm 10mm 8mn 501 20 ▲8 0.04 0.6 Fig. 16. Measurements of transverse detonation cell size a in JP. 10-additive-air mixture at Po =100 kPa, To=353 K. points for hydrocarbon-air mixtures are from Ref [126]. Fig. 15. Summary of experimental results of Ref [129] on the for CH4-air mixture is 260 mm[130] I-no additive, 2 etonability limits of CH4-O2 mixture in tubes of different shape of dditive, 3--CHa-additive, and 4-C2He-additive cross-section. Solid line 1 represents limits for tubes with circular cross-section with points 2-4 corresponding to round tubes 20, 16, and 8mm in diameter, p 5-8 correspond to tubes of the limiting tube diameter. According to experimental data ctangular cross-section: 5--18x 18 mm.6--16x 16 mm. of Borisov et al. [124 ethylene added to methane in amount 7-38x8mm, and 8-16x8mm. Dashed lines indicate recipro. of 10% reduces the critical diameter below 70 mm cal values of the short and the long side of the rectangular tubes. (detonation propagates in the 70 mm inner diameter tube They are plotted at the measured limit concentration value stably within the 9-11% CH4 concentration range). With the roughness protrusions on the walls facilitate attaching 20% ethylene additives to methane, the mixture is detonable the reaction zone to the shock front within the 8-12% CHA range. Such active additives as Tubes used in practice are not necessarily round acetylene, organic-nitrates-, and NF2-containing com- therefore a question arises, how the shape of the channel pounds extend the detonation limits and reduce the limiting affects the critical conditions for detonation propagation. diameter even to a greater extent. Fig. 16[130] shows the Jost and Wagner [1291 investigated detonability limits of effect of various hydrocarbon additives(C2H2, C2H4, and H4-O, mixture in tubes with circular, square, and CHa) on the detonation cell size of stoichiometric JP-10 rectangular cross-section. Fig. 15 shows the summary of additive-air mixtures. The experiments were conducted their experimental findings in terms of the limiting methane the heated 280 mm diameter detonation tube. Similar data concentration vs. hydraulic diameter plot. Following Jost on the effectiveness of adding low-molecular weight fuels and Wagner, an estimate of the limits of detonability based as sensitizers to hexane-air mixture was reported in on hydraulic diameters gives a reasonable value as long as Ref [131. f a rectangular cross-section is larger than a In situ mixing of hydrocarbon fuel with HP can also certain lower limit. The concept of limiting hydraulic used to significantly widen detonability limits[95]. Fig 17 diameter does not take into account real processes behind shows the predicted dependencies of the transverse detona- the detonation front. Nevertheless it was found that in tubes tion cell size in iso-octane-air-hP (solid curve) and n of rectangular and even triangular cross-section the last heptane-air-HP (dashed curve) mixtures on HP molar mode of stable detonation propagation was quite similar to fraction Addition of HP(up to 20%)results in decreasing spinning detonation with a single transverse wave. Of the cell size by a factor of 20. As HP is commercially course, the flow pattern at the tube periphery is somewhat available in the form of concentrated aqueous solutions, it is different from that in round tubes, but the general features of interesting to evaluate the effect of water. Fig. 18 shows the the marginal detonation are similar. In rectangular tubes the predicted detonation cell size as a function of molar fraction single-head mode is still the last one before detonation of water l in the aqueous solution of HP for the system failure, provided the ratio of the channel width to its height o-octane--20% HP and iso-octane-60% HP. Clearly, the does not exceed 2. With larger ratios, the margina detonation cell size is affected by water but if highly detonation mode is multiheaded concentrated HP solutions are used (e.g. 85-95%o), the Additives of e fuels even in small amou detonability of the blend remains much higher than that of extend markedly the detonation limits and reduce ure hydrocarbon fuel
the roughness protrusions on the walls facilitate attaching the reaction zone to the shock front). Tubes used in practice are not necessarily round, therefore a question arises, how the shape of the channel affects the critical conditions for detonation propagation. Jost and Wagner [129] investigated detonability limits of CH4 –O2 mixture in tubes with circular, square, and rectangular cross-section. Fig. 15 shows the summary of their experimental findings in terms of the limiting methane concentration vs. hydraulic diameter plot. Following Jost and Wagner, an estimate of the limits of detonability based on hydraulic diameters gives a reasonable value as long as one side of a rectangular cross-section is larger than a certain lower limit. The concept of limiting hydraulic diameter does not take into account real processes behind the detonation front. Nevertheless, it was found that in tubes of rectangular and even triangular cross-section the last mode of stable detonation propagation was quite similar to spinning detonation with a single transverse wave. Of course, the flow pattern at the tube periphery is somewhat different from that in round tubes, but the general features of the marginal detonation are similar. In rectangular tubes the single-head mode is still the last one before detonation failure, provided the ratio of the channel width to its height does not exceed 2. With larger ratios, the marginal detonation mode is multiheaded. Additives of more reactive fuels even in small amounts extend markedly the detonation limits and reduce the limiting tube diameter. According to experimental data of Borisov et al. [124], ethylene added to methane in amount of 10% reduces the critical diameter below 70 mm (detonation propagates in the 70 mm inner diameter tube stably within the 9–11% CH4 concentration range). With 20% ethylene additives to methane, the mixture is detonable within the 8–12% CH4 range. Such active additives as acetylene-, organic-nitrates-, and NF2-containing compounds extend the detonation limits and reduce the limiting diameter even to a greater extent. Fig. 16 [130] shows the effect of various hydrocarbon additives (C2H2, C2H4, and CH4) on the detonation cell size of stoichiometric JP-10– additive–air mixtures. The experiments were conducted in the heated 280 mm diameter detonation tube. Similar data on the effectiveness of adding low-molecular weight fuels as sensitizers to hexane–air mixture was reported in Ref. [131]. In situ mixing of hydrocarbon fuel with HP can also be used to significantly widen detonability limits [95]. Fig. 17 shows the predicted dependencies of the transverse detonation cell size in iso-octane–air–HP (solid curve) and nheptane–air–HP (dashed curve) mixtures on HP molar fraction. Addition of HP (up to 20%) results in decreasing the cell size by a factor of 20. As HP is commercially available in the form of concentrated aqueous solutions, it is interesting to evaluate the effect of water. Fig. 18 shows the predicted detonation cell size as a function of molar fraction of water c in the aqueous solution of HP for the systems iso-octane—20% HP and iso-octane—60% HP. Clearly, the detonation cell size is affected by water but if highly concentrated HP solutions are used (e.g. 85–95%), the detonability of the blend remains much higher than that of pure hydrocarbon fuel. Fig. 15. Summary of experimental results of Ref. [129] on the detonability limits of CH4 –O2 mixture in tubes of different shape of cross-section. Solid line 1 represents limits for tubes with circular cross-section with points 2–4 corresponding to round tubes 20, 16, and 8 mm in diameter, points 5–8 correspond to tubes of rectangular cross-section: 5—18 £ 18 mm, 6—16 £ 16 mm, 7—38 £ 8 mm, and 8—16 £ 8 mm. Dashed lines indicate reciprocal values of the short and the long side of the rectangular tubes. They are plotted at the measured limit concentration value. Fig. 16. Measurements of transverse detonation cell size a in JP- 10–additive–air mixture at p0 ¼100 kPa, T0 ¼353 K. All data points for hydrocarbon–air mixtures are from Ref. [126], cell size for CH4 –air mixture is 260 mm [130]; 1—no additive, 2—C2H2- additive, 3—CH4-additive, and 4—C2H4-additive. G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672 563
G.D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 energies, limiting diameter, concentration limits of detona- tion, etc ). As is well established, the major mechanism governing the heat release in detonation waves is self ignition of th for direct onset of detonation in the course of ddt Therefore to assess the effect of additives on detonation processes, one has to find out how the additives affect the basic self-ignition stages. Before analyzing the effect of ider the peculiarities of spontaneous 10 nditions relevan to those existing in detonation waves or DDT processes. A great body of experimental data and numerical modeling show that the range of characteristic times inherent in the processes at issue is sub-milliseconds, at longer times normally no strong coupling between the shock (or ompression wave) and chemical reaction has ever been observed. This range is covered by the shock tube experiments, which provide much more reliable kinetic data than do direct measurements in detonation waves Fig. 17. Predicted dependencies of the transverse detonation cell s moreover, the conditions for ignition in shock tubes are a in stoichiometric iso-octane-air-HP(solid curve)and -heptane- similar to those in detonation waves, except the absence of air-HP(dashed curve)mixtures on HP molar fraction vA [951 traveling transverse waves in the shocked mixture Although a detonation wave is characterized by a great This section focuses on the effect of chemically active variety of representative chemical reaction times,its additives mostly on the parameters pertaining to a critical arginal behavior is controlled by the longest of them, behavior of detonation waves. It has been discussed in therefore there is no need to analyze the effective heat release Section 2.2. 1 that small additives can hardly influence the profiles throughout the wave and restrict consideration only characteristics of steady CJ waves. Indeed, a change in the to local self-ignition process, which can be adequately rate of a chemical reaction can affect only the detonation characterized by shock-tube data. The basic conclusion ell size, which, in multihead detonation waves has nothing drawn from these data is that ignition never occurs to do with the averaged detonation parameters. The simultaneously throughout the preheated mixture volume. chemical kinetics becomes a crucial factor only when Ignition in exothermic centers (hot spots)arising due to the critical phenomena are concerned(minimum initiation gasdynamic fluctuations is a well-established fact in shock ubes, and this ignition seriously affects the time history of heat release. As experience suggests, hot spot ignition is herent in all techniques used to study self-ignition How does the hot-spot mechanism affect the overall heat release in a shocked mixture? A comparison of the data on spontaneous ignition with kinetic modeling of adiabatic chain-thermal explosions reveals that hot spots reduce the effective ignition delay, however, not drastically. But when the overall heat release profile (which is the result of averaging the reaction course in many elementary mixture volumes subjected to various fluctuations) is considered. these volumes would significantly extend the time range within which the reaction runaway is observed, affecting the overall ignition delay onl little, except when the ignition delay becomes commensurate with the runaway time. An analysis of kinetic measurements in a wide range of reaction times shows that for hydro- molar fractioned transverse deto carbon -air mixtures the runaway time is close to 100 us and solution of HP for the only insignificantly depends on temperature and initial iso-octane--20% HP (solid cur pressure [132]. It is also affected only little by chemical lines 1.2. and 3 corres. additives. Global kinetic heat release equations often used in pond to the predicted cell sizes in the corresponding systems with ID simulations must take into account this peculiarity of 0% H202, 20% H2O2, and 60% H2O2, respectively. at a=0 [95]. the thermal explosion development(which is reflected in
This section focuses on the effect of chemically active additives mostly on the parameters pertaining to a critical behavior of detonation waves. It has been discussed in Section 2.2.1 that small additives can hardly influence the characteristics of steady CJ waves. Indeed, a change in the rate of a chemical reaction can affect only the detonation cell size, which, in multihead detonation waves has nothing to do with the averaged detonation parameters. The chemical kinetics becomes a crucial factor only when the critical phenomena are concerned (minimum initiation energies, limiting diameter, concentration limits of detonation, etc.). As is well established, the major mechanism governing the heat release in detonation waves is selfignition of the mixture. This mechanism is also responsible for direct onset of detonation in the course of DDT. Therefore, to assess the effect of additives on detonation processes, one has to find out how the additives affect the basic self-ignition stages. Before analyzing the effect of additives, we consider the peculiarities of spontaneous ignition in shock-preheated gases under conditions relevant to those existing in detonation waves or DDT processes. A great body of experimental data and numerical modeling show that the range of characteristic times inherent in the processes at issue is sub-milliseconds, at longer times normally no strong coupling between the shock (or compression wave) and chemical reaction has ever been observed. This range is covered by the shock tube experiments, which provide much more reliable kinetic data than do direct measurements in detonation waves, moreover, the conditions for ignition in shock tubes are similar to those in detonation waves, except the absence of traveling transverse waves in the shocked mixture. Although a detonation wave is characterized by a great variety of representative chemical reaction times, its marginal behavior is controlled by the longest of them, therefore there is no need to analyze the effective heat release profiles throughout the wave and restrict consideration only to local self-ignition process, which can be adequately characterized by shock-tube data. The basic conclusion drawn from these data is that ignition never occurs simultaneously throughout the preheated mixture volume. Ignition in exothermic centers (‘hot spots’) arising due to gasdynamic fluctuations is a well-established fact in shock tubes, and this ignition seriously affects the time history of heat release. As experience suggests, hot spot ignition is inherent in all techniques used to study self-ignition. How does the hot-spot mechanism affect the overall heat release in a shocked mixture? A comparison of the data on spontaneous ignition with kinetic modeling of adiabatic chain-thermal explosions reveals that hot spots reduce the effective ignition delay, however, not drastically. But when the overall heat release profile (which is the result of averaging the reaction course in many elementary mixture volumes subjected to various fluctuations) is considered, asynchronous mixture ignition in these volumes would significantly extend the time range within which the reaction runaway is observed, affecting the overall ignition delay only little, except when the ignition delay becomes commensurate with the runaway time. An analysis of kinetic measurements in a wide range of reaction times shows that for hydrocarbon–air mixtures the runaway time is close to 100 ms and only insignificantly depends on temperature and initial pressure [132]. It is also affected only little by chemical additives. Global kinetic heat release equations often used in 1D simulations must take into account this peculiarity of the thermal explosion development (which is reflected in Fig. 17. Predicted dependencies of the transverse detonation cell size a in stoichiometric iso-octane–air–HP (solid curve) and n-heptane– air–HP (dashed curve) mixtures on HP molar fraction cA [95]. Fig. 18. Predicted transverse detonation cell size a as a function of molar fraction of water c in the aqueous solution of HP for the iso-octane—20% HP (solid curve) and iso-octane—60% HP (dashed curve) systems. Horizontal dashed lines 1, 2, and 3 correspond to the predicted cell sizes in the corresponding systems with 0% H2O2, 20% H2O2, and 60% H2O2, respectively, at c ¼ 0 [95]. 564 G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672