550 G.D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 the detonation wave. Lewis applied the theory of chain- Ferrie and Manson[47 Schelkin [48] reported pioneering branching reactions developed by Hinshelwood [371 and results on the effect of wall roughness on the ddt distance Semenov [38] to put forward the chemical mechanism of and time, as well as on the detonation propagation velocity. tonation propagation. within this model, the detonation By using various wire spirals inserted into the detonation wave propagates due to energy transfer from detonation tube he controlled the ddt distance and time within a wide products to the fresh mixture with active molecules inge. Of particular importance was Shchelkin's finding that possessing the energy sufficient for self-sustained reaction detonation can propagate at velocities considerably less than propagation. Detailed experimental studies of the effect of the thermodynamic CJ velocity initial mixture pressure and temperature, as well as tube In 1940, Zel'dovich [491 developed a theory of length and diameter on the run-up distance to detonation detonation wave structure and detonability limits. The were reported. The existence of concentration limits of keystone of his theory is the necessity of close coupling detonation was identified. In 1926, Campbell and between the lead shock wave and the finite-rate combustion Woodhead [39 have discovered the spinning detonation chemistry. The lead shock wave provides adiabatic propagating at oscillatory velocity. This discovery initiated compression and heating of the fresh explosive mixture. numerous studies of the detonation wave structure The compressed mixture autoignites after a certain induc- Campbell, Miga d, many researchers(Ricardo, Edgar, tion period and a part of the energy released is consumed to In this support constant-speed propagation of the lead shock Serruys, Schnauffer, Sokolik, Voinov and others, see corre- According to the theory, the structure and velocity of a sponding references in Ref. [40)) were involved in studies of detonation wave propagating along the tube is affected by combustion control in internal combustion engines it has been heat and momentum losses at the tube walls via variation of observed that at elevated compression ratios piston engines the chemical induction time and momentum and ener exhibited a sharp decrease in the effective pressure and, as a fluxes behind the lead shock. At a certain level of losses result-decrease in engine power. The term knocking in (governed by tube diameter, dilution ratio, etc. ) steady-state combustion comes from the fact that the mentioned decrease propagation of the detonation wave becomes impossible, as engine power is accompanied by a characteristic ringing noise. the lead shock and the reaction zone tend to decouple from As knocking combustion restricted the allowable compression each other. Later on, von Neumann [50] and Doering [511 ratio, there was mucheffort to study the mechanism of'knock have independently put forward similar models of a Ricardo [41] attributed this mode of combustion in the engine detonation wave comprising a lead shock followed by the to pre-flame autoignition of the end-gas in the cylinder. In his reaction front, taking into account the finite-rate chemistry. interpretation, autoignition of the end-gas results in a sharp At present, this model is known as Zel'dovich -Neumann pressure rise and formation of a blast wave that, similar to Doering(ZND)model of detonation hammer, hits cylinder walls. In 1930, Aubert and duchene Based on the theory, a number of important results have applied photographic method to study combustion phenomena been obtained in 1940-1950s. For example, it was proved in engines. In a knocking engine they detected high-speed theoretically in Refs. [52-54] that (i) there exist nonplanar luminous fronts propagating both into fresh mixture and into (cylindrical or spherical) detonation waves propagating at the combustion products-phenomena resembling detonation same constant velocity as planar detonations, (i)the critical onset in a tube with a characteristic retonation wave. In initiation energy of detonation is proportional to t;(where f; is 1934, Sokolik [40] substantiated the idea of Nernst[42 that the reaction induction time behind the lead shock front and vis detonation in tubes and knock in internal combustion the geometry index equal to 1, 2, and 3 for plane, cylindrical re essentially the same phenomena. His comparative analysis and spherical waves, respectively), (iii) there exists a critical of available evidence of detonation and knock onset revealed radius of the blast wave produced by the initiator at which its that physical conditions for these phenomena are completely amplitude drops to the value corresponding to the CJ similar. Experimental observations of autoignition in the detonation, and this critical radius depends on the reaction preflame zone [43] revealed the existence of exothermic rate and defines both the critical energy of the initiation centers that give rise to fast flames and shock waves resulting and the minimum size of a cloud which can support detonation. in flame flashback. Apparently due to technical reasons, most The ZND model allowed reasonable predictions of of studies dealing with knocking combustion in piston engines tration limits of detonations as well as dependencies of the vere aimed at searching for effective anti-knock chemicals to miting tube diameter on initial pressure, temperature and inhibit preflame autoignition[44] dilution ratio(see review articles [55, 56 ) A considerable progress in understanding detonation Although the ZND model is physically well-based and isa physics occurred during the 1940-1950s period. Exper very helpful idealization of a real detonation wave, later on it iments indicating a possibility of spherical flame accelera- has been clearly demonstrated both experimentally and tion and transition to detonation(i.e. DDT) were reported by theoretically that a detonation is essentially three-dimen- Rakipova et al. [45] and Zel'dovich and Roslovsky [46]. sional (3D) and steady-state only on average. Voinov [57 The first comprehensive publication in which observations based on detailed observations of spinning detonations, of spherical detonations were thoroughly discussed was by discovered transverse waves behind the lead shock front
the detonation wave. Lewis applied the theory of chainbranching reactions developed by Hinshelwood [37] and Semenov [38] to put forward the chemical mechanism of detonation propagation. Within this model, the detonation wave propagates due to energy transfer from detonation products to the fresh mixture with active molecules possessing the energy sufficient for self-sustained reaction propagation. Detailed experimental studies of the effect of initial mixture pressure and temperature, as well as tube length and diameter on the run-up distance to detonation were reported. The existence of concentration limits of detonation was identified. In 1926, Campbell and Woodhead [39] have discovered the spinning detonation propagating at oscillatory velocity. This discovery initiated numerous studies of the detonation wave structure. In this period, many researchers (Ricardo, Edgar, Campbell, Midgley, Boyd, Brown, Watkins, Dumanois, Pye, Serruys, Schnauffer, Sokolik, Voinov and others, see corresponding references in Ref. [40]) were involved in studies of combustion control in internal combustion engines. It has been observed that at elevated compression ratios piston engines exhibited a sharp decrease in the effective pressure and, as a result—decrease in engine power. The term ‘knocking’ in combustion comes from the fact that the mentioned decrease in engine power is accompanied by a characteristic ringing noise. As knocking combustion restricted the allowable compression ratio, there was much effort to study the mechanism of ‘knock’. Ricardo [41] attributed this mode of combustion in the engine to pre-flame autoignition of the end-gas in the cylinder. In his interpretation, autoignition of the end-gas results in a sharp pressure rise and formation of a blast wave that, similar to hammer, hits cylinder walls. In 1930, Aubert and Duchene applied photographic method to study combustion phenomena in engines. In a knocking engine they detected high-speed luminous fronts propagating both into fresh mixture and into combustion products—phenomena resembling detonation onset in a tube with a characteristic retonation wave. In 1934, Sokolik [40] substantiated the idea of Nernst [42] that detonation in tubes and knock in internal combustion engines are essentially the same phenomena. His comparative analysis of available evidence of detonation and knock onset revealed that physical conditions for these phenomena are completely similar. Experimental observations of autoignition in the preflame zone [43] revealed the existence of exothermic centers that give rise to fast flames and shock waves resulting in flame flashback. Apparently due to technical reasons, most of studies dealing with knocking combustion in piston engines were aimed at searching for effective anti-knock chemicals to inhibit preflame autoignition [44]. A considerable progress in understanding detonation physics occurred during the 1940–1950 s period. Experiments indicating a possibility of spherical flame acceleration and transition to detonation (i.e. DDT) were reported by Rakipova et al. [45] and Zel’dovich and Roslovsky [46]. The first comprehensive publication in which observations of spherical detonations were thoroughly discussed was by Ferrie and Manson [47]. Schelkin [48] reported pioneering results on the effect of wall roughness on the DDT distance and time, as well as on the detonation propagation velocity. By using various wire spirals inserted into the detonation tube, he controlled the DDT distance and time within a wide range. Of particular importance was Shchelkin’s finding that detonation can propagate at velocities considerably less than the thermodynamic CJ velocity. In 1940, Zel’dovich [49] developed a theory of detonation wave structure and detonability limits. The keystone of his theory is the necessity of close coupling between the lead shock wave and the finite-rate combustion chemistry. The lead shock wave provides adiabatic compression and heating of the fresh explosive mixture. The compressed mixture autoignites after a certain induction period and a part of the energy released is consumed to support constant-speed propagation of the lead shock. According to the theory, the structure and velocity of a detonation wave propagating along the tube is affected by heat and momentum losses at the tube walls via variation of the chemical induction time and momentum and energy fluxes behind the lead shock. At a certain level of losses (governed by tube diameter, dilution ratio, etc.) steady-state propagation of the detonation wave becomes impossible, as the lead shock and the reaction zone tend to decouple from each other. Later on, von Neumann [50] and Doering [51] have independently put forward similar models of a detonation wave comprising a lead shock followed by the reaction front, taking into account the finite-rate chemistry. At present, this model is known as Zel’dovich–Neumann– Doering (ZND) model of detonation. Based on the theory, a number of important results have been obtained in 1940–1950s. For example, it was proved theoretically in Refs. [52–54] that (i) there exist nonplanar (cylindrical or spherical) detonation waves propagating at the same constant velocity as planar detonations, (ii) the critical initiation energy of detonation is proportional to t n i (where ti is the reaction induction time behind the lead shock front and n is the geometry index equal to 1, 2, and 3 for plane, cylindrical, and spherical waves, respectively), (iii) there exists a critical radius of the blast wave produced by the initiator at which its amplitude drops to the value corresponding to the CJ detonation, and this critical radius depends on the reaction rate and defines both the critical energy of the initiation source and the minimum size of a cloud which can support detonation. The ZND model allowed reasonable predictions of concentration limits of detonations as well as dependencies of the limiting tube diameter on initial pressure, temperature and dilution ratio (see review articles [55,56]). Although the ZND model is physically well-based and is a very helpful idealization of a real detonation wave, later on it has been clearly demonstrated both experimentally and theoretically that a detonation is essentially three-dimensional (3D) and steady-state only on average. Voinov [57], based on detailed observations of spinning detonations, discovered transverse waves behind the lead shock front. 550 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)545-672 551 Voitsekhovsky [58 and Denisov and Troshin [59] have ven s a discovered the multihead detonation and analyzed the flow shock wave reflection at contact discontinuities patterns at the triple wave configurations with transverse walls were visualized shock waves and reaction fronts arising at the detonation Flame acceleration, DDT, and detonation propagation in front and changes in the flow patterns upon collisions of these ough-walled tubes were first visualized by babkin and figurations. Instability of realistic detonation waves and Kozatchenko [80, 81]. It has been shown that the structures their 3D structure raised serious questions concerning the of detonations in rough and smooth tubes can differ validity of the Arrhenius kinetics with an average tempera- considerably. In a tube with rough walls, mixture ignition ture in ID ZND modeling of detonation initiation and is facilitated by roughness elements due to high local propagation. Direct photographs and soot imprints [60-62] temperatures behind reflected shock waves. One-dimen- uivocally the fish-scales like cellular structure sional model predicts that due to this fact, detonations in not only of cj detonations but of the initial detonation kernel rough tubes should exhibit higher stability and wider which meant that the mixture was actually ignited behind the concentration limits [55, 56]. However, experimental obser shock front in hot spots where temperature is significantly vations [82,83] show somewhat narrower concentration higher than the average temperature limits of low-velocity regimes as compared to detonation in Based on this understanding numerous models of single smooth tubes and quite large wave velocity fluctuations and head (spinning) and multihead detonations have been recovery of a detonation wave upon its entry from a rough suggested since 1950s(see review articles [63, 641). tube into a smooth tube occurs within still narrower limits With the growing availability of diagnostics with This is evidently attributable to an essentially multidimen- mproved temporal and spatial resolutions and powerful sional nature of the reactive waves in rough tubes omputing resources, the progress in the detonation science One of the questions of practical importance is, how after the 1960s has been overwhelming First of all, it became detonation wave originated in a narrow tube behaves when it possible to visualize the ignition process behind a reflected enters a tube of a larger volume or unconfined mixture? The shock wave and discover two different modes of shock- answer to this question should provide information about induced ignition of a reactive gas, namely, 'strong'an al ways of detonation initiation in large volumes, mild ignition[65, 66]. violent volumetric ignition of shock because a mixture in a narrow duct can be initiated much compressed gas in which no local fluctuations of the ignition easier than in wide ones. Transition of detonation waves delays were resolved by the photographic technique was from narrow to wide ducts has been systematically studied termed strong ignition in contrast to mild ignition of the by a number of investigators, starting as early as in 1956 shock-compressed gas in clearly visible exothermic centers 1541. Visualization of detonation transmission from a (hot spots) giving rise to an accelerating flame fronts that run channel into an unconfined volume was probably first up to detonation in some cases. It has been unambiguously lade by mitrofanov and Soloukhin [84 in 1964. demonstrated that it is strong ignition mode that is relevant to Extensive experimental data on detonability of various detonation. However, the ignition process still remains fuels has been provided by research groups from all over the pendent on flow fluctuations even in this case. A world [64, 85-88. Based on well-documented experimental xperimental evidence shows [67 the ignition front behind data on detonation initiation, propagation and transition. the lead shock is quite irregular. This is supported by the well- several important empirical criteria have been extracted. The known nonuniform pattern of soot prints of multihead characteristic size in the fish-scales like structure of realistic detonations. An anal Ref [68] shows that the driving detonation waves, referred to as the detonation cell size, was mechanism of ignition delay fluctuations are gasdynamic found to be a representative parameter to qualitatively grade pulsations of the flow parameters due to collisions of weak detonability of the mixture: the larger the cell size the less coustic and quasi-acoustic waves traveling behind the shock sensitive is the mixture. The cell size was found to be a wave front and affecting it(because of the subsonic nature of function of the initial pressure, temperature, mixture the flow behind the shock wave). Interestingly, these composition and tube diameter. The cell size was proved fluctuations show up even in overdriven waves in which to be directly relevant to detonation transition from a channel the heat release is relatively very low(the temperature rise to an unconfined volume [64 to the limiting tube diameter due to the reaction not exceeding 400 K[691 1891, and to the critical energy of detonation initiation [90 Numerous theoretical works on ID and two-dimensional Detonations in heterogeneous media containing gaseous (2D) analysis of detonation wave instability predict the oxidizer and liquid fuel spray or film, or solid fuel virtually all waves with realistic reaction kinetics are unstable uspension is a topic of growing interest since the 1950s and develop a spinning or multihead structure [70-76] in view of industrial safety and military applications. In the series of elaborate photographic studies Detonations in such media were extensively studied bot Oppenheim et al. [62,77-79 revealed various scenarios experimentally [91] and theoretically [92]. It has been found of detonation onset during DDT in tubes with smooth walls. that detonability of heterogeneous mixtures depends Fast ejection of fame tongues and detonation kernel significantly on the fuel vapor concentration, in particular, formation near the accelerating flame brush, as a result of for heavy hydrocarbon fuels
Voitsekhovsky [58] and Denisov and Troshin [59] have discovered the multihead detonation and analyzed the flow patterns at the triple wave configurations with transverse shock waves and reaction fronts arising at the detonation front and changes in the flow patterns upon collisions of these configurations. Instability of realistic detonation waves and their 3D structure raised serious questions concerning the validity of the Arrhenius kinetics with an average temperature in 1D ZND modeling of detonation initiation and propagation. Direct photographs and soot imprints [60–62] showed unequivocally the fish-scales like cellular structure not only of CJ detonations but of the initial detonation kernel, which meant that the mixture was actually ignited behind the shock front in hot spots where temperature is significantly higher than the average temperature. Based on this understanding numerous models of singlehead (spinning) and multihead detonations have been suggested since 1950s (see review articles [63,64]). With the growing availability of diagnostics with improved temporal and spatial resolutions and powerful computing resources, the progress in the detonation science after the 1960s has been overwhelming. First of all, it became possible to visualize the ignition process behind a reflected shock wave and discover two different modes of shockinduced ignition of a reactive gas, namely, ‘strong’ and ‘mild’ ignition [65,66]. Violent volumetric ignition of shockcompressed gas in which no local fluctuations of the ignition delays were resolved by the photographic technique was termed strong ignition in contrast to mild ignition of the shock-compressed gas in clearly visible exothermic centers (hot spots) giving rise to an accelerating flame fronts that run up to detonation in some cases. It has been unambiguously demonstrated that it is strong ignition mode that is relevant to detonation. However, the ignition process still remains dependent on flow fluctuations even in this case. As experimental evidence shows [67] the ignition front behind the lead shock is quite irregular. This is supported by the wellknown nonuniform pattern of soot prints of multihead detonations. An analysis in Ref. [68] shows that the driving mechanism of ignition delay fluctuations are gasdynamic pulsations of the flow parameters due to collisions of weak acoustic and quasi-acoustic waves traveling behind the shock wave front and affecting it (because of the subsonic nature of the flow behind the shock wave). Interestingly, these fluctuations show up even in overdriven waves in which the heat release is relatively very low (the temperature rise due to the reaction not exceeding 400 K [69]. Numerous theoretical works on 1D and two-dimensional (2D) analysis of detonation wave instability predict that virtually all waves with realistic reaction kinetics are unstable and develop a spinning or multihead structure [70–76]. In the series of elaborate photographic studies, Oppenheim et al. [62,77–79] revealed various scenarios of detonation onset during DDT in tubes with smooth walls. Fast ejection of flame tongues and detonation kernel formation near the accelerating flame brush, as a result of collision of flame-driven shock waves, and as a result of shock wave reflection at contact discontinuities and tube walls were visualized. Flame acceleration, DDT, and detonation propagation in rough-walled tubes were first visualized by Babkin and Kozatchenko [80,81]. It has been shown that the structures of detonations in rough and smooth tubes can differ considerably. In a tube with rough walls, mixture ignition is facilitated by roughness elements due to high local temperatures behind reflected shock waves. One-dimensional model predicts that due to this fact, detonations in rough tubes should exhibit higher stability and wider concentration limits [55,56]. However, experimental observations [82,83] show somewhat narrower concentration limits of low-velocity regimes as compared to detonation in smooth tubes and quite large wave velocity fluctuations and recovery of a detonation wave upon its entry from a rough tube into a smooth tube occurs within still narrower limits. This is evidently attributable to an essentially multidimensional nature of the reactive waves in rough tubes. One of the questions of practical importance is, how a detonation wave originated in a narrow tube behaves when it enters a tube of a larger volume or unconfined mixture? The answer to this question should provide information about optimal ways of detonation initiation in large volumes, because a mixture in a narrow duct can be initiated much easier than in wide ones. Transition of detonation waves from narrow to wide ducts has been systematically studied by a number of investigators, starting as early as in 1956 [54]. Visualization of detonation transmission from a channel into an unconfined volume was probably first made by Mitrofanov and Soloukhin [84] in 1964. Extensive experimental data on detonability of various fuels has been provided by research groups from all over the world [64,85–88]. Based on well-documented experimental data on detonation initiation, propagation and transition, several important empirical criteria have been extracted. The characteristic size in the fish-scales like structure of realistic detonation waves, referred to as the detonation cell size, was found to be a representative parameter to qualitatively grade detonability of the mixture: the larger the cell size the less sensitive is the mixture. The cell size was found to be a function of the initial pressure, temperature, mixture composition and tube diameter. The cell size was proved to be directly relevant to detonation transition from a channel to an unconfined volume [64], to the limiting tube diameter [89], and to the critical energy of detonation initiation [90]. Detonations in heterogeneous media containing gaseous oxidizer and liquid fuel spray or film, or solid fuel suspension is a topic of growing interest since the 1950s in view of industrial safety and military applications. Detonations in such media were extensively studied both experimentally [91] and theoretically [92]. It has been found that detonability of heterogeneous mixtures depends significantly on the fuel vapor concentration, in particular, for heavy hydrocarbon fuels. G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672 551
G.D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 A considerable progress has been made in understanding advantage of detonation is capitalized properly, consid the mechanism of detonation initiation in the course of flame benefits are expected to be achieved in terms of development. Two principal concepts are worth mentioning: consumption, manufacturing and operational costs, pollutant Oppenheim's concept of predetonation point explosions emissions, etc. It is the authors'profound belief that the giving rise to detonation bubbles[62], and the Zel'dovich existing knowledge and the on-going research will lead to the gradient mechanism of detonation onset [93]. Somewhat of olutions of this challenging problem a mixed concept(shock wave amplification through coherent energy release(SWACER)) has been put forward by Lee and 2. 2. Gaseous detonations o-workers [94]. The Oppenheim's concept implies that, attaining the autoignition conditions, shock-compressed gas 2. 2. 1 General properties explodes in several exothermic centers resulting in gener In this section, steady reaction waves propagating at ation of spherical blast waves. Collision of the blast waves supersonic velocities are considered. This is necessary to he onset of detonation kernels that give rise to understand the kind of unsteady regimes that can be Zel'dovich's gradient mechanism implies that anticipated in combustible mixtures. Steady-state analysis of shock-compressed gas, of gasdynamic equations, which predicts only restricted with the minimum ignition delay, then moves towards the ranges of reaction wave velocities seems to be inconsistent locations with longer ignition delays (i.e. along the vector of with the experimental evidence of reactive waves propa- ignition delay gradient). As the apparent velocity of the 'self gation at any velocity between those of detonation and ignition wave'approaches the characteristic gasdynamic normal-flame. This contradiction is eliminated assuming velocity(e.g. local speed of sound), a shock wave is formed in that the observed waves that do not obey the steady the compressible reactive mixture followed by spontaneous equations are unsteady reactive waves (or quasi-detona- coupling of the shock with exothermic reaction and eventual tions). Interestingly, the reaction zone velocity relative to transition to detonation. SWACER concept implies that the fluid immediately ahead of it never exceeds(even in localized microexplosion in the shock-compressed mixture unsteady waves)the maximum found from the slope of the gives rise to a blast wave (like in the Oppenheim's concept) Rayleigh line(actually Rayleigh-Michelson line [35, 36],to that is further amplified according to the gradient mechanism give a tribute of respect to Michelson, who pioneered in the All these concepts differ only at first glance. Indeed detonation theory [30,31 tangent to the lower branch of the detonation onset in the detonation kernels should essentially Hugoniot curve plotted for the initial state corresponding to be based on Zel'dovich's mechanism of coupling between the gas compressed in the precursor shock wave the compression wave and exothermic reaction, otherwise For applications, the dependence of detonation para- fame would never accelerate to velocities sufficient to drive a meters on the initial conditions and their sensitiveness to the nock wave capable of self-igniting the mixture with delays mixture equivalence ratio are of importance. Normally, this inherent in detonation waves. On the other hand, as dependence is bell-shaped descending both towards lean experiment shows, incipience of detonation waves never and rich mixtures, except for hydrogen mixtures where the occurs throughout the whole mixture volume, thus support- detonation velocity keeps rising far into the region of rich ing the idea of hot spot self-ignition. Thus, all the concepts are mixtures. based on considering'microexplosion(s)in the exothermic In homogeneous hydrocarbon-air mixtures, the detona- center(s) formed in the shock-compressed gas. Zel'dovich's tion velocities peak in slightly rich mixtures. The maximum concept is less formal than the others because it includes the detonation velocity is attained in air mixtures with the evolution of reaction inside the exothermic center, provides a equivalence ratio ps 1. 2 for saturated hydrocarbons, and complete physical explanation of the hot spot development p= 1.3 for unsaturated hydrocarbons and clear criteria for detonation origination, thus avoiding Fig. I shows the predicted dependencies of the detonation speculations on the strength of the blast wave produced by velocity Dc(a), temperature of detonation products Tc(b), dimensionless pr of detonation products pc/po (c). Historically, the two fundamental modes of combustion, and molecular mass of detonation products uc(d)on molar amely flame and detonation, have found a wide variety of fraction of fuel in gaseous iso-octane-air(solid curve)and applications in human activities. It is a slow flame that has n-heptane-air(dashed curve)mixtures, calculated by using been extensively utilized in propulsion, power engineering, thermodynamic code SAFETY [95]. Here, indices 0 and CJ material science, and chemical technology, while detonations label quantities ahead of the detonation front and at the used basically for military purposes. As the knowledg CJ plane, respectively. The dependencies of detonation in detonation physics and chemistry is continuously advan- elocity, temperature and pressure exhibit a characteristic cing, one inevitably arrives at the time when this knowledge is bell shape, attaining detonability limits on both sides from to be used for constructive purposes as well to help humanity the stoichiometric composition. n-Heptane and iso-octane at large. Detonation is a very attractive phenomenon from the mixtures show very similar properties. viewpoint of the thermodynamic efficiency of chemical Fig. 2 shows the calculated dependencies of the detona- energy conversion into thermal and kinetic energy. Once this tion velocity Dc(a), temperature Ta (b), dimensionless
A considerable progress has been made in understanding the mechanism of detonation initiation in the course of flame development. Two principal concepts are worth mentioning: Oppenheim’s concept of predetonation point explosions giving rise to detonation ‘bubbles’ [62], and the Zel’dovich ‘gradient’ mechanism of detonation onset [93]. Somewhat of a mixed concept (shock wave amplification through coherent energy release (SWACER)) has been put forward by Lee and co-workers [94]. The Oppenheim’s concept implies that, at attaining the autoignition conditions, shock-compressed gas explodes in several exothermic centers resulting in generation of spherical blast waves. Collision of the blast waves results in the onset of detonation kernels that give rise to detonation. Zel’dovich’s gradient mechanism implies that self-ignition of shock-compressed gas, starting at location with the minimum ignition delay, then moves towards the locations with longer ignition delays (i.e. along the vector of ignition delay gradient). As the apparent velocity of the ‘selfignition wave’ approaches the characteristic gasdynamic velocity (e.g. local speed of sound), a shock wave is formed in the compressible reactive mixture followed by spontaneous coupling of the shock with exothermic reaction and eventual transition to detonation. SWACER concept implies that localized microexplosion in the shock-compressed mixture gives rise to a blast wave (like in the Oppenheim’s concept) that is further amplified according to the gradient mechanism. All these concepts differ only at first glance. Indeed, the detonation onset in the detonation kernels should essentially be based on Zel’dovich’s mechanism of coupling between the compression wave and exothermic reaction, otherwise flame would never accelerate to velocities sufficient to drive a shock wave capable of self-igniting the mixture with delays inherent in detonation waves. On the other hand, as experiment shows, incipience of detonation waves never occurs throughout the whole mixture volume, thus supporting the idea of hot spot self-ignition. Thus, all the concepts are based on considering ‘microexplosion(s)’ in the exothermic center(s) formed in the shock-compressed gas. Zel’dovich’s concept is less formal than the others because it includes the evolution of reaction inside the exothermic center, provides a complete physical explanation of the hot spot development and clear criteria for detonation origination, thus avoiding speculations on the strength of the blast wave produced by ‘microexplosion’. Historically, the two fundamental modes of combustion, namely flame and detonation, have found a wide variety of applications in human activities. It is a slow flame that has been extensively utilized in propulsion, power engineering, material science, and chemical technology, while detonations were used basically for military purposes. As the knowledge in detonation physics and chemistry is continuously advancing, one inevitably arrives at the time when this knowledge is to be used for constructive purposes as well to help humanity at large. Detonation is a very attractive phenomenon from the viewpoint of the thermodynamic efficiency of chemical energy conversion into thermal and kinetic energy. Once this advantage of detonation is capitalized properly, considerable benefits are expected to be achieved in terms of fuel consumption, manufacturing and operational costs, pollutant emissions, etc. It is the authors’ profound belief that the existing knowledge and the on-going research will lead to the solutions of this challenging problem. 2.2. Gaseous detonations 2.2.1. General properties In this section, steady reaction waves propagating at supersonic velocities are considered. This is necessary to understand the kind of unsteady regimes that can be anticipated in combustible mixtures. Steady-state analysis of gasdynamic equations, which predicts only restricted ranges of reaction wave velocities seems to be inconsistent with the experimental evidence of reactive waves propagation at any velocity between those of detonation and normal-flame. This contradiction is eliminated assuming that the observed waves that do not obey the steady equations are unsteady reactive waves (or quasi-detonations). Interestingly, the reaction zone velocity relative to the fluid immediately ahead of it never exceeds (even in unsteady waves) the maximum found from the slope of the Rayleigh line (actually Rayleigh–Michelson line [35,36], to give a tribute of respect to Michelson, who pioneered in the detonation theory [30,31]) tangent to the lower branch of the Hugoniot curve plotted for the initial state corresponding to the gas compressed in the precursor shock wave. For applications, the dependence of detonation parameters on the initial conditions and their sensitiveness to the mixture equivalence ratio are of importance. Normally, this dependence is bell-shaped descending both towards lean and rich mixtures, except for hydrogen mixtures where the detonation velocity keeps rising far into the region of rich mixtures. In homogeneous hydrocarbon–air mixtures, the detonation velocities peak in slightly rich mixtures. The maximum detonation velocity is attained in air mixtures with the equivalence ratio F < 1:2 for saturated hydrocarbons, and F < 1:3 for unsaturated hydrocarbons. Fig. 1 shows the predicted dependencies of the detonation velocity DCJ ðaÞ; temperature of detonation products TCJ ðbÞ; dimensionless pressure of detonation products pCJ=p0 ðcÞ; and molecular mass of detonation products mCJ ðdÞ on molar fraction of fuel in gaseous iso-octane–air (solid curve) and n-heptane-air (dashed curve) mixtures, calculated by using thermodynamic code SAFETY [95]. Here, indices 0 and CJ label quantities ahead of the detonation front and at the CJ plane, respectively. The dependencies of detonation velocity, temperature and pressure exhibit a characteristic bell shape, attaining detonability limits on both sides from the stoichiometric composition. n-Heptane and iso-octane mixtures show very similar properties. Fig. 2 shows the calculated dependencies of the detonation velocity DCJ ðaÞ; temperature TCJ ðbÞ; dimensionless 552 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 中f ig. 1. Predicted dependencies of (a) detonation velocity Dc, (b) temperature TcJ, (c) dimensionless pressure Pc/po, and(d) molecular I Ac of detonation products on fuel molar fraction in gaseous iso-octane-air(solid curves)and n-heptane-air(dashed curves) mixtures [95]- Vertical lines correspond to stoichiometric fuel molar fraction vf.st 2900 To/K T。/K Fig. 2. Calculated dependencies of (a)detonation velocity Dc. (b)temperature Tc, (c)dimensi sure pcpo detonation products Ac on the initial temperature and pressure for stoichiometric iso-octa ture95}:1-po=0.5atm,2-10 -20.4-5.0.and5-10.0atm
Fig. 1. Predicted dependencies of (a) detonation velocity DCJ; (b) temperature TCJ; (c) dimensionless pressure pCJ=p0; and (d) molecular mass mCJ of detonation products on fuel molar fraction in gaseous iso-octane–air (solid curves) and n-heptane–air (dashed curves) mixtures [95]. Vertical lines correspond to stoichiometric fuel molar fraction cf;st: Fig. 2. Calculated dependencies of (a) detonation velocity DCJ; (b) temperature TCJ; (c) dimensionless pressure pCJ=p0; and (d) molecular mass of detonation products mCJ on the initial temperature and pressure for stoichiometric iso-octane–air mixture [95]; 1—p0 ¼ 0:5 atm, 2—1.0, 3—2.0, 4—5.0, and 5—10.0 atm. G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672 553
G.D. Roy et al. Progress in Energy and Combustion Science 30(2004)545-672 mpensates for the initial energy increase, so that the detonation velocity is virtually independent of the initial temperature. In line with this logic, the temperature of detonation products increases only slightly with the initial temperature(Fig 2b). An important parameter such as the detonation pressure(Fig. 2c)decreases with temperature because the pressure ratio is proportional to the initial fluid density. Due to dissociation, the molecular mass of detona- tion products decreases, however, insignificantly. At the low end, the initial pressure should not affect the detonation velocity, but at higher pressures the equilibrium in the reaction products is shifted towards polyatomic molecules, which lie at lower energy levels. Hence, reduced dissociation of the products increases slightly the detonation Fig 3. Detonation properties of homogeneous JP-10-air mixture velocity(Fig. 2a), temperature(Fig. 2b), and molecular btained by using thermodynamic code tEP [96,97: 1-dcj mass(Fig. 2d). Dimensionless detonation pressure is almost insensitive to the initial pressure(Fig. 2c). It should be noted that at very low initial pressures the detonation parameters pressure Pay/po(c), and molecular mass ua(d)on the initial e affected by losses to the walls of even quite wide tubes temperature To and pressure Po of a stoichiometric homo- (this effect is not taken into account in thermodynamic geneous iso-octane-air mixture [95]. The effect of the initial calculations of Fig. 2). All the features of Fig. 2 are temperature on the detonation velocity is insignificant confirmed by the measurements and are typical for (Fig. 2a). According to elementary considerations, the initial detonations of high hydrocarbons internal energy is just added to the reaction heat and an As JP-10 is considered as one of prospective fuels for ease in the initial temperature should slightly increase the PDE applications, Fig. 3 shows the calculated detonation detonation velocity. However, the actual influence of the properties of homogeneous JP-10-air mixture [96] that initial temperature on the detonation velocity is more are very similar to those presented in Fig. 1. The complex since due to dissociation the reaction heat drops as properties presented in Fig. 3 were obtained by usin the final temperature in the products rises. This partl thermochemical equilibrium code TEP [971 which does c2750 A Fig. 4. Predicted dependencies of (a)detonation velocity Dc.(b)temperature Tc, (c)dimensionless pressure Pcr/po, and(d)molecular mass uc of detonation products on the molar fraction of HP vapor a admixed to the stoichiometric homogeneous iso-octane-air(solid curves)and
pressure pCJ=p0 ðcÞ; and molecular mass mCJ ðdÞ on the initial temperature T0 and pressure p0 of a stoichiometric homogeneous iso-octane–air mixture [95]. The effect of the initial temperature on the detonation velocity is insignificant (Fig. 2a). According to elementary considerations, the initial internal energy is just added to the reaction heat and an increase in the initial temperature should slightly increase the detonation velocity. However, the actual influence of the initial temperature on the detonation velocity is more complex since due to dissociation the reaction heat drops as the final temperature in the products rises. This partly compensates for the initial energy increase, so that the detonation velocity is virtually independent of the initial temperature. In line with this logic, the temperature of detonation products increases only slightly with the initial temperature (Fig. 2b). An important parameter such as the detonation pressure (Fig. 2c) decreases with temperature because the pressure ratio is proportional to the initial fluid density. Due to dissociation, the molecular mass of detonation products decreases, however, insignificantly. At the low end, the initial pressure should not affect the detonation velocity, but at higher pressures the equilibrium in the reaction products is shifted towards polyatomic molecules, which lie at lower energy levels. Hence, reduced dissociation of the products increases slightly the detonation velocity (Fig. 2a), temperature (Fig. 2b), and molecular mass (Fig. 2d). Dimensionless detonation pressure is almost insensitive to the initial pressure (Fig. 2c). It should be noted that at very low initial pressures the detonation parameters are affected by losses to the walls of even quite wide tubes (this effect is not taken into account in thermodynamic calculations of Fig. 2). All the features of Fig. 2 are confirmed by the measurements and are typical for detonations of high hydrocarbons. As JP-10 is considered as one of prospective fuels for PDE applications, Fig. 3 shows the calculated detonation properties of homogeneous JP-10–air mixture [96] that are very similar to those presented in Fig. 1. The properties presented in Fig. 3 were obtained by using thermochemical equilibrium code TEP [97] which does Fig. 4. Predicted dependencies of (a) detonation velocity DCJ; (b) temperature TCJ; (c) dimensionless pressure pCJ=p0; and (d) molecular mass mCJ of detonation products on the molar fraction of HP vapor cA admixed to the stoichiometric homogeneous iso-octane–air (solid curves) and n-heptane–air (dashed curves) mixtures [95]. Fig. 3. Detonation properties of homogeneous JP-10-air mixture obtained by using thermodynamic code TEP [96,97]; 1—DCJ; 2—pCJ=p0; 3—TCJ=T0: 554 G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672