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), dimensionlessA 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 gener￾ation 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 ‘self￾ignition 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 support￾ing 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 advan￾cing, 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 propa￾gation 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-detona￾tions). 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 para￾meters 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 detona￾tion 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 detona￾tion velocity DCJ ðaÞ; temperature TCJ ðbÞ; dimensionless 552 G.D. Roy et al. / Progress in Energy and Combustion Science 30 (2004) 545–672