Abstract (English):
The main objective of this book is to acquaint the reader with the main modern problems of the multisensor data analysis and opportunities of the hyperspectral shooting being carried out in the wide range of wavelengths from ultraviolet to the infrared range, visualization of the fast combustion processes of flame propagation and flame acceleration, the limit phenomena at flame ignition and propagation. The book can be useful to students of the high courses and scientists dealing with problems of optical spectroscopy, vizualisation, digital recognizing images and gaseous combustion. The main goal of this book is to bring to the attention of the reader the main modern problems of multisensory data analysis and the possibilities of hyperspectral imaging, carried out in a broad wave-length range from ultraviolet to infrared by methods of visualizing fast combustion processes, propagation and flames acceleration, and limiting phenomena during ignition and flame propagation. The book can be useful for students of higher courses and experimental scientists dealing with problems of optical spectroscopy, visualization, pattern recognition and gas combustion.

Keywords:
Remote measurements, optoelectronic methods, multisensor data analysis, hyper spectral shooting, ramjet engine, Catalytic Stabilization

The method of high-speed filming was used to study the instabilities arising from the propagation of hydrogen and hydrocarbon flames. The regimes of flame propagation during combustion of weak hydrogen-air mixtures with additives under conditions of central initiation by the method of high-speed filming are considered. The onset of acoustic instability in hydrogen-air mixtures in a closed reactor with central initiation by a spark discharge is analyzed. The regularities of the interaction of spherical flames of hydrogen-air and methane-air mixtures with fine-mesh obstacles at central initiation by a spark discharge have been established. The features of thermal ignition in gas eddies are studied. Key words: instability, hydrogen, hydrocarbon, spherical flames, cellular obstacle, thermal ignition, gas eddy. Every day, at home or in the workplace, we meet with devices that are used or in which combustion occurs. In this case, the combustion process can be useful, for example, a primitive fire, cooking ovens, various technological processes, including an internal combustion engine. This process can be extremely harmful, in particular forest fires, mine fires, etc. Such a wide application and significance of combustion in our life requires knowledge of the laws of this phenomenon. If ignition has occurred, the flame spreads through the combustible mixture. Under certain conditions, the flame can accelerate and detonation occurs - a complex consisting of a shock wave fed by the energy released during combustion and a combustion zone that propagates at a supersonic speed. Obviously, such processes leading to the destruction of industrial and residential premises and the death of people should be excluded. Combustion must be strictly controlled; reliable methods of preventing combustion should be available. Combustion suppression methods can be divided into chemical (using active additives that break the reaction chains) and physical (flame arresters). Methods for extinguishing with foam and aerosol formulations are intermediate, since the substances introduced into the flame zone are usually reactive. Active additives that suppress combustion (inhibitors) have many disadvantages, despite their apparent ease of use, for example, the possibility of mixing with a combustible gas in advance. Hydrogen combustion inhibitors, such as unsaturated hydrocarbons, are flammable in themselves and are effective only in stoichiometric and rich mixtures. These inhibitors accelerate, on the contrary, combustion in poor mixtures. Metal carbonyls are poisonous and cannot be used in the presence of human personnel. Practically safe freons in case of an abnormal fire lead to the formation of toxic fluorophosgene. Physical methods such as barriers and grids can also serve as combustion turbulators along with a suppressive effect. Under certain conditions, they can lead to an acceleration of the combustion front with undesirable consequences. On the other hand, many combustion devices require complete combustion (diesel engines) or accelerated combustion (detonation engine). This is ensured by the use of nozzles, turbulators and other obstacles to accelerate the flame, which, on the contrary, is desirable in this situation. The presentation of the foundations of the theory of combustion was not included in the tasks of the authors of this book. However, the authors draw the reader's attention to the fact that the modern theory of combustion is given in a number of references to the fundamental works and monographs for each subsequent Chapter, and the reader can get acquainted with the fundamentals of this field of science thanks to them. As far as is known, the processes of gaseous combustion proceed under conditions of unsteady flows, fluctuations in density and pressure in real conditions, i.e. are nonstationary in nature. Sound vibrations are a manifestation of these instabilities. It is known that there is a significant acceleration of various heat-and-mass transfer processes (mixture formation, evaporation, heat transfer from gas to walls, heat transfer when the flow interacts with heated bodies, etc.) in unsteady flows. Particle agglomeration and coagulation of aerosols are improved. In addition, during vibration combustion, the level of emission of toxic substances NOx decreases. Acoustic vibrations during combustion are caused by instabilities arising from the propagation of the flame front. These instabilities manifest themselves in combustion processes in various forms and can be classified as thermal diffusion, hydrodynamic, and thermoacoustic. Thermal-diffusive instability is observed in flames in which the rates of heat transfer and diffusion are different, i.e. Le ≠ 1 (Lewis number Le = D / a, where D is the diffusion coefficient of the component that determines the combustion process, and is the thermal diffusivity). This instability leads, for example, to the cellular nature of the propagation of flames in hydrogen-poor combustible mixtures. Hydrodynamic instability is determined by the difference in the densities of the burnt and unburned gas associated with the thermal expansion of the reaction products and also, under certain conditions, can lead to the appearance of cellular flames. Thermoacoustic instability is determined by the resonant relationship between the unsteady combustion mode and the acoustic modes of the reactor. Non-stationary heat release leads to the generation of acoustic vibrations, which, reflecting from the walls of the reactor, interact with the combustion process. Since combustion is sensitive to changes in gas flow conditions, if the phase between acoustic oscillations and unsteady combustion satisfies certain conditions, feedback and, accordingly, combustion instability can occur. The criterion for the occurrence of this instability was proposed by Rayleigh and consists in the fact that acoustic oscillations are maintained if maximum heat is imparted to the oscillating gas at the moment of its maximum compression. It is known that a flat flame is unstable from a hydrodynamic point of view. For a spherical FF, its stability was explained by the fact that the radius and, accordingly, the surface of the flame front grow so rapidly that instability does not have time to develop against this background. Therefore, at the initial stage of combustion, when the flame front has a spherical shape, hydrodynamic instability should not manifest itself. However, after the flame front touches the walls of the reactor, it propagates in the cylindrical channel. At this stage of combustion, the conditions for the rapid growth of the FF surface disappear and the hydrodynamic instability of the flame should manifest itself. Recently, much attention has been paid to the use of hydrogen-containing fuels in the automotive industry and power plants, including the combustion of the most ecological weak hydrogen-air mixtures, accelerated by the addition of hydrocarbons. The expected results on FF visualization are important both for the experimental verification of theoretical concepts of the propagation of gas flames and for solving the issues of explosion safety. Let us note in conclusion that in the modern scientific literature there is no systematic information about the conditions leading to the unstable propagation of the FF of mixtures of hydrogen and hydrocarbons with air in a cylindrical reactor with a central spark ignition. § 1. Studying by the method of high-speed filming of flame propagation modes during combustion of weak hydrogen-air mixtures with additives under conditions of central initiation As indicated above, in the absence of special conditions, gas-phase combustion processes proceed under conditions of unsteady flows, fluctuations in density and pressure, i.e. are nonstationary [1-3]. For example, weak hydrogen-air mixtures are characterized by a inhomogenuity of combustion front caused by thermal-diffusive instability, which leads to the appearance of flame cells [3-5]. For the first time, flame cells during the combustion of lean (up to 10% H2) hydrogen-air mixtures were observed in [6]. It was shown in [1, 7] that flame cells in lean mixtures of hydrogen with air are also observed under microgravity conditions. In other words, the gravity field is not a prerequisite for the formation of flame cells. When studying the propagation of flames in weak mixtures of hydrogen with air in narrow vertical pipes, it was found that the propagation of the flame “upward” is accompanied by the unburning of the fuel. In addition, in this case, the concentration of the fuel at the limit of propagation is less than in the “downward” direction [4, 8]. In two-dimensional simulations of the combustion of hydrogen-poor mixtures, convection and gravity were neglected [9]. However, the calculated burning rates turned out to be close to the experimental ones. The analytical theory of a cellular flame, based on the representation of a flame as a dense flat structure of hexagonally packed flame balls [2], also gives good agreement with experiment on the values of combustion rates with a good selection of parameters. Finding out the limits of applicability of hydrogen flame models that do not take into account convection and compressibility of the medium for describing the experimentally observed flame velocities [2,4,5,7,9,10] in comparison with models that take into account convection [2, 11] and medium compressibility is of interest. For this purpose, in this section, a study of the structure of flames of lean mixtures of hydrogen with air in a bomb of constant volume at atmospheric pressure is carried out by the method of high-speed filming. The results obtained are compared with numerical calculations and experimental data known from the literature. Experimental part The experiments were carried out with lean mixtures of hydrogen (6.25-15%) with air at initial atmospheric pressure and temperature To = 298 K. A horizontally located cylindrical stainless steel reactor 15 cm long and 13 cm in diameter was used as a setup. At one of the ends, the reactor was equipped with an optical quartz window. In the center of the reactor, spark ignition electrodes were placed, the distance between which was 0.5 mm. The experiments were carried out in the following sequence. If necessary, carbon tetrachloride CCl4, and then hydrogen and air to atmospheric pressure, were fed into the reactor pumped out to 10-2 Torr. It should be noted that an inert addition of Сl4 up to 4% is used to visualize a hydrogen flame [12]. The mixture was kept for 15 min for complete mixing, and ignition was initiated with a spark (the discharge power was 1.5 J). The dynamics of the ignition and propagation of the FF was recorded through the optical window using a Casio Exilim F1 Pro color high-speed film camera (frame rate - 60 - 1200 s-1). The resulting video file was written into the computer memory and then created frame-by-frame. The change in pressure during combustion was recorded using a piezoelectric sensor, the signal from which was fed to an S9-8 digital storage oscilloscope. The pressure in the reactor during the composition of the gas mixture was monitored with an exemplary vacuum gauge. Before each experiment, the reactor was evacuated using a 2NVR-5D foreline pump. Gas H2, carbon tetrachloride CCl4 were used of chemically pure grade. The degree of expansion of combustion products T was determined on the value of the maximum pressure developed during the combustion of the Рb mixture [7]: Рb/Po = 1 + T -1) (1.1) The value of the normal speed of flame propagation in the initial section Un was determined from the relation [13]: Un = Vv/T (1.2) In expressions (1), (2) Pb is the maximum pressure, P0 is the initial pressure, γ is the adiabatic index of the initial mixture, Vv is the apparent flame velocity in the initial section. Results and discussion of the experiment. As far as seen from Fig. 1, the flame front at the initial stage of development has a spherical shape. Cells are well visualized at the flame front, and the diameter of the sphere can be measured experimentally. For mixtures with H2 concentration <10%, the flame front has a spherical shape only at the initial stage after initiation (Fig. 1a). Fig. 1. The result of high-speed filming a) the process of propagation of a cellular flame front 4% CCl4 + 8% H2 + 88% air, To = 298K, initiation energy is 1.5 J. Frame rate 60 s-1 [9]; b) the process of propagation of a flame front illuminated with 4% CCl4 in a mixture of 10% H2 + 86% air at atmospheric pressure. Film speed 60 frames/s; c) the process of propagation of a flame front illuminated with 4% CCl4 in a mixture of 15% H2 + 81% air at an initial atmospheric pressure. Film speed is 600 frames/s. The number on the frame corresponds to the frame number when shooting. The first frame corresponds to the occurrence of a spark discharge; d) a frame from high-speed filming of the propagation of the flame front illuminated with 2% CCl4 in a mixture of 12.5% H2 + 87.5% air at atmospheric pressure [8]. Film speed is 60 frames/s; e) a frame from high-speed filming of the flame front propagation under microgravity conditions, 7.0% H2 in air, addition of 0.4% CF3Br. 1.18 s after initiation has passed [7]. Further, in the combustion process, the effect of gravity is manifested. The flame front takes the form of a hemispherical segment moving upward (Fig. 1 a, b). For mixtures containing H2> 10%, the flame front velocity increases so much that the effect of gravity does not have time to manifest itself, and the flame propagates spherically symmetrically (Fig. 1c, d). The flame front remains cellular, while the size of the flame cells decreases with an increase in hydrogen content up to 15%. It can be seen from fig. 1a, that for 8% H2 in air at the initial stage, the combustion front is spherical (Fig. 1a, frames 2-6). Figure 1b shows the results of high-speed shooting for flame propagation in a mixture of 10% H2 in air, illustrating the sphericity of the flame front. The apparent flame velocity Vv measured by us for a mixture of 4% CCl4 + 10.0% H2 + 86.0% air (Fig.1a) is 36 cm/s, while the normal velocity Un calculated by formula (1.2) is 21 cm/s taking into account the experimental value of εT for this mixture is 1.6. The apparent flame velocity Vv for a mixture of 4% CCl4 + 15.0% H2 + 81.0% air (Fig. 1 c) is 2.4 m/s, while the normal velocity Un calculated by formula (1.2) is 60 cm/s, taking into account that for this mixture the experimental value of εT is 4. As far as seen from Fig. 1c combustion is cellular in nature at this hydrogen concentration. These values of the normal velocity agree with the value of Un known from the literature data. They are also close to the results of the numerical calculation of Un obtained using the laminar flame model without taking into account convection [9], i.e. without taking into account the cellular structure of the flame. This means that the perturbations of a thermodiffusion nature observed in the flame front at the initial stage of combustion do not have a significant effect on the propagation rate of the lean mixture flame. It is possible to indicate the concentration boundaries of various modes of propagation of a cellular flame in lean hydrogen-air mixtures from fig. 1 and the data [4,8]: a) “gravitational” with the content of H2 <10%, which corresponds to different velocities of propagation of the flame front “up” and “down” in narrow tubes [4, 8] and a spherically symmetric regime at the initial section of combustion; b) spherically symmetric with an H2 content in the range of 10% ÷ 15%, while there is no difference between the “up” and “down” propagation velocities. The publication also describes a spherically symmetric mode of propagation of a cellular flame under microgravity conditions at a hydrogen concentration of less than 10% [1,7]. It should be noted also that under zero gravity there is also a little-studied mode of the appearance of separate isolated stationary combustion cells during the combustion of lean mixtures [1]. We point out that the experimental values of the lower concentration limit of flame propagation in microgravity (Сmicro) have a noticeable scatter, which does not allow us to judge with certainty whether its value is close to the "upward" or "downward" propagation limit. According to [7], this concentration limit is close to the value of the limit when the flame propagates upward in the gravity field and is 5.5% H2 in air. However, according to [1], (Сmicro) is 7% H2 and according to [7] (Сmicro) is 7% H2 in presence of 2.5% CF3Br. From the above, we can conclude that the spherical shape is inherent in the propagation of cellular flames of lean mixtures at the initial stage. The gravity field only then distorts the shape of the combustion front for mixtures near the lower concentration limit of flame propagation (Fig. 1.1 a, b). However, we point out that a careful approach is required to the concept of sphericity or the degree of sphericity of flames in reaction volumes of different shapes and sizes. In this work, a two-dimensional projection of the FF onto the end plane of a cylindrical reactor is used for conclusion on the sphericity. Let us consider some of the results obtained in the numerical simulation of cellular flames. A two-dimensional plane problem was considered in [10, 14] and the model of thermal convection was used in the Boussinesq approximation for analyzing the combustion front in lean hydrogen-air mixtures. The reduced kinetic scheme of the hydrogen oxidation reaction, which included 13 reactions, as well as the thermochemical parameters, were taken from [8]. However, in the absence of gravity, but taking into account convection associated with gas expansion during combustion, the cellular regime was absent in the calculation. Thus, the calculation in the Boussinesq approximation does not allow simulating the experimentally observed propagation of a cellular flame under microgravity conditions. In order to establish which physical processes should be taken into account when describing the propagation of a cellular flame under microgravity conditions, a numerical analysis by the finite element method was carried out using the FlexPde 6.0 software package [15]. At the same time, since it was shown in [11, 14] that, within the Boussinesq approximation, the laws of propagation of lean hydrogen flames do not depend on the nature of the most rapidly diffusing intermediate product, but are determined by the diffusion coefficient of the initial component that is in short supply [4, 8], the chemical reaction was set by one equation in the Arrhenius form. The authors note that such a simplified approximation can introduce uncertainties associated with the replacement of the combustion mechanism by one activated reaction. The results of calculating the propagation of the combustion zone in the Boussinesq approximation is shown in fig. 2. These results are demonstrated at a) g = 0 (g is the acceleration of gravity), b) g = 980 cm/s2, c) - calculation of the propagation of the combustion zone at g = 0 based on the analysis of the Navier–Stokes equations for a compressible medium [16] (see Annex). It can be seen from Fig. 2 that taking into account the convection associated with gas expansion during combustion does not lead to the appearance of a cellular combustion mode in the absence of gravity in a weakly compressible medium (Fig. 2a). In this case, one of the possibilities to describe the cellular regime in the absence of gravity is to take into account the compressibility of the medium in the Navier–Stokes equations (Fig. 2c). We point out that when analyzing the system of equations in the Boussinesq approximation, which takes into account the reduced kinetic mechanism of hydrogen oxidation from 12 elementary reactions [10, 14] in the absence of gravity, the cellular combustion mode is also absent, as in Fig. 2a. This means that the simplified approximation used (replacing the reaction mechanism with one activated reaction) does not noticeably affect the results of the qualitative calculation. Fig 2. Calculation by the finite element method [16] (see Annex) of the propagation of the combustion zone in the Boussinesq approximation a) g = 0, b) g = 980 cm/s2, c) calculation of the propagation of the combustion zone at g = 0, solving the Navier–Stokes equations for a compressible medium,  = 16. Thus, the Boussinesq approximation is applicable to simulate cells in the gravitational (H2 <10%) mode of flame propagation in lean hydrogen-air mixtures [11]. The Navier–Stokes equations for a compressible medium should be used to describe a spherically symmetric regime under microgravity conditions. Clarifying the limits of applicability of hydrogen flame models that do not take into account convection and compressibility of the medium for calculating the experimentally observed flame velocities [2,4,5,7,9,10,13] in comparison with models that take into account convection [2, 11] and compressibility of the medium is of interest. Let us compare the data available in the literature on measuring and calculating the combustion rates of lean hydrogen-air mixtures, taking into account our results. A large set of publication data is presented in [2]. We also use the data from [13], which presents the results of several groups of authors. A comparison of the measured and calculated normal flame velocities for lean hydrogen-air mixtures at 1 atm and an initial temperature of 298 K, depending on the fuel content in the mixture ( is the excess ratio of fuel in a mixture with air: Н2 + 0.5 (О2 + 3.76N2 )) is shown in fig. 3. Fig. 3. Comparison of measured and calculated normal flame velocities for lean hydrogen-air mixtures at 1 atm and an initial temperature of 298 K depending on the fuel content in the mixture ( is the excess ratio of fuel in a mixture with air: H2 + 0.5 (O2 + 3.76N2)). The bold curve is the calculation of the one-dimensional problem [2], the thin curve is the calculation by the analytical relation [2], the points are the data of experimental studies cited in [2] (see Fig. 1 from [2]). The crosses are the experimental data [10, 11], thin circles - data of two-dimensional calculation without taking into account convection [9], bold circles - data of two-dimensional calculation taking into account convection and gravity [10], triangles - experimental data in the absence of gravity [7]. The area in which the experimental values of the propagation velocities of hydrogen-air flames are located according to [13], which contains the data of several groups of authors, are highlighted in gray. The bold curve represents the simulation results within the framework of the one-dimensional problem [2], the thin curve is the calculation using the analytical relationship obtained in [2]. The dots in the figure represent the experimental data cited in [2] (see Fig. 1 from [2]), crosses — experimental data [10], thin circles — two-dimensional calculation data without convection (Fig. 2 from [9] ]), bold circles - data of two-dimensional calculation taking into account the velocity field (Fig 3 and Fig. 4 from [10]), triangles - experimental data in the absence of gravity [7]. The area in which the experimental values of the propagation velocities of the flame of hydrogen-air flames from [13] are found is highlighted in gray. As far as seen from fig. 3 the results obtained in [9] using a two-dimensional model without taking into account convection (crosses) are in the range of experimental values of the propagation velocities of the flame of hydrogen-air flames from [13]. It follows from fig. 3 that the error in experimental data on flame propagation in lean mixtures does not make it possible to consider in detail the kinetic mechanism of hydrogen combustion. It is necessary to describe the combustion of lean hydrogen-air mixtures and even distinguish between the results of a two-dimensional model with and without convection. In other words, a good selection of parameters allows one to obtain agreement with a specific experience. It should be noted that even the calculations according to the one-dimensional model (the bold curve in Fig. 3), which agree very much with the experiment, are also in the region of the experimental values of the propagation velocities of the flame of hydrogen-air flames. It should be noted that the above discussion applies only to hydrogen-air mixtures in the absence of other combustible additives, for example, hydrocarbons. It is known that the addition of hydrogen to hydrocarbon fuels is promising for increasing the level of environmental safety of combustion products [1]. Combustion of lean hydrogen mixtures in this aspect is the most environmentally friendly, but the burning rates of such mixtures are low. The combustion rate can be increased by adding a small amount of hydrocarbon to the lean mixture (see, for example, [18]). The foregoing determines the relevance of the below experimental study of the rates and dynamics of combustion of lean hydrogen mixtures in the presence of a small addition of hydrocarbon, which is isobutene is chosen in this work. The results of high-speed filming of combustion of lean mixtures of hydrogen with the addition of C4H8, the content of which in all cases does not exceed the lower concentration limit of ignition, which is 1.8% [12] are shown in fig. 4 (a-f). Fig. 4. The result of high-speed filming a) the process of propagation of a flame front illuminated with 4% CCl4 in a mixture of 10% H2 + 86% air at atmospheric pressure. Filming speed is 60 frames/s; b) - the result of high-speed filming of the propagation of the flame front in a mixture of 1.5% C4H8 + 10% H2 + 88.5% air at atmospheric pressure. The speed of filming is 300 frames/s. c) - the result of high-speed filming of the propagation of the flame front in a mixture of 1.5% C4H8 + 7.5% H2 + 91% air at the initial atmospheric pressure. Filming speed is 60 frames/s; d) - the result of high-speed filming of the propagation of the flame front, in a mixture of 0.5% C4H8 + 7.5% H2 + 92% air at the initial atmospheric pressure. e) - the result of high-speed filming of the propagation of the flame front, in a mixture of 1% С4Н8 + 5.8% Н2 + 93.2% air at atmospheric pressure. The number on the frame corresponds to the frame number when shooting. Filming speed is 60 frames/s. f) - the result of high-speed filming of the propagation of the flame front, in a mixture of 1% С4Н8 + 6.5% Н2 + 92.5% air at atmospheric pressure. Filming speed is 60 frames/s. The number on the frame corresponds to the frame number when shooting. The first frame corresponds to the occurrence of a spark discharge. From a comparison of the video sequences shown in Fig. 4 (a-f), it can be seen that in the presence of this additive, the combustion of mixtures containing two combustible components is noticeably accelerated. In other words, in accordance with [18], isobutene accelerates the oxidation of hydrogen, which burns faster than in the absence of isobutene; the addition of isobutene C4H8, in such quantities, is not combustible. Indeed, it follows from Fig. 4 (a, b) that a 1.5% addition of isobutene accelerates the combustion of 10% H2 in air as compared to 10% H2 in air without an addition by several times. Figure 4 (c, d) shows that an increase in isobutene addition by a factor of 3 accelerates the combustion of 7.5% hydrogen with air also approximately by a factor of 3. Even near the combustion limit, the addition of isobutene significantly accelerates the combustion of hydrogen in Fig. 4 (e, f). In addition, as can be seen from Fig. 4 (b, c, f), the gas-dynamic features of the propagation of the combustion front of lean hydrogen mixtures in the presence of a hydrocarbon additive also qualitatively change. With an increase in the content of the hydrocarbon additive, inhomogeneities appear no longer in the form of cells, but in the form of “folds” on the surface of the flame front, which are not observed during combustion of lean hydrogen-air mixtures in the absence of a hydrocarbon additive. This means that the stability of the combustion front increases. Note that the chemical mechanism of combustion of combined fuels based on lean hydrogen mixtures in the presence of hydrocarbons has not been considered in the publication. At the same time, the solution of this issue is necessary for correct numerical simulation of combustion of poor binary mixtures of hydrogen and hydrocarbon with air. The normal flame propagation velocities of hydrogen-air mixtures in the presence of isobutene and СО2 additives, measured at the initial stage of the combustion process (from the first video frames, when the flame front still retains a spherical shape) using equations (1.1) and (1.2). Normal combustion rates in the absence of additives (0% isobutene (iso) in Fig. 5) measured in this work are consistent with [12]. As far as it is seen from fig. 5 the 1.5% addition of isobutene is the most effective and provides an increase in the normal flame speed of the combined fuel in comparison with the combustion of a lean hydrogen mixture in air by more than 5 times. Addition of СО2 that phlegmatizes combustion [12] leads to a decrease in the flame speed (Fig. 5). It can also be seen from fig. 5 that to achieve the same flame propagation speed, for example, 5.8% hydrogen in air requires either 1% С4Н8 or 2% Н2 (dashed lines in Fig. 5). Fig. 5. Normal combustion rates of hydrogen-air mixtures in the presence of isobutene and CO2 additives. One of the reasons for the observed efficiency of the hydrocarbon additive may be associated with the fact that the thermal effect of oxidation of isobutene is 2549.7 kJ/mol, and of hydrogen - 242.9 kJ/mol [12] and, accordingly, when the hydrocarbon additive burns, heat is released in 10 times more than in the combustion of hydrogen. This provides an increase in flame speed by increasing the adiabatic combustion temperature. Another reason may be a change in the kinetics of combustion in the presence of a hydrocarbon additive. It is important at the initial stage of the flame propagation process, when initiation by a spark discharge leads to the appearance of active centers that initiate combustion, both with the participation of hydrogen and hydrocarbon. We note in conclusion that in lean hydrogen-air mixtures, in contrast to rich ones [18], the addition of hydrocarbon burns completely in an excess of oxidizer (which is accompanied by glow, see Fig. 4b-e. Therefore, it is necessary to introduce an effective process with the participation of a hydrocarbon and subsequently take into account the most important elementary reactions of combustion of a hydrocarbon to calculate the flame velocity in the presence of a hydrocarbon additive, along with by the mechanism of hydrogen oxidation. We briefly summarize the results obtained. It was found that cellular flames of lean hydrogen-air mixtures propagate spherically symmetrically at the initial stage of combustion. Therefore, it is possible to use the change in the visible radius of a spherical flame to calculate the rate of cellular combustion of lean hydrogen-air mixtures. Only after that the gravity field distorts the shape of the combustion front for mixtures near the lower concentration limit of flame propagation. It is shown that the Boussinesq approximation is applicable to describe the appearance of cells in a gravity field with an H2 content <10%. The involvement of the Navier-Stokes equations for a compressible medium makes it possible to describe the spherically symmetric in all directions of the mode observed during the combustion of lean mixtures under microgravity conditions. It is shown that the error in experimental data on flame propagation in lean hydrogen-air mixtures does not make it possible to carry out reliable verification of various calculation models and, all the more, to detail the kinetic mechanism of hydrogen combustion, which is necessary to describe the combustion of lean hydrogen-air mixtures. It was shown that additives of isobutene С4Н8 in amounts less than the lower concentration limit of ignition (up to 1.5%) lead to an increase, and the addition of СО2 leads to a decrease in the flame speed using the method of color high-speed filming. It was found that the gas-dynamic features of the propagation of the combustion front of lean hydrogen mixtures in the presence of a hydrocarbon additive also change qualitatively. With an increase in the content of the hydrocarbon additive, inhomogeneities appear no longer in the form of cells, but in the form of “folds” on the surface of the flame front, which are not observed during combustion of lean hydrogen-air mixtures in the absence of a hydrocarbon additive. This indicates an increase in the stability of the combustion front. One of the reasons for the increase in the flame front velocity may be an increase in the adiabatic combustion temperature. Another reason may be a change in the combustion kinetics in the presence of a hydrocarbon additive. Annex We use the example BUOYANT.PDE from the software package of the finite element method FlexPde 6.0 [15] to solve a two-dimensional problem for a qualitative consideration of the conditions for the emergence of cellular structures. A reactor of circular cross-section with firing by a step on the horizontal axis is considered. The calculation is carried out in the upper half of the area (Figure 1.2). The chemical process is represented by one reaction in the form of Arrhenius. In the Boussinesq approximation [17], we assume that the medium is incompressible, except for the thermal effects of expansion. The form of the Navier-Stokes equations for an incompressible medium: grad (U) = 0, ∂U/∂t + U grad (U) + grad (p) =  div (grad (U)) + F where U is the velocity vector, p is the pressure, - the kinematic viscosity, F - the vector of mass forces. The first equation expresses conservation of momentum, while the second one expresses conservation of mass. We obtain the momentum equation using the relations grad (U) =0 and grad (rot (U)) =0, and the definition of w= rot (U): ∂w/∂t + u ∂w/∂x + v ∂w/∂y =  div(grad(w)) – g ∂/∂x taking into account the fact that in two dimensions the velocity has only two components, u and v, and the vortex has only one, represented as w. Let us now consider the continuity equation. If we define a scalar function  in such a way that u = ∂∂y , v = - ∂∂x, then grad(U) = ∂2 /∂x∂y - ∂2 /∂y∂x = 0, and the continuity equation is satisfied exactly, then div (grad ()) = - w If F – is the force of gravity, then F = (0,-g ) and rot (F) =-g ∂ /∂x where  - the density and g - the acceleration of the gravity. If the liquid expands linearly with temperature T, then 0 (1+ (T-T0)) и rot (F) =-g ∂T/∂x temperature - div(grad(Т)) = 0 Сp(∂T/∂t + u ∂T/∂x + v ∂T/∂y),  coefficient of thermal conductivity, Сp – thermal heat capacity at constat pressure.. The Arrhenius law gives the first order reaction rate RC(C,Temp) = (1-C) exp[ (1-1/T)]. Taking diffusion into account, the system of equations takes the form: ∂w/∂t + u ∂w/∂x + v ∂w/∂y =  div(grad(w)) – g ∂/∂x div (grad ()) =-w div( grad(Т)) + 2 RC= 0 Сp (∂T/∂t + u ∂T/∂x + v ∂T/∂y) div(D grad(C)) + 1 RC= ∂C/∂t + u ∂C/∂x + v ∂C/∂y and the state equation p =  The temperature of the walls of the outer cylinder is T0, the concentration C on the wall of the outer cylinder is zero, the boundary condition of the second kind is specified for the density on the wall of the outer cylinder. Boundary conditions of the second kind for temperature, concentration and density are specified on the segment of the abscissa axis separating the upper and lower halves of the cylinder. The initial temperature of flame initiation at the step is 5T0, the initial temperature in the volume is T0, the initial concentration is C0 = 0; other parameters are set equal to Т0 =1, D=1, 2, , g =0 (fig. 1.2а), g=980 (fig. 2б). For a compressible medium, the Navier-Stokes equations in the absence of gravity are written as follows [16]: ∂U/∂t + U grad (U) + grad(p) =  div (grad(U)) + U) + F, ∂∂t +grad(U) = 0 When introducing the function w, the moment equation taking into account the identical relation rot(rot(w)) =w) - div(grad(w)) becomes: ∂w/∂t + u ∂w/∂x + v ∂w/∂y =  div(grad(w))+ (rot(rot(w))-div(grad(w))) along with the continuity equations, temperature and concentration: ∂∂t +grad(U) = 0 Cp/( Re Pr) div(grad(Т)) + 2 RC – (∂T/∂t + u ∂T/∂x + v ∂T/∂y) = Cp (Cp-1)/( Re) (( ∂u/∂y + ∂v/∂x)2 +⅔((∂u/∂x + ∂v/∂y)2)+ (∂v/∂y)2+(∂u/∂x)2)) div(D grad(C)) + 1 RC= ∂C/∂t + u ∂C/∂x + v ∂C/∂y In the calculation, we used the same initial and boundary conditions that are given above. We also assumed Re =105, Pr =1,  (fig. 2d). The scales for dimensioning were chosen as follows [16]: L - length, Т0 – initial temperature, pressure R0T0, speed – (RT0)1/2, time – L/(RT0)1/2 . Dimensionless parameters =Ср/Cv, Pr =  Ср  coefficient of heat conduction), Re = RT0)1/2 L §2. The onset of acoustic instability in hydrogen-air mixtures in a closed reactor upon central initiation by a spark discharge As you know, combustion is a source of sound vibrations. The sound generated by combustion plays an important role in ensuring the stable operation of engines, turbines, etc. [19]. In particular, intense pressure fluctuations lead to undesirable additional loads on the walls of the combustion device. On the other hand, it is known [20] that in oscillating flows there is a significant acceleration of various heat and mass transfer processes (mixture formation, evaporation, heat transfer from gas to walls, heat transfer when the flow interacts with heated bodies, etc.), particle agglomeration and coagulation of aerosols are improved. In addition, during vibration combustion, the level of NOx decreases [21]. Acoustic vibrations during combustion are caused by instabilities arising from the propagation of the flame front [20, 22]. These instabilities manifest themselves in combustion processes in various forms and can be classified as follows (see the beginning of this Chapter)). Thermal diffusion instability is observed in flames in which the rates of heat transfer and diffusion are different, i.e. Le ≠ 1 (Lewis number Le = D/, where D – where D is the diffusion coefficient of the component that determines the combustion process,  - is the thermal diffusivity) [23, 24]. The hydrodynamic instability is determined by the difference in the densities of the burnt and unburnt gas associated with the thermal expansion of the reaction products [22, 25]. Thermoacoustic instability is determined by the resonant relationship between the unsteady combustion mode and the acoustic modes of the reactor [20, 22, 25]. The criterion for the occurrence of this instability was proposed by Rayleigh [26]. In [27] this hypothesis is formulated as follows: if the phase shift between pressure fluctuations and fluctuations in the rate of heat supply is less than π/2 in absolute value, the oscillations are excited; if the phase shift is in the range from π/2 to π, the oscillations are damped. Pressure fluctuations accompanied by sound during combustion in closed vessels are usually associated with thermoacoustic instabilities that occur during spontaneous ignition, detonation, etc. [28]. Until now, the nature of this phenomenon is not completely clear [28]. In [29], fluctuations in the sound range were recorded in rich mixtures of pentane with air. However, in the same mixtures of benzol with air, fluctuations were not observed. In [12], sound vibrations were recorded during the combustion of a hydrogen-air mixture with. However, during the combustion of a hydrogen-air mixture (60), there were no sound vibrations. The possibility of self-ignition in the process of flame propagation in explosive bombs was pointed out in [30]. A sufficiently high rate of change in heat release during combustion with such self-ignition or with acceleration of the flame [29] can induce pressure oscillations and thermoacoustic oscillations. In turn, that can lead to an increase in the rate of heat release. Experiments carried out in [42] showed that during the ignition of rich mixtures of isooctane and lean mixtures of hydrogen with air, strong pressure fluctuations arise. The appearance of acoustic oscillations in [42] was associated with the development of hydrodynamic instability during the propagation of flames. However, during combustion of a stoichiometric mixture of hydrogen with air, pressure oscillations were not observed in [42]. Although it is known that the combustion of a stoichiometric mixture of hydrogen with air in cylindrical reactors is accompanied by a characteristic sound [12]. In the publication, for modeling thermoacoustic phenomena, the analysis of the inhomogeneous wave equation for acoustic pressure with a thermoacoustic source is used [21, 31, 32]: (2.1) where - acoustical velocity, - acoustic pressure,  the ratio of heat capacities at constant pressure, - the rate of heat release [W/m3]. If we assume the feedback mechanism as a linear function - from [32], then it can be shown [36] that equation (2.1) is an acoustic oscillator that is excited or attenuated depending on whether the Rayleigh criterion is met or not. This section presents the results of experiments on the observation of acoustic instabilities arising from the ignition of mixtures of hydrogen with air in a cylindrical bomb of constant volume with a central ignition. Experimental part Stoichiometric mixtures of hydrogen with air were used at total atmospheric pressure and initial temperature T0 = 298K. The experiments were carried out in a horizontal cylindrical stainless steel reactor 15 cm long and 13 cm in diameter. The reactor was equipped with an optical quartz window at one of the ends. In the center of the reactor, spark ignition electrodes were placed, the distance between which was 0.5 mm. In order to change the material and shape of the inner surface of the reactor in various experiments, titanium foil 0.1 mm thick was introduced into the reactor, covering the entire inner side surface of the reactor, tantalum foil 0.1 mm thick, covering ¼ of the inner side surface of the reactor, and platinum foil 12x6 cm with a thickness of 0.3 mm. In a number of experiments, a titanium foil 0.1 mm thick was introduced into the reactor, which covered 1/3 of the inner side surface of the reactor with three longitudinal corrugations 12 cm long, protruding into the reactor by 1 cm and located at a distance of 4 cm from each other. We point out that the introduction of Ti foil can be considered as the treatment of the inner surface of the reactor with titanium dioxide TiO2, since titanium metal is always covered with a thin oxide layer. In a number of experiments, filming was carried out through NS-1 filters to reduce the illumination intensity of the camera matrix. For the same purpose, in some experiments, optical glass was covered with a thin layer of talc. The experiments were carried out in the following sequence. If it is necessary, CCl4 was fed into the reactor, then hydrogen, air were added to atmospheric pressure so that the H2 content in the mixture was 30% and 15%, kept for 15 min in the reactor for complete mixing. After that spark initiation was carried out. The registration of the ignition and propagation of the FF was carried out through the optical window with a color high-speed film camera Casio Exilim F1 Pro (frame rate - 60 - 1200 s-1). The resulting video file was recorded into the computer memory and then processed frame-by-frame. To visualize the hydrogen flame, 2-3% carbon tetrachloride (CCl4) was added to the mixture. It should be noted that the addition of less than 3% CCl4 for this mixture is inert and does not have a noticeable inhibitory effect on the combustion of hydrogen with air [12]. The change in pressure during combustion was recorded using a piezoelectric sensor, the signal from which was fed through an ADC to a computer. Before each experiment, the reactor was evacuated using a 2NVR-5D foreline pump. The pressure in the reactor was also monitored with a pattern vacuum gauge. The gases Н2, carbon tetrachloride CCl4, were of chemically pure grade, the purity of the used foils was: Ti - 99.9%, Ta - 99.99%, Pt - 99.99%. Results and discussion of the experiment The experiments have shown that the features of the glow during the afterburning of a stoichiometric hydrogen-air mixture under conditions of central spark initiation do not depend on the material of the inner surface of the reactor (stainless steel, TiO2, Ta, Pt) but depend on its shape. The normal speed of a spherical flame is also independent of the surface material. Experiments have also shown that acoustic oscillations during combustion of hydrogen-air mixtures in a cylindrical reactor at atmospheric pressure are excited differently than in a spherical reactor. Fig. 6. Filming of the process of propagation of a spherical flame front. The number on the frame corresponds to the number of the frame when shooting, To = 298K, Eo = 1.5 J. a - (H2 + air) stoich + 5% CCl4, frame rate 600 s-1 b - 14.5% H2 + air + 3% CCl4, frame rate 300 s-1 c - (H2 + air) stoich, HC-1 filter, optical window treated with talcum powder, surface - stainless steel, frame rate 600 s-1, d - (H2 + air) stoich, 2 NS-1 filters, Ti foil with corrugations (marked on frames 7 and 15) is located in the lower part of the reactor, the frame rate is 600 s-1. The results of filming of a spherical front propagation process of a stoichiometric hydrogen-air flame with a frame rate of 600 s-1 is demonstrated in fig. 6a. The frames of FF development in a stoichiometric hydrogen-air mixture containing + 5% CCl4 is demonstrated in fig. 6a. It is seen that the front of the developing flame has a spherical shape without disturbances. The results of filming the process of flame propagation in a mixture of 15% H2 + air + 3% CCl4 is indicated in fig. 6b. It can be seen that the FF consists of small cells, while in the process of its propagation, long-wave disturbances arise. Figure 7 shows oscillograms of pressure changes during the ignition of combustible mixtures of 30% H2 + air and 15% H2 + air + 3% CCl4. Figure 7 shows that acoustic oscillations are excited after reaching the maximum pressure. In 15% of the mixture these oscillations are excited later than in the stoichiometric mixture, in contrast to [28]. In [28], acoustic oscillations in a spherical reactor were observed only in lean hydrogen-air mixtures and before reaching the maximum pressure, and in mixtures close in composition to stoichiometric, they were not observed at all (Fig. 3 [28]). Perturbations of the spherical FF in a lean mixture burning in a cylindrical reactor caused by thermal diffusion instability [23, 24] and indicated in fig. 7b develop until the flame front touches the side walls of the reactor. However, these perturbations do not lead to the excitation of acoustic oscillations during the propagation of a spherical FF. Obviously, the perturbations did not have time to develop and ensure the excitation of acoustic oscillations due to the smaller diameter of the reactor used in this work (13 cm) compared to [28], in which the diameter of the spherical bomb was 38.4 cm (see Fig. 3 from [28 ], curve  = 0.4). In our reactor, thermoacoustic instabilities, as can be seen from Fig. 6 a, b and 7, are excited noticeably later than the moment the flame front touches the side walls of the reactor. The data obtained are an argument in favor of the existence of a scale effect when this type of instability occurs. It should be noted that in [25], cellular flames that arise in dilute stoichiometric hydrocarbon-air mixtures after the flame front touches the walls of a cylindrical reactor were discovered and are caused by the occurrence of gas-dynamic instability (see also Chapter 4). This means that the nature of the pressure fluctuations observed by us (Fig. 7) can also be caused by the gas-dynamic instability arising after the flame touches the side walls of the reactor [27]. It is due to the fact that both instabilities, gas-dynamic and acoustic, are experimentally observed in the same time interval. Verification of this assumption requires further research. The results of video recording of the combustion of a stoichiometric hydrogen-air mixture in the time interval corresponding to the appearance and development of pressure oscillations for various materials of the reactor surface are demonstrated in fig. 6 c, d and Fig. 8 a, b (stainless steel, TiO2 with corrugations, Fig. 6; Pt and Ta, Fig. 8). Fig. 7. Oscillograms of pressure changes during ignition of combustible mixtures, 1 - signal at initiated ignition, 2 - comparison signal, bold points - time interval: a, b, c - (H2 + air) stoich, different time intervals; d - 15% H2 + air + 3% CCl4, 3 - extended time interval. The figures show that after the flame touches the side wall of the reactor, the afterburning of the combustible mixture occurs unevenly in the vertical section of the reactor, while the symmetric picture of the afterburning corresponds to the realization of longitudinal gas oscillations in the reactor. This means that the high-speed filming method makes it possible to visualize the longitudinal vibrations of the after-burning gas. Fig. 8. Filming of the process of propagation of a spherical flame front with a frame rate of 600 s-1. The number on the frame corresponds to the frame number during shooting, To = 298K, Eo = 1.5 J. а - (Н2 + air) stoich, 1 filter НС-1, Pt foil is located in the lower part of the reactor, b - (Н2 + air) stoich, 2 filters НС-1, Ta foil is located in the lower part of the reactor. It can be seen from these figures that in the case of a smooth inner surface of the reactor, the observed character of the afterburning of the combustible mixture (compare frame 8 in Fig. 6c, frame 6 in Fig. 8a, frame 8 in Fig. 2.3b) does not depend on the material of the reactor surface. In the next series of experiments, non-uniform gas flows were provided by introducing into the reactor a titanium foil with three longitudinal corrugations protruding 1 cm deep into the reactor (see experimental part). It was found (Fig. 6d, TiO2 foil with corrugations) that in the case of a nonsmooth inner surface of the reactor, the most intense afterburning of the combustible mixture occurs in the region of inhomogeneous gas flows, namely, in the region of corrugations. Comparing the oscillation frequencies observed directly on the pressure oscillograms (Fig. 7) and the natural frequencies of the longitudinal oscillations of the cylinder filled with gas (Fig. 6c, Fig. 8), observed visually from different spatial intensities of the afterburning of the combustible mixture is of interest. To determine the longitudinal modes of a cylindrical reactor, it is sufficient to set the right-hand side of equation (2.1) equal to zero. If P(x,y,z,t)=exp(i w t) v(x,y,z) we obtain the well-known [15, 32] eigenvalue equation: (2.2) Where - the frequency of the gas vibration mode. The solution of this problem by the finite elements method for the natural frequencies of longitudinal vibrations of a cylinder filled with an inert gas with fixed walls and a height equal to the diameter was carried out. It was performed using the software package (FlexPDE 6.08, A Flexible Solution System for Partial Differential equations, 1996-2008 PDE Solutions inc. [15]), in which this problem appears as an example. Since combustion takes place under conditions close to adiabatic, it is possible to estimate the temperature in the reactor at a given time from the relation on the pressure oscillogram. For the moment of time 21 ms in fig. 7b P = 4, P=1, and, accordingly, T = 273*4 ≈ 1000 0C for this temperature с0 ≈ 1000 m/s [33], and for the moment of time 27 ms P = 3.5, P=1, and, accordingly, T = 273*3.5 ≈ 900 0C; for this temperature с0 ≈ 900 m/s [33]. The video frame 7 from Fig. 6 and frame 41 from Fig. 7 and the calculated modes of air oscillations in the cylinder is demonstrated in fig. 9: mode 36 and mode 4. It is seen that the calculated vibrational modes correlate well with the visually observed afterburning pattern for a stoichiometric hydrogen-air mixture. Taking into account the cylinder length of 0.15 m for the 36th vibration mode, we obtain w = 1.11 KHz, at с0 = 900 m/s (Т ≈ 900 0C) we obtain w = 0.7 KHz for the 4th mode. We obtain an oscillation frequency of ~ 1.9 KHz, which agrees with the value w = 1.11 KHz, calculated from equation (2.2) according to the algorithm [15] from fig. 7b in the time interval 20.5 ms - 26 ms and Fig. 7d in the time interval 112.5 ms - 116.7 ms from the pressure oscillograms. Fig. 9. Video shots from Fig. 6 and Fig. 7 and the calculated modes of air oscillations in the cylinder, a - 36th mode, b - 4th mode. It can also be seen from fig. 7 that at the end of the afterburning process of the combustible mixture in the final sections of the pressure oscillograms corresponding to the cooling reactor, the oscillation frequency decreases noticeably and reaches 1 kHz in oscillogram 3 in Fig. 7. It also agrees with the calculation performed for the lower mode of longitudinal vibrations w = 0.7 kHz. The above comparison is illustrative and does not allow, for example, to interpret the more complex mode structure of oscillations observed for a 15% hydrogen-air mixture (Fig.6b, frame 49). We briefly summarize the results obtained. Using the combustion of hydrogen-air mixtures (30% and 15% H2) as an example, it is shown that the high-speed filming method allows visualizing the longitudinal oscillations of the after-burning gas. It was found that the features of flame propagation in a stoichiometric hydrogen-air mixture with central spark initiation do not depend on the material of the inner surface of the reactor (stainless steel, TiO2, Ta, Pt) but depend on the degree of its roughness. It was found that thermoacoustic oscillations during the combustion of hydrogen-air mixtures in a cylindrical reactor at atmospheric pressure are excited differently than in a spherical reactor, and at the same time depend on the size of the reactor. § 3. Interaction of spherical flames of hydrogen-air and methane-air mixtures with fine-mesh obstacles at central initiation by a spark discharge The influence of obstacles located in different volumes filled with a reactive mixture on the propagation of the flame front has been studied for a long time. These studies are carried out in order to clarify the dependence of the nature of combustion on the type of obstacles and the possibility of influencing the intensity of combustion by varying the geometrical arrangement of the obstacle. We point out that this issue will also be discussed in Chapter 6. It is known that if the combustible mixture is at a sufficient distance from the concentration limits of ignition, then the speed of flame propagation in the presence of obstacles can rapidly increase to supersonic values [34, 35]. However, the speed of the supersonic combustion wave in the presence of obstacles is significantly lower than the Chapman-Jouguet speed [36, 37]. Therefore, from a practical point of view, the most important aspect in the study of accelerating flames is due to explosion safety problems and is mainly associated with the transition of fast combustion to nonstationary (detonation-like), the destructive effect of which is stronger than the steady-state Chapman – Jouguet wave [38]. It should be noted that the effect of obstacles, can manifest itself both in maintaining a detonation wave as a result of reflections of shock waves, and in damping and dispersion a detonation wave as a result of heat and momentum abstraction according to [34]. The foregoing can be attributed to the initial stage of flame acceleration, namely, to the moment when the laminar flame meets an obstacle in the form of a grid, which is the subject of this study. In this case, the development of flame instability occurs, which contributes to its acceleration [12]. On the other hand, upon contact of the flame with the surface, one should expect an increase in the contribution of heterogeneous reactions, in particular, the termination of reaction chains [39], which should contribute to the deceleration and extinction of the flame. Such a dual mechanism of action of obstacles causes the fact that physical methods of suppressing detonation (nets, nozzles, etc.) [40] are not always effective. In [35], the effect of turbulizing obstacles (grids and perforated spheres with minimum cells of 2x2 mm and a hole diameter of 4 mm) located inside a combustible gas mixture on the apparent combustion velocity of stoichiometric hydrogen-air and hydrogen-oxygen mixtures was studied. In experiments, combustion acceleration was always observed by a factor of 1.5–2.5 after obstacles. For hydrogen-oxygen mixtures, a transition from combustion to detonation was observed, which depended on the initiation energy [35]. However, information on the interaction of flames of lean hydrogen-air mixtures with mesh obstacles is practically absent in the publication. Although such experiments are of interest for establishing the influence of oppositely acting factors accelerating the development of instability and slowing down the flame (breakage of active centers on the obstacle surface). The purpose of this section was to study the dynamics of propagation of flames of lean hydrogen-air mixtures and a stoichiometric mixture of natural gas with air inside the grid sphere, passing through the grid sphere and further propagation outside the grid sphere. Experimental part The experiments were carried out with lean mixtures of hydrogen (7.5-15%) with air and a stoichiometric mixture of natural gas (NG) with air at initial atmospheric pressure and temperature To = 298K. A horizontally located cylindrical stainless steel reactor 15 cm long and 13 cm in diameter was used. The reactor was equipped with an optical quartz window at one of the ends (Fig. 10). In the center of the reactor, spark ignition electrodes 6 were placed, the distance between which was 0.5 mm. On partially insulated electrodes 6, a sphere 5 with cut-out slots for electrodes, made of a mesh, consisting of two hemispheres and fastened by a spring 7 was fixed. In this case, the volume enclosed in the mesh sphere and the external reaction volume were in contact only through the mesh cells. We used mesh spheres with a diameter of d = 3 cm (wire diameter 0.2 mm, cell size 0.04 mm2), d = 4 cm (wire diameter 0.25 mm, cell size 0.08 mm2), d = 6 cm (wire diameter 0.3 mm, cell size 0.1 mm2). The mesh material was aluminum wire. As you know, the surface of aluminum is always coated with its oxide. Consequently, the surface of the grid was aluminum oxide Al2O3, which effectively terminates the reaction chains [12]. Fig. 10. Photo of the experimental setup. 1 - stainless steel reactor, 2 - folding mirror, 3 - high-speed color film camera Casio Exilim F1 Pro, 4 - vacuum valve for gas inlet and evacuation, 5 - mesh sphere d = 6 cm, 6 - ignition electrodes, 7 - spring. The inset shows a view of the interior of the reactor with a grid sphere. The experiments were carried out in the following sequence. If necessary, CCl4, then hydrogen, or natural gas (NG) was poured into the reactor, then air was added to atmospheric pressure. The mixture was kept for 15 min for complete mixing, and then spark initiation was performed (the discharge energy was 1.5 J). The dynamics of ignition and the propagation of the flame front (FF) was studied through the optical window using a Casio Exilim F1 Pro color high-speed film camera (frame rate - 60 ÷ 1200 s-1). The resulting video file was recorded into the computer memory and then processed frame-by-frame. To visualize the hydrogen flame, 4% carbon tetrachloride (CCl4) was added to the mixture. It should be noted that the addition of up to 4% CCl4 for these mixtures is inert [12]. The change in pressure during combustion was recorded using a piezoelectric sensor, the signal from which was fed to an S8-2 digital storage oscilloscope. The pressure in the reactor during the composition of the gas mixture was monitored with a pattern vacuum gauge. Before each experiment, the reactor was evacuated using a 2NVR-5D forvacuum pump. Gases Н2, carbon tetrachloride С were used of chemically pure grade, PG contained 2% propane and butane according to the data of chromatographic analysis. The value of the degree of expansion of the combustion products T was determined from the value of the maximum pressure developed during the combustion of the Рb [23], as in Section §1: Рb/Po = 1 + T-1) (3.1) The magnitude of the normal flame propagation velocity Un was determined from the relation [23]: Un = Vv/T (3.2) In expressions (3.1), (3.2) Pb – maximum pressure, γ – adiabatic index of the initial mixture, Vv - apparent flame velocity. Results and discussion of the experiment. In all experiments, the flame initiated inside the grid sphere passed through the grid cells (except for a mixture of 4% CCl4 + 7.5% H2 with air). This means that the interaction of a relatively slowly spreading flame (the normal flame velocity in a mixture of 15% H2 with air is ~ 6 times less than in a stoichiometric mixture (≈ 50 cm/s) in a mixture of 10% H2 with air and ~ 15 times less than in a stoichiometric mixture (≈ 20 cm/s) [12]) with a surface providing effective termination of reaction chains (Al2O3) does not lead to flame-out. Thus, the effect of heterogeneous termination of active combustion centers on flame propagation under our conditions is not sufficient to blow off the flame. It was found that mixtures of 4% CCl4 + 7.5% H2 with air do not pass through the nets. However, individual flame cells are observed inside the mesh. In the absence of a grid, the cellular flame of this mixture, as in [13], rises up to the reactor wall. Under our conditions, there is a critical concentration of hydrogen at which the flame does not pass through the grid. This is consistent with the results of calculation work [9], where it was shown that the effect of heterogeneous termination on flame propagation should be observed in the immediate vicinity of the lower concentration limit of flame propagation (which for a hydrogen-air mixture is ~ 5% H2 [12]). A sequence of video images of the propagation of a flame front illuminated with 4% CCl4 in mixtures of 10% H2 and 15% H2 with air, respectively, illustrating the effect of the grid sphere on the dynamics of flame propagation is shown in fig. 11. It can be seen that, after passing through the obstacle, the flame front in these mixtures is noticeably disturbed in comparison with the flame propagation in the absence of the obstacle. It can be seen from fig. 11 IIa, b that the FF consists of small cells, while in the process of its propagation, long-wave disturbances arise. Figure 11c shows the dynamics of an increase in the radius of the flame front in the absence and in the presence of a grid sphere. It can be seen from the figure that the flame slows down when approaching the grid, but after passing the obstacle it noticeably accelerates, in agreement with the results of [35]. Then, flame retardation is again observed at the reactor wall, associated with a change in the conditions for the expansion of combustion products [12, 23]. Worthy of note is the appearance of streams of hot glowing gas from the volume bounded by the grid, which appears after the flame reaches the walls of the reactor (frames 17-19 Fig. 11 IIb). In accordance with the existing ideas about the combustion mechanism of hydrogen - air mixtures, there should be no secondary exothermic reactions in this mixture [12]. The presence of the grid should also lead to a faster cooling of the gas inside it. Therefore, the gas flow must be directed towards the inside of the mesh. Fig. 11. I - the result of high-speed filming of the propagation of the flame front illuminated with 4% CCl4, in a mixture of 10% H2 + 86% air at atmospheric pressure. The number on the frame corresponds to the frame number when shooting. Filming speed is 60 frames/s. a) - in the absence of a grid; b) - in the presence of a grid sphere d = 6 cm. II - the result of high-speed filming of the propagation of the flame front illuminated with 4% CCl4 in a mixture of 15% H2 + 81% air at the initial atmospheric pressure. The number on the frame corresponds to the frame number when shooting. The first frame corresponds to the occurrence of a spark discharge. Filming speed is 600 frames/s. a) - in the absence of a grid; b) - in the presence of a grid sphere d = 4 cm; c) - dynamics of an increase in the radius of the flame front in the absence (1) and in the presence (2) of a grid sphere d = 4 cm (15% H2, II a, b). However, the gas flow is directed outside the grid sphere. Identification of the cause of this phenomenon requires a more detailed study. It was also found that in the presence of a mesh sphere, flame propagation of both 10% H2 and 15% H2 in the air is accompanied by a characteristic sharp sound, i.e. acoustic vibrations of gas. It should be noted that the propagation of a flame in a mixture of 10% H2 with air in the absence of obstacles inside the reactor is not accompanied by a sound effect. Figure 12 shows the dependences of the total pressure change on time for the indicated mixtures during flame propagation in the presence of a grid. It follows from Fig. 12 Ib that, in the presence of a grid in a 10% mixture of H2 and air, acoustic oscillations are excited, and the rate of pressure rise becomes higher compared to the process in the absence of a grid, in accordance with [35]. Figure 12 II shows that in a 15% mixture of H2 with air in the absence of a grid, acoustic oscillations are excited after reaching the maximum pressure. In the presence of a grid with d = 3 cm, acoustic vibrations occur much earlier than the pressure maximum is reached. The presence of a grid leads to a more rapid development of instability and provides an intensification of the combustion process. It should be noted that in a spherical bomb 38.4 cm in diameter, i.e. larger than that used in this work (see Fig. 3 from [28], curve  = 0.4), acoustic oscillations appear before the pressure maximum is reached. Attention should be paid to the fact that the larger the diameter of the mesh sphere, the later the acoustic vibrations occur, recorded by the pressure sensor (cf. Fig. 12 IIb and IIc, ~ 10ms and ~ 25ms, respectively). This means that the presence of a mesh barrier leads to the development of instabilities at the combustion front and the appearance of acoustic vibrations. In the next series of experiments, it was shown that the process of chemical conversion in a stoichiometric mixture of NG with air for all mesh spheres used in this work completely covers the volume of the reactor. Fig. 12. Oscillograms of pressure changes during ignition of combustible mixtures. I - 4% CCl4 + 10% H2 in air; a) - in the absence of a grid; b) - in the presence of a mesh d = 6 cm. II - 4% CCl4 + 15% H2 in air; a) - in the absence of a grid; b) - in the presence of a mesh d = 3 cm; c) - – in the presence of a mesh d = 4 cm; 1 - signal at initiated ignition, 2 - comparison signal, bold points - time interval; 3 - extended time interval. However, the flame actually stops with the disappearance of the glow in contrast to the combustion of hydrogen-air mixtures, near the inner surface of the grid (Fig. 13). This means that the mechanism for the penetration of such a flame through an obstacle is different from the mechanism for hydrogen-air mixtures. Figure 13a shows a sequence of video images when the flame of a mixture of NG with air propagates through a mesh obstacle. In fig. 13b dynamics of an increase in the radius of the flame front in the presence of a grid sphere is demonstrated. It can be seen from the figure that when the flame front approaches the grid sphere, the flame is practically extinguished. After the onset of combustion outside the mesh obstacle, the flame front is not accelerated, but propagates at an almost constant speed. Therefore, the excitation of acoustic vibrations due to the acceleration of the flame during the combustion of this mixture is not observed. There is an estimation of the normal speed of flame propagation outside the mesh obstacle using relations (1) and (2) gives ~ 27 cm/s - a value close to the normal speed of a spherical flame for this mixture composition (35 cm/s [12]). It can be assumed that the extinction of the NG - air flame is associated with the intense heterogeneous death of active intermediate combustion products on the mesh material. However, stable intermediate combustion products (for example, hydroperoxides) diffuse through the mesh cells and initiate flame propagation outside the mesh sphere. The absence of acoustic vibrations during the combustion of this mixture supports this assumption, i.e. the presence of a mesh barrier does not lead to turbulence of the combustion front and the appearance of acoustic vibrations. We point out that the normal flame velocities of mixtures of 10% H2 and 15% H2 with air are, respectively, 21 and 45 cm/s according to [13], which presents the data of several groups of authors on the definition of Un and the curve of the average values of this value. It should be noted that the normal flame propagation velocity in the NG-air mixture is 35 cm/s, i.e. the Un values for the three mixtures under consideration are close. Fig. 13. a) - the result of high-speed filming of the propagation of a flame front, a stoichiometric mixture of a steam generator with air at atmospheric pressure in the presence of a grid sphere d = 4 cm. The number on the frame corresponds to the number of the frame during shooting. Filming speed is 600 frames/s. b) - dynamics of an increase in the radius of the flame front in the presence of a grid sphere. In this case, the molar heat of combustion of natural gas is much higher than that of hydrogen [12]. Thus, according to only the thermal theory [23], the stopping of the NG-air flame near the mesh obstacle has no explanation. This means that the work obtained direct evidence that the active centers of combustion of methane and hydrogen, which determine the propagation of the flame, have a different chemical nature [41, 42]. The reason for the stopping of the NG-air flame is because hydrogen atoms easily penetrate through the mesh obstacle, and the carriers of the chains in the combustion of methane, on the contrary, actively die on Al2O3. Let us summarize the results obtained. It is shown that spark-initiated flames of lean hydrogen mixtures (8% -15% H2 in air) pass through mesh spheres with a mesh size of 0.04-0.1 mm2, while the flame of a mixture of 15% H2 in air accelerates after passing through an obstacle. In the presence of an obstacle during the propagation of flame in mixtures of 10% and 15% H2 in air, acoustic oscillations of the gas are initiated the earlier, the smaller the diameter of the grid sphere. Flame of 7.5% H2 in air does not pass through mesh spheres. It is shown that the process of chemical conversion in a stoichiometric mixture of NG with air for all mesh spheres used in this work covers the entire volume of the reactor, but is not accompanied by acoustic vibrations. The appearance of streams of hot glowing gas from the volume bounded by the grid, which appear after the flame reaches the walls of the reactor, is found. It is shown that the active centers of combustion of methane and hydrogen, which determine the propagation of the flame, have a different chemical nature. §4. Thermal ignition in gas vortices In laboratory [36, 37, 43, 44] and in large-scale experiments [45, 46], it was demonstrated that obstacles located in the path of a propagating flame can provide a rapid acceleration of the flame. Under these conditions, the detailed kinetic mechanism of the process falls by the wayside and the representation of the gross process by the effective Arrhenius reaction is sufficient. Thus, the gas-dynamic features of the process are of paramount importance. Qualitatively, the mechanism of this acceleration of the flame is well understood. Thermal expansion of the hot reaction products causes the unburned gas to move. In the presence of obstructions, turbulence can occur in this flow. Turbulence increases the local combustion velocity by increasing the surface area of the flame and the velocity of transfer of mass and energy. The increasing velocity of combustion provides, in turn, a higher flow rate in the unburnt gas. This feedback leads to continuous acceleration of flame propagation. Under appropriate conditions, this can lead to a transition to detonation. Depending on the sensitivity of the mixture, high intensity turbulence can reduce the overall combustion rate when the flame is highly distorted and the combustion products and cold unburnt mixture rapidly mix. If the temperature of the reaction zone is lowered to a value at which the flame cannot propagate, the flame can be extinguished locally. Turbulent quenching plays a role when the speed of the unburnt gas increases. For some weakly initiated mixtures, this can destroy the described positive feedback mechanism and lead to extinguishing the flame in general. Consequently, both the degree of flame acceleration and the final result (the maximum achieved flame velocity) depend on the competing effects described above due to gas turbulization [47]. Let us consider the main control parameters of processes in reacting gas streams and some features of the modern approach to the theory of turbulence. In a laminar flame of a premixed mixture, changes in the shape of the flame are described in terms of flame extension, which is a combination of its deformation and curvature. Flame expansion is caused by hydrodynamic effects in the flow, which disturb the flame front and local curvature of the flame. We point out that the main types of instability of subsonic flames can be classified for reasons that cause them as thermodiffusion, thermoacoustic, and gas-dynamic [48]. Flame expansion can have a positive or negative effect on the flame propagation speed, depending on the directions of deformation and curvature, as well as the Lewis number, which is the ratio of the thermal diffusivity (α) and diffusion (D) coefficients [12, 24, 49]: Le = α/D = λ/ρCp D (4.1) Figure 14 shows possible examples of stress and curvature at the flame front, which is built according to the Huygens principle [23]. As the flame spreads in the area of diverging streams (Fig. 14a), the flame is deformed so as to accelerate the diffusion of unreacted gas into the reaction zone, but also to cool the reaction zone. If Le > 1, then such a deformation will lead to a decrease in the flame propagation speed, since the reaction zone cools faster than the diffusion rate increases. On the contrary, with the same deformation, the flame propagation velocity will increase for mixtures with Le < 1. Figure 14b shows a flame propagating into a converging flow, which leads to an increase in the flame velocity for Le > 1 and a decrease in the flame velocity for Le < 1. For a Lewis number of the order of unity, the curvature practically does not affect the propagation velocity. In areas of a convex flame (Fig. 14c, peak), the flame surface increases while the reaction zone cools. The opposite happens in areas with a concave flame (Figure 14c, bottom). Fig. 15 illustrates the stabilizing and destabilizing effects associated with the Lewis number. For Le > 1, the heat propagation rate is higher than the diffusion rate. This stabilizes the flame as concave areas spread faster than convex areas. As a result, initial disturbances along the flame surface tend to level down, stabilizing the flame. Fig. 14. Disturbances and curvature of the flame front: a) disturbance in the direction of propagation of the flame front, b) disturbance in the opposite direction, c) curvature and propagation [23, 50]. Fig. 15 Stabilizing and destabilizing effects determined by the Lewis number. For Le < 1, the disturbances of the flame structure are intensified as the concave regions slow down relative to the convex regions, and this leads to flame instability. For Le = 1, the diffusion and heat transfer rates are balanced and do not affect the flame structure. The hydrodynamic effects associated with convection can increase if the gas flow is accelerated. For example, in a partially closed channel (hole), the expansion of combustion products leads to the propagation of compression waves ahead of the flame to the open end. That causes the flow of unburnt gas. This ultimately leads to an increase in the speed of the SF flame, which is the sum of the unburnt gas speed and the laminar speed of the SL flame. As the flame further spreads into the unburnt gas, it is accelerated due to the additional flame region created initially by the axial velocity profile along the width of the hole. Turbulence leads to a wrinkled flame, whereby the surface of the flame increases from the level of laminar combustion A to the level of turbulent combustion AT. The consequence of an increase in the flame area is an increase in the volumetric combustion rate up to the so-called turbulent combustion rate ST. Since the products are mixed with reagents during turbulence in case of turbulence-accelerated transfer processes, the laminar flame thickness δL increases to the thickness of the turbulent flame brush δT. There is, obviously, an inverse relationship between the flame propagation process and the turbulence of the gas medium. As the unburnt gas is consumed by the flame, baroclinic vortex flow [51] can occur, which is the result of changes in density and pressure. This process is viewed as turbulence generated by a flame. In this case, an increase in the kinematic viscosity in the flame due to an increase in temperature weakens the local turbulence. Historically, the study of turbulent combustion was initially focused on predicting the control parameters of turbulence such as ST and δT [49]. Unfortunately, ST and δT depend on local flow conditions, and therefore predictions are not as easy as in the case of a turbulent flame. Instead, it is wise to focus on the various turbulent combustion regimes that exist and make certain simplifications for the analysis of each regime. For a given mixture, the effect of turbulence on flame propagation will vary with the intensity and scale of the turbulence. When the flame accelerates in an obstructed channel, leading to a deflagration-to-detonation (DDT) transition, the entire spectrum of turbulent combustion modes is likely to pass through. It should be noted that the main dimensionless criteria in the analysis of the phenomena associated with turbulence, in addition to the Reynolds number, are the Karlovitz and Damköhler numbers [49]: Ka = τc / τη= (δ/SL)/(η/uη) (4.2) Da = τT / τc = (l T/ u′T)/( δ/ S L) (4.3), where τc is the time scale of chemical transformations. Integral time, length and scales of turbulence velocities, designated as τT, lT and u′T, characterize the highest energy containing eddies that exist in a turbulent flow. These scales are often determined by the geometry of the structure that restricts the flow. Energy is transferred along the turbulence scale to smaller and smaller eddies through a cascade process that ends on the so-called Kolmogorov scale. In other words, any turbulent flow includes a continuous spectrum of eddies structures. Large eddies are created due to the instability of the mean flow, then they transfer their energy to smaller eddies, which in turn transfer their energy to even smaller ones. The flow in the mixing layer in shown fig. 16 where one can see a cascade of eddies (Fig. 17) from the largest eddies to the smallest ones. Fig. 16. Flow in the mixing layer. Vortex Cascade (Brown, Roshko, 1974) The kinetic energy is dissipated only at the last stages of this process, when the vortex structures become so small that the Reynolds number, determined by the size of small eddies, becomes of the order of unity Re = ul/ ~ 1. In this sense, viscosity plays a rather passive role. Fig. 17. Energy cascade. Let us determine the characteristic size of the smallest eddies in a turbulent flow (Kolmogorov scale). Suppose u and v represent the characteristic velocities associated with the largest and smallest eddies sizes, respectively. In addition, suppose l and  be the characteristic dimensions of the largest and smallest structures that is, eddies transfer most of their energy to smaller eddies during a characteristic time ~ l / u. Therefore, the speed with which energy (per unit mass) is transferred down the cascade of eddies from the largest eddies is defined as π ~ u2/(l/u). When conditions are statistically stationary, the rate at which the energy of the largest eddies is transferred down the cascade must match the rate of energy dissipation at the level of the smallest eddies. If this were not so, then in this case the energy would accumulate at some intermediate stage of the eddies cascade. We exclude this possibility, since we are considering the case when the statistical structure of the turbulent flow does not change over time. The rate of energy dissipation at the level of the smallest eddies is defined as  ~ Sij Sij , where Sij is the velocity-strain tensor, which in a turbulent flow (due to the presence of a wide range of eddy scales) is associated precisely with the smallest eddies, since the local velocity gradients are determined precisely by the smallest eddies. Sij = ½ (∂ui/∂xj + ∂ui/∂xi) ~ v /. This leads to the estimate  ~  (v / Since the dissipation of turbulence energy  must coincide with the production of turbulence, we have u3/l ~ (v / We also know that the Reynolds number, determined from the characteristic values of the velocity and the size of the smallest eddies, must be of the order of unity: v/ ~ 1. Combining the last two relations, we find l ~ 1/Re3/4 or, as well as v/u ~ 1/Re1/4, или v = , where Re is the Reynolds number calculated from the size of the largest vortices, Re – ul/ . In a conventional wind tunnel experiment, the Reynolds number can be of the order of Re=103 at l=1 sm. From the above formulas, one can easily estimate the size of the smallest eddies, we obtain  mm. Suppose most of the energy of the global flow dissipate at the level of the smallest eddies, which have a size less than a millimeter. Obviously, the turbulent flow at the level of small eddies has a very fine structure, and the larger the value of the Reynolds number, the smaller the size of the smallest eddies. Two turbulent jets at two different Reynolds numbers are shown in the fig. 18. As the Reynolds number increases, the size of the smallest eddies decreases. Thus, the larger the Reynolds number, the finer the turbulent flow at the level of the smallest eddies. The characteristic size of the smallest eddies  and velocities v is called the Kolmogorov scale, l is the integral scale. It should be noted that all of the above estimates appear to agree surprisingly with experimental data. In fact, these results appear to be the most reliable in the theory of turbulence. Fig. 18. Influence of the Reynolds number on the structure of turbulent jets. The lower jet has a higher Reynolds number (P.E. Dimotakis - Physics of Fluids, California Institute of Technology) So, Kolmogorov's time, length and scale of velocities are indicated as τη, uη ′, and η, and are defined as [52]: τη = (ν /ε)1/2; η =(ν3/ε) 1/4 ; uη′ =(νε)1/4 (4.4) According to Kolmogorov, the directions of displacement of large scales disappear in the chaotic process of scale reduction, when energy is transferred to successively smaller eddies. Kolmogorov hypothesis of local isotropy indicates that at sufficiently high Re, small-scale turbulent flows are statistically isotropic. Here, the term "local isotropy'' means small scale isotropy. Large-scale turbulence can still be anisotropic. The first Kolmogorov similarity hypothesis indicates that in every turbulent flow in a sufficiently high Reynolds number, the statistics of small-scale motions have some universal form, which is exclusively determined and  through three equations (4.4) and: uη′/= 1/τη; Re = uη′/ν = 1 The fact that, according to Kolmogorov, Re = 1 is consistent with the statement that the cascade of eddies continues to smaller and smaller scales until Re decreases sufficiently for the dissipation to be effective. Initially, the flame acceleration is responsible for the geometric increase in the flame area caused by large-scale structures in the flow, which arose, for example, due to the interaction of the FF with obstacles. At the same time, when the acceleration of the flame continues and the flow of unburnt gas is turbulized, the processes of mass and momentum transport into the flame are accelerated. An increase in the combustion rate further contributes to the acceleration of the flame. The structure of a flame brush is highly dependent on the intensity of the turbulence and the characteristic scales of combustion and turbulence. If the time scale of combustion is less than the turnover time of the turbulent eddy, the flame brush can be modeled by a structure consisting of a large number of different laminar flamelets. If the combustion is slow compared to the eddy turnover time, then the reaction zones in the “flame brush” become dispenced and require the use and comparison of different model approaches. A scheme of turbulent combustion regimes, known as the Borchi diagram (Fig. 4.6), illustrates the influence of the Karlovitz and Damköhler criteria on turbulent combustion. When the fluctuations of the unburnt gas u 'are less than the laminar combustion rate SL, the final effect of turbulence is to distort the shape of the laminar flame without disturbing the internal structure of the flame. The different zones in fig. 19 are based on conditional dimensions of coordinates and only give an estimate of the order of magnitude of the transition limits. The transitions between combustion modes within these limits do not occur abruptly. This is an area of intensive research devoted to the establishment of new criteria in order to more accurately characterize and describe the transitions between combustion modes. In this case, we point out that in most practical calculations of turbulent combustion, combustion models are valid only for a certain combustion mode. It follows directly from the above that the experimental values measured using a particular setup may not necessarily be reproduced under the conditions of another setup, even if both plants are of the same type, for example, in a static fast-flood reactor. Fig. 19. Borja diagram. Combustion areas [53]. The original English terminology has been retained. Obviously, the experimental results (for example, ignition delay times) relate only to the installation by which they were obtained, since the behavior of gas flows arising in a reactor when a gas mixture is poured into it can differ significantly even for installations of the same type. This situation was described by one of the authors in [54], and the main results of this work are presented below. It should be noted that distributed combustion in eddies was investigated in [55, 56] to determine the effect of such flows on the environmental friendliness and combustion efficiency in a gas turbine with ultra-low NOx emissions. The authors of [55, 56] have shown that the eddy flow provides a high speed regime in the core of the combustion chamber and, accordingly, better mixing of components. In [54], a deeper understanding of the effect of tangential gas puffing was demonstrated, both on the regularities of gas combustion and on the interpretation of experimental results. As is clear from the above, the study of the propagation and stabilization of a flame in a rotating combustible gas is of interest both for a deeper understanding of the laws of turbulent combustion and thermal ignition in turbulent flows implemented in various technical devices. The specific effects of a eddy flow observed during the propagation of a flame in rotating flows can also manifest themselves in the modes of thermal ignition in eddy gas flows. The problem of flame propagation and stabilization in a separate eddy flow has received considerable attention from researchers [57–59]. Experiments carried out in [57] showed that when the mixture is ignited at the maximum distance from the axis of rotation, the resulting flame chamber in the form of an irregular segment moves to the axis of rotation. Having reached the center, the seat of the flame is transformed into a body of revolution. The flame propagation speed is approximately equal to or less than the apparent speed in the medium at rest. The movement of the flame to the center of the reactor is easily explained by the presence of centripetal forces leading to the appearance of a radial convective flow in a system in which there are regions with very different densities (initial mixture and combustion products). In [58], flame extinguishing in a rotating gas was studied. The mixtures of methane and air were used. The mixture was ignited with an electric spark in the center of the vessel. Experiments have shown that the flame propagates only up to a certain critical radius Rcr and diminishes. The authors of the work explain the flame extinguishing effect by the fact that the processes of combustion and cooling of the rotating gas are accompanied by complex radial movements of fresh gas and combustion products, which, in turn, lead to gradients of the gas rotation speed along the radius. This gradient can cause turbulence or flame extinguishment. The most detailed review of the publication on the problem of combustion in eddies can be found in [59]. Thus, it follows from the publication that the propagation of flame in eddy flows of combustible mixtures has a number of specific effects due to the presence of centripetal forces in the rotating gas. Unfortunately, their effect on the self-ignition of gas eddies arising in real flows, including flows with developed turbulence, under conditions with strongly differing temperatures in different regions of the flow has hardly been studied. The radial stratification of the eddy flow in terms of density and the arising convective flows during the eddy flow of gas and two-phase mixtures should affect both the appearance of point of origin of thermal ignition and the development of the process of flame propagation from them (including the induction mechanism of Ya. B. Zel'dovich [60]). These flows significantly change the temperature field and heat-exchange conditions. In a number of technical installations, for example, a hypersonic ramjet, these effects can turn out to be very important from the point of view of improving the ignition conditions and intensifying the combustion of fuel in the air flow. Therefore, their study seems to be practically valuable. In this regard, in [54, 61], the task was posed to fill the gaps in the understanding of ignition processes in difficult conditions of a eddy flow. In other words, it is also necessary to study experimentally the effect of radial stratification of a eddy flow on self-ignition and the resulting combustion of fuel-air mixtures. Experimental part The peculiarity of the experimental setup consisted in the method of creating a rotating eddy of the gas mixture. In [57, 58], a rotating gas flow was formed due to the rotation of the reactor around its axis. This technique makes it difficult for the long-term heating of the reactor, which is necessary for the study of thermal ignition, and cannot provide high rates of tangential flow. In [15], the rotation of the combustible mixture was carried out in a stationary heated reactor due to the swirling of the gas flow with tangential puffing into the evacuated vessel. The installation diagram is shown in Fig. 20. Fig. 20. Installation diagram: 1 - reactor, 2 - electric furnace and thermal insulation, 3 - high pressure chamber (HPC), 4, 5, 6 - electric heater, thermal insulation and thermocouple, measuring the HPC temperature, 7 – voltmeter. 8 - mixing chamber, 9 - valve, 10 - electromagnetic valve, 11 - pressure sensor and registration system, 12 - inlet port, 13 - thermocouple, 14 - voltmeter, 15 - thin thermocouple made of tungsten and perrhenic wires with a diameter of 30 microns. The bypass vessel, heated reactor and supply communication lines were made of stainless steel. Both vessels were connected by a communication equipped with an electromagnetic valve. The time during which the valve can be open is set from 50 ms to several seconds. The inner diameter of the reactor was 14 cm. The reactor could be used in two modifications: as a spherical chamber, in this case, only pressure registration is possible, and as a spherical-cylindrical vessel. In this version, high-speed video filming was carried out through a quartz window 14 cm in diameter and 2 cm thick. The experimental technique and measurement of the ignition delays did not differ from the technique adopted for a conventional bypass installation. The ignition was registered with a pressure sensor, thermocouple, or photodiode. The reactor was evacuated and heated to a predetermined temperature. A pre-prepared mixture was fed into the bypass vessel from the mixer, the time for mixing the gases was at least 48 hours. During the experiment, pressure was recorded with a "Courant DI" pressure sensor and an information collection system based on an analog-to-digital converter. The sampling frequency in all experiments was 1000 Hz. Results and discussion Experiments carried out with well-studied mixtures, such as air stoichiometric mixtures of methane, propane, pentane and rich mixtures of hydrogen with air, showed a discrepancy between the measurement results and the known experimental data. First of all, the ignition delays turned out to be much shorter than those expected at a given temperature of the reactor walls. The results also showed that the minimum reactor temperatures at which autoignition occurs are significantly lower than their literature values. For example, an air mixture containing 40% hydrogen ignited at a reactor temperature of only 558 K (285 0C) instead of 773 K (500 0C) at a pressure of about 1.0 atm. The stoichiometric air mixture of propane ignited at a reactor temperature of 630 K (357 0C), while, according to the literature data given in [15], this temperature is 743 K (470 0C). The corresponding oscillograms of ignition are shown in Fig. 21. Fig. 21. Oscillograms of pressure obtained by passing a mixture of 40% H2 and 60% air (a) and stoichiometric air mixture of propane (b) into a heated reactor. Wall temperature: 1 - 558 K, 2 - 552 K; 3 - 630K; 4 - 620 K. The obtained effect of lowering the temperature of thermal ignition in a eddy flow does not fit into the existing concepts of self-ignition of combustible gases and requires an explanation of its mechanism. Fig. 22. Records of thermocouple signals recorded in the center of the reactor at different pressures P in the HPC. Reactor and HPC temperature - room temperature; ; 1 - P = 0.3 MPa, 2 - P = 1.0 MPa. The valve opening time is 0.05 s. Fig. 22 shows thetemperature-time relationship recorded in experiments in which air was introduced into an evacuated reactor at room temperature. The pressure in the HPC is 0.3 and MPa. As you can see, the higher the pressure in the HPC, the higher the temperature peak in the center of the reactor. It was shown that the absolute value of the temperature peak in the heated reactor is significantly higher than its value in the reactor at room temperature. The ratio of the temperature at the peak to the initial temperature of the reactor (in degrees K) decreases slightly with an increase in the temperature of the latter. Experiments show that temperature peaks are also observed when the high pressure gas is injected not into an evacuated reactor, but into a reactor containing the low pressure gas. Thus, the tangential injection of gas into the reactor leads to the formation of an unsteady eddy flow, the temperature distribution in which reaches a maximum in the center of the eddy (see below). To obtain additional information on the processes occurring during the filling of a combustible mixture into a heated reactor and its spontaneous combustion, a series of experiments was carried out using high-speed video filming. The shooting was carried out with a Casio Exilim EXFH25 camera with a frequency of 1000 fps and a high-speed FANTOM camera with a speed of 10,000 fps. Examples of such video filming in the form of several separate frames are shown in Fig. 23 and 24. Fig. 23. Development of a point of origin of thermal ignition in time. Mixture - air + 4% C3H8. The temperature of the walls of the reactor is 630 K (357 ◦C): (a) t = 2 ms; (b) 5; (c) t = 9 ms. High-speed footage of the central region of the reactor is demonstrated in fig. 24. It turned out that in the case of tangential puffing of the mixture into a heated reactor and the formation of a swirling eddy flow, ignition always occurs in the central region, and only then does the flame propagate throughout the volume of the vessel. In contrast to the results of work [58], in which spark ignition of the mixture was carried out in a rotating reactor, flame extinguishing was not observed. In all the mixtures considered, once having appeared in the center of the reactor, the flame spread throughout the entire volume without extinguishing. Obviously, a certain radial temperature distribution is established in the reactor by the time of ignition: in the central region, the highest temperature at which self-ignition occurs; at the periphery, in the near-wall region, the temperature corresponds to the temperature of the walls of the reactor Fig. 24. The center of thermal ignition in the central region of the reactor at different moments in time. The difference between frames is 0.1 ms. Mixture - 40% H2 + 60% air. Reactor wall temperature is 558 K (285 0C) This suggests that the radius of the region heated enough to create conditions providing the induction mechanism of flame propagation proposed by Ya. B. Zeldovich [60] is greater than the critical radius rcr [58]. The glow of the cooling products confirms the fact of the eddy flow in the reactor. Shooting the central region of the reactor with a high-speed camera showed that at the moment of thermal ignition, the gas in it is practically stationary. Such a picture of thermal ignition differs significantly from that observed in a static setup with an axial filling of the mixture under study [48, 62], i.e. in the absence of rotation of the gas mixture. The experiments carried out on the high-speed registration of thermal ignition without rotation showed that the primary ignition source arises on the surface of the reactor. At the same time, the place of origin of the focus changes in each subsequent experiment under the same conditions (Fig. 25a). Fig. 25. a) - Video images of primary ignition centers in stoichiometric mixtures of n-pentane - air in four successive experiments at a wall temperature of 1 - 650K; 2 - 643K; 3-645K; 4-649K. 600 frames/s, P = 1 atm. The numbers in each image correspond to the sequential number of the experiment. b) - Sequences of video images of the spatial development of thermal ignition in stoichiometric mixtures of n-pentane - air at a reactor wall temperature of 649K, 600 frames/s. P = 1 atm. The numbers on the frames correspond to the sequential number of the video image. c) Diagram of the experimental setup: (1) reactor, (2) electric heater, (3) thermal insulation, (4) valves, (5) mixer, (6) digital video camera, (7) optical window, (8) hemispherical insert, (9) pressure transducer, (10) ADC data acquisition system, (11) digital voltmeter, and (12) spark ignition circuit. This means that the reactivity of different parts of the surface changes from one experiment to the next. Obviously, the observed character of the onset of combustion corresponds to the mode of ignition by a heated surface [50, 62]. The main feature of the ignition process is that ignition occurs in separate areas of the surface, at the same temperature of the reactor surface. Figure 25b shows video sequences of the spatial development of ignition recorded at a rate of 600 frames/s in a stoichiometric mixture of pentane with air at a reactor wall temperature of 620 K, which correspond to the development of one of the point of origin shown in Fig. 25a. It can be seen that, first, a hemispherical flame develops from the point of origin, which loses its symmetrical shape as new combustion centers appear. In the presented series of experiments, the induction period was at least 7 s. Therefore, steady heating of the combustible mixture, according to direct measurements [54, 61], was practically ensured, since the rapid filling of the mixture and the resulting turbulization reduce the heating time of the mixture. Consequently, the combustion process begins on the surface of the steel reactor even under conditions of practically steady heating of the combustible mixture. Thus, the ignition of combustible mixtures in a heated reactor in a rotating stream is completely homogeneous. If there is no eddy flow, or there is a different flow structure, then in the installation shown in Fig. 25V, thermal ignition is ununiform, i.e. thermal ignition modes are qualitatively different. These regimes are obviously not determined by the kinetics of the reaction, which remains the same. They are only related to gas dynamics. It should be noted that, after studies carried out by the high-speed filming method, thermal ignition in a heated reactor, which was considered as a steady ignition in volume, turned out to be in fact the propagation of a flame from a primary focus of a chemical or thermal nature, depending on the experimental conditions. In the case of tangential puffing, the flow of the reacting gas outflowing from the bypass vessel at the speed of sound (at the initial moment of time) flows around the heated spherical wall of the reactor. According to estimates [54, 61], overloads of more than 100,000 g occur in the rotating gas. The appearance of centripetal forces inevitably leads to radial stratification of the reacting gas flow in terms of density. The first portions of the inflowing gas are heated very quickly (high flow velocity and low pressure, i.e., a very high thermal diffusivity). The warmest, that is, the least dense, gas masses appear in the center of the eddy [59], and the coldest ones - on the periphery, where fresh cold portions of gas continue to flow. Together with the radial stratification of the gas in terms of density, the temperature distribution is also observed. In the central region of the reactor, a slow-moving gas is collected, initially heated to the temperature of the reactor wall. Heat outflow from this area is difficult due to its remoteness from the reactor walls and low convective heat transfer. A further increase in the pressure in the reactor due to the continued puffing of a fresh mixture into it will lead to adiabatic compression and, consequently, heating of the combustible mixture in the central part to a temperature exceeding the wall temperature. Let us estimate this value of the gas temperature in the central region, at which thermal ignition occurs. Based on the condition of adiabatic compression, we have: Tk / Ti = (Pk / Pi) (γ − 1) / γ. Here, the index i indicates the initial state of the gas in the reactor, and the index k indicates the final state, γ is the ratio of the heat capacities. The available experimental data make it possible to make a reasonable estimate of the ratio of the Pk / Pi values. We will assume that the combustion of the mixture in the reactor will be complete if the central region of the reactor, in which self-ignition occurs, has a radius R not less than the critical flame extinguishing radius rcr, R ≥ rcr [58]. Therefore, as the initial pressure Pi of the mixture in the reactor, we will take the pressure of that amount of the mixture, which, being compressed to the final pressure Pk, will occupy the volume of the central region of the reactor, limited by the radius rcr. The temperature will correspond to the minimum temperature of thermal ignition taken from the literature sources. We will numerically estimate the Pk/Pi value using the example of a stoichiometric mixture of propane and air and a rich mixture of hydrogen and air. Oscillograms of pressure during spontaneous ignition of these mixtures are shown in Fig. 21b and 21a, respectively. It is known from the reference literature that the minimum temperature of thermal ignition of propane in air is T = 743 K (470 0C). In accordance with [23], we take the ratio of the specific heat capacities for this mixture γ = 1.369. Thus, taking into account that the minimum reactor temperature at which ignition occurs is 630 K (357 0C), it is easy to estimate the value of Pk / Pi ≈ 1.84. Arguing in the same way, let us numerically estimate the Pk / Pi value for a rich mixture of hydrogen and air. Proceeding from the fact that at atmospheric pressure the minimum temperature of thermal ignition of hydrogen is 773 K (500 0C), and the value of the ratio of specific heat capacities γ = 1.396, according to the data of [63], it is easy to estimate Pk / Pi ≈ 3.15. This local adiabatic heating of the test gas in the central region of the reactor causes the gas to ignite at a low temperature. To make sure that the observed effect was caused by the eddy rotation of the gas, control experiments were carried out in which the formation of the eddy motion of the gas was suppressed at the moment the mixture was poured into the reactor. For this, an annular rib was installed in the reactor in the transverse direction to the gas flow outflowing from the bypass vessel. The outer diameter of the ring was equal to the inner diameter of the reactor and was 14 cm, and the inner diameter was 11 cm. This barrier excluded the swirling of the reacting gas flow, without interfering with the turbulent movement of the medium and providing rapid mixing of heated and cold layers of gas, as well as convective heat exchange with the walls of the reactor. The suppression of the flow swirling of the combustible mixture led to the disappearance of the effect under consideration. The results of this series of experiments have convincingly shown that the effect of ignition of combustible mixtures at a low temperature is associated precisely with the eddy nature of the flow that occurs in the bypass installation with tangential filling of the mixture under study. Let us summarize the results obtained. The effect of thermal ignition of combustible mixtures at reactor temperatures significantly lower than the thermal ignition temperature was experimentally observed in a static bypass installation with a tangential inlet of the mixture under study. In this case, the difference between the temperature of the reactor and the temperature of thermal ignition can reach more than 150 K. This effect is primarily caused by the presence of centripetal forces that inevitably arise during the formation of a eddy gas flow. The result of the action of these forces on the flow is the radial stratification of the gas in terms of density and, therefore, in terms of temperatures. The rotational motion of the gas in a flow with a temperature gradient leads to the formation in the center of the eddy of a region with an increased temperature relative to the peripheral layers of the gas. In the central region, the hottest and least mobile gas is formed. In addition, it is well insulated from the walls of the reactor. Depending on the average temperature of the gas and the degree of pressure increase in it, this difference can reach several hundred degrees, which is confirmed by a significant decrease in the autoignition temperature of combustible mixtures in comparison with the values known from the literature sources. The pressure increase in the reactor caused by the mixture puffing leads to adiabatic compression and additional heating of the gas. The centripetal forces contribute to the fact that the heat, which begins to generate with the onset of a chemical reaction, is accumulates in the central region of the reactor, thus creating favorable conditions for thermal ignition. The study of the discovered effect can be important for understanding the mechanism of thermal ignition of turbulent flows in various technical devices. This effect can be used in a hypersonic ramjet to improve ignition conditions and intensify combustion. In addition, an emergency situation with the formation of eddy flows of combustible mixtures under conditions that would seem to exclude the possibility of their thermal ignition is possible in industry. The discovered effect of local adiabatic heating of the mixture under study can be used to measure ignition delays in the so-called intermediate temperature range and ignition delays of fuel-air mixtures, namely, between temperatures and delays characteristic of experiments in shock tubes and in bypass installations for initial pressures ≤ 1 atm. This range is practically not covered in the literature source, since the results of experiments in installations of adiabatic compression refer to pressures significantly higher than atmospheric, and the results of measurements in jet installations are very rare. Conclusions for Chapter 3 Experiments proved that spherical flames of lean (6–15% H2) hydrogen-air mixtures have a cellular structure. In mixtures containing 6–10% H2, flames propagate spherically symmetrically at the initial stage near the lower concentration limit. Then the gravity field distorts the shape of the combustion front. Flames of mixtures containing 10-15% H2 propagate spherically symmetrically. It is shown that the Boussinesq approximation is applicable to obtain cells with H2 <10%, taking into account the force of gravity. Calculations by the Boussinesq model in the absence of gravity do not allow the formation of cells. The use of the Navier-Stokes equations for a compressible medium makes it possible to describe the spherically symmetric mode of propagation of a cellular flame under microgravity conditions. It is shown that the analysis of experimental data on flame propagation in lean mixtures does not make it possible to distinguish between the calculation results using a two-dimensional model with and without convection. It has been shown experimentally that additions of isobutene С4Н8 in amounts below the lower concentration limit (up to 1.5%) lead to an increase, and additions of СО2 to 15% - to a decrease in the flame propagation rate in lean hydrogen-air mixtures. The reasons for the acceleration of combustion in the presence of a hydrocarbon additive are considered. It is shown that the detected glow inhomogeneities can be associated with the presence of acoustic waves by using the combustion of hydrogen-air mixtures (30% and 15% H2) as an example. It was found that the flame propagation rates in a stoichiometric hydrogen-air mixture with central spark initiation do not depend on the material of the inner surface of the reactor (stainless steel, TiO2, Ta, Pt) but depend on the shape of the inner surface of the reactor. It is shown that spark-initiated flames of lean hydrogen mixtures (8% - 15% H2 in air) pass through aluminum mesh spheres with a cell size of 0.04-0.1 mm2, while the flame of a mixture of 15% H2 in air is accelerated after passing through an obstacle. In the presence of an obstacle during the propagation of flame in mixtures of 10% and 15% H2, acoustic oscillations of the gas arise in the reactor. The onset of oscillations occurs earlier in time in the presence of a sphere of a smaller diameter. The flame of a mixture of 7.5% H2 in air does not pass through the mesh spheres. It was found that the flame of a mixture of 8% natural gas with air passes through the mesh spheres. However, after the obstacle, the flame speed remains the same, while acoustic oscillations are not observed. It is shown that the active centers of combustion of methane and hydrogen, which determine the propagation of the flame, have a different chemical nature. In a static bypass installation with a tangential inlet of the mixture under study, the effect of thermal ignition of combustible mixtures at reactor temperatures significantly lower than the thermal ignition temperature was experimentally discovered. In this case, the difference between the temperature of the reactor and the temperature of thermal ignition can reach more than 150 K. This effect is caused primarily by the presence of centripetal forces, which inevitably arise during the formation of a eddy gas flow. The result of the action of these forces on the flow is the radial stratification of the gas in terms of density and, therefore, in terms of temperatures. In the central region, the hottest and least mobile gas is formed and. In addition, it is well insulated from the walls of the reactor. The possibility of mixing it with fresh cold masses of gas is excluded. The pressure increase in the reactor caused by the mixture puffing leads to adiabatic compression and additional heating of the gas. The centripetal forces contribute to the fact that the heat, which begins to generate with the onset of a chemical reaction, is accumulated in the central region of the reactor, thus creating favorable conditions for thermal ignition.

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