 Нижану. Она только что прошла, но почему? Good morning dear colleagues, let me introduce myself. My name is Viktor Golub. I'm from Institute of High Temporation Academy of Science because there is not chairman. I have to start myself. I appreciate very much the possibility. Just a moment. I appreciate very much the possibility to meet with you today and I'd like to tell you about acceleration of the spherical expanding hydrogen air flames. Acceleration of the flame fraud is a very complex process, influenced by very different phenomena. Just, sorry, some problems at the moment. Excuse me, 5 minutes ago it was very good, but nothing, some problem. Nevertheless, I will try. Immediately after initiation, the flame front is smooth and spherical, but with increasing size, the flame front is deformed and accelerated. It's because there are a lot of different instability, thermal diffusion, Daryl-Andau instability, Ray-Tail instability and turbulence. When the flame front reaches a critical value, its acceleration becomes first non-themed, same severe and then self-similar. Пекле-Намба, it is ratio of radius of a front and flame front thickness. Up to date, there are a lot of approaches to modeling the acceleration of the flame. Analytical models, fractal approach, analysis of individual instability, interaction of the flame front with turbulence, statistical turbulence approach of Kalmogorov-Обухов and numerical methods. Flame-Fretian numerical methods, Reynolds average, Navier-Stokes equation, the methods of large vertices and direct numerical simulation. The motivation of this work is the velocity of flame propagation is important factor for risk assessment. The knowledge of acceleration of spherical expanding hydrogen-air flames in big volume is limited. And following task we must solve, generalization of this knowledge about influence of individual physical phenomena on the acceleration of spherical premixed flames, experimental determination of the flame acceleration in a large volume. The description of the acceleration of the spherical expanding hydrogen-air flames by means Kalmogorov-Low. Ламинер-боргинг velocity. It is very important value. It is fundamental value, depending on the composition of the fuel mixture, which is defined as a velocity of the flame element in stationary combustible gas. As a result of thermal expansion during combustion, the visible flame velocity exceeds the normal combustion rate as a coefficient of thermal expansion. It is coefficient of thermal expansion. Real effect of flame curvature on chemical kinetics, diffusion, thermal conductivity and flame velocity is possible obtained with help of Markstein approach. On this graph you can see here dependence of Markstein lengths on equivalent ratio. This part of graph is lean mixture, less than one year. This part of graph is rich mixing. Markstein lengths, it is a dimensional parameter, which connects the flame curvature and boarding rate. For different combustible mixtures, the effect may have an opposite sign. When the front of flame is deformed, its velocity changes. You can see here, sigma t, it is areas of the corvette front and it is line, it is areas of the flat one. But nevertheless, the amount of combustible mixture passes through the corvette front the same as through the flat front. Это area of corvette front, it is laminar velocity, it is area of flat front, it is turbulent velocity. And we can obtain equation for turbulent velocity and the velocity of the deformed flame front exceeds the velocity of the flat front as the ratio of the areas of corvette front and the flat one. It is need to have some equation describing the turbulent flame velocity taking into account various factors. And this equation includes, of course, very well factor, thermal expansion factor, then diffuser of thermal stability, velocity coefficient, derriere landau instability, velocity coefficient, relay terrain stability, velocity coefficient and turbulent pulsation velocity coefficient. Here you can see the initial stage of informed spherical spread of the flame. It is sharing image of spherical flame front down moment for millisecond. And in this case, it is only one coefficient, it is real coefficient, another equal one. Immediately after initiation, the propagation of spherical flame is determined by the normal flame velocity, the thermal expansion of combustion products and curvature of the front. Different instability lead to different patterns of flow. You can see sharing image of spherical flame propagation for millisecond and 25 milliseconds. Depending on kind of type of instability and condition, the patterns can be informed of cells different size or oscillation different fluctuation. To determine the measure of diffuser of thermal instability, as usual, use so-called Lewis Criterion. Criterion, it is ratio of thermal diffusivity to the diffusion coefficient. You can see here expression. In this case, when Lewis more than Lewis critical, the transfer, you can see red and blue line, heat diffusion and mass diffusion. In this case, the transfer of heat is more intense than the transfer of reagent. We can in this case stable case of instability. When transfer of the mixing reagent is more intense than heat transfer, we have unstable kind of diffuser of thermal instability. But what is limiting value of this Lewis Criterion? The limiting value of Lewis Criterion is determined through the Zeldowich Criterion. You can see, as usual, it's about 0.8 value. And Zeldowich Criterion, it is ratio of thickness of the heating layer and chemical reaction layer. The next surface factor of diffusive thermal instability. It is one of these factors. It is when Lewis number is less than critical value. You can see factor here. The formula approximates, but is suitable for most of estimation. But when Lewis number is above the critical value, it is sort of factor of diffusive thermal instability. You can see here, target pattern of spherically expanding clean butane flame at 30 atmosphere. It's another scale. In this case, you can see this value 1. In this case, when Lewis number is above critical value, it's possible to say that diffusive thermal instability is manifested in the vibrational modes and makes no significant contribution to the surface area of the flame. Next, instability Darya Landau. You can see here very simple sketch, deviation of flow lines, leading to Darya Landau instability. And it is a positive feedback scheme. A sense of Darya Landau instability is very simple. Increase in the flame, flame convex increases to the flame velocity, which is stored increases the convex of flame. Positive, usual positive feedback. Landau in 1944 showed that flame becomes unstable when Reynolds number more than 1. Of course, it's a surprise, but he suggested the flame is infinity sin. Стратов Лебрович in 1966 showed that flame becomes unstable when Reynolds number more than 1,000. He suggested, he showed that flame thickness and velocity depends on chemical kinetics, diffusion and thermal conductivity. This process prevents the development of perturbation with small wavelengths. As a result, the decreasing flame thickness promotes the hydrodynamic instability. Next surface factor for Darya Landau instability you can see here. It's obtained from different question. Real characteristic times and special scales of Darya instability growth presented in this table. It is different column, different concentration of hydrogen. It is minimal time of Darya Landau instability growth. You can see that value are calculated by the algorithm proposed by Stratov and Librovich. With increase in hydrogen concentration, Darya Landau instability begins early. You can see here very small time. It is a peninsula of instability of spherical expanding flames. This graph shows the range of unstable modes for given Peclet number. As the size of flame grows, the Peclet number increases, correspondingly more harmonic oscillations are amplified. It is needed to obtain dependence of critical Peclet number on Markstein number. It is possible to use two types. We know two types of these dependence. One of them you can see here from this graph. Another one from this equation. But ten times difference between Peclet number from this and this possibility case. Why, what is the reason of this difference? The reason is because Markstein number, it is Markstein length divided on the thickness of flame. But you can see here on this graph the flame thickness very, very different value. It is possible obtained in literature. And it is reason why the critical Peclet number depends on the Markstein number. Markstein number depends on thickness of flame front. But the thickness of the flame front can differ by the factor of tens. It is our experimental setup used in this investigation. It is very 900 meters. It is some envelope of 4.5 meters and sub-bubble of 5 liters. This slide shows an image of different flame front propagation in sub-bubble. Relative instability occurs at the interface between two fluids of different densities when subjected to acceleration in the direction from the lighter to the heavier. It is need to obtain the surface factor for this value. You can see here very, very important Borgi diagram is useful classification of turbulent combustion regimes. You can see here different picture with different regime and flame propagating regime is terms of turbulence intensity and another kind of special coefficient connected with this problem. Of course, there are a lot of models for integration of flame with turbulence. It is some critical review of this model. Runs describe large-scale and temporal variations of the mean flow velocity that require model of influence of turbulent fluctuation on this variation. Large AD simulation is simulation technique that deals with transport equation averaged from the small spatial volume using a low pass filter. The less equation resolves turbulent edges larger than the filter width. Then there is solution of transport equation using a numerical grid that is sufficiently fine to resolve the smallest turbulent edges and mixture non-uniformity. BML, approach of modeling premixed turbulent combustion developed by Bray, Mos and Libya by assuming that various in mixture characteristic are localized to flame leads. There is a result, these models are quite complex and complex adapted to the solution of a specific problem under strictly limited condition. There are more simple estimates of the effects of turbulence on the flame front. First of all, it is shocking in 1943 when pulsation more than laminar velocity. In this case, the flame velocity proportional to turbulent pulsation this coefficient. Another case, when turbulent pulsation less velocity turbulent pulsation less than laminar velocity in this case it's a Scarlet equation the flame velocity is proportional to the square rod of the turbulent pulsation. Very important part is fractal. Фрактал development of the flame surface with spherical flame from propagates you can see here it is first, second on this picture you can see three scale of in gamaganges and with the growth of the flame the number of scales increases. Acceleration of flame caused by fractal structure of flame front. Here you can see the area of turbulent red line area of turbulent flame front and green line it is area of laminar turbulent front. The volume of burned gaze enveloped by wrinkling sphere grows proportionally to the wrinkling flame surface. Of course you can see here substitution the power acceleration equation obtained by Gastin will find the flame area of fractal growth with the exponent 7th thought that means one thought fractal excess. It's simple to obtain the wrinkling flame surface equation and you can see here difference between flame area of flame turbulent and area of flame laminar one thought it is fractal excess fractal excess arises in turbulent flame when later are treated as passive front passive front moving through the Kalmogorov flow field. Of course there are different reports devoted to numerical simulation of fractal structure. You can see here succession position of the flame front showing fractal like structure it was obtained flame tracking numerical method and this graph shows acceleration exponent and fractal excess calculated by different methods for different degree of expansion you can see it is different degree of expansion sigma it is value of exponent the value of exponent at fractal excess depend both on the properties of combustible mixture and on the method of results interpretation now you can see fractal structure dynamics it is our experiment on the flame front development it is saw bubble hydrogen air mixture lean mixture 10% hydrogen you can see different time moment it is 25 millisecond there are very interesting similarity of the large spherical flames and other turbulent objects on this table you can see different gases different mixture and clothes and something in ocean but all of them it is possible to express this this function similarity of low low governing propagation of large spherical flames and the transfer of velocity pulsation in the atmosphere in the ocean and the temporal dependence of the flame radius is nearly identical for all phenomena discussed that relates to Kolmogorov theory it is Kolmogorov scale Kolmogorov time but nevertheless for all of this case it is one one low conclusion spherical propagation of flame is a multi-stage process that cannot be described by single universal theory during the propagation of the flame various front instability occurs which at a certain stage make the main contribution to acceleration аналитик solution of varying degrees of approximation unknown which describe various type of instability there are many models for numerical simulation created by solving specific tasks and completely unsuitable for related problems approximate engineering estimation methods give a satisfactory accuracy to the results a variety of combination of similarity criteria and fundamental quantities characteristic of different gas mixture causes many scenarios of flame acceleration when flame reaches sufficiently large size it begins to accelerate according to the power low of course there are a lot of attempts to describe flame acceleration with power low you can see here some report hints of the acceleration of the flame front is approximately by power low with different exponents in many works also attempt to cover the wide range of flame scales with the power dependences but satisfactory coincidence is observed only in small segments what function describe the initial stage of flame acceleration you can see its results of our experiment some analysis of the application of power of function with constant exponent it is power of function with constant exponent without initial distance shift it is with initial distance shift but nevertheless in some segments the flame moves faster it is not so good there are you can see results paper for Kim 2015 it is acceleration dependent on Pecler very interesting results you can see too much oscillation it is our experiment approximately the same the exponent calculated as the ratio of logarithm of radius and time changes markedly as diameter of the flame increases the pre-exponent and its dimensionality also changes the problem you can see here all of this point another dimensionality it's impossible when value acceleration exponent variation A pre-exponent value variation A value variation dimension variation it is incorrect use of equation the use of power function to describe the acceleration of flame in transient mode forces us to solve incorrect problem of determining the pre-exponent it is our results the dependence of radius of flame front on time in the initial stage you can see uneven flame propagation with acceleration and deceleration it is so wobble hydrogen air mixture of course you can see here flame front velocity non monotonic from 0.8 up to 1.9 and relative instability condition change you can see at what number it is our case at what number is constant but you can see here field with positive and negative acceleration and at initial stage the condition for development of relative instability arrives and then decrease it is our infrared image of sequence of hydrogen air flame propagation concentration 50% cylinder diameter 1.5 meter high 2.4 meters it is image sequence at hydrogen air flame propagation up to 50 milliseconds the hemispherical flame propagation is absorbed in horizontal direction slows down in vertical direction decrease slows down in vertical decrease now it is comparison of flame front propagation with literature done the data of near stoichiometric hydrogen air mixture large scale we compare it with the data obtained at different states stands of different times unfortunately data of flame propagation in large volume of lean hydrogen mixture are not available but it is very important for point of some explosion here you can see for different hydrogen concentration dynamic of flame propagation in various lean hydrogen air mixture it is 30% 20% 50% and very lean 12% flame velocity strongly depends on the hydrogen content and there are two stages hemispherical stage and quasi parallel flame front on the left graph you can see dependence of flame position on time at hemispherical propagation in all cases with exponent close to 1.1 on the right graph you can see dependence of the flame position on time at quasi planar propagation the exponent close to 3 the flame is accelerated by power low with a constant exponent both in hemispherical and quasi planar stage of flame propagation for exponent increases monotonically with increasing hydrogen concentration here you see some attempt of application of low to dynamics of flame front it is black line it is case when velocity of specific velocity of turbulent energy dissipation is constant you can see that constant value of specific rate of turbulent energy dissipation assumes the flame propagation only by power low with exponent 1.5 so specific dissipation rate of turbulent energy cannot be constant and you can see some equation for specific rate of turbulent energy dissipation dependence on time here it is possible obtained value and it is possible obtained value of specific velocity of dissipation turbulent energy specific rate of turbulent energy dissipation makes it possible to describe flames expanding in accordance with power low with exponent different from 1.5 you can see here acceleration of flame with variable specific rate of turbulent energy dissipation you can see here very good results summary the series of experiments of propagation of the flame front in hydrogen air mixture of the various composition in cylindrical shell with volume 4.5 meter and 5 liter so bubble was carried out propagation of the flame front was detected with infrared video registration and sharing visualization the dependence of the position of the flame front on time for various gas mixture and characteristic picture of the flame front are obtained at the initial stage of flame propagation both acceleration and acceleration occurs in this case the condition of the development of relative instability arise and then decrease Results of large scale experiments with lean mixture in cylindrical envelope demonstrate flame acceleration by power low with constant exponent different from 1.5 interpretation of the results by the means of turbulent gas flame acceleration model based on the Kalmogorov-Obukhov low revealed the need for correction this model the model was supplemented by variable specific rate of turbulent energy dissipation which allowed the model dependencies in accordance with experimental date thank you because there is not chairman oh it's nice to meet you