3. SPREAD OF FLAME IN GAS MIXTURES

Speed flame spread during the combustion of solid, liquid and gaseous substances, it is of practical interest in terms of preventing fires and explosions. Let us consider the speed of flame propagation in mixtures of flammable gases and vapors with air. Knowing this speed, it is possible to determine safe gas-air flow rates in a pipeline, shaft, ventilation unit and other explosive systems.

3.1. FLAME SPREAD RATE

As an example in Fig. Figure 3.1 shows a diagram of exhaust ventilation in a coal mine. From the drifts of mine 1, a dusty mixture of air and coal dust, and in some cases – methane released in coal seams. If a fire occurs, the flame front 3 will spread towards the drifts 1. If the speed of movement of the combustible mixturew will be less than the speed of propagation of the flame frontAnd relative to the walls of the tube, the flame will spread into the shaft and lead to an explosion. Therefore, for normal operation of the ventilation system, it is necessary to comply with the conditions

w > u.

The speed of removal of the explosive mixture must be greater than the speed of propagation of the flame front. This will prevent flames from entering the mine shafts.

Rice. 3.1. Scheme of flame propagation in the mine:

1 – shaft; 2 – pipeline; 3 – flame front

The theory of flame propagation, developed in the works of Ya.B. Zeldovich and D.A. Frank-Kamenetsky, is based on the equations of thermal conductivity, diffusion and chemical kinetics. Ignition of a combustible mixture always begins at one point and spreads throughout the entire volume occupied by the combustible mixture. Let's consider a one-dimensional case - a tube filled with a combustible mixture (Fig. 3.2).

If the mixture is ignited at one end of the tube, then a narrow flame front will spread along the tube, separating the combustion products (behind the flame front) from the fresh combustible mixture. The flame front has the form of a cap or cone, with its convex part facing the direction of the flame movement. The flame front is a thin gas layer (10 -4 ÷10 -6) m wide. Chemical combustion reactions take place in this layer, which is called the combustion zone. The temperature of the flame front, depending on the composition of the mixture, is T= (1500÷3000) K. The released heat of combustion is spent on heating the combustion products of the fresh combustible mixture and the walls of the tube due to the processes of thermal conductivity and radiation.

Rice. 3.2. Scheme of flame front propagation in a tube

When the flame front moves in the tube, compression waves arise in the combustible mixture, which create vortex movements. Swirls of gases bend the flame front without changing its thickness and the nature of the processes occurring in it. On a unit surface of the flame front, the same amount of substance always burns per unit time . The value is constant for each combustible mixture and is called the mass burning rate . Knowing the flame front areaS, you can calculate the mass of a substance M, burned in the entire combustion front per unit time:

Each element of the flame front dSalways moves relative to the fresh mixture in the direction of the normal to the flame front at a given point (Fig. 3.2), and the speed of this movement:

where is the density of the fresh combustible mixture.

Magnitude is called the normal flame propagation speed and has the dimension m/s. It is a constant value of the combustion process of a given mixture and does not depend on the hydrodynamic conditions accompanying the combustion process. The normal speed of flame propagation is always less than the observed speed And, that is, the speed of movement of the combustion front relative to the walls of the tube:

u n< u .

If the flame front is flat and directed perpendicular to the axis of the tube, then in this case the observed and normal flame propagation speed will be the same

u n = u .

Area of ​​convex flame frontS issueAlways more area flat frontS pl, That's why

> 1.

Normal flame propagation speedu nfor each combustible mixture depends on the admixture of inert gases, the temperature of the mixture, humidity and other factors. In particular, preheating the combustible gas increases the speed of flame propagation. It can be shown that the speed of flame propagationu nproportional to the square of the absolute temperature of the mixture:

u n .= const · T 2.

In Fig. Figure 3.3 shows the dependence of the speed of flame propagation in the combustible mixture “air - carbon monoxide” depending on the concentration of CO. As follows from the graphs above, the speed of flame propagation increases with increasing temperature of the mixture. For each temperature value, the flame propagation speed has a maximum in the concentration region carbon monoxide CO equal to ~ 40%.

The speed of flame propagation is affected by heat capacity inert gas. The greater the heat capacity of an inert gas, the more it reduces the combustion temperature and the more it reduces the speed of flame propagation. So, if the mixture of methane and air is diluted carbon dioxide, then the speed of flame propagation can decrease by 2÷3 times. The rate of flame propagation in mixtures of carbon monoxide with air is greatly influenced by the moisture contained in the mixture, the presence of soot particles and admixtures of inert gases.

Rice. 3.3. Dependence of flame propagation speed

on the concentration of carbon monoxide in the mixture

A change in the shape of the flame significantly affects the nature of combustion, as it is associated with a change in the front surface. The size of the flame surface is the main factor determining the burning rate of a system of a given composition. This follows from the fact that all sections of the flame, regardless of their shape, are equivalent provided that the radius of curvature of the flame is much greater than the width of its front, i.e. in almost all important cases. With an increase in the surface of the flame, the combustion process intensifies, and the total amount of substance burned per unit time increases. A change in the shape of the flame is usually associated with the movement of gas near the combustion zone, its turbulization; in this case, the flame front is divided into a number of small foci and its total surface increases. This feature is used, for example, to intensify the combustion process by artificial turbulization of the burned gas.

Let's consider what shape a flame acquires spontaneously when spreading through a stationary flammable medium in the absence of influence on it external forces– indignation. Since the medium is homogeneous, all directions are equal and the speed of the flame along them is the same. In this case, the flame front propagating from a point source will have the shape of a spherical surface of continuously increasing radius. When a spherical flame propagates, the expansion of the gas leads to the fact that the original unburned medium will be pushed to the periphery. However, the gas does not turbulize, the speeds of movement of both the gas and the flame are the same in all directions, the shape of the flame, and at constant pressure, its speed remains unchanged.

Another characteristic mode of propagation of an undisturbed flame occurs when a flammable medium is ignited by a similar point pulse at the open end of a long pipe. The resulting flame will initially be spherical until it touches the walls of the pipe (Fig. 1.1).

Since the flame propagation stops near the walls, the flame takes the form of the outer surface of a spherical segment limited by the cross-section of the pipe. As the flame moves away from the ignition point and the radius of its curvature increases, it becomes more and more flat, coinciding in the limit with the cross section of the pipe.

Rice. 1.1.

The above considerations made it possible to establish that when a flame propagates in the absence of external disturbances, two forms of flame are stable: spherical for an unlimited space (three-dimensional problem) and flat for an infinite pipe (one-dimensional problem). The shape of any flame, whatever it may be at the beginning, will approach these two types in the limit.

Normal combustion

In the absence of disturbances to the combustion process, the shape that the flame front takes during its propagation can be determined based on the following considerations. Each point on the flame surface can be considered as an independent ignition pulse, around which a new elementary flame front is created. After a certain short period of time, as a result of the superposition of such elementary fronts, a new total flame front is formed, coinciding with the envelope of all elementary spherical fronts generated along the initial front.

We will assume that the flame section under consideration is flat AB(Fig. 1.2); with an arbitrary flame shape, any sufficiently small portion of it can also be considered flat. Application of the described construction principle leads to the conclusion that the new flame position A"B" will be parallel to the original one. Extending the same principle to the movement of the flame front free form, we come to the conclusion that the movement of an undisturbed flame occurs at each point of the front along the normal to its surface. Therefore, such combustion is called normal (or deflagration). The speed of a flame moving through a stationary flammable medium along the normal to its surface is called the normal flame speed U n.

Rice. 1.2.

Magnitude U n is the main characteristic of a flammable medium. This is the minimum speed at which a flame can spread through a given medium; she matches flat shape flame. Magnitude U n characterizes not only the linear, but also the volumetric combustion rate, determining the volume of the flammable medium converted into reaction products per unit time per unit flame surface. Accordingly, the dimension U n, can be expressed as cm/s or cm3/(cm2-s).

Magnitude U n, strongly depends on the composition of the flammable medium. In addition to the chemical specificity of the reacting components, the flame speed is significantly influenced by the ratio of fuel and oxidizer contents and the concentration of inert components. Changes in the initial temperature of the flammable medium and total pressure have a weaker effect. Below are the maximum values U n of some flammable mixtures under normal conditions (in m/s):

• С2Н2 + O2 – 15.4;
• H2 + O2; - 13;
• H2 + C12 – 2.2;
• CO + O2 + 3.3% H2O- 1.1;
• H2 + air – 2.7;
• CO + air + 2.5% H2O – 0.45;
• saturated hydrocarbons + air – 0.32–0.40.

The expansion of gas when heated during the combustion process leads to the fact that gas movement always occurs near the flame front, even if it was initially stationary. The following considerations explain how heat affects

expansion of gas and its turbulization by external disturbances on the course of adiabatic combustion. When gas burns inside a long open pipe, a flat flame coinciding with the cross section of the pipe will be motionless if flammable environment is blown into the pipe at a constant cross-sectional speed equal to U n. Combustion products flow out of the other end of the pipe.

Let us denote by p the gas density, by the index 0 the values ​​characterizing the initial flammable medium, and by the index b– combustion products. Since gas expands during combustion, the rate of reaction products leaving the flame U b , >U n. For every 1 cm2 of flame surface the flow brings every second U n cm3 of flammable medium, the mass of which is equal to U n r o. The volume of reaction products moving away from the same area of ​​the flame is equal to Ub, and the mass is Ubrb. The masses of the initial gas and reaction products are equal, which means that

Unro=Ubrb. (1*1)

Equation (1.1) expresses the law of conservation of matter for the combustion process.

We have established that even with a flat front shape, the flame can have different speeds:Un either U b depending on which medium is stationary. The velocity ratios in burning gas are illustrated by the diagram shown in Fig. 1.3.

Rice. 13.

U n – normal flame speed; U b is the rate of reaction products leaving the flame; T 0 – initial temperature of the source medium; T b – temperature of reaction products; r0, rb – densities of the initial gas and reaction products

In a situation 1 the flame is motionless; the flammable medium flowing into the pipe moves to the right at a speed U n ; in the same direction, but with speed U b combustion products move. If the flammable medium is motionless (situation 2), which occurs during combustion in a pipe closed at one end, then the flame moves along it at a speed U n, and the reaction products flow out in the opposite direction at a speed U b – U n. In a situation 3 when ignited at the closed end of the pipe, the combustion products are motionless. In this case, the flame moves at a speed U b in relation to the pipe walls (and burnt gas); in the same direction at speed U b -U n the combustion gas moves, displaced from the pipe by the expanding reaction products. The flame speed in relation to the combustion products is much greater than in relation to the source gas - r0/rb times.

Magnitude G=U r, called the mass burning rate, determines the mass of the substance burned per unit time on a unit flame surface. Naturally, it is the same for both the initial and final environments, as well as in all intermediate zones.

Let us consider the combustion conditions in a flame front of arbitrary shape located motionless in the flow of combustion gas (in a pipe).

The flame is stationary when the amount of gas burned is exactly compensated by the amount of incoming gas. If the flame surface is F, then the total volume of gas burned per unit time is equal to U T F. The same volumetric velocity can be defined in another way: as the product W.S. Where W – average (over the flow cross section) linear speed gas; S – cross section flow. From the equality of both greatnesses it follows:

This result is also valid for a stationary flammable medium, then w– the speed of movement of a curved flame along it. This speed is as many times greater than the normal flame speed as the flame surface is larger than the cross section of the flow. As a flat flame bends and its surface increases, the flame speed increases accordingly. Equation (1.2), usually called law of areas, expresses a fundamental feature of the combustion process: with an increase in the flame surface, combustion intensifies, and the limit of such intensification is caused only by the gas-dynamic features described below.

Curvature of the flame surface is a consequence of turbulization of the combustion gas, spontaneous or forced.

If the combustion gas is highly turbulized and small elementary areas of the cold combustible medium are largely mixed with hot combustion products, then the flame can no longer be considered as a surface separating the two media. A diffuse turbulent zone appears in which the total rate of chemical transformation is high, which is due to the extremely developed surface of the flame.

Flagration combustion modes for a medium of a given composition differ only in the speed of flame propagation at different degrees of development of its surface. This circumstance is essential for clarifying the conventions of frequently used terminology. The concept of “explosion” in relation to flame propagation cannot be characterized otherwise than a fairly rapid combustion in a highly turbulent environment with a flame speed of the order of ten to one hundred meters per second. “Slow” combustion differs from “explosion” only in the degree of development of the flame surface. Other types of flame propagation, for example, characterized by the terms “flash” and “clap,” are fundamentally indistinguishable from those described. Only when the flame speed becomes close to the speed of sound in a flammable medium does the combustion process acquire a new, qualitatively special character.

Disturbances that bend a flat or spherical flame always arise, even in the absence forced movement gas; they are caused by gravity and friction. The first leads to the appearance of convective flows caused by differences in the densities of the combustible medium and combustion products, the second manifests itself when the gas burning in the pipe moves and is slowed down by the walls. It is convenient to trace the effect of disturbances on the laws of combustion in a long pipe placed vertically, open at one end. If you ignite a flammable medium at the lower, open end of the pipe (Fig. 1.4, A), then conditions favorable for the development of convective flows are created, since the unburned source gas, which has a high density, is located above the light combustion products. The flame tends to stretch along the axis of the pipe. When ignited at the upper, closed end of the pipe (Fig. 1.4, b), no convective flows arise, but the combustion zone is intensively turbulized by friction forces. Burning and expanding gas flows out of the pipe. The flow rate of the flammable medium, under the influence of viscosity, changes along the cross section of the pipe; it is maximum along the axis and equal to zero at the walls (Fig. 1.5).

Rice. 1.4.

The flame front bends accordingly. When igniting, the upper open end is rough (Fig. 1.4, V) the possibility of turbulization of the combustion zone is minimal: the combustion products are located above the combustion gas, and the cold gas is motionless. However, as the flame moves away from the edge of the pipe, the frictional force increases, and turbulence spreads to the burning gas.

If combustion is not accompanied by heat losses, i.e. proceeds adiabatically, then the reserve of chemical energy of the combustible system is completely converted into thermal energy reaction products. Since the flame temperature is high, the rates of reactions occurring in it are high and a state of thermodynamic equilibrium can quickly be established. The temperature of the products of adiabatic combustion does not depend on the reaction rates in the flame, but depends only on the total thermal effect and heat capacities of the final products. This temperature is called the thermodynamic combustion temperature T b. Magnitude T b – the most important characteristic of a flammable environment; for common flammable media, it has values ​​of 1500–3000 K. In what follows, we consider in detail to what extent the assumptions made correspond to reality and what significance the thermal combustion regime has for the problems of explosion safety technology. In an adiabatic process and the equilibrium state of combustion products T b – Maximum temperature, achieved in the flame. The actual temperature of the equilibrium reaction products is lower when heat losses from the burning gas occur. The issue of heat losses, as can be seen from what follows, is of decisive importance for solving problems of ensuring explosion safety. During stationary flame propagation, intense heat transfer occurs by conduction into the cold initial combustible environment. However, this process is not associated with heat losses from the combustion zone. The removal of heat from each burning layer of gas to the adjacent one, which has not yet reacted, is exactly compensated by the equivalent supply of heat to the same layer at the previous stage, when it itself was cold. Non-stationary, uncompensated heating occurs at the initial moment when the flammable medium is ignited by the initial impulse. However, as the flame moves away from the ignition point, this additional amount of heat is distributed among an ever-increasing amount of combustion products, and its role in additional heating continuously decreases.

Rice. 1.5.

From the above it follows that during combustion, heat loss is possible as a result of radiation of the heated gas and when it comes into contact with a solid surface. The role of heat removal by radiation is discussed in the following discussion, but for now we will assume that such losses are negligible for the zone whose thermal regime determines the flame speed. Cooling by conduction of combustion products when they come into contact with the walls of vessels and apparatus occurs very intensively, which is due to the large temperature difference between the walls and the gas. Therefore, after combustion is completed in vessels of common sizes, significant cooling of the combustion products in them is completed in less than 1 s.

Cooling the burning gas by walls is also essential for our tasks. Since heat dissipation into the walls begins only after they are touched by the flame, such losses strongly depend on the shape and size of the vessel in which the reaction occurs and the position of the ignition point. During combustion in a spherical vessel and central ignition, heat losses by conduction occur only after combustion is completed.

The combustion temperature is determined by the law of conservation of energy during the adiabatic transition of the chemical energy of the combustible medium into the thermal energy of the combustion products. It is obvious that the components of the combustible mixture are not equivalent. The reserve of chemical energy is determined by the content of the component missing according to the stoichiometric ratios, which is completely consumed during the reaction. Part of the other component, excess, remains unreacted during the interaction. It is equal to the difference between the initial content of the excess component and the amount required to completely bind the missing component. If you increase the content of the missing component due to the content of an inert component that does not participate in the reaction, then the molar reserve of chemical energy of the combustible mixture will increase. Such a replacement for the excess component leaves the chemical energy unchanged.

Let us explain approximately how the law of conservation of energy during combustion is implemented. The reserve of chemical energy of the combustible system will be considered equal to π1Q), where π1 is the concentration of the missing component; Q– the thermal effect of its combustion. The heat of reaction is spent on heating all components of the mixture: the resulting reaction products, excess and inert components. If WITH – average heat capacity the amount of combustion products that was formed from 1 mole of the initial mixture, then the increment in the physical heat reserve is equal to WITH(T b – T 0), where T 0 – initial temperature flammable environment. According to the condition of adiabaticity

Accurate calculation of the state of adiabatic combustion products is much more difficult.

In adiabatic combustion, the combustion temperature determines the density of the final products, and therefore the relationship between flame velocities U n and U b. It is necessary to take into account that as a result of the reaction the number of molecules per unit mass changed by P once. According to the laws of ideal gases

Meaning P in combustion processes it is mostly close to unity. Thus, during the transformation of the stoichiometric mixture 2CO + O2 (combustion to 2CO2) P= 2/3, for a similar mixture of CH4 + 2O2 (combustion to CO2 + 2H2O) n = 1, etc. During the combustion of mixtures of non-stoichiometric composition and mixtures containing inert components, the total number of molecules (taking into account the contents of components not participating in the reaction) changes even less.

During adiabatic combustion, the gas temperature increases 5–10 times. If during combustion the pressure remains constant and the gas expands freely, and n= 1, then its density changes by the same amount and the same ratio U b to normal flame speed. If adiabatic combustion occurs without gas expansion, in a closed vessel, then the pressure increases to approximately the same extent. This determines the destructive effect of rapid combustion in a closed vessel.

The concept of “combustion” cannot be formulated unambiguously. We will call combustion a self-accelerating rapid chemical transformation accompanied by intense heat release and emission of light. Accordingly, we will call the flame (hot) gaseous medium, in which an intense chemical reaction leads to glow, heat generation and significant self-heating.

Such definitions are convenient, but not entirely clear and universal. It is difficult to pinpoint exactly what reaction is fast enough to be considered combustion. The concept of an explosion is even less clear. In the future, we will become acquainted with the existence of cold flames, in which a chemical reaction is accompanied by a glow, but proceeds at a moderate speed and without noticeable heating.

According to D.L. Frank-Kamenetsky, “combustion is the occurrence of a chemical reaction under conditions of progressive self-acceleration associated with the accumulation of heat or catalyzing reaction products in the system.” Here the desire to cover the phenomena of both thermal and autocatalytic development of the reaction is obvious. However, such a generalization leads to the fact that this definition includes phenomena that cannot in any way be classified as combustion processes. These will include flameless reactions in the gas and liquid phases, accompanied by limited self-acceleration, but not turning into a thermal or explosive explosion when the reaction rate reaches a moderate maximum or splashing of the components of a heterogeneous flammable medium occurs.

It would be unacceptable to limit combustion processes to the condition of completeness of the reaction, since in many definitely explosive processes the reaction remains incomplete.

Difficulties in defining combustion are recognized by B. Lewis and G. Elbe: “The concepts of combustion, flame and explosion, although quite flexible, are still used somewhat arbitrarily.”

Complications in determining combustion reflect the lack of sharp boundaries in the complex of physicochemical phenomena specific to combustion. Self-acceleration of the reaction, self-heating, accumulation of active products, radiation of various intensities and wavelengths exist in processes both related and not related to the category of combustion; the difference turns out to be only quantitative. For this reason, any definition of combustion will be inaccurate or incomplete.

Developed ideas suggest that for a combustion-type process to occur, only two conditions must be met: this reaction must be exothermic and must accelerate with increasing temperature. The latter is typical for most chemical processes, so it would seem that any exothermic reaction can develop in the combustion mode. From what follows it follows that for the existence of stable combustion it is necessary to fulfill one more important additional condition associated with the propagation of the flame front in horizontal pipe.

Some features of the course of an exothermic reaction differ when it occurs in a pipe. When a flammable medium is ignited from the open end, the flame acquires a specific shape, elongated and tilted forward (Fig. 1.6).

Rice. 1.6.

1 – flame contact boundary; 2 – the front boundary of the flame image (the intersection of the front and the plane of symmetry); M– point of maximum gas velocity

On a certain part of the path after initiation, combustion proceeds stationary, with constant speed. As the ratio increases h/d, Where h– the height of the column of combustion products, in the limit – the length of the pipe; d– the diameter of the pipe, the friction forces of the gas against the walls increase so much that they cause progressive turbulization of the gas in the combustion zone and unsteady acceleration of the flame in accordance with the law of areas.

The oblique shape of the flame in a horizontal pipe is due to the large difference in the densities of the source medium and combustion products. The flame front is the interface between these two media. To explain the consequences of differences in their densities, we use the following analogy. In a horizontal pipe (Fig. 1.7, A) there are two immiscible liquids of different densities, for example, mercury (right) and water (left), separated by a vertical partition. If the partition is removed, the difference in density causes the movement of liquids: heavy mercury will flow to the left and down, water will be located above the mercury, moving to the right and up. The interface will be inclined forward, its surface continuously increases (Fig. 1.7, b). Similar flows arise during gas combustion, but the transformation of a heavy flammable medium into light reaction products prevents an unlimited increase in the surface of the flame, the size and shape of which become stationary. The deviation of the upper section of the flame front towards the combustion products is due to the deceleration of the gas near the wall under the influence of friction.

Rice. 1.7.

A– before removing the septum; b– after removal of the septum

The shape of a stationary flame (in an area of ​​uniform propagation) is determined by the relationship between the normal flame speed and the speed of gas movement in the corresponding sections of the front. Let us consider these relations for the most advanced point of the front M(see Fig. 1.6), where the flame is normal to the axis of the pipe, and therefore to the direction of movement of the entire front. Total flame speed along the pipe axis U f at point M also consists of the flame speed relative to the gas U n and the component of the speed of movement of the gas itself in the same direction W M :

For any small inclined flame section AB(Fig. 1.8), forming an angle in with the axis of the pipe, the flame moves through the gas along the normal to AB with speed U n (to position A"B") is obviously associated with the movement of the flame element along the pipe axis at a speed U n / sinβ. The total speed of movement of the flame element along the pipe axis is the same as for the point M, consists of the combustion speed itself in this direction and the gas flow velocity component W. Since the shape of the flame is stationary, this means that the speeds of all its elements are equal:

(1.6)

At each point of the flame, its slope is determined by the local value of the gas flow velocity component along the axis. Because U n/sinβ > U n ,W M >W, gas velocity is maximum at point M. Magnitude W decreases near the walls and even becomes negative (where the flammable medium “leaks” under the layer of combustion products). Flame surface area AB, moving in bottom part pipes, replaced by a new one generated at the ignition point M.

Rice. 1.8.

WITH By increasing the diameter of the pipe, the convection of the burning gas increases, while the total flame speed increases approximately in proportion to square root from d. As the normal flame speed increases, so does U f (at d= const), slower than U n. At a certain value U n there is a sharp transition of the flame shape from oblique to hemispherical.

A stationary combustion mode in a flow is often encountered when using a Bunsen burner. This seemingly simplest device is a tube through which a flammable medium is continuously supplied. When it is ignited, a stationary flame is formed at the exit from the burner - a Bunsen flame, the shape of which is close to conical. The laws characterizing the Bunsen flame were established by the work of one of the founders of the theory of combustion, V. A. Mikhelson.

Stationary combustion in a Bunsen flame is possible with various speeds flow. When this speed changes, the shape of the Bunsen cone changes accordingly, and with it its surface - according to the law of areas. In this case, the base of the cone remains unchanged, approximately coinciding with the outlet section of the burner, and the height increases in a fast flow and decreases in a slow flow. Steady combustion, in which such self-regulation of the flame shape occurs, is possible in a wide range of gas flow velocities. Only at a very high gas velocity does the flame fail and die out. If the gas velocity becomes sufficiently low, on average close to U n, the flame spreads towards the flow, entering the inside of the burner - a “breakthrough” of the flame occurs.

Rice. 1.9.

Combustion in a Bunsen flame is complicated by secondary interaction of products incomplete combustion With atmospheric air, if the combustion mixture contains excess fuel. In this case, a secondary, so-called external Bunsen cone of flame is formed in addition to the main, internal one. To prevent external coning, the burner flame is sometimes surrounded by an inert gas environment.

The laws that determine the shape of a Bunsen flame can be established by considering the behavior of a flat (small) section of a stationary flame L V in the combustion gas flow (Fig. 1.9).

If the gas were stationary, then the flame would move along the normal to AB with speed U n, and along the flow - with speed U n/sin β, where β is the angle between AB and the axis of the pipe. This component of the combustion rate is equal to the local flow rate W, since the flame is motionless:

Equation (1.7), obtained by V. A. Mikhelson, is a special case of equation (1.6) - for a stationary flame ( U f = 0); a negative gas velocity value indicates that the directions of gas and flame velocity are opposite. Equation (1.7) determines for each point of the flame surface the value of the angle β, and therefore the stationary shape of the entire flame as a whole. If at any point of the Bunsen cone the component of the gas flow velocity normal to the flame turns out to be greater than the normal flame speed, then the gas flow will relate this element flame from the burner mouth. In this case, the inclination of the flame element to the flow axis increases (since the base of the cone is fixed), and the angle β will decrease until the flow velocity component equals U n. Reverse changes will occur when Wsin β< U n.

If the gas velocity were constant over the entire cross-section of the flow, then the flame would not have any bending and the Bunsen cone would be straight. At laminar flow gas in a pipe, the velocity distribution over the cross section is parabolic, it is determined by Poiseuille’s law

(1.8)

Where W(r) – flow velocity at a distance r from the pipe axis; R 0 – pipe radius; W 0 = W(r= 0) – maximum flow speed.

Average flow rate W, equal to the gas flow per unit section of the pipe, we calculate by averaging:

(1.9)

those. W half as much W 0. It should be borne in mind that after the gas leaves the burner, the distribution of velocities in the flow will change somewhat. In the case of distribution of gas velocities according to Poiseuille’s law at equal W The flame cones for all burners are geometrically similar.

We have already seen that the existence of a Bunsen flame in a wide range of combustion gas flow rates is due to the stability of the base of the cone and the fixation of the flame at the burner cutoff ring. This stabilization is due to the combustion characteristics in this zone. Experience shows that there is a small gap between the base of the flame and the burner cut, and combustion begins at a certain distance from the edge of the pipe. This is due to the fact that combustion is impossible at the surface, since the stationary temperature of the gas in this zone is too low. For the same reason, it is impossible for the flame to penetrate the pipe along the walls, where the gas flow velocity is lower U n.

In the zone of the stabilizing ring at a certain distance from the edge of the burner, combustion becomes possible, but the flame speed in this zone is lower U n due to heat losses. As you move away from the edge of the burner and the flow is no longer slowed down by the wall, the gas velocity along the ring increases. r = R 0. At a certain height it is compared to the speed of the flame.

At these points the flame is stably fixed: closer to the edge of the burner combustion is impossible, at a greater distance the flame speed is greater than the gas speed and the flame will approach the burner until both speeds are equal. By the same mechanism, the flame can be stabilized in the flow of a flammable medium near various stationary obstacles, for example, near a wire ring placed above the burner, or at the end of a rod located inside the burner. In the latter case, a so-called inverted Bunsen cone is formed, turned upside down and stabilized at one fixed point - at its apex.

As the analysis shows thermal regime combustion, when there is a stationary flame inside the pipe, heat is removed from the gas to the wall, and the flame is convexly directed towards the unburned gas, i.e. has the shape of a meniscus. At high heat removal intensity, i.e. at the wall itself, it cannot exist at all and breaks off at some distance from it, just as when it is outside the pipe, above the mouth of the burner. We see that combustion in a Bunsen flame, despite the simplicity of this device, is a very complex process, distinguished by many specific features.

When a moving mixture burns, the resulting flame propagation speed will be the sum of
.

The condition that the flame front be stationary (i.e. motionless) is
- the resulting speed is zero,
.

As a model, consider a Busen burner.

When gas and air are supplied to the mouth of the tube at a speed W, a cone will form, and an increase in speed will lead to an increase in the height (surface) of the cone and a decrease in the angle at the apex. Or the opposite is also possible.

4.3. Processes in a flat flame front.

R
Let's look at the flame front. It will constitute a narrow area where h f is the thickness of the front, and h X – thickness of the chemical reaction zone. Moreover, it can be divided into 2 zones: a heating zone and a reaction zone.

A fresh mixture of gas and air enters zone 1, the gas concentration in the air remains constant because the chemical reaction has not yet begun, but is only being heated due to the heat released in the reaction zone. It begins where the heat input becomes equal to the heat sink, or in mathematical language
, which corresponds to the ignition temperature T B. In the heating zone, the heat supply is greater than the heat sink
, and in the reaction zone
. Heat transport in the flame front is carried out by thermal conductivity. And the maximum heat release lies in the reaction zone, and decreases to 0 at the end of the front.

The propagation of the flame front is affected not only by the rate of the chemical reaction, but also by the transport of substances and combustion products.

4.4 Stabilization of the laminar flame front.

P
When actual gas is supplied to the burner, the propagation speed changes from a maximum in the center to its minimum value at the periphery. In this case, the flame front is bent from a conical shape. And the normal speed of flame propagation can only be compensated
, and the other component
will carry the point to the top of the torch. At the periphery due to the cooling ability of the walls U n is significantly reduced compared to its average value, creating the possibility of direct compensation of the flow rate W speed U n. Due to this, the flame front at the edge turns into a horizontal plane and a stable combustion zone is formed - an incendiary ring. This area may well exist on its own.

The flame front is generally determined by the cosine law, and its stability is determined by the stabilization of the ignition ring. Therefore, we will determine the main dependencies of a stable flame.

Because Since all burners operate in variable modes, situations are possible when the flow rate exceeds U n, or the opposite situation is possible.

The separation of the flame is associated with the existence of the incendiary ring and its destruction. Separation will occur if the flow speed exceeds the critical separation speed (zone II in Figure 8).

Several factors will influence the magnitude of the lift-off speed. WITH increasediameter burner cooling capacity decreases, And maximum flame breakout speedincreases(straight 3,2,1). With mixture leaner (increase in primary air) is decreasing maximum lift-off speed. And with a decrease in the amount of primary air (diffusion flame), the maximum speeds will increase.

A slip occurs when U n exceeds the flame flow speed (zone 3 in Fig. 8).

Flame breakthrough is related to the cooling capacity of the burner walls. No slip condition
. As the diameter increases, the normal combustion rate increases, the more, all other things being equal, the probability of breakthrough increases, the greater must be the flow velocity that prevents flame breakthrough (curves 1,2,3 in Fig. 8) 1 . Maximum speeds absence of breakthrough will be observed at excess air values ​​slightly less than stoichiometric. Cooling of the burner mouth is used to reduce the likelihood of breakthrough.

There are also methods to stabilize the flame.

Fig. 9. Stabilization using Fig. 10. Flame stabilization

igniting the ring with a V-shaped body.

N
and fig. Figure 9 shows a device that carries out stabilization due to the fact that gas enters the annular slot 3 through channels 2. This creates a stable ignition ring that prevents the flame from breaking off. In Fig. Figure 10 shows stabilization of the flow by a V-shaped body. Due to the turbulence, a semblance of an incendiary ring is created, and the probability of flame separation decreases (the maximum speed increases).

The tunnel stabilizer is shown in Fig. eleven. Gas-air mixture exits burner 1 into tunnel 3, where torch 2 is formed. Combustion products are sucked into the root of the torch, creating a zone for their return movement, forming a stable ignition ring. Because if it sucked cold air, then this would significantly worsen the ignition conditions.

Topic 7. SPREAD OF FLAME.

7.1. Thermal theory of combustion.

At adiabatic, i.e. combustion not accompanied by thermal losses, the entire supply of chemical energy of the combustible system is converted into thermal energy of the reaction products. The temperature of the products of adiabatic combustion does not depend on the rate of reactions occurring in the flame, but only on their total thermal effect and the heat capacities of the final products. This value is called the adiabatic combustion temperature Tg. It is an important characteristic of a flammable medium. For most combustible mixtures, the value of Tg lies in the range of 1500-3000° K. Obviously, Tg is the maximum temperature of the reaction products in the absence of external heating. The actual temperature of the combustion products can only be less than T g in case of heat loss.

According to the thermal theory of combustion developed by Soviet scientists Ya.B. Zeldovich and D.A. Frank-Kamenetsky, flame propagation occurs by transferring heat from combustion products to the unburnt (fresh) mixture. The temperature distribution in the gas mixture, taking into account the heat release from the chemical reaction and thermal conductivity, is shown in Fig. 26.

Flame front, i.e. the zone in which the combustion reaction and intense self-heating of the combustion gas occurs begins at the self-ignition temperature Tst and ends at the temperature Tg.

In front of the flame front propagating to the right there is a fresh mixture, and behind there are combustion products. It is believed that in the heating zone the reaction proceeds so slowly that the release of heat is neglected.

The heat transfer process during stationary flame propagation does not lead to heat loss and a decrease in temperature compared to Tg directly behind the flame front. The heat removal from each burning layer of gas when the adjacent, not yet heated one is ignited, is compensated by a similar amount of heat previously received in the igniting layer during its own ignition. The additional heat of the initial igniting pulse does not noticeably distort the steady-state combustion regime, since its role decreases more and more as the amount of burned gas increases.

Combustion products lose heat only as a result of radiation and upon contact with a solid surface. If the radiation is insignificant, such combustion turns out to be practically adiabatic. Noticeable heat losses are possible only at a certain distance behind the flame front.

Thus, the initiation of combustion of a gas mixture at one point leads to heating of the nearby layer, which is heated by thermal conduction from the reaction products until self-ignition. The combustion of this layer entails the ignition of the next one, etc. until the combustible mixture burns out completely. The heat removed from the reaction zone into the fresh mixture is completely compensated by the release of reaction heat and a stable flame front appears. As a result of layer-by-layer combustion, the flame front moves through the mixture, allowing the flame to spread.

If the fresh mixture moves towards the flame front at a speed equal to the speed of flame propagation, then the flame will be motionless (stationary).

A theoretical justification for the conditions for flame propagation can be given when considering a stationary flame, when the speed of its propagation Upl is equal to the supply speed of the gas mixture υ g: Upl =υg (Fig. 27). In this case, the relationship between the normal burning rate U n and the flame propagation speed U pl will be expressed by the equation:

Un = Upl* sinφ. (7.1)

An amount of heat is supplied to the fresh mixture from a unit of flame surface per unit of time by thermal conductivity:

(7.2)

where: - thermal conductivity coefficient;

Flame front width.

This heat is spent on heating the fresh mixture from the initial temperature T o to the combustion temperature T g:

Where: With– specific heat capacity;

Density of the mixture.

Taking into account equations (7.2) and (7.3) at U pl =υ g, the flame propagation speed is determined by the relation:

(7.4)

where: - thermal diffusivity coefficient.

Since the combustion rate very much depends on temperature, the combustion of the bulk of the gas occurs in a zone whose temperature is close to Tg.

The rate of a chemical reaction, as discussed in § 6.1., is determined by the equation:

. (7.5)
Then the speed of flame propagation is:

Where: b– indicator depending on the properties of the mixture, .

Thus, the flame will not be able to spread through the combustible mixture if its temperature is below the theoretical combustion temperature by an amount exceeding (see § 9.3).

- characteristic temperature range in chemical kinetics. A change in temperature by this amount leads to a change in the reaction rate by “e” times.

The limiting value of the flame propagation speed UPR is determined by the relation:

(7.7)

Unlike the considered case of normal combustion, in real conditions of explosions in confined space the process of deflagration combustion self-accelerates. This is due to the expansion of the combustion surface, the occurrence of gas movement and an increase in pressure during combustion.

7.2. Combustion in a closed volume.

When gases burn in open pipe and in the flow the reaction products expand freely, the pressure remains almost constant. Combustion in a closed vessel is associated with an increase in pressure. This is of great importance for solving explosion safety problems. An increase in pressure during combustion in closed apparatus, as well as in rooms, can lead to destruction and accidents.

During combustion without heat losses (adiabatic combustion) in a closed volume, as a result of an increase in temperature from T o to the combustion temperature T g and a change in the number of gram molecules during the reaction, the pressure increases from P o to P g:

(7.8)

where: m, n – number of moles of substances before and after the explosion, stoichiometric

th composition of the mixture.

However, the greatest pressure does not develop for stoichiometric mixtures, although they have the highest heat of combustion and create the maximum T g, but for mixtures enriched with combustible substances, which have a maximum combustion rate. During deflagration combustion, the pressure reaches 7-10 atm, during detonation it is much higher.

A characteristic feature of the combustion process in a closed volume is the uneven distribution of the temperature of the reaction products immediately after combustion. The initially burning part of the combustible mixture, located in the center of the vessel, reacts at the initial pressure p o; the last layer, burning at the wall, reacts at a final pressure R.

Heating of each layer of gas occurs in two stages: during chemical transformation and adiabatic compression. Although the composition of combustion products and pressure are the same at all points in the volume, the final temperature depends significantly on the sequence of both heating processes. Under adiabatic compression from pressure p o up to pressure R the temperature increase from T o to T is determined by the Poisson equation

, (7.9)

where: g = s r / sv.

The final temperature of the combustion products will be higher if the gas is first heated during a chemical transformation, and then its temperature increases during compression according to equation (7.9), than in the case of the reverse sequence of both processes.

7.3. Movement of gases during combustion.

The expansion of gases in a flame (according to Gay-Lussac's law) leads to the fact that combustion is always accompanied by the movement of gases. Let us denote by ρ g - the density of the initial medium, ρ pr - the density of combustion products, their speed relative to the stationary flame front is equal to u pr. For each square centimeter of the front surface, the flow brings u n cm 3 of combustible mixture every second, its mass is equal to u n* ρ g, respectively, from this section of the flame is removed in 1 sec u pr cm 3 reaction products with mass u pr* ρ pr. Since the masses of the burning mixture and the reaction products are equal, then

u n* ρ g = u pr* ρ pr (7.10)

Equation (7.10) expresses the law of conservation of mass during combustion.

The value upr exceeds the normal flame speed by as many times as the density of the initial medium is greater than the density of the combustion products. An increase in the speed of gas flow during combustion is a consequence of the expansion of gases.

Absolute temperature upon combustion it increases 5–10 times. If combustion occurs at constant pressure, the gas expands in r o / r pr once. Let us consider the combustion of a stationary flame front in an open pipe, shown in Figure 28.

Rice. 28. Scheme for explaining the area law: S – pipe cross-section, F – surface of the flame front, ω – speed of the initial combustible mixture, T 0 – temperature and density of the initial mixture, U H – normal combustion speed, U PL – flame propagation speed, U PR is the speed of combustion products, T PR is the temperature and density of combustion products.

Since the flame is stationary, ω = U PR. Then, for example, on 1 cm 2 of the surface of the flame front F, the flow brings ω cm 3 / s of the combustible mixture. Its mass is equal to ω. Accordingly, U PR cm 3 /s of combustion products with a mass of U PR are removed from this section. Then, according to the law of conservation of mass (equation 7.10) at ω = U PL:

(7.11)

Thus, the volumetric velocity of combustion products exceeds the combustion speed as many times as the density of the original medium is greater than the density of combustion products.

On the other hand, if U N cm 3 /s of the mixture burns on 1 cm 2 of the surface of the flame front, then U N * F cm 3 /s burns over the entire area F. At the same time, the volume of combustion gas is equal to the volumetric velocity of the gas flow ω*S cm 3 /s. Then U H *F = ω*S, or ω = U H *F / S.

With equality ω =U PL:

UPL= U H* F / S. (7.12)

We get area law: the speed of flame propagation in the pipe will be as many times greater than normal as the surface of the flame exceeds the cross section of the pipe.

If we consider a stationary combustible mixture, then as the flame front spreads, the sharply heated gases do not have time to expand, and the pressure in the combustion zone sharply increases, which “expands” and pushes the gases to both sides of the flame, and not only combustion products are pushed out, but there is also a movement of the initial mixture ahead of the flame front, as in Figure 29:

The speed of the gases increases as the initial mixture burns and, accordingly, the gas pressure. In this case, compressed hot burnt gases are ejected from one end of the pipe, and a compressed initial mixture is ejected from the other, which ignites explosively from the ejected flame in the atmosphere of the room, followed by a shock wave, fire and destruction.

7.4. Combustion acceleration factors.

Different modes of deflagration combustion differ only in the speed of flame propagation due to the unequal development of the surface of the flame front. The combustion of an initially stationary gas is always complicated by external disturbing influences that distort the shape of the flame. The most important of them are gravity, friction and turbulence of the burning mixture.

Thus, when ignited in the middle of a vertical pipe, as shown in Figure 30, the heavy initial mixture is located above the light combustion products. In this case, convective flows of the initial mixture move downward, and combustion products move upward. Under their influence, the flame front stretches and combustion accelerates.

When the flame spreads downwards, the flammable medium is stationary and the disturbance of the flame front is insignificant. At low combustion rates and pipe length, the flame shape is close to flat.

However, in this case, the gas also moves down the pipe due to expansion during combustion. The friction of the moving gas against the walls leads to a decrease in its speed at the periphery and stretching of the flame front, and the flame front velocity profile also takes the form of a dome. The surface of the flame progressively increases and combustion accelerates.

Quite fast combustion, in which the flame speed reaches hundreds of m/sec, occurs during turbulization of the gas mixture and, accordingly, during turbulization of the flame front. Turbulization causes a significant expansion of the flame front, acceleration of heat exchange between the combustion products and the initial mixture and, accordingly, combustion. This type of combustion is often called an explosion.

7.5. Conditions for an explosion.

As we found out earlier, an explosion is a chemical or physical transformation of a substance, accompanied by an extremely rapid transition of its energy into the energy of compression and movement starting materials, products of their transformation and environment. Based on this, a chemical explosion is an extremely fast combustion reaction, accompanied by a sharp transition of the released thermal energy into the energy of compression and movement of the starting substances, combustion products and the environment.

The explosion consists of three stages:

1) conversion of chemical reaction energy into thermal energy;

2) conversion of thermal energy into the energy of highly compressed gas;

3) propagation of compressed gas in the form of a shock wave.

The main conditions for the occurrence of a chemical reaction in the form of an explosion are:

1. Exothermicity, which is due to the fact that the strength of the bonds between atoms in the reaction products is much higher than in the starting substances, so “extra” energy is released. In endothermic reactions, an explosion does not occur.

2. Gas formation, because:

· firstly, the transition to a gaseous state during a chemical reaction of any substance in a constant volume leads to an increase in pressure;

· secondly, gases have a very high coefficient of volumetric expansion when heated. Without the presence of gases, only heating of the substance will occur.

3. High reaction rate and its ability to self-propagate and self-accelerate. Self-propagation occurs due to either a thermal “wave” carried out by thermal conductivity (deflagration explosion) or a shock wave of compressed gases (detonation).

The heat wave is supported by the heat released during combustion, and shock wave– ourselves compressed gas.

Automatic acceleration of the reaction and the occurrence of an explosion occurs as a result of an increase in the temperature of the reacting substances due to the heat of reaction, or an increase in active radicals, or an increase in pressure in the shock wave.

Requirements for combustion chambers and their characteristics

Combustion chambers of gas turbine plants operate over a wide range of loads. They must have small dimensions, weight, and be operational when burning various types of fuel. In addition, the CS must ensure an acceptable level harmful emissions with combustion products (nitrogen oxides, sulfur). Special requirements were placed on the CS from the point of view of operational reliability, since they are located in difficult temperature conditions.

In addition, combustion chambers must have:

· high combustion efficiency;

· low pressure losses;

· small dimensions, i.e. high thermal intensity;

· specified temperature field;

· fast and reliable start;

· sufficiently large resource;

· sufficient ease of installation and preventative maintenance.

The combustion efficiency coefficient (or combustion chamber efficiency) is defined as:

Where Q 1– the amount of heat actually released in the working volume of the chamber; Q 2 – full quantity heat that theoretically could be released during complete combustion of the fuel.

The flame in the combustion chamber, developing under conditions of forced movement with a central fuel supply, consists of three main zones: internal zone I, mixture formation and combustion zone II, and zone III - external air zone Fig. 4.2.

In zone II 0 ≤ α ≥ ∞. There is no air in the inner zone α = 0.

In zone 2, mixture formation and combustion take place. It is divided into two: internal - a, and external - b.

The internal zone is filled with a mixture of flammable gas and combustion products, and external mixture combustion products and air. The boundary between the zones is the combustion flame front. In this interval there are all regions from α = 0 to α = ∞. In the thickness of the combustion front α= 1; the fuel, moving from the root to the tail zone, is diluted with combustion products, and the air is saturated with combustion products. This leads to the fact that in the combustion zone the heat of combustion of the fuel decreases, i.e. the amount of heat decreases,

Rice. 4.2. Combustion flame front.

per unit surface of the combustion front, combustion conditions worsen until the flame may go out and some of the unburnt fuel will be removed. It should be borne in mind that this process is typical for unlimited space. In real combustors, the nature of combustion, due to the fact that the flow is limited, is largely determined by the aerodynamic properties of the combustor. Moreover, a high temperature is maintained in the combustion zone, which leads to combustion of the mixture at very high rates; in this case, the combustion rate is determined primarily by the rate of mixture formation, because the rate of chemical reactions will be many times greater than the rate of mixture formation. This process is called diffusion combustion. It is easily controlled by changing the conditions of mixture formation, which, in turn, can be changed by design measures - the use of blade ring grids as turbulators, etc.

One of the main characteristics of the combustion chamber is the magnitude of the thermal stress, which is the ratio of the amount of heat released in the combustion chamber to its volume at combustion pressure.

J/m 2 MPa (4.10)

Where R KS– pressure of the working fluid in the combustion chamber, MPa; V– combustion chamber volume, m3.

Based on the value of the specific heat intensity, the volume of the combustion chamber is determined.

To create stable combustion over the entire range of operating modes, the organization of the combustion process is important, which is characterized by the surface of the combustion flame front and is determined from the equation:

Where U T – turbulent flame propagation speed, which is usually taken in the range (40 ÷ 60 m/s); F f – combustion flame front; – heat of combustion of the mixture; ρ cm - mixture density.

The lower calorific value of the mixture is determined from the equation:

The density of the mixture is determined from the Mendeleev-Clayperon equation:

Where T KS is the temperature of the mixture in the combustion chamber.

Combustion flame front according to the equation:

Stable combustion is possible with F tf≥ F f.