PHYSICAL AND CHEMICAL CONDITIONS FOR THE FORMATION AND DEVELOPMENT OF A STABLE PROCESS OF SURFACE FLAMELESS COMBUSTION OF GASES

Norkin N. N.

I. Introduction

There exist various views and theories that attempt to explain the mechanism of flameless combustion*); however, in these theories there is, in our opinion, no attempt to relate flameless combustion to other forms of gas combustion. Meanwhile, there can be no doubt that the various forms of combustion are mutually transformable; thus, for example, ordinary flame combustion, under appropriate conditions, can be converted into diffusion or flameless combustion, while the latter, when stability is disturbed, passes either into the form of an explosion or into the form of ordinary combustion**).

In this connection there arises the idea of the need to investigate the question of the physical and chemical conditions that promote the transformation of a normal conical flame front into such a form as merges with the surface of a catalytic material. Moreover, as is known, flameless combustion is extremely sensitive to changes in the physical conditions under which it is regulated—a sharp change entails disruption of the stability of the process; the limits of stability are extremely restricted. It is therefore necessary to investigate the question of the influence of internal and external actions on the limits of stability of flameless combustion.

The present theoretical-experimental work is an attempt to illuminate the questions posed, without claiming completeness of physico-chemical analysis, but only to the extent to which this can be used in engineering and industrial practice.

II. Principal Forms of Gas Combustion at Constant Pressure and the Conditions for Their Mutual Transformations

The principal forms of gas combustion at constant pressure are the following three: 1) torch laminar-diffusion combustion; 2) torch turbulent-diffusion combustion (ordinary flame combustion); and 3) surface catalytic (flameless) combustion.

Torch laminar-diffusion combustion can be organized if the following conditions are observed:

a) the outflow of gas and air from the burner must occur as plane-parallel or concentric streams without preliminary mix—

*) In the monograph of Professor M. B. Ravich [1] a brief analysis of the theories of flameless combustion is given, and an exhaustive bibliography on this question is provided.

**) It is interesting to note that in the discussion that unfolded at the Paris Thermal Conference in 1937 concerning the reports of Guffe and Cassan [2], the very concept of “flameless” combustion was called into question.

their combustion in a burner; mixing of the gas and air streams takes place in the working space of the heat installation (in the furnace, in the oven), as a result of molecular diffusion of the components of the gas and air;

b) the velocities of outflow of the gas and air streams from the burner must be identical and must lie within the limits of the laminar regime. These conditions for the course of the diffusion-combustion process can be calculated in advance with sufficient accuracy by means of the following equations:

Fick’s diffusion equation,

\[ \frac{\partial p}{\partial \tau}=K\frac{\partial^{2}p}{\partial x^{2}} \tag{1} \]

\[ w_{\text{gas}}=w_{\text{air}}=\text{idem} \tag{2} \]

\[ Re=\frac{wd\rho}{\mu}<2320. \tag{3} \]

In the equations the following are denoted: \(p\)—the partial pressure of the diffusing component; \(\tau\)—the diffusion time, which, for uniform motion, may be expressed as the ratio of the length of the diffusion zone \(l\), identified with the flame length, to the velocity of uniform motion of the flame \(w_{\phi}\)

\[ \tau=\frac{l}{w_{\phi}}; \]

\(K\)—the diffusion coefficient of the mixture component;
\(x\)—the current linear coordinate, which in the present case has the meaning of the thickness of the diffusion layer;
\(w_{\text{gas}}\)—the velocity of gas outflow;
\(w_{\text{air}}\)—the same for air;
\(d\)—the diameter of a round burner, or the reduced diameter of a slotted or otherwise shaped burner;
\(\rho\)—the density of the stream;
\(\mu\)—the viscosity of the stream.

Investigations carried out by the author on the combustion of illuminating and water gases under the conditions of open atmospheric burners, both slotted and concentric, as well as in a shielded furnace chamber, showed that the actually attained length of the diffusion-flame torch is \(0.75 \div 0.85\) of the calculated length, owing to the curvature of the rectilinear path of the torch under the influence of the temperature field [3].

Regulation of the length of the diffusion-combustion flame depends to a large extent on the thickness of the diffusion gas and air streams, determined by the geometrical dimensions of the burner, and to a lesser, indeed very slight, extent on the initial velocity of outflow of the streams. The influence of the composition of the combustible gas on the length and temperature of the flame is manifested through the diffusion coefficients of the components entering into the gas mixture. The more hydrogen there is in the gas, the shorter the flame; the more methane there is in the gas, the longer the flame. When a gas containing considerable quantities of hydrocarbons (for example, illuminating*) or coke-oven gases) is burned, the diffusion flame has great luminosity owing to the thermal decomposition of hydrocarbons with the liberation of carbon in finely dispersed—

* The author carried out an experimental study of the influence of preheating of the gas and air and of changing the angle of encounter of the gas and air streams on the length of the flame and the distribution of temperature along the length of the flame, and also determined the conditions under which the flame lifts off from the mouth of the burner and burns steadily at some distance from it [11].

state; the degree of blackness of the flame is rather high, on the order of 0.4–0.45 of the degree of blackness of absolutely black radiation. The area of practical application of diffusion combustion and its advantages are described in considerable detail in Hepburn’s article [4].

The second form of gas combustion is torch turbulent-diffusion combustion, the most widespread in practice. In organizing this type of combustion, the mixing of gas and air is carried out partly in the burner (primary air), and partly in the working space of the furnace firebox. The factors affecting the degree of mixing and the length of the torch are: a) unequal velocities of outflow of the streams; b) the direction of the streams at a greater or lesser angle; c) the use of artificial turbulizers. The length of the flame torch and the temperature distribution in the torch do not lend themselves to exact preliminary calculation, although rather successful attempts in this direction exist [5, 6, 7, 8, 9, 10].

The third form of gas combustion is surface catalytic flameless combustion; this combustion is characterized by the following: a) the gas and air, before entering the burner, are preliminarily and thoroughly mixed to the state of a homogeneous mixture; b) the combustible mixture is burned on the surface of the refractory material of the burner, which has a high temperature and exerts a catalytic effect on the combustion process.

The external signs of surface combustion are the complete or almost complete absence of a visible flame front. The flame front coincides with the surface of the catalytically active refractory materials or is located in the pores of the granular layer. Owing to the high thermal density of combustion, the surface of the burner or of the layer possesses intense thermal radiation.

The three indicated forms of gas combustion can transform one into another in the presence of the corresponding conditions; in order to trace the transformation of some forms of combustion into others, let us take as the initial form torch turbulent-diffusion combustion, carrying it out in a simple injection burner, for example, in a Bunsen burner. Let a homogeneous combustible mixture be supplied through such a burner with an amount of air less than is required by stoichiometric ratios; then the air in the combustible mixture will play the role of primary air, while the remaining amount of air necessary for complete combustion of the gas (secondary) is brought to the torch from the surrounding medium. Under these conditions a two-cone flame torch is formed (position 1, Fig. 1).

If the gas and the primary air are sufficiently well mixed, then the inner, i.e., “blue,” cone has a sharply outlined contour; its surface is the first, inner flame front. In this front a greater or lesser part of the gas burns, depending on the amount of primary air. The outer cone does not have a sharply outlined contour; its surface is the second flame front, in which the remaining part of the gas burns at the expense of diffusion of secondary air from the surrounding medium.

If the velocity of outflow of the combustible mixture is increased by increasing its flow rate at the same composition, then the height of the inner “blue” cone increases; the height and outline of the outer cone also change (position 2, Fig. 1).

If we decrease the amount of primary air in the combustible mixture, leaving the gas flow rate the same as in position 1, then the heights of the cones will increase and the flame will be drawn out (position 3, Fig. 1). This occurs as a result of a decrease in the velocity of flame propagation. The decrease in the velocity of flame propagation is explained by the impoverishment of the combustible mixture in the oxygen of the air, which is in agreement with ex-

experimental data of Le Chatelier [12] and Michelson [13], who investigated the flame-propagation velocity as a function of the composition of the combustible mixture. If the admission of primary air to the burner is stopped, while maintaining the turbulent regime of gas outflow, then the inner cone

Increases the flow rate of the combustible mixture →
Decreases the amount of primary air

Position 1  Position 2  Position 3  Position 4

Combustion with the theoretically required amount of air

The flame front is deformed

Position 5  Position 6  Position 7

Surface flameless combustion

Position 8

Fig. 1. Diagram of the transformation of torch combustion into surface flameless combustion

will disappear, and the outer cone will have the greatest length at the given mean outflow velocity (position 4, Fig. 1).

Let us increase the amount of air in the combustible mixture in comparison with position 1 and bring it to that theoretically required for complete combustion; then the two-cone flame will turn into a one-cone flame (position 5). Since the flame-propagation velocity is greatest at the stoichiometric ratio between the combustible gas and air, the height of the cone at the given mean outflow velocity will be minimal. Further increase in the flow rate of the combustible mixture with the theoretically required ...

a significant amount of air entails deformation of the conical flame front into an elliptical one as a result of a change in the velocity profile at considerable Reynolds numbers \(Re\) (position 6). A turbulent flame differs from a laminar one in that, unlike the laminar flame, a loud whistling is heard, the flame front is not sharply outlined but blurred, and sometimes the upper part of the flame is considerably wider than the base [14]. If a grate (metal or refractory) is now inserted into the burner tube, the previously single flame cone is broken up into a number of elementary cones above each opening of the burner grate (position 7). By regulating the outflow velocity one can cause the flame to penetrate into the grate, and then combustion becomes surface (flameless) combustion, which is carried out chiefly by means of channel refractory or layered granular refractory burners (position 8).

III. Deformation of the Normal Flame Front in the Process of Surface Combustion

In surface combustion the flame front, unlike in the torch process, is considerably deformed under the influence of hydrodynamic, thermal, catalytic, and other phenomena. As is known, the stability of the conical flame front in torch combustion is determined, according to Michelson [13], by the equations:

\[ \cos \alpha = \frac{u}{w_m} \tag{4} \]

\[ h = r \sqrt{\frac{w_m^2}{u^2} - 1} \tag{5} \]

In these equations the following are denoted: \(\alpha\)—the angle between the generatrix of the cone and the radius of the base; \(u\)—the flame propagation velocity; \(w_m\)—the mean, over the cross section, outflow velocity of the combustible mixture, equal to the per-second flow rate of the combustible mixture divided by the cross-sectional area of the tube (burner); \(h\)—the height of the cone; \(r\)—the radius of the tube (burner) (Fig. 2).

Fig. 2. Diagram of the normal conical flame front

The equations (4) and (5) are valid under the condition of laminar outflow, when a parabolic velocity profile occurs over the cross section, and also when a flame front of regular conical form is formed. Under these conditions, \(u\)—the flame propagation velocity—is determined experimentally by measuring the angle \(\alpha\) or the height of the cone, by the method known as the “dynamic method” [13, 15, 16].

For a normal conical flame front the characteristic relation is

\[ \frac{u}{w_m} = \mathrm{const} = \cos \alpha \tag{4'} \]

Across the burner cross section the outflow velocity varies from \(w = 0\) to \(w = w_{\max}\), reaching a maximum on the axis of the tube; consequently, in the same

the ratio, the magnitude \(u\) changes, while the angle \(\alpha\) remains unchanged. But even under a laminar outflow regime there is some distortion of the regular geometrical shape of the flame front; therefore it is more correct to measure the angle \(\alpha\) not over the entire surface of the cone, but at the point where the actual outflow velocity is equal to the mean velocity; this point can be determined from the following considerations: according to Hagen–Poiseuille, the flow rate under laminar outflow is determined from the equation

\[ V=\frac{\pi}{8\mu}\cdot\frac{\Delta p}{\Delta l}r^4, \tag{6} \]

the mean velocity over the cross-section is

\[ w_m=\frac{V}{\pi r^2}=\frac{\Delta p}{\Delta l}\cdot\frac{r^2}{8\mu}, \tag{7} \]

the velocity at any point of the velocity profile is

\[ w_i=\frac{1}{4\mu}\cdot\frac{\Delta p}{\Delta l}(r^2-x^2). \tag{8} \]

Comparing equations (7) and (8) and solving with respect to \(x\), we find

\[ w_m=w_i, \]

\[ x=\frac{r}{\sqrt{2}}=0.707r, \tag{9} \]

i.e., the flow velocity at the point \(x\), located at a distance \(0.707\,r\) from the axis, is equal to the mean outflow velocity.

In the equations given above, the symbols denote: \(V\) — the volumetric flow rate per second of the combustible mixture; \(\dfrac{\Delta p}{\Delta l}\) — the pressure gradient; \(\mu\) — the viscosity of the flow; \(x\) — the variable radius of the tube (burner).

In accordance with equations (4) and (5), at a high flame-propagation velocity the height of the cone, the inclination angle of the generatrix, and the surface of the cone decrease, which entails combustion of the mixture in a smaller volume. An increase in the flame-propagation velocity is achieved by increasing the temperature of the combustion process, by preheating the combustible mixture, and by the catalytic action of the burner surface. This is one of the reasons affecting the deformation of the normal flame front during the transition from ordinary flame combustion to surface flameless combustion.

To avoid disturbance of the stability of the combustion process, it is necessary to increase the outflow velocity of the combustible mixture, since at the limit, when \(w_m=u\), flashback of the flame will occur; but increasing the outflow velocity entails a transition from a laminar regime to a turbulent one. In the turbulent regime, as the Reynolds number \(Re\) increases, the velocity profile changes its parabolic form to another, flatter one, with a less pronounced maximum along the tube axis; thus, according to experimental data [17], at \(Re=50000\) the jet velocity at a distance \(0.9\,r\) from the tube axis is \(0.72\,w_m\); at \(Re=200000\) the jet velocity at the same distance is \(0.75\,w_m\); and at \(Re=800000\) the jet velocity is \(0.8\,w_m\), whereas under laminar motion the jet velocity at the same distance from the tube axis is only \(0.22\,w_m\). In connection with the change in the velocity profile at large values of \(Re\), a flattening (deformation) of the conical flame front occurs.

It should be noted that, as a result of the equalization of the velocity profile over the flow cross-section, there also occurs an equalization of the flame-propagation velocity along the flame front.

In practice, surface flameless combustion is carried out by means of channel burners with small-diameter channels, in a granular bed, in porous plates, diaphragms, etc.; above the opening of each pore, channel, etc., an elementary cone of combustion is formed. The following formulation of the question is not without interest: how will the total lateral surface of all the elementary combustion cones change in comparison with the surface of a single cone, if in both cases the burner radius and the efflux velocities are the same? The surface \(S\) of a single cone above the opening of a burner of radius \(r\), with height \(h\), will be

\[ S = \pi r \sqrt{h^2 + r^2} \tag{10} \]

Expressing the cone height \(h\) in terms of the radius of the burner opening \(r\), the mean efflux velocity \(w_m\), and the flame-propagation velocity \(u\), according to equation (5), we obtain another equation for determining the surface of a single cone \(S\)

\[ S = 3.14\, r^2 \frac{w_m}{u}. \tag{11} \]

If a grate is inserted into the burner opening or it is filled with a granular bed of grains of diameter \(d\), then the number of combustion cones \(N\), equal to the number of elementary openings or pores, is determined from the equation

\[ N = \frac{\pi r^2}{f}\,\eta . \tag{12} \]

Here \(\eta\) is the relative free cross-section of the granular bed or grate, and \(f\) is the cross-sectional area of an elementary pore.

For a granular bed, according to Slichter [18], the relative free cross-section of the granular bed \(\eta\) and the cross-sectional area of an elementary pore can be determined approximately from the equations

\[ \eta = 1 - \frac{\pi}{4\sin\Theta} \tag{13} \]

\[ f = 0.0369d^2 . \tag{14} \]

Here \(\Theta\) is the angle between lines drawn through the centers of adjacent grains, taken as spheres. With the densest arrangement of grains (spheres), \(\Theta = 60^\circ\), and therefore

\[ \eta = 1 - \frac{\pi}{4\sin 60^\circ} = 0.0921 . \]

Substituting the values of \(\eta\) and \(f\) into equation (12), we obtain

\[ N = \frac{\pi r^2}{0.0369d^2}\cdot 0.0921 = 7.85\,\frac{r^2}{d^2}. \tag{15} \]

Assuming approximately that the pore cross-section is circular, we determine the pore radius \(r'\)

\[ r' = \sqrt{\frac{f}{\pi}} = \sqrt{\frac{0.0369\,d^2}{3.14}} = 0.1085\,d \tag{16} \]

and the surface \(s'\) of an elementary cone of height \(h'\)

\[ s' = \pi r'\sqrt{h'^2 + r'^2}, \]

Then the lateral surface \(S'\) of all elementary combustion cones with radii \(r'\) and height \(h'\) will be equal to

\[ S' = Ns' = 7.85 \frac{r^2}{d^2}\cdot \pi r' \sqrt{h'^2 + r'^2}. \]

Substituting the value of \(r'\) from (16), we shall have

\[ S' = 2.67 \frac{r^2}{d}\sqrt{h'^2 + 0.01175d^2}. \tag{17} \]

The height of an elementary undeformed cone according to equation (5) is

\[ h' = r'\sqrt{\frac{w_m'^2}{u'^2} - 1}. \]

Substituting \(h'\) and \(r'\) into equation (17), we obtain

\[ S' = 0.29 r^2 \frac{w_m'}{u'}. \tag{18} \]

Comparing the magnitude of the total lateral surface of the elementary cones formed in the layer of a burner of radius \(r\) with the lateral surface of a single cone in the same burner, and taking into account that, for a stable combustion process, in both cases the ratios must be identical,

\[ \frac{w_m}{u} = \frac{w_m'}{u'}, \]

we obtain

\[ \frac{S'}{S} = \frac{0.29 r^2 \dfrac{w_m'}{u'}} {3.14 r^2 \dfrac{w_m}{u}} = 0.092 . \tag{19} \]

It follows from this that deformation of the combustion surface entails concentration of heat release over a smaller surface, although the flow rate of the combustible mixture through the layer must undoubtedly be greater, since the rate of flame propagation in the layer is substantially increased, which must also cause a considerable increase in the mean flow velocity of the combustible mixture. Furthermore, the surface of the flame front has a definite thickness; on one side of the front surface, facing toward the burner mouth, there is an unignited combustible mixture, and on the other side there are combustion products heated to a high temperature. The combustion surface is a zone of chemical reaction within which the combustion process itself takes place. This thickness of the combustion surface, as far as is known, has not been determined experimentally, but it can be calculated from the kinetic equations for the rate of the combustion reaction. For example, in the combustion of hydrogen in a mixture with air the thickness of the combustion surface is 0.11 mm [19]; in the combustion of hydrogen in air the thickness of the combustion surface is 0.16 mm, and in the combustion of carbon monoxide in air it is 0.3 mm [20]. If the velocity of motion of the combustible mixture through the flame front is of the order of 10 m/sec, then the actual time of the combustion reaction will be determined by a value of the order of \(0.5\cdot 10^{-5}\)—\(1.5\cdot 10^{-5}\) sec. The extent of the reaction zone, or, what is the same, the thickness of the combustion surface, depends on the rate of the chemical reaction, i.e., on the chemical composition of the combustible mixture, on temperature, and on other kinetic

factors, among which the catalytic action of the surface of the burner refractory plays a rather important role. In surface flameless combustion, all kinetic factors that increase the rate of the combustion reaction are present, such as: intensive heating of the combustible mixture under the influence of the incandescent surface of the burner refractory, and its catalytic action. As a result, the surface of the blue cone becomes vanishingly small. This is also one of the causes leading to deformation of the normal flame front.

IV. Increase in the Rate of Flame Propagation in Surface Flameless Combustion

Strictly speaking, the concept of the flame-propagation rate is not entirely definite, since the method for determining the magnitude of this rate is quite varied, and the results obtained in its determination do not always agree with one another.

In the present work, the concept of the flame-propagation rate is used in the sense in which it is treated by V. A. Mikhelson [13], N. N. Semenov [21], [20] [22], [3].

In order to form an approximate idea of the influence of the principal kinetic factors on the flame-propagation rate under conditions of surface combustion, certain quantitative relationships are discussed below. The influence of the preheating temperature of the combustible mixture on the flame-propagation rate can be revealed from an analysis of the formula of Zel’dovich and Frank-Kamenetskii [21]

\[ U=\frac{1}{L\gamma_0}\sqrt{ 2\lambda \frac{C_p^2\gamma_0}{L} \left(\frac{T_0}{T_2}\right)^2 \left(\frac{n_0}{n_2}\right)^2 \left(\frac{\lambda}{D C_p \gamma}\right) \left(\frac{RT_2}{E}\right)^3 e^{-E/RT_2} } \tag{20} \]

Here

\[ U\ \frac{\mathrm{cm}}{\mathrm{sec}} \]
— flame-propagation rate at constant pressure;

\[ L\ \frac{\mathrm{cal}}{\mathrm{g}} \]
— calorific value of the combustible mixture;

\[ \gamma_0\ \frac{\mathrm{g}}{\mathrm{cm}^3} \]
— specific weight of the initial mixture;

\[ \lambda\ \frac{\mathrm{cal}}{\mathrm{cm}\,\mathrm{sec}\,\mathrm{g}} \]
— coefficient of thermal conductivity of the reaction products at \(T_2\);

\[ C_p\ \frac{\mathrm{cal}}{\mathrm{g}\,\mathrm{deg}} \]
— heat capacity of the combustion products;

\[ T_0\ ^\circ\mathrm{K} \]
— initial temperature of the combustible mixture;

\[ T_2\ ^\circ\mathrm{K} \]
— theoretical combustion temperature;

\[ n_0 \]
— number of moles of the initial substance according to the stoichiometric reaction equation;

\[ n_2 \]
— the same for the reaction products;

\[ D\ \frac{\mathrm{cm}^2}{\mathrm{sec}} \]
— coefficient of diffusion of the reacting substance in the reaction products;

\[ R\ \frac{\mathrm{cal}}{\mathrm{mol}} \]
— gas constant;

\[ E\ \frac{\mathrm{cal}}{\mathrm{mol}} \]
— activation energy of the chemical reaction.

Combining all the physical constants for the combustible mixture of the given composition into a single quantity \(K\), and, for simplicity, not taking into account their variation with the initial temperature, we rewrite equation (20) in a form that makes it possible to establish the direct dependence between the initial temperature \(T_0\) and the flame-propagation velocity:

\[ u=K\left(\frac{T_0}{T_2}\right)\left(\frac{RT_2}{E}\right)^{1/2} \sqrt{\frac{1}{e^{E/RT_2}}}. \tag{21} \]

When the initial temperature of the combustible mixture is changed to \(T_0'\) and, consequently, to \(T_2'\), the flame-propagation velocity will be \(u'\), and the ratio between \(u\) and \(u'\) may be expressed as

\[ \frac{u'}{u} = \left(\frac{T_0'}{T_2'}\cdot\frac{T_2}{T_0}\right) \left(\frac{T_2'}{T_2}\right)^{3/2} \sqrt{ e^{\frac{E}{R}\left(\frac{1}{T_2}-\frac{1}{T_2'}\right)} } \tag{22} \]

As an example, let us take the combustible mixture carbon monoxide—air, for which \(T_0=273+15=288^\circ\mathrm{K}\); the theoretical combustion temperature will be \(T_2=2500+273=2773^\circ\mathrm{K}\). When the combustible mixture is heated to \(500^\circ\mathrm{C}\), \(T_0'=773^\circ\mathrm{K}\) and \(T_2'=3173^\circ\mathrm{K}\). Taking the value of the gas constant \(R=1.985\ \frac{\mathrm{kcal}}{\mathrm{mol}}\) and the activation energy \(E=34000\ \frac{\mathrm{kcal}}{\mathrm{mol}}\), and substituting them into equation (22), we obtain the ratio of flame-propagation velocities:

\[ \frac{u'}{u} = \left(\frac{773}{3173}\cdot\frac{2773}{288}\right) \cdot \left(\frac{3173}{2773}\right)^{3/2} \sqrt{ e^{\frac{34000}{1.985}\left(\frac{1}{2773}-\frac{1}{3173}\right)} } =2.9, \]

i.e., the flame-propagation velocity in a combustible mixture preheated to \(500^\circ\mathrm{C}\) increases approximately threefold in comparison with that at an initial temperature of \(15^\circ\mathrm{C}\). Let us examine equation (20) with respect to the effect of a decrease in the activation energy, owing to the catalytic action of the incandescent surface of the refractory material, on the flame-propagation velocity. For different values of \(E\), all other conditions being equal, the ratio between the flame-propagation velocities is expressed in the form

\[ \frac{u'}{u} = \frac{E}{E'} \sqrt{ e^{\frac{1}{RT_2}(E-E')} } \tag{23} \]

Having no experimental material for determining \(E\) under the action of an incandescent refractory surface, let us assume that the activation energy decreases by a factor of 2, which is probably quite admissible if one takes into account that the ignition temperature of the combustible mixture is considerably lowered. Then, for the preceding example, i.e., for the combustible mixture carbon monoxide—air, the ratio of flame-propagation velocities will be

\[ \frac{u'}{u} = \frac{34000}{17000} \sqrt{ e^{\frac{1}{1.985\cdot3173}(34000-17000)} } =7.7, \]

i.e., the flame-propagation velocity increases approximately eightfold under the influence of the catalytic action of the incandescent surface of the burner.

In flameless combustion, high outflow velocities of the combustible mixture are necessary. But at high outflow velocities and strong turbulence, the flame-propagation velocity increases considerably in comparison with that under laminar outflow. It has been determined experimentally [14] that, under a turbulent outflow regime, the propaga-

the flame-propagation velocity increases approximately in proportion to \(\sqrt{Re}\), for example, at \(Re = 4000\),

\[ \frac{u_{\text{turb.}}}{u_{\text{lam.}}} = 2.9 \]

and at \(Re = 23300\) this ratio is

\[ \frac{u_{\text{turb.}}}{u_{\text{lam.}}} = 5.95. \]

If the value \(Re = 23300\), i.e., a comparatively large value, is adopted, and accordingly the increase in the flame-propagation velocity due to the influence of turbulence is estimated as a quantity of the order of 6, then the total increase in the flame-propagation velocity under conditions of surface combustion will be expressed by quantities of the order of: a) without taking into account the catalytic influence of the incandescent surface of the refractory material of the burner, \(3 \cdot 6 = 18\) times; b) taking into account the catalytic influence of the incandescent surface of the refractory material of the burner, \(3 \cdot 8 \cdot 6 = 144\) times.

Applied to a combustible mixture of carbon monoxide and air, for which under ordinary conditions of flame combustion the flame-propagation velocity is estimated at \(0.6\ \text{m/sec}\), under conditions of surface (flameless) combustion this quantity increases to

\[ 0.6 \cdot 18 = 10.8\ \frac{\text{m}}{\text{sec}} \]

or

\[ 0.6 \cdot 144 = 86.4\ \frac{\text{m}}{\text{sec}} \]

However, it does not follow from the above that at comparatively low rates of outflow of the combustible mixture and correspondingly low pressures it is impossible to achieve a stable process of surface combustion. In the investigations of M. B. Ravich [1], the pressure of the combustible mixture was in the range of 50–100 mm water column, and the surface combustion was stable for a long time. In Sitov’s experiments [25], the pressure of the combustible mixture likewise did not exceed 150 mm water column. In the author’s experiments, the results of which are presented below, the pressure of the combustible mixture illuminating gas–air did not exceed 100 mm water column, and when burning the combustible mixture water gas–air, the pressure was of the order of 100–150 mm water column. By suitably selecting the length of the channels in channel burners and the thickness of the layer in granular burners, stable surface combustion can be achieved even at low pressures of the combustible mixture.

In surface (flameless) combustion of gas, an enormous quantity of heat is liberated per unit volume per unit time, compared with the heat liberation in ordinary flame combustion. According to the experimental data of M. B. Ravich [1], when burning Moscow municipal gas in an experimental furnace installed at the Power Engineering Institute of the Academy of Sciences of the USSR and equipped with channel burners, a heat-release intensity of the order of

\[ 700 \cdot 10^6\ \frac{\text{kcal}}{\text{m}^3\text{hour}} \]

was achieved, instead of the heat-release intensity usually attained in flame combustion,

\[ 300000\text{–}1000000\ \frac{\text{kcal}}{\text{m}^3\text{hour}}. \]

It may be considered that, with the selection of appropriate conditions (catalysts, temperature), the practical limits of heat-release intensity are unlimited. Owing to the high heat-release intensity, the burner surface is heated to a high temperature and becomes an intense thermal radiator.

V. Conditions for the Stability of Surface Combustion

In order for the process of surface combustion to be stable, the following conditions must be observed: constancy of the composition of the combustible mixture, constancy of the temperature regime, and constancy of the shape and dimensions of the cross sections of the channels and pores in the burner.

If these conditions are observed, the surface combustion achieved will be characterized by definite values of the heat intensity and heat density of combustion and by the fuel consumption.

It is necessary to maintain the composition of the combustible mixture constant because, when the composition changes, the magnitude of the flame-propagation velocity changes; as a result, a redistribution of zones may occur along the length of the burner channel or through the thickness of the granular layer, entailing a change in the temperature regime.

The requirement that the temperature regime in the burner be kept constant entails: a) the necessity of dynamic equilibrium between the process of material exchange and the process of chemical transformation (combustion); b) the necessity of dynamic equilibrium between the process of heat exchange and the process of heat release during combustion.

The dynamic equilibrium between the process of material exchange and the process of chemical transformation (combustion) may be expressed by the equality of the rate of transformation \(U_n\) and the rate of exchange \(U_0\)

\[ U_n = U_0 \tag{24} \]

or

\[ \frac{\partial c}{\partial \tau} = -\operatorname{div}(w_n c)+\operatorname{div}(D\operatorname{grad}C) \tag{25} \]

Here \(\dfrac{dc}{d\tau}=U_n\ \dfrac{\text{mol}}{\text{m}^3\,\text{sec}}\) is the rate of transformation, i.e., the quantity of reacting substance per unit reaction volume per unit time;

\[ U_0\ \frac{\text{mol}}{\text{m}^3\,\text{sec}} \]

is the rate of exchange, i.e., the quantity of mixture delivered by convective and diffusional transfer per unit time into a unit reaction volume;

\[ w_n=\frac{\text{m}}{\text{sec}} \]

is the component, normal to the flame front, of the mean linear velocity of transfer;

\[ C\ \frac{\text{mol}}{\text{m}^3} \]

is the concentration of fuel in the mixture;

\[ D\ \frac{\text{m}^2}{\text{sec}} \]

is the diffusion coefficient.

Let us refer the terms of equation (25) to a unit surface, since the characteristic geometrical quantity in flameless combustion is the surface of the flame front; then let us assume that diffusional transfer under the conditions of surface combustion is of little significance in comparison with convective transfer; let us exclude the influence of changes in the concentration of fuel on the rate of transformation of a mixture of definite composition, which is permissible, since the combustible mixture is always taken in equimolecular quantities and is irreversibly transformed into combustion products,

then the quantity $U_n$ acquires the meaning of the flame-propagation velocity $\left(\dfrac{\mathrm{m}^3}{\mathrm{m}^2\sec}\right)$, and the quantity $U_0$ becomes the component, normal to the flame front, of the mean velocity of motion of the combustible mixture through the flame front.

Thus, the condition for dynamic equilibrium of the processes of transformation and material exchange is the equality of the flame-propagation velocity $U$ and the normal component of the mean velocity of motion of the combustible mixture $w_n$

\[ U = w_n \tag{26} \]

This condition is specific to surface (flameless) combustion, since in other forms of combustion, especially in torch laminar combustion, diffusive transfer is of predominant importance.

The dynamic equilibrium between the process of heat exchange and the process of heat release during combustion can be expressed by the equation

\[ \frac{D}{d\tau}(C_p \rho \theta) - qU_n = Q_0 . \tag{27} \]

It follows from this equation that the change in the heat content of the system (the substantial derivative $\dfrac{D}{d\tau}(C_p \rho \theta)$) depends on the heat release in the transformation process $(+qU_n)$ and on heat exchange $Q_0$.

But

\[ Q_0 = - div\,(C_p \rho \theta w) - div(-\lambda grad\,\theta) + Z \tag{28} \]

Here $div\,(C_p \rho \theta w)$ is the flow transfer of heat per unit volume, $\rho$ is density, $\theta$ is temperature; $w$ is the flow velocity; $div(-\lambda grad\,\theta)$ is the conductive transfer of heat per unit volume; $\lambda$ is the coefficient of thermal conductivity; $Z$ is the radiative transfer of heat per unit volume.

Since

\[ \frac{D}{d\tau}(C_p \rho \theta) = \frac{\partial}{\partial \tau}(C_p \rho \theta) + w\,\frac{\partial}{\partial x}(C_p \rho \theta) \]

and for a stationary process

\[ \frac{\partial}{\partial \tau}(C_p \rho \theta)=0, \]

then

\[ w\,\frac{\partial}{\partial x}(C_p \rho \theta) = div\,(C_p \rho \theta w), \]

\[ qU_n = -div(-\lambda grad\,\theta) + Z \tag{29} \]

With constant composition of the combustible mixture and with constant reaction-kinetic conditions observed,

\[ qU_n = \mathrm{const}. \tag{30} \]

Since $qU_n$ is the thermal intensity of combustion, condition (30) means that stable surface combustion is accompanied by a constant thermal intensity of the volume of the reaction space.

From (29) and (30) it follows that

\[ -div(-\lambda grad\,\theta) + Z = \mathrm{const}. \tag{31} \]

This condition can be fulfilled when $\theta = \mathrm{const}$, i.e., there must be a constant temperature regime. Let us clarify the circumstances on which

depends on maintaining a constant temperature regime in the various zones of a burner for surface (flameless) combustion. In a burner (of any design) intended for flameless combustion of gas, three zones may be distinguished: 1) a preflame preparatory zone, in which the temperature of the combustible mixture rises from the initial \(t_0\) to the ignition temperature \(t_z\); 2) a reaction flame zone, where the temperature of the combustion products rises from the ignition temperature almost to the theoretical combustion temperature \(t_{\text{theor.}}\); 3) a postflame zone, in which the combustion temperature decreases to the temperature of the outgoing gases \(t_{\text{out.g.}}\).

To analyze the temperature regime in the preparatory preflame zone, we shall adopt the assumptions: a) that in this zone, owing to the negligibly small rate of the chemical reaction, \(-qU_n=0\); b) that heat transfer from the flame front directly to the combustible mixture is of little importance in comparison with heat transfer from the heated surfaces of the channel or of the granular bed. This assumption is quite appropriate; it follows from comparison of an ordinary torch process with surface combustion.

Under these assumptions, the thermal state of the system in the preparatory zone, made in the form of a cylindrical channel of diameter \(d_k\) and length \(l\), can be expressed by the equation

\[ w\,\frac{\partial}{\partial x}(C_p\rho \Theta)\,\frac{\pi d_k^2}{4}\,dx = \alpha(t_{\text{p.z.}}-t)\pi d_k dx . \tag{32} \]

According to this equation, the heat content of the combustible mixture in the preparatory zone, of volume \(\dfrac{\pi d_k^2}{4}dx\), changes as a result of heat transfer from the surface \(\pi d_k dx\) bounding the given volume; the temperature of the combustible mixture changes from \(t_0\) to \(t_z\), and the surface temperature \(t_{\text{surf.}}\) has an average value; the heat-transfer coefficient \(\alpha\) has the value of the total coefficient

\[ \alpha=\alpha_k+\alpha_{\text{rad.}}, \]

i.e., due to convection, \(\alpha_k\), and due to radiation, \(\alpha_{\text{rad.}}\). Integrating equation (32) within the limits \(t/t_0^{t_z}\) and \(x/0^l\), with average values of the physical constants and velocity, we obtain

\[ l= \frac{t_{\text{surf.}}\,d_k\,\bar{w}\,\bar{C}_p\,\bar{\rho}}{4\alpha} \ln \frac{t_{\text{surf.}}-t_0}{t_{\text{surf.}}-t_z} \tag{33} \]

If the value of \(l\) calculated from equation (33) is less than the actual length of the burner channel, then ignition of the combustible mixture will occur inside the channel; if \(l\) is equal to the actual length of the channel, then ignition will occur at the outlet mouth of the burner channel.

For a burner made in the form of a granular bed, the characteristic quantities are the specific surface of the granular bed \(\sigma\left(\dfrac{m^2}{m^3}\right)\) and the height of the bed \(h\); in this case the thermal state of the system in the preparatory zone may be expressed by the equation

\[ w\,\frac{\partial}{\partial h}(c_p\rho \Theta)=\alpha(t_{\text{surf.}}-t)\sigma \tag{34} \]

After integration within the limits \(t/t_0^{t_z}\) and \(h/0^h\), we obtain the height of the bed in the preparatory zone—

\[ h= \frac{t_{\text{surface}}\,\bar{w}\,\bar{c}_p\,\bar{\rho}}{\sigma\alpha} \ln \frac{t_{\text{surface}}-t_0}{t_{\text{surface}}-t_z} \tag{35} \]

In accordance with equations (33) and (35), the length or height of the proposed preparatory zone must be quite definite; moreover, the temperature difference

\[ t_{\mathrm{surf.}} - t_z \]

must be positive, i.e., \(t_{\mathrm{surf.}} > t_z\).

In the flame reaction zone, the change in the heat content of the combustible mixture and of the combustion products occurs as a result of heat liberation in the course of the chemical combustion reaction and of heat removal by convective transfer, conduction, and radiation. The magnitude of the heat removal by conduction and radiation may be taken into account by introducing the concept of the pyrometric combustion coefficient \(\eta_{\mathrm{pyr.}}\), showing the ratio of the actual flame temperature to the theoretical one,

\[ \eta_{\mathrm{pyr.}}=\frac{t_{\mathrm{flame}}}{t_{\mathrm{theor.}}}. \]

Owing to conduction and, chiefly, radiation at the moment of heat liberation, \(t_{\mathrm{flame}} < t_{\mathrm{theor.}}\), and the coefficient \(\eta_{\mathrm{pyr.}} < 1\).

The thermal state in the flame reaction zone may be expressed by the equation

\[ w\frac{\partial}{\partial x}\left(C_p\rho\eta\Theta\right)=qU_n . \tag{36} \]

But

\[ U_n=K_0 e^{-E/RT} f(c_A,c_B,\ldots). \]

Here \(K_0\) is the pre-exponential factor, depending on the chemical nature of the reacting substances and on the reaction mechanism; \(f(C_A C_B,\ldots)\) is a function of the concentrations of the reacting substances, depending on the reaction mechanism.

For a constant composition of the reacting combustible mixture under the conditions of an irreversible process,

\[ K_0 f(C_A,C_B\ldots)=\mathrm{const}=K, \]

then equation (36) takes the form

\[ qK e^{-E/RT}=w\frac{\partial}{\partial x}\left(C_p\rho\eta\Theta\right) \tag{37} \]

Integrating this equation over the limits from the ignition temperature \(t_z\) to the flame temperature \(\eta t_{\mathrm{theor.}}\) along the length of the reaction zone, with mean values of the physical constants \(\overline{C_p}, \rho\) and the mean velocity of motion \(\overline{W}_{\mathrm{av}}\), we obtain

\[ h=\frac{\overline{w}}{qK}\,\overline{C_p}\rho\,\frac{R}{E} \left( T_z^2 e^{\frac{E}{RT_z}} -\eta^2 T_{\mathrm{theor}}^2 e^{\frac{E}{R\eta T_{\mathrm{theor}}}} \right) \tag{38} \]

An exact quantitative calculation of the extent \(h\) of the reaction zone is difficult to carry out by this equation, because a considerable number of variable quantities were taken as mean constants in the integration; however, qualitative conclusions useful for discussing the question of the conditions for stability of the reaction zone can be drawn.

If the first term in the parentheses is compared with the second, then, in absolute value, the first is approximately \(10^5\) times greater than the second; from this it may approximately be concluded that the theoretical combustion temperature and the pyrometric combustion coefficient have little influence on the position of the reaction zone. An exceptionally great influence on the stable position of the reaction zone is exerted by the ratio \(\frac{E}{T_z}\). Under conditions of surfac—

of surface combustion the value of \(E\) tends to decrease, and the more so the more active the catalyst; as a result, \(h\)—the extent of the reaction zone—decreases.

Thus, the stability of the reaction zone is due to the catalytic action of the surface of the burner material, since it is precisely on this action that the value of \(E\) and the ignition temperature \(T_z\) of the combustible mixture depend.

In the post-flame zone the temperature of the combustion products decreases from \(\eta t_{\mathrm{theor}}\) to \(t_{\mathrm{ex}}\) as a result of heat transfer to the surface of the burner material; the quantity of heat given up by the combustion products in the post-flame zone depends on its accumulation by the burner material, on the conductive heat transfer of the burner material into the pre-flame zone, and on radiation from the open surface of the burner into the working space of the furnace, kiln, etc. Under steady-state conditions the heat of accumulation is equal to zero; the heat transferred into the pre-flame zone is comparatively small, since its quantity is determined by the expenditure for heating the combustible mixture from the initial temperature \(t_o\) to the ignition temperature \(t_z\). Consequently, the predominant influence on the change in the heat content of the combustion products in the post-flame zone is exerted by radiation from the open surface of the burner; the stability of the combustion process, which depends on the temperature regime in the post-flame zone, will be determined mainly by the magnitude of the open surface of the burner.

Fig. 3. Diagram of the temperature regime within the limits of stable surface combustion.

Legend:

— temperature of the combustible mixture,
— temperature of the layer,
— ignition temperature.

The considerations set forth above regarding the influence of the temperature regime on the stability of surface combustion are illustrated by the curves in the “diagram of the temperature regime within the limits of stable surface combustion” (Fig. 3).

The curves marked 1 refer to the case of the most stable regime, when the reaction zone is located inside the channel or layer of the burner; the curves marked 2 refer to the case of unstable combustion, since small fluctuations in the regime may cause the transition of surface combustion into explosive combustion in the mixer; the curves marked 3 refer to another case of unstable combustion, since small fluctuations in the regime may cause the transition of surface combustion into flame combustion, outside the burner.

The straight line parallel to the abscissa axis characterizes the conventionally constant ignition temperature. The curves corresponding to the case of the most stable regime characterize the following phenomena: the solid curve 1 shows the change in the temperature of the combustible mixture from the initial \(t_o\), at

at entry into the burner to the final \(t_{\text{out.g.}}\) at exit from the burner. The section of the burner in the interval \((t_{0} \div t_{z})\) is the pre-flame zone. In this zone, owing to heat transfer from the surface of the channel or the burner bed, the combustible mixture is heated to the ignition temperature. At the point where the temperature curve of the combustible mixture intersects the straight line of the ignition temperature \(t\), the combustion reaction occurs almost instantaneously.

In the reaction flame zone the curve \(t_{0}\) of the combustible mixture sharply changes into the flame-temperature curve \(\eta t_{\text{theor.}}\). In the post-flame zone the temperature of the combustion products decreases from \(\eta t_{\text{theor.}}\) to \(t_{\text{out.g.}}\), owing to heat transfer to the surface of the channel or the burner bed. Fluctuations in the temperature regime near the stability curves, i.e., the curves marked 1, although they may cause displacement of the reaction zone to one side or the other and thus alter the relationship between the remaining zones, will not disrupt surface combustion. However, considerable fluctuations in the temperature regime may cause displacement of the reaction zone to the boundaries of unstable combustion, 2 or 3, as a result of which surface combustion will be disrupted and will pass into another form. The causes that may bring about a disturbance of the stability of surface combustion include the following:

a) a change in the ratio between the amounts of gas and air in the combustible mixture;

b) a change in the free cross section of the burner, caused by clogging of the channels and pores in the burner, melting, etc., which entails an increase in resistance, a decrease in the rate of outflow of the combustible mixture, and displacement of the reaction zone toward the boundaries of unstable regimes;

c) an abrupt change in the thermal load of the burner. With a sharp increase in thermal load, and consequently in the flow rate of the combustible mixture, there will occur a lengthening of the pre-flame zone, displacement of the combustion zone toward the open surface of the burner, and transformation of surface combustion into flame combustion.

With a sharp decrease in flow rate, the reaction zone will shift toward the surface of entry into the burner, and combustion may then pass into explosive combustion in the mixer.

Summarizing the discussion of the question of the conditions for the stability of surface combustion, it may be said that surface combustion, while being the most perfect method of burning gas, at the same time requires a high degree of automation in the monitoring and control of the combustion process.

VI. Experimental investigations of the conditions for the formation and stable development of surface (flameless) combustion of illuminating gas and water gas

The experimental investigation of the conditions for the formation and stable development of surface (flameless) combustion is being carried out by the author in the laboratory of thermal apparatus of the Tomsk Polytechnic Institute.*) The following series of experiments were set up: a) surface combustion of illuminating gas in a granular bed in a burner with an open surface; b) surface combustion of illuminating gas in a granular bed in a burner with a water heater; c) surface combustion of illuminating gas in porous tiles; d) combustion of water gas in quartz tubes; e) combustion of water gas in a furnace with a granular bed.

*) At various times the following laboratory staff members took part in the work: G. D. Speshchits, P. G. Fedotov, V. V. Sigova, A. A. Starikov, N. D. Vylegzhanin, V. V. Piotukh, Pakhtusova.

In the experiments, illuminating gas from the retort furnaces of the institute’s gas works was used for combustion. The average gas composition was

\[ \mathrm{CO_2}—4.4\%; \qquad \mathrm{O_2}—1.4\%; \qquad \mathrm{CH_4}—34.05\%; \qquad \mathrm{N_2}—13.10\%. \]

\[ \mathrm{C_2H_2}—1.00\%; \qquad \mathrm{CO}—9.00\%; \qquad \mathrm{H_2}—35.64\%; \]

The calorific value according to the Junkers calorimeter averaged \(4254\ \mathrm{kcal}/\mathrm{m^3}\).

Water gas was supplied from plant No. 660; its composition was

\[ \mathrm{CO}—38\%; \qquad \mathrm{O_2}—0.2\%; \qquad \mathrm{N_2}—3.3\%. \]

\[ \mathrm{CO_2}—5\% \qquad \mathrm{H_2}—53.5\%; \]

The calorific value was \(2470\ \mathrm{kcal}/\mathrm{m^3}\).

The gas and air flow rates were measured by calibrated sharp-edged orifices, manufactured in the laboratory and installed in the gas pipeline and air duct, in accordance with the appropriate rules. The gas was supplied to the experimental installations either directly from the mains or, beforehand, passed through a gas blower, as a result of which the pressure was increased. Air was supplied to the installations by means of a fan either of the “Sirocco” type or of the “Schiele” type.

A. Surface (flameless) combustion of illuminating gas in a granular bed with an open surface

The layout of the experimental installation is shown in Fig. 4. Illuminating gas, by means of a gas blower (capacity up to \(2.8\ \mathrm{m^3/hour}\), motor power \(1\ \mathrm{kW}\), and number of revolutions \(n = 1440\ \mathrm{rpm}\)), was supplied through a gas pipeline of diameter \(D_1 = 11\ \mathrm{mm}\) through a sharp-edged orifice \(d_1 = 5\ \mathrm{mm}\) into the mixer.

The pressure in the gas pipeline did not exceed \(100\ \mathrm{mm}\) water column. When regulating the gas flow rate, the excess gas was burned in an atmospheric Bunsen-type burner. Air was supplied by the fan to the mixer through a pipeline of diameter \(D_2 = 50\ \mathrm{mm}\) through a sharp-edged orifice \(d_2 = 27\ \mathrm{mm}\). The mixer was tubular, with a conical nozzle. After the mixer, the combustible mixture passed through a pipeline of diameter \(D_3 = 25\ \mathrm{mm}\), through a sharp-edged orifice \(d_3 = 12\ \mathrm{mm}\). The combustible mixture was introduced into the experimental chamber through a manifold,

equipped with 9 branch pipes. The surface-combustion chamber had a rectangular shape, 300 by 330 mm, and consisted of two parts:

1) the lower part of the chamber, for uniform distribution of the combustible mixture over the cross section; it was equipped with a water jacket with continuous circulation of water;

2) the upper part of the chamber, with a mesh bottom. The total area of the bottom was 0.099 m², the free cross section of the mesh 0.021 m². The upper part of the chamber was filled with a layer of grains of fireclay refractory material, with various layer heights and grain diameters.

Six thermocouples were inserted into the side walls of the upper chamber at three heights: 80 mm, 40 mm, and 20 mm from the level of the mesh surface.

The hydraulic resistance of the layer of fireclay grains was determined by the formula

\[ \Delta p = \xi \frac{w^2}{2g}\gamma \frac{l}{d}. \tag{39} \]

Here \(l\) is the height of the layer (m);

\(d\) is the grain diameter (m);

\(\gamma\) is the specific weight of the gas (kg/m³);

\(w\) is the velocity of motion of the gas (m/sec); in this case the velocity is calculated as the quotient obtained by dividing the air flow rate per second by the free cross section of the surface of the granular layer, i.e.

\[ w=\frac{V}{f}\left(\frac{\text{m}^3}{\text{sec m}^2}\right); \]

\(\Delta p\) is the pressure drop (mm water column);

\(\xi\) is the resistance coefficient.

The magnitude of this coefficient was found experimentally for a layer of grains 3–5 mm in diameter:

\[ \xi = 29.2. \]

In processing the results of the investigation it is necessary to know the velocity at which the combustible mixture passes through the granular layer. The velocity of passage of the combustible mixture through the layer was calculated as the ratio of the volume per second of the combustible mixture to the free cross section of the granular layer. The free cross section is

\[ f = F \cdot \eta, \]

where \(F\) m² is the open surface of the granular layer; in our case

\[ F = 0.3 \cdot 0.33 = 0.099\ \text{m}^2. \]

\(\eta\) is the coefficient of surface porosity; its value was determined according to Slichter (equation 13).

For the densest arrangement of grain spheres \(\eta = 0.0921\); consequently, the free cross section of the granular layer in the experimental gas-combustion chamber was

\[ f\,0.099 \cdot 0.0921 = 0.00911\ \text{m}^2. \]

A series of experiments on burning illuminating gas in a granular layer with an open surface had the following aims: a) visual observation of the transformation of flame combustion into surface (flameless) combustion; b) study of the question of the optimal height and granulometric composition of the layer under conditions of a stable combustion process; c) study of the question of the temperature distribution in the layer, the thermal intensity, and the thermal density of combustion.

Observations of the transformation of flame combustion into surface combustion were carried out as follows: into the gas-combustion chamber with a filled-

...with a layer of fireclay grains poured into it (grain diameter 3–5 mm, layer height 85 mm), first only one gas was supplied, and then air was gradually added through the mixer.

When there is insufficient air for complete combustion, an oscillating flame of indefinite shape forms above the layer. As air is added, an internal “blue” cone appears inside the flame; it seems to “settle” onto the surface of the layer, and then breaks up into a number of elementary “blue” cones. When the theoretically required amount of air is reached in the combustible mixture, the elementary “blue” cones “disappear”; acoustically this is accompanied by a slight crackling. Soon after the elementary cones have “disappeared,” the surface of the layer becomes strongly incandescent. Thermocouples inserted into the layer make it possible to judge the place in the layer where the highest temperature develops.

A smooth, gradual increase or decrease in the flow rate of the combustible mixture caused the high-temperature zone to shift along the height of the layer; with a sharp change in the mixture flow rate, popping usually occurred—explosions of the combustible mixture in the lower part of the combustion chamber, accompanied by ejection of the granular layer. Sometimes the explosions propagated as far as the mixer.

For this reason, the mixer initially used, in the form of a metal cylinder, was replaced by a tubular injector mixer.

It was also established that the water jacket in the lower part of the gas-combustion chamber has no noticeable effect on preventing popping; therefore, in subsequent investigations water was not supplied to the jacket.

In studying the question of the optimal height and granulometric composition of the layer, the following were selected as evaluation criteria: a) uniform incandescence of the surface of the granular layer without visible “blue” cones; b) combustion of the gas with the theoretically required amount of air; and c) absence of popping and of local combustion foci in the layer. The characteristics of the investigated layers are given in Table 1.

Table 1

Height and granulometric composition of the granular fireclay layer in an open burner

Layer No.	Grain size, mm	Layer height, mm	Combustion conditions
I	1–3	13	Incandescence of the surface is nonuniform, frequent explosions. Surface combustion is unstable.
I	3–4	25	Incandescence of the surface is nonuniform, frequent explosions. Surface combustion is unstable.
I	4–5	5	Incandescence of the surface is nonuniform, frequent explosions. Surface combustion is unstable.
I	5–6	10	Incandescence of the surface is nonuniform, frequent explosions. Surface combustion is unstable.
I	6–7	12	Incandescence of the surface is nonuniform, frequent explosions. Surface combustion is unstable.
I	7–10	15	Incandescence of the surface is nonuniform, frequent explosions. Surface combustion is unstable.
I		80
II	1–3	8	Local combustion foci in the layer; incandescence of the surface is nonuniform; frequent explosions.
II	3–4	4	Local combustion foci in the layer; incandescence of the surface is nonuniform; frequent explosions.
II	4–5	5	Local combustion foci in the layer; incandescence of the surface is nonuniform; frequent explosions.
II	5–6	6	Local combustion foci in the layer; incandescence of the surface is nonuniform; frequent explosions.
II	6–7	7	Local combustion foci in the layer; incandescence of the surface is nonuniform; frequent explosions.
II	7–10	10	Local combustion foci in the layer; incandescence of the surface is nonuniform; frequent explosions.
II		40

Continuation of Table 1

Layer No.	Grain size, mm	Layer height, mm	Combustion conditions
III	1—3 3—4 4—5	7 8 5	The same, but to a greater degree than in layer II.
		20
IV	7—10	80	With changes in the flow rate of the combustible mixture—frequent popping.
V	7—10	40	The same
VI	6—5	80	Comparatively uniform incandescence of the surface.
VII	6—5	40	The same.
VIII	5—4	80	Uniform incandescence of the surface, stable flameless combustion.
IX	5—4	40	The same.
X	4—3	40	The same.
XI	4—3	80	Uniform incandescence of the surface; regulation of the flow rate of the combustible mixture over wide limits does not disturb the stability of flameless combustion.
XII	2—3	80	The same, but less uniform incandescence.
XIII	3—1	80	Nonuniform incandescence of the surface.

Of the 13 layers studied, the most suitable proved to be layer No. XI, 80 mm high, with grains 3—4 mm in diameter. Further work was carried out with this layer.

The velocity of passage of the combustible mixture through the layer was

\[ w_0 = 0.15 \div 0.32 \ \text{m/sec}. \]

The porosity of the layer, as the ratio of the sum of the volumes of the pores to the total volume of the layer, according to Slichter [18], is

\[ m = 1 - \frac{\pi}{6(1-\cos\Theta)\sqrt{1+2\cos\Theta}} \tag{40} \]

For the densest packing of the spheres—grains, \(\theta = 60^\circ\), and then \(m = 0.2295\).

The specific surface area of the granular layer $\sigma$, as the ratio of the sum of the surfaces of all the spheres-grains to the volume of the layer, is

\[ \sigma = 1321 \frac{\mathrm{m}^2}{\mathrm{m}^3} \]

In studying the question of the temperature distribution in the granular layer, the thermal intensity and the thermal density of combustion, the gas and air flow rates were varied while maintaining an excess-air coefficient approximately equal to unity. The temperature was measured by thermoelements ($Pt—PtRh$ thermocouples) placed at heights of 20, 40, and 80 mm from the level of the surface of the screen supporting the granular layer. The results of the measurements are given in Table 2.

Table 2

Temperature distribution in a granular layer, 80 mm high,
of fireclay grains with \(d = 3—4\) mm

Gas, m³/hr	Air, m³/hr	Excess-air coefficient	Temperature distribution, 20 mm	Temperature distribution, 40 mm	Temperature distribution, 80 mm
0.775	3.673	1.065	20°C	100°C	690°C
0.950	4.645	1.095	20°C	168°C	750°C
1.097	5.625	1.150	20°C	210°C	800°C
1.344	6.560	1.090	20°C	275°C	835°C
1.550	7.580	1.1	40°C	750°C	850°C
1.731	8.400	1.09	40°C	780°C	875°C
1.731	8.500	1.1	60°C	950°C	880°C

At a gas flow rate from 0.775 m³/hr to 1.344 m³/hr, combustion occurs near the outer open surface. If, at this gas flow rate, the height of the combustion zone is taken approximately as equal to the height of the upper half of the layer, i.e. 40 mm, then the thermal intensity of the combustion zone, referred to the volume of pores, will be

\[ q = \frac{V_{\mathrm{gas}} Q_{\mathrm{H}}^{\mathrm{P}}}{m V_1}, \]

where \(V_{\mathrm{gas}}\) is the hourly gas flow rate from 0.775 m³/hr to 1.344 m³/hr; \(m\) is the porosity of the layer, equal to 0.2295; \(Q_{\mathrm{H}}^{\mathrm{P}}\) is the calorific value of the gas, equal to

\[ 4254 \frac{\mathrm{kcal}}{\mathrm{m}^3}; \]

\(V_1\) is the volume of the layer, equal to

\[ 0.3 \cdot 0.33 \cdot 0.040 = 0.00396 \ \mathrm{m}^3; \]

then

\[ q = \frac{0.775 \cdot 4254}{0.2295 \cdot 0.00396} = 3.6 \cdot 10^6 \ \frac{\mathrm{kcal}}{\mathrm{m}^3 \ \mathrm{hr}} \quad \text{to} \quad \frac{1.334 \cdot 4254}{0.2295 \cdot 0.00198} \]

\[ = 6.2 \cdot 10^6 \ \frac{\mathrm{kcal}}{\mathrm{m}^3 \ \mathrm{hr}}. \]

At a gas flow rate from 1.550 m³/hr to 1.731 m³/hr, combustion occurred in the middle of the layer. If, at this gas flow rate, the height of the combustion zone is taken approximately as equal to \(2/3\) of the height of the layer, i.e. 53 mm, then the thermal intensity of the combustion zone, referred to the volume of pores, will be from \(5.5 \cdot 10^6\) kcal/m³·hr to

\[ 6.2 \cdot 10^6 \frac{\mathrm{kcal}}{\mathrm{m}^3 \ \mathrm{hr}}. \]

The principal mode of heat transfer in surface combustion is radiation from the heated surface of the layer. The calculation of heat transfer by radiation was made from the equation

\[ Q=C\left[\left(\frac{T_n}{100}\right)^4-\left(\frac{T_0}{100}\right)^4\right]F\ \frac{\text{kcal}}{\text{m}^2\cdot\text{h}}. \]

Here \(C\) is the reduced radiation coefficient;

\[ C=C_{\text{layer}}=3.72; \]

\(T_n\) is the temperature of the open surface of the layer;
\(T_0\) is the temperature of the surrounding medium;
\(F\) is the open surface of the layer.

Table 3

Heat transfer from the surface of the granular layer

Gas, m³/h	Air, m³/h	Combustion products, m³/h	Temperature at surface of layer, °C	Heat release rate of combustion, kcal/(m²·h)	Heat of combustion, kcal/h	Heat transfer by radiation, kcal/h	Heat content of combustion products, kcal/h	Fraction of heat for radiation
1	2	3	4	5	6	7	8	9
0.775	3.673	4.030	690	\(33\cdot10^3\)	3300	2350	950	0.71
0.950	4.645	4.940	750	\(40.5\cdot10^3\)	4050	2779	1271	0.68
1.097	5.625	5.700	800	\(46.7\cdot10^3\)	4670	3088	1582	0.66
1.341	4.560	6.980	835	\(57.2\cdot10^3\)	5720	3675	2045	0.64
1.550	7.580	8.070	850	\(66\cdot10^3\)	6600	4195	2405	0.64
1.731	8.400	9.010	875	\(78.8\cdot10^3\)	7880	5142	2738	0.65
1.731	8.500	9.625	880	\(78.8\cdot10^3\)	7880	4820	2960	0.62

The results of the calculations are given in Table 3. It also gives the heat release rate of combustion, kcal/m²·h, conventionally referred to the open surface of the layer, as well as the heat content of the combustion products leaving the layer.

Thus, by a series of experiments on burning illuminating gas in a granular layer with an open surface, it has been demonstrated that:

a) stable surface combustion is possible at low outflow velocities and low pressures;

b) combustion is concentrated in the pores of a granular layer of height less than 80 mm;

c) the heat intensity of combustion is of the order of \(3\cdot10^6\) to \(6\cdot10^6\) kcal/m²·h;

d) heat transfer by radiation from the surface of the granular layer averages 0.66 of all the heat released during combustion.

This method of surface flameless combustion can be successfully used for muffle and crucible furnaces.

B. Surface (flameless) combustion of illuminating gas in a granular layer with a water heater above the layer

The arrangement of the experimental installation is shown in Fig. 5. Above a round burner 130 mm in diameter there was mounted a cylindrical chamber made of refractory material, fitted at the top with a metal box through which water flowed continuously. The granular layer, 80 mm high, consisted of chamotte grains 3–4 mm in diameter.

In studying a stable combustion process, the following measurements were made: a) the flow rate of illuminating gas from the pressure drop across a sharp-edged orifice; b) the same for air; c) the temperature of the layer surface;

Fig. 5. Diagram of the installation for surface combustion of gas in a granular bed with a water heater.

1—lined burner casing; 2—granular bed;
3—mixer; 4—air blower; 5—water heater;
6—water cooling; 7—orifice in the gas pipeline;
8—orifice in the air duct; 9—differential manometers;
10—thermocouple; 11 and 12—mercury thermometers.

d) the temperature of the water at the inlet to the water heater and at the outlet from it; e) analysis of the outgoing combustion products.

The measurement results are presented in Table 4.

Table 4

Flow rate of gas, air, and water in a burner with a granular bed, with a water heater above the bed

Gas, m³/hour	Air, m³/hour	Excess-air coefficient	Amount of water passed, kg/hour	Increase in water temperature, Δt°	Temperature of layer surface	CO₂	CO	O₂
0.32	1.54	1.08	4.2	18°	650°	9.45	0.3	0.0%
0.33	1.56	1.06	18.79	54°	710°	9.40	0.4	0.0%
0.42	2.02	1.08	9.40	70.8°	654°	9.50	0.1	0.0%
0.45	2.20	1.10	5.65	76.2°	795°	9.48	0.2	0.0%
0.50	2.42	1.09	18.48	49.2°	783°	9.46	0.2	0.0%
0.52	2.43	1.05	3.42	73.7°	848°	9.40	0.35	0.0%
0.63	3.00	1.07	4.20	80.0°	945°	9.50	0.05	0.0%
0.65	2.90	1.00	18.23	46.9°	811°	9.50	0.06	0.0%
0.66	3.18	1.08	7.42	90.3°	657°	9.48	0.15	0.0%
0.67	3.06	1.03	15.70	79.5°	812°	9.44	0.32	0.0%
0.90	4.40	1.10	14.08	25.7°	960°	9.42	0.36	0.0%
1.28	6.05	1.06	8.20	74.5°	728°	9.50	0.1	0.0%

The measurement results given in Table 4 make it possible to draw the following conclusions:

a) the heat-release intensity of combustion, referred to the volume of the pores in the granular bed, amounted to a value from \(5.6 \cdot 10^6\) to \(22.4 \cdot 10^6\) kcal/m³·hour.

b) the thermal density of combustion, conventionally referred to the open surface of the granular bed, 130 mm in diameter, amounted to a value from \(103\cdot 10^3\) to \(408\cdot 10^3\) kcal/m²·h.

c) the heat absorbed by the water screen constitutes the following fraction of the total heat released during combustion (Table 5).

Table 5

Distribution of the heat released during combustion

Amount of heat released \(V_{\text{gas}}\cdot Q_n^p\), kcal/h	Amount of heat absorbed by the water screen, \(G_{\text{water}}\Delta t\), kcal/h	Fraction of heat absorbed by the heat screen
\(0.32\cdot 4254=1360\)	\(15\cdot 54.5\)	0.75
\(0.33\cdot 4254=1400\)	\(18.79\cdot 54\)	0.72
\(0.42\cdot 4254=1780\)	\(18.40\cdot 70.8\)	0.73
\(0.45\cdot 4254=1910\)	\(19.30\cdot 76.2\)	0.77
\(0.50\cdot 4254=2127\)	\(21.50\cdot 69.2\)	0.70
\(0.52\cdot 4254=2210\)	\(21.20\cdot 73.7\)	0.71
\(0.63\cdot 4254=2680\)	\(25.20\cdot 80\)	0.74
\(0.65\cdot 4254=2760\)	\(43.23\cdot 46.9\)	0.73
\(0.66\cdot 4254=2800\)	\(21.42\cdot 90.3\)	0.69
\(0.67\cdot 4254=2850\)	\(25.10\cdot 79.5\)	0.70
\(0.90\cdot 4254=3820\)	\(30.40\cdot 85.7\)	0.68
\(1.28\cdot 4254=5450\)	\(55.50\cdot 74.5\)	0.76

Thus, the fraction of heat absorbed by the water screen averaged 0.72; the remaining heat—0.28—was lost with the outgoing combustion products and as heat losses to the surroundings.

Consequently, the experiments of series B demonstrated the possibility of stable surface (flameless) combustion in a granular bed in the presence of heat transfer to the heating surface. This method can be used in various heat apparatuses employed in the chemical industry.

B. Surface (flameless) combustion of illuminating gas in refractory channel and porous plates

The layout of the experimental apparatus is shown in Fig. 6.

A steel cylindrical burner. In the casing of the cylinder, along its height, 2 rectangular “windows” were cut, closed with mica, for observing flame flashback. At the top of the cylinder a steel ring is installed, in which a channel refractory plate is fastened, with a diameter equal to the diameter of the cylinder. The plates were made of refractory clay (15 specimens), of a refractory mass composed of 65% corundum and 35% clay (11 specimens), and of fired magnesite (3 specimens). The diameter of all plates was the same and was 50 mm. The thickness of the plates varied: from 7 to 50 mm. The channels in the plates had various diameters: from 1 to 4.2 mm. The number of channels in the plates ranged from 52 to 495. In addition to plates with channels of a definite diameter, porous plates were made by pressing in sawdust and subsequently burning it out.

During the tests the following measurements were made: 1) the amount of gas and air; 2) the temperature of the outer surface of the plate; 3) the temperature inside the burner cylinder.

1. Burner
2. Water manometer
3. Thermocouple
4. Mixer
5. Air vessel
6. Fireproof plate
7. Sight window
8. Burner body

Fig. 6. Diagram of the apparatus for studying the surface combustion of lighting gas in channel and porous plates.

The results of the measurements are presented in Table 6, which includes measurements not for all experiments, but only for some of the experiments characterized by a prolonged process of stable surface combustion.

Table 6

Materials	Plate diameter, mm	Plate thickness, mm	Channel diameter, mm	Number of channels	Gas, m³/hour	Air, m³/hour	Excess-air coefficient	Temperature at the plate surface, °C
Mixture: 65% corundum, 35% clay	50	30	1.5	209	0.54	2.41	1.03	840
Mixture: 65% corundum, 35% clay	50	20	2.5	89	0.56	2.50	1.05	760
Mixture: 65% corundum, 35% clay	50	30	2.5	89	0.56	2.49	1.04	920
Fireclay	50	30	1.5	209	0.46	2.05	1.01	810
Fireclay	50	33	2.5	89	0.56	2.50	1.00	950
Fireclay	50	50	4.2	52	0.46	2.06	1.01	890
Calcined magnesite	50	40	2.0	120	0.64	2.85	1.0	840
Calcined magnesite	50	20	2.0	120	0.64	2.90	1.04	780
Porous mass of fireclay	50	30	Porosity was not determined	Porosity was not determined	0.63	2.80	1.00	860
Porous mass of 65% corundum and 35% clay	50	30	Porosity was not determined	Porosity was not determined	1.30	5.9	1.04	870
Porous mass of 93% magnesite and 7% clay	50	30	Porosity was not determined	Porosity was not determined	0.65	2.9	1.02	790

As indicated above, Table 6 includes only those experiments in which stable surface combustion, easily regulated over a long period of time, was achieved with uniform incandescence of the surface.

On the basis of the data in Table 6, the velocity of passage of the combustible mixture through the channels of the plates ranged from 1 m/sec to 2.58 m/sec.

The heat intensity of combustion, conventionally referred to the volume of the channels, ranged from \(65 \cdot 10^6\) kcal/m³·hour to \(235 \cdot 10^6\) kcal/m³·hour.

The thermal intensity of combustion, conventionally referred to the outer surface of the tile, is from \(1 \cdot 10^6\ \text{kcal}/\text{m}^2\cdot\text{h}\) to \(3 \cdot 10^6\ \text{kcal}/\text{m}^2\cdot\text{h}\).

Direct observations of the process of surface combustion with channel and porous tiles make it possible to draw the following conclusions: a) for the same channel diameter in the tiles, the thicker the tile, the more stable the process. Tiles 30–40 mm thick proved the most suitable; b) the most easily regulated combustion process is achieved in porous tiles.

Experiments in which surface combustion was not stable are characterized by the following data: a) in tiles 7 to 10 mm thick, with channels 1 mm in diameter and 495 in number, stable combustion could not be achieved; b) in tiles of the same thickness, but with channels 2.5 to 4.2 mm in diameter and 89 to 52 in number, stable surface combustion likewise could not be achieved.

Thus, the experiments of series B proved the possibility of stable surface (flameless) combustion using channel and porous tiles and revealed the optimal ratios among their geometric dimensions. A method of surface combustion of this kind may be applied in bath-type industrial furnaces, for heating the bath mirror by radiation from the surface of the tiles.

G. Experiments on the Combustion of Water Gas in a Quartz Tube

As is known, the flame-propagation velocity of water gas is considerably greater than the flame-propagation velocity of hydrocarbon gases, for example, coke-oven or illuminating gas. Thus, the flame-propagation velocity of illuminating and coke-oven gas is expressed by the value 1.6 m/s, whereas the propagation velocity of water gas is 2.8 m/s. Consequently, preliminary experiments on the combustion of water gas in a granular bed were accompanied by frequent flashbacks into the mixer.

The water producer gas used for the experiments is obtained at electric-lamp plant No. 660, adjacent to the institute, in generators of the Pintsch system from Aralich lean bituminous coal of the semi-anthracite type.

Composition of the moist gas, saturated at \(20^\circ\text{C}\): \(\mathrm{CO}\)—37.13%; \(\mathrm{CO}_2\)—4.87%; \(\mathrm{O}_2\)—0.19%; \(\mathrm{H}_2\)—52.3%; \(\mathrm{H}_2\mathrm{O}\)—2.3%; \(\mathrm{N}_2\)—3.21%.

The calorific value of the gas, calculated for this composition and repeatedly determined in a Junkers calorimeter both in the laboratory of the department and in the laboratory at plant No. 660, is

\[ Q_{\mathrm{H}}^{p} = 2470 \frac{\text{kcal}}{\text{m}^3} \]

The specific gravity of the gas is \(\gamma_0 = 0.669\ \text{kg}/\text{m}^3\).

For the combustion of this gas with the theoretically necessary quantity, \(2.12\ \text{m}^3/\text{m}^3\) of air is required. The quantity of combustion products thereby formed is \(2.67\ \text{m}^3/\text{m}^3\).

The calorimetric combustion temperature of water gas (heat-producing capacity) when burned with the theoretically necessary quantity of air in the cold state (temperature of the gas and air about 15–20°C), \(t_{\text{calor.}} = 2050^\circ\text{C}\).

The gas flow rate was determined by means of a normal sharp-edged orifice plate installed in the gas pipeline. The gas pipeline has an internal diameter \(D = 15\) mm; the orifice plate has an internal diameter \(d = 7.5\) mm.

The air flow rate was determined by means of a normal orifice plate installed in the air duct. The internal diameter of the air duct is \(D = 25\) mm; the internal diameter of the orifice plate is \(d = 12.5\) mm.

In the experiments a quartz tube of internal diameter 15 mm and length 1100 mm was used. The cross section of the tube was

\[ f=\frac{\pi d^{2}}{4}=0.785\cdot(0.015)^{2}=0.000175\ \text{m}^{2}. \]

In one series of experiments the investigation was carried out with the aid of a glass injector. Water gas was supplied from the mains under pressure, and the air was injected from the surrounding atmosphere.

The arrangement of the experimental setup is shown in Fig. 7.

The gas was supplied to the injector under a pressure of 218 mm water column, in an amount of 0.55 m³/h. The air flow rate was not measured; in any case it was less

Fig. 7. Combustion of water gas in a quartz tube

than that theoretically required for combustion, i.e., less than \(0.55\cdot 2.12\) m³/h; consequently, the amount of combustible mixture was less than 1.72 m³/h, and accordingly the velocity of passage of the combustible mixture through the tube was less than

\[ \frac{1.72\cdot 4}{3600\cdot 3.14\cdot(0.015)^{2}}=2.7\ \text{m/sec}. \]

Under these conditions, in an empty quartz tube, when the combustible mixture was passed through, flashback of the flame occurred from the open end of the tube to the injector nozzle. Then spirals made of copper wire were placed in the tube at various distances from the end of the tube. The spirals had the following dimensions: a) length 125 mm, diameter 14 mm, number of turns 5; b) length 70 mm, number of turns 20; and c) length 30 mm, number of turns 10.

When the wire was placed at a distance of 510 mm from the outlet end of the tube (position A), the flame flashed back to A and went out; it was not possible to hold the flame in position A. When the wire was placed closer to the outlet end, at a distance of 370 mm (position B), the same phenomenon was observed, i.e., flashback of the flame to position B and extinction; but when the wire was placed at a distance of 220 mm (position C), upon ignition the flame flashed back to C and burned steadily; localization of the flame occurred in position C. The temperature of the outer surface of the tube in the section occupied by the wire over a length of 25 mm rose to 800–850°C.

When the pressure in the mains was reduced to 60 mm water column, the spirals in all positions were penetrated by the flame, and it was not possible to localize the flame in the tube.

Experiments were then carried out with metal meshes instead of spirals. The mesh (tungsten) was fixed in a holder in 3 rows, and the holder was inserted into the quartz tube (Fig. 8).

At a gas pressure in the mains of 100 mm water column and under the same air-injection conditions, it was not possible to arrest the flame in any position along the entire length of the quartz tube.

If an igniting burner is constantly kept at the open outlet end of the tube, then a periodically recurring flashback of the flame is obtained. The periodicity of the flashback is 70 times per minute. Apparently, the periodicity of the flashbacks should be explained by the duration of propagation of the flame through the tube. Approximately, the duration of flame propagation is expressed—

is expected in \(\frac{60}{70}=0.85\) sec.; consequently, the flame propagation velocity under these conditions will approximately be equal to:

\[ \frac{1.08}{0.85}=1.28\ \text{m/sec.} \]

In investigating the combustion of water gas in a quartz tube with forced supply of gas and air into the mixer (in contrast to the preceding experiments, when the air was injected from the atmosphere), it was found that localization of the flame on the metal screen occurs under the following regime: gas flow rate \(0.935\ \text{m}^3/\text{hr}\); air flow rate from \(2.94\ \text{m}^3/\text{hr}\) to \(3.14\ \text{m}^3/\text{hr}\); velocity of the combustible mixture in the tube from 6.15 to 6.45 m/sec.

At the same time it should be noted that localization of the flame on the screen did not begin immediately; for some time periodic flashbacks of the flame to the screen occurred. Suspecting that the cause of the periodic flashbacks was the cooling action of the walls of the quartz tube, and that this action was the greater the longer the distance to the screen, in subsequent experiments, at the same gas flow rate, the screen was moved toward the outlet end of the tube to a distance of 350–370 mm; in this case the number of flashbacks before flame localization was considerably reduced, and combustion on the screen was established more rapidly. Subsequently, in order to eliminate the cooling influence of the tube walls, the latter was insulated with asbestos cylinders placed over the tube. With such insulation of the walls of the quartz tube, localization of the flame at the above-mentioned flow rate of the combustible mixture occurred on the screen at any distance from the outlet end of the tube, in any position of the holder with the screens, and, moreover, immediately, without preliminary periodic flashbacks. A thermocouple inserted into the insulation made it possible to measure the temperature of the insulated surface of the quartz tube; this temperature varied within the range from 950 to 1200°C.

Fig. 8. Tungsten holder

When the gas flow rate was increased to \(1.08\ \text{m}^3/\text{hr}\) and the air flow rate to \(3.84\ \text{m}^3/\text{hr}\), and, consequently, the velocity of the combustible mixture in the tube to 8 m/sec., insulation of the tube walls was no longer required for localization of the flame on the screen; the insulating asbestos cylinders were removed from the tube, and retention of the flame on the screen occurred immediately in any position along the length of the quartz tube.

Experiments on gas combustion were then repeated in an empty quartz tube, without a screen and without metal spirals, but at an increased flow rate of the combustible mixture. At a gas flow rate of \(2.7\ \text{m}^3/\text{hr}\) and an air flow rate of \(7\ \text{m}^3/\text{hr}\), and at a combustible-mixture velocity of 15.4 m/sec., the flame was held in the tube at a distance of 400 mm from the outlet end of the tube. When the velocity and flow rate were decreased or increased, localization of the flame occurred at a nearer or more distant distance from the outlet end of the tube.

In burning water gas in a quartz tube filled with fireclay grains, it was found (the tube was filled tightly with fireclay grains 3–4 mm in diameter, in a layer 600 mm long, counting from the inlet end of the tube) (Fig. 9):

at a gas flow rate of \(0.864\ \text{m}^3/\text{hr}\) and an air flow rate of \(2.22\ \text{m}^3/\text{hr}\) (excess-air coefficient 1.2 and mixture velocity 5 m/sec.), the flame, ignited at the out-

from the inlet end, stopped for a short time at position A, then shot through to B, remained for some time at B, again shot through to C, and was localized there for a long time. No flame flashback into the mixer was observed. Then, at the same flow rate, the experiment was repeated, but the layer of fireclay grains was shortened to 170 mm and shifted 300 mm from the inlet end of the tube.

Fig. 9. Combustion of water gas in a quartz tube with refractory grains

In this case the phenomenon was repeated; that is, the flame remained for a short time at position A, then jumped to B, and there the combustion was stable for an indefinitely long time.

D. Flameless combustion of water gas in a small-model furnace

The small-model furnace had the following dimensions: internal cylinder diameter 547 mm; internal cylinder height 115 mm; internal cylinder volume

\[ \frac{\pi d^{2}h}{4}=\frac{3.14}{4}(0.047)^2=0.00173\ \mathrm{m^3} \]

On the refractory grate, in a layer 10 mm high, there were quartz grains 3 mm in diameter; above them, to a height of 105 mm, were magnesite grains 3–4 mm in diameter. Pyroscopic cones were placed in the layers: No. 16 at the bottom (melting temperature 1460°C); No. 13 in the middle (1380°C); and No. 12 at the top (1350°C). The gas and air flow rates were: gas from 1.7 m³ to 1.95 m³, and air from 3.14 m³/hour to 3.52 m³/hour (air-excess coefficient from 0.80 to 0.84). During the experiments it was found that:

a) the lower layer of quartz grains was carried by the stream to the surface; on the surface the quartz grains were in a mobile state;

b) the pyroscopic cones were likewise forced out to the surface;

c) after 1 hour 15 minutes, cone No. 12 (1350°C) melted. Taking the mean open cross section of the layer as equal to 0.22, we obtain: the velocity of passage of the combustible mixture (in the cold state) was from 3.5 m/sec to 4 m/sec.

The velocity of passage of the combustion products at the measured temperature of 1350°C was from 19.2 m/sec to 21 m/sec.

The heat release rate per unit volume (relative to the entire volume of the cylinder) was approximately \(20 \cdot 10^{6}\) kcal/m³·hour.

Then experiments were conducted with a granular layer made of larger grains.

Magnesite grains 6–9 mm in diameter were placed in the small-model furnace, in an amount of 250 pieces (by count). The volume of the grains was \(0.0000670\ \mathrm{m^3}\); the volumetric porosity of the layer was

\[ \frac{0.0001955-0.0000670}{0.0001955}=0.66. \]

Gas flow rate—1.22 m³/h; air flow rate—2.72 m³/h. Air-excess coefficient—1.04.

Pyroscopes were placed in the bed: at the bottom—No. 34 (1750°C); No. 35 (1770°C); in the middle—No. 28 (1630°C); at the top—No. 27 (1610°C).

The experiment lasted about 8 hours. After the furnace had cooled, it was found that cones No. 27 and 28 had melted, No. 34 had glazed over, and No. 35 remained without visible changes. Consequently, the temperature in the granular bed was of the order of 1630–1700°C.

The thermal intensity of the bed (referred to the entire volume of the cylinder) was

\[ 15 \cdot 10^6 \frac{\text{kcal}}{\text{m}^3 \cdot \text{h}} . \]

The thermal intensity referred to the pore volume was

\[ 23.5 \cdot 10^6 \frac{\text{kcal}}{\text{m}^3 \cdot \text{h}} . \]

Taking the average free cross-section as equal to 0.22, we obtain: the velocity of passage of the combustible mixture (in the cold state) through the bed is 2.9 m/sec.

The velocity of passage through the bed of the combustion products, at the measured temperature

\[ \frac{1630+1700}{2}=1665^\circ\text{C}, \]

will be 14.2 m/sec.

As indicated above, the experiment lasted 8 hours; no carry-over of grains from the bed was observed, and the grains in the bed were in a calm state, since the kinetic energy of the stream corresponding to a velocity of 14.2 m/sec is insufficient to overcome the weight of the particle, which is also confirmed by the following calculation. It is generally accepted that, as a result of the interaction of gravity and the resistance force according to Stokes, the flow velocity at which a solid particle is entrained can be found from the equation (according to Prokat):

\[ w_0 = 3.15 \sqrt{d \frac{\gamma_m}{\gamma_2}} \left(\frac{\text{m}}{\text{sec}}\right) \tag{41} \]

Here \(d\) is the particle diameter (m); in our case \(d = 0.008\) m; \(\gamma_m\) is the specific (volumetric) weight of the material; in our case, for magnesite, \(\gamma = 2600\) kg/m³; \(\gamma_2\) is the specific weight of the gas; in our case, at a temperature of 1665°C, \(\gamma_2 = 0.184\); hence \(w_0 = 33.6\) m/sec, that is, at a flow velocity greater than 33.6 m/sec, carry-over of particles from the bed should be observed; since in the experiments described the velocity of the combustion products was 20.6 m/sec, and no popping or explosions were observed, carry-over of particles likewise did not occur.

The experiment was then repeated, with magnesite grains of still larger size being taken, namely 10 mm. The number of grains (by count) was 250.

The volume of the grains was 0.00013 m³.

With the total furnace volume equal to 0.0001955, the volumetric porosity was

\[ \frac{0.0001955 - 0.00013}{0.0001955} = 0.34 . \]

Note: if the volumetric porosity of the bed is calculated according to Slichter,

\[ m = \frac{\pi}{6(1-\cos\theta)\sqrt{1+2\cos\theta}}, \]

then a volumetric porosity of 0.34 corresponds to an angle of arrangement of the spherical grains \(\theta = 65^\circ\).

The specific surface of the granular bed, as the ratio of the surface area of all spherical grains to the volume of the bed, is expressed as

\[ \sigma=\frac{N\pi d^2}{\frac{N\pi d^3}{6(1-m)}}=\frac{6(1-m)}{d} \]

\[ \sigma=\frac{6(1-0.34)}{0.01}=384\ \mathrm{m^2/m^3}. \]

In this experiment the gas flow rate was \(1\ \mathrm{m^3/hour}\); the air flow rate was \(2.33\ \mathrm{m^3/hour}\); the excess-air coefficient was \(1.08\).

Pyroscopes were placed in the bed: at the bottom No. 34 \((1750^\circ\mathrm{C})\), in the middle of the bed No. 28 \((1630^\circ\mathrm{C})\), and at the top No. 27 \((1610^\circ\mathrm{C})\); the experiment lasted about 3 hours, and was then stopped, since flameless combustion, with all its characteristic signs, was stable. All the cones melted; consequently, the temperature in the bed was not lower than \(1750^\circ\mathrm{C}\).

The heat intensity of the bed (referred to the entire volume of the cylinder) was

\[ 12.6\cdot 10^6\ \frac{\mathrm{kcal}}{\mathrm{m^3\,hour}}. \]

The heat intensity referred to the pore volume was

\[ 37.2\cdot 10^6\ \frac{\mathrm{kcal}}{\mathrm{m^3\,hour}}. \]

The heat intensity referred to the surface of the grains (combustion density) was

\[ 32.8\cdot 10^3\ \frac{\mathrm{kcal}}{\mathrm{m^2\,hour}}. \]

With an average open cross section equal to \(0.22\), the velocity of passage of the combustible mixture (in the cold state) through the bed was \(2.45\ \mathrm{m/sec}\).

The velocity of passage of the combustion products through the bed, at the measured temperature of \(1750^\circ\mathrm{C}\), was \(15.3\ \mathrm{m/sec}\).

Under these conditions the flameless combustion was stable; no entrainment of grains was observed.

The pyrometric combustion coefficient, as the ratio of the measured temperature to the calorimetric combustion temperature, was

\[ \frac{1750}{2050}=0.85. \]

E. Flameless combustion of water gas in the enlarged-model furnace

The enlarged-model furnace has the following dimensions: internal diameter of the cylinder \(90\ \mathrm{mm}\), internal height of the grain bed \(155\ \mathrm{mm}\), internal volume of the cylinder

\[ \frac{\pi d^2 h}{4}=\frac{3.14}{4}\cdot(0.09)^2\cdot 0.155=0.001255\ \mathrm{m^3}. \]

The furnace body is turned from a round cast-iron blank; the wall thickness is \(10\ \mathrm{mm}\). The cast-iron walls are coated on the inside with asbestos insulation \(8\ \mathrm{mm}\) thick and with a magnesite refractory luting \(20\ \mathrm{mm}\) thick. On the outside, the cast-iron walls of the cylinder are covered with asbestos insulation \(30\ \mathrm{mm}\) thick. The granular bed is located on a refractory grate \(15\ \mathrm{mm}\) thick, with holes \(3\ \mathrm{mm}\) in diameter; the number of holes in the grate is 35; consequently, the open cross section of the grate is

\[ \frac{\pi d_0^2}{4}\,n=0.000264\ \mathrm{m^2} \]

The grate is located above the burner at a height of 50 mm, so that between the outlet opening of the burner and the grate there is a free volume of 0.00032 m³.

The burner is of the injection type: water gas from the mains was supplied to the burner nozzle under a pressure of 500 mm water column; air was forced into the burner by an Alma fan under a pressure of 200 mm water column. The gas and air flow rates were measured from the pressure drop across sharp-edged orifices. The temperature inside the bed was measured with pyroscopes and a Pt—PtRh thermocouple, and on the open surface of the grains with an “Ardometer” radiation pyrometer. A graphite crucible, filled with a batch for glass melting, was placed in the granular bed. The granular bed consisted of magnesite grains 9–10 mm in diameter. The arrangement of the installation is shown in Fig. 10.

The furnace is ignited in the usual way, i.e., at first gas alone is admitted and ignited from outside the bed. Then air is gradually added; the flame “settles” on the surface of the bed and penetrates to a certain depth inside the bed. As the bed heats up, the amount of air is increased

and is brought up to the theoretically necessary amount or to a slight excess. After 1 hr. 30 min. from the start of the gas supply, the combustion becomes externally flameless—the entire granular bed is incandescent, and no flame is present. Usually the experiments on melting the batch lasted 2–3 hours. Throughout the entire time the flameless combustion was completely stable, without any disturbances. The gas consumption ranged from 2.76 m³/hr to 2.86 m³/hr; the air consumption from 6.5 m³/hr to 7 m³/hr; the excess-air coefficient from 1.09 to 1.14. At the bottom of the bed above the grate, pyroscopes No. 19 (1520°C) were placed; at the location of the crucible, a thermocouple was installed. The temperature reached during operation was: at the bottom not less than 1500°C (the pyroscope melted), at the crucible location—1480°C according to the thermocouple readings, and the temperature on the surface of the bed—1440°C (according to the pyrometer readings). In the cruc—

the charge, consisting of 80% \(SiO_2\) and 20% \(Na_2CO_3\), melted, and glass was formed.

The thermal intensity of the layer, referred to the entire volume of the furnace,

\[ \text{from } \frac{2470 \cdot 2.76}{0.001255} = 5.45 \cdot 10^6 \ \text{kcal}/\text{h}\,\text{m}^3 \]

\[ \text{to } \frac{2470 \cdot 2.86}{0.001255} = 5.83 \cdot 10^6 \ \text{kcal}/\text{h}\,\text{m}^3 . \]

The average thermal intensity of the layer, after subtracting the volume of the grains and of the crucible (volumetric porosity of the layer 0.34, volume of the crucible \(0.00008 \ \text{m}^3\)), is

\[ \frac{2470 \cdot 2.82}{0.001255 \cdot 0.34 - 0.00008} = 20 \cdot 10^6 \ \text{kcal}/\text{m}^3\text{h}. \]

The velocity of passage of the combustible mixture (in the cold state) through the layer, with a clear cross section of the layer of 0.22, was on average

\[ \frac{2.82 + 6.75}{3600 \cdot 0.00635 \cdot 0.22} = 1.9 \ \text{m/s}. \]

The velocity of passage of the combustion products through the layer at the measured temperature of \(1520^\circ C\) was \(10.2 \ \text{m/s}\).

At the narrowest point of the layer, where the crucible, 50 mm in diameter, was placed, at a temperature of \(1480^\circ C\) the velocity of the combustion products was \(15.1 \ \text{m/s}\).

No entrainment of grains from the layer was observed.

The velocity of passage of the combustible mixture through the openings in the grate separating the granular layer from the burner was

\[ \frac{2.82 + 6.75}{3600 \cdot 0.000264} = 10 \ \text{m/s}. \]

Conclusions and Final Remarks

1. In this work an attempt has been made to describe the mechanism of surface flameless combustion of gases, proceeding from the general conception of gas combustion and the mutual transformability of some forms of gas combustion into others. By appropriately changing the physical and chemical conditions, it is possible to bring about the transformation of flame combustion of gases into a stable flameless surface process; conversely, when the conditions of stability are disturbed, the flameless process turns into torch flame combustion.

2. In the transition of torch flame combustion to flameless surface combustion, the normal flame front is substantially deformed; the deformation of the normal flame front is influenced by hydrodynamic factors (increased efflux velocity, change in the velocity distribution, etc.) and by physicochemical conditions (flame-propagation velocity, catalytic influence of the surface, temperature, etc.).

3. The inevitable increase in the flame-propagation velocity in flameless combustion also entails the necessity of increasing the velocity of efflux of the combustible mixture through a burner of one design or another (granular layer, pores, channels, etc.); as a consequence, flameless combustion is concentrated in small furnace volumes, thereby creating considerable values of thermal intensity \(\left(\frac{\text{kcal}}{\text{m}^3\text{h}}\right)\) and heat-release density of combustion \(\left(\frac{\text{kcal}}{\text{m}^2\text{h}}\right)\).

1. The stability of the flameless surface combustion process is determined by the conditions of thermokinetic equilibrium in the zones: pre-flame, reaction, and post-flame, as well as by the relationship between the zones. Mathematical relations have been established that make it possible to determine the influence of the principal physical and chemical factors on the dimensions of the individual zones within the limits of stable flameless combustion. The causes are also indicated as a result of which the stability of the flameless combustion process is disturbed.

2. In the experimental part of the study, six series of experiments were carried out in the laboratory; in the first three series of experiments illuminating gas was used (series A, B, C), and in the last three series of experiments water gas was used (series G, D, E).

In the flameless combustion of illuminating gas, the objective was set—to organize stable flameless combustion at low gas and air pressure under various conditions of flameless combustion, namely: combustion in a granular bed with an open bed surface, combustion in a granular bed with water heating above the bed, and combustion in refractory channel and porous tiles. The stated objective was achieved; in addition, the optimal structure of the granular bed and the minimum dimensions of channel tiles (channel diameter, their length) were determined.

In the flameless combustion of water gas, the objective was set—to increase the pyrometric combustion coefficient.

In the experiments with water gas, the pyrometric combustion coefficient reached a value of 0.85. At the same time it was found that an essential criterion for evaluating the structure of the granular bed is the product of the grain diameter by its specific gravity. To avoid disturbing the stability of the flameless process, this product must be greater than the critical value; otherwise, as a result of entrainment or oscillation of the grains in the bed, the flameless process is disrupted.

Incidentally, the idea was put forward (only preliminarily tested) that, in contrast to the existing methods for determining the rate of flame propagation (static and dynamic), a method of continuous pulsations may be proposed; but this proposal is the subject of a special additional investigation.

LIST OF REFERENCES CITED

1. M. B. Ravich.—Surface combustion, Publishing House of the Academy of Sciences of the USSR, 1946.

2. Chaleur et Industrie 213, 185–190, 1938.

3. N. Norkin. Diffusion combustion of gases. Report; abstract published in the Bulletin of the All-Union Chemical Society named after D. I. Mendeleev No. 4, 1–44.

4. W. Hupburn. Diffusion combustion heating reduces shaling loss of steel. Steel 10, 25–27, 12.21, 1932.

5. D. N. Lyakhovskii and S. N. Syrkin—Aerodynamics of an elementary flame. Journal of Technical Physics 5, 505–514, 1937.

6. M. A. Kuzmin—On the question of the calculation of flame furnaces. Metallurg 9, 46–58, 1934.

7. D. N. Lyakhovskii, S. N. Syrkin—Turbulent diffusion in a flame. Soviet Boiler Construction 9, 5–8, 1935.

8. B. A. Shvab.—The relation between the temperature and velocity fields of a gas flame. Journal of Technical Physics 5, 431–442, 1941.

9. V. Heiligenstaedt.—Thermal-engineering calculations for the design of furnaces and their operation. Translated from the German, 1937.

10. K. V. Brod.—Methodology for calculating the temperature of the flame of coke ovens when heated by blast-furnace gas. Coke and Chemistry 6, 19–21, 1939.

11. N. Norkin.—Report on scientific-research work (unpublished), located in the scientific-technical library of TPI.

12. E. Mallard—et le Chatelier. Ann. min. 8, 1883.

13. V. A. Mikhelson. On the normal ignition velocity of explosive gas mixtures. Collected Works, vol. I, 1930.

1. G. Damköhler—Der Einfluss der Turbulenz auf die Flammengeschwindigkeit in Gasgemischen, Ztschr. f. Electroch. u. angew. Physik. Chemie, B. 46, No. 11, 1940.

2. Gouy.—Recherches photometriques sur la flammes colorees. Ann. de Chem. et Phys., vol. 5, No. 18, pp. 1—101, 1879.

3. Ubbelohde and Anwander. J. f.—Gasbeleuchtung. 225, 1917.

4. Nikuradze.—Cited from Gröber and Erk. Principles of the Theory of Heat Exchange. Translated from German, 1936.

5. Slichter.—Cited from Leibenzon. Oil-Field Mechanics. Part II, ONTI, 1934.

6. Nusselt.—ZVDJ 59, 1918.

7. Ribaud—Chaleur et Industrie 213, 1938.

8. N. N. Semenov.—Thermal Theory of Combustion and Explosions. Advances in the Physical Sciences, XXIII, issue 3, pp. 251—292, 1940.

9. W. Bone and Townend.—Flame and Combustion in Gases. London, 1927.

10. W. Payman.—Jnd. a Eng. Chem. 20, 10. 1928.

11. E. B. Zel’dovich, N. N. Semenov.—ZhETF, 9—10. 1940.

12. K. A. Syugov.—Collection of Scientific-Research Works of the Ural Branch of VTI, issue 4, 1939.