Flame Length in the Combustion of Partially Prepared Combustible Mixtures of Water Gas with Air

N. N. Norkin

(Presented by Prof. I. V. Gebler, Doctor of Technical Sciences)

With the aid of atmospheric burners, the combustion of partially prepared combustible gas mixtures is carried out; mixture formation takes place in the burner by injection of primary air by the gas, usually in an amount less than that theoretically required, that is, at an excess-air coefficient less than unity (hence the name “partially prepared” combustible mixture). Atmospheric burners often operate as two-pipe burners with forced supply of gas and air.

When combustible gas mixtures containing primary air in an amount insufficient for complete combustion are burned, a two-cone flame with two combustion fronts is formed. On the surface of the inner cone—the inner front—the gas burns in an amount equivalent to the content of primary air in the combustible mixture. The oxygen of the primary air enters completely into the combustion reaction. The inner combustion front is the kinetic part of the flame.

On the surface of the outer cone—the outer front—the remaining portion of the gas burns with air (secondary) diffusing from the surrounding medium. The outer combustion front is the diffusion part of the flame.

Such complex kinetic-diffusion combustion we call flame combustion in partially prepared combustible mixtures. The geometrical dimensions of the flame are influenced by: the burner diameter, the velocity and regime of discharge, and the composition of the combustible mixtures.

Our study, carried out in the laboratory of the Tomsk Polytechnic Institute and verified at one of the plants, is an attempt to establish certain generalized dependences of the kinetic-diffusion flame, proceeding from the basic principles of hydrodynamics and chemical kinetics by directly studying a burning flame. The experiments were performed with burners of diameter 1.18—1.54—2.9—3.7 mm. For combustion, water producer gas of the following composition was used: CO₂—4.5%, O₂—0.4%, CO—28.4%, H₂—51.0%, CH₄—6.6%, N₂—7.1%, and H₂O—2.0%. The theoretically required amount of air is equal to 2.5 m³/m³. The composition of the combustible mixtures varied within the limits from 15.8 to 73.2% water gas in the combustible mixtures, that is, within the limits of the excess-air coefficient from \(\alpha = 2.13\) to \(\alpha = 0.14\).

The efflux velocities of the combustible mixtures varied from 1.58 to 123.3 m/sec. The Reynolds numbers \(Re\) varied from 738 to 9260.

The gas and air flow rates were measured with gas meters. The flame length was measured with an optical instrument of the cathetometer type. The composition of the combustible mixtures was determined with a combustion gas analyzer.

The measurement results are presented in the table. The following notation is used in the table:

\(\alpha\) — excess-air coefficient;

\(w\) — velocity of efflux of the combustible mixture from the burner;

\(l\) — length of the inner (kinetic) flame;

\(L\) — total length of the kinetic-diffusion flame;

\[ Re=\frac{wd}{\mu}\rho \]

calculated for the combustible mixture during efflux from the burner;

\(u\) — flame-propagation velocity;

\[ \frac{w}{u}=Mi \]

— the Michelson criterion (the name is proposed by the author of the article).

As can be seen from the table, the ratio \(\frac{w}{u}\) varied in the experiments from 3.4 to 70.5. Within these ratios, combustion is stable. Attempts to obtain stable combustion when this ratio was decreased ended with flashback of the flame into the burner, and when \(\frac{w}{u}>70.5\) it ended with separation of the flame from the burner.

Table

Flame length of water-gas flame as a function of the composition of combustible mixtures, efflux velocity, and burner diameter

Burner diameter 1.54 mm

Burner diameter 2.9 mm

Burner diameter 3.7 mm

In Fig. 1 a straight line is shown with experimental points on it, indicating the dependence of the relative length of the kinetic part of the flame on the Michelson criterion

\[ \frac{l}{r} = \varphi\left(\frac{w}{u}\right) \tag{1} \]

for four burners.

Thus, for burners of different diameter, the length of the inner (kinetic) cone is

\[ l = r \frac{w}{u}, \tag{2} \]

which corresponds to Michelson’s equation

\[ l = r \sqrt{\frac{w^2}{u^2}} - 1, \tag{3} \]

if the unity is discarded, which is entirely permissible, since in our experiments \(\left(\frac{w}{u}\right)^2\) varied from 36 to 4900.

Fig. 1. Dependence of the relative length of the kinetic part of the flame on the Michelson criterion.

The criterion \(Mi\) is a measure of the relationship between the chemical and hydrodynamic kinetics in the flame combustion process. The criterion \(Mi\) characterizes the stability of the flame process; for \(Mi < 1\) the flame process is unstable and is not stabilized. The critical value is

\[ Mi_{\mathrm{crit}} = 1. \]

If, in ordinary flame combustion, the stability of the process is determined by the value \(Mi > 1\) (for example, in our experiments at \(Mi \geq 3.4\)), then in homogeneous–heterogeneous combustion on a heated surface (thin channels, granular bed, porous bodies) a stable combustion process is possible at \(Mi = 1\).

The upper stability limit of the flame combustion process in experiments with water gas is equal to \(Mi = 70.5\).

The relative length of the kinetic flame is uniquely determined by the criterion \(Mi\). In the case of complex kinetic–diffusion combustion, the total flame length (external combustion front) depends mainly on the criterion \(Mi\).

Fig. 2. Dependence of the length of the external flame on the Michelson criterion.

In Fig. 2 are shown curves indicating the dependence of the total flame length \(L\) on the criterion \(Mi\). As is seen from the curves, \(L\) is not determined uniquely by the value of \(Mi\), but also depends on the burner diameter.

Let us assume this dependence in the form

\[ L = A d^n Mi . \tag{4} \]

Here \(L\) is in mm, \(d\) is in mm.

By processing the experimental data for burners of diameter \(2.9\) mm and \(3.7\) mm, it was established that \(A=\mathrm{const}=0.535\), \(n=\mathrm{const}=1.9\).

Attention is drawn to the fact that outflow from these burners occurred predominantly in a conditionally laminar regime at \(Re<2320\). Outflow from burners of diameter \(1.18\) mm and \(1.54\) mm occurred in a conditionally turbulent regime. For these cases it is necessary to introduce the correction factor

\[ m=\sqrt{\frac{Re}{2320}} . \tag{5} \]

Thus, the generalized equation for the dependence of the total length of the kinetic-diffusion flame has the form

\[ L=Amd^nMi, \tag{6} \]

where for the laminar regime

\[ m=1 \]

and for the turbulent regime

Fig. 3. Generalized curve. \(\dfrac{L}{A d^n}=Mi\) and \(\dfrac{L\cdot 2320^m}{A d^n Re^m}=Mi\)

\[ m = \left( \frac{Re}{2320} \right)^{0.5}. \tag{7} \]

The generalized straight line described by the equation is shown in Fig. 3.

We use the terms “conditionally laminar” and “conditionally turbulent” outflow regime in order to emphasize that, for a burning jet, the critical value of \(Re\) calculated for flow in a tube is conditional.

Conclusions

In a flame plume that forms two combustion fronts, the length (height) of the inner kinetic combustion front is calculated by Michelson’s equation. To calculate the total length (height) of a plume with an external diffusion-combustion front, a new equation is proposed that reflects the influence of the character of motion, the Michelson criterion, and the burner diameter. The equation has been verified in the combustion of combustible mixtures of water gas with air.