LOOKING at the familiar sight of a flame of natural gas burning in air, one might wonder what would happen if the gas and the air were interchanged, that is, if a jet of air were introduced into an atmosphere of natural gas. Would one see some kind of reverse flame, with the same shape, height, color and temperature distribution as a normal flame? These questions occurred to Stuart Travis of Akron, Colo., who with his investigation of a reverse flame of air in an atmosphere of methane won second place in the physics division of this year's International Science and Engineering Fair. The reverse flame is similar to a normal one but displays some surprising differences that neither Travis nor I can fully explain.

The normal and reverse flames investigated by Travis are diffusion flames: the burning requires the mutual diffusion of the fuel and the oxidizer into the flame front, the surface where the burning takes place. In the other general type of flame, premixed flames, the fuel and the oxidizing agent are mixed before they reach the flame, as in a Bunsen burner. Diffusion flames and premixed flames can be either laminar (that is, smoothly flowing) or turbulent, depending on the rate of flow of the participating gases. Travis limited his attention to laminar diffusion flames. The commonest example of this type of flame is a candle flame, which I discussed in this department for April, 1978.

One might think that laminar diffusion flames are well understood, since candle flames have been investigated for a long time, but it is not so. Flames are exceedingly difficult to understand even in general terms, much less in detail, because of the wide variety of phenomena occurring in them. Many chemical reactions take place, and many of them are complex. Light is emitted by both chemical and thermodynamic phenomena. Gases expand as they are heated. Heat is transferred across the surface of the flame in several ways. The flow is in three dimensions. Probing the flame usually distorts it in inexplicable ways.

Students of flames concentrate on several key features: color, shape, temperature distribution and burning velocity. Burning velocity is the rate at which the flame propagates perpendicular to the flame front. The propagation can be either through a stationary gas or, as in a flame on a stove, through a flame that remains stationary while the gas flows. It is easy to calculate the burning velocity when the flame front is flat but more difficult when the flame front is curved, as it is with most burners.

Another matter of interest in the investigation of a flame is the reaction zone, the region where the fuel and the oxidizer meet. Part of the light from the flame emerges from the chemical reactions in this zone. In a normal diffusion flame the reaction zone is blue, largely because of the blue emissions of the molecules excited by the chemical reactions in the zone. If the rate of flow of fuel is sufficiently low, the entire flame may be blue. An example is the flame of a candle with a thin wick.

With a somewhat greater flow of fuel a yellow or white tip develops near the top of a normal diffusion flame. As the flow of fuel is increased further the yellow or white region grows, eventually dominating the flame and relegating the blue reaction zone first to the sides of the flame and then finally to just the side regions near the base. The yellow-white tip consists of carbon particles that have become hot enough to emit radiation more or less continuously across the entire visible spectrum.

The combustion chamber employed by Travis for his investigation was made out of a 500-milliliter round-bottom flask. The flask was held upside down on ring stand by a clamp. Projecting upward from the round surface was a tube that had been annealed to the flask. A similar tube projected sideways from the neck. A stopper in the neck carried a short burner. To make a normal diffusion flame Travis supplied methane to the burner tube and air to the side tube. For a reverse flame he interchanged the supplies. A small hole in the side of the flask gave access for a thermocouple to probe the temperature of the flame. Also passing through the stopper in the neck were two electrical leads to the Nichrome wire Travis employed to start the flame inside the flask. His air and methane came from tanks in his school laboratory.

To light a reverse flame Travis placed the length of Nichrome wire across the mouth of the burner tube and then turned on the methane. After about 15 seconds the flask was filled with methane and he could light the gas escaping through the vent at the top of the flask. (He needed the 15 seconds to avoid having a mixture of a small amount of methane and a large amount of air, which would explode.) He adjusted the flow of methane until the flame at the vent was four or five inches high. After the reverse flame was created inside the chamber the flame at the vent burned off the excess methane escaping from the chamber.

The Nichrome wire was connected by two leads to a current source, which was then turned on enough to make the wire glow red. Next the air tank was turned on to supply air at a low rate (about .6 liter per minute). The flow of air had to be low at first or the amount of oxygen supplied by it might have caused the flask to explode. The hot wire ignited a flame at the mouth of the burner; this was the reverse flame. The current on the wire was then turned off and the leads through the stopper were wiggled until the wire was brought down from its position over the mouth. The flame was more distinguishable in the dark, so that most of these things were done in dim light. To extinguish the flame Travis turned off the air first to avoid any danger of explosion.

Travis lighted the normal flame by a similar procedure. Again he carefully avoided lighting the flame at the top of the flask while a small amount of methane was in a large amount of air. He turned on the methane first to fill the flask before he turned on the air. To turn off the flame he first turned off the air. When I asked him about the danger of explosion, he replied that he had had no problem with the reverse flame but that with the normal flame he had occasionally had an explosion that blew the stopper out of the flask. To guard against a more serious accident anyone doing this kind of experiment should wear a face shield. Moreover, a combustion chamber larger than Travis' 500-milliliter flask should not be used or the hazard of explosion will be greater.

The distribution of temperature in the flames was measured with the thermocouple probe slipped into the combustion chamber through the small hole. Travis got his thermocouple from the Edmund Scientific Company (6975 Edscorp Building, Barrington, N.J. 08007). He ground down the tip of the Chromel-Alumel wire, rebrazed it and ground it down again to make it as small as possible. Still the probe was relatively large compared with the flame and therefore could measure only average temperatures. One must also bear in mind two unmeasurable effects of the probe: it distorts the flame, and by carrying off heat it distorts the temperature distribution.

To record the location of the probe in the flame Travis mounted a ruler outside the chamber in such a way that the distance from the tip of the thermocouple to the hole in the side of the chamber equaled the distance from the hole to the ruler. Hence when the tip was moved a certain distance within the flame, the stiff wire moved an equal distance across the ruler, enabling him to measure the displacement in the flame.

Travis measured the rate of flow of gas with two relatively inexpensive flow meters (Dwyer brand) that worked in the range of a few liters per minute. (Local distributors for flow meters are listed in the yellow pages of the telephone book.) For very low gas flows Travis approximated the rate of flow by bubbling the gas through a container of water. He estimated the average bubble size and then counted the number of bubbles passing through the water each minute. A simple calculation gave him the volume flow rate.

The spherical combustion chamber distorted photographs of the flames, and so Travis replaced it with a rectangular chamber made out of ordinary plate glass. When he lighted a flame, he had to work fast because the heat soon cracked the glass. More expensive glass designed for thermal stress could have been substituted to avoid the problem. Travis made his photographs with a 35-millimeter camera fitted with a 55-millimeter lens and a one-power extender. He mad black-and-white pictures, using Kodak Tri-X film at an aperture of f/2.8 and a exposure time of a thirtieth of a second

To measure the burning velocity of the flames Travis employed a technique known as Gouy's method, which is based on the total surface area of the flame front. The burning velocity is assumed to be constant over the entire flame front in spite of the front's curvature. The volume flow rate of gas from the burner is equal to the area of the mouth of the burner multiplied by the velocity of the gas issuing from the mouth (as measured by a flow meter) Since the flame is stationary, the volume flow rate must also equal the burning velocity multiplied by the total surface area of the flame front. If the surface area can be determined, the only unknown is the burning velocity.

To determine the total surface area of the flame front a photograph is made of the flame and then the flame in the picture is divided in half along its central vertical axis. One of the halves is split into several sections as is shown in the illustration on the next page. For each such section two sides are radii from the central axis out to the flame front and another side is the sloping side along the flame front. The surface area along the circumference of the flame corresponding to one of these sections is calculated by multiplying pi by the average of the two radii for the section and then multiplying by the length along the slope. The calculation is done for each of the sections. The total area obtained is approximately the total surface area of the flame front.

How accurate is the result? The calculation can be in error for several subtle reasons. One is that determining the position of the flame front can be difficult if the reaction zone is thick, as it is likely to be in flames with low burning velocities. Another source of error stems from the difficulty of calculating the surface area at the top of the flame, where the flame front may be substantially curved. A larger error may arise because the base of the flame is often poorly defined in a photograph. Finally, the burning velocity of the flame may be distorted by the thermal expansion of the gases when they enter the reaction zone and are heated.

Predicting the shape or height of a normal diffusion flame is no easy matter either. Both depend on a complex interaction of heat transfer, diffusion and the rates of the chemical reactions. In a simple analysis the height of a diffusion flame should be proportional to the volume flow rate and inversely proportion al to the average rate of diffusion of the gases.

The reverse flames Travis created in his apparatus are just as difficult to analyze as normal diffusion flames, and perhaps even more so. They are noticeably different from the normal flames in size, shape and color. A reverse flame is usually rounded at the top instead of having the conical tip of a normal flame. A normal flame with a certain volume flow rate of methane is much higher than a reverse flame with the same volume flow rate for its air. The normal flame usually has a poorly defined base, whereas the reverse flame has a distinct base. Moreover, its base is separated from the mouth of the burner by a relatively wide dead space.

The outstanding difference between the two flames is in their color. A normal flame with a small flow of fuel is blue throughout. As the flow of methane is increased a yellow or white tip appears at the top of the flame, and the blue regions are reduced and shifted downward to the base. A reverse flame is entirely blue until a large amount of air is forced into the flame. Then the top turns orange.

The temperature distribution of the two flames is slightly different. The normal flame tends to be hottest along the side of the inner cone of darkness; the reverse flame has somewhat hotter areas over the inner cone. Bear in mind that these measurements are affected by the introduction of the thermocouple probe into the flame and by the fact that the thermocouple averages the temperatures over a region, even though the region can be a small one.

The reverse flame also has a higher burning velocity. When Travis adjusted a normal flame and a reverse one so that they were the same height, the reverse flame had about twice the burning velocity of the normal one. When he adjusted the flames to have equal flow rates (methane for the normal flame and air for the reverse flame), the ratio was about 10. In both types of flame the burning velocity decreased (from a few centimeters per second) as he increased the flow rate because the area of the flame front did not increase as much as the flow rate.

Why does the reverse flame differ from the normal flame? I am not sure, because even the normal diffusion flame is not completely understood. The reverse flame and the normal one are similar when the flow rates of each are low. Then both flames are rounded at the top and blue in the reaction zone. As the methane flow rate for the normal flame is increased, the yellow or white tip quickly appears. The corresponding orange tip of the reverse flame develops less rapidly because the flow of air must be increased considerably to bring it out.

It is puzzling that the colors of the tops are not the same. They should be (as far as I know) because in both flames the color of the top is due to the visible emissions from incandescent particles of carbon. Since the air supply in the reverse flame must be relatively high to create an orange tip, the formation of incandescent carbon particles may also require a relatively large supply of air.

The fact that the methane diffuses from the outside of the reverse flame rather than from the inside as it does in the normal flame may be a key to the differences between the two types. Methane needs a fairly high temperature for decomposition. If the methane comes from inside the flame, it enters the very hot regions of the flame rather quickly. The means by which it eventually forms solid carbon particles is not understood, although the process is thought to be incomplete until the gases have risen to the top of the flame. When methane diffuses into a reverse flame, it enters from the cooler regions and is gradually heated, and so the reactions that form the particles may be different. My speculations on these matters can be only rough guesses, however, until more work has been done on reverse flames.

A normal diffusion flame that is stable will sit slightly above a burner opening at a height where the burning velocity matches the gas velocity. If one velocity changes significantly, the flame will move either away from the mouth or into it. The gas velocity decreases somewhat as the gas stream spreads from the mouth of the burner, so that the flame front settles at the point above the mouth where the two velocities match. Certain flames (such as ethylene jets) may lift a good deal higher above the burner and then stabilize for a time. Such lifted flames are not easy to achieve because they call for a perfect balance between the gas velocity and the burning velocity that is difficult for the experimenter to achieve.

Travis could not make his normal flame lift off in this way but could easily make the reverse flame do it. He turned the methane supply off and then quickly turned it back on. The flame lifted several centimeters above the burner mouth, remaining there for up to four minutes. I am not sure why the reverse flame does this, but I suspect that the relatively high burning velocity may be the key.

When the methane supply in a normal flame is turned up high, the flame becomes turbulent. The reverse flame does not show such turbulence. When its air supply is turned up high, the flame moves away from the mouth of the burner and dies.

I can find no mention of reverse flames in the printed material on flames. Travis may be the first person to have investigated them. If you want to pursue the study, much further experimentation could be done. Try hydrocarbon gases other than methane. (Be careful if they are toxic or highly explosive.) Travis also experimented with propane; you might start there. In my earlier discussion of a candle flame I described how a simple spectroscope can serve for observing the line emissions of the chemical radicals CH and C₂ from the reaction zones. You may want to make similar observations on the reaction zones of reverse flames. If the emissions are missing, the chemistry of the reaction zones in the two types of flame would be quite different.

Several people have written to me about the similarity between falling trees and the falling chimneys I discussed in this department for February. James D. Plimpton of Albuquerque, N.M., pointed out that a falling tree with full foliage may float briefly just before hitting the ground because of the large air resistance encountered by its branches. A more dangerous aspect of falling trees was described by Paul R. Burnett of Temple Hills, Md. A tree that is to be felled is first notched on one side and then given a single horizontal cut on the side opposite the notch. When the tree begins to fall, it hinges around the inch or so of wood remaining between the notch and the straight cut. If the tree is young, it may be noticeably bent by air resistance as it falls, but a live tree will not snap because of the high tensile strength of the living wood. The hinge, however, does snap, hurling the butt end of the tree upward with considerable force. Then that end may move in the direction of fall of the tree, as the lower end of a falling chimney does. If the tree has many full branches, much energy may be stored in the branches as they bend while striking the ground. The branches may then suddenly push the trunk back toward the stump with great force. Burnett has seen stumps almost knocked out of the ground by the impact. This sudden, violent recoil is particularly dangerous for anyone who remains at or even near the stump after felling the tree.

The falling behavior of snags (dead and partly decayed trees) is even curiouser. John D. Engels of North Bend, Ore., has seen falling snags fracture much the way chimneys do. Highly decayed snags sometimes break in half, and the two pieces land on opposite sides of the stump, presenting a serious problem for the logger trying to decide which way to run. Engels has also seen trees with much green foliage bend as they fall. In some instances the tree straightens rapidly as it nears the ground, so that the upper half reaches the ground before the lower half.

After reading my description (in the same article) of how pencil points break Gerald R. Martin of Napa, Calif., sent a description of a strange effect chemistry students first noticed with glass stirring rods. If the rods are dropped, they often break into three pieces of equal length and a small number of chips. This breaking pattern was dubbed the "pi rule," since the rods break into approximately 3.1 pieces. Martin and other mathematicians generalized the result (as mathematicians are likely to do) to include lengths of fresh chalk. Are there other examples of the pi rule?

I tested the rule by dropping pieces of chalk onto the floor after marking each piece so that I could reconstruct the fragments and locate the point of impact. Although the rule was not obeyed exactly, the chalk usually broke into three sections (rarely of the same length) with fractures similar to those in pencil points that have been broken. My work drew several comments from my colleagues at Cleveland State University. (A professor repeatedly dropping pieces of chalk on the floor is bound to attract attention.) Karl Casper discovered that if the chalk is reduced in length by a third, it will usually break into two sections rather than three. It could be that a full-length piece first snaps about a third of the way along its length and then the remaining two-thirds of a piece snaps approximately in half when the top section hits a moment later. You might try high-speed photography to find out whether my speculation is right or whether the entire piece of chalk vibrates and breaks in two places simultaneously.

Another example of fracturing, which seems at first to be unrelated, was sent to me by J. G. Nandris of the University of London. In about 2000 B.C. a huge menhir (an upright monolith), Le Grand Menhir Brise, was erected at what is now Carnac in France. The stone was some 70 feet high and weighed more than 300 tons. How men with primitive tools could fashion and then erect such a stone is not understood. The stone stood until about 700 years ago, when it toppled and broke into four pieces. The upper half now lies in three pieces aligned east and west. The lower half is aligned toward the northwest, apparently after having fallen in a direction almost opposite to that taken by the upper half.

Why did the stone fall? Was it broken by lightning or pulled down by peasants? Why did the two halves fall in opposite directions? Most likely the stone was felled by an earthquake that snapped it at its midpoint. When the upper half struck the ground, it broke into three pieces much like the chalk lengths I dropped. The fracture surfaces on all four pieces even appear to be similar to the chalk fractures. The lower half of the stone continued to ride the heaving ground (if indeed the stone was toppled by an earthquake) until it too was knocked down, but it happened to fall in a different direction from that of the upper half. Both the menhir and the earthquake that shattered it must have been awesome.

The type of fracturing common to pencil points, chimneys, chalk and even the menhir is called mixed-mode fracturing because it involves two general modes of fracture, as was explained to me recently by Anthony R. Ingraffea of Cornell University. The illustrations on page 202 show how to cut and tear sheets of paper to demonstrate these modes. A fracture of the type named Mode I occurs when the material is under either pure bending stress or pure tensile stress, neither of which will cause the two sides of the resulting crack to slide over each other. To demonstrate this phenomenon cut a slit in a sheet of paper and pull or rotate the ends as shown in the top two illustrations on page 202. The crack propagates in a straight line parallel to the scissors cut.

If the two faces of a crack are made to slide over each other without being separated, the fracture is of the type named Mode II. Cut two sheets of paper as shown in the bottom illustration on page 202 and then push and pull as required. This time the fracture propagates in a curved manner.

The cracks that propagate across the width of a falling chimney or a pencil point under stress are of mixed modes: bending (Mode I) and shearing (Mode II). Therefore the crack displays some of the fracture pattern of each mode. The direction in which the crack curves during the latter part of the propagation is different for chimneys and pencil points because of the direction of shearing. For example, if the chimney falls to the left, a clockwise shearing makes the crack curve downward as it travels across the chimney. In a pencil point the direction of shearing sends the crack curving upward, away from the point.

There was an error in the illustration 1 of the amplifier circuit for the seismograph described in this department for July. The line from the .4-microfarad capacitor to the pin labeled "2" on the second gate should be connected to the line between the one-kilohm resistor and the 100-kilohm resistors.

Bibliography

THE OPTICS OF FLAMES. Felix J. Weinberg. Butterworth & CO., 1963.

FLAME STRUCTURE. R. M. Fristrom and A. A. Westenberg. McGraw-Hill Book Company, 1965.

FLAMES: THEIR STRUCTURE, RADIATION AND TEMPERATURE. A. G. Gaydon and H. G. Wolfhard. Chapman and Hall, Ltd., 1970.

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