Although the anatomy of the vortex is not a major preoccupation of physics, many questions of vortex behavior continue to interest designers of ships and aircraft, those who construct hydroelectric power stations and foresters concerned with fire prevention. Vortexes in the wake of ships and aircraft represent wasted fuel; their generation requires substantial expenditure of energy. Air entrained by a whirlpool in water entering a penstock limits the power of a water turbine. Vortexes become a serious menace during forest fires because they are capable of picking up large flaming timbers and dropping them elsewhere to start new fires. According to Vincent J. Schaefer of the Atmospheric Sciences Research Center of the State University of New York, fire vortexes are of prime concern to foresters who undertake to burn over an area in order to clean it up before planting it with new trees. Even when care is taken to protect the surrounding area by lanes cleared of all combustible rubble, a vortex can develop during the burn and spread the fire.

What conditions induce the formation of vortexes and what factors determine their intensity and direction of rotation? The answers to these questions developed by theorists during the l9th century are of only casual interest to foresters and engineers because all are based on the analysis of "perfect" (nonviscous) fluids. The behavior of real fluids such as air and water, which exhibit the properties of adhesion and internal friction, does not conform to the theoretical predictions. Apart from observations made in wind tunnels and towing tanks, vortex motion in real fluids still awaits intensive investigation. A series of experiments that illustrates one simple procedure for observing vortex motion in flame and water was made last year by Robert A. Singer of Elmont, N.Y., as a project for a Junior Research Fellowship under Shaefer at a field station of the Atmospheric Sciences Research Center. The techniques Singer describes suggest a number of interesting variations.

"The first requirement of an apparatus designed for experimenting with vortexes," he writes, "is a means of imparting rotary motion to a fluid. Still water in containers up to about five feet in diameter that discharge through a centered port in the bottom always drains in a straight, radial flow. The whirlpool that usually forms in a kitchen sink is initiated by eddies set up in the wate1 when the drain is opened; the direction of the rotation is determined by the sense of the eddy rotation. This can be demonstrated by swirling the water gently one way or the other before opening the drain. The slightest perceptible rotary motion is sufficient to trigger a vortex in a container the size of a kitchen sink, even as little as one revolution per minute.

"Continuous circulation can be developed in water merely by directing the inflow along the edge of the container. I use essentially the same stratagem for generating vortexes in flame. The fire is enclosed by a container in the form of one or more spirals of sheet metal that admits air at a tangent to the base of the flame. In a typical setup for experimenting with gas flame a spiral of sheet metal about six inches in diameter and 10 inches high is overlapped one inch to make a slit about a quarter of an inch wide. The spiral rests on a base of aluminum foil supported by a pair of bricks set on edge. The top of a Bunsen burner projects through a hole in the middle of the foil. When the burner is lighted, air drawn through the slit by convection sets up a general circulation inside the spiral. A similar apparatus for burning solid alcohol can be made by fitting the alcohol container with a pair of spirals in the form of interlocking C's cut from aluminum foil and taped to the container. The strength of the resulting vortex can be increased by enclosing the flame with a smooth flue supported on rubber stoppers or small blocks to admit air at the bottom.

"Another version of the apparatus that provides forced draft as well as the required rotary motion has been constructed by George M. Byram and Robert Martin of the U.S. Forest Service. A cylinder of cardboard 26 inches in diameter and 30 inches high is cut and overlapped one inch to form an entrainment slit half an inch wide. The spiral rests on a flat surface and is capped with a cardboard disk fitted with a 80inch length of 10-inch stovepipe for increasing the draft by convection. A small pan of liquid alcohol serves as fuel; the vortex is examined through a window of clear plastic 14 inches wide and two feet high. Incidentally, when versions of this apparatus are constructed for use indoors, fireproof material is substituted for the cardboard. Lumberyards stock several varieties of thin composition sheets that are fire-resistant; sheet aluminum of the kind stocked by hardware stores can also be used. Several aluminum sheets can be fastened together with metal screws to make large spirals. I made one 36 inches wide and 48 inches high for experimenting outdoors with wood fires. Spirals of this size can be set on a bed of sand or supported by rocks of various sizes, depending on the amount of draft desired.

"Other variations of the spiral include compound baffles for observing the interaction of twin fire vortexes. A pair of sheets bent in the general form of an interlocking E and 8, for example, generates vortexes that rotate in the same direction; three sheets bent to form two C's that interlock with a sheet in the form of a 8 generate a counterrotating pair of vortexes. By making a series of compound baffles of increasing height the experimenter can study the interaction of flames that extend above the baffle.

"Accessory apparatus should include instruments for measuring flame temperature and fuel consumption, for observing the flow pattern of the gases and for regulating the input of fuel and air. Temperature can be measured by a pair of Chromel-Alumel thermocouples connected either to a recording potentiometer or, if desired, to a vacuum-tube voltmeter calibrated for a full-scale indication of 50 millivolts. Thermocouples are easily assembled by the method previously described in 'The Amateur Scientist [SCIENTIFIC AMERICAN, December, 1961]. I measured the rate of fuel inflow, when experimenting with gas flames, by means of a wet-test meter. If an instrument of this type is not available, the rate can be determined by transferring gas to a container of known size, such as a glass jug, displacing the fuel at constant pressure by water and timing the combustion interval. The effect of forced draft is conveniently investigated by means of a small motor-driven blower. Flow paths constituting the vortex can be easily observed by introducing particles of soot into the base of the flame. The soot can be generated by a small smudge pot that burns turpentine. I made mine by boring a hole through a rubber stopper for a cloth wick and fitting the assembly into a small test tube that contained the turpentine.

"When I perform an experiment with a new apparatus, I first examine the flow patterns that appear during the interval between the lighting of the fire and the formation of the vortex. In the case of a wood fire the flame begins to rotate slowly around the center of the container in the same direction as the surrounding air and simultaneously to spiral around its own axis. I refer to these motions respectively as external and internal rotation. The flame in the apparatus that burns gas initially exhibits almost pure external rotation that quickly reaches a constant rate of rotation if the fuel input and related factors such as air inflow do not change. In addition the gas flame displays a periodic oscillation I refer to as radial translation. The bright outer gases spiral inward until the flame is concentrated close to its axis. Both the frequency of rotation and the upward velocity then increase appreciably, and internal rotation predominates. In a well-constructed apparatus the internal rotation persists for only a few seconds. The flame then expands to its original radius and initiates the next cycle. In the case of alcohol flames, particularly when they are observed in an apparatus of the Byram and Martin type, the flow pattern begins as a slow external rotation and is followed by radial translation until the flame hugs its axis in the form of a stable vortex of high intensity. When the entrained air is free of eddies, the entrainment slit properly adjusted and the fuel supply aderluate, one cycle of radial translation establishes the intense vortex. During most experiments, however, several cycles are observed.

"The type and intensity of any fire vortex appears to be determined by the amount of friction between the surrounding air and the gases that constitute the flame, by the presence or absence of stagnant air and by temperature differences between the several parts of the flame. A vortex of high intensity can form only if the neighboring air rotates in the same direction as the flame and, in the case of small fires, at a higher velocity than is normally induced by convection inflow from the entrainment slit. In the absence of forced draft the required velocity must be gained by the loss of energy from the flame to the environment. As the neighboring air gains momentum, friction is reduced and the intensity of the vortex increases.

"The intensity of vortex burning also appears to be related to the efficiency of combustion. A given quantity of alcohol is consumed by a weak vortex flame in approximately half the time required for nonvortex burning. A high-intensity vortex quarters the nonvortex burning time. On the assumption that a vortex that burns its fuel in zero time has an intensity of 100 per cent and a normal burning efficiency of 100 per cent, the flames illustrated in the accompanying drawings have burning efficiencies of 20, 50 and 70 per cent respectively. The first of these flames burned in open air without a spiral enclosure. The second was equipped with spiral baffles through which air was forced by a blower. The third was generated by an apparatus of the Byram and Martin type.

"Examination of a high-intensity flow pattern by means of soot particles discloses that most of the gases are entrained at the base; the general form resembles an inverted water vortex. Three patterns of flow can be distinguished: the core, a cylindrical region of substantial radius that borders the core and, beyond the cylindrical region, a surrounding environmental layer. Gases in the core spiral upward at high velocity. The radius of the core is short with respect to that of the neighboring cylindrical region, in which the rates of rotation and velocity are comparatively low but higher than in the surrounding environmental layer, where the flow is slightly downward.

"Experiment demonstrates that intensity is strongly influenced by the rate at which air enters the entrainment slit and by the angle of the inflow. In the case of an alcohol fire the intensity increases when air from a centrifugal blower is directed upward into one of the slits. The forced draft causes the vortex to incline away from the slit; beyond a critical angle the wind loses its effect. When the blast is directed into the slit horizontally, intensity decreases as a consequence of the disturbed circulation. Maximum intensity is achieved by directing the inflow downward at an optimum velocity that must be determined experimentally and at an angle that does not displace the vortex from the vertical. Suction applied-by a flue, for example-to the top spiral accomplishes much the same result.

"Within limits the velocity of air entrained by convection varies inversely with the diameter of the entrainment slit. A critical diameter exists for each apparatus at which the intensity is maximum. The intensity also varies with the ratio of the areas of the top and bottom of the container. Hence the production of intense vortexes is encouraged by narrow slits and an exhaust port of small area. Intensity decreases as the center of the outflow is displaced from the axis of the vortex; even small displacements can extinguish the vortex. As in the case of water vortexes, standing longitudinal waves appear in the core and increase in amplitude with the increasing displacement of the outflow.

"Temperature profiles were made by inserting thermocouples into the respective regions of the flow pattern and plotting the readings against distance from the core. Fluctuations of temperature that accompany periodic changes of internal and external rotation were plotted against time. In general the temperature is lowest in the center of the core, increases toward the edge and drops sharply at the boundary of the cylindrical region. The temperature profile appears to be related directly to the motion of the gases, because the rate at which the air rises is proportional to temperature differences along the core. The flow of glowing soot particles shows that velocity at the edge of the core is greater than in the center. The radial temperature gradient is also influenced by the spinning motion that tends to reduce the density of the inner core and cool the gases slightly. In a stable vortex, temperature decreases exponentially with height and-what is perhaps more significant-differences of temperature from point to point along the core are proportional to the temperature; the higher the temperature, the greater the differences. Periodic temperature fluctuations of more than 100 degrees centigrade were found just above the tip of the flame in the case of the vortex fueled by gas. The fluctuations occur at a period of about 70 seconds and are obviously caused by the periodic inward and outward spiraling of the flame. The external flame rotates at a rate of approximately one revolution per second.

"The behavior of adjacent vortexes appears to be determined by the relative direction of rotation and the relative intensities of the vortexes. When two neighboring vortexes of equal strength rotate in the same direction, an initial oscillation is observed as each attempts to entrain the other. A single large vortex then forms in the same direction and engulfs the original pair. When neighboring vortexes rotate in the same direction but differ substantially in intensity, the more intense member of the pair entrains the one of lesser intensity. Two vortexes of equal intensity rotating in opposite directions continue as individuals but with diminished intensity. The weaker vortex of an antiparallel pair may be entrained by the stronger, but the disparity in intensity must be large.

"Two types of apparatus have been used for experimenting with water vortexes: (1) a rectangular tank enclosing a smooth cylinder that is supported on three large rubber stoppers for equalizing the water level of the cylinder and tank and (2) a circular tank without an inner cylinder. Water is admitted at the top by a hose that directs a jet along the inner edge of the container for inducing rotational motion and initiating the vortex. The rectangular tank measures 15 inches in diameter and width and 24 inches in height. The outlet port is one inch in diameter. The companion cylinder is 10 inches wide and 15 inches high. The vortex forms inside the cylinder and can be displaced or otherwise manipulated by shifting the position of the cylinder. Cylinders in a range of sizes, as well as cones or other shapes, could be used in the tank, but I have not found time to try these variations.

"The circular tank is four feet in height and diameter. Both tanks were made of clear plastic reinforced by metal frames. The outlet port of the large tank is 15 inches in diameter and makes a snug fit with a size 20 rubber stopper. A set of stoppers was bored with holes that increased in diameter in quarter-inch steps from 1/2 inch to 1 1/4 inches for observing the effect of variations in outflow on the intensity of the vortex. Both water and time can be conserved by equipping the drain hose with a gate valve, so that the tank will not drain between experiments. In areas where water is in short supply the system can be equipped with a circulating pump. During observations of steady-state flow the water is maintained at a desired level by adjusting the inlet valve. An automatic float valve could be provided but is scarcely justified because the inflow is easily regulated by hand.

"If the outlet port is centered on the axis of the cylindrical container, the vortex forms almost immediately when the outlet valve is opened, and it is characterized by two waves. The first is a standing wave that twists the air core into a corkscrew shape of one or two turns that varies with the displacement of the outlet port from the center of the cylinder. The second is a moving wave on the surface of the core that resembles a loosely coiled helical spring of many turns. The moving wave is most evident when the vortex is unstable and in process of formation. Trains of moving waves are occasionally discharged by the core and generate con centric ripples on the flat surface of the water. The moving waves can be sup pressed by adding the oily substance hexadecanol to the water. The resulting increase in surface tension reduces the ripples and produces a core with straight walls. If detergent is added to the water, the surface tension is decreased; the vortex then becomes unstable and, de pending on the amount of detergent, may be destroyed.

"The flow pattern can be studied by sprinkling powdered dye or small crystals of potassium permanganate on the water. As in the fire vortex, three regions of flow can be distinguished: the core at the water-air interface, the cylindrical layer in the immediate vicinity of the core and the environmental layer beyond. Water in the vortex and in the cylindrical layer spirals downward, that in the environmental layer slightly upward. The formation of a vortex decreases the outflow, so that the difference between maximum outflow in the absence of a vortex and outflow when a vortex is present can be taken as a measure of vortex intensity. The rate of outflow can be determined by observing the time required to fill a container of known volume. Maximum outflow changes when either the diameter of the outlet port or the depth of the water in the apparatus is altered. In order to compare the intensity of vortexes formed in water of various depths and at various rates of outflow I substituted as an index the difference between maximum outflow (O_m) and vortex outflow (O_v) divided by the maximum outflow, expressed as a percentage; the equation is S (the percentage of intensity ) = (O_m - O_v)/O_m X 100. A series of experiments was made to determine the effect on intensity of varying the diameter of the outlet port, the displacement of the vortex, the angle of incidence of the inlet jet, the depth of the water and the rate of the core's rotation.

"In general the outflow increases with depth and the diameter of the outlet but the relation is not directly proportional. When a vortex is present, the outflow varies as the square root of the pressure head or depth and as the 3/2 power of the area of the outlet. Doubling the diameter (hence quadrupling the outlet area) results in only a threefold increase in outflow. The angle made by the inlet jet, measured from the horizontal, exerts a pronounced effect on the intensity of the vortex. As the angle is made larger, intensity increases, but the vortex becomes increasingly unstable and beyond a critical angle does not form. As previously mentioned, within limits the vortex is destroyed by shifting the outlet away from the center of the container or by surrounding the vortex with a cylinder that is not centered above the outlet.

"The rate at which the surface water of the core rotates was measured by directing the beam of a stroboscope on a small cork in the vortex. The rate decreases logarithmically with the water level and at any height is independent of the area of the outlet port. The radius of the core increases directly as the diameter of the outlet is increased, because higher angular momentum is required to reduce the pressure of the water to that of the atmosphere, otherwise the core would collapse. Equilibrium must be maintained between the pressure of the water at the surface of the core and the atmosphere, a requirement that determines the maximum surface velocity of the core at any depth as well as the ratio of the radius of the core to depth."

Bibliography

ELEMENTARY FLUID MECHANICS. John K. Vennard. John Wiley & Sons, Inc., 1940.

VORTEX MOTION IN A VISCOUS FLUID. Robert R. Long in Journal of Meteorology, Vol. 15, No. 1, pages 108-112; February, 1958.

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