Each of these elements can be made in a number of different forms depending on the size of the model and the speed and altitude at which the object represented by the model is designed to fly. A supersonic wind tunnel for investigating the flight characteristics of a high-velocity bullet, for example, will necessarily differ from one designed for observing the reentry characteristics of a space vehicle; the bullet travels through relatively dense air at a speed of perhaps 2,000 miles per hour whereas the space vehicle flies more than eight times faster in the near vacuum of the upper atmosphere. Hence the problem of designing a supersonic wind tunnel consists largely of selecting components from among the many existing designs.

Gary S. Settles, a student at Maryville High School in Maryville, Tenn., spent most of his free time during the past two years selecting components and constructing a supersonic wind tunnel. The apparatus displays flow patterns around objects of interest to many amateurs, including small scale models of rockets. The models are available in most hobby stores. The project, which included a series of photographs of flow patterns made with the tunnel, won four prizes last year at the regional science fair. Settles writes:

"All supersonic wind tunnels share one characteristic: when they are in operation, they consume power at an astonishing rate. About 300 horsepower must be expended to maintain a flow of air at 1,500 miles per hour through a pipe only one inch square and two inches long. The air compressor of a continuous tunnel measuring nine inches square at the Aberdeen Proving Ground in Maryland absorbs the output of a 25,000-horsepower motor.

"A way out of this difficulty lies in the fact that energy from a source of limited capacity, such as an electric outlet in the home, can be stored in the form of compressed air and discharged intermittently. This principle is employed in 'blowdown,' or high-pressure, wind tunnels. Air is compressed in a tank during a comparatively long interval and discharged abruptly into the atmosphere at supersonic velocity. Conversely, energy can be stored by exhausting a tank to which air is abruptly admitted. The inflow reaches supersonic velocity if it enters through a duct of the proper design. In such 'indraft' tunnels the atmosphere acts as the high-pressure supply. The indraft tunnel has two advantages from the amateur's point of view. It is safer than the high-pressure type; a weak or faulty tank will simply collapse instead of exploding. Moreover, a vacuum system provides its own pressure regulation, whereas high-pressure systems require some form of such regulation.

"In view of these considerations I decided to construct a small tunnel of the indraft type for intermittent operation. Small tunnels operate well if they are made aerodynamically 'clean,' that is, if sharp turns are avoided and obstructions such as rough walls are eliminated in the duct through which the air flows.

My tunnel consists of eight elements: a $2 drier, a stilling chamber, a nozzle, a test section, a diffuser, a vacuum tank, a pumping system and a schlieren apparatus for photographing the flow of air around the model [see Figure 3].

"Air at atmospheric pressure enters the nozzle through the drier and stilling chamber, which are designed to remove moisture and to accelerate the flow smoothly. Specially shaped blocks in the nozzle first constrict the entering stream of air and then allow it to expand. In this arrangement the air is accelerated to the speed of sound at the point where the blocks constrict the channel to minimum area. Immediately downstream from this point the channel becomes larger. The air expands and so is further accelerated to supersonic velocity.

"After passing through the enlarged channel the stream flows through a duct of constant area. This is the test section, where models are mounted. From the test section the stream enters another channel known as the diffuser, which conducts the spent air away from the test section without distorting the flow pattern. A quick-acting valve between the diffuser and the tank seals off the system during pumpdown.

"The size of the installation is determined by its intended use as well as by the available space and power. My installation had to be portable because I wanted to enter it in the science fair. The power had to be taken from an ordinary 110-volt outlet fused for 15 amperes. This was adequate for operating a motor rated at 1/4 horsepower. In 30 minutes a motor of this size can store enough energy to operate a supersonic tunnel with an area of half a square inch for about three seconds at a stream velocity of 1,500 miles per hour. That is about twice the speed of sound. My apparatus is assembled in a table-like framework, supported by casters, that is 30 inches wide, 30 inches high and 48 inches long. It can be wheeled through most doors.

"The amount of energy that can be stored is determined by the size of the vacuum tank as well as by the capacity of the pumping system. The length of a test run varies directly with the size of the tank. New tanks are costly, but I found that those from discarded water heaters are both inexpensive and effective. They can be obtained from dealers in scrap metal. The price depends on the condition of the tank and the length of time it has been discarded.

"Most of these tanks are designed to withstand a pressure of 150 pounds per square inch. The atmosphere exerts an inward pressure of only 15 pounds per square inch, so that even old water tanks are strong enough for wind tunnel purposes. I use three 30-gallon tanks that have a total volume of about 13 cubic feet. To connect the tanks I welded one-inch pipes directly into them. The tanks are stacked inside the framework and fastened in place with steel pipe straps. All joints in the plumbing system were welded and coated with a commercial gasket compound.

"The top of the framework consists of a sheet of 3/4-inch plywood on which the wind tunnel and the optical system are mounted A lead-in pipe extends vertically through the platform and terminates in a quick-acting gate valve operated by a self-contained motor. The valve, a surplus item, was secured from the Surplus Center, 900 West 'O' Street, Lincoln, Neb. 68510. It is listed as item No. JX07 and priced at $4.25. The valve is vacuum-tight when closed. Although the motor is designed for direct current at 12 volts, I power it with alternating current from a variable-voltage transformer. For quick operation I use up to 60 volts.

"The intake side of the gate valve connects to the diffuser through a 90degree pipe elbow. This arrangement makes it possible to mount the wind tunnel horizontally. The design of the diffuser depends on the shape and size of the test section. If the test section is rectangular, as it is in my apparatus, the diffuser must provide a smooth transition from the rectangular cross section at one end to the circular cross section at the other. The diffuser can be constructed by a variety of techniques. Mine was made by altering the shape of a pipe nipple that fitted the gate valve. A tapered bar of iron that matched the cross section of the test section was driven into the unthreaded end of the nipple after the nipple had been heated to redness with a blowtorch. A matching flange was welded to the rectangular opening of the diffuser. Four holes were drilled in the flange for attaching the assembly to the stilling chamber [see lower illustration below].

"The size of all components is determined by the cross-sectional area of the test section and by the maximum velocity of the airstream. In wind tunnel work velocity is expressed in the units called Mach numbers. The unit is 762 miles per hour, the speed of sound at sea level; it is named for the Austrian physicist Ernst Mach. Mach 1 is equal to the speed of sound, Mach 2 is equal to twice the speed of sound and so on.

"In the case of an indraft tunnel the maximum velocity of the airstream is fixed by the contour of the nozzle. The walls leading from the upstream side of the nozzle curve inward, gradually reducing the area of the duct, and then diverge. Air that flows beyond the point of minimum area decreases in density much faster than its volume increases.

For this reason the velocity increases as the air expands to fill the diverging portion of the duct and is independent of the difference between the upstream and the downstream pressure. A change in the downstream pressure merely alters the location in the duct at which supersonic flow changes to subsonic flow. Similarly, a change in the upstream pressure alters the pressure at which supersonic flow occurs. Neither of these changes affects the Mach number. Velocity can be changed only by altering the shape of the nozzle.

"The profile of my nozzle was supplied by R. W. Hensel of the Arnold Engineering Development Center in Tullahoma, Tenn. The dimensions of the profile are shown in the accompanying illustration [Figure 6]. The nozzle develops an airstream velocity of Mach 2 when the tanks have been exhausted to a pressure of 38 centimeters of mercury or less. In small indraft tunnels the upper limit of velocity is about Mach 3, according to authorities with whom I have discussed the matter. The density of the air decreases with increasing Mach number. Above Mach 3 the air is too thin for observing flow patterns optically. Below Mach 2 it is difficult to maintain supersonic flow with a model of reasonable size.

"The top and bottom of my nozzle and test section were made of a pair of aluminum blocks half an inch thick. The blocks were first clamped together. The profile was then cut in both blocks simultaneously by drawing a rattail file across the metal from front to back. The contour was checked periodically with a template cut from thin sheet metal. The filed surface was smoothed with successively finer grades of emery cloth and finally polished to a mirror-like finish with crocus cloth.

"One cannot take too much care at this point in the construction, because the performance of the tunnel will be no better than the accuracy with which the finished blocks conform to the specified profile. The blocks are assembled with the contoured edges facing each other to form a symmetrical duct and are fastened together by metal bezels, or frames, that also hold the plate glass walls. Flanges for bolting the unit between the diffuser and the stilling chamber were welded to the metal side walls that enclose the blocks.

"Air enters the nozzle-block assembly through the stilling chamber, where turbulence is suppressed by 50-mesh wire cloth at each end of the cavity. Wire cloth for this purpose can be obtained from the Cambridge Wire Cloth Co., Cambridge, Md. 21613. Air must be dried before it enters the stilling chamber or condensation will occur when heat is lost during expansion of the air. I dry the air by means of an apparatus consisting of a small motor-driven blower, a cardboard mailing tube packed with silica gel and a storage reservoir. My storage reservoir is a surplus weather balloon, obtainable from the Edmund Scientific Co., Barrington, N.J. 08007. The blower forces air through the mailing tube, where moisture is absorbed by the silica gel; the air then passes into the balloon for storage. A flange, cemented into an opening I made in the side of the balloon, connects to a duct through which the dry air flows to the stilling chamber. A gate valve I improvised from sheet metal closes the neck of the balloon after it has been filled.

"The stilling chamber can be made of wood. Fairing blocks should be inserted at the outlet end of the chamber to guide the air smoothly into the nozzle. Neither the curvature nor the finish of the blocks is critical, as it is in the nozzle-test-section assembly. My stilling chamber was made of 16-gauge sheet metal and faired with blocks of lightly sanded and varnished wood.

"The system does not impose a severe requirement on the vacuum pump. Any pump capable of reducing the pressure in the tanks to about 10 centimeters of mercury within a reasonable time, say 30 minutes, is adequate. Still lower pressures will increase the running time of the tunnel. It is possible to pump the tanks to a pressure of about one centimeter by using the compressor unit of an old electric refrigerator in reverse. Such compressors are available from dealers in refrigerators. Two or more units can be interconnected for reducing the time of pumpdown. I am now using an excellent and comparatively inexpensive pump that was obtained from the Groban Supply Company, 1139 Wabash Avenue South, Chicago, Ill. 60605. Designated model No. 480A, the unit is priced at $20. The price does not include a heavy-duty 1/4 horsepower motor, which is required for driving the unit. A check valve must be placed between the pump and the tank system to prevent air from leaking into the tanks when the pump is not operating.

"The model is supported in the test section by a length of 16-gauge steel wire that is flattened at one end and pointed at the other. The flattened end is clamped between the flanges of the test-section and diffuser assemblies. The pointed end is heated and pushed into the tail of the plastic model.

"Although I have made a few models, I have relied mostly on the miniature plastic rockets and bombs that are found on scale-model aircraft. I have also used cones, spheres and wedges. In general, models should not occupy more than 15 percent of the cross-sectional area of the test section. In no case should they reduce the area to that of the nozzle constriction The test section of the first tunnel I built measured only a quarter of an inch in width and half an inch in height. I had considerable difficulty finding models small enough to test. Large models block the airstream. Blockage seriously distorts the flow pattern around the model and results in the formation of shock waves upstream.

"Shock waves and other features of the flow pattern alter the density of the air and so change the amount by which a given volume of air can bend a ray of light. A similar effect causes stars to twinkle and explains why one can 'see' heat rising from a steam radiator or other hot objects. Advantage is taken of the effect to photograph patterns of airflow by the schlieren system [see "The Amateur Scientist, SCIENTIFIC AMERICAN, February, 1964].

"In this system divergent rays of light from a source of small area are made parallel by a spherical concave mirror. The parallel rays are then brought to focus by a similar mirror placed a few feet away. At the focal point half of the bundle of rays is blocked by an opaque object such as a knife-edge. If the column of air between the mirrors is of uniform density, the unobstructed rays will uniformly illuminate a screen placed beyond the knife-edge. If the density of the air is not uniform, some of the obstructed rays may be bent away from the knife-edge and will proceed directly to the screen, thus increasing the brightness of the screen in a certain area. Conversely, other rays that would normally fall on the screen may be deflected onto the knife-edge; this has the effect of reducing the brightness of the screen in certain areas. The net effect is the appearance on the screen of an image that represents variations in the density of the air.

"My schlieren system consists of the conventional light source, spherical mirrors and knife-edge and also of three plane first-surface mirrors, a lens and a camera equipped with a focal-plane shutter but no lens [see Figure 9]. The three plane mirrors are used for folding the light path so that the apparatus can be mounted on the tabletop. The light source is a 12-volt incandescent automobile lamp (GE 1133) equipped with a helical filament The lamp is positioned so that the rays proceed from the side of the helix, forming a rectangular source.

"The spherical mirrors are three inches in diameter. I bought them from the Edmund Scientific Co. The catalogue number is 50,082. They are priced at $7.65 each. The knife-edge consists of a safety-razor blade supported by a fixture equipped with an adjustment screw for advancing the blade into the cone of light. The lens focuses the image of the test section on the photographic film.

"After the apparatus has been assembled in the approximate positions illustrated, the schlieren system must be aligned and focused. The small first-surface mirror is positioned to flood the first spherical mirror with light. The distance between the filament and the surface of this mirror is adjusted to exactly half the mirror's radius of curvature by sliding the mounting fixture. The correct distance has been determined when the rays reflected by the spherical mirror become parallel. A simple test for parallelism can be made by holding a piece of white cardboard in the reflected beam. The spot of light should not change in diameter when the screen is moved toward or away from the mirror.

"The parallel beam is then directed at a right angle through the test section by rotating the second first-surface mirror and is directed onto the second spherical mirror by similarly rotating the third first-surface mirror. These adjustments are checked by removing the lens and placing the eye where the lens was. The second spherical mirror should appear as a glowing disk resembling the full moon.

"The knife-edge is now advanced into the beam. If the knife-edge is too close to the spherical mirror, a straight shadow will move across the glowing disk in one direction when the blade is moved across the beam. If the blade is too far away from the mirror, the shadow will move in the opposite direction. When the blade is in the proper position, the disk will darken uniformly as the knife-edge is advanced. No moving shadow will be observed. The knife-edge is in the proper transverse adjustment when the brightness of the disk has been reduced to roughly half its maximum intensity. The lens is now replaced. Finally, a model is mounted in the test section and the position of the camera is adjusted until a sharp silhouette of the model appears on the ground glass.

"The controls of my tunnel are assembled on a small panel that contains a switch for operating the room light as well as the vacuum pump, schlieren light and gate valve. One quickly learns the positions of the various switches; this saves a lot of fumbling when the system is operated in a darkened room.

"Making a test run involves only a few basic operations. A model is installed in the test section and the system is pumped down. After the schlieren system has been turned on and adjusted and the room has been darkened, the model is lighted obliquely from the front by a high-intensity lamp. (This step is not necessary if the experimenter does not mind having the model appear as a silhouette in photographs.) The gate valve is opened and a photograph is made during the two and a half seconds in which the tunnel is going supersonic. The film is developed and printed conventionally. Exposure time must be found by trial and error.

"I am now making a set of 20 manometers that will be connected to small ports distributed at various points in the vicinity of the model. These will indicate air pressure within the flow pattern and enable me to analyze in part the forces that arise from the flow."

Bibliography

AERODYNAMICS OF SUPERSONIC FLIGHT. Alan Y. Pope. Pitman Publishing Corporation, 1958.

SCHEIEREN METHODS. D. W. Holder and R. J. North in National Physical Laboratory Notes on Applied Science No. 31. Her Majesty's Stationery Office, 1963.

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