9.transonic - web viewthe key word in that last sentence was stationary. ... radius as compared to...
TRANSCRIPT
1.Problems in operating
Transonic wind tunnel
Testing at transonic speeds presents additional problems, mainly due to the reflection of the shock waves from the walls of the test section . Therefore, perforated or slotted walls are required to reduce shock reflection from the walls
Supersonic wind tunnel
1)The power required to run a supersonic windtunnel is enormous, of the order of 50 MW per square meter of test section.:2)adequate supply of dry air 3)wall interference effects 4)high-quality instruments capable of rapid measurements due to short run times on intermittent tunnels
Hypersonic Tunnels
1)supply of high temperatures and pressures for times long enough to perform a measurement2)reproduction of equilibrium conditions 3)structural damage produced by over-heating4)fast instrumentation 5) power requirements to run the tunnel
.2.
Schlieren is German for ‘striations’. The term was coined by Albert Töpler, who developed the technique in 1906 from a related technique used to identify figuring errors in telescope mirrors. Schlieren photography is a way of visualizing density variations in a gas, and is useful in wind tunnel studies and investigations into heat flow. It employs ashadowgraph principle. A collimated (i.e. parallel) beam of light passes through the test space and is brought to a focus at a knife edge; it then diverges on to a screen or a camera system. Any gas density gradient with a component perpendicular to the knife edge will deviate the light from the region, so that it either clears the edge, giving a bright area on the screen, or is intercepted by it, giving a dark area. The resolution can be improved by a further knife edge at the first focus of the system. Where large spaces are to be imaged, off-axis parabolic mirrors are used rather than lenses to collimate and focus the beam . An alternative to the knife edge is a band of three colour filters, red above and blue below, with a narrow strip of green in between.
Schlieren photography is sensitive enough to record the pattern of warm air rising from a human hand, but a more sensitive test uses interferometry, in a kind of hybrid of Schlieren photography and holography. A laser beam replaces the white light beam, and a beamsplitter and beam combiner form a Mach-Zehnder interferometer set-up . This shows density differences directly, rather than density gradients
3.A shock tube is a device used primarily to study gas phase combustion reactions. Shock tubes (and
related impulse facilities: shock tunnels, expansion tubes, and expansion tunnels) can also be used to
study aerodynamic flow under a wide range of temperatures and pressures that are difficult to obtain in
other types of testing facilities.
A simple shock tube is a tube, rectangular or circular in cross-section, usually constructed of metal, in
which a gas at low pressure and a gas at high pressure are separated using some form of diaphragm, see
for instance texts by Soloukhin, Gaydon and Hurle, and Bradley.[1][2][3] This diaphragm suddenly bursts
open under predetermined conditions to produce a wave propagating through the low pressure section.
The shock that eventually forms increases the temperature and pressure of the test gas and induces a flow
in the direction of the shock wave. Observations can be made in the flow behind the incident front or take
advantage of the longer testing times and vastly enhanced pressures and temperatures behind the reflected
wave.
The low-pressure gas, referred to as the driven gas, is subjected to the shock wave. The high pressure gas
is known as the driver gas. The corresponding sections of the tube are likewise called the driver and
driven sections. The driver is usually chosen to have a low molecular weight, hydrogen or helium, for
safety reasons, with high speed of sound, but may be slightly diluted to 'tailor' interface conditions across
the shock. To obtain the strongest shocks the pressure of the driven gas is well below atmospheric.
The test being conducted begins with the bursting of the diaphragm. Three methods are in common use to
burst the diaphragm.
A mechanically-driven plunger to pierce it or its destruction by an explosive charge have both been
practiced.
Another method is to use diaphragms, either of plastic or metals, generally annealed to ensure closely
defined bursting pressures, with plastics for the lowest burst pressures, aluminum andcopper at
somewhat higher levels and mild steel and stainless steel for the highest ones. They are frequently
scored in a cross-shaped pattern to a calibrated depth, to rupture evenly, contouring the petals so that
the full section of the tube remains open during the test time.
The third utilizes a mixture of combustible mixture of gases, with an initiator designed to produce
a detonation within it, producing a sudden and sharp increase in what already may have been a
pressurized driver.
The bursting diaphragm produces a series of pressure waves, each increasing the speed of sound behind
them, so that they compress into a shock propagating through the driven gas. This shock wave increases
the temperature and pressure of the driven gas and induces a flow in the direction of the shock wave but
at lower velocity than the lead wave. Simultaneously, a rarefaction wave, often referred to as the Prandtl-
Meyer one, travels back in to the driver gas. The interface, across which a limited degree of mixing
occurs, separates driven and driver gases is referred to as the contact surface and follows, at a lower
velocity, the lead wave.
Applications
In addition to measurements of rates of chemical kinetics shock tubes have been used to
measure dissociation energies and molecular relaxation rates[4] [5] [6] they have been used in aerodynamic
tests. The fluid flow in the driven gas can be used much as a wind tunnel, allowing higher temperatures
and pressures therein [7] replicating conditions in the turbine sections of jet engines. However, test times
are limited to a few milliseconds, either by the arrival of the contact surface or the reflected shock wave.
They have been further developed into shock tunnels, with an added nozzle and dump tank. The resultant
high temperature hypersonic flow can be used to simulate atmospheric re-entry of space
craftor hypersonic craft, again with limited testing times.
4.
On the figure, we show a schematic drawing of a blowdown wind tunnel. Blowdown tunnels are
normally used from high subsonic to high supersonic flow conditions. There are several possible
configurations for a blowdown tunnel. On the figure, we show completely closed supersonic
configuration. The test section sits at the end of a supersonic nozzle. The Mach number in the test section
is determined by pressure and temperature in the plenum and the area ratio between the test section on
the nozzle throat. As the flow expands in the nozzle, the pressure decreases and any moisture in the
tunnel may condense and liquify in the test section. To prevent condensation, air is brought into the tunnel
through a dryer bed. The air is pumped into a closed high pressure chamber upstream of the plenum. At
the same time, air is pumped out of a closed low pressure chamber downstream of the test section.
Test times are limited in blowdown wind tunnels. At the beginning of the test run, valves are opened
upstream and downstream of the test section. The pressure ratio establishes a supersonic flow in the test
section and the air flows from the high pressure chamber to the low pressure chamber. As air leaves the
high pressure chamber, the pressure in the chamber decreases. Likewise, as air enters the low pressure
chamber, the pressure in that chamber increases. Eventually, the pressure in the two chambers equalize,
the flow stops, and the test is finished. To provide constant conditions in the test section, a pressure
regulator valve is normally installed in the plenum. A second throat is often employed downstream of
the test section to shock down the supersonic flow to subsonic before entering the low pressure chamber.
A closed configuration with both high pressure and low pressure chambers is shown in the figure, but
there are other configurations of blowdwon tunnels. Some blowdown tunnels, called indraft tunnels, do
not use a high pressure chamber, but open the plenum chamber to the atmosphere. The indraft tunnel uses
the low pressure (vacuum) chamber downstream of the test section to produce flow. The advantage of this
configuration is that the conditions in the plenum remain constant and there is no need for a pressure
regulator. The disadvantage is that the pressure ratio across the test section is usually lower than a closed
confifguration and therefore the maximum Mach number is lower. Another configuration retains the high
pressure chamber, but exits to atmosphere instead of into a low pressure chamber. The advantage of this
configuration is that it is cheaper than a closed configuration in both construction and operation. But the
tunnel is very loud and normally requires some type of muffler downstream of the test section.
The blowdown tunnel has some advantages and some disadvantages relative to a closed continuous flow
tunnel.
Advantages of the Blowdown Tunnel
High Mach capability. Easy tunnel "starting".
Lower construction and operating costs.
Superior design for propulsion and smoke visualization. There is no accumulation of exhaust
products in an open tunnel.
Smaller loads on model during startup because of faster starts.
Disadvantages of the Blowdown Tunnel
Shorter test times require faster (often more expensive) instrumentation.
Need for pressure regulator valves.
Noisy operation.
5.Supersonic Wind Tunnels
Supersonic wind tunnels operate differently than subsonic and transonic wind tunnels. First, because fans are inefficient at supersonic speeds, they must run subsonic and the air must make a transition from subsonic to supersonic speeds. Second, supersonic wind tunnels require an enormous amount of power. Supersonic wind tunnels can require so much power that if run during periods of peak electricity demands they can cause a regional brown-out. Very few facilities have continuous supersonic wind tunnels for this reason. The key to making a supersonic wind tunnel is to employ a supersonic venturi. Figure 8.18 shows a schematic of a closed-circuit supersonic wind tunnel. The fan moves the air in a subsonic channel. During startup the subsonic section has been pressurized while the test section remains at a static pressure of 1 atmosphere. The air accelerates in the first venturi until the speed at the throat becomes Mach 1. As the channel opens up, since the air is flowinginto a region of lower pressure it accelerates, producing the supersonic flow in the test section. After the test section the airflow goes through a second venturi. Here the speed decreases until it becomes Mach 1 at the throat. Since the air is going into a region of higher pressure, as the channel opens up the flow slows down, becoming subsonic again. The supersonic wind tunnel has an additional source of power loss. In addition to the friction on the walls and the drag on the models, now there are losses associated with the inevitable shock waves. All of these losses mean a lot of heat is being generated. In order to run continuously, a supersonic wind tunnel must have a large cooler, which is placed in the airflow in the subsonic section. The great amount of power required for supersonic wind tunnels
means there are very few continuous wind tunnels and they are not very large. A 3 _ 3 foot (1 _ 1 m) test section is considered very large and requires half a million horsepower (375 megawatts) to operate at Mach 3. But there are other methods to test supersonic aircraft. One method is the “blowdown” supersonic wind tunnel depicted in Figure 8.19. A huge tank is filled with high-pressure air and then exhausted through a venturi. This kind of wind tunnel works quite well but will
only allow a few minutes of testing. However, a carefully planned test can gather a tremendous amount of data in a very short time. With this technique the energy required is generated and stored over time. This type of wind tunnel requires very little power but requires quite a long time between tests. The NASA Hypersonic Tunnel Facility at Plum Brook can generate speed up to Mach 7. This blowdown facility can accommodate a 5-minute test every 24 hours. The Twenty-Inch Supersonic Wind Tunnel at the Langley Research Center can generate flows with Mach numbers from 1.4 to 5 for 1.5 to 5 minutes. Another option, which is more common, is the vacuum supersonic wind tunnel shown schematically in Figure 8.20. Rather than pump a chamber to a high pressure, which is dangerous, the chamber is evacuated and the airflow is in the other direction through the test section. Thus, the upstream reservoir of air is just the atmosphere and the air is being drawn through the throat and test section into a vacuum. In all supersonic venturis, the air expands on the high-speed sideand thus cools. For continuous supersonic wind tunnels this is not a concern because all the energy losses cause the air to be hot to start with. For the blowdown wind tunnels the air is often heated before it reaches the venturi so that the test section remains at a reasonable temperature. Vacuum wind tunnels have a problem that the room air is used and thus it is not practical to preheat the air. Therefore, the test section is very cold. For
example, a Mach 3 test section would be _274°F (_170°C) if the air supply were at room
temperature
6.Hypersonic TestingWith the incredible power required for supersonic wind tunnels, how can anyone expect to create hypersonic flow conditions, typically above a Mach 5, in a test environment? The only effective method to do this with a stationary model is with the blowdown method, lots of preheating of the air, and a very small test section. The key word in that last sentence was stationary. Some hypersonic facilities actually use a combustion gun, where gases combust in the breach to propel the model. The problem with this technique is that the desired measurements must be made on a nonstationary model, one that is moving very fast. But there is another trick up an engineer’s sleeve. Hypersonic flight implies that the Mach number is typically greater than Mach 5. Up to this point we implicitly assumed that to achieve hypersonic speeds we have to increase the speed in the test section or of the model. What if we were to decrease the speed of sound instead? Sound speed differs for different gases. The speed of sound decreases as the weight of the gas molecules increases. So, instead of using air for our working gas, we could look for a heavier gas, like carbon dioxide, although this will only decrease the sound speed by 14 percent. The advantage of using an alternate gas is that the true speeds can be kept reasonable, while the Mach number is fairly high.
Hypersonic Wind TunnelsSince air is stored in the high pressure air flasks at ambient temperature, it must be heated in
order to avoid condensation during operation of the hypersonic tunnels. This is accomplished by
passing the air through a bed of aluminum oxide pebbles which is enclosed in a silicon carbide
cylinder surrounded by 12 electrical heating elements (Globars); the bed is maintained at the
desired temperature by radiation from these elements. The heater was designed for a maximum
operating pressure and temperature of 600 psia and 2500F, respectively. For effective utilization
of the tunnels and instrumentation equipment available in this facility, several hypersonic tunnels
are permanently connected to the heater.
At present there are three tunnels connected to the collector; these are the Mach 4.4, the Mach 8
and the Mach 12 tunnels. However, additional access ports are available on the collector which
have been used in the past for low speed, high temperature tests involving thermal ablation,
studies of thermal stresses, and heat transfer in tubes. At the present time the hypersonic tunnels
and the heater system are in a stand-down mode. Due to the resurgence of interest in hypersonics
there is an ongoing effort to reactivate this part of the facility.
The Mach 8 tunnel has a test section diameter of 2 ft. and consists of an axisymmetric inner
contoured nozzle surrounded by a pressure shell. Test models are supported from the horizontal
access ports, the vertical windows being used for flow visualization. Free stream static pressures
between 0.2 and 3 mm Hg can be obtained with a test duration of up to 90 seconds. Test
programs have been carried out in this tunnel relating to near wake studies, nose cone
configurations, mass transfer cooling, hypersonic boundary layers, and low density shock layers.
The Mach 12 tunnel is also axisymmetric in the throat region, but at the test section the tunnel
has a decagon cross section. The test section diameter is 4 ft. and therefore permits testing of
relatively large models. The decagon shape was chosen for economy and ease of construction
since an axisymmetric contoured nozzle of this size would be extremely expensive. As a result,
the tunnel was manufactured with a monocoque structural design; ribs and stringers were formed
with the proper contour and thin plates welded to these ribs form the nozzle. The resulting
contour has the same cross sectional area at any position as the corresponding axisymmetric
nozzle. A transition between the axisymmetric throat region and the decagon cross section is
achieved in the vicinity of the throat at fairly low Mach numbers. Due to the large boundary
layer thickness of the flow in this nozzle the test section flow is essentially axisymmetric and
quite uniform. The pressure in the test section varies between 0.1 and 0.3 mm Hg and run times
on the order of 3 to 4 seconds can be achieved in this tunnel. Experimental studies which have
been conducted in this tunnel include the investigation of the near and far wake of blunt and
slender bodies and viscous/inviscid interactions occurring in a low density, high Mach number
free stream environment. Both the Mach 8 and Mach 12 tunnels exhaust into the vacuum sphere
through two large butterfly valves which can be used to isolate either tunnel from the sphere.
7.Shock Tunnels –( Hydrogen and Helium Tunnels )
How Free Piston Shock Tunnels Work
In order to understand the methods of testing and limitations for free piston shock tunnels
their method of operation must be known. The type of shock tunnel discussed will be the Free Piston Shock Tunnel (FPST) which was developed in Australia. . In order to explain how a free piston shock tunnel operates the driving principles behind a conventional shock tunnel must be understood. A regular shock tunnel has 6 major components. The main structure of a shock tunnel is of a thick walled pipe. This structure must be strong enough to withstand the high temperatures and pressures of shock tunnel operation. This is the tunnel where the shock system is created and travels through. The length of this tunnel is dependent upon the size of the test section and the duration of test wanted. Inside this tunnel there are three main sections. The first section is the compression chamber. The compression chamber is filled with a high pressure gas. This gas can be of any composition as it does not flow over the test section. The choice of driver gas is usually driven the gases thermodynamic properties. Nitrogen (N2), helium (He) and hydrogen (H2) are often used as driver gasses. The type of driver gas used dictates the resulting enthalpy of the flow and hence the speed of the flow. Hydrogen generates the highest enthalpy flow but it is dangerous to use due to its high flammability. A more common selection of driver gas is helium,
this is because it behaves as a perfect gas up to high temperatures, less energy is required to raise the temperature than hydrogen and it is safe to use. The second section of the tunnel is the expansion chamber. The gas in the expansion chamber is the gas which flows through the test section. The third component in the shock tunnel is the diaphragm. This diaphragm separates the compression and expansion sections of the tunnel. It is made of strong metal and will rupture at a predefined pressure and temperature. This is important to make this out of a light weight material so only a small amount of energy is needed to accelerate the particles to the flow velocity of the gas. The shattered diaphragm absorbs energy in the rupturing process and also tends to impede the flow through the tube. 3 Connected to the end of the tunnel adjacent to the expansion section is the nozzle. In this section enthalpy in the flow is converted into kinetic energy. The test gas expands through the nozzle and as a result accelerates. This motion is governed by the continuity equation and thermodynamic properties of the flow. The nozzle must be specially designed such that the boundary layer does not separate through the nozzle. If there is boundary layer separation the flow over the test subject may not be as desired.
The final component of a shock tunnel is the test section. This is located downstream from the nozzle. This area has mounts and wiring such that a model can be placed inside and instrumented. This section usually has windows such that the flow can be visualised using Schlieren or shadow photography techniques. In a free piston shock tunnel a “piston” which is a
large piece of metal (often steel) is placed inside the compression tube. As the name suggests this piston is free to move within the compression tube. A reservoir tank is connected to a FPST upstream of the compression tube. This reservoir is filled with high pressure gas, typically 100 atm. When the reservoir is opened the piston is accelerated down the compression tube. The speed which the piston moves is determined by the reservoir pressure, initial compression tube pressure, L/D ratio and the piston mass. As the piston moves down the compression tube energy is transferred from the reservoir gas to the compression gas. The result of this energy transfer is an increase of temperature and pressure of the compression gas. When the compression gas reaches a predefined pressure (typically 900atm, 4600K) the diaphragm separating the compression and expansion chambers will rupture. As the pressure in the expansion tube is less than that of the compression tube the He in the compression tube will flow into the expansion tube. As the pressure of the compression gas is much higher than the test gas the expansion happens rapidly. In fact the contact surface between the driver and test gas creates a shockwave. This shockwave moves faster than the contact surface between the gasses. During this stage of the test both the contact surface and the shock wave move down the expansion tube towards the nozzle.When the shockwave reaches the nozzle a secondary diaphragm in the throat of the nozzle is ruptured. This diaphragm is to separate the expansion tube from the test section. The test section is held at a pressure lower than that of the expansion tube to ensure the nozzle starts properly. When the flow hits the nozzle a shock is reflected back down the tube. This reflected shock raises the enthalpy of the flow. The test gas expands through the nozzle at supersonic speeds. As this is the case the nozzles allows the flow to expand and hence accelerate. During this expansion process the static pressure and temperature reduce. The flow velocity and the Mach number increase in the expansion process.
As the flow escapes out through the nozzle the reflected shock wave moves through the expansion tube back towards the piston. The shockwave will travel through the contact surface and be partially reflected back towards the nozzle, this shock reflection causes a negligible rise in flow enthalpy. When the shock travels through the contact surface the contact surface stops moving down the expansion tube. Between the shock being reflected and the shock travelling through the contact surface an expansion wave is propagated from the piston end of the expansion tube. The expansion wave towards the nozzle. The test is completed when the expansion wave reaches the nozzle.
8..Wind Tunnel Balance BasicsA wind tunnel balance is a device that measures the aerodynamic loads a model experience during a wind tunnel test. A balance is just a multiple axis force transducer. Balances are designed to measure some or all of the three forces and three moments a model experience. In aerodynamics terms, these forces and moments are called: Normal, Side, and Axial Force and Pitch, Yaw, and Rolling moment.
Balances come in many different designs and configurations. Most balances use strain gauged elements that relate applied loads to voltage signals. In the past, wind tunnel loads where measured using weight scales, much like the ones that existed in doctor's offices, and that's why today they're called balances.
Variations in Wind Tunnel Balances
Size and Shape How it Attaches to the Model and to the Support System The Number of Forces and Moments it can Measure The Electronics, Type of Strain Gauges, and Wiring Composed of Single or Multiple Assembled Pieces Designed Operating Load Ranges
Common Balance Types( Strain Gauged )
Internal Multiple Component Balance, with a tapered end, measures six axis loads Internal Single Piece Balance, with a cylindrical end, measures six axis loads Semi-Span Balance, Single Piece, measures five axis loads Ring or Rotor Balance
Flow through Balance
How a Strain Gauged Balance Works
Physical Elements Balances are made of flexures that deflect with load is applied. These flexures are designed to respond to load in a particular axis. Balance that can measure multiple loads and moments have individual flexures that each measure load in one axis. Strain gauges are bonded to these flexures to measure the deflections.
Electrical Elements Applied loads cause the bonded strain gauges to stretch. When a strain gauge changes length its electrical resistance changes. Individual strain gauges are wired in a whetstone bridge so that these small resistance changes can be measured as voltage signals.
Balance Inspection
Ames Balance Calibration Lab does a basic inspection for each balance before use. It is recommended that customers do an inspection before using a balance. Although not comprehensive, a basic check will avoid aggravation that could result if a faulty balance is installed in a wind tunnel model.
NOTE See the detailed explanation and working principles in Aerodynamics by Clancy9.Transonic tunnel
High subsonic wind tunnels (0.4 < M < 0.75) or transonic wind tunnels (0.75 < M < 1.2) are designed on
the same principles as the subsonic wind tunnels. Transonic wind tunnels are able to achieve speeds
close to the speeds of sound. The highest speed is reached in the test section. The Mach number is
approximately one with combined subsonic and supersonic flow regions. Testing at transonic speeds
presents additional problems, mainly due to the reflection of the shock waves from the walls of the test
section (see figure below or enlarge the thumb picture at the right). Therefore, perforated or slotted walls
are required to reduce shock reflection from the walls. Since important viscous or inviscid interactions
occur (such as shock waves or boundary layer interaction) both Mach and Reynolds number are
important and must be properly simulated. Large scale facilities and/or pressurized or cryogenic wind
tunnels are used.
UNIT 4(Theory parts) for derivations see class notes
The drag divergence Mach number is the Mach number at which the aerodynamic drag on an
airfoil or airframe begins to increase rapidly as the Mach number continues to increase [1]. This increase
can cause the drag coefficient to rise to more than ten times its low speed value.
The value of the drag divergence Mach number is typically greater than 0.6; therefore it is a transonic
effect. The drag divergence Mach number is usually close to, and always greater than, the critical Mach
number. Generally, the drag coefficient peaks at Mach 1.0 and begins to decrease again after the
transition into the supersonic regime above approximately Mach 1.2.
The large increase in drag is caused by the formation of a shock wave on the upper surface of the airfoil,
which can induce flow separation and adverse pressure gradients on the aft portion of the wing. This
effect requires that aircraft intended to fly at supersonic speeds have a large amount of thrust. In early
development of transonic and supersonic aircraft, a steep dive was often used to provide extra
acceleration through the high drag region around Mach 1.0. In the early days of aviation, this steep
increase in drag gave rise to the popular false notion of an unbreakable sound barrier, because it seemed
that no aircraft technology in the foreseeable future would have enough propulsive force or control
authority to overcome it. Indeed, one of the popular analytical methods for calculating drag at high
speeds, the Prandtl-Glauert rule, predicts an infinite amount of drag at Mach 1.0.
Two of the important technological advancements that arose out of attempts to conquer the sound barrier
were the Whitcomb area rule and the supercritical airfoil. A supercritical airfoil is shaped specifically to
make the drag divergence Mach number as high as possible, allowing aircraft to fly with relatively lower
drag at high subsonic and low transonic speeds. These, along with other advancements including
computational fluid dynamics, have been able to reduce the factor of increase in drag to two or three for
modern aircraft designs[2
SUPERCRITICAL AIRFOIL
supercritical airfoil is an airfoil designed, primarily, to delay the onset of wave drag in the transonic
speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered
(curved) aft section, and greater leading edge radius as compared to traditional airfoil shapes. The
supercritical airfoils were designed in the 1960s, by then NASA engineer Richard Whitcomb, and were
first tested on the TF-8A Crusader. While the design was initially developed as part of the supersonic
transport (SST) project at NASA, it has since been mainly applied to increase the fuel efficiency of many
high subsonic aircraft. Research in 1940 by DVL's K. A. Kawalki led to subsonic profiles very similar to the
supercritical profiles, which was the basis for the objection in 1984 against the US-patent specification
for the supercritical airfoil.[1] The supercritical airfoil shape is incorporated into the design of a
supercritical wing.
Research aircraft of the 1950s and 60s found it difficult to break the sound barrier, or even reach Mach
0.9, with conventional airfoils. Supersonic airflow over the upper surface of the traditional airfoil
induced excessive wave drag and a form of stability loss called Mach tuck. Due to the airfoil shape used,
supercritical wings experience these problems less severely and at much higher speeds, thus allowing
the wing to maintain high performance at speeds closer to Mach 1. Techniques learned from studies of
the original supercritical airfoil sections are used to design airfoils for high-speed subsonic and transonic
aircraft from the Boeing 777 to the Hawker Siddeley Harrier.
Supercritical airfoils have four main benefits:
1. They have a higher drag divergence Mach number,
2. They develop shock waves farther aft than traditional airfoils,
3. They greatly reduce shock-induced boundary layer separation, and their geometry allows for
more efficient wing design (e.g., a thicker wing and/or reduced wing sweep, each of which may
allow for a lighter wing).
4. At a particular speed for a given airfoil section, the critical Mach number, flow over the upper
surface of an airfoil can become locally supersonic, but slows down to match the pressure at the
trailing edge of the lower surface without a shock. However, at a certain higher speed, the drag
divergence Mach number, a shock is required to recover enough pressure to match the pressures
at the trailing edge. This shock causes transonic wave drag, and can induce flow separation
behind it; both have negative effects on the airfoil's performance.
Supercritical airfoil Mach Number/pressure coefficient diagram.
The sudden increase in pressure coefficient at midchord is due to the shock. (y-axis:Mach number (or
pressure coefficient, negative up); x-axis: position along chord, leading edge left)
At a certain point along the airfoil, a shock is generated, which increases the pressure coefficient to the
critical value Cp-crit, where the local flow velocity will be Mach 1. The position of this shockwave is
determined by the geometry of the airfoil; a supercritical foil is more efficient because the shockwave is
minimized and is created as far aft as possible thus reducing drag. Compared to a typical airfoil section,
the supercritical airfoil creates more of its lift at the aft end, due to its more even pressure distribution
over the upper surface.
In addition to improved transonic performance, a supercritical wing's enlarged leading edge gives it
excellent high-lift characteristics. As a result, aircraft utilizing a supercritical wing have superior takeoff
and landing performance. This makes the supercritical wing a favorite for designers of cargo transport
aircraft. A notable example of one such heavy-lift aircraft that uses a supercritical wing is the C-17
Globemaster
The supercritical airfoil, below, maintains a lower Mach number over its upper surface than the
conventional airfoil, above, which induces a weaker shock.
AREA RULE
The area rule is an important concept related to the drag on an aircraft or other body in transonic and
supersonic flight. The area rule came into being in the early 1950s when production fighter designs
began pushing ever closer to the sound barrier. Designers had found that the drag on these aircraft
increased substantially when the planes traveled near Mach 1, a phenomenon known as the transonic
drag rise illustrated below. This increase in drag is due to the formation of shock waves over portions of
the vehicle, which typically begins around Mach 0.8, and this drag increase reaches a maximum near
Mach 1. Because of its source, this type of drag is referred to as wave drag.
Increase in wave drag at transonic Mach numbers
Since the physics of supersonic flight were still largely a mystery to manufacturers, designers had no idea
how to address this problem except to provide their aircraft with more powerful engines. Even though jet
engine technology was rapidly advancing in those days, the first generation of jet-powered fighters was
hampered by relatively low-thrust engines which limited them to subsonic flight. The US Air Force hoped
to overcome this deficiency with its first dedicated supersonic fighter, the F-102 Delta Dagger.
Since the transonic drag rise was still not fully understood, the F-102's designers chose an engine they
believed would provide enough thrust to reach a maximum speed of about Mach 1.2. However, initial
flight tests of the YF-102 prototype indicated that the aircraft couldn't even reach Mach 1. The Convair
engineers were baffled by this lack of performance until a NACA researcher named Dr. Richard
Whitcomb developed the area rule.
Whitcomb experimented with several different axisymmetric bodies and wing-body combinations in a
transonic wind tunnel. What he found was that the drag created on these shapes was directly related to the
change in cross-sectional area of the vehicle from the nose to the tail. The shape itself was not as critical
in the creation of drag, but the rate of change in that shape had the most significant effect. For the
mathematically inclined, we can say that wave drag is related to the second-derivative (or curvature) of
the volume distribution of the vehicle.
Whitcomb area rule test models: (a) cylindrical fuselage, (b) fuselage with wings, (c) bulged fuselage,
(d) waisted fuselage with wings
To illustrate the point, four of Whitcomb's experimental models are drawn above, representing a simple
cylindrical fuselage, the same fuselage with wings attached, a bulged fuselage, and a "pinched" fuselage
with wings. What Whitcomb discovered was that the addition of wings to the basic cylinder produced
twice as much drag as the cylinder alone. He also found that drag rose by the same amount if a simple
bulge were added to the cylinder, the bulge being of equivalent volume as the wings. However, if he
reduced the cross-sectional area of the fuselage over the region were the wings were attached, shown as
body "D," the total drag was about the same as that of the cylinder alone.
The conclusion of this research was that shaping the vehicle to create a smooth cross-sectional area
distribution from the nose to the tail could drastically reduce the drag on an aircraft. The area rule tells us
that the volume of the body should be reduced in the presence of a wing, tail surface, or other projection
so that there are no discontinuities in the cross-sectional area distribution of the vehicle shape.
Effect of the area rule on overall vehicle shape
Whitcomb's findings are related to a more theoretical concept called the Sears-Haack body. This shape
yields the lowest possible wave drag for a given length and volume. The variation in cross-sectional area
for a Sears-Haack body, illustrated in the following figure, tells us that wave drag is minimized when the
curvature of the volume distribution is minimized. The closer the volume distribution of an aircraft or
other high-speed vehicle comes to the ideal Sears-Haack body, the lower its wave drag will be.
Volume distribution of a Sears-Haack body
Whitcomb's research was a major breakthrough in supersonic aerodynamics and had an immediate effect
on the design of the aforementioned F-102 fighter. Convair engineers quickly redesigned the aircraft's
fuselage, taking the area rule concept into account, to create the "waisted" or "coke-bottle" fuselage. This
modification, plus a new engine, allowed the aircraft to easily exceed Mach 1 and achieve a maximum
speed over Mach 1.5.
Effect of the area rule on the F-102
Today's supersonic fighters are fitted with much more powerful engines than were available in the 1950s,
so the area rule is not as essential to their design as it used to be. However, it has found greater
application to subsonic aircraft, particularly commercial airliners since they cruise at the lower end of the
transonic regime. A good example is the Boeing 747, known for its distinctive "hump." This hump, which
houses the cockpit and upper passenger deck, increases the cross-sectional area of the forward fuselage
and has the effect of evening the volume distribution over the length of the aircraft. As a result, the 747 is
able to cruise efficiently at a slightly higher speed than most other airliners since the increase in transonic
wave drag is delayed.