Different Ways Air Moves

The following definitions are terms that aerodynamicists use to define the way a fluid moves in or around an object. In order to get a good picture of what is happening about a wing, for example, the aerodynamicist must know the velocity of the plane, the altitude of the plane, the size and shape of the wing, and the properties of the air. He or she will use the terms and concepts discussed in this list to define the fluid flow.

Speed of Sound

Sound travels in invisible waves of changing pressure through a fluid (usually air, but sometimes liquid). If a person is standing very far from an explosion, he or she will not hear it right away. It takes time for the sound waves to travel. A person standing closer to the explosion will hear it sooner. At sea level, on a typical day (not too hot, not too cold), the speed of sound (how fast the sound waves travel) is 340 meters per sec (m/s), 1115.54 feet per second (ft/s), or 760 miles per hour (mph).

The speed of sound is a function of the pressure and the density of the fluid in question. Since both the pressure and the density can change with temperature or altitude, the aerodynamicist must compute the speed of sound at the altitude, temperature, pressure, and density where the plane is flying.

Mach Number

Because aerodynamicists like to be able to compare results, they have defined a dimensionless (no units) value to measure the velocity of the airplane. The Mach number is defined as the velocity of the plane divided by the speed of sound computed for the airplane's altitude. An airplane at a low altitude flying at Mach 0.8 will have the same airflow behavior over the wing as the same airplane flying at a high altitude at Mach 0.8. The speed of sound decreases as the altitude increases, so in order for the airplane at the higher altitude to be flying at Mach 0.8, its velocity will be slower than that of the plane flying at the lower altitude! The behavior of the airflow over the wing, however, will be the same on both planes.

The Mach number is named for Ernst Mach (1838 - 1916), who conducted the first meaningful experiments in supersonic flight while a professor of experimental physics at the University of Prague.

The Mach number is useful to aerodynamicists in another way, too. They use the Mach number to define characteristics of the flow and to determine the correct mathematical procedures to use to compute the flow behavior. Mach numbers less than 1.0 define a flow regime that is called subsonic flow. Mach numbers greater than 1.0 define a regime called supersonic flow. If the Mach number is greater than 5.0, that regime is called hypersonic flow. Sonic conditions exist at Mach number equal to 1.0. Because flows from about Mach 0.75 to 1.20 can have areas that are both subsonic and supersonic, aerodynamicists have named it the transonic regime. They must be very careful how they manipulate the fluid equations in this regime.

Another way to look at the flow regimes based on the Mach number is to study the waves generated by the plane flying through the air. In the subsonic, or relatively slow speed regime, the waves of changing pressure about the planes travel out in all directions at the speed of sound for that altitude.

As the plane flies faster and approaches the transonic regime (still below Mach 1.0), the waves in front of the plane don't travel that much faster than the plane itself. The airplane's speed is approaching that of the speed of sound for the waves.

At the sonic barrier, Mach = 1.0, the front of the waves and the plane are traveling at the same speed. The velocity of the plane and the speed of sound for the waves are equal.

As the plane flies faster than the speed of sound (Mach number greater than 1.0), the waves compress into a cone-shaped envelope about the plane. The flow conditions of the air ahead of the plane remain unchanged or constant until after the plane flies past. Only the region inside the cone is affected by the plane. This conical compression is called a shock wave, and it will be discussed in greater detail in a later section.

Friction

Anything that moves against another object must overcome the resistance to motion between the two objects. If a person tries to push a box across the floor, he or she must push hard to overcome the resistance. This resistance is a force called friction. If the person applies a push, or force that is stronger (larger) than the frictional force, the box will move. If the push isn't strong enough, the box won't move.

The friction between two moving objects can be affected by the surfaces of the objects. For example, it is easier to push a heavy box across a smooth wood floor, or a sheet of ice, than it is to push it across a thick, bumpy carpet. That means the frictional force between the box and the smooth floor or ice sheet is less than the frictional force between the box and the thick carpet, so it takes less of a push to get it moving.

When a fluid like air flows across a surface such as a wing, there is friction resisting the motion. How much friction is dependent on mainly two factors, the viscosity of the fluid and the smoothness of the surface. A very viscous fluid like honey (a fluid with high viscosity) will resist flowing, even down a smooth surface. The friction force is very strong at the surface. A fluid like water with a much lower viscosity will travel much faster down a smooth surface; the frictional force between the water and the surface is much smaller. However, if water flows across a very rough surface, like carpet, it will travel down more slowly than on the smooth surface. Because the surface is rougher, the friction force is stronger, and the velocity is slower.

Boundary Layer

Because of this friction force, when a fluid flows over a surface, an interesting pattern develops. At the very surface, the fluid actually stops; there is no velocity or movement at the surface. But because the fluid is a deformable body, layers of the fluid above the surface move over the stopped flow. In addition, each layer experiences friction between it and the next layer, so each layer flows a little slower than the layer above it. Eventually, some distance away from the surface, there is no effect of the slowed flow, and the remaining layers of the fluid travel at the original velocity. This distance is called the boundary layer thickness, and all of the thickness all over the surface form the boundary layer.

In general, the boundary layer gets thicker as the flow moves along the surface. How fast and how big the boundary layer grows is a function of the smoothness of the surface, the shape of the surface, and how fast the flow is travelling.

Laminar Boundary Layer

For lower velocities, fluid flowing over a smooth surface that is relatively short and flat will only develop a very thin boundary layer. The flow inside the boundary layer will be smooth and orderly, meaning that the layers will basically stay in layers, without mixing. This condition is called a laminar boundary layer.

Unfortunately, nature tends towards disorder, so it is rare to be able to maintain a laminar boundary layer for very long.

Turbulent Boundary Layer

As a fluid moves over a long, relatively flat surface, the boundary layer will get thicker, and the layers will start to mix and swirl around each other. This swirling, rolling layer is called a turbulent boundary layer. The mixing and swirling is called turbulence; if the swirling is regular and repeatable, it is called a vortex or an eddy.

Since most of the boundary layers over an airplane will be turbulent, aerodynamicist will try to design the surfaces to minimize the amount of turbulence or disorder.

Transition

The region in the boundary layer where the orderly laminar layers start to mix together, but before they really start swirling, is called the transition region. Most of the time it is a fairly small region. In order to maintain control over the boundary layer, the aerodynamicist will often design "trip points" on the surface to trigger the transition to turbulent flow. They will try to design the surface to maintain a barely turbulent boundary layer.

Flow Separation

When a turbulent boundary layer really starts to swirl, the boundary layer thickness starts to grow even faster. Eventually the flow is so mixed, it starts to flow back towards the front of the surface! When this happens, the outside, original fluid is moving over a large bubble, and inside the bubble, the flow is moving back up the surface. This is called flow separation. The front of the bubble where the outside fluid turns sharply away from the surface is called the point of separation; the back of the bubble, where the outside fluid turns back to follow the surface again, is called the point of reattachment. If the region of flow separation extends past the surface, this region is called a wake.

Pilots and engineers usually don't like it when the flow separates on a wing. This is a condition known as stall, and when a wing stalls, the lift (a force that helps a plane to fly, see later section) decreases sharply. The plane loses altitude, and if the stall is not corrected, the plane will crash. To land a plane, however, a pilot will wait until the plane is close to the ground, then initiate a slight, controlled stall to gently drop the plane to the runway.

Buoyancy

The buoyancy force in fluids is one of the few forces that is not somehow related to the fluid velocity. It exists in a stationary fluid as well as for one that is moving. It is a force that is directed upwards, or opposite of the weight (which is considered a downward force). A body immersed in a fluid will always experience a buoyancy force. The Greek scientist Archimedes (287 - 212 B.C.) deduced that the buoyancy force was equal to the weight of the fluid displaced by the body.

The weight of the fluid displaced by a body immersed in it is computed by finding the volume of the object and multiplying it by the density of the fluid (remember, the density is mass per volume) to get the mass of the displaced fluid. This mass is then multiplied by the acceleration due to gravity to get the weight, a force which is then defined as the buoyancy force. If the buoyancy force is greater than the weight of the object, it will float. If the force is less than the weight of the object, it will sink.

Because the density of liquids is so much larger than the density of gases like air, the buoyancy force for a body immersed in a liquid is much, much higher than that of a body in a gas. Naval architects and ship designers must use the buoyancy forces in their calculations, but the buoyancy forces for airplanes are so small that they are usually ignored. Hot air balloons and blimps do use the buoyancy force to get afloat, but they displace such an extremely large volume of air that the computed buoyancy force exceeds their weight so that they can fly.

Streamlines and Flow Patterns

Aerodynamicists and other engineers prefer to visualize the ways a fluid moves for a given geometry. They like to know where the flow is going so they can compare experimental and flight test data to the theory. A streamline traces out the path of an element or piece of fluid as it travels in space and time around or through an object. These streamlines are computed mathematically from the velocities in the flow region. Streamlines are usually plotted as smooth lines, and they sometimes have arrows on them to show the direction of the flow.

Streamlines are very useful to illustrate how air moves. In the section earlier about flow separation, for example, streamlines were used to show how the outside flow traveled around the body and the region of separation and how the flow inside the separation bubble reversed direction. They can be used to show how the air travels around an airfoil (the cross-section or slice of a wing), with some of the air flowing over the top of the airfoil, and the rest flowing below the airfoil.

Shocks

As discussed in the Mach number section, when a plane flies faster than the speed of sound, the waves of changing pressure are compressed in to a single, infinitesimally thin layer. This is called a shock wave, and fluid properties such as pressure, density, temperature, and velocity change drastically and instantaneously through a shock wave.

Theoretically, once formed a shock wave travels on to infinity. In nature, however, atmospheric winds cause the shock to weaken and disperse. When an aircraft flying at supersonic speeds is at a high altitude, the shock wave is diffused long before it travels to the earth's surface. If a supersonic airplane flies too close to the ground, however, the shock will hit the earth's surface. It will be heard by observers on the ground (it's called a sonic boom), and if the shock is strong enough, it will cause buildings to shake and windows to break.

The space shuttle has a shock wave around it as it returns to earth through the atmosphere. There is a section of southwestern Georgia that is along the flight path of the returning shuttle when it lands at Cape Canaveral. When the shuttle travels along this path, it is still slightly supersonic, and it is close enough that the people on the ground hear the sonic boom as it travels overhead. The shuttle can't be seen, but it can be heard! Before the shuttle flies low enough for the shock to cause any damage, however, it has dropped its speed below Mach 1.0 and the shock is gone.

In the early days of flight, the aerodynamics of transonic and supersonic flight were not well understood. When pilots started flying faster and faster, their planes were not designed for the rigors of sonic flight. The fronts of the planes and the wings were relatively fat and blunt (rounded), which was fine for subsonic flight. As these early planes approached the sonic regime (called the sound barrier in those days), the pressure waves compressed together to form shock waves in the supersonic regions over the plane, causing vibrations and buffeting (bumpiness). Sometimes the vibrations and buffeting were enough to cause the planes to break up in flight! People were convinced that there was an invisible solid barrier at Mach 1.0, and that humans were not intended to go faster than the speed of sound.

In the late 1940's, designers started to understand high speed aerodynamics and began to design aircraft to fly in the supersonic regime. They designed planes that had sharp noses and sharp and thin airfoil shapes for the wings. This allowed the designers to control the strength of the shock waves that formed to sharply decrease the vibrations and buffeting. On October 14, 1947, flying the experimental aircraft Bell XS-1, Captain Charles Yeager flew the first successful supersonic flight. Today many pilots regularly fly faster than the speed of sound in planes designed for transonic and supersonic flight. The transition to supersonic is so smooth they only notice it because of changes in their instruments.

Perfect Gas Law

The perfect gas law establishes the relationship between the pressure, density , and temperature of a gas at any instant in time or space. Even though it is a mixture of gases, air is mostly nitrogen and can be treated as a perfect gas. Engineers regularly use the perfect gas law to compute air flow properties. The equations for the perfect gas law were found empirically, meaning that many, many experiments were run and data compared mathematically to get the equations.

The simplest and most commonly used formula for the perfect gas law says that the pressure of a gas is equal to the density of the gas multiplied by the gas constant (a function of the atoms in the gas molecules) multiplied by the temperature of the gas. It is very useful in defining how the properties of a gas will change when one of the properties is changed. For example, if the density of a gas is held constant, but the container is heated to raise the temperature, the perfect gas law says that the pressure must also rise. A dangerous example of this principle is illustrated when an aerosol can is thrown into a fire. The density of this can is fixed; neither the mass inside the can or its volume can change. When the can heats up, it will explode when the pressure inside becomes too high for the can to contain!

Bernoulli's Theorem

In order to better understand the changing flow field around an object, aerodynamicists needed a formula for the relationship between the velocities in the fluid and the pressures. Daniel Bernoulli (1700 - 1782) was the first to calculate an expression relating the two terms. For steady (unchanging in time), inviscid (no friction forces), incompressible (density is constant) flow, he found that the local pressure plus one half times the density times the local velocity squared was constant along a streamline. This meant that a particle on a streamline would have the same sum all along the streamline.

In front of an airfoil, for example, the particle would be at the freestream pressure, density, and velocity. The sum of the pressure plus one half times the density times the velocity squared could be computed. As the particle traveled up over the airfoil surface, its velocity would change; it would speed up as it turned up over the front of the airfoil, then slow down as it traveled down the back side of the airfoil. As it moved away from the airfoil trailing edge, it would have returned to the freestream velocity value. The Bernoulli equation shows that as the velocity changed, the pressure would have to change, as well, since the sum computed from the freestream values must remain the same.

Over time, other famous mathematicians and aerodynamicists have expanded the relationship between the pressures and the velocities in a fluid flow, but all show the same basic behavior as Bernoulli's Theorem: when the velocity in the flow increases, the pressure decreases, and when the velocity decreases, the pressure increases.

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