AERODYNAMICS

Definition:
When objects move through air, forces are generated by the relative motion between the air and the surfaces of the object. Aerodynamics is the study of these forces, generated by the motion of air.
Introduction:
The behavior of air in motion can be described in general terms using physical theories at various levels, going from the dynamics of huge masses of air such as hurricanes, down to the tiniest scales of atomic motion. However it is unnecessary to use these general, all-inclusive theoretical descriptions to solve most problems.  To design vehicles and predict their performance, we use several methods, each of which is restricted to a small range of parameters. Thus, for example, we divide the field of aerodynamics into categories based on the speed range of interest.
The behavior of air flows changes depending on the ratio of the flow speed to the speed of sound. This ratio is called the Mach number. The speed of sound is the speed at which information propagates through a gas. So if the vehicle moves faster than the speed of sound, the air ahead of it cannot "move away": there is no way for it to "know" of the approaching vehicle. This leads to the formation of "shock" waves in the air ahead of the vehicle.
Very close to a body surface, or at the interface between two streams of air moving at different speeds, we encounter friction.  This leads to many strange and beautiful effects, producing the sinuous structures which make us want to keep looking at flowing streams for hours. Unfortunately, these things are quite difficult to calculate, so we argue that the primary effects of friction are confined to a region very close to the surface, called the "boundary layer".  The boundary layer is a "shear layer". Likewise, the region between two streams of air, flowing at different speeds, is called a "free shear layer" because no solid surface boundary is involved. Away from surfaces, the flow can usually be considered to be "inviscid": it’s almost as if viscosity does not exist there.

Classification of speed ranges by relation to the speed of sound: Mach number regimes
1. "Incompressible" ; Low Speed Aerodynamics    (0 < M  < 0.33)
2. "Subsonic Aerodynamics" (0.33 < M < Mcritical )
3. "Transonic Aerodynamics" (Mcritical  < M < 1.2)
4. "Supersonic Aerodynamics" (1.2 < M < 4)
5.  Hypersonic Aerodynamics (4 < M < ?)
6. Relativistic Aerodynamics

1. "Low Speed Aerodynamics" (0 < M  < 0.33)
Here the speed range is from zero to roughly 1/3 the speed of sound. The speed of sound in the atmosphere is roughly 340 meters/second, so low-speed aerodynamics covers speeds of 0 to roughly 100 m/s. What is special about this range? The density of the air (mass per unit volume) does not change appreciably due to changes in velocity of this magnitude (i.e., from 0 to 0.3 times the speed of sound). The maximum variation in density is less than 5% of the value of density. Thus, in this speed range, the flow is said to be "incompressible" (by changes in velocity!).  With this assumption, we can treat air flow in a manner similar to water flow over a body.

2. "Subsonic Aerodynamics" (0.33 < M < Mcritical )
Here the speed range is from about 1/3 the speed of sound, to about 0.8 times the speed of sound. When vehicles move in this speed range, the flow variations occurring over the vehicle surfaces involve substantial density variations. This effect must be taken into account in performing calculations, or the results obtained will be quite wrong. The upper limit of this regime is the flight Mach number where the local flow somewhere over the aircraft becomes sonic. This flight Mach number is called the "critical Mach number". It depends on the aircraft configuration, and the attitude at which it is flying. Flying faster than the critical Mach number makes the flow supersonic over some part of the aircraft. When this flow decelerates, shocks are produced, with a large increase in drag.

3. "Transonic Aerodynamics" (Mcritical  < M < 1.2)
Most of today's airliners fly at speeds very close to the speed of sound. Today's engines work very well in this regime, and today's people want to reach their destinations quickly and as cheaply as possible. However, this is a very difficult flow regime to analyze, because the changes occurring over an aircraft flying at transonic speeds  involve changes from "supersonic" to "subsonic" and back.

4. "Supersonic Aerodynamics" (1.2 < M < 4)
The behavior of flows moving faster than the speed of sound is very different from that of flows moving slower than sound. The simple explanation for this is that sound cannot propagate upstream in such flows; so these flows cannot "know" of changes about to occur further downstream. Changes occur very suddenly, and through distinct flow features, rather than the curves and gradual changes of subsonic flows.

5. Hypersonic Aerodynamics (4 < M < ?)
As the Mach number increases, the changes caused by deceleration become very large. When a high-Mach number flow is stopped, say at the nose of a vehicle, the temperature, pressure and ensity increase by large amounts. This increase may be large enough that the properties of the air, such as the specific heat and even the molecular structure, change. This is generally considered to become significant above Mach 4.

In the hypersonic regime, the disturbance caused by the aircraft is not felt until the vehicle is very close indeed: the "shocks" lie so close to the surface that the layer of air between the shock and the vehicle is quite thin. The concept of Mach number begins to lose significance as these changes occur, and engineers resort to descriptions in terms of "enthalpy" rather than Mach number to deal with flows at very high speeds. We can still take the flight speed and divide by the speed of sound in the undisturbed atmosphere, and arrive at a flight Mach number. For spacecraft re-entering the atmosphere without aerodynamic controls (such as the Apollo capsules) this "Mach number" was about 35; the Space Shuttle glides in at around Mach 25; meteors might come in at Mach number of a thousand or more.

6. Relativistic Aerodynamics
No human-built object has started flying in this range; however, it is easy to think about a star which is part of one galaxy encountering of another galaxy moving at a vey different speed. Here the relative speeds may become a significant fraction of the speed of light. The flows inside the engines of spacecraft may  reach such speeds, as engineers explore propulsion devices to power spacecraft towards other stars.

Classification of Flows according to properties of significance

Engineers often use terms which are most relevant to the methods which they are using to describe a particular problem and solve it. The following list is certainly not all-inclusive, but illustrates the reasoning behind the terms. The terms are not mutually exclusive. Thus, one speak of a steady turbulent reacting flow, or an unsteady, high-temperature potential flow. One CANNOT speak of a laminar turbulent flow, or a steady unsteady flow, obviously.

This term is used to describe situations where there is no rapid change in properties over time. For example, an aircraft cruising straight and level in the upper atmosphere, well above where any gust can reach it. When such situations are being analyzed, a lot of effort can be saved by neglecting terms in the equations which describe rates of change of the flow properties or forces at any point on the aircraft.

Obviously, unsteady means "not steady", but it also means a lot more. Many situations of "not steady" can be made "steady" by appropriately changing coordinates. For example, an aircraft flying around in circles can be considered to be flying a steady, "coordinated turn", with the flow properties not changing at any point on the craft. The rotor blade of a helicopter hovering steady in still air, also sees the same flow properties from instant to instant.

Now if the aircraft starts rising or sinking, or stays in the coordinated turn long enough to burn a lot of fuel and thus require changes to the control surfaces and engine thrust, or if the helicopter starts flying forward very slowly,  there is a small rate of change of properties encountered, but this is slow enough to be broken up into several stages of steady flow. Likewise, if a wing flaps up and down very slowly, its attitude and the forces on it, change with time, but this can be analyzed by breaking the flapping motion into several steady steps and "joining the dots" of the answers at each step.

On the other hand, an aircraft wing encountering a gust is a situation which requires "unsteady aerodynamics". Likewise, a helicopter rotor in moderate forward flight speed encounters substantially different flow conditions within each revolution.  A shock forming at the inlet of a jet aircraft, and then disappearing, causes large unsteady effects. The flapping motion of an insect's wings is an extreme case of unsteady aerodynamics. In all these cases, the fact that there is a high rate of change has an important bearing on the result.

• Inviscid Flows
To describe flows which are away from surfaces, one can simplify the theory and neglect the influence of viscosity of the fluid. Such descriptions are adequate for situations where the flow velocity and the size dimensions are large. The resulting methods are adequate to explain most of the lift forces (forces perpendicular to the freestream direction) on vehicles; they can also explain the formation of parts of the drag forces, but not all.
• Potential Flows
When viscosity is neglected, and the effects of any rotation and shear in the flow are replaced by mathematical artifacts known as "singularities", the behavior of the rest of the flow can be analyzed by methods similar to those used to analyze electric fields and magnetic fields. These methods of "potential theory" are very powerful: they are used to do the initial calculation of  the air loads on the wings, rotors and fuselages of most airplanes flying today, and also to analyze what happens when the flow is unsteady.
• Viscous Flows
When flow close to a solid surface, or near any boundary where there is relative motion, is analyzed, the effects of fluid viscosity become important. So, analyses of such regions of flows must use equations which include the terms describing the effects of viscosity.

• Laminar Flows
Generally used in analyses of "viscous flow" problems, this term means that the flow is "smooth", and resembles layers of fluid with slightly different velocities. In such flows, the effects of forces due to viscosity are significant, when compared to the effects of the inertia of the fluid motion. In other words, the "Reynolds number" which describes the ratio of inertial forces to viscous forces, is not very large (it still can be of the order of 100,000, but probably not 1 million. )  In describing such flows, it is possible to arrive at an answer to the question: "what will the velocity be at this point one second from now?"  to a high degree of accuracy: unlike "turbulent flows", described below.
• Turbulent Flows
When there is some source of shear between different regions of fluid, and the Reynolds number is extremely high (on the order of a million or more),  flows become turbulent, with the velocity, flow direction, and all associated properties fluctuating from instant to instant. Analyses of such flows must thus account for the results of such fluctuations, which include increased skin friction drag, reduced occurence of flow separation and its drag, different rates of heat transfer between the flow and vehicle surfaces, the generation of noise, faster mixing between different fluid streams, and faster propagation of flames through gases.
• High Temperature Flow
Over a narrow range of temperature, the properties of air, such as its specific heat, molecular composition etc. can be assumed to hold constant. We generally don't even worry about this issue in most of aerodynamics. However, there are situations where the changes in temperature are large, and hence we have to include detailed models of how gas properties change with temperature, in solving such problems. An example is the shock wave in front of the nose of the space shuttle as it comes down through the atmosphere. If we ignored the changes in gas properties in analyzing the change of temperature through this shock, we would get ridiculous results: we would predict temperatures which do not occur except in nuclear explosions!!  As seen above, its not the actual "highness" of the temperature that matters for this definition: its the fact that the temperature can change over a large range.
• Reacting flow
If the chemical reactions occurring in the flow are significant to the changes in flow properties, one has to include them in the analysis. For example, a "flame" is a reacting flow, where there is a large and rapid release of heat occurring during a chemical reaction. The molecular composition also changes, of course, during the chemical reaction. The flow in the combustion chamber of a rocket is a reacting flow. However, the flow in the nozzle of the same rocket, though it is glowing hot, may or may not be classified as a reacting flow: this depends on whether the composition  changes substantially in the nozzle.

• Non-equilibrium flow
This is another of those "when did we assume that"? revelations. In most problems in aerodynamics, we assume that we have "equilibrium" in the flow. The rates of collisions between molecules is high enough that we can assume, for example, that the temperature and pressure in the flow in a nozzle adjust instantly to changes in the nozzle geometry.  In some flow situations, the changes in properties may be so large and so sudden that the flow has moved a significant distance before there is complete adjustment of the temperature and the chemical composition. This occurs in lasers, for example, where the medium is kept out of equilibrium. Non-equilibrium phenomena can cause important differences to the pressure distribution and hence the pitching moment on a high-speed aircraft, like the Space Shuttle at re-entry. Calculations of nozzle geometry and heat transfer for rocket engines and vehicles such as the X-33 also require non-equilibrium considerations.
• Multiphase flow
Sometimes, flows may include changes between solid, liquid and gas states, and may also include substantial amounts of material of different phases flowing along together. For example, as compressed air at room temperature is expanded through the throat of a supersonic wind tunnel, some of the constituent gases may begin to liquefy, and droplets of oxygen or nitrogen might form in the flow. The flow over the leading edge of a rotor blade operating under icing conditions may involve the formation of ice particles near the surface.
• Rarefied flow
In the upper reaches of the atmosphere, the density of the air becomes so low that air cannot be assumed to be a continuous medium or "continuum". The flow analysis must include consideration of this fact. Since collisions between molecules become rare, it is smarter to regard the flow as being composed of  many balls bouncing off the surface of the vehicle.
• Plasma
When the gases in the flow are ionized (electrons leave many atoms, so that there is a high concentration of positive ions and free electrons), the flow behavior can be modified, and forces generated, using magnetic fields. Such flows are called plasmas.
• Buoyant flow
These are probably the most common flows of air in the atmosphere: flows driven by the changes in their density due to heating or cooling, making them lighter or heavier than surrounding fluid. In most aerodynamics problems, we can neglect buoyancy effects because the flow velocities and the inertial effects are so large; however, buoyancy is a driver of atmospheric flows. Gliders, obviously, take advantage of buoyant flows when they rise on "thermals".

General Introduction
Classification by speed
Classification by flow phenomena
Course level

 0 1 2 3 4 5 6 7 8 9

Research Areas
Textbooks
References

External Resources

Matrix of Applications. Dominant Phenomena and Analysis Methods

 Application/Vehicle Phenomena/Problems Thin Airfoil Lifting Line Lifting Surface: linear Slender Wing Slender Body Vortex Cloud Vortex Ring Theodorsen Indicial Modal Uns. Lifting Surface Free Wake Betz Cross-Flow Polhamus Full Potential TSD Integral Layer Boundary Layer Conical Flow Vortex  Dynamics Euler Parabolized  Navier-Stokes Full Navier-Stokes:  Laminar Full N-S:  Turbulent microAV Wing Tip Vortex Persistence UCAV Rotor Blade Tip Vortex Tiltrotor Forebody Vortex Vortex Asymmetry Tail Buffeting Wing Buffeting Ornithopter Weiss-Fogh Effect Insect Blade-Vortex Interaction JSF Laminar Flow Control F-22 Dynamic Stall: 2D FA-18 Dynamic Stall: 3D X-31 Parachute Inflation X-33 Parafoil Collapse X-36 Rotor-Fuselage Interaction X-38 Vortex-Surface Interaction HSCT Cavity Flow NASP propwash/wing interaction

Richards, B.E., Brebner, G.G., Stahl, W., "Missile Aerodynamics". AGARD Lecture Series No. 98, February 1979. Technical
Editing and Reproduction Ltd., London.

Brebner, G.G., "A Brief Review of Air Flight Weapons". AGARD Lecture Series No. 98, February 1979. Technical Editing and
Reproduction Ltd., London, pp. 1-1 - 1-12.

Brebner, G.G., "General Missile Aerodynamics". AGARD Lecture Series No. 98, February 1979. Technical Editing and
Reproduction Ltd., London, pp. 2-1 - 2-16.

Stahl, W.H., "Aerodynamics of Low Aspect Ratio Wings". AGARD Lecture Series No. 98, February 1979. Technical Editing
and Reproduction Ltd., London, pp. 3-1 - 3-64.

Esch, H., "Bodies". AGARD Lecture Series No. 98, February 1979. Technical Editing and Reproduction Ltd., London, pp. 4-1 -
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Wardlaw, A.B., Jr., "High-Angle-of-Attack Missile Aerodynamics". AGARD Lecture Series No. 98, February 1979. Technical
Editing and Reproduction Ltd., London, pp. 5-1 - 5-53.

Delery, J., Sireix, M., "Ecoulements de Culot". AGARD Lecture Series No. 98, February 1979. Technical Editing and
Reproduction Ltd., London, pp. 6-1 - 6-78.

Brebner, G.G., "The Control of Guided Weapons". AGARD Lecture Series No. 98, February 1979. Technical Editing and
Reproduction Ltd., London, pp. 7-1 - 7-29.

Mathews, C.B., "Store Separation". AGARD Lecture Series No. 98, February 1979. Technical Editing and Reproduction Ltd.,
London, pp. 8-1 - 8-76.

Richards, B.E., "Kinetic Heating of High Speed Missiles". AGARD Lecture Series No. 98, February 1979. Technical Editing and
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Young, A.D, et al., (Ed): "Aerodynamics of Vortical Type Flows in Three Dimensions". AGARD Conference Proceedings No.
342, July 1983. ISBN 92-835-0334-1

Peake, D.J., Tobak, M., "On Issues Concerning Flow Separation and Vortical Flows in Three Dimensions". AGARD Conference
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Hornung, H.G., "The Vortex Skeleton Model for Three-Dimensional Steady Flows". AGARD Conference Proceedings No. 342,
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Roberts, L., "On the Structure of the Turbulent Vortex". AGARD Conference Proceedings No. 342, July 1983. ISBN
92-835-0334-1, pages 3-1 to 3-11.

Strange, C., Harvey, J.K., "Instabilities in Trailing Vortices: Flow Visualization Using Hot-Wire Anemometry". AGARD
Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 4-1 to 4-11.

Delery, J., Horowitz, E., "Interaction Entre Une Onde de Choc et Une Structure Tourbillonaire Entroulee". AGARD Conference
Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 5-1 to 5-19.

Poll, D.I.A., "On the Generation and Subsequent Development of Spiral Vortex Flow Over a Swept-Back Wing". AGARD
Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 6-1 to 6-14.

Verhaagen, N.G., "An Experimental Investigation of the Vortex Flow over Delta and Double-Delta Wings at Low Speed".
AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 7-1 to 7-16.

Werle, H., "Visualisation des Ecoulements Tourbillonaires Tridimensionnels". AGARD Conference Proceedings No. 342, July
1983. ISBN 92-835-0334-1, pages 8-1 to 8-20.

Vorropoulos, G., Wendt, J.F., "Laser Velocimetry Study of Compressibility Effects on the Flow Field of a Delta Wing". AGARD
Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 9-1 to 9-13.

Lamar, J.E., Campbell, J.F., "Recent Studies at NASA-Langley of Vortical Flows Interacting with Neighboring Surfaces".
AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 10-1 to 10-32.

Erickson, G.E., Gilbert, W.P., "Experimental Investigation of Forebody and Wing Leading Edge Vortex Interactions at High
Angles of Attack". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 11-1 to 11-20.

Byram, T., Petersen, A., Kitson, S.T., "Some Results from a Programme of Research into the Structure of Vortex Flow Fields
Around Missile Shapes". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 12-1 to 12-20.

Maskew, B., "Predicting Aerodynamic Characteristics of Vortical Flows on Three-Dimensional Configurations Using a
Surface-Singularity Panel Method". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 13-1 to
12-12.

Vollmers, H., Kreplin, H.P., Meier, H.U., "Separation and Vortical Type Flow Around a Prolate Spheroid - Evaluation of
Relevant Parameters". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 14-1 to 14-14.

Evangelou, P., "On the Generation of Vortical Flows At Hypersonic Speeds Over Elliptic Cones". AGARD Conference
Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 15-1 to 15-9.

Wickens, R.H., "Viscous Three-Dimensional Flow-Separation From High-Wing Propeller Turbine Nacelle Models". AGARD
Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 16-1 to 16-29.

Smith, J.H.B. "Theoretical Modeling of Three-Dimensional Vortex Flows in Aerodynamics". AGARD Conference Proceedings
No. 342, July 1983. ISBN 92-835-0334-1, pages 17-1 to 17-21.

Hoeijmakers, H.W.M., "Computational Vortex Flow Aerodynamics". AGARD Conference Proceedings No. 342, July 1983.
ISBN 92-835-0334-1, pages 18-1 to 18-35.

Weiland, C., "Vortex Flow Simulations Past WingsUsing the Euler Equations". AGARD Conference Proceedings No. 342, July
1983. ISBN 92-835-0334-1, pages 19-1 to 19-12.

Huberson, S., "Simulation d'Ecoulements Turbulents par Une Methode de Tourbillons Ponctuels". AGARD Conference
Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 20-1 to 20-8.

Rizzi, A., Eriksson, L-E., Schmidt, W., Hitzel, S., "Numerical Solutions of the Euler Equations Simulating Vortex Flows Around
Wings". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 21-1 to 21-14.

Steinhoff, J., Ramachandran, K., Suryanarayanan, K., "The Treatment of Convected Vortices in Compressible Potential Flow".
AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 22-1 to 22-12.

Leibovich, S., "Vortex Stability and Breakdown". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1,
pages 23-1 to 23-22.

Persen, L.N., "The Break-Up Mechanism of a Streamwise Directed Vortex". AGARD Conference Proceedings No. 342, July
1983. ISBN 92-835-0334-1, pages 24-1 to 24-5.

Escudier, M.P., Keller, J.J., "Vortex Breakdown: A Two-Stage Transition". AGARD Conference Proceedings No. 342, July
1983. ISBN 92-835-0334-1, pages 25-1 to 25-8.

Krause, E., "A Contribution to the Problem of Vortex Breakdown". AGARD Conference Proceedings No. 342, July 1983. ISBN
92-835-0334-1, pages 26-1 to 26-4.

Nakamura, Y., Leonard, A., Spalart, P.R., "Numerical Simulation of Vortex Breakdown by the Vortex Filament Method".
AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 27-1 to 27-13.

Solignac, J.L., Leuchter, O., "Etudes Experimentales d'Ecoulements Tourbillonaires Soumis a des Effets de Gradient de Pression
Adverse". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 28-1 to 28-25.

Maxworthy. T., Mory, M., Hopfinger, E.J., "Waves on Vortex Cores and their Relation to Vortex Breakdown". AGARD
Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 29-1 to 29-13.

Rao, D.M., "Vortical Flow Management for Improved Configuration Aerodynamics - Recent Experiences". AGARD Conference
Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 30-1 to 30-14.

Spillman, J.J., Fell, M.J., "The Effects of Wing Tip Devices on the Performance of the BAe Jetstream". AGARD Conference
Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 31A-1 to 31A-11.

Spillman, J.J., "The Effect of Wing Tip Devices on the Far-Field Wake of a Paris Aircraft". AGARD Conference Proceedings No.
342, July 1983. ISBN 92-835-0334-1, pages 31B-1 to 31B-9.

Baron, A., de Ponte, S., "Boundary Layer Segmentation on Sharp Highly-Swept Loading Edges and its Effects on Secondary
Vortices". AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1, pages 32-1 to 32-7.

Seginer, A., Salomon, M., "Augmentation of Fighter Aircraft Performance By Spanwise Blowing Over the Wing Leading Edge".
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Young, A.D., (Ed). "Round Table Discussion", AGARD Conference Proceedings No. 342, July 1983. ISBN 92-835-0334-1,
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