Aerodynamics

Aerodynamics is the study of the flow of gases. It is a branch of fluid dynamics. The solution of an aerodynamic problem normally involves calculating for various properties of the flow, such as velocity, pressure, density, and temperature, as a function of space and time. Once the flow pattern is understood it becomes possible to calculate or approximate the forces and moments acting on bodies in the flow. It is this mathematical analysis and empirical approximation that becomes the scientific basis for heavier-than-air flight.

Aerodynamic problems can be classified in a number of ways. The first classification criterion is whether the flow is external or internal. External aerodynamics is the study of flow around solid objects of various shapes. For instance, evaluating the lift and drag on an airplane, the shock waves that form in front of the nose of a rocket, and the flow of air over a hard drive head are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine or through an air conditioning pipe.

A second classification of aerodynamic problems is the ratio of the problem characteristic flow speed to the speed of sound. A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present (normally when the characteristic speed is approximately the speed of sound), supersonic when the characteristic flow speed is greater than the speed of sound, and hypersonic when the flow speed is much greater than the speed of sound. Aerodynamicians disagree over the precise definition of hypersonic flow; minimum Mach numbers for hypersonic flow range from 3 to 12. Most aerodynamicians use numbers between 5 and 8.

A third way to classify aerodynamic problems is by the importance of viscosity in the flow. In some problems, in which viscous effects on the solution are negligible, viscosity can be safely ignored and set to zero. The approximations to these problems are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

Table of contents

1 History of Aerodynamics
2 Aerodynamic Forces on Aircraft
3 Aerodynamics in Other Fields
4 Continuity Assumption
5 Conservation Laws
6 Subsonic Aerodynamics
7 Transonic Aerodynamics
8 Supersonic Aerodynamics
9 Hypersonic Aerodynamics

History of Aerodynamics

Aerodynamic Forces on Aircraft

One of the major goals of aerodynamics is to predict the aerodynamic forces on aircraft.

The four forces that act on a powered aircraft are lift, weight, thrust, and drag. Weight is the force due to gravity and thrust is the force generated by the engine. Lift and drag are aerodynamic forces. Lift is defined as the aerodynamic force acting perpendicular to the direction of travel of the aircraft relative to the surrounding air, and drag is defined as the aerodynamic force acting parallel to the direction of travel. Lift is positive upwards and drag is positive rearwards.

Aerodynamics in Other Fields

Continuity Assumption

Gases are composed of molecules which collide with one another and solid objects. In aerodynamics, however, gases are considered to have continuous quantities. That is, properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another. The discrete, molecular nature of a gas is ignored.

The continuity assumption becomes less valid as a gas becomes more rarified. In these cases, statistical mechanics is a more valid method of solving the problem than aerodynamics.

Conservation Laws

Aerodynamic problems are solved using the conservation laws, or equations derived from the conservation laws. In aerodynamics, three conservation laws are used:

Conservation of mass: Matter is not created or destroyed. If a certain mass of fluid enters a volume, it must either exit the volume or increase the mass inside the volume.
Conservation of momentum: Also called Newton's second law of motion
Conservation of energy: Energy is neither created nor destroyed. It may only change from one manifestation to another.

All aerodynamic problems are therefore solved by the same set of equations. However, they differ by the assumptions made in each problem. The equations become simpler as assumptions are made.

Note that these laws are based on Newtonian Mechanics, they are not applicable in Einsteinian Mechanics.

Subsonic Aerodynamics

In a subsonic aerodynamic problem, all of the flow speeds are less than the speed of sound. This class of problems encompasses nearly all internal aerodynamic problems, as well as external aerodynamics for general aviation aircraft, model aircraft, and automobiles.

In solving a subsonic problem, one decision to be made by the aerodynamicist is whether or not to incorporate the effects of compressibility. Compressibility is a description of the amount of change of density in the problem. When the effects of compressibility on the solution are small, the aerodynamicist may choose to assume that density is constant. The problem is then an incompressible problem. When the density is allowed to vary, the problem is called a compressible problem. In air, compressibility effects can be ignored when the Mach number in the flow does not exceed 0.3. Above 0.3, the problem should be solved using compressible aerodynamics.

Transonic Aerodynamics

Transonic aerodynamic problems are defined as problems in which both supersonic and subsonic flow exist. Normally the term is reserved for problems in which the characteristic Mach number is very close to one.

Transonic flows are characterized by shock waves and expansion waves. A shock wave or expansion waves is a region of very large changes in the flow properties. In fact, the properties change so quickly they are nearly discontinuous across the waves. Flow ahead of a shock wave is supersonic; flow behind a shock wave is subsonic.

Transonic problems are arguably the most difficult to solve. Flows behave very differently at subsonic and supersonic speeds, therefore a problem involving both types is more complex than one in which the flow is either purely subsonic or purely supersonic.

Supersonic Aerodynamics

Supersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating the lift on the Concorde is an example of a supersonic aerodynamic problem.

Supersonic flow behaves very differently from subsonic flow. The speed of sound can be considered the fastest speed that "information" can travel in the flow. Gas travelling at subsonic speed diverts around a body before striking it, it can be said to "know" that the body is there. Air cannot divert around a body when it is travelling at supersonic speeds. It continues to travel in a straight line until it reaches a shock wave and decelerates to subsonic speeds. Mathematically expressed, supersonic flow is hyperbolic while subsonic flow is elliptic.

Another example of the difference between supersonic and subsonic flow is the behaviour in a convergent duct (known as a nozzle in subsonic flow and a diffuser in supersonic flow). Subsonic flow in a convergent duct accelerates and supersonic flow decelerates.