Introduction
Aerodynamics, in its simplest form is the study of the motion of air and how it moves around things, notably an aeroplane wing. The first modern study of aerodynamics in the eighteenth century, however people new about some of the concepts much earlier. The majority of the first studies in aerodynamics were about achieving heavier-than-air flight, which was first demonstrated by the Wright brothers in 1903. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed a rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to compressible flow, turbulence, and boundary layers and has become increasingly computational innature.3
History
The word “aerodynamics” was not actually used until 1837. However, the investigation into aerodynamics was started in the 2nd and 3rd centuries BC, when the work of Aristotle and Archimedes show early fundamental aerodynamics concepts. [Anderson] Aristotle, in 350 B.C. the effect that fluids had on objects. He discovered that air has weight and he also observed that an object moving through a fluid has a resistance. Archimedes, in250 B.C. presented his law of floating bodies that formed the basis for the principle lighter-than-air vehicles. The next contribution to aerodynamics did not occur until the end of the1400s, when, in 1490, Leonardo da Vinci began writing down his aerodynamic theories and ideas for flying machines in personal notebooks. He used to sit down and watch the sky as many birds flew past, concluding that the flapping of the wings created forward motion. This forward motion allowed air to pass across the bird’s wings to create lift. It was the movement of the wing relative to the air and the resulting reaction that produced the lift necessary to fly. The numerical theory of air flow and aerodynamics was not discovered until the 18th century. Isaac newton became one of the first aerodynamicists when he presented Newton’s Laws of motion. In particular in his second Law of Motion, the conservation of momentum, which was used to figure out the Euler equations and Navier-Stokes equations. In 1738 the Dutch scientist Daniel Bernoulli described a relationship be-tween pressure, velocity, and density, in his Hydrodynamica publication. The relationship is now called Bernoulli’s principle, and provides a method of calculating lift, as the pressure in a fluid decreases as its velocity increases. In 1752 Jean le Rond d’Alembert developed a theory about drag. He wrote that the drag on a body immersed in an inviscid, incompressible fluid is zero, a theory now called D’Alembert’s paradox.[Alembert]The English engineer John Smeaton used a whirling arm device in 1759to calculate the drag exerted on a surface by moving air. He proposed the equation which those making the first attempts at flight, including the Wright brothers, used:D=kSV2(2.1) Where:D is the drag4
S is the surface area V is the air velocity k is a constant, called Smeaton’s coefficient. Despite all of these people’s work Sir George Cayley of England is generally known as the modern father of aerodynamics. He engineered a glider with a wing and tail that managed to fly successfully, as well as a model helicopter. He understood many of the basic forces that acted on the wing, and therefore realized the importance of the wing angle and that curved surfaces would have more lift. Figure 2.1: Drawing of a glider by Sir George Cayley. Before the turn of the 20th century, two problems were observed flight could be realized. The first problem was that wings had to be of low-drag and of high-lift. The second problem was to figure out what sort of power was needed for sustained flight. In 1884, an American physicist, J Montgomery, started to experiment with various designs in which a glider could be assembled. His experiment used a water table with water that circulated as well as a smoke chamber. By applying fluid dynamics he was able to observe the motions of air flow over curved surfaces.5
In 1889, a French engineer, Charles Renard, predicted the power that would be required for a continuous flight.[Renard1889]The wright brothers carried out much research in a wind tunnel, and because of this they had enough statistics to fly the first powered aircraft. in1903. This flight either confirmed or ruled out many aerodynamic theories. For example Newton’s theory about drag was incorrect.6
Theory
Compressible Flow
Compressible flow is when the density of the fluid varies with its pressure. i.e., there are changes in the mass density as the fluid flows. The first re-search into compressible flow was at the beginning of the 19th century. An investigation into the behaviour of bullets once fired was made and this led to an increased accuracy of weapons. There are some assumptions that have been made with the theory of compressible flow. The continuum assumption permits us to understand that a flowing gas is a continuous substance apart from at low densities. This simplifies the problem. The no-slip condition assumption states that the flow velocity on a solid exterior is the same as the velocity of the solid. This assumption implies that the flow is viscous, therefore a layer forms on the solid travelling through the air at high speeds. For compressible flow, there are 3 main equations which can solve 5 different unknowns, including density, pressure and the three different components of velocity [Reif1965]:1γ−1[DpDt−γpρDρDt]=χ+γpρ+κMR∇2[pρ](3.1)DvDt=−∇pρ−∇Ψ+μρ[∇2v+13∇(∇·v)](3.2)DρDt=−ρ∇·v,(3.3)7
Where: T is temperature in degrees Kelvinχ is the dissipation function is the density p is the pressure γ=cpcV=cV+RcVγ is the ratio of the molar specific heat at constant pressure, cp, to themolar specific heat at constant volume, cVκ,M, and Rare all constants Equation 3.1 was put together from the continuity equation, the energy conservation equation, and Reifs equations.3.2 Turbulence3.3 Pressure Difference Benoulle principle Fineness ratio8
Turbulence is a very serious problem that engineers have to take into account when designing planes. Turbulence caused by thunderstorms has in the past caused many accidents for the airplanes, because the sudden changes of direction of the wind can cause airplanes to change speed and altitude rapidly. This can be particularly dangerous near the ground.