AerodynamicsGeorge CT GrasslySummer 2017
Contents1 Abstract22 Introduction32.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43 Theory73.1 Compressible Flow . . . . . . . . . . . . . . . . . . . . . . . .73.2 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83.3 Pressure Difference . . . . . . . . . . . . . . . . . . . . . . . .81
Chapter 1Abstract2
Chapter 2IntroductionAerodynamics, in its simplest form is the study of the motion of air and howit moves around things, notably an aeroplane wing. The first modern studyof aerodynamics in the eighteenth century, however people new about some ofthe concepts much earlier. The majority of the first studies in aerodynamicswere about achieving heavier-than-air flight, which was first demonstratedby the Wright brothers in 1903. Since then, the use of aerodynamics throughmathematical analysis, empirical approximations, wind tunnel experimenta-tion, and computer simulations has formed a rational basis for the develop-ment of heavier-than-air flight and a number of other technologies. Recentwork in aerodynamics has focused on issues related to compressible flow, tur-bulence, and boundary layers and has become increasingly computational innature.3
2.1 HistoryThe word “aerodynamics” was not actually used until 1837. However, theinvestigation into aerodynamics was started in the 2nd and 3rd centuriesBC, when the work of Aristotle and Archimedes show early fundamentalaerodynamics concepts. [Anderson] Aristotle, in 350 B.C. the effect thatfluids had on objects. He discovered that air has weight and he also observedthat an object moving through a fluid has a resistance. Archimedes, in250 B.C. presented his law of floating bodies that formed the basis for theprinciple 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 aerodynamictheories and ideas for flying machines in personal notebooks. He used to sitdown and watch the sky as many birds flew past, concluding that the flappingof the wings created forward motion. This forward motion allowed air to passacross the bird’s wings to create lift. It was the movement of the wing relativeto the air and the resulting reaction that produced the lift necessary to fly.The numerical theory of air flow and aerodynamics was not discovereduntil the 18th century. Isaac newton became one of the first aerodynamicistswhen he presented Newton’s Laws of motion. In particular in his second Lawof Motion, the conservation of momentum, which was used to figure out theEuler 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. Therelationship is now called Bernoulli’s principle, and provides a method of cal-culating lift, as the pressure in a fluid decreases as its velocity increases.In 1752 Jean le Rond d’Alembert developed a theory about drag. Hewrote that the drag on a body immersed in an inviscid, incompressible fluidis 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 theequation which those making the first attempts at flight, including the Wrightbrothers, used:D=kSV2(2.1)Where:D is the drag4
S is the surface areaV is the air velocityk is a constant, called Smeaton’s coefficientDespite all of these people’s work Sir George Cayley of England is gen-erally known as the modern father of aerodynamics. He engineered a gliderwith a wing and tail that managed to fly successfully, as well as a model heli-copter. He understood many of the basic forces that acted on the wing, andtherefore realized the importance of the wing angle and that curved surfaceswould have more lift.Figure 2.1: Drawing of a glider by Sir George CayleyBefore the turn of the 20th century, two problems were observed flightcould be realized. The first problem was that wings had to be of low-dragand of high-lift. The second problem was to figure out what sort of powerwas needed for sustained flight.In 1884, an American physicist, J Montgomery, started to experimentwith various designs in which a glider could be assembled. His experimentused 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 flowover curved surfaces.5
In 1889, a French engineer, Charles Renard, predicted the power thatwould be required for a continuous flight.[Renard1889]The wright brothers carried out much research in a wind tunnel, andbecause 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
Chapter 3Theory3.1 Compressible FlowCompressible 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. Aninvestigation into the behaviour of bullets once fired was made and this ledto an increased accuracy of weapons.There are some assumptions that have been made with the theory ofcompressible flow. The continuum assumption permits us to understandthat a flowing gas is a continuous substance apart from at low densities.This simplifies the problem. The no-slip condition assumption states thatthe 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 onthe solid travelling through the air at high speeds.For compressible flow, there are 3 main equations which can solve 5 differ-ent unknowns, including density, pressure and the three different componentsof 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 Kelvinχis the dissipation functionρis the densityp is the pressureγ=cpcV=cV+RcVγis the ratio of the molar specific heat at constant pressure,cp, to themolar specific heat at constant volume,cVκ,M, andRare all constantsEquation 3.1 was put together from the continuity equation, the energyconservation equation, and Reifs equations.3.2 Turbulence3.3 Pressure DifferenceBenoulle principleFineness ratio8
Turbulence is a very serious problem that engineeres 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 perticuarly dangerous near the ground.