Aerodynamics

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The passage of the wing of a plane creates an identifiable vortex by the coloured smoke.

Aerodynamics is the branch of fluid mechanics that studies the actions that appear on solid bodies when there is a relative motion between them and the fluid that bathes them, the latter being a gas and not a liquid, this case being studied in hydrodynamics. Its study is basic for the lift and high lift surfaces of aircrafts and helicopters.

History

Modern aerodynamics only dates back to the 17th century, but aerodynamic forces have been harnessed by humans for thousands of years. of years in sailing ships and windmills, and images and stories of flight appear throughout history, such as the ancient Greek legend of Icarus and Daedalus. The fundamental concepts of continuum, drag, and gradient of pressure appear in the work of Aristotle and Archimedes.

In 1726, Sir Isaac Newton became the first person to develop a theory of air resistance, making him one of the first aerodynamicists. The Dutch-Swiss mathematician Daniel Bernoulli followed in 1738 with Hydrodynamica in which he described a fundamental relationship between pressure, density, and velocity of flow for incompressible flow known today as Bernoulli's principle, which provides a method for calculating aerodynamic lift. In 1757, Leonhard Euler published the more general Euler Equations that could be applied to both compressible and incompressible flows. Euler's equations were extended to incorporate the effects of viscosity in the first half of the 19th century, giving rise to the equations Navier-Stokes equations. The Navier-Stokes equations are the most general governing equations of fluid flow, but are difficult to solve for flow around all but the simplest forms.

A replica of the Wright brothers' wind tunnel is exhibited at the Virginia Air and Space Center. Wind tunnels were key in the development and validation of aerodynamic laws.

In 1799, Sir George Cayley became the first person to identify the four aerodynamic forces of flight (weight, lift, drag, and thrust) as well as the relationships between them, charting the path toward achieving heavier-than-air flight for the next century. In 1871, Francis Herbert Wenham built the first wind tunnel, allowing aerodynamic forces to be accurately measured. Resistance theories were developed by Jean le Rond d'Alembert, Gustav Kirchhoff, and Lord Rayleigh. In 1889, Charles Renard, a French aeronautical engineer, became the first person to reasonably predict the power required for sustained flight. Otto Lilienthal, the first person to have great success with glider flight, was also the first to propose thin, curved airfoils that produced high lift and low drag. Based on these developments and research conducted in their own wind tunnel, the Wright brothers flew the first powered airplane on December 17, 1903.

During the time of early flight, Frederick W. Lanchester, Martin Kutta, and Nikolai Zhukovsky independently created theories linking the circulation of fluid flow to lift. Kutta and Zhukovsky went on to develop a theory of two-dimensional wings. Expanding on Lanchester's work, Ludwig Prandtl is credited with developing the mathematics underlying thin-film and lift-line theories, as well as work with boundary layers.

As aircraft speeds increased, designers began to encounter problems related to the compressibility of air at speeds close to the speed of sound. Differences in airflow under such conditions cause problems in aircraft control, increased drag due to shock waves, and the threat of structural failure due to vibration induced by aeroelastic oscillations. The relationship between the speed of the flow and the speed of sound was called the Mach number after Ernst Mach, who was one of the first to investigate the properties of supersonic flow. Macquorn Rankine and Pierre Henri Hugoniot independently developed the theory of flow properties before and after a shock wave, while Jakob Ackeret led the initial work calculating lift and drag for supersonic profiles. Theodore von Kármán and Hugh Latimer Dryden introduced the term transonics to describe flow velocities between the critical Mach number and Mach 1 where drag increases rapidly. This rapid increase in drag caused aerodynamicists and aviators to disagree on whether supersonic flight was achievable until the sound barrier was broken in 1947 with the Bell X-1 aircraft.

By the time the sound barrier was broken, aerodynamicists' understanding of subsonic and low supersonic flow had matured. The Cold War prompted the design of an ever-evolving line of high-performance aircraft. Computational fluid dynamics began as an effort to solve the properties of flow around complex objects and has rapidly grown to the point that entire aircraft can be designed using computer programs, with wind tunnel testing followed by flight testing to confirm the computer's predictions. The understanding of supersonic and hypersonic aerodynamics has matured since the 1960s and the goals of aerodynamicists have shifted from fluid flow behavior to engineering a vehicle that interacts predictably with fluid flow. Aircraft design for supersonic and hypersonic conditions, as well as the desire to improve the aerodynamic efficiency of today's aircraft and propulsion systems, continue to motivate new research in aerodynamics, while continuing to work on important problems in basic aerodynamic theory. related to flow turbulence and the existence and uniqueness of analytical solutions of the Navier-Stokes equations.

Introduction

Aerodynamics is developed from Newton's equations. With the equations of continuity, momentum and energy, models that describe the movement of fluids can be obtained. A particular case occurs when the movement of the fluid is stationary, that is, the properties of the fluid only change with the position in the fluid field but not with time, and when the viscosity of the fluid can also be neglected. With these two characteristics, stationary and non-viscous motion, it is possible to obtain a potential function that, when derived, obtains the velocity of the fluid at each point in the field. Once we have obtained the velocity of the fluid, we can find other important magnitudes. The classical aerodynamics that explains how lift is generated on airfoils is based on potential motions. This type of movement is ideal, since zero viscosity is never achieved.

Modeling the fluid field is possible to calculate, in almost all cases, the forces and moments that act on the body or bodies submerged in the fluid field. The relationship between forces on a body moving in the bosom of a fluid and speeds is given by aerodynamic coefficients. There are coefficients that relate speed to the forces and coefficients that relate speed to time. Conceptually the easiest are the first, which give the strength of support ${L}$ aerodynamic resistance ${displaystyle {D}}$ and lateral force ${displaystyle {Y}}$ in terms of the speed square (V²), fluid density (ρ) and cross-sectional area (S_t):3:/:C:V

Sustaining coefficient ${displaystyle {C_{L}}={frac {L}{{frac {1}{2}}rho V^{2}S_{t}}}}$
Resistance coefficient ${displaystyle {C_{D}}={frac {D}{{frac {1}{2}}rho V^{2}S_{t}}}}$
Side force coefficient ${displaystyle {C_{Y}}={frac {Y}{{frac {1}{2}}rho V^{2}S_{t}}}}$

Due to the complexity of the phenomena that occur and the equations that describe them, both practical tests (for example wind tunnel tests) and numerical calculations of numerical aerodynamics are extremely useful.

Aerodynamic problems

Several classifications have been established, among which we must highlight:

according to its application: aerodynamic aeronautics (or simply aerodynamic) and civil aerodynamics
according to the nature of the fluid: understandable and incompressible
according to the number of Mach characteristic of the problem:
- subsonic (M habit1: incompressible subsonic M dose0,3 and understandable subsonic M≤0.8)
- transonic (M near 1)
- supersonic (M/2002/1)
- hypersonic (M/2003/6).

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