Introducing Aerodynamics

                Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with the difference being that gas dynamics applies to all gases.

Understanding motion of air (often called a flow field) around an object enables the calculation of forces and moments acting on the object. Typical properties calculated for a flow field include velocity, pressure, density and temperature as a function of spatial position and time. Aerodynamics allows the definition and solution of equations for the conservation of mass,momentum, and energy in air. The use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations form the scientific basis for heavier-than-air flight and a number of other technologies.

Aerodynamic problems can be classified according to the flow environment. External aerodynamics is the study of flow around solid objects of various shapes. Evaluating the lift and drag on an airplane or the shock waves that form in front of the nose of a rocket 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.

"According to the theory of aerodynamics, a 

flow is considered to be compressible if its 

change in density with respect to pressure is 

non-zero along a streamline."

Aerodynamic problems can also be classified according to whether the flow speed is below, near or above 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. Aerodynamicists disagree over the precise definition of hypersonic flow; minimum Mach numbers for hypersonic flow range from 3 to 12.

The influence of viscosity in the flow dictates a third classification. Some problems may encounter only very small viscous effects on the solution, in which case viscosity can be considered to be negligible. The approximations to these problems are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

Continuity assumption

The foundation of aerodynamic prediction is the continuity assumption. In reality, gases are composed of molecules which collide with one another and solid objects. To derive the equations of aerodynamics, fluid properties such as density and velocity are assumed to be well-defined at infinitely small points, and to vary continuously from one point to another. That is, the discrete molecular nature of a gas is ignored.

The continuity assumption becomes less valid as a gas becomes more rarefied. In these cases, statistical mechanics is a more valid method of solving the problem than continuous aerodynamics. The Knudsen number can be used to guide the choice between statistical mechanics and the continuous formulation of aerodynamics.

Laws of conservation

Aerodynamic problems are normally solved using conservation laws as applied to a fluid continuum. The conservation laws can be written in integral or differential form. In many basic problems, three conservation principles are used:

• Continuity: If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume. In fluid dynamics, the continuity equation is analogous to Kirchhoff's Current Law in electric circuits. The differential form of the continuity equation is:

Above,  is the fluid density, u is a velocity vector, and t is time. Physically, the equation also shows that mass is neither created nor destroyed in the control volume. For a steady state process, the rate at which mass enters the volume is equal to the rate at which it leaves the volume. Consequently, the first term on the left is then equal to zero. For flow through a tube with one inlet (state 1) and exit (state 2) as shown in the figure in this section, the continuity equation may be written and solved as:

Above, A is the variable cross-section area of the tube at the inlet and exit. For incompressible flows, density remains constant.

• Conservation of Momentum: This equation applies Newton's second law of motion to a continuum, whereby force is equal to the time derivative of momentum. Both surface and bodyforces are accounted for in this equation. For instance, F could be expanded into an expression for the frictional force acting on an internal flow.

For the same figure, a control volume analysis yields:

Above, the force  is placed on the left side of the equation, assuming it acts with the flow moving in a left-to-right direction. Depending on the other properties of the flow, the resulting force could be negative which means it acts in the opposite direction as depicted in the figure. In aerodynamics, air is normally assumed to be a Newtonian fluid, which posits a linear relationship between the shear stress (the internal friction forces) and the rate of strain of the fluid. The equation above is a vector equation: in a three dimensional flow, it can be expressed as three scalar equations. The conservation of momentum equations are often called the Navier-Stokes equations, while others use the term for the system that includes conversation of mass, conservation of momentum, and conservation of energy.

• Conservation of Energy: Although energy can be converted from one form to another, the total energy in a given closed system remains constant.

Above, h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and  is the viscous dissipation function. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted to heat. The term is always positive since, according to the second law of thermodynamics, viscosity cannot add energy to the control volume. The expression on the left side is a material derivative. Again using the figure, the energy equation in terms of the control volume may be written as:

Above, the shaft work  and heat transfer  are assumed to be acting on the flow. They may be positive (to the flow from the surroundings) or negative (to the surroundings from the flow) depending on the problem.

The ideal gas law or another equation of state is often used in conjunction with these equations to form a determined system to solve for the unknown variables.

Incompressible aerodynamics

An incompressible flow is characterized by a constant density despite flowing over surfaces or inside ducts. While all real fluids are compressible, a flow problem is often considered incompressible if the density changes in the problem have a small effect on the outputs of interest. This is more likely to be true when the flow speeds are significantly lower than the speed of sound. For higher speeds, the flow will compress more significantly as it comes into contact with surfaces and slows. The Mach number is used to evaluate whether the incompressibility can be assumed or the flow must be solved as compressible.

Subsonic flow

Subsonic (or low-speed) aerodynamics is the study of fluid motion which is everywhere much slower than the speed of sound through the fluid or gas. There are several branches of subsonic flow but one special case arises when the flow is inviscid, incompressible and irrotational. This case is called Potential flow and allows the differential equations used to be a simplified version of the governing equations of fluid dynamics, thus making available to the aerodynamicist a range of quick and easy solutions.

In solving a subsonic problem, one decision to be made by the aerodynamicist is whether 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 low-speed aerodynamics problem. When the density is allowed to vary, the problem is called a compressible problem. In air, compressibility effects are usually ignored when the Mach number in the flow does not exceed 0.3 (about 335 feet (102m) per second or 228 miles (366 km) per hour at 60 °F). Above 0.3, the problem should be solved by using compressible aerodynamics.

Compressible aerodynamics

According to the theory of aerodynamics, a flow is considered to be compressible if its change in density with respect to pressure is non-zero along a streamline. This means that - unlike incompressible flow - changes in density must be considered. In general, this is the case where the Mach number in part or all of the flow exceeds 0.3. The Mach .3 value is rather arbitrary, but it is used because gas flows with a Mach number below that value demonstrate changes in density with respect to the change in pressure of less than 5%. Furthermore, that maximum 5% density change occurs at the stagnation point of an object immersed in the gas flow and the density changes around the rest of the object will be significantly lower. Transonic, supersonic, and hypersonic flows are all compressible.

via wikipedia