Aerodynamics

The place of aerodynamics in engineering is discussed through the physical origin of the forces on aircraft and objects in the fluid. First, the concept of lift force is reminded with Archimedes' principle and the difference of this force from aerodynamic lift force is explained. The concepts of lift force, drag force, resultant aerodynamic force, moment, reference area, chord, span, aspect ratio and angle of attack are introduced. Basic L, D and R calculations are introduced with the definition of airspeed, relative velocity vector, lift and drag directions.

It is examined how aerodynamic forces and moments are obtained from the pressure and shear stress distributions on the surface. Pressure coefficient, friction coefficient, lift coefficient, drag coefficient and moment coefficient are defined. Force/moment components for two-dimensional airfoil and three-dimensional wing are studied by worked examples and problem solving. In this section, the concepts of aerodynamic center, center of pressure and moment reference point are particularly emphasized.

In terms of aerodynamic modeling, viscous-inviscid, compressible-incompressible, subsonic-transonic-supersonic and steady-unsteady flow distinctions are discussed. The concept of boundary layer, viscous effects, flow separation, wake formation and stall mechanism are explained physically. The effects of lift curve, lift-curve slope, stall angle and angle of attack on aerodynamic performance are interpreted through graphics.

Dimensional analysis and modeling approach in aerodynamic problems is handled through Buckingham Pi theorem. The physical meaning of dimensionless parameters such as Reynolds number, Mach number, lift coefficient, drag coefficient and moment coefficient are examined. Model-prototype similarity, geometric/kinematic/dynamic similarity, wind tunnel experiments and interpretation of experimental data through dimensionless coefficients are studied.

Fluid movement. It is examined through the concepts of velocity field, acceleration field, material derivative, streamline, pathline, streakline and control volume. In aerodynamic problems, appropriate model selection, modeling the flow as two-dimensional or three-dimensional, inviscid approach and small disturbance assumptions are discussed. In this section, the relationship between the mathematical representation of the flow field and the physical flow structure is established.

Mass and momentum conservation are discussed in differential and integral forms. The control volume approach, continuity equation, momentum equation and Euler equations under appropriate assumptions are connected to aerodynamic problems. In inviscid flow, the relationship between pressure gradient, velocity change and flow direction acceleration is interpreted. The role of the Bernoulli equation in aerodynamic applications is discussed.

Potential flow approach is developed under inviscid, incompressible and irrotational flow assumptions. Velocity potential, stream function, Laplace equation, stream function–velocity potential relationship and the physical meaning of streamlines are discussed. This section discusses why potential flow is used in aerodynamics and what limitations it has.

Basic potential flow elements such as uniform flow, source, sink, vortex and doublet are examined. Using the principle of superposition, complex flow fields are attempted to be created as the sum of simple elements. Rankine oval, flow around the cylinder and pressure distribution on the cylinder are addressed by worked examples and problem solving; d'Alembert's paradox is interpreted physically.

The concept of circulation, vortex flow, and lift generation through circulating flow around the cylinder are examined. Using the Kutta–Joukowski theorem, the relationship between the lift force per unit span and circulation is obtained. The Kutta condition, starting vortex, bound vortex and lift mechanism around the airfoil are physically explained.

Airfoil geometry. It is defined through chord, camber line, thickness distribution, leading edge, trailing edge and angle of attack. The relationship between pressure distribution on the airfoil, pressure coefficient graphs, upper and lower surface pressure difference and lift generation is examined. The effects of moment coefficient, aerodynamic center, pressure center and profile characteristics on lift/drag behavior are particularly emphasized.

Thin airfoil theory is developed under the assumptions of small angle of attack and thin profile. The lift curve slope, zero-lift angle and moment coefficient are obtained by using the vorticity distribution on the profile, boundary condition, basic integral equation and Fourier series approach. The results of thin airfoil theory for symmetric and cambered airfoils are studied with worked examples and problem solving.

Three-dimensional flow effects on finite wings are examined through the concepts of wing tip vortices, downwash and induced angle of attack. The lift generation of the finite wing is explained using the bound vortex, trailing vortex and horseshoe vortex model. The concepts of aspect ratio, spanwise loading and induced drag are interpreted physically.

Using the Prandtl lifting-line theory, the circulation distribution, downwash and induced drag relationship along the finite wing are discussed. Elliptical lift distribution, Oswald efficiency factor, aspect ratio effect and how the lift curve slope changes in the finite wing are examined. Finite wing performance. It is evaluated by worked examples and problem solving in terms of induced drag, wingspan, planform and design parameters.

The panel method is introduced as a numerical implementation of the potential flow approach. Separation of the airfoil surface into panels, source/vortex distribution, impermeability boundary condition and application of the Kutta condition are discussed at a basic level. How to interpret the panel method results in terms of Cp distribution, lift coefficient and airfoil aerodynamics is discussed.