# Aerodynamics

Topics covered in Aerodynamics course in PoliMi:

.Regular perturbations and asymptotic expansions: application with the theory of the boundary layer and Euler’s equations.
.Derivative of integrals with moving boundaries
.Flows around bluff bodies.
.3D and 2D dimensional flows around cylinders and vortex shedding phenomena.
.Flows around high angle of attack wings
.Stall: free and forced separation of flow.
. Delta wing at high incidence angle and canard configuration: leading edge vortex and vortex breakdown
.Vorticity.Equation of Vorticity. Lagrange theorems. Vortex lines, vortex surfaces and vortex tubes. Circulation and Kelvin’s Theorem. I, II, III Helmholtz’s Theorems and consequences of vorticity solenoidal fields.
.Mathematical modeling with potential flow and stream function.
.Laplace’s Equation and boundary conditions.
.Harmonics properties of potential flow and stream function and velocity components
.Lift generation.
.Complex analysis:analytical functions,multivariate calculus,branch point,branch cut,Cauchy’s integral, Morera’s theorem. Series expansion for analytical functions:Laurent’s series. Residuals theorem. Integrals via residual theorem.
.Complex potential and complex flow. Simple solutions: uniform flow, dihedral flow, source,vortex, doublet, flow around cylinders. Calculus of circulation and lift with integration of complex flow. I, II Blasius’ formula. Kutta-Joukowsky ‘s Theorem.
.Conformal mapping:constraints on the solutions.
.Circulation transformation and lift calculation. Moment coefficient on the transformed cylinder.
.Joukowsky’s transformation: critical points, inverse transformation and branch point. Flow around plate. Flow around arc of circle. Lift force and coefficient calculation in Joukowsky’s profile. Karman-Trefftz transformation.
. Thin airfoil theory: Plemelj’s formulas. Riemann-Hilbert equations. Complex velocity equation for thin airfoils. Laurent’s series expansion for the complex velocity with circulation for length span. Solution of Riemann-Hilbert equation. Lift coefficient. Null lift angle. Pressure coefficient. Theodorsen’s angle. Slats-Tabs surfaces properties. Moment coefficient.Aerodynamic Center. Criteria for design of airfoils. Stall and properties.
.Finite wing theory: Prandtl-Lanchester theory. Lift coefficient. Induced drag coefficient.Circulation distribution with minimal drag per lift. Cl-alfa curve. Roll and yaw coefficients.
.Numerical methods: panels methods: Hess-Smith. Vortex latex method. Weissinger method.Green method. Morino’s method. Wake conditions.

.Compressible flows: equation of motions for compressible flow. Continuity equation and momentum equation.Energy equations.Thermodynamics and fundamental relations.
Polytropic gasses. Compressible Navier-Stokes equations closure. High Reynolds number flow outside the boundary layer: compressible Euler’s equations. Sound equations. Crocco’s equation. Vorticity equation. Irrotational flow and potential flow. Bernoulli’s for isentropic irrotational flow. Limit velocity. Sonic velocity. Critical velocity. Complete equation of compressible potential flow. Prandtl-Glauert transformation. Compressible flow along a streamline. Mach’s cone and Shock waves:Rankine-Hugoniot’s relation. Oblique shock wave:shock wave polar. Expansion for supersonic flow. Prandtl-Meyer’s fan. Transonic regime airfoils. Shock stall. Supersonic regime airfoils