Analytical Subsonic Aerodynamics

Calendar

SES #	TOPICS	KEY DATES
1	Singular Perturbation Method Subject overview Motivation for the subject Concept map Compelling problems Dimensional analysis, similarity Asymptotics A singular perturbation problem and solution [ODE, Ordinary Differential Equations]
2	Seminar in Perturbation Methods A singular perturbation problem and solution [PDE, Partial Differential Equations] Conservation principles Pressure distribution and compressibility Pressure—velocity relations in isentropic flow
3	Singular Perturbation Methods; Formation of Shock Waves Similarity of flows Equations governing irrotational flows of a homentropic gas Velocity potential Calorically perfect gas Speed of sound
4	Fundamental of Fluid Mechanics Small perturbation theory Perturbation velocity potential Perturbation velocity potential equation Limit of small perturbations Boundary conditions [steady flows]
5	Linear Subsonic Flow Linearized pressure coefficient Linearized subsonic flow Transformation of independent variables Prandtl-Glauert Rule
6	Similarity Rules Similarity Rules Dynamic and geometric variables Afine body relationships von Karman Rules
7—9	Bodies of Revolution: Slender Body Theory Bodies of revolution—slender body theory Cylindrical coordinates: x, r, θ Continuity equation Linearized perturbation potential equation Boundary conditions: limit of r->0 Linearized pressure coefficient Axial symmetry Incompressible solution Source distribution Superposition Subsonic solution f(x), S(x), R(x) relation	Problem set 1 out
10	Slender Body Theory Slender body theory from a regular perturbation perspective Transonic limit Hypersonic limit	Problem set 1 due
11	Higher Approximation: Slope of the Lift and Moment About Mid-chord Higher approximations for lift and moment about mid-chord
12—14	Perturbation Methods / Overview Thin wing theory Thickness, angle of attack, camber Matched asymptotic expansions Kutta-Joukowsky condition Stretched variables Boundary conditions Inner and outer spaces Inner and outer solutions Downwash Drag due to lift Total drag
15	Thin Wing Theory Two dimensional flow over a wavy wall	Problem set 2 out
16	Non-linear, Unsteady Transonic Waves Summary Review	Porblem set 2 due