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