Aerodynamics

Course Outcomes

  1. Identify and formulate the correct set of assumptions and boundary conditions for aerodynamic force calculations for incompressible flow

  2. Apply analytical methods based on potential flow theory to estimate the aerodynamic force on finite wings in incompressible flow

  3. Develop numerical algorithms based on panel methods for aerodynamic analysis of simple configurations

  4. Use boundary layer theory to estimate viscous drag on simple configurations and apply corrections to potential flow based methods

Syllabus

Aerodynamic forces and moments – review of governing equations – potential flows – Kutta condition – vortex theorems – thin airfoil theory – finite wing theory – panel methods – flow over delta wings – boundary layer theory – effect of pressure gradient – flow separation and stall – high-lift devices – structure of turbulent boundary layer – Reynolds averaging.

Course Outline

  • Introduction

    • Aircraft Free body diagram (6 DOF)
    • Aircraft Free body diagram (3 DOF)
    • Aim (to calculate lift, drag and pitching moment coefficient)
    • Rationale for dimentionless Coefficients
      • Buckingham Pi theorem
      • Example calculation of drag coefficient
      • Does this result in a unique set of non-dimensional numbers?
      • Example of wrong non-dimensional numbers for lift force

  • Review of Fluid Statics

    • Continuum Hypothesis (range of validity, definition of density)
    • State of gas (what are all the things required to define the state of a gas)
    • Thermal Conductivity
    • Thermal Equation of State
    • Caloric Equation of State

  • Review of Fluid Mechanics

    • Definition of velocity
    • Definition of viscosity
    • Stress tensor
    • Kinematics (Lagrangian vs Eulerian)
      • Reynolds Transport Theorem
    • Laws of Motion
      • Conservation of Mass
      • Newton’s second law of motion (with viscous terms)
      • Conservation of Energy (with viscous terms)

  • Inviscid Compressible Flow

    • Chapter 7 and sections 8.1 - 8.4 of Liepman and Roshko
    • Equation of Angular Momentum Conservation
      • Show vorticity is constant along a streamline
    • Split the energy equation into two parts
    • Derivation of Euler’s equation
      • Along a strealine
      • In full domain
    • Derivation of Potential flow equation

  • Inviscid Barotropic Flow

    • Vorticity and circulation
    • Kelvin’s circulation theorem

  • Inviscid Incompressible Flow

  • Derivation of Bernoulli’s Equation

    • Along a streamline
    • For any two points in an irrotational flow

  • Kelvin’s theorem

  • Kutta-Jowkowski theorem

    • Proof for thin airfoil
    • General proof

  • Elementary flows (source/sink/doublet/vortex)

  • Non-lifting/lifting flow over a cylinder

    • D’Alembert’s paradox

  • Kutta Condition

  • Starting vortex for a 2D airfoil

  • NACA four digit airfoil definition

  • Definition of vortex filament and vortex sheet

  • Thin airfoil theory

    • Derivation for the symmetric airfoil
    • Derivation for a general cambered airfoil

  • Concept of Boundary Layer

  • Airfoil drag

    • Laminar and Turbulent BL
    • Numericals

  • High lift devices

Grading

There will be three assignments. One theoretical (5), one computational (10) and one numerical (5).

References

[@anderson2011Fundamentals] is available from Book bank. [@karamcheti1980] has a very good treatment of potential flow theory.

etc

Course Plan