Aerodynamics 3

Module aims

This module covers both compressible and incompressible aerodynamics relevant to aerospace vehicle design. The module builds on the Aerodynamics 1 and 2 modules. Topics covered include the derivation of the Reynolds-Averaged Navier Stokes equation, treatment of boundary layers, finite aspect ratio wing effects, effects of friction and heat transfer on compressible flow and the two-dimensional method of characteristics for compressible flows.

Learning outcomes

On successfully completing this module, you should be able to: 1. Demonstrate understanding of the intractability of the Navier-Stokes equations for aircraft applications and hence justify the need for simplifications such as the RANS equation or the linearisation of Navier-Stokes to Laplace's equation in order to analyse the pressure distribution around thin aerofoils of arbitrary geometry. 2. Appreciate the significance of the momentum integral equation in coupling viscous and inviscid solvers and employ approximate methods (i.e. Thwaite's method) to solve it. 3. Apply physical principles in order to derive the mean velocity profile in a zero-pressure-gradient laminar boundary layer and analyse the various regions of a turbulent boundary layer. 4. Solve Prandtl's lifting line model for the generation of lift on a finite aspect ratio wing for a generalised lift distribution represented as a Fourier series. 5. Evaluate the effects of friction and heat transfer on 1D compressible flows. 6. Apply the 2D method of characteristics to analyse unsteady gas dynamics problems and steady 2D compressible flows.

Module syllabus

The module consists of one section on incompressible flow and one section on compressible flow. 1). Incompressible flow The need for numerical methods.  Equations of motion: derivation of 3-D, incompressible, Navier Stokes equations.  Reynolds stresses.  Review of small perturbation theory: hierarchy of small disturbances.  Numerical solution of incompressible, potential flow.  Effects of thickness and camber.   Surface singularity methods.  Surface source method (A.M.O. Smith). Introduction to boundary layers: the thin-shear-layer approximation. Blasius solutions Laminar: Thwaites’ approximate method.  Turbulent boundary layers, Reynolds stresses, the concept of eddy-viscosity, the law of the wall. Lifting line theory: wings of large aspect ratio: basis of theory for wings of finite span.  Downwash and induced drag.  Prandtl’s theory.  Use of lifting line theory: solution method.  Elliptic loading.  Solutions for general planforms – collocation and iteration methods. Swept wings in incompressible flow. Comparison with/without sweep: the use of taper. 2). Compressible flow Compressible flow: governing equations.  Waves and speed of sound.  Validity of the incompressible assumption.  Normal and oblique shock waves.  Prandtl-Meyer expansion waves.  Shock expansion theory. Rayleigh flow, Fanno flow. Method of characteristics.  Introduction: 1-D unsteady inviscid flow.  Unsteady jump conditions.  Unsteady motion in a constant area duct.  Characteristic equations and compatibility conditions.  Examples: simple and non-simple regions.  Shock tube problem. Steady 2-D irrotational isentropic flow.  Governing equations.  Characteristic lines.  Compatibility conditions.  Example: nozzle design.

Pre-requisites

AERO40001 Aerodynamics 1
AERO50001 Aerodynamics 2

Teaching methods

  • Lectures (with gapped lecture notes and practical examples)
  • Six tutorial sheets
  • Surgeries to focus on specific areas of difficulty.
  • Laboratory sessions for low speed and supersonic wind tunnel testing

Assessments

Examined Assessment
2-hour written examination in January (80%).
Low Speed Flow Past a High Aspect Ratio Wing Lab (10%)
Compressible Flow Lab (10%)
Non-Examined Assessment
Peer-reviewed class questionnaire 

Reading list

Core

Supplementary

Module leaders

Dr Oliver Buxton