Aerodynamics course

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Airplane vortex


This course is planned as a graduate level aerodynamics course for mechanical engineers planning to have focus on thermo and fluid dynamics. By the end of this course, the students are expected

1. To get acquainted with the following fluid flow phenomena.

  • laminar and turbulent flows
  • subsonic, transsonic, supersonic and hypersonic flows
  • shock and expansion waves
  • separated flows
  • boundary layer flows

2. To classify different phenomenon of aerodynamics based on non-dimensional parameters, scaling laws and observed effects.

3. To have theoretical understanding of incompressible, compressible, inviscid and viscous aerodynamics. This will be achieved by giving the mathematical fundamentals of integral and differential modeling of fluid flows for the conservation laws of mass, momentum and energy. Simplification and solution of those equations for special flow states in aerodynamical flows.

4. To apply fluid mechanics and aerodynamics knowledge on the evaluation, design and optimization of flow devices.

Moreover, students have the chance to see the direct application of the content in the research and development work conducted by the lecturer.


The prerequisites of this course are

  • Fluid mechanics I
  • Thermodynamics I
  • Algorithms and programming

The following courses will be also helpful

  • Partial differential equations
  • Computer aided methods in mechanical engineering

Motivation of studying this aerodynamics course[edit]

Aerodynamics is a fundamental subject of aerospace and mechanical engineering and partially chemical, civil and medical engineering. As a matter of fact, it is a field where multiple physical effects can be met. Aerodynamic drag of transport vehicles, lift and drag characteristics of flying vehicles, performance of compressors and turbines, combustion chambers are applied examples, where aerodynamics plays a very important role. Knowledge on aerodynamics certainly help us to develop new flow devices and processes related with flow of gasses. Furthermore, application of the approaches of aerodynamics in other research subjects might be beneficial.

Airplane aerodynamics
Wind turbine aerodynamics
Car aerodynamics

Basic components of the course[edit]

This course is dominnatly a theoretical one. However, examples are provided in the form of visual media and laboratory experiments. Exercises are made and homeworks are given so that students get acquainted to the theoretical systematic in aerodynamics. In the last part of the course, relevant examples of research work are provided.

Chapters & Contents[edit]

The following chapters will be covered in this graduate level aerodynamics course. One unit lecture is 45 min. The course consists of 30 units of lecture material and 30 units of tutorial and laboratory exercises.

1.Introduction and motivation (1 unit)

2.Phenomena in aerodynamics (2 units)

  • Compressibility
  • Laminar, turbulent and transitional flows
  • Boundary and shear layers
  • Separated flows
  • Shock waves
  • Lift, drag and viscous losses

3.Integral and differential analysis of fluid flows (4 units,repitition)

4.Governing equations of aerodynamics, thermodynamics and boundary conditions (4 units)

  • Non-dimensional form of continuity, Navier-Stokes and energy equations
  • Euler equation, Bernoulli equation, Potential flow equations (incompressible and linearized-compressible), mechanical energy equation (for isothermal flows)
  • Basic thermodynamical relations for an ideal gas.

5.Inviscid and incompressible external flows: Low speed flows over airfoils and wings (4 units)

  • Potential flows
  • Flow over airfoils: The numerical vortex panel method
  • Flow over wings: Lifting-surface theory and the numerical vortex lattice method

6.Inviscid and compressible flows (7 units)

  • Normal, oblique and expansion waves
  • Flow over airfoils and wings
  • Flows through nozzles and diffusers

7.Viscous flows (6 units)

  • Boundary layer concept
  • Concept of fully-developed flow
  • Fundamental aspects of turbulent flows
  • Flow over a flat plate, a cyclinder and an airfoil
  • Laminar and turbulent internal flows and jet flows

8.Examples of contemporary studies (2 units)

Appendix 1. Scalars, Vectors and Tensors

Appendix 2. Dimensional Analysis

Appendix 3. Analytical solutions of internal flows

The course ends with a summary of the complete course material and a discussion on the red line of examination questions.


  • Derivation of continuity and Navier-Stokes equations and simplification of the equation system for different flow cases
  • Derivation of Betz's law for horizontal axis wind turbines
  • Development of a vortex-panel method for the calculation of a lifting flow over an airfoil
  • Simulation of a flow around an airfoil at subsonic, transonic and supersonic speeds
  • Design of a convergent divergent nozzle for required supersonic conditions at the exit

Laboratory exercises and demonstrations[edit]

  • Flow visualization around blunt bodies (airfoil, square and circular cylinders)
  • Simulation of a flow around an airfoil at subsonic, transonic and supersonic speeds
  • Chocked nozzle-flow experiment
  • Round jet experiment
  • Excursion to various wind-tunnels

Important Links[edit]


  • Anderson, J.D.: "Fundamentals of Aerodynamics", Mcgraw Hill Series in Aeronautical and Aerospace Engineering,2010.
  • Anderson, J.D.: "Modern Compressible Flow: With Historical Perspective", Mcgraw Hill Series in Aeronautical and Aerospace Engineering,2002.
  • Anderson, J.D.: "Hypersonic and High-Temperature Gas Dynamics", Second Edition (AIAA Education), 2006.
  • Aris, R:"Vectors, Tensors and the Basic Equations of Fluid Mechanics", Dover Books on Mathematics, 1990.
  • Ashley, H. and Landahl, M.: "Aerodynamics of Wings and Bodies",Dover Books on Aeronautical Engineering,1985.
  • Durst, F.: “Grundlagen der Strömungsmechanik: Eine Einführung in die Theorie der Strömung von Fluiden“, Springer, 2006.
  • Durst, F.: "Fluid Mechanics: An Introduction to the Theory of Fluid Flows",Springer, 2010.
  • Fox, R.W. and McDonald, A.T.:“Introduction to Fluid Mechanics”, John Willey and Sons.
  • Munson, B.R., Young, D.F., and Okiishi,T.H., Huebsch, W.W.: “Fundamentals of Fluid Mechanics”, John Willey and Sons.
  • Pozrikidis, C.: "Fluid Dynamics: Theory, Computation and Numerical Simulation", Springer, 2009.
  • Schlichting, H. and Gersten, K.: "Boundary-Layer Theory", Springer, 2000.
  • Schlichting, H. and Truckenbrodt, E.A.: "Aerodynamik des Flugzeuges: Teil 1 und Teil 2", Springer, 2000.
  • Spurk, J. and Aksel, N.:“Strömungslehre: Einführung in die Theorie der Strömungen“, Springer,2010.
  • Spurk, J. and Aksel, N.:“Fluid Mechanics“ , Springer, 2008.
  • White, F.:“Fluid Mechanics“ , McGraw-Hill Series in Mechanical Engineering,2010.
  • White, F.:"Viscous Fluid Flow", McGraw-Hill Mechanical Engineering, 2005.