Aerodynamics 2

Module aims

This module will build on existing knowledge of incompressible and compressible aerodynamics, and the basic prediction methods for aerofoil design at both low and high speed. The first part of the module extends the incompressible analyses of the first year Aerodynamics module and introduces potential flow. The second part of the module introduces compressible flow, shock waves and high speed aerodynamics. This module forms a direct link to the third year course in Aerodynamics.

Learning outcomes

On successfully completing this module, you should be able to:

1. Recall basic flow definitions such as compressible/incompressible, viscous/inviscid, steady/unsteady, and understand the concepts of rate of strain, angular velocity, vorticity, a free vortex and a forced vortex;
2. Perform a control volume analysis;
3. Demonstrate understanding of the circumstances under which stream function and velocity potential formulations may be used, and to study their basic solutions leading up to a circular cylinder with circulation; 
4. Use the complex potential and conformal transformation; 
5. Demonstrate understanding of wave propagation phenomena and the flow properties in compressible subsonic and supersonic flow;
6. Derive the governing equations of 1D compressible flow, extend them to obtain the equations for normal shocks and varying area ducts, and apply them to solve problems of stationary and moving normal shock waves, quasi-1D flow in ducts and supersonic wind tunnels;
7. Explain the relationships for 2D compressive and expansive wave systems and apply to solve problems using both exact and linearised approaches;
8. Differentiate the properties of high speed transonic and supersonic wing sections and describe the factors affecting the design of supercritical and supersonic aerofoils.

Module syllabus

 • Fundamentals: vorticity and circulation; free and forced vortex, Rankine vortex; equations of motion; Bernoulli equation; normal pressure gradient; relation between vorticity and gradient of total pressure.
• Control volumes:  Reminder of control volume formulation, examples including: force on a converging nozzle, total pressure loss on a duct with rapidly expanding area.
• Stream Function and Velocity Potential: stream function and velocity potential for uniform stream at incidence, source/sink, free vortex; superposition of solutions; source/sink combinations; Joukowski lift theorem; flow past a circular cylinder with and without lift.
• The Complex Potential: complex coordinates and complex velocity; basic solutions for uniform stream, source/sink, vortex; image reflection at walls.
• Conformal mapping; circle to ellipse and flat plate; relation between complex velocities in circle plane and transformed plane; flow past ellipse at zero incidence; flow past ellipse at incidence; control of circulation/lift by specifying rear stagnation point; Kutta condition; lift of a flat plate; pressure distribution on the flat plate; Joukowski aerofoil; effect of camber and thickness.
• Introduction and one-dimensional compressible flow: Speed of sound, Mach number, subsonic and supersonic flow; propagation of weak waves; Mach waves and Mach cones; physical differences between two-dimensional subsonic and supersonic aerofoils.
• One-dimensional compressible flow: one-dimensional flow, nozzle flow; continuity, momentum and energy equations; convergent-divergent nozzles, choking; the appearance of shock waves; stationary and moving shock normal waves; supersonic wind tunnel.
• Two-dimensional compressible flow: The oblique shock wave; sharp wedge, attached and detached shock waves; shock wave reflection; very weak shock waves; two-dimensional supersonic linear theory (Ackeret) and wave interactions using linear theory; wave drag; the Prandtl-Meyer function and isentropic supersonic expansion. Shock expansion theory and supersonic aerofoils.

Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological. The content is presented via a combination of slides, whiteboard and visualiser.

Learning will be reinforced through tutorial question sheets and laboratory exercises, featuring analytical, computational and experimental tasks representative of those carried out by practising engineers. 


This module presents opportunities for both formative and summative assessment.  
You will be formatively assessed through progress tests and tutorial sessions.
You will have additional opportunities to self-assess your learning via tutorial problem sheets.
You will be summatively assessed by a written examination at the end of the module as well as through practical laboratory assessments and a written laboratory report.

Assessment type Assessment description Weighting Pass mark
Examination Written examination 80% 40%
Practical Laboratory practical 12% 40%
Coursework Laboratory report 8% 40%
You will receive feedback both during the laboratory sessions and following the coursework submission.
You will receive feedback on examinations in the form of an examination feedback report on the performance of the entire cohort.
You will receive feedback on your performance whilst undertaking tutorial exercises, during which you will also receive instruction on the correct solution to tutorial problems.
Further individual feedback will be available to you on request via this module’s online feedback forum, through staff office hours and discussions with tutors.

Reading list