Transonic Aerodynamics (LR42)

Course coordinator(s): Bakker, prof.dr.ir. P.G.
Phone: (+31 15 278) 5907
faculty of Aerospace Engineering
[ Type: coarse | Code: lr42 | DUT credits: 2 | ECTS credits: 3 ]
Catalog Data:
Phenomenology of transonic flow; supercritical airfoils, Transonic Small Perturbation theory, basic solutions, similarity, hodograph theory, Tricomi equation, Tomotika-Tomada approximation, local supersonic regions, shock formation, viscous interactions.
[ Course year: 3,4 | Semester: 0/0/2/2 | Hours p/week: 2 | Other(s): - | Examination: essay | Exam. period(s): - ]
Prerequisites: a68, a180B, lr54, lr44.
Follow up: lr11, lr56I, lr56II.
Detailed description of topics:
  1. Phenomenology of transsonic flow : airfoil characteristics in transonic flow, critical Mach number, frozen conditions, shock free airfoils, transonic cont roversy.
  2. Equations for 2-D inviscid compressible flow : conservation of mass, momentum and energy, conservative- and non-conservative form, iso-enthalphy, Crocco relation, weak solutions for shockwaves, vorticity due to a curved shock, two-dimensional potential equation.
  3. Transonic small perturbation theory : regular and singular asymptotic expansions, Prandtl-Glauert equation for subsonic and supersonic flow. Guderley-von Karman equation, transonic similarity, applications : 2D-Laval nozzle, shock on a curved surface / Zierep solution.
  4. Hodograph theory : concept of the hodograph, Legendre and Molenbroeck-Chaplygin transformation, Chaplygin equations, limit lines and branch lines; application : Prandtl-Meyer flow, Ringleb flow.
  5. Approximation of the hodograph equations : compressibility function, Tricomi equation, Tomotika-Tomada equation, fundamental solutions, hypergeometrical functions, Airy functions, design of a supercitical airfoil, breakdown of hodograph solutions.
  6. Local supersonic flow regions : Nikolskii-Taganov rule, compression- and expansion waves, conditions for shock-free flow, design considerations for shock-free airfoil design, Peaky airfoils, shock-formation : convergence of compression waves, detached shock wave-anology.
  7. Viscous interactions : qualitative aspects, shock-induced separation, trailing-edge separation, Pearcy's interaction model.
Course material:
Transonic Aerodynamics (reader, in dutch).
Reference(s) to literature:
  1. Ferrari & Tricomi (1968): Transonic Aerodynamics, Academic Press.
  2. Bers. L. (1958): Mathematical aspects of subsonic and transsonic gas dynamics, Wiley, New York.
  3. Liepmann & Roshko (1957): Elements of Gasdynamics, Wiley, New York.
  4. Moulden, T.H. (1984): Fundamentals of transonic flow, Wiley, New York.
Remarks:
Goals:
This course is designed to get informed about the fundamentals of transonic flow and its applications in civil aerospace engineering.
Computer use:
Numerical simulations of Ringleb flow.
Laboratory project(s):
A Laboratory project (HSL 3) is in preparation.
Design content ( 25%)