Fluid mechanics II

Generalities

Fundamental equations (continuity, momentum & energy), complementary equations (constitutive equations, equations of state, 2nd principle), particular cases: inviscid flows, barotropic flows, Bernoulli formulas, constant density flows, two-dimensional flows & stream function.

Dimensional analysis and similarity

Experimental testing (geometric, kinematic and dynamic similarity), dimensional analysis (Vaschy-Buckingham theorem), non-dimensional form of the governing equations, non-dimensional parameters.

Two-dimensional incompressible potential flows

potential flows & potential equation, two-dimensional flows: stream function equation, complex potential, elementary flows (uniform flow, source, vortex & doublet flows), force & moment on a solid body, flow around a circular cylinder.

Laminar and turbulent flows

Qualitative aspects, Reynolds' experiment, engineering description of turbulent flows: Reynolds averaged Navier-Stokes equations, average velocity profile in turbulent wall-bounded flows (inner and outer layers), effect of roughness, turbulence modelling: eddy viscosity models, mixing length model

Boundary layers

Laminar boundary layer equations, flat plate boundary layer (self-similarity concept and Blasius solution, characteristic thicknesses), Falkner-Skan solutions, qualitative analysis of the effect of pressure gradient, separation and recirculation bubbles, integral methods, viscous-inviscid interaction, form drag.

Internal flows

Pipe flow: entrance flow, entry length, laminar and turbulent pipe flow, Moody chart, kinetic energy balance - head losses, singular head losses (contraction, expansion, bends and branches), gradual expansion (diffusor), piping networks, obstruction flowmeters (orifice, venturi and nozzle meters).

One-dimensional steady compressible flows

Stagnation properties, governing equations for steady (quasi-)one-dimensional flows, speed of sound and Mach number, isentropic flow in nozzles, adiabatic flow with friction, frictionless flow with heat transfer, shock waves.

General objectives

• Develop critical thinking when modeling a fluid mechanics problem
• Analyze the results of fluid mechanics experiments carried out in the laboratory

Specific objectives

• Apply the rules of dimensional analysis
• Calculate quantities of interest for engineering flows studied in the course:
  • Velocity and pressure  field in incompressible potential
  • Wall friction and characteristic thicknesses of laminar boundary layers
  • Pressure losses in pipes comprising straight sections and singularities
  • Distributions of speed, Mach number, pressure, temperature and density in (quasi-) one-dimensional compressible flows

Cours co-requis

Exposés (36h), Exercices (12h), Laboratoires (12h)

Références, bibliographie et lectures recommandées

• Y. A. Çengel & J. M. Cimbala. Fluid Mechanics, fundamentals & applications, 2nd edition, Mc Graw Hill, 2010.

• I. L. Ryhming. Dynamique des fluides, Presses Polytechniques Romandes, 1985.

Support(s) de cours

• Syllabus
• Université virtuelle

Contacts

Thierry Magin

Thierry.Magin@ulb.be

Campus

Solbosch

Méthode(s) d'évaluation

• Autre

Autre

Examen oral, examen écrit et rapport de laboratoire

Construction de la note (en ce compris, la pondération des notes partielles)

Examen oral (50%), examen écrit (30%), note de laboratoire (20%)

Langue(s) d'évaluation

• anglais
• français