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.

Support(s) de cours

• Syllabus
• Université virtuelle

Contacts

Thierry Magin

Thierry.Magin@ulb.be

Campus

Solbosch

Méthode(s) d'évaluation

• Examen écrit
• Examen oral
• Autre
• Rapport écrit

Examen écrit

Examen oral

Autre

Rapport écrit

examen oral, examen écrit et rapport de laboratoire

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

Examen oral (60%), examen écrit (20%), note de laboratoire (20%)

Langue(s) d'évaluation

• anglais
• français