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Turbulence Modelling



By Dr Rémi MANCEAU

This course is made of two parts:

  • Introductory lectures on turbulence modelling, a course common with students of the ENSMA engineering school;

  • A series of tutorials focused on particular aspects.
Outline of the introductory lectures:
  1. Introduction to CFD (Computational Fluid Dynamics)

    • Different phases and important points of a simulation: geometric modelling, meshing, physical modelling, computation, post-processing; Evaluation of computational costs linked with turbulence, computer power available today and implications for modelling;
    • Different existing methods (RANS, hybrid, LES, DNS) : objectives, formalism, modelling, maturity, fields of application;
    • CFD codes: commercial codes (Fluent, StarCD, CFX, Powerflow), in-house industrial codes, open-source codes (Open-Foam, Code_Saturne).

  2. Standard method used in industrial design: RANS modelling (Reynolds-averaged Navier-Stokes modelling):

    • Closure problem, different levels of modelling, history;
    • Similarity with continuum mechanics (constitutive relations), physical principles;
    • Eddy-viscosity models: hypotheses, selection of the constitutive relation, k-epsilon models, k-omega models, Spalart-Almaras model, etc.: limits, corrections, variations;
    • Reynolds-stress models: hypotheses, advantages, limitations, modelling of the different physical processes, algebraic models;
    • Wall regions: physics, joint selection of the mesh and the model, law of the wall, low-Reynolds number models.

  3. Eddy-resolving methods:

    • URANS and semi-deterministic models;
    • Large-eddy simulation (LES): filtering, subgrid-scale stresses, modelling;
    • Hybrid RANS/LES methods;
      • i. Zonal methods: principle, issue of the interface;
      • ii. Continuous methods: VLES, LNS, DES, SAS, PANS, PITM;

  4. Modelling of turbulent heat transfers:

    • Non-dimensional numbers, convection regimes and simplifying assumptions;
    • Simple models for the forced convection regime: simple and generalized gradient hypotheses, mechanical and thermal length/time scales;
    • Modelling in the mixed/natural convection regimes: influence of buoyancy on the Reynolds stresses, modelling of the transport equations for the turbulent heat fluxes.

List of tutorials:
  1. Quick review of Kolmogorov's theory and its link with length/time scale evaluation in turbulence modelling.
  2. The dynamics of homogeneous turbulence under various constraints (pure decay, plane strain, shear) and implications for turbulence modelling.
  3. Evaluation of turbulence length scales in wall bounded turbulence and consequences for the simulation of turbulent flows.
  4. Educated guess of the parameters to perform a good computation using different classes of turbulence models (mesh, computational domain, boundary conditions, numerical schemes).
  5. Accounting for curvature effects on turbulent boundary layers.
  6. Near-wall asymptotics and implications for turbulence models and boundary conditions.
  7. Application of the general principles of turbulence modelling to the case of the triple moments.
  8. Forced and mixed convection in plane channels.