7.15 Summary of turbulence modelling

  • The k model solves transport equations for turbulent kinetic energy eqn and dissipation rate , Sec. 7.1 .
  • It is the original of a family of two-equation models, which ultimately provide eqn to calculate the turbulent stresses.
  • Initial and inlet values for eqn and must be specified, which can be calculated from turbulent intensity eqn and mixing length scale eqn, respectively, Sec. 7.2 .
  • eqn and eqn are often estimated using functions that fit experimental data for fully developed turbulent flow, Sec. 7.3 .
  • The eqn models replace by specific dissipation rate eqn, with equivalent expressions for initial and inlet values, Sec. 7.10 .
  • The two “standard” eqn models today are the eqn SST model and eqn 2006 model, Sec. 7.11 .
  • Models can provide a turbulent conductivity eqn to calculate the turbulent heat flux for thermal problems, Sec. 7.12 .

Turbulent boundary layers

  • Turbulent boundary layers include a thin viscous sub-layer adjacent to the boundary with a linear velocity profile and, further from the boundary, the inertial sub-layer with a log law profile, Sec. 7.4 .
  • Profiles in temperature are similar to those for velocity, with equivalent linear and log law relationships, Sec. 7.13 .
  • Very thin cells are generally needed to resolve the viscous sub-layer to calculate the velocity gradient eqn at the wall accurately, Sec. 7.5 .
  • Such thin cells within the boundary layer region can increase the mesh to a size which is prohibitively costly to run.

Wall functions

  • Wall functions permit much larger cells near the wall, by exploiting the universal character of the velocity distribution.
  • The functions increase eqn at the wall to compensate for the under-prediction of eqn with larger cells, to improve the prediction of the wall shear stress, Sec. 7.5 .
  • Thermal wall functions similarly increase eqn at the wall to compensate for the under-prediction of eqn, in order to improve the prediction of the wall heat flux, Sec. 7.14 .
  • Standard wall functions make no adjustment to eqn when the near wall cell centre falls below the transition within a buffer layer, Sec. 7.5 .
  • Other models include a continuous function of eqn through the viscous sub-layer to the wall and adjustments for surface roughness, Sec. 7.6 .
  • Boundary conditions for turbulence fields with wall functions are based on observed profiles of those fields, Sec. 7.7 .

Models with resolved boundary layers

  • Turbulence models must predict the universal character of boundary layers when the viscous sub-layer is resolved with sufficiently thin cells, Sec. 7.8 .
  • Models like the Launder-Sharma k include source terms and damping functions to improve the predictions and to simplify boundary conditions, Sec. 7.9 .
Notes on CFD: General Principles - 7.15 Summary of turbulence modelling