## 7.15Summary of turbulence modelling

• The model solves transport equations for turbulent kinetic energy and dissipation rate , Sec. 7.1 .
• It is the original of a family of two-equation models, which ultimately provide to calculate the turbulent stresses.
• Initial and inlet values for and must be speciﬁed, which can be calculated from turbulent intensity and mixing length scale , respectively, Sec. 7.2 .
• and are often estimated using functions that ﬁt experimental data for fully developed turbulent ﬂow, Sec. 7.3 .
• The models replace by speciﬁc dissipation rate , with equivalent expressions for initial and inlet values, Sec. 7.10 .
• The two “standard” models today are the SST model and 2006 model, Sec. 7.11 .
• Models can provide a turbulent conductivity 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 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 at the wall to compensate for the under-prediction of with larger cells, to improve the prediction of the wall shear stress, Sec. 7.5 .
• Thermal wall functions similarly increase at the wall to compensate for the under-prediction of , in order to improve the prediction of the wall heat ﬂux, Sec. 7.14 .
• Standard wall functions make no adjustment to when the near wall cell centre falls below the transition within a buﬀer layer, Sec. 7.5 .
• Other models include a continuous function of 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 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 