# Turbulence Modeling

Three-dimensional industrial scale problems are concerned with the time averaged (mean) flow, not the instantaneous motion. The preferred approach is to model turbulence using simplifying approximations, and not resolve it.

Turbulence modeling is a procedure to solve a modified set of the Navier-Stokes equations by means of developing a mathematical model of the turbulent flow that represents the time-averaged characteristics of the flow. Turbulence modeling is used to compute the impact of eddies on the mean flow field. This approach is based on the assumption that the turbulent eddy motion is “universal” and can be related to the large-scale average motion.

- Large Eddy Simulation (LES)
- LES solves the filtered Navier-Stokes equations to resolve eddies down to the inertial range and it uses subgrid models to account for the influence of eddies in the dissipative range. The computing requirement is substantially less than that of DNS but is still not practical for many industrial applications containing wall bounded flows.
- Hybrid
- Hybrid simulations are the bridge between LES and RANS by utilizing RANS for attached boundary layers and LES for separated flow regions. In general, hybrid simulations need spatial filtering processes to determine the local sub grid turbulent viscosity. Compared to LES and DNS, hybrid simulations are much more tractable since the numerical requirement is less severe than the other two approaches.
- Reynolds-averaged Navier-Stokes (RANS)
- RANS simulations solve directly for the time averaged flow and model the effects of turbulent eddies on the mean flow. This method is the most computationally efficient CFD approach. Since most engineering problems are concerned with the time-averaged properties of the flow, this approach is used most frequently in the industry. The Reynolds averaging procedure introduces additional unknowns into the Navier Stokes equations, and it is thus necessary to develop additional turbulence model equations to close the set. These additional model equations can be categorized into turbulence models that use the Boussinesq assumption and turbulence models that do not use the Boussinesq assumption. The turbulence models with the Boussinesq assumption have two steps to compute Reynolds stresses for the RANS equations. First, turbulence models are needed for the computations of the eddy viscosity, second, the eddy viscosity is used for the estimation of the Reynolds stress with the Boussinesq assumption. The turbulence models without the Boussinesq assumption, for example, Reynolds stress models or nonlinear eddy viscosity models, determine the Reynolds (turbulent) stresses explicitly by solving an equation for each stress component.

CFD methods | Reynolds Number Dependence | Empiricism | Grid | Time steps |
---|---|---|---|---|

DNS | strong | none | 10^{16} |
10^{7.7} |

LES | weak | weak | 10^{11.5} |
10^{6.7} |

DES (hybrid) | weak | strong | 10^{8} |
10^{4} |

RANS | weak | strong | 10^{7} |
10^{3} |