Reynoldsavergerade

Reynoldsavergerade refers to the Reynolds-averaged approach in turbulence modeling, named for the Reynolds averaging method used to separate turbulent flows into mean and fluctuating components. In this framework, instantaneous flow quantities are decomposed into a time-averaged part and a fluctuating part, for example a velocity field u = U + u′, where U is the mean velocity and u′ the fluctuations. This leads to the Reynolds-averaged Navier–Stokes equations, which describe the evolution of the mean flow but include additional terms representing the transport of momentum by turbulence.

A central feature of the Reynolds-averaged equations is the appearance of the Reynolds stresses, a term that accounts for momentum transfer by velocity fluctuations. These stresses introduce a closure problem: the equations contain more unknowns than equations, so turbulence models are required to relate the Reynolds stresses to mean-flow quantities. Common closures include the Boussinesq eddy-viscosity model and more sophisticated models such as k–ε, k–ω, and shear-stress transport (SST) variants. In compressible or variable-density flows, density-weighted (Favre) averaging is often used to obtain a form of the equations suitable for such conditions.

Reynoldsavergerade methods, collectively known as RANS, are widely used in engineering for predicting steady or time-averaged flows due to their relatively low computational cost compared with direct numerical simulation or large-eddy simulation. They are well suited for aerodynamic design, pipe flows, and industrial applications where the long-term mean behavior is of primary interest. Limitations include limited accuracy for highly unsteady or transient phenomena and dependency on the chosen turbulence model and its constants.