Reynolds-Averaged Navier–Stokes Equations for Turbulence Modeling

Abstract

The approach of Reynolds-averaged Navier–Stokes equations (RANS) for the modeling of turbulent flows is reviewed. The subject is mainly considered in the limit of incompressible flows with constant properties. After the introduction of the concept of Reynolds decomposition and averaging, different classes of RANS turbulence models are presented, and, in particular, zero-equation models, one-equation models (besides a half-equation model), two-equation models (with reference to the tensor representation used for a model, both linear and nonlinear models are considered), stress-equation models (with reference to the pressure-strain correlation, both linear and nonlinear models are considered) and algebraic-stress models. For each of the abovementioned class of models, the most widely-used modeling techniques and closures are reported. The unsteady RANS approach is also discussed and a section is devoted to hybrid RANS/large methods.

Numerical study of blowing and suction slot geometry optimization on NACA 0012 airfoil

“…The Reynolds stresses were modeled via the Boussinesq approximation [34], in which the deviatoric part is considered proportional to the strain rate tensor through the turbulent viscosity. The incompressible form of the Boussinesq approximation is (3) (4) where ν t is the turbulent viscosity, k is the average kinetic energy of the velocity fluctuations, and δ ij is the Kronecker delta.…”

Numerical Analysis of Flow Erosion on Sand Discharge Pipe in Nitrogen Drilling

“…An Eulerian-Lagrangian approach is applied to analyze the continuum phase and particle tracking for sand particles, in which, compressible nitrogen flow is treated as the continuum phase evaluated by the RANS equations based on the Eulerian approach, while sand particles are treated as spherical particles added into continuum phase flow field as discrete phase, which are captured by DPM based on the Lagrangian approach. The RANS equations used to solve the continuum phase include continuity and momentum equations and are written as follows [16][17][18]:…”

Performances of Navier-Stokes Solver on a Hybrid CPU/GPU Computing System

“…Numerical simulation of turbulence implies the execution of the numerical integration of the three-dimensional unsteady NavierStokes equations on an appropriate computing domain, for an adequate number of time steps. Different numerical techniques, ranging from finite differences, finite elements, spectral methods and appropriate combinations of the basic techniques into mixed techniques, can be used, besides different approaches to the modeling of turbulence (where modeling is needed, see among others, [1]). …”