In
computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate ...
, the k–omega (''k''–ω) turbulence model is a common two-equation
turbulence model, that is used as an approximation for the
Reynolds-averaged Navier–Stokes equations
The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged
equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged ...
(RANS equations). The model attempts to predict
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
by two
partial differential equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
for two variables, ''k'' and ω, with the first variable being the
turbulence kinetic energy
In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuat ...
(''k'') while the second (ω) is the specific rate of
dissipation
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
(of the turbulence kinetic energy ''k'' into internal thermal energy).
Standard (Wilcox) ''k''–ω turbulence model
The
eddy viscosity ν
T, as needed in the RANS equations, is given by: , while the evolution of ''k'' and ω is modelled as:
For recommendations for the values of the different parameters, see .
Notes
References
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External links
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{{DEFAULTSORT:K-omega turbulence model
Turbulence models