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K-epsilon (k-ε) turbulence model is one of the most common models used in computational fluid dynamics (CFD) to simulate mean flow characteristics for turbulent flow conditions. It is a two equation model that gives a general description of turbulence by means of two transport equations ( partial differential equations , PDEs).
The Reynolds stress equation model (RSM), also referred to as second moment closure model, [12] is the most complete classical turbulence modelling approach. Popular eddy-viscosity based models like the k–ε (k–epsilon) model and the k–ω (k–omega) models have significant shortcomings in complex engineering flows. This arises due to the ...
Menter's Shear Stress Transport turbulence model, or SST, is a widely used and robust two-equation eddy-viscosity turbulence model used in Computational Fluid Dynamics.The model combines the k-omega turbulence model and K-epsilon turbulence model such that the k-omega is used in the inner region of the boundary layer and switches to the k-epsilon in the free shear flow.
Physically, the turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.
Models include k-ε (Launder and Spalding), [62] Mixing Length Model , [63] and Zero Equation Model (Cebeci and Smith). [63] The models available in this approach are often referred to by the number of transport equations associated with the method.
Turbulence models use different methods to model fluctuations inherent in the full Navier-Stokes equations. They are used because the use of the full Navier-Stokes equations is normally computationally impractical.
where ε is the average rate of dissipation of turbulence kinetic energy per unit mass, and; ν is the kinematic viscosity of the fluid.; Typical values of the Kolmogorov length scale, for atmospheric motion in which the large eddies have length scales on the order of kilometers, range from 0.1 to 10 millimeters; for smaller flows such as in laboratory systems, η may be much smaller.
One class of models, closely related to the concept of turbulent viscosity, are the k-epsilon turbulence models, based upon coupled transport equations for the turbulent energy density (similar to the turbulent pressure, i.e. the trace of the Reynolds stress) and the turbulent dissipation rate .