k-epsilon (k-ε) & k-omega (k-ω)

The k-epsilon (k-ε) turbulence model is the most common model 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 first transported variable is the turbulent kinetic energy (k) and the second transported variable is the rate of dissipation of turbulent kinetic energy (ε)².

The k-omega (k-ω) turbulence model is another common two-equation turbulence model used in CFD as an approximation for the Reynolds-averaged Navier–Stokes equations (RANS equations). The model attempts to predict turbulence by two partial differential equations for two variables, k and ω, with the first variable being the turbulence kinetic energy (k) while the second variable is the specific dissipation rate (ω)³.

Menter's Shear Stress Transport (SST) turbulence model combines both k-omega and k-epsilon turbulence models 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 flow¹. 

(1) K-epsilon turbulence model - Wikipedia. https://en.wikipedia.org/wiki/K-epsilon_turbulence_model.
(2) k–omega turbulence model - Wikipedia. https://en.wikipedia.org/wiki/K%E2%80%93omega_turbulence_model.
(3) Menter's Shear Stress Transport - Wikipedia. https://en.wikipedia.org/wiki/Menter%27s_Shear_Stress_Transport.

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The k-epsilon model is best suited for flow away from the wall, say free surface flow region, whereas the k-omega model is best suited for near the wall flow region, where adverse pressure gradient is developed¹.

(1) What is the differece between k- omega , k- epsilon and Spalart-allmaras turbulent .... https://www.researchgate.net/post/What_is_the_differece_between_k-omega_k-epsilon_and_Spalart-allmaras_turbulent_models2.
(2) What is the difference between k epsilon and k omega models in CFD and how does it .... https://www.researchgate.net/post/What_is_the_difference_between_k_epsilon_and_k_omega_models_in_CFD_and_how_does_it_affect_flow_in_a_shell_and_tube_heat_exchanger.
(3) What is the difference between k-epsilon and K-Omega?. https://vidque.com/what-is-the-difference-between-k-epsilon-and-k-omega/.
(4) Difference between K-epsilon and K-omega Turbulence Model - Ansys Learning Forum. https://forum.ansys.com/forums/topic/difference-between-k-epsilon-and-k-omega-turbulence-model/.

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