The k-epsilon model is a type of turbulence model that is used in computational fluid dynamics (CFD) simulations. It is based on two transport equations for the turbulence kinetic energy (k) and its dissipation rate (epsilon). The k-epsilon model can capture the effects of mean velocity gradients, buoyancy, compressibility, and heat and mass transfer on the turbulent flow. It is one of the most widely used turbulence models in engineering applications because of its robustness, economy, and reasonable accuracy for a wide range of flows¹².
Ansys Fluent is a software package that allows users to perform CFD simulations using various turbulence models, including the k-epsilon model. Ansys Fluent provides three variants of the k-epsilon model: the standard, the RNG, and the realizable k-epsilon models. Each variant has different methods of calculating the turbulent viscosity, the turbulent Prandtl numbers, and the generation and destruction terms in the epsilon equation³. The k-epsilon model in Ansys Fluent can be used for modeling internal and external flows, separated flows, jets, flows with high-pressure gradients, and flows through curved geometries⁴⁵.
Source:
(1) ANSYS FLUENT 12.0 User's Guide - 33.3.3 Viscous Model Dialog Box - ENEA. https://www.afs.enea.it/project/neptunius/docs/fluent/html/ug/node1022.htm.
(2) 12.4.1 Standard k Model Overview - University of Washington. https://courses.washington.edu/mengr544/handouts-10/Fluent-k-epsilon.pdf.
(3) ANSYS FLUENT 12.0 User's Guide - 12.4 Steps in Using a Turbulence Model. https://www.afs.enea.it/project/neptunius/docs/fluent/html/ug/node411.htm.
(4) Difference between K-epsilon and K-omega Turbulence Model - Ansys .... https://forum.ansys.com/forums/topic/difference-between-k-epsilon-and-k-omega-turbulence-model/.
(5) k-epsilon and Laminar differrence - Ansys Learning Forum. https://forum.ansys.com/forums/topic/k-epsilon-and-laminar-differrence/.
What are the limitations of k-epsilon model?
The k-epsilon model is a popular and widely used turbulence model, but it also has some limitations that affect its accuracy and applicability. Some of the limitations are:
- It assumes that the turbulence is isotropic, which means that the ratio between Reynolds stress and mean rate of deformation is the same in all directions. This is not true for flows with strong anisotropy, such as swirling, rotating, or curved flows²³.
- It requires a high Reynolds number, which means that the inertial forces are much larger than the viscous forces. This is not true for flows near the wall, where the viscous effects are important. Therefore, the k-epsilon model needs a near-wall treatment, such as wall functions or low-Reynolds number corrections, to account for the wall effects¹².
- It does not capture the effects of history and rapid distortion on the turbulence. This means that the model cannot handle flows with large adverse pressure gradients, boundary layer separation, or shock waves. Therefore, the k-epsilon model may under-predict the extent of recirculation zones or over-predict the turbulent kinetic energy at stagnation points¹⁴⁵.
These limitations can be overcome by using more advanced turbulence models, such as Reynolds stress models, large eddy simulation, or detached eddy simulation, which can account for the effects of anisotropy, compressibility, history, and distortion on the turbulence. However, these models are also more complex, computationally expensive, and sensitive to initial and boundary conditions. Therefore, the choice of the turbulence model depends on the trade-off between accuracy and efficiency for a given flow problem.
Source:
(1) The k-Ξ΅ Turbulence Model - COMSOL Multiphysics. https://doc.comsol.com/5.5/doc/com.comsol.help.cfd/cfd_ug_fluidflow_single.06.088.html.
(2) OpenFOAM: User Guide: k-epsilon. https://www.openfoam.com/documentation/guides/latest/doc/guide-turbulence-ras-k-epsilon.html.
(3) K-epsilon turbulence model - Wikipedia. https://en.wikipedia.org/wiki/K-epsilon_turbulence_model.
(4) Validation and analysis of turbulence modeling in pipe elbow under .... https://link.springer.com/article/10.1007/s40430-022-03899-9.
(5) Limitations and empirical extensions of the k-epsilon model as applied .... https://ntrs.nasa.gov/search.jsp?R=19840035309.
Is k-epsilon model good for low quality meshes ?
The k-epsilon model is not very suitable for low quality meshes, especially near the wall regions. This is because the k-epsilon model requires a high Reynolds number, which means that the inertial forces are much larger than the viscous forces. This is not true for flows near the wall, where the viscous effects are important. Therefore, the k-epsilon model needs a near-wall treatment, such as wall functions or low-Reynolds number corrections, to account for the wall effects¹². However, these treatments are sensitive to the mesh quality and resolution, and may not work well for coarse or skewed meshes³⁴.
A better alternative for low quality meshes is the k-omega model, which is more robust and accurate for near-wall flows. The k-omega model does not require a high Reynolds number, and can handle flows with large adverse pressure gradients, boundary layer separation, or shock waves. The k-omega model is also good in resolving internal flows, separated flows and jets and flows with high-pressure gradient and also internal flows through curved geometries³. However, the k-omega model may be more computationally expensive and sensitive to initial and boundary conditions than the k-epsilon model². Therefore, the choice of the turbulence model depends on the trade-off between accuracy and efficiency for a given flow problem.
Source:
(1) K-epsilon Turbulence Model | Global Settings | SimScale. https://www.simscale.com/docs/simulation-setup/global-settings/k-epsilon/.
(2) K-epsilon turbulence model - Wikipedia. https://en.wikipedia.org/wiki/K-epsilon_turbulence_model.
(3) Difference between K-epsilon and K-omega Turbulence Model. https://forum.ansys.com/forums/topic/difference-between-k-epsilon-and-k-omega-turbulence-model/.
(4) k-epsilon model: which criteria do I have to meet for the near wall mesh?. https://forum.ansys.com/forums/topic/k-epsilon-model-which-criteria-do-i-have-to-meet-for-the-near-wall-mesh/.
What is the difference between k-epsilon and k-omega models?
The k-epsilon and k-omega models are both types of turbulence models that are used in computational fluid dynamics (CFD) simulations. They are based on two transport equations for the turbulence kinetic energy (k) and either its dissipation rate (epsilon) or its specific dissipation rate (omega). The main difference between them is that the k-epsilon model is more suitable for flow away from the wall, while the k-omega model is more accurate for near-wall flow regions¹².
The k-epsilon model assumes that the turbulence is isotropic, which means that the ratio between Reynolds stress and mean rate of deformation is the same in all directions. This is not true for flows with strong anisotropy, such as swirling, rotating, or curved flows. The k-epsilon model also requires a high Reynolds number, which means that the inertial forces are much larger than the viscous forces. This is not true for flows near the wall, where the viscous effects are important. Therefore, the k-epsilon model needs a near-wall treatment, such as wall functions or low-Reynolds number corrections, to account for the wall effects. However, these treatments are sensitive to the mesh quality and resolution, and may not work well for coarse or skewed meshes¹².
The k-omega model does not assume isotropy, and can handle flows with large adverse pressure gradients, boundary layer separation, or shock waves. The k-omega model does not require a high Reynolds number, and can resolve the viscous layer without wall functions. The k-omega model is also good in resolving internal flows, separated flows, jets, flows with high-pressure gradients, and flows through curved geometries¹³. However, the k-omega model may be more computationally expensive and sensitive to initial and boundary conditions than the k-epsilon model².
A common variant of the k-omega model is the SST (shear stress transport) model, which blends the k-epsilon and k-omega models to achieve the best of both worlds. The SST model uses the k-omega formulation in the near-wall region and switches to the k-epsilon formulation in the free-stream region. The SST model can capture the effects of mean velocity gradients, buoyancy, compressibility, and heat and mass transfer on the turbulent flow. The SST model is one of the most widely used turbulence models in engineering applications because of its robustness, economy, and reasonable accuracy for a wide range of flows¹⁴.
Source:
(1) Which Turbulence Model Should I Choose for My CFD Application?. https://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-application/.
(2) Use of k-epsilon and k-omega Models - CFD Online. https://www.cfd-online.com/Forums/main/75554-use-k-epsilon-k-omega-models.html.
(3) Difference between K-epsilon and K-omega Turbulence Model. https://forum.ansys.com/forums/topic/difference-between-k-epsilon-and-k-omega-turbulence-model/.
(4) What is the difference between k-epsilon and k-omega model .... https://rampfest-hudson.com/what-is-the-difference-between-k-epsilon-and-k-omega-model/.
(5) What is the difference between k-epsilon and K-Omega?. https://vidque.com/what-is-the-difference-between-k-epsilon-and-k-omega/.
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