[CFD] The k - epsilon Turbulence Model

Summary

In this video, Aiden provides a comprehensive overview of the k-epsilon turbulence model used in CFD simulations. He explains its evolution from early models, detailing the role of Reynolds stresses, the Boussinesq hypothesis, and the development of the eddy viscosity concept. Aiden also dives into the importance of damping functions in the low Reynolds number formulation and compares the k-epsilon model with the k-omega SST model for different flow regimes. The video concludes with a practical guide on how to select the appropriate model and coefficients for accurate turbulence modeling near walls and high Reynolds number applications.

Takeaways

• 😀 The k-epsilon model is widely used in CFD to simulate turbulence in fluid flows through transport equations for turbulent kinetic energy (k) and dissipation rate (epsilon).
• 😀 The original k-epsilon model was introduced in the 1970s and has evolved over time, with damping functions applied in low Reynolds number formulations to better capture flows near walls.
• 😀 Damping functions like F1, F2, and Fmu are used to adjust model coefficients (C1, C2, and Cmu) in low Reynolds number flows to better predict turbulent behavior close to the wall.
• 😀 The low Reynolds number form of the k-epsilon model is useful for accurate wall shear stress and heat transfer predictions in flows with a small Y+ (less than 5).
• 😀 For external aerodynamic and turbomachinery simulations, it’s crucial to consider alternative models like the K-Omega SST, which has superior performance for low Reynolds number applications.
• 😀 The k-epsilon model remains a top choice for high Reynolds number flows (Y+ greater than 30), where turbulence dominates, as it does not require damping functions.
• 😀 The key difference between the k-epsilon and K-Omega SST models lies in their performance near walls and in resolving low Y+ flows, where K-Omega SST is more accurate.
• 😀 Damping functions reduce the value of epsilon near the wall, which improves the model's ability to resolve turbulent kinetic energy in the viscous sublayer.
• 😀 The K-Omega SST model, introduced 20 years after the k-epsilon model, is more effective for capturing low Reynolds number turbulence near walls, especially in simulations with small grid sizes.
• 😀 While the k-epsilon model is preferred for high Reynolds number flows, its low Reynolds number variants can still be used to simulate wall-bounded turbulent flows when properly tuned with damping functions.
• 😀 The lecture encourages viewers to consult CFD user manuals or original research papers on the k-epsilon model for deeper insights into its implementation and variations.

Q & A

What does the K-epsilon model predict near the wall in a low Reynolds number formulation?

The K-epsilon model predicts an increased dissipation of turbulent kinetic energy near the wall, as expected from molecular viscosity. This behavior is captured through damping functions applied to the model coefficients.

Why were damping functions introduced in the K-epsilon model?

Damping functions were introduced to allow the K-epsilon model to resolve the equations all the way into the viscous sublayer. They reduce the value of epsilon near the wall, similar to how the mixing length was reduced in earlier turbulence models.

In which cases should you use the K-epsilon model with low Reynolds number formulation?

The low Reynolds number formulation of the K-epsilon model is useful when you are interested in flows close to the wall, particularly when accurate wall shear stress and heat transfer predictions are required, such as in external aerodynamic or turbomachinery simulations.

Why is the K-Omega SST model preferred for low Reynolds number applications?

The K-Omega SST model is preferred because it has been shown through extensive comparison to provide better performance for low Reynolds number flows, particularly those with Y+ values less than 5 or 1, compared to the K-epsilon model.

What is the significance of Y+ in turbulence modeling?

Y+ is a dimensionless wall distance used in turbulence modeling to determine how well the model resolves the flow near the wall. Low Y+ values indicate that the simulation resolves the viscous sublayer more accurately, which is crucial for accurate wall shear stress and heat transfer predictions.

What is the main difference between the high and low Reynolds number formulations of the K-epsilon model?

The main difference is that the low Reynolds number formulation includes damping functions applied to model coefficients to resolve the equations closer to the wall, while the high Reynolds number formulation does not use these functions and is typically used for flows where Y+ is greater than 30.

In what kind of simulations is the K-epsilon model with high Reynolds number formulation typically used?

The high Reynolds number formulation of the K-epsilon model is commonly used in simulations where Y+ is greater than 30, such as for large-scale flows in external aerodynamics and industrial applications where the flow does not need to be resolved near the wall.

What is the historical context of the K-epsilon and K-Omega SST models?

The K-epsilon model was introduced in the early 1970s, whereas the K-Omega SST model was developed nearly 20 years later. The K-Omega SST model was based on advancements in turbulence modeling that led to improved performance for low Reynolds number applications.

How does the K-epsilon model handle turbulence near the wall?

The K-epsilon model uses a set of damping functions to reduce the value of epsilon near the wall, which helps to resolve turbulence more accurately in the viscous sublayer, especially in low Reynolds number flows.

What resources are provided for further study of the K-epsilon model?

The speaker has linked three key research papers on the K-epsilon model in the video description for those interested in exploring the original papers and theory behind the model.