[CFD] The k-omega Turbulence Model

Summary

This video delves into turbulence modeling in CFD, specifically the K-Omega, K-Epsilon, and K-Omega SST models. The speaker discusses the sensitivity of the K-Omega model to free stream turbulence conditions and how this affects predictions of skin friction and flow separation. To address this, the K-Omega SST model blends the strengths of both the K-Omega and K-Epsilon models, improving accuracy for external aerodynamic applications. The video highlights the importance of choosing the right turbulence model for reliable results, emphasizing the advantages of the K-Omega SST model in overcoming the limitations of its predecessors.

Takeaways

• 😀 The K-Omega model is more accurate than the K-Epsilon model when predicting flows with adverse pressure gradients, making it ideal for wall-bounded flows.
• 😀 The K-Omega model's primary limitation is its sensitivity to free-stream turbulence conditions, which can lead to significant variations in predictions based on small changes in the turbulence level.
• 😀 Researchers have proposed several ways to address the K-Omega model’s free-stream dependence, including tuning the model coefficients or adding cross-diffusion terms.
• 😀 The K-Epsilon model is less sensitive to free-stream turbulence and is more stable in regions far from the wall, where wall effects are minimal.
• 😀 The K-Omega SST model, proposed in 1992, blends the K-Epsilon model in far-field regions with the K-Omega model near the wall, overcoming the free-stream dependence issue.
• 😀 The blending of the K-Epsilon and K-Omega models in the SST model provides more accurate and reliable results for external aerodynamic applications.
• 😀 A plot of turbulent kinematic viscosity shows how the K-Omega model’s sensitivity to free-stream turbulence can cause large variations in predicted values depending on the turbulence level.
• 😀 The skin friction coefficient is used to assess the impact of the K-Omega model’s sensitivity on practical applications, with variations in the coefficient occurring depending on free-stream turbulence conditions.
• 😀 Adverse pressure gradients can lead to flow separation, which occurs at different locations depending on the value of free-stream turbulence, further complicating the use of the K-Omega model in such cases.
• 😀 Despite the identified issues with free-stream sensitivity, the K-Omega SST model remains the preferred choice for external aerodynamic simulations due to its improved accuracy and stability.

Q & A

What is the primary difference between the K-epsilon and K-omega models in turbulence simulation?

The primary difference is that the K-epsilon model is more suited for flows where the turbulence intensity is high, and the boundary layers are fully developed, while the K-omega model performs better in situations with adverse pressure gradients and in predicting the separation of flow, particularly near solid boundaries.

Why is the K-omega model sensitive to free-stream turbulence conditions?

The K-omega model is sensitive to free-stream turbulence conditions because small changes in the turbulence kinetic energy (K) at the free-stream can significantly affect the prediction of the turbulence properties near the wall, influencing quantities such as the skin friction coefficient.

What does the term 'free-stream turbulence' refer to in the context of turbulence modeling?

Free-stream turbulence refers to the turbulence level in the flow far from the surface of the object being studied, typically outside the boundary layer where the flow is unaffected by the surface. Changes in this turbulence can impact the accuracy of turbulence models like K-omega.

How does the K-omega SST model address the sensitivity issue in the original K-omega model?

The K-omega SST model combines the strengths of both the K-epsilon and K-omega models. It uses the K-epsilon model far from the wall, where the turbulence is less sensitive to free-stream turbulence conditions, and switches to the K-omega model close to the wall, where it provides more accurate predictions of turbulence effects near boundaries.

What is the reason for using a blending approach in the K-omega SST model?

The blending approach is used to combine the advantages of both K-epsilon and K-omega models. The K-epsilon model is more stable and less sensitive to free-stream conditions, while the K-omega model is more accurate near the wall, where flow separation and adverse pressure gradients are important.

What are the key challenges associated with the K-omega model?

The key challenge of the K-omega model is its sensitivity to small variations in free-stream turbulence conditions, which can lead to significant changes in the predicted results, such as the location of flow separation and skin friction coefficient.

Why is the K-omega SST model recommended over the standard K-omega model?

The K-omega SST model is recommended because it eliminates the sensitivity to free-stream turbulence conditions that is present in the standard K-omega model, making it more accurate and reliable for external aerodynamic simulations, such as those involving flow over aircraft surfaces.

What role does the 'specific dissipation rate' (Omega) play in turbulence modeling?

The specific dissipation rate (Omega) is a key variable in turbulence modeling, representing the rate at which turbulence energy is dissipated. It is used in the K-omega model to predict the turbulence behavior and flow characteristics near walls, and its accuracy is critical for simulations involving adverse pressure gradients.

How do small modifications in model coefficients affect the K-omega model?

Small modifications to the model coefficients in the K-omega model can reduce its sensitivity to free-stream turbulence, potentially mitigating the issue of dependency on turbulence conditions. However, tuning these coefficients is complex and not a guaranteed fix for all scenarios.

What are some suggested improvements or fixes for the K-omega model's limitations?

Some suggested improvements include introducing a cross-diffusion term (present in the K-omega SST model), tuning the model coefficients more effectively, or using hybrid models like the K-omega SST model to overcome the issues associated with free-stream turbulence sensitivity.