Turbulence Modeling: Comparison and Best Practices for Accurate Results

Turbulence is a complex phenomenon present in various applications:

• Industrial processes: in chemical and process engineering to optimize the design of reactors, heat exchangers, and other industrial equipment.
• Aerospace engineering: to predict the behavior of air flows around aircraft wings, fuselages, and control surfaces to ensure that the aircraft is stable and efficient.
• Automotive engineering: in the design of automotive components such as engine intake manifolds, exhaust systems, and aerodynamic components to improve engine efficiency and reduce drag.
• Energy production: in the design of wind turbines and wind farms, and other renewable energy systems to optimize the efficiency of energy production.
• Climate modeling: to simulate atmospheric circulation and the transport of heat, moisture, and pollutants.
• Environmental engineering: in water treatment and pollution control to predict the behavior of contaminants in water and air flows.
• Sports: in the design of sports equipment, such as golf balls and tennis rackets, to optimize their aerodynamics and improve performance.

To simulate turbulent flows, different approaches can be used. Each approach has its advantages and disadvantages, and the choice of method depends on the specific application and desired level of accuracy.

1. Turbulence approaches

• DNS: Direct Numerical Simulation is a turbulence modeling approach that solves the Navier-Stokes equations without any turbulence modeling assumptions. DNS models provide the most accurate predictions of turbulent flows and are particularly useful for fundamental studies of turbulence. However, DNS models are computationally very expensive and are limited to low-Reynolds-number flows and simple geometries.
• LES: Large Eddy Simulation is a turbulence modeling approach that resolves the large-scale turbulent structures and models the small-scale turbulence using a subgrid-scale model. LES models provide accurate predictions of unsteady flows and are particularly useful for flows with large-scale coherent structures, such as turbulence in boundary layers, jets, and wakes. However, LES models are computationally expensive and require a fine grid resolution, which can be challenging for complex geometries and high-Reynolds-number flows.
• RANS: Reynolds-averaged Navier-Stokes is a widely used turbulence model that averages the turbulent quantities in space and time. RANS models solve the time-averaged Navier-Stokes equations and provide statistical information about the turbulent flow field. RANS models are computationally efficient and can be used for a wide range of applications. However, RANS models are limited by their inability to capture unsteady structures in turbulent flows.
• DES: Detached Eddy Simulation is a hybrid RANS-LES model that combines the advantages of both approaches. DES models use RANS equations in the near-wall regions, where the flow is typically smooth, and LES equations in the outer regions, where the turbulence is dominant. DES models are computationally efficient and provide accurate predictions of wall-bounded flows and unsteady flows. However, DES models can be sensitive to grid resolution and require careful calibration of the model constants.

2. Comparison between approaches: Works from the literature

Hattori et al. investigate a thermal field in a turbulent boundary layer with changing wall thermal conditions using DNS [1]. Two types of wall thermal conditions are investigated using DNS and predicted by LES and RANS. The study shows that the predictions of both LES and RANS almost agree with the DNS results, but the predicted temperature variances near the wall by RANS give different results as compared with DNS due to the difficulty in predicting the dissipation rate of temperature variance. The study concludes that DNS is a useful method to investigate turbulent heat transfer, while RANS and LES can be used for practical applications.

Zheng and Yang evaluated the wind flow and pollutant dispersion in a street canyon with traffic flow using LES and RANS [2]. The standard k-ε (SKE) turbulence model is found to be the most accurate in the RANS simulations, while the LES simulation with the wall-adapting local eddy-viscosity subgrid-scale model outperforms all RANS models.

On the accuracy of CFD simulations of cross-ventilation flows for a generic isolated building, Hoof et al. compared 3D steady RANS simulations and LES with experiments [3]. The study finds that the LES dynamic Smagorinsky subgrid-scale model provides better results for all three measured parameters, namely velocity, turbulent kinetic energy, and volume flow rate. However, the use of LES increases computational demand significantly. The authors conclude that the choice of model depends on the target parameter.

In a comparison of unsteady RANS to hybrid RANS/LES, Athkuri et al. investigated the performance of different turbulence models for simulating flow past a circular cylinder in the "drag-crisis" region. The hybrid RANS-LES models outperformed the URANS models in the fully turbulent trans-critical region and better represent the physics in the wake region [4].

3. Best practices for turbulence modeling

• Understanding the different types of turbulence approaches. Each model has its strengths and weaknesses, and selecting the appropriate model depends on the specific problem and the available computational resources.
• Choosing the right boundary conditions: Boundary conditions play a critical role in turbulence modeling and can have a significant impact on the accuracy of the results. Understanding how to specify boundary conditions correctly for different turbulence models is crucial for obtaining accurate simulations.
• Choosing a good quality mesh: Mesh resolution is critical for accurate turbulence modeling, as the smallest eddies in a turbulent flow can be orders of magnitude smaller than the larger-scale features. Understanding how to properly resolve the mesh for different turbulence models and flow regimes is essential for obtaining accurate results.
• Conducting sensitivity analyses: A mesh sensitivity should be performed to make sure that the grid is sufficiently good to provide accurate results. The sensitivity analyses, concern also the most significant parameters and assumptions in a turbulence model and provide insights into the accuracy and reliability of the results.
• Validating the results: Validating the results of a turbulence simulation against experimental data or other reference solutions is crucial for assessing the accuracy and reliability of the model and ensuring that the results are physically meaningful.

By following these best practices, engineers and scientists can improve the accuracy and reliability of their turbulence simulations and obtain meaningful insights into complex fluid flow problems.

Conclusion

Turbulence modeling plays a critical role in predicting fluid flow behavior in a wide range of applications, from aerospace and automotive engineering to oil and gas production and environmental modeling. The development of accurate turbulence models has been a major focus of research for several decades, and significant progress has been made in this field. Despite the challenges associated with turbulence modeling, it continues to be an active area of research, with new approaches and techniques being developed to improve the accuracy of predictions. The continued development and application of turbulence models are essential to solve real-world problems and enhance our understanding of fluid dynamics.

References

[1] Hirofumi Hattori, Shohei Yamada, Masahiro Tanaka, Tomoya Houra, Yasutaka Nagano, DNS, LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions, International Journal of Heat and Fluid Flow, Volume 41, 2013, Pages 34-44, https://doi.org/10.1016/j.ijheatfluidflow.2013.03.014.

[2] Xing Zheng, Jiachuan Yang, CFD simulations of wind flow and pollutant dispersion in a street canyon with traffic flow: Comparison between RANS and LES, Sustainable Cities and Society, Volume 75, 2021, https://doi.org/10.1016/j.scs.2021.103307.

[3] T. van Hooff, B. Blocken, Y. Tominaga, On the accuracy of CFD simulations of cross-ventilation flows for a generic isolated building: Comparison of RANS, LES and experiments, Building and Environment, Volume 114, 2017, Pages 148-165, https://doi.org/10.1016/j.buildenv.2016.12.019.

[4] Sai Saketha Chandra Athkuri, M.R. Nived, R. Aswin, Vinayak Eswaran, Computation of drag crisis of a circular cylinder using Hybrid RANS-LES and URANS models, Ocean Engineering, Volume 270, 2023,113645, https://doi.org/10.1016/j.oceaneng.2023.113645.