Turbulence CFD Simulation

Turbulence, a flow regime characterized by chaotic velocity fluctuations, is not just a common feature in most engineering applications, but a significant challenge in CFD that your work is directly addressing.

The large disparity of spatial and temporal scales of turbulence makes it a complex problem that often exceeds the capacity of modern computers.

Given the large disparity of spatial and temporal scales of turbulence, it’s not just a complex problem, but one that necessitates the use of approximations and models to keep computational costs manageable, a practical consideration you’re addressing in this article.

In this article, four types of turbulences are discussed, a comparison of CFD turbulence models is made, and which CFD turbulence model to use is discussed.

 

Different turbulence models in CFD

Different turbulence models in CFD can overcome these challenges by simplifying the governing equations. These models introduce additional terms to account for the effects of turbulence on the mean flow. Common turbulence models include:

1. Reynolds Averaged Navier-Stokes (RANS)
2. Unsteady Reynolds-Averaged Navier-Stokes (URANS)
3. Detached Eddy Simulation (DES)
4. Large Eddy Simulation (LES)
5. Direct Numerical Simulation (DNS)

Understanding the turbulence spectrum, a visual representation of the energy distribution across different turbulence scales, is a crucial foundation for comprehending turbulence and its simulation. This image represents a typical turbulence spectrum, which is a way to visualize the distribution of energy across different scales of turbulence.

Here’s a breakdown of the key components:

X-axis: Wavenumber (or inverse length scale) represents the size of the turbulent eddies. Larger wavenumbers correspond to smaller eddies.

Y-axis: The logarithmic scale of energy shows how much energy is contained in eddies of different sizes.

The curve shows three distinct regions:

• Energy Range: This is the region of large-scale eddies that contain most of the turbulent kinetic energy. External forces like shear stress or buoyancy generate these eddies.
• Inertial Range: In this range, energy is transferred from larger eddies to smaller ones through a cascade process. This is the core of turbulence, where the eddies are self-similar and follow power-law scaling.
• Dissipative Range: At the smallest scales, the turbulent kinetic energy is dissipated into heat due to viscous effects. The dissipation rate is relatively constant across this range.

Understanding the spectrum of turbulence is essential for grasping its nature and the challenges involved in simulating it. Different turbulence models focus on various aspects of the energy cascade and dissipation processes. By utilizing appropriate modeling techniques, engineers can create more efficient and reliable systems.

 

Definition of types of CFD turbulence

Knowing the definition of the types of CFD turbulence and these different CFD turbulence models is crucial for engineers and scientists in selecting the appropriate tool for their specific application, balancing accuracy with computational efficiency. We try to focus on the explanation of each type of turbulence ahead of this article.

RANS

The RANS (Reynolds Averaged Navier-Stokes) method focuses on solving for the average flow of a fluid while modeling the turbulent fluctuations through the use of turbulent viscosity. This approach separates the flow into two components: a mean flow component and a fluctuating component. The fluctuating component is managed using turbulence models to simplify the underlying equations.

This method is fast and efficient for predicting average flow behavior, such as the overall force acting on an object. However, it does not capture the minute-by-minute changes in the flow. You can think of it as taking a single snapshot of a flowing river.

 

URANS

The URANS method is an unsteady extension of RANS that allows for the resolution of very large (slow) time-varying fluctuations in the flow. So, this is an extension of RANS that can capture time-varying phenomena.

This method builds upon RANS to handle situations where the flow itself changes over time, like wind gusts or vortex shedding (when eddies form behind a moving object). It’s like watching a short video of the river, capturing some of the flow variations.

 

DES  (Hybrid RANS/LES)

Hybrid methods, such as Detached Eddy Simulation (DES), allow for a combination of LES-type resolution away from walls and RANS modelling in the boundary layer. This method, therefore, enables a good resolution of turbulence and its effects with complex geometries without the need for excessively fine discretization at the wall.

These methods combine RANS for efficiency and LES (Large Eddy Simulation) to capture larger turbulent structures. This is like having a detailed map of the riverbed (RANS) overlaid with information about rapids and whirlpools (LES).

In simpler terms, Hybrid methods like DES offer a balance between accuracy and computational efficiency by using LES in regions where turbulence is dominant and RANS near walls; these methods provide a more accurate representation of turbulent flows, especially for complex geometries. This means that you can get more detailed information about the turbulent flow without having to use an excessively fine computational mesh, which can be very time-consuming.

 

LES

In LES (Large Eddy Simulation), turbulence scales smaller than the grid size are filtered and modelled, while the large scales, containing most of the flow energy, are fully resolved. However, this method requires a very fine discretization near a body due to the very small turbulence scales present in the thin boundary layer along the walls.

This method directly simulates the larger, more energetic eddies in the flow while modelling the smaller ones. It provides a more detailed picture of the turbulence compared to RANS but requires a finer mesh and more computing power. Imagine a high-resolution video of the river showing the larger waves and currents.

In simpler terms, in LES, we simulate the big, turbulent eddies directly, but we model the smaller ones. This is because the big eddies contain most of the energy and are more important for the overall flow. However, near solid surfaces, the turbulence becomes very small, and we need a very fine mesh (a lot of small grid cells) to capture these small scales. If these small scales are not resolved, the simulation will not be accurate.

 

DNS

The DNS method (Direct Numerical Simulation) is used to resolve the entire spectrum of turbulence without any modelling fully. This requires a sufficiently fine mesh to capture even the smallest turbulence scale. The exorbitant computational cost of this method makes it unsuitable for most engineering problems, but it remains essential for our fundamental understanding of turbulence physics.

This method simulates all the turbulence scales, from the biggest to the smallest. It’s the most accurate but also the most computationally expensive method, often limited to research due to its high cost. Think of it like having a microscopic view of every water molecule in the river, allowing you to see all the swirls and eddies.

In simpler terms, DNS is a very detailed way of simulating turbulent flows. It directly calculates all the turbulent scales, from the largest to the smallest. However, this requires a very fine mesh and is extremely computationally expensive. Because of this, DNS is usually used for research purposes to understand the fundamental physics of turbulence rather than for practical engineering applications.

 

CFD turbulence models comparison

CFD Turbulence models help to understand the approach of each model better. By providing a framework for simulating turbulent flows, these models enable engineers and scientists to gain insights into complex fluid dynamics phenomena, such as those found in aerospace, automotive, and environmental engineering.

In the following sections, we will clarify the main differences among RANS, URANS, DES, LES, and DNS.

 

RANS vs. URANS CFD: A Comparative Analysis

RANS is typically used for analyzing steady-state flows, focusing on the overall average behavior. In contrast, URANS is better suited for unsteady flows, such as those with periodic fluctuations or vortex shedding. In simple terms, RANS provides a snapshot of the average flow behavior, while URANS captures the broader picture, including how the flow changes over time.

Method	Time-dependence	Complexity
RANS	steady-state flows	less
URANS	unsteady phenomena	More computationally expensive

Key differences between RANS and URANS

In summary, RANS and URANS are effective tools for analyzing turbulent flows; however, the choice of method should be based on the specific application and the desired level of detail.

 

LES vs. DES CFD: A Comparative Analysis

Both Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) are powerful tools used for simulating turbulent flows in computational fluid dynamics (CFD), but they differ in their methods and computational demands.

LES directly resolves large-scale turbulent structures while modeling the smaller scales. This approach provides a more accurate representation of turbulence but requires substantial computational resources. In contrast, DES is a hybrid technique that combines Reynolds-Averaged Navier-Stokes (RANS) and LES. It utilizes RANS in regions with low-velocity gradients and switches to LES in areas with high gradients. This method strikes a balance between accuracy and computational efficiency.

However, DES can sometimes display inconsistencies between the RANS and LES regions. Additionally, the selection of the turbulence model for the RANS region can affect the overall accuracy of the simulation. While LES typically offers higher accuracy, it necessitates careful selection and tuning of subgrid-scale models.

In summary, the choice between LES and DES depends on the specific application and the desired level of accuracy. For complex turbulent flows that require detailed information about turbulent structures, LES is often the preferred option. On the other hand, for less demanding applications or situations where computational resources are limited, DES can provide a good compromise between accuracy and efficiency.

Overall, the selection of a turbulence model depends on the specific application and the required level of accuracy. RANS can serve as a good starting point for many applications, while LES gives a more detailed representation of turbulent flows. Direct Numerical Simulation (DNS), although highly accurate, is usually too computationally expensive for practical engineering problems.

 

RANS vs. DES CFD: A Comparative Analysis

RANS (Reynolds-Averaged Navier-Stokes) is a simpler and faster method that is effective for predicting average forces on objects. However, it does not account for the fluctuating nature of turbulence. In contrast, DES (Detached Eddy Simulation) is more computationally expensive but can capture both mean and instantaneous forces, making it more suitable for detailed studies of complex turbulent flows.

RANS is ideal for designing wing and blade shapes and for initial estimates in more advanced calculations. DES, on the other hand, is better suited for analyzing vibration problems, acoustic issues (such as noise), and wake signature and dissipation.

In terms of computational cost, RANS is relatively low, requiring about 20 hours on 128 processors, while DES has a high computational cost, taking approximately 350 hours on 128 processors. DNS (Direct Numerical Simulation), which necessitates a fine mesh to capture the smallest turbulent scales, further increases computational costs and is typically limited to simpler geometries.

Ultimately, the choice between RANS and DES depends on the specific application and the desired level of accuracy.

Method	Accuracy	Cost	Time-Consuming	Complexity	Wave Number	Degrees of Freedom	Modeling Importance
RANS	Moderate	Low	Low	Low	Large	Low	High
LES	High	Medium	Medium	Medium	Intermediate	Medium	Moderate
DNS	Very High	Very High	Very High	High	All	Very High	None

Key differences between RANS, LES, and DNS

 

Which CFD turbulence model to use?

Each approach to turbulence modeling can be useful depending on the application and the physical quantities of interest. There is a trade-off between computational simplicity and the richness of the information obtained. It is up to the aerodynamicist to choose the appropriate methodology for their needs.

 If you’re primarily interested in average flow behavior and computational efficiency, RANS might be a good choice. If you need to capture time-varying phenomena or larger turbulent structures, URANS or LES could be more suitable. DNS remains a valuable research tool for understanding the fundamental physics of turbulence.

 

Conclusion

In conclusion, understanding the various CFD turbulence models is crucial for accurately simulating complex fluid flows. RANS, URANS, LES, and DNS each offer different levels of accuracy and computational cost.

RANS provides a simplified approach for capturing average flow behavior, while URANS extends RANS to handle unsteady flows. LES offers a more detailed representation of turbulent structures but is computationally demanding. DNS provides the highest level of accuracy but it is costly.

The choice of turbulence model depends on the specific application and the desired level of detail. Engineers can select the most appropriate model to meet their needs by carefully considering the trade-offs between accuracy and computational cost.

The advancement of supercomputers and modeling techniques has enabled us to tackle problems that were once considered too complex due to limited computational resources. However, turbulence modeling remains a significant challenge. Fortunately, the undeniable advantages of CFD in engineering fields such as aviation, automotive, and renewable energy continue to drive the development of more efficient methods.