# Part 5: Turbulence

# 1.0 Introduction

How we address turbulence is **the defining feature** of modern computational fluid dynamics (CFD). No modern computer has the power to directly compute the full details of turbulence (as of 2019). Instead, we make approximations and develop empirical models. What type of approximation, and which models should you select? This invokes our discussion on turbulence modeling in CFD.

## 1.1 Laminar Flow and CFD

Before we dive into turbulence modeling, any CFD engineer should first check their assumptions. Is the flow truly turbulent? Speeds below a Reynolds Number of 1 x 10^{4} may be laminar. At that point, the CFD engineer must decide if the best option is to turn off the turbulence model. These models act like a lite bulb, on or off. Either the flow is turbulent everywhere in the domain, or nowhere.

# 2.0 Source of Turbulence

First, a quick refresher on the source of turbulence. Look at the mixing storm clouds in Figure 2‑1. Imagine a pocket of slower air near the bottom of the cloud suddenly gets shoved up into the faster air near the top of the cloud. This happens so fast that the slower pocket does not have time to change velocity. It arrives in the faster air at an entirely different speed. That speed difference acts like a traffic jam, generating eddies, more circulation, and more turbulence. The exchange of air at different speeds and resulting sheer stresses generates turbulence.

**When we have a steady, but non-uniform flow of fluid, turbulence introduces fast and random fluctuations in that flow velocity. **

# 3.0 Turbulence Definition in RANS

As mentioned before, modern computers do not have the power to fully calculate turbulence. It encompasses too much detail, transitioning down to scales of millimeters and time periods of milliseconds. If we tried to capture that level of detail in the scope of industrial fluid flow, the computer would never complete the simulation.

Instead, we developed an approximation: Reynolds Averaged Navier Stokes (RANS). In the RANS approach, the velocity gets separated into two components. (Equation 1) the first component, *U*, is the steady velocity. The second component, *u’*, represents the fluctuating turbulent velocity. With *u’*, we don’t worry about every single fluctuation. Instead, we only consider the average effect. This average effect gets approximated with empirical models, vastly simplifying the detail required. The RANS approach made turbulence modeling achievable.

The practical implementation of the RANS turbulence scheme depends on the actual turbulence model. The CFD program solves for the steady velocity U. We supplement this with empirical models to calculate the averaged effect of the turbulent fluctuation. Several different groups developed empirical models to calculate appropriate predictions.

## 3.1 Other Methods of Handling Turbulence

Despite its breakthrough for CFD, the RANS method is not perfect. More advanced methods exist to more accurately capture turbulent effects, with greater detail:

- Large eddy simulation (LES)
- Detached eddy simulation (DES)

These both require advanced CFD modeling and are beyond the scope of this article.

# 4.0 Turbulence Models

Turbulence models introduce additional transport equations to model the creation and dissipation of turbulence in CFD. Turbulence changes. It grows and spreads, reacts to the flow patterns and influences them. To capture all that elegance, turbulence models range from the overly simplistic to the massively complex. Each model has some basis in physics. But all models include empirical constants and coefficients, usually derived from extensive experimental testing.

As the CFD engineer, we get to see these empirical constants, but *Don’t edit the empirical values!* They are very precisely chosen. Unless you personally created the turbulence model, don’t touch the values. The CFD engineer does select different models, based on the situation. There are too many to count. Two of the best known models are:

- K-ε model: works well for internal flow – pipes, valves, etc.
- K-ω model: works well for boundary layer flow – wings, control fins, etc.

The gold standard for selecting the best turbulence model is to conduct validation studies. Compare all your available turbulence models and see which ones fit best.

## 4.1 K-ω SST Turbulence Model

Many turbulence models have a special niche application, but one turbulence model gained wide acceptance as a general purpose model. In the marine world this model serves for 80% – 90% of all RANS simulations. The k-ω shear stress transport (SST) model provides a combination of the k-ε and k-ω models. It employs the k-ω model for boundary layer flow near walls, and it switches to the k-ε model away from the wall in the main domain. The actual change is gradual, based on Y+ distance from the wall. The SST model employs the best strengths of both worlds, making it an excellent general purpose turbulence model.

# 5.0 Conclusion

Without turbulence models, modern CFD fails to capture a major component of fluid flow. We simply cannot calculate this directly with current computer resources. That said, these models still require some level of approximation, some distortion from a perfect representation. The CFD engineer decides which turbulence model forms the best fit for each situation, with the k-ω SST model usually a good starting point. Despite their imperfections, we all agree that empirical turbulence models are far preferable to no model at all.

# 6.0 References

[1] |
Max Pixel, “Cumulus Storm Turbulence Thunderstorm Cloud Roller,” Max Pixel, 01 Jan 2019. [Online]. Available: https://www.maxpixel.net/Cumulus-Storm-Turbulence-Thunderstorm-Cloud-Roller-567678. [Accessed 01 Jan 2019]. |

[2] |
V. R. Raj, “Quadratic Profile Used in QUICK Scheme,” Wikimedia Commons, 12 Nov 2012. [Online]. Available: https://commons.wikimedia.org/wiki/File:Quadratic_profile.jpg. [Accessed 01 Jan 2019]. |

[3] |
S. Wasserman, “Choosing the Right Turbulence Model for Your CFD Simulation,” Engineering.com, 22 Nov 2016. [Online]. Available: https://www.engineering.com/DesignSoftware/DesignSoftwareArticles/ArticleID/13743/Choosing-the-Right-Turbulence-Model-for-Your-CFD-Simulation.aspx. [Accessed 01 Jan 2019]. |

[4] |
Q. Wang, C. Yan and T. Hui, “Mechanism Design for Aircraft Morphing Wing,” Research Gate, <https://www.researchgate.net/figure/y-plus-value-for-the-CFD-model-10-degree-of-extension-angle-of-attack-6_fig4_268478784>, Accessed: 2019, Jan, 01, April 2012. |

[5] |
S. Tao, F. Yuqing, L. Graeme and J. Kaixi, “CFD simulation of bubble recirculation regimes in an internal loop airlift reactor,” in |