Fluids are all around us, including the air we breathe, the water we drink, and the blood flowing in our body. Understanding how fluids interact with our surroundings allows us to harness their potential for endless applications in multiple disciplines. For example, reducing the air resistance/drag on cars and airplanes so we can travel faster while utilizing less fuel, generating renewable energy using wind turbines, and biological processes such as predicting blood flow through a blocked artery as a non-invasive medical analysis.

Most fluid motion that we encounter is turbulent. To accurately analyze and predict fluid motion, it is vital to understand and characterize turbulence. So, what exactly is turbulence and how can we define and characterize it, and what are some methodologies that allow us to accurately predict?

## What is Turbulence?

Fluid flow can generally be classified into three types: laminar flow, transitional flow, and turbulent flow.

- Laminar flow is smooth and streamlined, where fluid flows in parallel layers.
- Turbulent flow can be described as random or chaotic fluctuations in fluid flow in both space and time. Specifically, instantaneous fluctuations are present in the velocity and pressure field of a turbulent flow.
- Transitional flow is the mixture of laminar and turbulent flow and is the flow regime where laminar flow transitions into a turbulent flow.

Figure 1 shows the schematic of laminar and turbulent flows. Figure 2 shows flow over an airfoil in a wind tunnel at high angle of attack, where both laminar (upstream and far away regions) and turbulent flow (directly over the airfoil surface and in the wake) regions can be clearly seen.

Figure 1: Schematic of Laminar and Turbulent flow

Figure 2: Airflow separating from a wing at high angle of attack showing laminar and turbulent flow regions (Image source: By DLR, CC-BY 3.0, CC BY 3.0 de, https://commons.wikimedia.org/w/index.php?curid=61072555)

Turbulence in a flow generally occurs due to high flow velocity, lower fluid viscosity, or due to disturbances, such as change in geometry and shape, obstacles and/or changes in the flow path, etc. Whether a flow is turbulent or not can be determined with the help of a dimensionless number, called the Reynolds number.

## The Reynolds Number

The dimensionless number called Reynolds number is used as an indicator to predict if the flow is in the laminar or turbulent regime. Reynolds number is defined as

Here *U* is the characteristic velocity, *L* is the characteristic length scale, and *v* is the kinematic viscosity of the fluid. Generally, if the Reynolds number is large for a particular fluid system, the flow is turbulent. That is, if the inertial forces are much larger than the viscous forces, the flow transitions into turbulence. A critical value for the Reynolds number (Re_{cr}) exists for every fluid system, below which the flow remains laminar, and above which, the flow transitions into turbulence. For example, a commonly cited Re_{cr} for pipe flow is known to be around 2000 to 4000. For a flow over a flat plate, Re_{cr} ~ 500,000.

## Applications of Turbulent Flows

Turbulent flows find important and diverse applications in all engineering and sciences ranging from aerospace and mechanical engineering, biofluid mechanics, industrial mixing, meteorology, etc. In aerospace, they influence aircraft efficiency and wing design. Hydraulic engineers study turbulent flows in rivers for erosion control and pollutant dispersion. Turbomachinery efficiency hinges on understanding turbulence within turbines and pumps. Weather and climate models rely on turbulent flow dynamics for accurate predictions. Industrial processes such as chemical reactions and heat transfer benefit from controlled turbulent mixing. Oceanographers analyze turbulent ocean currents for climate research. Fundamental turbulence research advances fluid dynamics understanding. Applications extend to heat transfer in HVAC systems, aerodynamics in sports equipment, and environmental fluid mechanics. Turbulent flows thus play critical roles in engineering, environmental science, and beyond.

## Turbulence Modeling in Computational Fluid Dynamics

As mentioned in our previous blog post, Computational Fluid Dynamics (CFD) is a tool that is used to model fluid flow using numerical computations.

To accurately predict fluid flow behavior, it is important to take all the scales of turbulence motion into consideration. This can be done by directly solving the Navier-Stokes equations, assuming an appropriate spatial and temporal discretization is used in the numerical scheme (for example, Direct Numerical Simulation (DNS)). Resolving all the scales of turbulent motion is computationally very expensive, and is only possible for some simple fundamental problems, even with current state of the art super-computing resources. For practical applications, this is infeasible. Hence, turbulence modeling is used in lieu of directly resolving turbulence in a CFD simulation. Reynolds Averaged Navier Stokes (RANS) and more recently, Large Eddy Simulation (LES) are two of the commonly used methodologies for accurately resolving turbulence in flows for practical applications. In the upcoming blogs, we will take a closer look at some of these turbulence modeling methodologies.

## Final Thoughts

This post mentions a brief introduction to turbulent flows. The applications of turbulent flows, along with how they can be modeled using CFD are also briefly mentioned. In future blog posts, we will take a closer look at some of the intricacies of turbulence modeling in CFD, deep dive into some of the mathematics behind turbulence modeling and share some useful tips and tricks on successfully running a CFD simulation to accurately resolve turbulence.

If you need help with CFD analysis, or just want to chat about simulation in general, don’t hesitate to **reach out to the expert team at Fidelis**!