Turbulent Boundary Layer

Key Takeaways

• What is a turbulent boundary layer?

• The causes of boundary layer turbulence.

• Methods of analyzing turbulent boundary layers.

Airplane experiencing a turbulent boundary layer

If you are one of the few billion passengers that fly in any given year, chances are that you have experienced a bump or two in the air. If this was your first excursion into the ‘friendly’ skies, this event may have caused you some alarm. However, if you are a seasoned air traveler you know this turbulence is not uncommon. 

There are many reasons why the airflow around an aircraft boundary layer might result in turbulence. For example, flying through the chaotic environment of a lightning storm is a common reason for a rocky flight. In fact, if the weather conditions are severe enough, planes will be grounded. When designing systems for flight, this is but one of the causes of a turbulent boundary layer of which you should be aware.  

What Is a Turbulent Boundary Layer?

Understanding how an aeronautical system will behave due to changes in its environment is critical for designing and building aircraft that will reliably meet performance objectives and provide safe transport. Central to this study is analyzing fluid flow around aircraft boundaries, such as symmetrical or cambered airfoil or fuselage surface.

For boundary layer analysis, fluid flow is often categorized as either laminar or turbulent. Similar to internal fluid flow, where values less than 2300 indicate laminar flow, Reynolds numbers for external boundary layer laminar flow are lower than for turbulent flow. Additionally, streamlines for laminar fluid flow are unidirectional and parallel. Turbulent boundary flow regimes, on the other hand, exhibit lateral mixing, non-parallel streamlines, and chaotic pressures and temperatures. These boundary layer conditions can have various root causes.

The Causes of Boundary Layer Turbulence

Unless the aircraft is flying in an unstable environment such as a storm, the fluid flow at the leading edge of the boundary layer is typically laminar. However, as the air flows over the surface, the laminar flow (which is unstable) thickens and breaks down and the boundary layer transitions to turbulent, as shown in the figure below. 

Turbulent boundary layer formation. (Image from Symscape)

Note the arrows in the figure above only indicate the time-averaged velocity in the general direction of air along the boundary and not the internal activity within the airflow. There are several factors that may contribute to this transition. For example, moisture, the transfer of momentum, temperature changes, and the object surface roughness all affect to what extent the turbulent boundary layer forms. For analyses, greater detail of how the fluid in the boundary layer is changing is required.

Methods of Analyzing Turbulent Boundary Layers

The transition from full laminar flow to a fully turbulent boundary layer is not instantaneous. In fact, the turbulent flow goes through an energy cascade that consists of three intervals. 

Energy Cascade Levels

1. Generation - where eddies form due to changing flow parameters.
2. Inertial - during which energy is lost due to direct and reverse energy transfers between large and small eddies. 
3. Dissipation - characterized by almost exclusive loss of energy, primarily as a result of viscosity.

The study of turbulence is essentially an evaluation of the kinetic energy of the boundary layer. The most often applied method for this analysis – and indeed for fluid mechanics problems in general – is the Navier-Stokes equation shown below.

Navier-Stokes equation

The Reynolds-Averaged Navier-Stokes (RANS) equations are also utilized, as they provide a practical model that separates the velocity in time-dependent and time-invariant components. 

The models above are effective for evaluating turbulent boundary layers, provided they are implemented using CFD solver tools that include fast, accurate numerical computation and high-quality geometrical mesh generation, which are included in Cadence’s advanced suite of CFD tools.

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