December 5, 2023

# Turbulent wedge – a small disturbance with a large effect

The boundary layer, a tiny layer on the surface of a body in a flowing fluid, such as an airplane wing in the air, is of paramount importance for the future of flight. Just over 100 years ago, Ludwig Prandtl introduced the term boundary layer to distinguish the area close to the wall, where the viscosity of the air is of importance, from the outer flow, where viscosity can be neglected in aerodynamic considerations.

On the wing of a commercial aircraft, the boundary layer only grows to a few centimeters along the direction of the flow but within it the entire increase in flow velocity between the fluid at rest directly at the wall of the body and the external flow takes place. The frictional forces acting on the aircraft, which account for almost half of the total drag, depend directly on this wall-normal velocity gradient: if the boundary layer flow is laminar and therefore ordered, the relevant velocity gradient directly at the wall is more moderate and friction is reduced. If the flow within the boundary layer is turbulent, the drag increases due to a larger velocity gradient at the wall. Today's commercial airplanes do not show any relevant laminar flow areas during cruise flight, as the boundary layer flow becomes turbulent almost immediately. This is precisely where the scientists at the German Aerospace Center (DLR) come in.

### Transition – from laminar to turbulent

One way to make flying more ecologically efficient is to shift the change from laminar to turbulent boundary layer flow as far downstream as possible. This change from laminar to turbulent flow is called boundary layer transition. The transition location can be shifted by means of a suitable wing design, as the change in pressure along the flow results from the shape of the wing. If the flow remains accelerated over a larger distance, the flow will, in general, stay laminar in this part of the boundary layer.

### Combining experiment and simulation for future aircraft

In addition to wind tunnel tests, numerical computer simulations on high-performance computers are used to design and evaluate such laminar wings and aircraft. As the transition location cannot be predicted exactly in the computer models, correlations are used at least in parts of the modeling approach. These transition models are validated by suitable wind tunnel experiments, as carried out in the aviation research project ULTIMATE (LuFo VI-2, project partners involved: AIRBUS, DLR, ETW, Liebherr, TU Berlin, TU HH) in the European Transonic Windtunnel (ETW). Figure 1 shows the wind tunnel model of the NLF-ECOWING-FSW in the test section of the wind tunnel - a model with a forward swept laminar wing for an aircraft the size of an AIRBUS A320.

### Turbulent wedges as an unwanted phenomenon in the experiment

In the wind tunnel, the temperature-dependent light emission of certain surface coatings (TSP technology) can be recorded by cameras. As the heat transfer between flow and body and thus the surface temperature depends on the mixing within the boundary layer, laminar and turbulent flow areas show different light intensities. The transition location can therefore be determined experimentally and compared with a computer simulation. This is shown in Figure 2: The calculated transition location is superimposed on the TSP measurement and good agreement is shown in large parts of the wing. However, there are also turbulent wedges that arise near the leading edge. Such turbulent wedges occur at irregularities, surface imperfections, and other disturbances that cause the laminar boundary layer to trip. In a wind tunnel, for example, these can be ice crystals that form in the test section.

### Turbulent wedge models as an important step in transition modeling

The right part of Figure 2 shows the result of a computer simulation with the DLR γ transition model, in which the turbulent wedges are taken into account. Just as in the experiment, the flow model is disturbed at a single point at the tip of the wedge and the turbulent wedge forms by itself. The effect is illustrated using the skin friction coefficient cf : at the location where the boundary layer flow becomes turbulent, the skin friction increases, which increases the overall frictional drag of the wing.

The effect of the turbulent wedges on the aerodynamics of the wind tunnel model is illustrated in Figure 3 using the lift coefficient. The lift coefficient is the lift normalized by the dynamic pressure and a reference surface. It is an important dimensionless quantity to assess the aerodynamics of a wing. The difference between the computer simulation, in which the DLR TAU-Code flow solver (CFD - computational fluid dynamics) is coupled with an ANSYS® Mechanical Enterprise structural model (CSM - computational structural mechanics), and the experimental data can be significantly reduced if the turbulent wedges measured in the wind tunnel are modeled.

The turbulent wedge model can therefore help to represent and understand wind tunnel data more accurately, which in turn can be used for further improvements in the flow models. At the same time, turbulent wedge models will lead to a better overall assessment of future laminar aircraft by including the effect of local disturbances on the laminar boundary layer.

### Author:

Dr. Michael Fehrs, DLR-Institute of Aeroelasticity, Department Aeroelastic Simulation