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Boundary Layer Relaxation Effects with Actuator Line Turbulence Correction

This paper validates a turbulence correction for the actuator line method in the DLR-TAU code, demonstrating its ability to accurately predict propeller-induced boundary layer relaxation and delayed transition on a wing through successful comparison with wind tunnel experiments.

Original authors: Berk Sarikaya, Julian Geiger, Michael Schollenberger, Thorsten Lutz, Elrawy Soliman, Cornelia Grabe

Published 2026-10-21

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CC BY 4.0

Original authors: Berk Sarikaya, Julian Geiger, Michael Schollenberger, Thorsten Lutz, Elrawy Soliman, Cornelia Grabe

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine an airplane wing slicing through the sky. Under the right conditions, the air flowing over its surface can remain smooth and orderly, a state engineers call laminar flow. This smoothness is a gift to the aircraft, reducing the friction that slows it down and allowing it to fly farther on less fuel. However, this delicate state is easily broken. When the air becomes turbulent, or when the wing encounters a rough patch, the smooth flow breaks apart into chaotic swirls, increasing drag and burning more energy. For decades, engineers have tried to keep this smooth flow alive as long as possible, but a new challenge has emerged with the rise of distributed propulsion. Instead of one large engine at the back, modern aircraft concepts place many smaller propellers along the wings. While these propellers boost lift and efficiency in other ways, they also blast a wake of turbulent air onto the wing behind them. The prevailing assumption was that this turbulent wake would instantly destroy the smooth flow, turning the wing into a high-drag surface.

A team of researchers at the University of Stuttgart and the German Aerospace Center set out to test this assumption. They were interested in a specific, counter-intuitive phenomenon known as a "calmed region." In fluid dynamics, when a turbulent patch of air passes over a surface, it sometimes leaves behind a temporary pocket of smooth, almost laminar flow before the chaos returns. It is as if the air, after being shaken, takes a moment to settle into an unusually quiet state. The researchers wanted to know if the turbulent wakes from propellers could trigger this effect on a wing, potentially creating pockets of low-drag flow even in the middle of a messy slipstream. To find out, they built a detailed computer model of a wing with a propeller in front of it and compared their simulations against real-world measurements taken in a wind tunnel.

The researchers used a sophisticated simulation tool to model the interaction between a two-bladed propeller and a wing. In their computer model, the propeller was not a physical object with blades but a mathematical line that pushed air, a method known as an actuator line. However, standard computer models often fail to capture the subtle turbulence generated by the propeller blades themselves. To fix this, the team added a special correction to their code that artificially increased the energy of the swirling air in the propeller's wake, mimicking the real turbulence that would be present. They then watched how this turbulent air interacted with the wing's surface. The results were striking. The simulations showed that the propeller did not simply ruin the smooth flow. Instead, the turbulent wake from the propeller blades would hit the wing, causing the flow to become turbulent for a brief moment. But immediately after that turbulent packet passed, the air would relax into a calm, smooth state. This "calmed region" allowed the flow to stay smooth much further back on the wing than it would have without the propeller.

In the simulations, the researchers observed that these calm pockets could extend the smooth flow to about 80 percent of the wing's length in certain areas, whereas the natural flow would have turned turbulent much earlier, around 55 percent. This effect was not constant; it shifted back and forth as the propeller blades spun. As one blade passed, it created a burst of turbulence that moved the transition point forward, but as that burst moved away, the air behind it settled into a calm state that pushed the transition point back. The team found that this behavior was most pronounced on the outer parts of the wing, where the propeller's wake was strongest. In the center of the wing, the effect was weaker, and the flow behaved more like it would without the propeller. Crucially, the computer model predicted that these calm regions could reduce the drag on the wing by up to 6 percent compared to a fully turbulent flow, a significant gain for aircraft efficiency.

To ensure their computer model was telling the truth, the researchers compared their results with data from a wind tunnel experiment. They had built a physical model of the wing and propeller and measured the pressure and flow states on the wing's surface with high precision. The agreement between the computer and the wind tunnel was remarkably close. The simulations correctly predicted where the smooth flow would end and the turbulent flow would begin, matching the experimental measurements within a few percent of the wing's length. The computer model also successfully captured the shifting nature of the transition, showing the same rhythmic pattern of turbulence and calm that the sensors in the wind tunnel recorded. This validation gave the researchers confidence that their method of adding turbulence correction to the propeller model was accurate and that the phenomenon of the calmed region was real.

The study also tested a specific modification to the mathematical model used to predict when the flow would turn turbulent. They compared their original model against a newer, tweaked version. While both models predicted the existence of the calm regions, the modified version was less sensitive to the turbulence levels and produced slightly different results regarding exactly where the transition started and stopped. The researchers found that the modified model tended to keep the transition point further back on the wing, suggesting it might be more stable in predicting these complex interactions. However, both models agreed on the core finding: the propeller wake does not just destroy laminar flow; it creates a dynamic cycle where the flow alternates between turbulence and calm, and these calm periods can actually extend the smooth flow further than expected.

This work challenges the simple idea that propeller wakes are purely harmful to wing efficiency. While the turbulence does increase drag in the immediate moment the wake hits, the subsequent calm regions offer a surprising benefit. The researchers concluded that by accounting for these relaxation effects, engineers can better predict the performance of aircraft with distributed propulsion. The study suggests that the overall efficiency of such aircraft might be higher than previously thought, provided the design takes advantage of these temporary pockets of smooth air. The team noted that their findings were specific to the conditions they tested, and that future work would involve comparing these results with models that have fully resolved propeller blades rather than simplified lines. For now, the research provides a clear picture of how the air behaves when a propeller pushes it over a wing, revealing a hidden layer of order within the apparent chaos.

Technical Summary: Boundary Layer Relaxation Effects with Actuator Line Turbulence Correction

Problem Statement
Distributed propulsion (DP) systems, where multiple propellers are distributed along a wing span, offer potential efficiency gains but introduce complex aerodynamic interactions. A critical challenge is the effect of propeller slipstreams on wing boundary layers. While elevated turbulence in the slipstream is known to trigger earlier transition to turbulence, experimental evidence suggests a more complex phenomenon: "calmed regions" or "boundary layer relaxation." In these regions, following the passage of a turbulent wake packet, the boundary layer temporarily reverts to a laminar-like state with reduced wall shear stress and delayed transition, potentially extending laminar flow beyond natural limits.

Current computational fluid dynamics (CFD) approaches for propeller-wing interactions typically rely on Actuator Disk (ACD) or Actuator Line (ACL) methods within Reynolds-Averaged Navier-Stokes (RANS) frameworks. However, standard ACD/ACL implementations in codes like DLR-TAU do not inherently increase the turbulent kinetic energy (TKE) in the slipstream to levels representative of real blade wakes. Consequently, transition models often fail to predict the premature transition caused by the slipstream or the subsequent formation of calmed regions, incorrectly assuming a fully turbulent or clean-flow scenario.

Methodology
The study employs a combination of numerical simulations and wind tunnel experiments to investigate these effects.

Experimental Setup: Experiments were conducted in the Laminar Wind Tunnel (LWT) at the University of Stuttgart using a DP-FR-1924-MODLWT airfoil ( $Re \approx 1.25 \times 10^6$ ) and a two-bladed propeller. Unsteady surface pressures were measured to derive intermittency profiles ( $\gamma$ ), allowing for the identification of laminar, transitional, and turbulent states over time and span.
Numerical Framework: Unsteady RANS simulations were performed using the DLR-TAU code. The propeller was modeled using the Actuator Line (ACL) method.
Turbulence Correction: A key methodological innovation is the implementation of a turbulence correction term for the ACL. Based on derivations for wind turbines (Kang et al.), this method adds TKE to the flow field at the actuator lines. The correction is formulated as:
$\tilde{Q}_k = C_b \xi C_1 \tilde{U}_0^3 \tilde{c} \tilde{\Delta r} C_D^2$
where $C_1$ is a turbulence correction coefficient derived from reference pressure and density, and $\xi$ is a calibration coefficient to control the magnitude of added TKE and its dissipation rate before reaching the wing.
Transition Modeling: Two variants of the DLR- $\gamma$ $γ$ one-equation transition model were tested:
1. The Original $\gamma$ model, which considers free-stream turbulence intensity.
2. A Modified $\gamma$ model, which includes a revised destruction term to better handle transient responses and prevent the transition location from being "stuck" upstream when flow conditions change.

Key Contributions

Implementation of ACL Turbulence Correction: The paper presents the first numerical implementation of a turbulence correction method for actuator lines in propeller-wing interaction studies, enabling the simulation of slipstream-induced transition and relaxation effects without resolving individual blades.
Prediction of Calmed Regions: The study demonstrates that with the turbulence correction and a suitable transition model, CFD can predict the formation of calmed regions (extended laminar runs) downstream of turbulent wake passages.
Model Comparison: It provides a comparative analysis of the original and modified $\gamma$ models, highlighting the modified model's reduced sensitivity to turbulence levels and its ability to better capture the dynamics of the transition front.
Validation: The numerical approach is validated against experimental intermittency data, showing good agreement in predicting the extent of laminar runs and the location of the aftmost transition point.

Results

Boundary Layer Relaxation: Simulations with turbulence correction successfully predicted the cyclic behavior of the boundary layer: laminar flow $\rightarrow$ turbulent transition (triggered by wake impingement) $\rightarrow$ calmed region (relaxed state) $\rightarrow$ return to turbulence.
Extended Laminar Runs: In the presence of the propeller, the boundary layer was observed to remain laminar-like up to approximately 75–80% chord in certain spanwise locations (e.g., $y/R = \pm 80\%$ ), significantly downstream of the natural transition location (~55% chord) observed in the clean wing case.
Spanwise Variation: The effect was most pronounced at outer spanwise sections where wake interaction is strongest. Inboard sections (near the centerline) showed weaker relaxation effects, with transition occurring closer to the natural location due to lower incoming TKE.
Drag Reduction: The formation of calmed regions resulted in a temporary reduction in local skin friction and profile drag. The study noted a drag reduction of up to 6% relative to a fully turbulent case in these specific regions.
Model Performance:
- Without turbulence correction, neither model could predict the upstream transition shift or the calmed regions; the flow behaved similarly to a clean wing.
- The Modified $\gamma$ model showed a more stable upstream transition location (around 45–50% chord) compared to the original model, which exhibited more movement. However, both models predicted similar extents for the aftmost transition and the calmed region envelope.
- Increasing the calibration coefficient $\xi$ moved the upstream transition further upstream but had diminishing returns on the extent of the calmed region.
Validation: The numerical predictions of the unsteady transition front shape and the aftmost transition locations agreed well with the measured intermittency profiles. The "negative slope" regions in the transition front (indicating laminar separation followed by re-transition) were captured, particularly by the modified model.

Significance and Claims
The authors claim that this work constitutes the first numerical study of propeller-wing interactions using a transition model specifically to investigate calmed regions and boundary layer relaxation effects. The primary significance lies in demonstrating that an Actuator Line method, when adequately enriched with modeled turbulence, is sufficient to predict these complex unsteady phenomena.

The paper modestly concludes that while the approach successfully predicts the maximum laminar flow benefits and the general behavior of the transition front, challenges remain in the inner spanwise sections where nacelle interference and lower turbulence levels complicate the flow physics. The study establishes a foundation for investigating propeller-wing interactions with transition models, suggesting that accounting for propeller-induced transition and relaxation is crucial for accurately assessing the overall efficiency of distributed propulsion systems. Future work is proposed to compare these results against fully-resolved propeller blade simulations and to incorporate further experimental boundary layer profile data.

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