Three-Dimensional Flow Separation on a Wall-Bounded Wing at Transitional Reynolds Numbers: An Experimental and Numerical Study

Core Concepts

Wall boundaries significantly influence the three-dimensional flow separation and reattachment dynamics on a wing at transitional Reynolds numbers, even at the midspan, highlighting the limitations of two-dimensional flow assumptions in such scenarios.

Abstract

This research paper investigates the complex flow patterns that emerge on a wall-bounded NACA 65(1)412 airfoil at transitional Reynolds numbers (Re = 10^4 - 10^5). The study employs experimental techniques (Particle Image Velocimetry) and Direct Numerical Simulations (DNS) to analyze the impact of varying angles of attack (α) and Reynolds numbers on the flow separation characteristics.

Research Objective:
The primary objective is to examine the three-dimensional flow topology, particularly the behavior of shearing surfaces, in the transitional Reynolds number regime for a wall-bounded wing with an aspect ratio of 3.

Methodology:

• Experiments were conducted in a water channel using a 3D-printed NACA 65(1)412 airfoil model with transparent end walls to simulate wall boundaries.
• PIV measurements were performed at midspan and within the end wall boundary layer to capture flow velocities.
• A curved laser sheet technique was employed to obtain near-wall velocities at the suction surface.
• DNS simulations were conducted for comparison with experimental results.

Key Findings:

• Laminar separation occurs over the airfoil surface, leading to complex three-dimensional flow structures downstream.
• The presence of wall boundaries significantly influences the flow field, even at the midspan, indicating that a two-dimensional flow assumption is not valid in this scenario.
• Strong spanwise flows originating from the wall towards the midspan are consistently observed, regardless of the Reynolds number.
• A critical angle of attack (αcrit) exists, where the flow transitions from a low-lift state with no reattachment to a high-lift state with turbulent reattachment.
• The shear layer shedding frequency exhibits a dependence on both the angle of attack and Reynolds number.
• DNS simulations with no-slip spanwise boundary conditions show good agreement with experimental observations, highlighting the importance of considering wall effects.

Main Conclusions:

• Wall boundaries play a crucial role in shaping the flow separation and reattachment dynamics on a wing at transitional Reynolds numbers.
• The three-dimensional nature of the flow field, particularly the presence of strong spanwise flows, necessitates a departure from two-dimensional flow assumptions.
• Understanding the complex flow phenomena observed in this study is essential for developing effective flow control strategies for airfoils operating in this Reynolds number regime.

Significance:
This research provides valuable insights into the intricate flow behavior around wall-bounded airfoils at transitional Reynolds numbers, which is relevant to various applications, including unmanned aerial vehicles (UAVs), wind turbines, and micro air vehicles (MAVs).

Limitations and Future Research:

• The study focuses on a specific airfoil geometry and a limited range of Reynolds numbers.
• Further investigations are needed to explore the influence of different airfoil shapes, surface roughness, and turbulence levels.
• Future research should also consider the impact of active flow control techniques on the observed flow phenomena.

Stats

Chordwise Reynolds numbers tested: Re = 2, 4, 6, 8 × 10^4.
Aspect ratio of the wing: AR = 3.
Chord length of the airfoil model: c = 200 mm.
Span of the airfoil model: b = 600 mm.
Free stream speeds corresponding to the tested Reynolds numbers: U = 0.1, 0.2, 0.3, 0.4 m/s.
Dominant shear layer shedding frequency: St ≈ 3.
Scaled dominant frequency: St/√Re ≈ 0.027.

Quotes

Key Insights Distilled From

The Footprint of Laminar Separation on a Wall-Bounded Wing Section at Transitional Reynolds Numbers

by Charles Klew... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.05926.pdf

Deeper Inquiries

How would the observed flow patterns and separation characteristics change with different wing aspect ratios and planform shapes?

Answer:
Modifying the wing aspect ratio and planform shape significantly influences the observed flow patterns and separation characteristics, particularly at transitional Reynolds numbers (Re = 104 - 105) where laminar separation bubbles (LSBs) dominate. Here's a breakdown of the potential impacts:
Aspect Ratio:

Lower Aspect Ratios: Decreasing the aspect ratio amplifies the influence of the wall-induced spanwise flows. This leads to a more pronounced three-dimensional flow field, potentially causing earlier separation and larger, more unstable LSBs. The critical angle of attack (αcrit) for the transition between low-lift (SI) and high-lift (SII) states might decrease, and the transition itself could become less abrupt.
Higher Aspect Ratios: Increasing the aspect ratio reduces the impact of the wall, promoting a flow field closer to two-dimensional behavior, especially near the midspan. The separation line might become more uniform, and the LSBs could become smaller and more stable. However, even at higher aspect ratios, the wall effects wouldn't completely disappear, and three-dimensional flow features would still persist near the wing-wall junctions.
Planform Shape:

Sweep Angle: Introducing a sweep angle can either stabilize or destabilize the flow depending on the sweep direction and angle. Forward sweep tends to stabilize the flow, potentially delaying separation and reducing the size of LSBs. Conversely, backward sweep can promote earlier separation and lead to larger, more unstable LSBs.
Taper Ratio: A higher taper ratio (smaller chord length at the tip) can reduce the strength of the wingtip vortices, which in turn, can influence the spanwise flow patterns and separation characteristics. This effect might be more pronounced at lower aspect ratios.
Wingtip Devices: Adding wingtip devices, such as winglets or wingtip fences, can alter the wing's effective aspect ratio and modify the wingtip vortex structure. This can impact the spanwise flow and separation behavior, potentially delaying separation and improving lift-to-drag ratios.
In essence, understanding the interplay between aspect ratio, planform shape, and the resulting flow patterns is crucial for optimizing aerodynamic performance at transitional Reynolds numbers.

Could the addition of passive flow control devices, such as vortex generators, mitigate the negative impact of wall-induced spanwise flows on lift and drag?

Answer:
Yes, passive flow control devices like vortex generators (VGs) can potentially mitigate the negative impact of wall-induced spanwise flows on lift and drag, especially at transitional Reynolds numbers. Here's how:

Energizing the Boundary Layer: VGs work by generating streamwise vortices that energize the boundary layer. This added energy makes the boundary layer more resistant to separation, even under the influence of adverse pressure gradients and spanwise flow.
Disrupting Spanwise Flow: Strategically placed VGs can disrupt the formation and strength of the horseshoe vortices that form at the wing-wall junction. By modifying the flow structure in this region, VGs can reduce the extent of the spanwise flow and its impact on the overall flow field.
Controlling Separation and Transition: By delaying separation, VGs can lead to a smaller separation region and a more controlled transition to turbulence. This can result in a thinner, more stable wake, reducing pressure drag and improving lift.
Effectiveness and Considerations:
The effectiveness of VGs in mitigating wall effects depends on several factors:

VG Placement and Design: The location, size, and angle of attack of the VGs are crucial for their effectiveness. Optimal placement requires a thorough understanding of the flow field and the specific spanwise flow patterns.
Reynolds Number and Angle of Attack: The performance benefits of VGs might vary with Reynolds number and angle of attack. Optimization for a specific operating range is essential.
Drag Penalty: While VGs can improve lift and reduce pressure drag, they also introduce a small amount of parasitic drag. The overall benefit depends on the trade-off between these factors.
Other Passive Flow Control Devices:
Besides VGs, other passive flow control devices that could be explored include:

Boundary layer trips: These devices promote an earlier transition to turbulence, potentially delaying separation and reducing the size of LSBs.
Trailing edge modifications: Modifying the trailing edge geometry, such as adding serrations or a Gurney flap, can alter the wake structure and improve lift-to-drag ratios.
In conclusion, passive flow control devices like VGs offer a promising avenue for mitigating the negative impact of wall-induced spanwise flows. However, careful design and optimization are crucial for maximizing their effectiveness and achieving the desired aerodynamic improvements.

How can the insights gained from this study be applied to develop more efficient and robust aerodynamic designs for small-scale aircraft and wind turbines operating at low Reynolds numbers?

Answer:
This study provides valuable insights into the complex flow phenomena at transitional Reynolds numbers, crucial for designing efficient and robust small-scale aircraft and wind turbines. Here's how these insights can be applied:
1. Aerodynamic Design Optimization:

Aspect Ratio and Planform Selection: The study highlights the significant impact of aspect ratio and planform shape on separation characteristics. For small-scale aircraft and wind turbines, where wall effects are more pronounced, designers should carefully consider these parameters. Lower aspect ratios might be unavoidable in some applications, necessitating strategies to mitigate the amplified 3D flow features.
Tailoring Airfoil Sections: The study used a NACA 65(1)-412 airfoil, known for its sensitivity to transitional flow phenomena. Designers can use this knowledge to select or tailor airfoil sections that exhibit more desirable stall characteristics and are less prone to large-scale separation at lower Reynolds numbers.
2. Flow Control Implementation:

Strategic Placement of Vortex Generators: The study demonstrates the potential of VGs in mitigating wall-induced spanwise flows. By strategically placing VGs, designers can delay separation, reduce drag, and improve lift, leading to increased efficiency and performance.
Exploration of Other Passive Control Devices: The study encourages the exploration of other passive flow control devices, such as boundary layer trips and trailing edge modifications, to further enhance aerodynamic performance at low Reynolds numbers.
3. Computational Fluid Dynamics (CFD) Validation and Refinement:

Experimental Data for CFD Validation: The detailed experimental measurements, particularly the three-dimensional flow field data, provide valuable validation data for CFD simulations. This validation is crucial for improving the accuracy and reliability of CFD predictions at transitional Reynolds numbers.
Incorporating Wall Effects: The study emphasizes the importance of accurately modeling wall effects in CFD simulations. Designers should ensure their simulations adequately capture the influence of the wall on the flow field, especially for low aspect ratio wings.
4. Robustness and Stability Considerations:

Designing for Flow Unsteadiness: The study reveals the inherent unsteadiness of flows at transitional Reynolds numbers. Designers should consider this unsteadiness when assessing the structural integrity and stability of small-scale aircraft and wind turbines.
Control System Development: Understanding the flow dynamics and potential for flow control can aid in developing robust control systems that can adapt to the changing flow conditions and maintain stability.
5. Wind Turbine Applications:

Optimizing Blade Design: The insights into separation control and three-dimensional flow features are directly applicable to wind turbine blade design. By minimizing flow separation and optimizing blade geometry, designers can enhance energy capture and improve the efficiency of wind turbines operating at lower wind speeds.
Enhancing Turbine Performance: The study's findings can contribute to developing more effective stall control mechanisms for wind turbines, allowing them to operate safely and efficiently across a wider range of wind conditions.
In conclusion, this study provides a deeper understanding of the complex flow phenomena at transitional Reynolds numbers. By applying these insights, designers can develop more efficient, robust, and stable aerodynamic designs for small-scale aircraft and wind turbines, pushing the boundaries of performance in this challenging flow regime.