Here, we present a protocol to observe unsteady vortical flows over a delta wing using a modified smoke flow visualization technique and investigate the mechanism responsible for the oscillations of the leading-edge vortex breakdown locations.
It is well known that the flow field over a delta wing is dominated by a pair of counter rotating leading edge vortices (LEV). However, their mechanism is not well understood. The flow visualization technique is a promising non-intrusive method to illustrate the complex flow field spatially and temporally. A basic flow visualization setup consists of a high-powered laser and optic lenses to generate the laser sheet, a camera, a tracer particle generator, and a data processor. The wind tunnel setup, the specifications of devices involved, and the corresponding parameter settings are dependent on the flow features to be obtained.
Normal smoke wire flow visualization uses a smoke wire to demonstrate the flow streaklines. However, the performance of this method is limited by poor spatial resolution when it is conducted in a complex flow field. Therefore, an improved smoke flow visualization technique has been developed. This technique illustrates the large-scale global LEV flow field and the small-scale shear layer flow structure at the same time, providing a valuable reference for later detailed particle image velocimetry (PIV) measurement.
In this paper, the application of the improved smoke flow visualization and PIV measurement to study the unsteady flow phenomena over a delta wing is demonstrated. The procedure and cautions for conducting the experiment are listed, including wind tunnel setup, data acquisition, and data processing. The representative results show that these two flow visualization methods are effective techniques for investigating the three-dimensional flow field qualitatively and quantitatively.
Flow field measurement via visualization techniques is a basic methodology in fluid engineering. Among the different visualization techniques, smoke wire flow visualization in wind tunnel experiments and dye visualization in water tunnel experiments are the most widely used to illustrate flow structures qualitatively. PIV and laser Doppler anemometry (LDA) are two typical quantitative techniques1.
In smoke wire flow visualization, smoke streaklines are generated from oil droplets on a heating wire or injected from the outer smoke generator/container during the experiments. High-power lights or laser sheets are used to illuminate the smoke streaklines. Images are then recorded for further analysis. This is a simple but very useful flow visualization method2. However, the effectiveness of this method may be limited by various factors, such as the short duration of smoke wires, the complex three-dimensional flow field, the relatively high velocity of the flow, and the efficiency of smoke generation3.
In PIV measurements, a cross-section of a flow field with entrained particles is illuminated by a laser sheet, and instant positions of the particles in this cross-section are captured by a high-speed camera. Within an extremely small time interval, a pair of images is recorded. By dividing the images into a grid of interrogation areas and calculating the average motion of particles in interrogation areas through cross-correlation functions, the instantaneous velocity vector map in this observed cross-section can be obtained. However, it is also known that compromises must be reached for factors including the size of the observation window, the resolution of the velocity map, the velocity magnitude in the plane, the time interval between the pair of images, the orthogonal velocity magnitude, and the particle density4. Therefore, many exploratory experiments may be needed to optimize the experimental settings. It would be expensive and time-consuming to investigate an unknown and complex flow field with PIV measurement alone5,6. Considering the above concerns, a strategy to combine smoke flow visualization and PIV measurement is proposed and demonstrated here to study the complex flow over a slender delta wing.
Numerous studies of LEV flows over delta wings have been conducted7,8, with flow visualization techniques used as the primary tools. Many interesting flow phenomena have been observed: spiral type and bubble type vortex breakdowns9,10, an unsteady shear layer substructure11,12, oscillations of LEV breakdown locations13, and effects of pitching and yaw angles14,15,16 on the flow structures. However, the underlying mechanisms of some unsteady phenomena in the delta wing flows remain unclear7. In this work, the smoke flow visualization is improved using the same seeding particles used in PIV measurement, instead of a smoke wire. This improvement greatly simplifies the operation of the visualization and increases the quality of the images. Based on the results from the improved smoke flow visualization, PIV measurement focuses on those flow fields of interest to acquire the quantitative information.
Here, a detailed description is provided to explain how to conduct a flow visualization experiment in a wind tunnel and to investigate unsteady flow phenomena over a delta wing. Two visualization methods, the improved smoke flow visualization and PIV measurement, are used together in this experiment. The procedure includes step-by-step guidance for device setup and parameter adjustment. Typical results are demonstrated to show the advantage of combining these two methods for measuring the complex flow field spatially and temporally.
1. Wind Tunnel Setup
2. Running the Experiment
3. Data Processing
Figure 2d shows the time histories of the LEV breakdown locations. The black curve indicates the portside LEV and the red curve indicates the starboard LEV. The time scale is nondimensionalized by the free stream velocity and chord length. The correlation coefficient between these two time histories is r = −0.53, indicating a strong anti-symmetric interaction of the LEV breakdown location oscillations. This result agrees well with the work of others13,19,20.
Figure 3 shows the LEV flow structure in the longitudinal cross section at α = 34° and Re = 75,000. The original image was captured by the digital camera in RGB form, with an exposure duration of 1/500 seconds. In this figure, the coordinate is normalized by the delta wing chord length. A 10 mm scale is plotted at the upper right corner for reference. The result clearly demonstrates the primary LEV core, which develops from the tip of the delta wing to the downstream in a straight line. Near the position at x = 0.19 c, the vortex core suddenly expands. This is known as the leading edge vortex breakdown9,21. After the breakdown location, the wake becomes turbulent. Around the primary LEV core are small vortical structures. These substructures originate from the leading edges and swirl around the primary vortex core within the rolling up shear layer12,22,23. As the substructures move into the inner layer of the LEV, their shape is stretched due to the relatively high velocity component in the longitudinal direction near the vortex core. During the experiment, it is noted that the flow structure of the LEV is quite stationary, except at the LEV breakdown location. This result shows that this smoke flow visualization method can achieve a good balance between the local small flow structure and the global flow structure evolution.
Figure 4 shows the typical particle images in a 64 x 64 pixel region, captured from PIV measurement. In the 32 x 32 pixel interrogation area in Frame A, there are 10 identified particles, marked by yellow circles. After the time interval between two frames, these particles displace to new locations, as shown in Frame B. The displacements are about one-quarter of the interrogation area, resulting in an almost 70% overlap between these interrogation areas. Additionally, almost all of the particles remain in the laser sheet plane, indicating that the setup parameters were appropriately chosen for this case.
Figure 5 shows the time-averaged PIV results in the streamwise and spanwise cross sections. Before these measurements are carried out, the improved smoke flow visualization is conducted to identify the primary vortex core position, following steps 2.1.1 – 2.1.3. The coordinates in Figure 5 are normalized by the delta wing chord length c and the local semispan length SL. The vorticity is normalized as ω* = ωU∞/c. According to this result, the primary vortex core can be easily identified by the inflection line of the positive and negative vorticities, and it is marked by the black dotted line. In the upper and bottom regions, the rolling shear layers show large vorticities. The λci criterion24,25 is used to identify the vortices from PIV measurement. In Figure 5, the solid lines illustrate the region with a local swirling strength lower than zero, indicating the existence of vortices. Near the core, the substructures are stretched and do not appear in the swirling strength contour. However, the concentrated vorticity contour still suggests the substructures here, marked by the white dotted line. In Figure 5b, the velocity vector map clearly illustrates that on each side, the flow separates at the leading edge and forms a strong shear layer, which later rolls into the LEV core. Complementary to the flow structure in the streamwise cross section, the spanwise flow structure clearly shows the evolution of the outer vortical substructures.
Figure 1: Schematics of setups. (a) The delta wing model; (b-d) setups for PIV measurement in the longitudinal cross-section, the spanwise cross-section, and the transverse cross-section, respectively. Please click here to view a larger version of this figure.
Figure 2: Measurement of the LEV breakdown location. (a) A smoke flow visualization result showing the leading-edge vortex structure in the transverse cross section: α = 34° and Re = 50,000; the marked area is rotated and further processed. (b) The binary image of the marked area in (a), clearly showing the LEV core and breakdown. (c) The summation of each column in the binary image (b) and the identified LEV breakdown location in the streamwise direction (x-direction), normalized by the chord length c. (d) The time histories of the LEV breakdown locations. is the time-averaged position and is the instant distance to the time-averaged position. Please click here to view a larger version of this figure.
Figure 3: The leading-edge vortex structure in the longitudinal cross section at α = 34° and Re = 75,000, obtained from the smoke flow visualization. Please click here to view a larger version of this figure.
Figure 4: Particle images in a 64 x 64 pixel region. The corresponding interrogation area is 32 x 32 pixels. The time interval between Frames A and B is 80 microseconds. The identified particles in the original interrogation area are marked by yellow circles. Please click here to view a larger version of this figure.
Figure 5: Time-averaged PIV results. (a) Dimensionless vorticity ω* contour with solid lines marking the regions with local swirling strength lower than zero in the longitudinal cross section. (b) Dimensionless vorticity ω* contour with velocity vectors in the spanwise cross section at x = 0.4c; coordinates are normalized by the local semispan length SL (α = 34° and Re = 50,000). Please click here to view a larger version of this figure.
This article presents the two flow visualization methods, improved smoke flow visualization and PIV measurement, to investigate flow structure over the delta wing qualitatively and quantitatively. The general procedures of the experiment are described step by step. The setups of these two methods are almost the same, while the devices involved are different. The basic principle of these two flow visualization methods is to illuminate the particles in the flow via the laser sheet. The improved smoke flow visualization can obtain the global flow structure and small local structures at the same time, which is helpful for obtaining an overview of an unknown flow structure. The quantitative PIV analysis provides a detailed vector map of the interesting flow field. Thus, combining these flow visualization methods can significantly improve research efficiency.
Compared with normal smoke wire flow visualization, the smoke flow visualization method demonstrated here is rather efficiently conducted. Because the particles are uniformly distributed, small flow structures are easily identified. In a complex three-dimensional flow, this method allows the laser sheet to be set up at any spatial position to observe the flow fields in different cross-sections, whereas in the traditional smoke wire method, the laser sheet must always be aligned with the smoke direction and the observation window is accordingly limited26. Additionally, this improved method should not miss any flow details caused by the absence of the smoke in some regions during a smoke wire experiment. However, this method would not be suitable for open-loop wind tunnel facilities due to how seeding is conducted. Flow visualization data should be carefully analyzed to avoid the pitfalls of imaginary illuminations3,27.
Because the flow field over the delta wing is highly three-dimensional and sensitive to any disturbance, non-intrusive investigations are recommended21. For measurements in planes, it is essential to consider the orthogonal velocity component on the observation plane during PIV measurement28,29. In this case, the time interval between two frames and the laser sheet thickness should be a compromise with the orthogonal velocity to ensure that most of the particles do not move out the laser sheet. For similar measurements, it is suggested to run several cases with different setup parameters in advance to identify the most suitable ones.
The flow visualization methods described in this paper are convenient, efficient, and low-cost. In the future, these techniques will be applied to complex flow fields with active flow control, such as bluff body drag reduction and vortex-structure interaction, to evaluate control effects quickly, understand control mechanisms, and accelerate the optimization of control parameters.
The authors have nothing to disclose.
The authors would like to thank Hong Kong Research Grants Council (no. GRF526913), Hong Kong Innovation and Technology Commission (no. ITS/334/15FP), and the US Office of Naval Research Global (no. N00014-16-1-2161) for financial support.
532 nm Nd:YAG laser | Quantel Laser | Evergreen 600mJ | |
High speed camera | Dantec Dynamic | HiSense 4M | |
camera lens | Tamron | SP AF180mm F/3.5 Di | |
PIV recording and processing software | Dantec Dynamic | DynamicStudio | |
cylindrical lens | Newport | Φ=12 mm | |
convex lens | Newport | f=700 mm | |
neutral density filter | Newport | ||
Calibration target | custom made | ||
aerosol generator | TSI | TSI 9307-6 | |
PULSE GENERATOR | Berkeley Nucleonics Corp | BNC 575 | |
continuous laser | APGL-FN-532-1W | ||
Digital camera | Nikon | Nikon D5200 | |
Image processing | Matlab | custom code | |
wind tunnel support | custom made | ||
laser level | BOSCH | GLL3-15X | |
angle meter | BOSCH | GAM220 |