Visualization of vortical flows around a rapidly pitching wing and propeller

Abstract

This study was conducted to visually investigate flows related to fixed-wing vertical-takeoff-and-landing micro air vehicles, using the smoke-wire technique. In particular, the study examines transition between forward flight and near-hover. The experimental model consists of a rigid Zimmerman wing and a propulsion system with contra-rotating propellers arranged in a tractor configuration. The model was pitched about the wing’s aerodynamic center at approximately constant rates using a five-axis robotic arm. Constant-rate pitching angles spanned 20° to 70°. No-pitching and four pitching-rates were used, along with three propulsive settings. Several observations were made during no-pitching tests. Turbulent wakes behind blades and laminar flow between them produces pulsations in the boundary layer. These pulsations alter the boundary layer from a laminar to turbulent state and back. An increase in lift and drag in the presence of a slipstream is a result of competing effects of the propulsive slipstream: (a) suppression of flow separation and increased velocity over the wing and (b) decrease of the effective angle of attack. Higher nose-up pitching-rates generally lead to greater trailing-edge vortex-shedding frequency. Nose-up pitching without a slipstream can lead to the development of a traditional dynamic-stall leading-edge vortex, delaying stall and increasing wing lift. During nose-up pitching, a slipstream can drive periodically shed leading-edge vortices into a larger vortical-structure that circulates over the upper-surface of a wing in a fashion similar to that of a traditional dynamic-stall leading-edge vortex. At lower nose-up pitching-rates, leading-edge vortices form at lower angles of attacks. As a slipstream strengthens, a few things occur: separation wakes diminish, separation occurs at a higher angle of attacks, and downward flow-deflection increases. Similar effects are observed for nose-up pitching, while nose-down pitching produces the opposite effects.

Introduction

The term micro air vehicle (MAV) refers to aircraft that are significantly smaller than conventional aircraft. MAVs typically have a maximum linear dimension between 15 and 30 cm and can be classified according to their mode of flight: fixed-wing, rotary-wing, or flapping-wing. Fixed-wing MAVs typically utilize either a single-propeller, contra-rotating propellers, or counter-rotating propellers and can be remotely controlled, fully autonomous, semi-autonomous, or switchable between the three. MAVs are often used as sensor platforms; carrying cameras, chemical sensors, or anything that is sufficiently small and light. Unlike their larger cousins (UAVs), many MAVs can operate close to the ground, in cluttered environments and even indoors. Some advantages of these small craft include: low visual signatures, high maneuverability, and low-cost manufacturing, maintenance, and storage.

Each of the three classes of MAVs possesses different strengths and weaknesses. Rotary-wing MAVs have the maneuverability and low-speed flight capability necessary to be effective in restrictive operational environments, but they generally lack the range, endurance, payload capacity, and dash speed of their fixed-wing cousins. Conventional fixed-wing craft are incapable of either hovering or operating in cluttered environments. To combine the desirable features of both classes, fixed-wing vertical-takeoff-and-landing (VTOL) MAVs have been developed at the University of Arizona.^1,2

An article written by Shkarayev et al. ² summarizes fixed-wing VTOL MAV aerodynamics and design. A related study by Randall et al. ³ characterized the steady aerodynamics of fixed-wing VTOL MAVs and their propulsion systems from 0° to 90° angle of attack. The study ³ included different freestream velocities, throttle-settings, and elevator deflections and found that the slipstream has a profound effect on wing aerodynamics—delaying stall, increasing lift coefficient, and increasing drag coefficient. Non-dimensional coefficients were also discussed and new coefficient formulations were proposed.

A recent study by Randall et al. ⁴ addressed unsteady forces and moments exerted on a VTOL MAV dynamically pitching at constant rates, spanning 20°–70°. Pitching rates from −114° to +114° per second were used, based on free-flight data presented in a study by Chu et al. ⁵ This study found that propulsion system aerodynamics are not sensitive to pitching-rate, but wing aerodynamics are. For this and the previous study, ⁴ angle of attack during dynamic pitching is defined as the angle between the instantaneous wind tunnel flow direction and the instantaneous root chord-line of the wing. This definition allows for comparison of static and dynamic data. Nose-up pitching was found to delay stall, generally increase wing lift and drag coefficients throughout the angle of attack domain and decrease wing moment coefficient. Nose-down pitching was found to have the opposite effects. Also of note, pitch-damping appeared irrespective of angle of attack effects, and from 30° to 70° for angle of attack (at Re = 86 K), wing aerodynamic efficiency was virtually independent of pitching-rate, throttle-setting, and elevator deflection.

During the course of the previous study, ⁴ several questions were raised related to constituent frequency-signals in the force and moment data. To surmise the nature of the constituent signals, it was necessary to determine whether or not vortex-shedding occurred and, if so, at what frequencies. The present study is something of an extension to the previous study. ⁴ Potential vortex-shedding is investigated via vertical-plane smoke-wire flow visualization; a technique that has been used by many researchers.^6–8 Smoke-wire flow visualization involves coating a thin metal wire with a solution that vaporizes as the wire is heated. Combustion does not take place, so there is no “smoke.” Batill and Mueller ⁹ studied the smoke wire technique and published information related to the selection of smoke wire alloys and solutions.

Smoke-wire techniques were used extensively in studies of unsteady vortical phenomena over stationary and dynamic delta wings. ¹⁰ In a delta wing at high angle of attack, the shear layer emanates from the leading edge and forms the primary vortex. The vortex breakdown occurs downstream near the trailing edge. Spiral and bubble modes of vortex breakdown were identified in the study. ¹¹ Velocity profiles in vortex cross-sections were obtained showing the development of the jet-like core flow before the vortex breaks down into a wake-like structure.

The shear layer instabilities in delta wings form secondary small-scale vortices observed in experiments ¹¹ and numerical studies. ¹² Vortex wandering has been found over the surface of delta wings as well as for wingtips. Gursul and Xie ¹³ showed that this motion is induced by small vortices related to the Kelvin–Helmholtz instability in the shear layer. The shear layer unsteadiness and roll-up are closely linked to the vortex/surface interaction and boundary-layer separation. ¹²

The low aspect ratio wing promotes strong wingtip vortices, therefore, studies of wingtip vortex dynamics are of significant scientific importance for MAV design. Measurements of the near-field of the wingtip vortex were conducted in Igarashi et al. ¹⁴ using stereoscopic PIV. A rectangular wing with a NACA 0012 airfoil was tested in a wind tunnel. The evolution of the wingtip vortex at four downstream locations revealed the interaction of the wake of the wing and the wingtip vortex. By tracking the vortex center, vortex wandering amplitude was determined and its changes with angle of attack were quantified.

Computational modeling and experimental measurements were performed in Khabatta et al. ¹⁵ to investigate flow characteristics around a MAV wing. A highly three-dimensional flow around the wing was found, especially at high angles of attack. Interestingly, the wingtip vortices grow and shrink alternating between wingtips over time.

Experimental PIV results revealed discrepancies in the numerical predictions: a premature large scale separation over the wing surface at near stall angle of attack and much smaller vorticity magnitude within the wingtip vortex.

Experimental studies were conducted ¹⁶ on a MAV model with an inverse Zimmerman wing. The results ³ showed an increase in lift coefficient and delays in stall due to propeller-induced flow, which were confirmed in Arivoli et al. ¹⁶

Choi and Ahn ¹⁷ modeled the flow induced by a pusher propeller and studied its effects on MAV aerodynamic characteristics using Fluent (a CFD code). When the propeller is turned on, flow separation is delayed by 4°–6° and reattachment of separated flow is promoted. Despite changes in the flow structure, lift-to-drag ratio is decreased by 1–2%. Similar results were reported in article. ³

Much can be learned from studies of dynamically pitching airfoils. Visbal and Shang^18,19 noted several qualitative flow features, including the leading-edge vortex (LEV). They found that LEVs develop for nose-up pitching airfoils. They also found that increasing pitching rate made the LEV structure more coherent and moved its center closer to the LE of an airfoil. Visbal and Shang suggested that LEV formation is related to: vorticity diffusion from the surface of the rotating body, an effective angle of attack at the vicinity of the leading edge, as well as time-dependency for both vorticity convection and shear-layer “rolling up.” This time-dependency has been used to explain why LEVs form at higher angles of attack for higher pitching-rates.

The overall objective of this study is to investigate the effect of rapid-pitching on the aerodynamics of fixed-wing VTOL MAVs that utilize a Zimmerman wing and contra-rotating propellers in a tractor configuration. A better understanding of related aerodynamics should lead to improved autopilot control algorithms for autonomous flight-mode transition.

Model and experimental apparatus

The experimental model consists of two main parts: a wing and a propulsion system. The wing has a Zimmerman planform and uses a thin reflexed-airfoil, while the propulsion system features contra-rotating motors and propellers arranged in a tractor configuration. A picture of the disassembled experimental model is provided in Figure 1, and relevant technical information is provided in Table 1. Flow measurements for static tests are performed in the Earth-fixed frame of reference with the origin at the center of the leading edge of the wing as illustrated in Figure 1. Coordinate axes $\overline{x}$ , $\overline{y}$ , and $\overline{z}$ are oriented parallel to freestream and wingspan, and in the vertical direction, respectively. Coordinates are non-dimensionalized by half of the wingspan: $\overline{x}$  = x/l, $\overline{y}$  = y/l, $\overline{z}$  = z/l.

Figure 1.

Experimental model and frame of reference.

Table 1.

Model information.

Wingspan, 2l	252.0 mm
Root chord length	168.0 mm
Mean aerodynamic Chord	142.6 mm
Wing AC location	At root 42 mm aft of Wing LE
Wing area	332.5 cm2
Aspect ratio	1.91
Elevon area	41.0 cm2
Airfoil	S5010-TOP24C-REF
Propellers (2)	APC 140 × 115 mm2

The model has been tested under steady conditions at different facilities, including the University of Arizona low-speed wind tunnel, ¹ the Institut Superieur de l’Aeronautique et de l’Espace, ² the University of Florida’s Research Engineering and Education Facility ⁴ and, at present, a new wind tunnel facility located at the University of Arizona (UA). The new wind tunnel facility at UA is a closed-loop; open-section tunnel that is capable of airspeeds up to 15 m/s. Flow speed is actuated using a variable frequency drive that controls the excitation frequency sent to a 7.5 horsepower motor, which rotates a fan to generate suction. The wind tunnel test section is contained within a small room to minimize potential ambient disturbances on the flow. The area of the nozzle outlet is 0.16 m² and it is 1.24 m away from the diffuser’s inlet. An industrial erector set was installed in the test section (outside of the flow) to mount various experimental apparatus including: a robotic arm, a backdrop, a stopwatch clock, and a pitot-static tube. The outside of the wind tunnel is depicted in Figure 2 and a picture of the test section is provided in Figure 3.

Figure 2.

Wind tunnel exterior.

Figure 3.

Wind tunnel test section.

Of particular importance to this study is the robotic arm used to produce desired model motions. The arm is manufactured by ST Robotics, ²⁰ and it is referred to as the R12. The controller for the robotic arm accepts discretely prescribed positions specified in either Cartesian or joint-angle format. The arm has five rotational axes driven by encoded motors, which allow for feedback-control as well as position recording. The robot is designed similarly to a human arm, including: a waist (for yaw), a shoulder, elbow, and wrist (for pitch), and a hand (for roll). These components are labeled in Figure 4 and specifications are provided in Table 2.

Figure 4.

Joint labels for the R12 robotic arm.

Table 2.

R12 specifications. ¹⁰

Max torque (at hand)	2 N. m
Max payload (at flange)	1000 g
Nominal payload (at flange)	500 g
Nominal repeatability	0.1 mm
Nominal max rates	Shoulder 180°/s Elbow 270°/s Waist 180°/s
Overall length (erect from  base-to-hand)	835 mm

Procedure and processing

Procedure and processing are broken down into three parts, A, B, and C. In part A, the selection of testing parameters is described, including: non-dimensional pitching-rates, advance ratios, angles of attack, and Reynolds number. Part B addresses the setup and specific procedures used during a typical test to produce: desired wind tunnel flow speed, intended model motion, target propeller rotation-rate, adequate “smoke” for visualization, and proper lighting conditions. Part B also addresses image acquisition and video processing. Part C addresses verification of constituent processes and data.

Test parameter selection

This study is a continuation of a previous study, ⁴ for which a test matrix has been published. The previous study’s test matrix was selected based on free-flight data obtained using a successful fixed-wing VTOL MAV and restrictions imposed by the experimental testing system. For this study, non-dimensional pitching-rates, advance ratios, and α for dynamic-pitching match those used in the previous study, namely −0.031 ≤ Ω ≤ 0.031, 0.47 ≤ J ≤ 0.60, and 20 ≤ α ≤ 70°, where α is defined (for our purposes) as the angle between the wind tunnel flow direction and the instantaneous root chord-line of the wing (Figure 1). Reynolds number for the previous study was 86,000, but practical limitations associated with the current testing system limited Reynolds number to 21,500, which will be explained shortly.

Development of a Karman-Vortex Street behind a circular cylinder will occur at a Reynolds number above approximately 40 and may cause significant flow-disturbance downstream of a smoke-wire.^21,22 Thus, there is an upper-limit to the product of wire diameter and freestream velocity. Unfortunately, if a smoke-wire is too thin, it will not hold a sufficient quantity of solution for proper flow visualization, especially when the wire is oriented vertically and gravity pulls the solution downward. Therefore, freestream velocity must be restricted. To allow for as thin a wire as possible, an iterative procedure was employed to develop a superior smoke-wire solution consisting of turbine oil, petroleum jelly, and iron powder. In addition, saw-tooth bends were added to the wire to reduce run-off.

Ultimately, two flow speeds were chosen: 2.5 and 4 m/s corresponding to a model Reynolds number of 21,500 and 34,400, respectively, and to a wire Reynolds number of 30 and 48, respectively. An upgrade to the testing system has been planned for the future, which involves positioning smoke-wire apparatus at the inlet of the wind tunnel’s nozzle, rather than its outlet. Because the nozzle’s contraction ratio is four, repositioning should justify flow speeds up to 10 m/s with the same wire and solution.

Experimental setup and procedure

To determine wind tunnel flow speed, a small pitot-static tube was positioned in the lower-right corner of the nozzle’s exit. Using silicon tubing, the ports on the pitot-tube were connected to two ports on a Honeywell SCXL010DN dynamic pressure gauge. This differential pressure gauge has a range from 0 to 2500 Pa with a sensitivity of 10 mV per 249 Pa. This gave steady readings within  ± 2 Pa range over the testing flow speed range.

This system was verified by eliminating system offset and noise using readings at zero flow conditions. The pressure sensor was connected through Labview hardware to a desktop computer. A virtual instrument (VI) was written to interpret signals from the pressure sensor and output dynamic pressure. Air density was determined using a connected thermocouple and a stand-alone barometer. With density and dynamic pressure known, flow speed was calculated and displayed through the VI.

To produce desired model motions the R12 robotic arm was installed in the open test section of the wind tunnel. Custom attachment hardware was machined to attach the experimental model to the hand of the robotic arm. Digital calipers were used to carefully measure the position of the model’s AC relative to the robot’s hand. Matlab was used to determine coordinate positions and angles needed to produce desired motions. Calculated positions were specified at constant time intervals. Rates of motion were adjusted by changing the length of the time-intervals. Calculated positions and time intervals were sent to the controller via a desktop PC running Robowin software. Desired motions were produced.

Propeller rotation rate was controlled using a signal generator connected to an electronic speed controller (ESC), which connected to three-phase propulsive motors. The ESC received power from an off-board DC power supply, which was set to 11.0 V. Propeller rotation rate was not instantaneously recorded or controlled throughout motions, because the motors were not encoded. Instead, a laser tachometer was setup on a tripod inside the test section. Before each test, the model was positioned at 45° α with the wind on. Throttle-setting was manually adjusted until the desired rotation rate was obtained, and then a test was performed. While throttle-setting did remain nine constant throughout each motion, the aerodynamic load on the propulsive motors changed. As a result, there was some variation of propeller rotation-rate during tests. Variation has been estimated and is presented in Part C.

Smoke-production is a key part of the experimental setup and procedure. A 300 V DC power supply was connected to an external toggle-switch controlling current through two electrical wires. The wires were fixed to the top and bottom of the nozzle outlet and their ends were stripped, soldered, and bent into circular loops. A 34 gauge nichrome wire was bent into a saw-tooth pattern and strung between the two electrical wires. A weight was attached to the lower end of the nichrome wire, which passed freely through the lower-loop of one of the electrical-wires. The power supply was turned on and it “warmed up” to the desired voltage. The toggle-switch was flipped and electrical current passed through the smoke-wire, heating it. As the wire thermally expanded the attached weight maintained constant-tension, reducing vibration and taking up “slack.” The heated wire vaporized the solution, which was carried downstream by the flow.

Several lights were carefully positioned in the test section to properly illuminate “smoke” for visualization. One floodlight shone downward from above the nozzle exit, while another floodlight shone upward from below. Two halogen lights were positioned above and below the diffuser shining toward the nozzle exit. One light was positioned on the floor and was directed toward the side of the experimental model to provide backlight and illuminate two small holes used for model point-tracking.

The images are obtained by two high-speed Phantom V9.1 cameras and the Phantom video acquisition system. The video can be output as Cine and AVI format. The camera could provide 14-bit image depth, and 1000 frames per second at a full resolution of 1632 × 1200 pixels. One camera was positioned carefully on a tripod outside of the test section to acquire side-view images of the model during tests, while the top view of the images was captured by mean of placing the camera over the model facing downward.

Verification of results

Verification was performed at each step of the process to ensure accurate production and measurement of test parameters. Since the pitot-static system was newly installed dynamic pressure results were compared against measurements acquired with a larger pitot tube connected to a manometer. Flow speed measurement proved to be accurate at 2.5 m/s and above (manometer resolution was insufficient to accurately test at speeds below 2.5 m/s).

The maximum error of 7% corresponded to the lowest test speed of 2.5 m/s. The relationship between fan RPM and flow speed was found to be linear.

Since the facility itself is new (December 2011), a brief investigation of flow quality was conducted. Significant growth of shear-layer vortices was discovered, which spoil much of the otherwise useful flow region downstream of the nozzle exit (Figure 5). At a flow speed of 2.5 m/s, shear-layer vortices are shed at a frequency of 13.8 Hz. Shear-layer vortex behavior over different “slices” and flow speeds was studied and a laminar, undisturbed flow region was mapped. As a result, the model was positioned as closely to the nozzle exit as possible, within the undisturbed laminar flow region. Inclusion of vortex generators at the nozzle exit should alleviate the problem in the future.

Figure 5.

Shear layer vortex growth in test section flow.

Another concern was the size of the model relative to the area of the flow region. The wingspan is 252 mm and the width of the nozzle exit is 450 mm. The distance from the trailing-edge of the wing to the tip of the leading propeller is 253 mm, while the height of the nozzle exit is 350 mm. The fit was tight, but ingestion of shear-layer vortices into the slipstream was not observed within the dynamically investigated 20°–70° α range. Other potential proximity effects have been neglected.

Propeller rotation-rate was measured under static conditions for different α to estimate its deviation from target values during dynamic tests. The lowest target rotation-rate (29.6 Hz) had the greatest proportional deviation, as high as 9.5% of its value (Figure 6(a)). Accordingly, there was variation of advance ratio, which is provided in Figure 6(b) for Ω = 0.

Figure 6.

Propulsive variation with α: (a) rotation rate and (b) advance ratio.

Points were added to the video backdrop to provide an absolute frame of reference (Figure 7). Two points were made perfectly horizontal and two points were made perfectly vertical (within 0.1°), using a digital inclinometer. In addition, two holes were drilled into the fuselage of the model and were tracked at each frame using point-tracking software developed by Hedrick. ²³ One point was placed directly over the aerodynamic center (AC) of the wing and the other point was placed near the trailing edge, as seen in Figure 7. Because the flow was essentially horizontal, pitch angle is equal to α, given the definition of α for this study. Pitch angles were determined based on the absolute reference frame, tracked body-fixed points, and the known offset between point-pitch and wing pitch. Accordingly, the location of the AC and α of the wing are known with certainty for each frame.

Figure 7.

Points for motion verification.

Point-tracking was performed for each of the static tests over 100 frames. For static tests, AC position and wing α were intended to be constant. Naturally, some oscillation and noise were observed. For static tests, α never deviated more than 0.96° from its mean value, and position never deviated more than 2.38 mm from its mean value. Maximum deviations occurred at J = undefined, α = − 3°.

Point-tracking was performed for images acquired before, during, and after each dynamic test. A linear curve fit was applied to α vs. time throughout the constant pitching-rate region (20°–70°). The lowest coefficient of determination (R ² ) was 0.99905, which indicates that pitching rate was approximately constant for all tests and was within 0.5°/s of its desired value for all tests. The angle of attack deviation (from its best-fit linear curve) was always less than 1.67°. The worst case of variance and α deviation occurred for Ω = −0.0310, J = 0.47. Maximum deviation of AC position was 5.73 mm. The most severe cases of deviation for static and dynamic tests are depicted in Figure 8. α_d is desired α and linear position deviation (ΔAC) is defined as the linear distance from the mean (x,z) position of the AC, where positive values correspond to z greater than its mean and negative values correspond to z less than its mean. There is an apparent overall drift of approximately 9 mm, which does not appreciably contribute to variation of effective freestream velocity during tests.

Figure 8.

Motion-tracking results for worst-case α and AC deviation: (a) static and (b) dynamic.

An additional step was taken to avoid error during the course of video-processing, editing, and analysis. A stopwatch clock was mounted behind the backdrop and it ran during each test (Figure 7). The smaller numbers denote hundredths of a second and the larger numbers denote seconds. Tests do not start at 00⁰⁰ because the clock was allowed to run continuously as testing was performed. With temporal data embedded directly into each acquired image, results could be verified without regard to outside-image information. Video playback speed and pitching-rate could be determined directly from the videos and flow speed could be estimated (as streaklines first begin to appear).

Results

Results are presented in parts A and B. First, static flow field variation with α is explored as a baseline for interpretation of later static and dynamic results. Phenomena observed during static tests are quantified and discussed, including the effect of propeller rotation-rate on the flow. Next, dynamic results are presented against one another with pitching-rate varied. The effect of non-dimensional pitching rate on the structure of the flow is discussed and quantifiable phenomena are tabulated. Flow-field trends are compared with force trends that were observed and presented in a previous studies.^3,4

Results of static tests

Viewing slow-motion video compilations is probably the most effective means of gaining a qualitative understanding of related flow-fields, but comparing rows and columns of images will have to suffice for the purposes of this article. An array of images corresponding to static conditions (α = constant, no pitching) is provided in Figure 9 for a freestream velocity of 2.5 m/s. Nominally stated α values are expected to be within 1.2° of actual values, based on point-tracking results. The smoke-wire was positioned vertically in front of the nozzle at $\overline{y}$  = 0.05 (see Figure 1).

Figure 9.

Effects of J and α on flow patterns on plane y = 0.05.

The first column of images in Figure 9 corresponds to the no-slipstream case (n = 0 and J = undefined), where propellers have been removed, but the motor and its mount have been retained. There appears to be a separation bubble at 16.5° with fully separated flow and periodic trailing-edge vortex-shedding apparent at 26.5°. When the slipstream is introduced (J = 0.60) separation and reattachment is not apparent until 26.5°, with periodic TE vortex-shedding occurring at 41.0°. For J = 0.47, TE vortex-shedding is not seen to occur until 57.5°. One may conclude that the slipstream delays TE vortex-shedding.

When the flow is separated, regions of rotating fluid form over the top surface of the wing. Induced rotation in the separation region may cause air near the wing’s surface to flow toward the back of the propellers, especially in the presence of a large quasi-stable vortex attached to the leading edge of the wing. These separation regions are typically influenced by periodically shed vortices of varying frequency and are unsteady in nature.

Recall that the smoke-wire was offset from the centerline of the model by 6 mm. As a result, there is a spanwise flow at high α, which causes some streaklines to separate away from the wing-root. Consequently, for J = 0.47, α = 67.0° there are two “layers” of observable flow. Flow near the root of the wing at the LE is swept into a near-wake circulating region, but away from the wing-root LE vortices separate and convect downstream with the flow.

General observations may be made about the slipstream. For visualized flow three obvious things happen as the strength of the slipstream is increased: (a) the size and extent of each separation wake is diminished, (b) separation occurs at a higher α, and (c) downward deflection of the flow increases, even when separated. Therefore, it may be concluded that the slipstream significantly reduces the severity of flow separation, delays stall, and increases lift. The effect of the slipstream on stall-delay and wing lift has been noted by Kuhn and Draper ²⁴ and by the present authors in previous studies.^3,4

Another interesting flow feature is observable from Figure 9. As the α of the wing is increased to very high values, oncoming flow is displaced both downward and upward as it moves around the wing (as seen for J = undefined, α = 86°). This up/down deflection is also observed when the slipstream is present. Notice that flow can enter the propeller discs from behind when the wing is present, which is most apparent at J = 0.47, α = 86°. For that case, streakline curvature over the top of the propeller discs is extreme and the flow above the wing is forced downward toward its LE. This dramatic example suggests that the wing may significantly affect propulsion-system aerodynamics, especially at high α. The effect of the wing on the aerodynamics of the propulsion system has been neglected in previous studies,^1,3–5 which may have introduced some error, particularly at high α. Wing-propulsion system coupling should be studied further; in the future, a balance should be placed between the wing and the propulsion system to obtain aerodynamic forces on separate components, simultaneously.

Table 3 is provided to summarize phenomena observed under different conditions for static flow fields. Tables 4 and 5 allow for trend-extrapolation.

Table 3.

Summary of description of flow-fields for Ω = 0.

α/J	Undefined	0.60	0.47
−3.5	Attached flow	Attached flow	Attached flow
16.5	Separation bubble	Attached flow	Attached flow
26.5	Separated flow vortex-shedding from TE	Attached flow	Attached flow
41.0	Separated flow vortex-shedding from LE, TE	Separated flow vortex-shedding from TE	Attached flow (upper surface) Vortex-shedding from TE
57.5	Separated flow vortex-shedding from LE, TE Streaklines bend out-of-plane	Separated flow vortex-shedding from LE, TE	Separated flow vortex-shedding from TE
	toward wingtip	Streaklines bending out-of-plane toward wingtip	Streaklines bend out-of-plane toward wingtip
67.0	Separated flow vortex-shedding from LE, TE Streaklines bend out-of-plane	Separated flow vortex-shedding from LE, TE	Separated flow vortex-shedding from LE, TE
	toward wingtip	Streaklines bending out-of-plane toward wingtip	Streaklines bending out-of-plane toward wingtip
86.0	Separated flow vortex-shedding from LE, TE Streaklines bend out-of-plane	Separated flow vortex-shedding from LE, TE	Separated flow vortex-shedding from LE, TE Streaklines bend out-of-plane
	toward wingtip Approximate wake symmetry	Streaklines bending out-of-plane toward wingtip	toward wingtip

Table 4.

Approximate leading-edge vortex-shedding frequency for Ω = 0 (Hz).

α/J	Undef	0.60	0.47
26.5	–	–	–
41.0	10.9	–	–
57.5	17.9	6.4	–
67.0	39.3	4.6	7.1
86.0	Undet	5.7	8.6

Table 5.

Approximate trailing-edge vortex-shedding frequency for Ω = 0 (Hz).

α/J	Undef	0.60	0.47
26.5	8.0	–	–
41.0	7.0	8.6	–
57.5	5.2	7.9	9.2
67.0	5.6	7.2	6.8
86.0	6.0	5.7	5.2

Table 4 suggests that the frequency of LE vortex-shedding generally increases with α. This does not appear to agree with expectation, based on Strouhal number for an inclined flat plate.

Table 5 suggests that the frequency of TE vortex-shedding decreases with α, which agrees with expectation based on Strouhal number for an inclined flat plate. Table 5 suggests that the slipstream generally increases TE vortex-shedding frequency, except at 86°.

In order to investigate three-dimensional flow effects over the wing, a series of tests was performed at eight different spanwise cross-sections. Flow pictures were obtained in vertical planes from $\overline{y}$  = 0.125 to $\overline{y}$  = 1.0 at increments of 0.125. Recall that propellers were removed in the previous no-slipstream tests. In the present series of tests, propellers have been fixed in the vertical position. Also, the initial position of the smoke wire was set at y = 0.125.

The wind tunnel speed was set at 4 m/s. More details of the flow are seen at higher wind tunnel speed when Figures 10 and 11 are compared to Figure 9. Figure 10 presents images of flow patterns at α = 16.5°. Under no-slipstream conditions, a small leading edge separation bubble is seen over the inner part of the wing at $\overline{y}$  ≤ 0.25. Similar flow patterns were observed in Figure 9 for the same angle of attack. Shortly after the flow reattachment, the boundary layer separates again through the trailing edge.

Figure 10.

Spanwise changes in flow at α = 16.5°.

Figure 11.

Spanwise changes in flow at α = 26.5°.

For no-slipstream experiments at $\overline{y}$  ≥ 0.25, the laminar boundary layer on the suction side separates completely and the instability waves develop in the upper shear layer (Kelvin–Helmoholtz instabilities). These waves roll up to form small-scale vortices.

The leading edge bubble disappears and flow patterns radically change when the propulsion system is turned on.

One benefit of the tractor-propeller configuration is the suppression of flow separation. The wing now is submerged in a slipstream following its contour. It results in flow reattachment on the upper surface. The four blades of the two propellers intersect the smoke plane creating disturbances in flow patterns. These disturbances consist of blade tip vortices and blade wakes. Their periodicity depends on the free stream velocity and on the propeller-induced pulsating slipstream. Traces of blade wakes are turbulent and inclined to the wing surface. The latter can be explained by a non-uniform propeller-induced velocity distribution. Specifically, the velocity profile behind propeller exhibits a single-hump shape, with the maximum of velocity near the midpoint of a blade. ² Streaklines between propeller wakes are well-defined and laminar. Turbulent wakes behind blades and laminar flow between them produce pulsations in the boundary layer. Effects of propeller-induced pulsations on the boundary layer velocity profile were observed in Miley et al. ²⁵ These pulsations alter the boundary layer from a laminar to turbulent state and back.

The slipstream diminishes and flow separates outboard the station of $\overline{y}$  = 0.625, which is behind the propeller blade tip line $\overline{y}$  = 0.55. Also, the current propulsion system consists of two propellers and does not produce a swirling slipstream. However, as seen in Figure 10, the flow separation region is smaller than in the no-slipstream case at the same distance, which can be explained by a spanwise flow generated by the propellers.

The outer area of the wing $\overline{y}$  ≥ 0.875 is affected by the wingtip vortex flow as seen in Figures 10 and 12. In the top view setup in Figure 12, the smoke wire was positioned vertically in front of the nozzle of the wind tunnel and aligned with the wingtip at $\overline{x}$  = 1.5 and $\overline{y}$  = 1. According to Figure 12 for J = undefined, the wingtip vortex is weak and covers a relatively small region. With the power on, the wingtip vortex is stronger and is expended for lower advance ratio. This stronger vortex system interacts with the longitudinal flow circulation by entraining a separated flow. It results in a decrease of the size of the flow separation area at $\overline{y}$  = 0.875 and $\overline{y}$  = 1 as observed in Figure 10.

Figure 12.

Top view of wingtip vortices.

Images of a flow over the wing at α = 26.5° are presented in Figure 11. Contrasting the previous case for propulsion-off at α = 16.5°, there is no leading edge bubble in the inner region of the wing. The flow separates at the sharp leading edge and trailing edge corners.

When the power is turned on, the flow reattaches and redevelops over the upper surface of the inner region of the wing $\overline{y}$  ≤ 0.375 (see also Figure 9). The flow becomes more turbulent in close proximity to the upper surface and at the stronger slipstream corresponding to J = 0.47.

Flow separates at $\overline{y}$  = 0.50 and J = 0.6, but reattaches near the trailing edge at the next section $\overline{y}$  = 0.625 forming a separation bubble. Wingtip vortices are entrained into the separation flow nearby the wingtip accelerating the mixing in downstream flow. Owing to the wingtip induced mixing, the separated flow shortly reattaches after getting separated. For the stronger slipstream (J = 0.47), the reattachment point moves toward the leading edge because more energy is entrained into the separated flow by stronger wingtip vortices as explained in following.

The curling of flow around the trailing edge and wingtip can be clearly seen in Figure 11 in the presence of a slipstream at $\overline{y}$  = 0.625. From Figure 12 and similarly to the case of α = 16.5°, the strength of the spiral motion of the streamline increases with an increase of propeller rotation speed (advance ratio decrease). At α = 26.5°, the region covered by wingtip vortices becomes slightly larger than the case of 16.5°.

Presented discussion on flow patterns over the wing with propellers can provide some explanations and insights to the aerodynamic force measurement results. ³ The inner part of the wing covered by the slipstream represents 64% of the wing area. Therefore, it is reasonable to assume that flow over the inner part of the wing contributes the most to aerodynamic force production.

When a slipstream is present, streaklines bend downward behind the blades and approach the leading edge at an angle that is smaller than in the no-slipstream case, as depicted in Figures 10 and 11. This angle is an effective angle of attack that the wing sees near its leading edge. Figures 10 and 11 show that the effective angle of attack is smaller with a slipstream present, as compared to the no-slipstream case. The reduction in AOA is greater at higher angles of attack.

There are two competing effects of the propulsive slipstream on wing aerodynamics: (a) suppression of flow separation and increased velocity over the wing and (b) decrease of the effective angle of attack. The lift increases with a suppression of flow separation and speed increase. The drag force decreases with the flow reattached, but increases with the speed increase. Both lift and drag decrease with the effective angle of attack decrease.

In Randall et al., ³ lift and drag forces were measured on the current wing-propeller model at a wind tunnel velocity of 5 m/s. Also, the throttle was set to 55% and 65%, which approximately correspond to advance ratios of J = 0.6 and 0.47, respectively. Lift and drag coefficients are provided in Tables 6 and 7, respectively. They were generated based on force data ³ by using wind tunnel velocity ³ of 5 m/s. Correlations of the force coefficients s with observed features in flow structures are sought in the following discussion. Results for α = 16.5° show that for slipstream as compared to the no-slipstream case values of lift (see Table 6) are within 3% of each other and values of drag coefficient increase almost twice (see Table 7). Evidently, an increase in the speed is countered by a decrease in the effective angle of attack. The total flow produces significant increase in a drag, as compared to the no-slipstream case.

Table 6.

Lift coefficients ³ for Ω = 0 (Hz).

α/J	Undef	0.60	0.47
16.5	0.711	0.733	0.714
26.5	0.649	1.309	1.317

Table 7.

Drag coefficients ³ for Ω = 0 (Hz).

α/J	Undef	0.60	0.47
16.5	0.162	0.153	0.242
26.5	0.268	0.589	0.739

Data presented in Tables 6 and 7 for α = 26.5° show that lift and drag at J = 0.47 are much higher, as compared to the no-slipstream case. The significant increase in lift coefficient can be attributed to a relative increase in effective angle of attack (even though it is still smaller than α), as seen from comparison of Figure 11 to 10 along with suppression of flow separation and flow speed increase.

Dynamic results

Point-tracking was used for Figures 13–17 to precisely identify frames corresponding to desired model α within 0.3° of nominally stated values. Figure 15 shows the effect of the slipstream at Ω = + 0.0310 and Ω = −0.0310.

Figure 13.

Effect of J and α: (a) Ω = + 0.0310 and (b) Ω = −0.0310.

Figure 14.

Effect of Ω for J = undef.

Figure 15.

Effect of Ω for J = 0.60.

An attached leading edge vortex (LEV) is a common feature of dynamic stall for airfoils during nose-up pitching.^10,11 At α = 30° for J = undefined (Figure 13(a)), a separation bubble is evolving into a nascent LEV. For J = 0.60, there is a shadow over the leading edge, which is turbulent flow coming off of the motor and its mount. The flow remains fully attached to the upper-surface of the wing. At J = 0.47, there is no visible wake behind the motor and the flow remains fully attached.

Looking at positive-pitching (Figure 13(a)) for α = 45°, the J = undefined case features a salient LEV covering the entire upper-surface of the wing. At J = 0.60, there is a recirculation region over the upper-surface of the wing, which we will refer to as a “quasi-LEV.” The quasi-LEV is quasi-steady in the sense that it evolves relatively smoothly as the wing pitches. At J = 0.47, the visualized flow remains fully attached to the wing’s upper-surface.

For the J = undefined case at α = 60°, the flow forms a large LEV; TE vortices begins to impinge on the LEV, which separates at 68°. At J = 0.60, there is a quasi-LEV recirculation region above the wing. For J = 0.47, the flow remains attached at the root of the wing, while further outboard the flow fully separates from the leading edge and convects downstream, effectively dividing the flow field into two distinct regions. Notice that the slipstream reduces the coherence and distinction of LEVs during nose-up pitching.

For separated slipstream-absent nose-down pitching (Figure 13(b), first column), the flow over the upper-surface of the wing mixes as LE and TE vortices are periodically shed. Nothing like an LEV forms, and there are no well-defined LEVs for the static cases presented in Figure 9.

Broadly viewing Figure 13 shows that the slipstream has clear effects on the flow, regardless of pitching-rate. Relative to the no-slipstream case, the slipstream: delays flow-separation, hastens flow reattachment, reduces the severity and extent of wakes, and causes greater downward-deflection of the flow, which is particularly apparent comparing J = undef with J = 0.47 for the Ω = − 0.0310, α = 60° case. These observations suggest that the wing will experience delayed stall and greater lift when the slipstream is present, even during dynamic-pitching. The suggestion has been confirmed by previously acquired force-data. ⁴

Figure 14 describes the effect of pitching on the aerodynamics of the wing, without the presence of a slipstream. In Figure 14, at Ω = 0.0310, the LEV starts developing at 30° and is seen to cover the entire upper-surface of the wing by 45°. More precisely, videos show that the LEV recirculation-region covers the entire upper-surface of the wing at 33.8° and is shed at 68.0°. For Ω = 0.0155, the LEV covers the entire upper-surface at a lower α = 27.5° and it is shed at a lower α = 61.5°. This suggests that LEVs develop sooner at lower positive pitching-rates for this three-dimensional case, in agreement with previous studies involving dynamically pitching airfoils.^10,11

Figure 14 includes both positive and negative pitching-rate flow fields. It is apparent that positive pitching-rates produce greater downward deflection of streaklines and wakes, implying greater lift. Positive-rate fields also have smaller wake-regions. These observations are also true relative to static cases (Figure 9). For example, at α = 26.5°, the static-case flow is fully separated, while flow is reattached during upward pitching at Ω = + 0.0310, α = 30°. Furthermore, for Ω = +0.0310 at α = 60°, the LEV dramatically increases downward deflection of the flow, as compared to Ω = 0°, α = 57.5° (Figure 11). Figure 14 showcases the benefits of positive-pitching, which increase as pitching-rate increases. We conclude that positive-pitching leads to development of an attached stable LEV that delays stall and increases maximum lift. This agrees with previously published force data. ⁴

Turning to negative-rates (nose-down pitching), flow field images suggests that negative-rate pitching has a generally deleterious effect on wing lift because flow separates at a lower α and there is less downward deflection at a given α. Accordingly, one would expect hastened stall and lower lift relative to zero and positive pitching-rate flows (referenced to α). This has been confirmed in a previous study. ⁴

Changes in the visualized field with pitching-rate become less-pronounced when the slipstream is introduced (Figure 15), but they are noticeable. At 45°, the flow just above the wing for Ω > 0 begins to resemble a quasi-LEV. Quasi-LEVs are strongest at 60°. Some previously noted trends hold: higher nose-up pitching-rate results in less-severe wakes and greater downward flow deflection. Positive-pitching provides a beneficial boost to wing-lift even in the presence of a slipstream. Negative pitching has a deleterious effect on wing lift and stall α, even in the presence of a slipstream. These assertions have been verified via force-data presented in our previous study. ⁴ Careful observation of the flow in the vicinity of the propulsion system, at different pitching-rates, suggests that rapid-pitching has little affect on propulsion system aerodynamics because flow structure, streakline direction, and streakline curvature is similar throughout. The suggestion is supported by our previous study, ⁴ for which propulsive thrust was always within 10% of its Ω = 0 value and propulsive normal force was always within 0.1 N of its Ω = 0 value; also, propulsive moment was found to be insensitive to pitching-rate.

At Ω = +0.0155 and α = 60°, the propulsive jet helps to drive flow around the periphery of a quasi-LEV, with some of the flow becoming entrained (increasing the size of the quasi-LEV) and with some of the flow deflected downward, and convecting downstream. Because this is difficult to resolve in Figure 15, an enlarged image is provided in Figure 16 for clarification. Note the absorption of periodically shed LE-vortices into the larger quasi-LEV structure.

Figure 16.

Slipstream interaction with quasi-LEV for Ω = 0.0155 and α = 60°.

Figure 17.

Effect of Ω for J = 0.47.

Figure 17 examines pitching-rate effects at the strongest slipstream setting, J = 0.47. The most interesting behavior occurs at α = 60°. For Ω = +0.0310, the flow circulates in the slipstream region, but outside of the region flow separates from the LE and convects downstream. At + 0.0155, flow sheds from the LE of the wing and circulates over its top surface. At − 0.0155, streaklines are periodically shed from the LE of the wing, forming diffuse vortices while more-salient vortices are shed from the TE. Previous conclusions hold with regard to pitching-rate effects.

Since various flow events, including periodic phenomenon, are observable in acquired videos, it is natural to tabulate related data and extrapolate trends. There is some subjectivity in interpreting precise moments at which events take place, such as the onset of reattachment. Accordingly, values presented in Tables 4–7 should be viewed as approximate.

Flow separation from the leading-edge of the wing was observed at different α under different conditions. Observations were limited to regions illuminated by the smoke, so flow separation may have occurred at different α in unilluminated regions. The lowest α for observed LE flow separation is presented in Table 8. Note that during nose-down pitching the flow begins in a separated condition and appears to reattach as α is reduced. One clear trend is observable from Table 8—a stronger slipstream results in attached flow at a higher α, implying that the slipstream has a stall-delaying/reattachment-hastening effect, in agreement with published force-data.^3,4 When the slipstream is absent, nose-up pitching seems to delay LE flow separation and nose-down pitching seems to hasten it. During nose-down pitching the LE of the wing moves downward, increasing the upward component of “effective” freestream velocity in the vicinity of the LE. This increases the effective angle of attack there, causing separation at a lower pitch-angle. When the slipstream blows over the LE, there is no clear trend with regard to observed LE flow separation and pitching-rate. Unfortunately, we were unable to reliably determine approximate mean-frequencies for observed leading-edge vortex-shedding.

Table 8.

Lowest α for observed flow separation at leading-edge (Hz).

Ω/J	Undef	0.060	0.47
+0.0310	18.7	35.4	50.4
+0.0155	19.4	35.5	44.5
−0.0310	14.5	35.7	48.6
−0.0155	15.9	37.9	50.0

Table 9 provides estimates of the α at which TE vortex-shedding begins. As pitching rate increases, so too does the lowest α for observed TE vortex-shedding, especially when the slipstream is absent. This suggests that increasing pitching-rate delays TE vortex-shedding (referenced to α). Generally speaking, the stronger the slipstream, the higher the α at which TE vortex-shedding becomes observable.

Table 9.

Lowest α (°) for observed trailing-edge vortex-shedding.

Ω/J	Undef	0.060	0.47
+0.0310	40.8	37.2	39.0
+0.0155	28.6	32.5	40.5
−0.0155	15.2	32.1	33.0
−0.0310	17.2	31.9	37.5

Because the model is changing its α, during dynamic tests, the frequency of vortex-shedding varies. For constant pitching-rate motions, the mean frequency of trailing-edge vortex-shedding was estimated over α at which it was observable (Table 10). The general trend is that higher positive pitching-rate leads to greater TE vortex-shedding frequency, especially for the slipstream-absent case. This makes sense, as nose-up pitching forces the TE toward the oncoming flow increasing the “effective” freestream velocity in the vicinity of the TE. The flat-plate Strouhal number formulation suggests that higher freestream velocity should increase vortex-shedding frequency, when other parameters are held constant.

Table 10.

Mean frequency of observed trailing-edge vortex-shedding (Hz).

Ω/J	Undef	0.060	0.47
+0.0310	12.7	6.6	9.6
+0.0155	10.3	9.2	14.3
−0.0155	7.8	8.9	6.4
−0.0310	7.5	4.6	6.5

Conclusions

MAVs are small aircraft that can fulfill many practical operational roles when used as sensor platforms. Different MAVs use different devices for lift generation, including: fixed, rotary, and flapping wings. Fixed-wing VTOL MAVs combine the advantages of both fixed and rotary-wing MAVs. Autonomous operation is desirable and has been successfully demonstrated for some, but not all, flight conditions. Aerodynamic research was conducted toward improving understanding of the transition-maneuver, which involves rapid-pitching. Improved understanding should lead to improved autonomous-execution of rapid-pitching maneuvers.

The static (Ω = 0) cases explored in this study led to several conclusions. A contra-rotating slipstream blowing over the LE of a wing can cause a delay in the onset of TE vortex-shedding within its vicinity, and it generally increases the frequency at which TE vortices are shed. TE vortex-shedding frequency decreases with increasing α. There is no conclusive trend in the effect of the slipstream on LE vortex-shedding frequency, but LE vortex-shedding frequency seems to increase with α. Three things happen to the flow field as the slipstream is strengthened: (a) separation wakes diminish, (b) separation occurs at a higher α, and (c) downward deflection of the flow increases. Due to circulation in the wake, flow may travel upward from the TE of the wing toward the LE of the wing within the slipstream region. Last, the wing may significantly affect flow in the vicinity of the propellers, especially at high α. Accordingly, related interference should not be neglected, unless investigated further.

Three-dimensional effects in flow over the wing with running propeller were investigated. A series of tests was performed for two values of α (16.5° and 26.5°) at eight vertical cross-sections placed spanwise. The blades of the propellers intersect the smoke plane creating disturbances in flow patterns. These disturbances consist of blade tip vortices and blade wakes. Traces of blade wakes are turbulent and inclined to the wing surface. The latter can be explained by a non-uniform propeller-induced velocity distribution. Streaklines between propeller wakes are well-defined and laminar. Turbulent wakes behind blades and laminar flow between them produce pulsations in the boundary layer. These pulsations alter the boundary layer from a laminar to turbulent state and back.

The slipstream diminishes and flow separates in the outer area of the wing. Due to the spanwise flows generated by the propellers, the outboard flow separation region is smaller when there is a slipstream. The slipstream is not the only factor influencing reattachment in the outer area. Other contributing factors are wingtip vortices, which are entrained into the separated flow near the wingtip. They accelerate mixing in downstream flow. From the flow patterns on the top view, it was found that the strength of the spiral motion of the streamline increases with increasing propeller rotation rate.

Correlations exist between features in flow patterns and aerodynamic forces. It was observed that a slipstream effective angle of attack reduces and the reduction is smaller at higher angles. For α = 16.5°, an increase in the speed is countered by a decrease in the effective angle of attack. The total flow with a slipstream produces small changes in lift and drag, as compared to the no-slipstream case. At α = 26.5° in the presence of a slipstream, significant increase in lift and drag is attributed to a smaller decrease in effective angle of attack along with a suppression of flow separation and an increase in flow speed.

Nonzero pitching-rate tests also lead to several conclusions. Positive-pitching without a slipstream may lead to development of a stable LEV and a contra-rotating propulsive jet may help to drive flow around the periphery of a quasi-LEV, with some flow becoming entrained and with some flow deflecting downward and convecting downstream. Higher positive pitching-rate generally leads to greater TE vortex-shedding frequency, especially when the slipstream is absent. Nose-up pitching delays stall and increases downward flow deflection, while nose-down pitching hastens stall and reduces downward flow deflection. These observations hold true regardless of pitching-rate or slipstream strength. As with static cases, a stronger slipstream results in attached flow at a higher α, which implies that the slipstream has a stall-delaying/reattachment-hastening effect.