Topology of a Trailing Vortex Flow Field with Steady Circulation ...

AIAA 2015-1706 AIAA SciTech 5-9 January 2015, Kissimmee, Florida 53rd AIAA Aerospace Sciences Meeting

Topology of a Trailing Vortex Flow Field with Steady Circulation Control Blowing Adam M. Edstrand∗ and Louis N. Cattafesta III†

Downloaded by Louis Cattafesta on June 12, 2016 | http://arc.aiaa.org | DOI: 10.2514/6.2015-1706

Florida State University, Florida Center for Advanced Aero-Propulsion, Tallahassee, FL 32310, USA

Trailing vortices adversely affect many applications and are robust to control efforts. In this study, a 1 mm slot placed along the suction-side of the airfoil tip spans 70% of the chord that blows pressurized air in the spanwise direction in an attempt to oppose the vortex motion via the Coanda effect. First, this experimental study uses stereo particle image velocimetry to observe the effects of different control levels along surface of the wing. These results show that the control jet appears to behave more akin to a jet in crossflow, bending backwards and rolling up with the vortex rather than oppose the vortex motion. The vortex separates from the surface further upstream (relative to the baseline case) with increased turbulent kinetic energy within the core. Investigation into the intermediate field shows a larger, more diffuse vortex relative to the baseline case. This diffuse vortex reduces the wake-hazard by as much as 40% in the first 5 chords downstream, potentially improving aircraft safety.

I.

Introduction

Trailing vortices are caused by equalizing pressure at the tip of a finite wing. These vortices cause adverse effects such as increased drag, increased wake hazard, and reduced stealth in maritime applications.1, 2 Induced drag is created because the vortex redirects streamwise velocity to transverse downward velocity. This downward velocity reduces the effective angle attack by effectively tilts the lift vector aft, resulting in a drag component. These vortices are hazardous because the transverse momentum may be transferred to trailing aircraft that could cause a destabilizing rolling moment resulting in a crash. In addition, these vortices persist far downstream, leaving a long footprint, making them detectible in maritime applications when stealth is desired. Research efforts to reduce the strength of these vortices have only been modestly successful due to the stable nature of the vortices. Despite the high Reynolds number of flight, these vortices re-laminarize because of the solid-body rotation of the vortex core decaying the turbulence within the core.3 There are two primary philosophies of vortex control: instability excitation and turbulence injection into the core. For instability excitation, the Crow instability4 is usually excited through displacement of the vortex in a manner that accelerates the growth of this instability.5 Turbulence injection attempts to reduce the vorticity by enhancing the mixing of the vortex within the core. Which method is superior remains controversial. In the present study, we address the flow topology of a trailing vortex when spanwise blowing along the suction side of the wingtip is introduced. Examining the literature, initial work showed that blowing along the symmetry line in the spanwise direction increased the effective aspect ratio of the wing.6 This blowing resulted in changes in aerodynamic forces on the aircraft. Many other studies included spanwise blowing using discrete jets,7, 8 including a computational study,9 that showed promising results. Unsteady pulsing has also been investigated8, 10 showing similar benefits for reduced (or zero) mass flow rate. More recently, an extensive parametric study by applying blowing at the wingtip in various directions and for various tip geometries is performed. The results indicated that usually (but not always) slots positioned on the pressureside resulted in a more diffuse vortex.11 In addition, a novel method that exploited the controllability of a separated shear layer through zero mass-flux perturbations to control the vortex, which resulted with control ∗ Graduate † Eminent

Student, Department of Mechanical Engineering, Member, AIAA Scholar & Professor, Department of Mechanical Engineering, Associate Fellow, AIAA

1 of 15 American Institute of Aeronautics and Astronautics Copyright © 2015 by Adam Edstrand. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

z y

Ujet

y

U∞

x

z

Cross-sectional view


Figure 1. Schematic of the trailing vortex model with the coordinate system presented. Note the coordinate system is fixed when the airfoil is at 0◦ angle of attack. The plane shows a schematic of the cross-section of the internal plenum of the airfoil.

of the vortex position and axial velocity deficit.12 Despite these research efforts, trailing vortices continue to persist in practical application. In this paper, we perform an experimental study on the effect of spanwise blowing from a slot on the suction side of a wingtip on the trailing vortex (Figure 1). Stereo particle image velocimetry measurements along the airfoil surface and in the intermediate field provide physical insight into how the control is affecting the development of the vortex. In the next section, we provide the experimental setup and methodology. Then, we present and discuss the results, emphasizing the physical insight drawn from the near field measurements. Then, we look at the control’s effect on quantitative metrics. Last, we summarize the results and draw conclusions.

II.

Experimental Setup and Methodology

This section describes the experimental setup. First, the model is presented and the control methodology and parameters are provided. Second, we present the static characterization to quantify the control we are applying into the flowfield. Third, the Florida State Anechoic Tunnel (FSAT) is introduced. Then, the stereo particle image velocimetry (SPIV) setup is presented and the processing parameters of the SPIV are discussed. Last, the metrics for various adverse effects are introduced and discussed. A.

Wing Model

All test cases are performed at a chord Reynolds number of 530k, corresponding to a test-section speed of 27 m/s. The trailing vortex is generated by a NACA0012 with a chord of c = 0.3048 m and a half-span of b/2 = 0.3810 m positioned at an angle of attack of 5◦ . When the angle of attack is varied, the airfoil rotates about the quarter-chord point. The wingtip is a half-revolution of the airfoil’s profile, resulting with a rounded wingtip. A nominally 1 mm slot located on the suction-side of the airfoil spans from the leading edge to 70% of the chord. Pressurized air issues from the slot tangentially to the rounded trailing edge. Without freestream velocity, the jet then wraps around the wingtip due to the Coanda effect, ideally counteracting the vortex motion during testing. The wing is mounted to the ceiling of the closed test section configuration of the Florida State Aeroacoustic Tunnel described below. For the baseline flow configuration, the slot is taped shut to prevent the influence of Helmholtz resonance caused by the dynamics of the slot and the plenum. To expel air from the slot, the interior of the airfoil is a pressurized plenum ranging from 0 to 1 psig. Air is initially pressurized to 150 psig by a compressor and is then reduced to 30 psig with a coarse adjustment pressure regulator. The air then passes through a filter with a resistance temperature detector attached for temperature measurements. The air then flows through a long straight pipe and a Venturi meter to measure mass flow rate. Downstream of the Venturi meter, a precision pressure regulator is used for fine tuning of the pressure within the plenum. To protect the system from accidental over-pressurization, a 4 psi pressure relief 2 of 15 American Institute of Aeronautics and Astronautics

valve is connected in parallel to a 3.66 m long 3.81 cm diameter hose that guides the air into a transition piece attached to the root of the airfoil. The transition piece connects the round hose to the square entrance at the root of the airfoil. Within the plenum, a miniature Pitot tube measures the stagnation pressure within the plenum. The air then continues through the plenum, reaching the slot at the wingtip. The control must be quantified by some input parameter. For circulation control airfoils, the input is commonly determined in terms of momentum flux through the slot normalized by the momentum of the flow about the airfoil. This is given by the non-dimensional momentum coefficient


Cµ =

m ˙ jet Ujet q∞ S

(1)

where m ˙ jet denotes the mass flow rate through the slot, Ujet denotes the speed of the jet exiting the slot, q∞ denotes the freestream dynamic pressure, and S denotes the planform area of the wing. When examining the quantitative metrics, two blowing configurations are explored, both shown in Figure 2. The first, termed the uniform blowing configuration, consists of the jet issuing from the entire length of the slot. In the second, termed the segmented blowing configuration, the jet blows from the slot in a chordwise periodic manner. The spacing is determined by matching the wavelength of the secondary instability of flow over a cylinder.13 Because the radius of the “cylinder” is varying, the average radius across the slot region is used. From this result, the spacing is λs ≈ 0.03 m.

Ujet

Ujet

U∞

U∞

(a) Uniform Blowing Configuration

(b) Segmented Blowing Configuration

Figure 2. Schematic of the (a) uniform blowing configuration and (b) segmented blowing configuration. For the segmented blowing configuration, tape covers the slot at a spacing of λs ≈ .03 m corresponding to the wavelength of the secondary instability of flow over a cylinder.13

It is also important to define the different regions of the vortex development. Along the airfoil surface, the vortex develops in what we term the near field of the vortex. As the vortex reaches the trailing edge, it separates from the wing, ending the near field and beginning the intermediate field. In the intermediate field, the vortex sheet and vortex are clearly present. When the vortex sheet fully rolls up into the vortex, the intermediate field ends and the vortex enters the far field. In the far field, the vortex is fully rolled up and self-similar.3 B.

Static Characterization

It is important to quantify the control’s input to the overall system. To do this, a static characterization is performed in a bench-top setup. Constant temperature anemometry (CTA) is used to measure the jet velocity leaving the slot. A hotwire probe is placed approximately in the center of the slot at different chordwise locations and different plenum pressures. These results provided an experimental verification of

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the isentropic relations used to predict the jet velocity. The relation is v u γ−1 ! u γ P∞ γ t Ujet = 2RT0 1− γ−1 P0

(2)

where ( )0 is the stagnation conditions and γ is the ratio of specific heats. This relation assumes the plenum is large enough such that there is no flow within the plenum. Testing this assumption, the velocity within the plenum is calculated, again with the isentropic relations, for a jet velocity of 100 m/s. The plenum velocity is found to be approximately 6 m/s, or less than Mach 0.02, which is negligibly small. The hotwire probe is calibrated with a Dantec Streamline frame with a CTA Module 90C10 used to keep the 5 µm diameter, 1 mm long platinum-plated tungsten wire at a constant temperature. Flow passes over the 55P11 probe, resulting in forced convection that attempts to reduce the probe temperature. To maintain constant temperature, a control circuit increases the voltage, providing more current to the probe, heating the probe further to offset the cooling effects of convection. The voltage change is then measured by a DAQ system. The low thermal mass of the wire and the high temperature of the wire relative to ambient temperature results in rapid heating and cooling of the wire. The rapid heating and cooling allows for a fast time response, providing time resolution on the order of kHz.14 The voltage to velocity relation is a power law, known as King’s law, and states that E 2 = A + BU n .

(3)

Here, E denotes the measured voltage, U denotes the velocity, and A, B, and n are calibration constants. A Streamline free jet calibrator calibrates the probe with 30 points over the entire measured velocity range. The constants are then determined through a least-squares curve fit. C.

Florida State Anechoic Tunnel

The FSAT is an open-return wind tunnel installed in an ISO-3745-2003-certified 250 Hz anechoic chamber. The 0.91 m by 1.22 m open-jet test section extends 3.05 m in the flow direction. A 550-hp centrifugal fan produces test section speeds of 5-70 m/s with turbulence intensities below 0.1% above a frequency of 10 Hz.15 For fluid dynamics testing, a modular closed-walled test section connects to the inlet, extending the full length of the test section. This closed test section contains optically clear acrylic on the ceiling and floor allowing for optical access. D.

Stereo Particle Image Velocimetry Setup

To measure the flowfield, a New Wave Solo 120XT Nd:Yag laser passes through a series of spherical and cylindrical lenses to create an approximately 2 mm thick light sheet. The light sheet is perpendicular to the flow direction. A TSI 9307-6 seeder produces 1 µm particles that are fed into a 2.5 cm steel pipe positioned within the settling chamber. The steel pipe increases the turbulence intensity of the FSAT to 1%. The seed illuminated by the light sheet is then captured by two Imager Pro X 4 megapixel CCD cameras with 16-bit resolution. Two Nikon 105 mm f/2.8 lenses with 1.4x teleconverters are attached to the cameras and focused with an aperture of f/5.6. This aperture provided a good balance of depth of field and available light intensity. Scheimpflug mounts are attached to each camera to correct for the non-parallel nature of the laser plane and the image plane of the cameras. A LaVision portable timing unit synchronizes the camera and laser for simultaneous firing. To ensure convergence of turbulence statistics, 1000 images are acquired for each case. All image acquisition and processing is performed by LaVision DaVis software. The laser and cameras are rigidly mounted under the wind tunnel connected to a traversing system, allowing for simultaneous repositioning to minimize the number of required calibrations. This setup forces the cameras into backscatter, reducing the intensity of the seed particles. To reduce the effect of surface reflections, the airfoil is initially sprayed with commercially available glossy black spray paint. In addition, a second layer of dark red spray paint is applied to help further reduce these surface reflections. 1.

Processing Parameters

The intensity levels of the 1000 raw images are first averaged, resulting with an image of the background and averaged laser reflections. This averaged image is then subtracted from each individual image in an attempt 4 of 15 American Institute of Aeronautics and Astronautics


to reduce the effect of surface reflections and increasing the signal-to-noise ratio of the seed particles. These individual images then undergo stereo cross-correlations that estimate the displacement of the particles. Initially, a 96x96 pixel interrogation window makes two passes with 50% overlap and a square weighting function before stepping down to a 32x32 window making four passes with 50% overlap and an adaptive weighting function. This results in an estimate of the individual vector fields; however, many spurious vectors are still present in regions of low seeding density. To address these spurious vectors, the data undergo further post-processing. First, an allowable pixel shift is given, removing any vectors outside this range effectively keeping the velocity within a physically realizable range. Then, should the correlation coefficient be below 35%, the vector is assumed to be spurious and removed. From this point, a universal outlier rejection routine is applied. The parameters of the outlier rejection are varied from case-to-case since the control parameters resulted in different constraints for the flow field. The parameters are varied such that the regions of high velocity gradients are retained while the spurious regions due to lack of seeding are removed. Finally, all images are averaged and their RMS-value is calculated with a minimum of 75 vectors required for an average. The vectors are then averaged again removing any vectors outside the range of ±3 the RMS value, assuming that vectors outside this range are outliers. E.

Quantitative Metrics

Because the trailing vortex has a number of adverse effects, multiple metrics must be used to determine the control’s effectiveness for each effect. The following subsections describe three metrics: vortex strength metric, wake-hazard metric, and wake-detection metric. 1.

Vortex Strength Metric

In general, the strength of a vortex is quantified by the circulation of the vortex, Γ. The circulation can be computed by integrating the vorticity flux through a plane, shown as ZZ ZZ Γ= (∇ × V) · dS = ω · dS (4) S

S

where V denotes the velocity vector and ω denotes the vorticity. This metric reduces if the control annihilates vorticity in the flow field and increases if it adds vorticity within the flow field. 2.

Wake-Hazard Metric

Should a trailing aircraft fly into the wake of leading aircraft, the wake causes potentially hazardous forces and moments on the trailing aircraft. These forces are short in duration and generally are caused by the transverse velocity of the wake. Therefore, the instantaneous velocity should be examined. Because the time scales of SPIV are much smaller than the time scales of the flow field, each image pair provides an instantaneous flow field information. From this, the wake hazard metric is defined to be the mean of the maximum instantaneous transverse velocity, denoted Vˆtr,max . To calculate this value, first the maximum transverse velocity of the flow field is found and recorded. This results with 1000 maximum transverse velocity. We then take a mean of these data, resulting in the average maximum transverse velocity. The value of this metric provided mathematically as Vˆtr,max = E[max (Vtr,i )]. 3.

(5)

Wake-Detection Metric

For maritime detection, optical imaging techniques have been used to measure the wakes.2, 16 However, a large number of averages is required for sufficient convergence of the data. Therefore, to examine the wakedetection metric, the flow field should be examined after time-averaging. In addition, the largest velocity component should be examined as well. Therefore, the maximum of the time-average swirl velocity is used as the wake-detection metric, denoted V θ,max . To determine this value, the flow field is first time-averaged and the vortex center is determine through the maximum of the vorticity magnitude. The velocity vectors from SPIV are then converted from Cartesian


to cylindrical coordinates and the maximum of the swirl velocity is then determined. This is expressed mathematically as V θ,max = max (E[Vθ,i ]) . (6)

III.

Experimental Results

The results of experiments performed in the FSAT are now presented and discuss. First, the flow leaving the slot is characterized. Second, the baseline case is explored and characterized in both the near field and the intermediate field. Then, the near field and intermediate field a cases is examined: uniform blowing configuration with a Cµ = 0.0048. Last, quantitative results are presented and different metrics are examined. A.

Static Characterization

120 I se nt ropic R e lat ions Hotw ire Dat a

100

U j e t ( m /s)


Prior to applying the control, the input must first be compared with the predicted velocity of Equation 2. The solid line in Figure 3 shows the isentropic relations given in Equation 2. The circles (◦) signify the results from the hotwire data. As shown, the agreement is excellent. The hotwire data are slightly lower than the isentropic relations. This reduced velocity is attributed to the viscous losses in the thin slot.

80 60 40 20 0

0

0.2

0.4

0.6 P 0 ( p sig )

0.8

1

Figure 3. Measured slot velocity for various plenum pressures as compared with the isentropic relation. The slight reduction relative to the isentropic relations is attributed to viscous losses in the thin slot.

B.

Baseline Case

In the near field, the pressure difference between the lower and upper surface of the airfoil drives the flow about the wingtip. The vorticity within the boundary layer separates from the body and forms the vortex that continues to convect downstream. This vortex develops along the suction side of the wing as it convects downstream along the wing until it separates at the trailing edge. This separation forms a free-shear flow with a developing vortex. To confirm this qualitative description, SPIV data in the near field are presented (for the baseline case) in Figure 4. As shown, the pressure difference between the lower and upper surface of the wing causes a net flow about the wingtip. Due to the high Reynolds number of the flow, the vortex core remains attached to the surface beyond x/c = 0.75. At both x/c = 0.5 and 0.75, the upper region of the vortex core is visible through the region of velocity surplus. Just downstream of the trailing edge, at x/c = 1.01, the vortex is clearly present along with the velocity deficit of the wake behind the trailing edge. The vortex sheet shed from the trailing edge is also present. Within the vortex core, there is a velocity surplus near U/U∞ = 1.40. Further insight can be drawn from examining the vorticity of the flow field, shown in Figure 5. Similar to the streamwise velocity surplus, the vorticity remains in the vortex core, where at x/c = 0.75 the upper region of the vortex core is resolved. However, at x/c = 1.01, there is a strong coherent vortex present with large amounts of vorticity within the core. In addition, the vortex sheet is present as well.



Figure 4. Stereo particle image velocimetry data representing the mean flowfield for the baseline flowfield along the airfoil. Contours represent the streamwise velocity normalized by the freestream velocity. The planes correspond to x/c = 0.25, 0.50, 0.75, and 1.01 from the leading edge. The streamwise velocity within the flow is accelerated within the core.

Figure 5. Stereo particle image velocimetry data representing the streamwise vorticity and streamlines for the baseline flowfield. Contours represent the streamwise vorticity normalized by the freestream velocity and the chord. The planes correspond to x/c = 0.25, 0.50, 0.75, and 1.01 from the leading edge. The data show there is little (resolvable) vorticity along the airfoil surface until the x/c = 1.01 position where the vorticity in the vortex core and the vortex sheet is clearly present.


ωc U∞

y c

z c

x c


Figure 6. Time-averaged non-dimensional streamwise vorticity field for the baseline case in the intermediate field from 50 image pairs for the downstream positions between x/c = 1.5 − 5.0. The data show the vortex sheet shed from the wing and a clear coherent vortex core just downstream of the wing. The vortex sheet appears fully rolled up by x/c = 3.0.

The vortex then progresses from the near field to the intermediate field upon separation from the trailing edge of the wing. Figure 6 shows the normalized streamwise vorticity in the intermediate field. As shown, the vortex sheet shed from the wing is present and connected to the vortex core. With downstream progression, this vortex sheet rolls up into the core. Upon reaching an x/c = 3.0, the vortex sheet is no longer present and the vortex core appears to be fully rolled up. Throughout this process, the vortex clearly undergoes diffusion. The diffusion is a combination of two physical mechanisms: viscous diffusion and wandering. These data are not corrected for wandering because upon application of control, the vortex core becomes obfuscated, making wandering corrections break down. However, for the baseline case, when wandering corrections are applied, it is clear that the diffusion shown in Figure 6 is due more to vortex wandering rather than viscous diffusion. With the baseline characterized, we now have an idea of how the vortex flow field develops along the wing, separates from the trailing edge, and progresses into the intermediate field. With this understanding, it is now possible to look into the effect of control. For the control configurations, uniform blowing along the entire slot is examined. C.

Control Case: Cµ = 0.0048, Uniform Blowing Configuration

With the application of control, the jet emits from the slot, interacting with the surrounding flowfield. Figure 7 shows the control case with a momentum coefficient of Cµ = 0.0048, corresponding to a jet velocity of Ujet = 30 m/s. The jet-flowfield interaction causes a clear change to the near field. From Figure 7, we can draw some physical insight into the nature of these dynamics. Initially examining the x/c = 0.25 plane, the jet is bent backwards, acting like a jet in cross flow rather than opposing the vortex motion as expected. This lifts the vortex off the surface of the airfoil as early as x/c = 0.25, and the jet appears to promote growth of the vortex as it progresses downstream. Furthermore, as the vortex progresses to x/c = 0.50 and 0.75, the vortex core no longer has an axial velocity surplus, but rather, a deficit. It appears that the jet lifts the low-momentum region of the boundary layer along the wingtip’s edge and wraps it around the vortex core. Upon separation of the vortex from the trailing edge, the velocity deficit of the vortex sheet is clearly present with a velocity deficit surrounding the core region. The deficit proves interesting because the presence of an axial velocity deficit in a Batchelor vortex results in the presence of instabilities17 and has shown to cause more rapid vortex growth.8, 9 The growth is apparent at the x/c = 1.01 location, showing a larger and shifted vortex relative to the baseline case. The larger, more diffuse vortex matches well with previous experiments.11 The streamwise vorticity for the control case, shown in Figure 8, illustrates that the vorticity remains within the vortex core, similar to the baseline case. Further upstream, at x/c = 0.25 and 0.50, the vorticity magnitude is fairly large within the core. However, upon progression to x/c = 1.01, the vorticity appears smeared out with reduced vorticity magnitude within the core. The larger, less intense vortex in Figure 7 matches the vortex shown in the intermediate field at x/c = 1.50, shown in Figure 9. Upon progression downstream, the vortex sheet rolls up at a similar rate to the baseline 8 of 15 American Institute of Aeronautics and Astronautics


Figure 7. Stereo particle image velocimetry data representing the mean flowfield for the control case corresponding to a Cµ = 0.0048. Contours represent the streamwise velocity normalized by the freestream velocity. The planes correspond to x/c = 0.25, 0.50, 0.75, and 1.01 from the leading edge. The flow field is vastly changed from the baseline case, lifting the vortex core off the surface as early as x/c = 0.25. At x/c = 1.01, the vortex is larger relative to the baseline case.

Figure 8. Stereo particle image velocimetry data representing streamwise vorticity and streamlines for the control case corresponding to a Cµ = 0.0048. Contours represent streamwise vorticity normalized by the freestream velocity and the chord. The planes correspond to x/c = 0.25, 0.50, 0.75, and 1.01 from the leading edge. The vorticity magnitude in the core appears large at x/c = 0.5, however, the jet appears smeared out as it reaches x/c = 1.01.


case. ωc U∞

y c x c

z c


Figure 9. Time-averaged non-dimensional streamwise vorticity field for the control case corresponding to Cµ = 0.0048 in the intermediate field from 50 image pairs. This is for the downstream positions between x/c = 1.5 − 5.0. The data show a larger vortex with reduced vorticity magnitude relative to the baseline case.

D.

Turbulent Kinetic Energy

The turbulent kinetic energy (TKE) of the flow field provides insight into contrasting turbulent energy within the flow field with and without control present. The mean kinetic energy equation, derived by taking the scalar product of the mean velocity with the Reynolds averaged momentum equation and rearranging, is expressed as18 DK + ∇ · T = −P − E. (7) Dt Here, K denotes the mean kinetic energy, T is a convective term, E is the mean kinetic energy dissipation term, P is a TKE production term defined as P ≡ −ui uj

∂U i . ∂xj

(8)

Further examining the TKE equation derived by taking the scalar product of the turbulent fluctuation and the Reynolds averaged momentum equation and rearranging, is expressed as18 Dk + ∇ · T ′ = P − ǫ. Dt

(9)

Here, k represents the TKE, T ′ is the fluctuating counterpart to T , ǫ denotes the dissipation of TKE, and P denotes the TKE production term expressed in Equation 8. From the sign of P in Equations 7 and 9, it is apparent that TKE production term acts as a sink to the mean kinetic energy from the Equation 7 and a source of TKE from Equation 9. The production of TKE, from Equation 8, is generated due to large levels of shear in the mean flow. Figure 10 shows the TKE field for the baseline case. As shown, the freestream is relatively free of TKE. Previous studies19 have shown that the Reynolds stresses and turbulent energy from the boundary layer roll up into the vortex core along the airfoil surface. The TKE localized to the vortex sheet and vortex at x/c = 1.01 confirms these results. When control is applied for a Cµ = 0.0048, TKE is apparent in the core lifted from the surface of the airfoil, shown in Figure 11. At x/c = 0.25, there are high levels of TKE near the control jet interacting with the flow field. This implies that there is a region of large amounts of shear from Equation 8. As the vortex convects downstream, the TKE diffuses outward but remains in the region of large shear. At x/c = 1.01, the TKE is again localized to the vortex sheet in vortex core region with increased levels relative to the baseline case. From the previous figures, the effect of control is qualitatively characterized relative to the baseline case. The control induces earlier separation of the vortex core from the airfoil’s surface, promoting growth of the vortex along the surface. Upon separation into the intermediate field, the vortex is larger with lower vorticity magnitude in the core. In addition to the alterations in the mean flow, the TKE levels are increased in the 10 of 15 American Institute of Aeronautics and Astronautics


Figure 10. Stereo particle image velocimetry data of the turbulent kinetic energy (TKE) for the baseline case. The planes represent x/c = 0.25, 0.50, 0.75, and 1.01 from the leading edge. It is apparent that there is limited TKE in the free field and slight TKE present at the edge of the core at x/c = 0.75. At x/c = 1.01, there is TKE present in the vortex sheet and the vortex core region.

Figure 11. Stereo particle image velocimetry data of the turbulent kinetic energy (TKE) for the control case corresponding to a Cµ = 0.0048. The planes represent x/c = 0.25, 0.50, 0.75, and 1.01 from the leading edge. The control appears to produce TKE in the core near the leading edge at x/c = 0.25. With increasing development of the vortex with downstream progression, the TKE diffuses and spreads outward. At x/c = 1.01 the TKE is localized to the vortex sheet and in the vortex core.


flow field as well. The TKE still remains localized to the vortex core and the vortex sheet upon separation, but the increased levels of shear introduced by the control produces TKE within the overall flow field. Though these results provide insight into the qualitative effects of the control, they do not provide insight into how the control influences the adverse effects of trailing vortices. To quantify this, the metrics outlined previously are examined.

IV.

Quantitative Metrics

Due to the many adverse effects of trailing vortices, different metrics are necessary to determine the effectiveness of control. For the present study, a vortex strength metric, a wake-hazard metric, and a wakedetection metric are examined. These metrics are examined for both the uniform and segmented blowing configuration. Circulation

To quantify the strength of the vortex, circulation is used as the parameter. Recall that circulation is the flux of vorticity through the plane; therefore, should the circulation increase, it signifies that vorticity (and thus the circulation) is being added to the flow, whereas should circulation be reduced, vorticity annihilation is occurring. Circulation versus various Cµ values are shown in Figure 12 for the streamwise location of x/c = 5.0. Examining the uniform configuration first, it is evident that there is a monotonic increase in circulation relative to the baseline case. For the control case shown in the previous section (Cµ = 0.0048), there is a 14% increase in circulation. This indicates that though the vorticity magnitudes are reduced in Figure 9, the vorticity is in fact added to the flow field. Therefore, the control appears to smear the vortex by increasing the vortex diffuseness. 0.7 Unif orm C onfigurat ion Se gme nt e d C onfigurat ion

0.65 0.6 0.55

Γ/Γ B


A.

0.5 0.45 0.4 0.35 0

0.005

0.01

0.015

0.02

0.025

Cµ Figure 12. Vortex strength, Γ, non-dimensionalized by the theoretical bound circulation, ΓB for varying momentum coefficients. The plot shows results for the uniform blowing configuration (◦) and segmented blowing configuration (×). The baseline case corresponds to when Cµ = 0.

For the segmented blowing configuration, there is no appreciable change in the circulation a Cµ = 0.0023, however, circulation increases thereafter. These results show that, the vorticity is actually increasing rather than reducing as expected. However, though the vortex strength is technically increasing, there may be benefits in the other metrics despite the increase in vortex strength. B.

Wake-Hazard Metric

If the trailing aircraft encounters the wake of a leading aircraft, the velocity field will induce a momentum on the trailing aircraft, potentially causing a hazardous rolling moment and disrupting the intended flight


1

Vˆ t r , m a x

0.9

0.8

0.7

0.6 Unif orm C onfigurat ion Se gme nt e d C onfigurat ion 0.5

0

0.005

0.01

0.015

0.02

0.025


Cµ Figure 13. The non-dimensionalized wake-hazard metric, Vˆtr,max , for varying momentum coefficients. The metric is non-dimensionalized by its baseline value. For the uniform blowing configuration (◦), there is a 40% peak reduction in the wake-hazard metric. However, for the segmented blowing configuration (×), the peak reduction is about 15%. These measurements are taken at x/c = 5.0 because the far field region is of interest.

path. Figure 13 shows the wake-hazard metric non-dimensionalized by the baseline wake-hazard metric value, implying a value of less than 1 is desirable. Examining Figure 13 shows that the uniform blowing configuration (◦) significantly outperforms the segmented blowing configuration. For low values of Cµ , there is approximately a 40% reduction in Vˆtr,max with an increase after. For the segmented blowing configuration, there is approximately a 15% reduction in Vˆtr,max . This shows that the uniform blowing configuration vastly outperforms the segmented blowing configuration for this metric. Another point to note is that there is a clear optimum in Cµ for this metric. Due to the coarse sweep of Cµ for this experimental configuration, the values between Cµ = 0 and Cµ = 0.0021 are unresolved. The control being optimal at lower values of Cµ has an added benefit. The lower Cµ levels affords more opportunities for actuators to be used for the trailing vortex control. C.

Wake-Detection Metric

When a maritime vehicle maneuvers through the water, its wake leaves behind a footprint that could be detected by underwater detection techniques. Because these techniques generally look at the flow field in a time-averaged sense, the time-averaged flow field is examined for this metric. Figure 14 shows the wakedetection metric non-dimensionalized by its baseline value, implying a value of less than 1 is desirable. Contrary to the wake-hazard metric, the uniform blowing configuration underperforms relative to the segmented blowing configuration. As shown in Figure 14, the uniform blowing configuration has a modest improvement of less than 10% for low Cµ values. However, the segmented blowing configuration has nearly a 20% reduction in the wake-detection metric. This result shows that depending on which metric is of interest, different blowing configurations should be implemented. Similar to the wake-hazard metric, there is a clear optimum at low values of Cµ . Again, to determine the true optimum, the coarse sweep must be reduced to a finer variation in Cµ . The low values of Cµ resulting in the best performance is beneficial for the increase in the potential control options.

V.

Conclusions

From these results, it is clear that the control has a drastic effect on the flow field; albeit not as expected. Rather than oppose the vortex motion as was hypothesized, the flow altered the formation of the vortex.


1.5 Unif orm C onfigurat ion Se gme nt e d C onfigurat ion

1.4

V¯ θ , m a x

1.3 1.2 1.1 1 0.9 0.8 0

0.005

0.01

0.015

0.02

0.025


Cµ Figure 14. The non-dimensionalized wake-detection metric, V θ,max , for varying momentum coefficients. The metric is non-dimensionalizzed by its baseline value. For the uniform blowing configuration (◦), there is less than a 10% reduction in the metric. However, for the segmented blowing configuration (×), there is nearly a 20% reduction in the metric. These measurements are taken at x/c = 5.0.

The flow around the wingtip bent the jet backwards similar to a jet in crossflow. This resulted in formation of the vortex as early as x/c = 0.25. As the vortex convected downstream, the control promoted the growth of the vortex, resulting in a more diffuse vortex without a streamwise velocity surplus in the core. This result translated to a vortex with a larger vortex core and lower vorticity magnitudes in the intermediate field when compared with the baseline case. Though the magnitude of vorticity in the core was reduced, examining the circulation showed that vorticity was not being annihilated, but rather more vorticity was being introduced to the flow field. The control, however, appeared to smear the vorticity as shown in the contours in Figure 9. As a result, though the control is technically increasing the strength of the vortex, the spreading of the vorticity over a larger area may be beneficial in other metrics. The uniform blowing configuration vastly outperformed the segmented blowing configuration for the wake-hazard metric. A nearly 40% reduction in Vˆtr,max was found for the uniform blowing configuration. However, for the segmented blowing configuration, only a 15% reduction was found. These results are promising for increasing safety in the landing of consecutive aircraft. Contrary to the wake-hazard metric, the wake-detection metric showed better performance out of the segmented blowing configuration relative to the uniform blowing configuration. The segmented blowing configuration had nearly a 20% reduction in the wake-hazard metric, whereas the uniform configuration had a modest reduction of less than 10%. The dependency on the blowing configuration on different metric illustrates the importance of the blowing configuration. From Figures 13 and 14, it is clear that there is a clear optimum for low values of Cµ . This is encouraging because it increases the number of viable control options. In addition, steady blowing was performed throughout this study. Because of the low velocity requirements, forcing at non-zero frequencies could potentially provide a more optimal control configuration. This could be done with either synthetic jets10 or plasma actuators.20

Acknowledgments This work is supported by the National Science Foundation PIRE grant OISE-0968313 and the Office of Naval Research grant number N00014-10-1-0832 monitored by Dr. Ronald Joslin.


References 1 Spalart,

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2 Wren,


Topology of a Trailing Vortex Flow Field with Steady Circulation ...

Topology of a Trailing Vortex Flow Field with Steady Circulation ...

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