Effect of a jet on vortex merging

Transcription

1 37th AIAA luid Dynamics Conference and Exhibit June 27, Miami, L AIAA Effect of a jet on vortex merging D. Marles * and I. Gursul University of Bath, BA2 7AY, United Kingdom Experiments were conducted in order to understand the effect of an axial jet on the merging process of a simulated flap-edge and wing-tip co-rotating vortex pair in the near wake. Cross-flow velocity measurements and flow visualization were performed for three realistic jet positions on both equal and unequal strength like-signed vortices for a range of momentum coefficients. he main finding was that the initial jet position has a vastly contrasting effect on the merging process. If the jet turbulence interacts rapidly with only one of the vortices, severe diffusion of that vortex occurs which ultimately wraps around and becomes consumed by the unaffected vortex structure. he jet causes a reduction in the vortex spacing and an increase in the rotation angle, hence merging is promoted. If the jet turbulence does not interact directly with either vortex, but instead interferes with the mechanism in the outer-recirculation region that advects vorticity to a larger radius, then merging can be retarded. In this case, an increase in vortex spacing and reduction in rotation angle was observed. Increasing the momentum coefficient, hence introducing more turbulence into the flow, has a greater effect on the merging process. Nomenclature a = vortex radius A = area of integration c = wing chord length = momentum coefficient, m& ju j /.5ρ U 2 cs d j = jet exit diameter h = vortex spacing = initial jet-to-flap vortex spacing = initial vortex spacing m& j = jet mass flow rate Re = Reynolds number based on chord, U c/ ν Re Γ = Reynolds number based on circulation, Γ/ν s = submerged semi-span t = time t o = two-point vortex rotational period, 2π 2 h 2 v /Γ t* = normalized orbit time, t/t o U j = axial jet velocity U std = standard deviation of cross-flow velocity U = free stream velocity x = downstream distance from trailing edge of generic wings y = spanwise distance y c = spanwise coordinate of vorticity centroid z = normal distance z c = normal coordinate of vorticity centroid α = angle of attack Γ = circulation Γ o = total circulation ν = kinematic viscosity ρ = density of free stream ω = axial vorticity subscript f = flap-edge vortex t = wing-tip vortex * Postgraduate Student, Department of Mechanical Engineering, Student Member AIAA Professor, Department of Mechanical Engineering, Associate ellow AIAA Copyright 27 by Dave Marles and Ismet Gursul. Published by the, Inc., with permission.

2 I. Introduction AKES generated by lifting aircraft wings consist of spanwise vorticity sheets that rapidly roll-up into distinct W vortex structures. he exact configuration of the lifting surface governs the strength and number of vortices produced. Cruise conditions generate a pair of discrete counter-rotating vortices at the extremities of the wings. During low speed flight, which occurs in close proximity to airfields, lift augmentation devices are deployed. A co-rotating vortex pair emanates from the flap-edge and wing-edge tips which subsequently merge into a single vortex within 5 to spans downstream, resulting in a structure similar to that during cruise 2. hese vortices pose a serious hazard to trailing aircraft and limit airport capacity due to their longevity. he fluid dynamics of vortex merging has recently received renewed enthusiasm due to its applicability to the decay of two- dimensional turbulence, three-dimensional turbulence and mixing layers. or the purpose of this article, its relevance to aircraft wakes will be discussed. Depending on the particular setting of the high-lift devices, equal and unequal strength co-rotating vortices can be generated which is an important factor in the merger process. Vortices of comparable strength undergo a symmetric merger which takes place at the extremities of the vortex. or an unequal strength pair, the stronger vortex dominates the dynamics, splitting the weaker structure radially with severity depending on their relative strengths 3. or large differences in strength, catastrophic merger occurs very rapidly as the weaker vortex is first split axially, then wrapped around the dominant vortex. Previously vortex merging of equal strength like-signed vortices has been divided into three distinct stages 4 with Cerretelli and Williamson 5 adding a fourth to describe a second diffusion of the vortices at the end of merging. Merging is a two-dimensional laminar process at Reynolds number less than, Re Γ 2. he vortex cores rotate due to their mutually induced velocity. Numerical simulations performed by Leweke et al 6 on Lamb-Oseen vortices with a Gaussian vorticity profile demonstrated merging was initiated when the critical core size to separation distance exceeded a value of a/h =.25 ±.. Experiments revealed merger commenced once the time-dependent core exceeded approximately 29% of the vortex separation distance for low Reynolds number flow 4,5,7. Recently, Meunier et al. 8 suggested this value to be slightly over predicted, proposing a merging criterion a/h =.24 ±. from experimental results. Inviscid simulations show no merger if the ratio a/h is less than the critical value. he vortex pair will rotate around each other indefinitely at a fixed separation. However, viscous diffusion in real flows always causes merger as a result of the growth of the vortex cores. his initiates the second stage known as the convective phase in which the separation distance of the pair decreases. Arms of vorticity are ejected radially outward as a result of the fluid being advected by the outer-recirculation region. he antisymmetric vorticity field generated induces an inward velocity that drives the vortex cores together 5. Alternatively, this idea can be viewed as the spiral arms cause the approach of the vortex cores in order to conserve angular momentum 2. As the vortex spacing approaches zero, the inward induced velocity applied to the cores becomes negligible. his leaves the vortices at a spacing approximately equal to 2% of the initial separation according to Cerretelli and Williamson 5. he resulting pair of close vorticity peaks mature into a single core by a second diffusive stage. he structure is transformed into an approximate axisymmetric vortex with about twice the area of the original individual vortices 4,6. he phenomenon of instabilities occurring between a pair of vortices is well documented. Long-wavelength and shorter-wave elliptical instabilities have been observed in counter-rotating vortices by Crow 9 and Leweke and Willamson respectively. or co-rotating vortices, the longer-wavelength Crow type instability is known to be suppressed by the rotation of the vortex pair. Recently and for the first time, Meunier and Leweke 4 observed that co-rotating vortices with prolonged diffusive periods (diffusive stage is proportional to Reynolds number) exhibited elliptical instabilities. his occurs for Reynolds number greater than, Re Γ 2 or small initial core size to vortex spacing, allowing time for the growth of three-dimensional instabilities. Experiments performed by Meunier et al. 2 revealed that three-dimensional merger can be initiated earlier (in terms of viscous time period), for core sizes as low as 9% of the vortex separation, even though the entire merger process may actually take longer (in terms of convective units, t o ). he instability causes sinusoidal distortion of the vortex line with a wavelength similar to the vortex separation. his deformation aids the transfer of vorticity across the separatrices, allowing the outer-recirculation region to advect this fluid to a larger radius. Another effect of merging involving elliptical instabilities is that the final merged vortex has a core area 3.5 times that of the unmerged pair. In contrast, two-dimensional merger only produces approximately.5-2. times the area increase, resulting in a more concentrated vortex core with larger peak vorticity 2,4. his has the effect of increasing the maximum azimuthal velocity of the final vortex by approximately.5 times over the case where instabilities were present. Extensive experimental and numerical studies have been performed on the interaction of a jet with a single vortex 2. Research revealed that there are two methods of interaction between the jet and vortex. or small initial jet-vortex spacing, similar to a Batchelor q-vortex 3, strong injection of axial perturbations into the core cause severe diffusion of the vortex structure 4. his arrangement is analogous to an engine located close to a flap-edge on aircraft with four engines. Interactions for larger initial jet-vortex spacing has a vastly differing flow topology. indings reveal that the wake development can be divided into two phases. he first of these, known as the jet 2

3 regime, sees the simultaneous turbulent mixing of the jet with ambient fluid and roll-up of the wing-generated vorticity sheet around discrete vortices. Jet growth is known to be dominated by the Kelvin-Helmoltz type instability which has been studied by Michalke and Herman 5 for a simple inviscid incompressible axisymmetric jet. or numerical simulations it is assumed that minimal interaction occurs between the jet and vortex during this stage 4. he next phase, known as the interaction regime, is dominated by the entrainment of the jet around the vortex. Interaction between the jet axial and vortex tangential velocities causes secondary vortices to be generated around the periphery of the vortex. No strong perturbations were found to be injected into the vortex core. Wang et al. 6 performed experiments on a co-flowing jet immersed in an induced velocity field which was generated by the vortex wake of a delta wing. he jet was significantly modified by the vortices, losing its axisymmetric shape, undergoing vertical compression and lateral stretching. However, little effect was observed on the trajectory of the vortices. urther experiments performed by Wang and Zaman 7 revealed the presence of additional vortical structures of significant strength around the jet. hese secondary vortices are the mechanism responsible for the deformation of the jet structure which ultimately results in a more rapid decay in maximum axial velocity. Margaris et al. 8 performed a parametric study on the effect of a co-flowing jet on a single wing-tip vortex. he jet turbulence was observed to elongate and wrap around the vortex, producing a more diffuse vortical structure with reduced levels of botorticity and cross-flow velocity. Smaller initial jet-vortex separations and larger momentum coefficients allowed a more rapid ingestion of the turbulence into the vortex, which had the greatest effect on the coherence of the vortical flow. he objective of the present paper is to provide an insight into the effect of jet turbulence on co-rotating vortex merger in the near wake. Extensive simulations and experiments have been performed on the merger process, which is now relatively well understood. However, there remains a large void in the knowledge of cold engine jet interaction and its effect on the merging process. his study uses a pair of generic rectangular wings to generate a vortex pair and a round nozzle to simulate the co-flowing engine exhaust. Both equal and unequal strengtortices were produced to replicate aircraft with lift augmentation devices deployed. he initial jet nozzle position relative to the vortices was varied along with the vortex separation distance. II. Experimental System and echniques A. Experimental Setup. acilities and Models Experiments were conducted in an Eidetic Model 52 closed circuit free surface water tunnel at the University of Bath. he co-rotating vortex pair was generated using generic rectangular wings suspended vertically (igure ) in the.38 m x.58 m x.524 m test section. his produced a submerged semi-span of 23 mm and aspect ratio of.5 (based on the full span). All experiments were performed at.3 ms - on 5% cambered airfoils with 4 mm chord. he aluminium wings were of constant thickness of 5% chord with rounded leading and trailing edges. his provided a Reynolds number based on chord of 2. lorescent dye was introduced into the vortices using a.5 mm tube embedded in the pressure surface of the wings. Engine exhaust flux was simulated via a round nozzle aligned with the free stream having d j = 6 mm and a.5 mm wall thickness. he nozzle support was U-shaped to minimize interference allowing the jet to be located between the vortex generating wings. A constant diameter, 4 mm long straight section extending from the support, released the jet fluid in the same cross-flow plane as the trailing edges of the generic wings (igure ). Dye was introduced into the jet via a mm tube located in the nozzle support structure. Measurements were taken at numerous cross-flow planes downstream of the model between x/c = 4 and 24 as illustrated in igure 2. he maximum downstream distance was chosen to ensure limited endeffects and is measured from the trailing edge of the wings. 2. Instrumentation Quantitative measurements were obtained using a 2-D SI Digital Particle Image Velocimetry (DPIV) system which produces up to 2 mj pulses from a pair of mini Nd:YAG laser heads at a rate of 3.75 pairs/second. Images were taken with an 8 bit grayscale 248 x 248 pixel digital CCD camera. he tunnel was seeded with hollow glass spheres of mean diameter 8 2 µm. Cross-correlation was performed on image pairs using Hart algorithm with a 32 x 32 pixel interrogation window and 5% overlap. his produced a vector spatial resolution at the measurement stations x/c = 4 and 24 of approximately 4 and 2% of the chord length respectively. Uncertainty in the velocity data was estimated to be 2%. low visualization was achieved by illuminating fluorescent dye via a Coherent Innova7 4 Watt continuous emission Argon-Ion laser, emitting a 55 nm wavelength beam. Green (Rhodamine 6G) and red (Rhodamine B5%) dyes were used to distinguish between the vortex and jet flows respectively. Instantaneous images were extracted from video footage recorded at a rate of 25 frames per second. 3

4 B. Data Analysis Circulation was calculated for eacortex to verify their relative strengths. his was achieved by separating the vector field in two along a division that runs tangentially through the midpoint of a line connecting the vortex centers. Circulation was then determined by performing a line integral of the velocities around a closed loop. he integration path was incrementally expanded around the vortex centre until the resulting circulation value reached an asymptotic maxima. A typical method of defining the vortex centre location is using the peak vorticity associated with the core. his approach is reasonably reliable for axisymmetric vorticity distributions. However, vortex merger in conjunction with the diffusion generated by jet turbulence produces elongated vorticity structures, making the peak vorticity method unreliable. his problem was overcome by means of calculating the vorticity centroid for eacortex as documented by Chen et al. 3 he centroid is found by independently considering the vorticity distribution in the y and z direction as detailed in Eq. () and (2) respectively. y c z c yωda = Γ zωda = Γ () (2) or this method to work accurately and consistently, vorticity with an absolute value less than 5% of the maximum was removed. his prevented background noise with large moment arms having a major influence on the centroid location. If two distinct axisymmetric vorticity patches exist in the time-averaged flow, this was treated as an unmerged vortex pair. o gain an initial approximate vortex centre location, the peak vorticity for each patch was found. he field was then divided perpendicular at the mid-point of a line joining the points of peak vorticity. In an iterative process, the vortex centroid (Eq. () and (2)) was evaluated for each half of the vorticity field and the flow was then divided using the new improved vortex centre locations. his provided a reliable method for finding the vortex centre location for each of the vortices based on the vorticity distribution. However, diffusion of one or both vortices by jet turbulence makes the process of deciding whether a vorticity patch has merged into a single structure very subjective. At downstream measurement stations the flow field typically consisted of an elongated patch of vorticity, rendering the above method inappropriate. In an attempt to remove this ambiguity and make the process quantitative the following procedure was performed. Large number of streamlines were plotted which tended to converge at the centre of the more dominate vortex structure. his position was cross-checked by finding the vorticity centroid of the entire flow field. or a fully merged axisymmetric vortex in the flow, there should be a negligible difference between the locations produced by the two methods. o automate the process, a criterion was applied to classify merged and unmerged vortices. If the difference between the locations was.5c then the flow contains unmerged vortices and vice versa. his criterion is approximately equivalent to 7% of a vortex core diameter. If the flow was unmerged, the field was divided into two and the vorticity centroid found for eacortex as detailed above. If the flow was merged then the vorticity centroid for the entire field was used. urbulence produced in the wake was calculated by taking the standard deviation of cross-flow velocities. his term is a little misleading because the low frame rate PIV system does not give true turbulence data. However, this is sufficient to provide information on the magnitude and location of the largest fluctuations in the cross-flow velocity field. III. Results A. Experimental Parameters he present setup generates a pair of vortices using two cambered aerofoils. his arrangement is not identical to that of real wings but the trailing vortical field created mimics that of an aircraft with high lift devices deployed. his experimental setup offers greater flexibility as the vortex spacing and jet positions can be altered with ease (igure ). he separation distance was a compromise between minimizing interference between the aerofoils and ensuring merger will occur within the length of the water tunnel test section. he coordinate system is based on the effective starboard aircraft wing being represented by the model in igure. he trailing edge tip of the effective wing is taken as the origin (in other words the trailing edge tip of the wing generating the tip vortex), hence positive x is downstream, y is outboard and z is in the normal direction upwards. or this investigation the main spacing 4

5 between the vortices was /c =.75 with some additional testing performed at /c =.. able reveals how these values compare with the spacing taken from real aircraft configurations. Aircraft Span (m) able. Aircraft parameters lap Chord span/wing (Mean aerodynamic) span ratio (m) Number of Engines A B A B /c Realistic momentum coefficients were taken from Margaris et al. 8 who supply a comprehensive analysis of vortex strength to jet flux ratio for real aircraft configurations. Experiments were performed for jet exit velocities of U j /U =, 2., 2.85 and 4.3 corresponding to momentum coefficients =,.25,.5 and. (based on a single vortex generating wing). heir data shows a minimum initial spacing of hj/c =.6 ensures the least interference effects from the jet nozzle structure. he jet was located in three positions relative to the vortex generating wings. hese were chosen for their physical similarity to real aircraft designs. able 2 provides a description of these positions along with a schematic of the experimental arrangement and effective real aircraft geometry being modeled. Configuration I represents the approximate jet/vortex positioning for aircraft with two engines such as the A33 or B757. he outboard engine on four engined aircraft are modeled in configuration II and III which represent the A34 and B747 respectively. able 2. Summary of the experimental setup and effective aircraft arrangement being modeled. Schematic views are looking upstream in the water tunnel for a starboard aircraft wing. Experimental Arrangement Effective Aircraft Configuration Description /c /c Setup Configuration I Jet in same spanwise plane as flap-edge and wing-edge tips II Jet below tip vertically flap-edge III Jet vertically below centre of flap-edge and wing-edge tips..6 Both equal and unequal strength co-rotating vortices were generated in an attempt to model a realistic aircraft wake structure. or an equal strength pair the wings were set at α = o. his produced a circulation ratio, at x/c = 4 with no jet nozzle structure in the flow, of / =.6 and Reynolds number based on circulation Re Γ = 65 (for a single vortex). or an initial vortex spacing of /c =.75 the rotational period was t o = 2.83s. Hence, it can be inferred that one orbit will be completed at x/c 2. Assuming the vortex radius is taken as the distance from the 5

6 vortex centre to maximum tangential velocity, at x/c = 4. with no nozzle in the flow, we estimate a radius to separation ratio, a/h.2. or the purposes of this paper, it is assumed that the physical spacing of the generic wing tips is equal to the initial vortex spacing. Likewise the jet-to-flap separation is assumed to be synonymous with the initial jet-to-vortex spacing. hroughout the paper the vortices will be referred to as flap and tip, which correspond to the flap-edge and wing-tip vortices respectively. Cross-flow measurements were taken at four chord length intervals which equates to a normalized orbit time, t* =.9. Unequal strengtortices occur when the high lift devices are configured for take-off and landing flight regimes, having a circulation ratio < and > respectively. Setting the angle of attack to α f = o, α t = 5 o and α f = 5 o, α t = o produced unequal strengtortices with ratios / =.54 and / =.65 respectively at the most upstream measurement location. B. Equal Strength Vortex Merging low visualization was performed to illustrate the interaction between the jet and vortex pair as they develop downstream. igure 3 and igure 4 compares the results for two differing jet positions which both have the same initial vortex spacing /c =.75. In both figures the jet nozzle structure is present with the left and right column representing the = and.25 cases respectively. igure 3 shows the results for the case with the nozzle centre located /c =.6 horizontally inboard of the flap (configuration I). Repositioning the nozzle centre in a normal direction beneath the flap (configuration II) is shown in igure 4. igure 3a to 3e shows the downstream development of the vortex pair from x/c = 4 to 24 for =. he vortices appear to approach each other, but remain unmerged at the most downstream distance. igure 3f to 3j shows the =.25 case where the red jet fluid is observed to become rotated and stretched by the flow field generated by the vortex pair. However, the counter-clockwise rotation rate of the vortices appears to be greater than that of the jet fluid. It emerges that moving downstream the jet slowly interacts with the vortices. Comparing the = and.25 case reveals the influence of the jet on the vortex system. Up to x/c = 8, the jet appears to have little effect on the vortices. However further downstream at x/c = 6, the jet clearly causes a reduction in rotation angle of the vortex pair. Positioning the jet nozzle vertically below the flap (igure 4a to 4e) appears to cause interference that increases the rotation angle of the vortex pair at a given downstream location when compared to igure 3a to 3e, even though =. It emerges that at the most downstream measurement location x/c = 24 the increase in rotation angle has caused the vortex pair to be closer to a merged condition. Introducing a jet flux of =.25 (igure 4f to 4j) produces a vastly different interaction between the jet and vortex structures than that observed in igure 3f to 3j. It is clear that at x/c = 4 the red jet fluid has been elongated and wrapped around the flap vortex. Reasoning for this is probably because the rotation of the vortex pair tends to move the flap vortex into the path of the jet flux. Moving further downstream causes the tip vortex to wrap the jet fluid around itself. he images reveal that the presence of the jet flux has produced a single merged structure and this is confirmed at x/c = 24 where the remnants of the jet fluid can be seen to roll-up around the solitary vortex. he flow visualization has revealed very different results when comparing the two jet configurations. It appears that configuration I has a reduced rate of rotation when compared to configuration II. At x/c = 24 this difference is clearly visible because the spanwise jet location (igure 3j) demonstrates an unmerged vortex pair whereas configuration II (igure 4j) promotes a well merged structure. Instantaneous PIV results comparing the vorticity field of configurations I and II at x/c = 4 can be found in igure 5. he reason for using instantaneous data is because time-averaging conceals the weak vorticity produced by the jet. he reference case in igure 5a demonstrates the vorticity field for the vortex pair with the nozzle structure removed. he horizontal line represents the effective starboard aircraft wing with the ends of the thicker and thinner line being the flap-edge and wing-tip respectively. Introducing the nozzle in igure 5b at /c =.6 inboard of the flap, as shown, generated small scale axial vorticity even though = (due to the wake generated by the nozzle). Increasing the jet flux to =. in igure 5c introduces both positive and negative vorticity with magnitude similar to that of the vortex cores. his is consistent with findings made by Wang and Zaman 7. Similar to the flow visualization, the vorticity generated by the jet appears to trail behind the rotating vortex pair. he main vortex structures in igure 5a, igure 5b and igure 5c are all very similar with perhaps only a small change in vortex spacing being visible. Moving the nozzle structure vertically below the flap in igure 5d again introduces very small scale background vorticity when compared with the reference case. Increasing the momentum of the jet to =. produces large scale vorticity patches that move alongside the flap vortex (similar to the flow visualization). his vorticity may have the ability to alter the structure of the vortices as its magnitude is comparable to that of the vortex cores. Again it emerges that the vortex pair tends to rotate into the path of the turbulence generated by the jet. his appears to be accompanied by a change in vortex rotation angle and spacing (compare igure 5c and igure 5e). urbulence plots showing the downstream development of the equal strengtortex pair for jet configurations I and II can be found in igure 6 and igure 7 accordingly. he left and right columns compare the = and. 6

7 cases respectively. Analyzing the horizontal jet location (configuration I), the turbulence generated by the jet fluid at the most upstream location (x/c = 4) is clearly visible by comparing igure 6a and igure 6e. Again the jet appears to trail the flap vortex as seen in the flow visualization. he = case reveals some background turbulence at x/c = 4 which disappears on moving downstream. his can be attributed to the wake from the vortex generating wings and nozzle structure. At x/c = 4 the intensity of the jet turbulence for =. appears to be comparable to that of the vortex cores. his turbulence decays rapidly on moving downstream and interacts partially with the flap vortex at x/c = 8. Moving further downstream, the flap vortex begins to rotate away from the bulk of the jet turbulence. Comparing the = and =. cases at x/c = 6, its clear the jet flux has not only caused a change in the turbulence levels of the flap vortex but also the orientation of the vortex pair. In fact the blowing appears to have reduced the angle through which the pair has rotated. Moving to the vertically orientated jet, igure 7 shows just how rapidly the turbulence interacts, becoming elongated and ingested into the flap vortex. At x/c = 8 only a single vortex structure is visible which is trailed by what can only be assumed to be the remains of the flap vortex and jet fluid. Only a single vortex is observed further downstream with a decaying tail of turbulence. It s clear that the presence of the jet flux dramatically alters the flow field, appearing to promote merger. igure 8 and igure 9 show the jet effect on vortex merger using contours of time-averaged axial vorticity. At x/c = 6 the reference case with no nozzle in the flow can be seen in igure 8a. he vortices at this station have become slightly elongated, an expected result of being close to merging. Introducing the nozzle structure at /c =.6 horizontally from the flap as in igure 8b, clearly has an effect on the merging process. A reduction in rotation angle and a small break in the lowest level vorticity contour between the pair suggest a delay in merger. his trend is continued as the momentum coefficient is increased to =.25,.5 and. in igure 8c, igure 8d and igure 8e respectively. Clearly the jet turbulence has retarded merger, causing an increase in separation distance and decrease in the angle the pair has rotated through. rom the conservation of momentum, a change in separation will be accompanied by an adjustment in the rate of rotation. Increasing momentum flux produces a more diffuse flap vortex while the tip vortex becomes more concentrated. Vorticity contours for the jet vertically below the flap (configuration II) can be found in igure 9. he measurement station has been moved upstream to x/c = 8 because it appears the jet in this configuration promotes merger, hence only a single vortex exists further downstream. he reference case with no nozzle in the flow, igure 9a, shows two discrete vortex structures that are far from merging. Introducing the jet nozzle in igure 9b causes the approach of the vortex pair and a small increase in rotation angle. igure 9c reveals the effect of increasing the jet flux to =.25. Clear diffusion of the flap vortex occurs as the still high intensity jet turbulence interacts rapidly with this vortex as illustrated by the flow visualization in igure 4b and plots in igure 7f. In addition, the tip vortex appears to succumb to the jet turbulence, causing a slight diffusion. Interaction of the jet turbulence with the tip vortex was also observed in the flow visualization by x/c = 8. Increasing the strength of the jet to =.5 and =. in igure 9d and igure 9e respectively, reveals how effective the jet is at diffusing the flap vortex. he results suggest that the more diffuse flap vortical structure begins to stretch and wrap around the more concentrated tip vortex. he lower levels of vorticity around the edge of a diffuse vortex can be removed in a process known as strain-induced vortex stripping as documented by Dritschel 9. It appears the jet flux reduces the separation distance, increases the rotation angle and causes significant diffusion of the flap vortex. Another explanation comes from the idea that unequal strengtortices merge more rapidly than if they were of equal strength 3. Examination of this revealed a negligible difference in circulation of around.5% when comparing the = and. cases. igure, igure and igure 2 revert back to the horizontal jet case at x/c = 6 in an attempt to explain how the tip vortex becomes more concentrated for larger momentum coefficients in igure 8. A vorticity profile through the time-averaged vortex centers can be found in igure. he reference case with no nozzle in the flow produces a symmetric distribution with only 6% difference in peak vorticity. On introduction of the nozzle structure, a large reduction in peak value is observed for the flap vortex. his is expected because the nozzle is placed.6c from the flap-edge, causing some unwanted interference. his is accompanied by a very small increase in vorticity for the tip vortex. Increasing the momentum coefficient to =.25 produces a large increase in both flap and tip vorticity peak of 23% and 6% respectively over the = case. his is unexpected because generally the jet causes diffusion. he obvious parameter to check was circulation but this offers a negligible change in the order of %. urther increase in momentum coefficient begins to reduce the flap vorticity but has little further effect on the tip. Another observation that can be made is the turbulence generated by the jet fluid reduces the vorticity value between the vortex pair and increases the separation of the vorticity peaks. his tends to suggest the influence of the jet moves the pair further from a merged state. o confirm whether the changes in peak vorticity in the time-averaged result is a function of vortex wandering or an actual reduction in vorticity, instantaneous data was analyzed. igure a and igure b show the maximum vorticity values taken from the time-averaged and instantaneous fields as a function of momentum coefficient for the flap and tip vortices respectively. he reference case (when there is no nozzle in the flow) is also included. he 7

8 reduction in maximum vorticity for the time-averaged flap vortex on the introduction of the nozzle structure ( = ) is not reflected in the instantaneous data in igure a. his suggests an increase in vortex wandering and is confirmed by comparing igure 2a and igure 2b where the flap vortex wandering appears to increase significantly in the spanwise direction. hese figures illustrate the instantaneous peak vorticity location for each vortex along with the standard deviation of the vortex positions plotted as error bars at the time-averaged centre location. he tip vortex shows little response to the introduction of the nozzle structure. Increasing momentum flux to =.25 increases the time-averaged vorticity peak for both flap (igure a) and tip (igure vortices but again there is little change in the instantaneous value. Both these changes can be attributed to a reduction in wandering (igure 2c), perhaps because of the vortices moving away from a merged condition. Increasing the momentum coefficient further sees a major reduction in time-averaged maximum vorticity which is accompanied by a decrease in the instantaneous maxima for the flap vortex (igure a). However for the =. case the reduction in time-averaged results is approximately 6% (compared to the reference case), whereas the instantaneous value only undergoes a 2% decrease (compared to the reference case). he greater reduction seen in the time-averaged data can be accredited to severe wandering of the flap vortex in igure 2e. he more concentrated tip vortex, hence larger peak vorticity values, for =.25,.5 and. is associated with a reduction in wandering in igure 2c, igure 2d and igure 2e respectively as the pair move further away from a merged state. igure 3 and igure 4 illustrate the vortex pair spacing and rotation angle as they progress downstream for the horizontal and vertical jet configurations respectively. Concentrating on the horizontal jet with no nozzle in the flow, igure 3a shows an approximately constant rate of rotation to just over 36 o or one orbit. igure 3b follows this trend with the pair approaching each other at an approximate linear rate up to x/c = 2. he data terminates at this point because for the next measurement station, x/c = 24, only a single vortex exists. he dashed line represents the collapse of the vortex pair into a single structure. here appears to be only a very small diffusive period, because a reduction in vortex spacing occurs immediately at x/c = 4. his suggests the convective merger stage is active which is possible because the pair have fulfilled the criterion required for the production of three-dimensional instabilities during merger. hat is at the upstream measurement location (x/c = 4) a/h =.2 and Re Γ > 2. Introducing the nozzle structure into the flow causes a small increase in separation distance at all downstream locations. he corresponding reduction in rotation angle is not visible until x/c = 8 is reached. or momentum coefficients of =.25 and greater, merging is clearly delayed as two vortex structures exist even at x/c = 24. An interesting observation is that between x/c = 8 and 2 the gradients of all lines are approximately constant in igure 3b. his indicates the vortices approach each other at the same rate. he jet flux has the greatest effect at the upstream locations where the gradients of the lines vary dramatically with blowing. he data indicates the spacing remains approximately constant up to x/c = 8, as the strength of the jet is raised. Even though the initial gradient of the lines varies, extrapolating the lines back to the ordinate axis suggests a convergence of the data at unity. Hence the mechanism behind this could be interpreted as a delay in the onset of the convective stage. At x/c = 2 the jet turbulence generated by a momentum flux of =. produced approximately a 63 o reduction in rotation angle and a 4% increase in vortex spacing over the = case. igure 4 suggests that moving the jet vertically below the flap has the exact opposite effect in that merging is promoted. Introducing the nozzle into the flow produces sufficient turbulence to cause an increase in rotation rate and a corresponding reduction in spacing. Merger now occurs upstream of x/c = 2. In fact, increasing the momentum flux moves the merger point as far upstream as x/c = 2 for =.. here appears to be an increase in rotation angle for the blowing cases, however this change is not as pronounced as for the horizontal jet. Another observation is the gradient of the lines in igure 4b appear to become more negative as blowing increases. Physically this means the inward radial velocity of the vortex pair has increased. Extrapolating the data back to the ordinate axis, the lines tend to converge at non-dimensional spacing of unity. Increasing the momentum coefficient to =. produces a 2% reduction in vortex spacing over the = case at x/c = 8. So far it has been shown that placing the jet in two different positions produces vastly dissimilar results. his suggests the merging process is sensitive to the initial conditions. o analyze merging in detail, it is common for the velocity field to be transformed into a rotating frame. igure 5 and igure 6 show the results of this with turbulence contours overlaid by streamlines at x/c = 4. igure 5a places the jet /c =.6 horizontally inboard of flap. he small asymmetry in the outer-recirculation region is a result of the nozzle interference. Increasing the blowing to =.5 in igure 5b shows the jet turbulence trailing the flap vortex in close proximity which disturbs the organized streamline patterns. his disturbance is located at the point where vorticity laden fluid from the inner region is advected to a larger radius by the rotation of the outer-recirculation region. herefore it is clear that the jet has a major effect on the mechanism that produces convective merger. his idea can be used to aid the understanding of the trends produced in the vortex separation diagrams (igure 3. At upstream locations, where the jet turbulence intensity is still large, the gradient of the lines reduced, as discussed previously. Hence the jet affects the convective stage which impedes the approach of the vortex pair. As the turbulence decays or its position 8

9 moves relative to the vortex pair (see igure 6), the outer-recirculation region regains its structure and ability to advect vorticity. herefore all lines have the same gradient (igure 3 downstream of x/c = 8 because the convective stage can proceed unaffected. Moving the jet to the vertical configuration in igure 6 does not appear to disrupt the streamlines as previously observed in igure 5. In this arrangement high intensity jet turbulence interacts directly with the flap vortex, causing rapid diffusion. urther experiments were performed at a larger initial vortex spacing of /c =.. hese data are useful because it will confirm whether the trends already discussed can be repeated with a different experimental arrangement. An additional jet location was included vertically below the centre of the flap and tip as seen in configuration III (able 2). his arrangement gives more information about the importance of the initial jet location. low visualization in igure 7 was performed in exactly the same manner as previously seen. With the jet located.6c inboard of the flap (igure 7a and igure 7, similar results to those in igure 3 are produced at x/c = 4. he jet fluid trails the flap vortex as the pair rotates due to their self induced velocities. However slightly more interaction is observed at x/c = 6, probably because the rate of rotation is lower than in the previous case. Moving the jet vertically below the flap in igure 7c causes the bulk of the jet fluid to become elongated and stretched alongside the flap vortex. At x/c = 6 (igure 7d) a severe interaction between the vortex pair and jet has occurred. inally moving the jet vertically below the centre of the flap and tip (configuration III) as in igure 7e produces a different result. It might be expected to perform similar to configuration II in igure 7c because the flap would still tend to rotate into the path of the jet. At x/c = 4 no interaction with either vortex has occurred. his is similar to the horizontal case, except the jet fluid is now in the advancing side of the flap vortex. he downstream image reveals that the jet tends to interact with the tip vortex more than the flap. Comparing the rotation of the vortex pairs at x/c = 6 for all three jet positions, it is clear configuration II aids merging whereas configuration I retards merging the most. Axial vorticity fields for the three nozzle locations at x/c = 2 can be found in igure 8 to igure 2. With the jet located inboard of the flap, increasing the jet flux from = to. appears to cause severe diffusion of the flap vortex. his is accompanied by a very small reduction in rotation angle. More diffusion appears to have occurred for this case than for /c =.75 (igure 8e) which is probably an effect of the reduced rate of rotation, rather than the measurements being taken at different downstream locations. Moving the nozzle vertically below the flap in igure 9, results in a single diffuse vortex for =.. he final jet location vertically below the centre of the flap and tip (igure 2) causes the diffusion of botortices for =.. hey appear to be in a state of merger as the vortices are not distinct vorticity patches as for =, but instead the lowest vorticity levels have connected. Analyzing the vortex spacing for the /c =. experiments in igure 2, it is clear that locating the jet vertically below the flap in configuration II provided the greatest promotion of merger compared to the other positions. Vertically below the centre does aid merging slightly but only for larger momentum coefficients. Again the horizontal case actually interferes and delays the merger process, consistent with previous findings. he changes in spacing may not be as pronounced as the /c =.75 cases which again is probably a function of the reduced rotation rate for the larger spacing. hese results have been consistent with those performed at /c =.75. Detailed discussion on the mechanism behind retarding the merging process has already been presented. However it is still unclear whether merging can actually be promoted or if instead the large scale diffusion reduces the vorticity levels so severely that it only leaves one recognizable vortex structure. In an attempt to solve the problem, the circulation for the tip vortex was calculated as it should provide a quantitative measure of merging. Of the three jet configuration, the only case to show an increase in tip circulation was configuration II, when the jet was located vertically below the flap as in igure 9. or =, the circulation of the tip vortex was approximately 5% of the total, which is expected because they are an equal strength pair. Larger momentum coefficients of =.5 and =. saw the tip vortex circulation increase to /Γ o =.56 and /Γ o =.95 respectively. his suggests vorticity from the flap vortex has combined with the tip vortex and that the system has moved closer to a fully merged state. As previously mentioned the vorticity plot for the =. case, refer to igure 9b, only shows a single vortical structure and it has just been revealed the circulation of that vortex has not increased to % of total. his is probably because some low level vorticity, which can be seen in the plot, has not yet been ingested by the dominant vortical structure. he other jet positions (configuration I and III) show little circulation change with increasing momentum coefficient, which suggests little transfer of vorticity. It is clear the three jet positions produce vastly differing results, even though all configurations had approximately the same initial distance from the flap tip. In an attempt to find a trend between the initial vortex to jet distance, the jet location with respect to the centre of vortex pair rotation was analyzed. However this does not produce a consistent relationship because the smallest initial jet to centre of rotation distance occurs for configuration III, but this position does not produce the best promotion of merging. In addition, vortices with different initial spacings do not have the same rotation rate. Hence this suggests that in order to produce a beneficial jet/vortex interaction, careful selection of the initial engine location is required. 9

10 C. Unequal Strength Vortex Merging Merging of unequal strength co-rotating vortices is more representative of real aircraft wakes. Experiments have been performed with an initial vortex spacing /c =.75 and the jet in configurations I and II (able 2). Aircraft on approach produce a pair of vortices with relative strength >. he vorticity fields for these experimental results which have an initial circulation ratio / =.54, can be found in igure 22. At x/c = 6, the no nozzle reference case (igure 22a) shows the pair having approached and begun to form a single structure. he weaker tip vortex has clearly been elongated and deformed by the strain field imposed by the flap vortex. Introducing the nozzle structure produces a small reduction in rotation angle as visible in igure 22b. However no obvious change occurs to the structure of the vortices. Increasing the momentum coefficient to =.25,.5 and. in igure 22c, igure 22d and igure 22e respectively, shows three main trends. he first is there is a clear reduction in rotation angle with increasing jet turbulence as already observed for equal strengtortex cases. he second is the flap vortex becomes dramatically more diffuse. his is a function of the momentum flux and has also been observed previously. he third point is the weaker tip vortex becomes more axisymmetric. Possible reasons for this include the pair move further from merging or the less coherent flap vortex loses its ability to deform and strip vorticity from the weaker vortex. igure 23 provides a detailed analysis of spacing and rotation for the vortices which appear to be consistent with results from the equal strengtortex cases. Upstream of x/c = 8 the jet has little effect on rotation (igure 23a), however downstream the momentum flux causes the data to diverge. he presence of the nozzle structure produces a small reduction in rotation angle over the reference case. his reduction is enough to delay merger from a point downstream of x/c = 6 to x/c = 2. Increasing the momentum flux consistently reduces the rotation angle and for =. at x/c = 6 there is a 6 o decrease (/6 of an orbit) over the = case. he separation plot in igure 23b shows the same trend, that the spanwise jet increases the vortex spacing. Increasing the momentum flux reduces the gradient of the lines between x/c = 4 and 8. Extrapolating the data back to x/c =, all lines converge at a value close to unity. Generally the approacelocity of the pair is constant at points downstream of x/c = 8. At x/c = 6 the jet turbulence generated by a momentum flux of =. produces an increase of approximately 7% over the = case. A similar merging delay mechanism, as already seen for equal strengtortices, must be present. Moving the jet nozzle to configuration II causes a gradually more diffused flap vortex as momentum coefficient is increased at x/c = 8 (igure 24). Merging is clearly promoted as rotation angle increases and the lowest vorticity level begins to combine into a single structure for =. (igure 24e). As the vortices move closer to a state of merger, igure 24c shows the weaker tip vortex becoming more elongated and deformed. Interestingly for the largest jet flux, the very diffuse flap vortex also appears to have elongated. his is an effect from the strain field emanating from the weaker tip vortex which suggests the flap structure loses its coherency as it moves into the path of the jet flux, allowing the stripping of the lowest vorticity levels. he analysis in igure 25 shows consistent findings with equal strengtortex merger. Interference from the nozzle structure produces a promotion of merger over the reference case which is clear from the rotation and separation plots, igure 25a and igure 25b respectively. Increasing the momentum coefficient moves the merged vortex location to a point just upstream of x/c = 6 from x/c = 2. Changing the momentum coefficient from = to. produces a 5 % reduction in spacing at x/c = 2. Adapting the setup to simulate a take-off configuration was achieved by increasing the strength of the tip vortex relative to the flap vortex. he circulation ratio measured in the wake at x/c = 4 was / =.65. Vorticity contour plots at x/c = 6 for the jet located in the spanwise plane (configuration I) can be found in igure 26. he reference case shows severe elongation of the weaker vortex compared to a more axisymmetric tip vortex. Introducing the jet nozzle and increasing the momentum flux consistently reduces the rotation angle. he greater merger is retarded, the closer the weaker flap vortex tends to an axisymmetric structure. igure 27 summarizes this data and shows that again a delay in merging is present. A consistent decrease in rotation angle and increase in vortex spacing occurs as turbulence from the jet is introduced into the flow. Comparing the = and. at x/c = 6 reveals a slightly larger increase in separation distance (approximately 23%) than that observed for the approach case ( / =.54) in igure 23. However at x/c = 24, all experimental results have collapsed to a single structure. Results at x/c = 8 for the jet vertically beneath the flap (configuration II) can be found in igure 28. he jet turbulence rapidly interacts with the flap vortex causing severe diffusion. his result is in agreement with previous data for this jet configuration. or the =. case in igure 28e the jet turbulence implements catastrophic diffusion of the flap vortex causing it to become unrecognizable. igure 29 indicates that the results are again consistent with those already observed for cases where turbulence is introduced vertically below the flap. Rotation angle is increased and vortex separation is reduced. he jet appears to be more effective at promoting merger in this case than for the approach circulation ratio ( / =.54) in igure 25, because here the weaker vortex emanates from the flap which is known to rotate into the path of the jet flux. his has the effect of moving the merged location further upstream.

11 IV. Conclusions his experimental study investigates the effect of a cold engine jet on the process of vortex merging in the near wake. Equal and unequal strength co-rotating vortices were produced to replicate the outboard flap-edge and wing-tip vortex structures generated by real aircraft. low visualization and particle image velocimetry measurements were performed in order to provide a detailed understanding of the jet effects on the vortical flow. he sensitivity of vortex merging to the introduction of external turbulence has been revealed in this investigation. Severe effects on merging can occur if the turbulence interacts with the vortical structures before its intensity decays. he parameter that dictates whether merging will be promoted or delayed is the initial relative positions of the vortices and jet plume. he largest promotion of merger occurs when the high intensity jet turbulence interacts directly with only one of the two vortices. his would occur on four engined aircraft where the outboard jet is located vertically beneath the flap-edge vortex. Self-induced rotation of the vortex pair tends to move the flap vortex directly into the path of the exhaust plume. he consequence is a severe diffusion and reduction in coherence of the flap vortex. Merging is promoted as the flap vorticity begins to wrap around the unaffected and more concentrated tip vortex. he diffusion could also cause additional amounts of vorticity laden fluid from the flap vortex to cross the separatrices into the outer-recirculation region. Advection of this fluid to a larger radius would result in the approach of the cores to conserve angular momentum. Repositioning the jet vertically beneath the centre of the flap-edge and wing-tip vortices is again realistic of an outboard engine on a four engined aircraft. he rotational flow induced by the vortices tends to carry the jet fluid with the vortex pair, causing a more symmetric jet interaction and diffusion of botortices. his does not leave a more concentrated vortex to dominate the merging process and consume the vorticity from the less coherent vortex structure. Merging was promoted but on a much smaller scale than seen previously. A small reduction in vortex spacing was observed which was likely to be facilitated by the transfer of vorticity across the rotating reference frame separatrices to the outer-region where it can be advected outwards. Locating the jet along the spanwise plane inboard of the flap is approximately representative of aircraft with only two engines. It could be predicted that the jet fluid would interact directly with only the flap vortex, therefore promoting merger. However the results clearly indicate that the collapse of the vortex pair into a single structure is delayed. Analysis revealed that the jet turbulence tended to trail the flap vortex as the vortices rotated. herefore, negligible interaction between the jet fluid and flap vortex was observed and the analysis revealed the jet flux to have little effect on the circulation of the vortices. he probable mechanism responsible for the delay was exposed when viewing the cross-flow rotating reference frame at the most upstream measurement location. he jet turbulence appears to alter the streamline pattern in the outer-recirculation region. he disturbance occurred at the point where vorticity is advected radially outward which clearly inhibits the convective merger stage, limiting its ability to reduce the separation of the vortex pair. Moving downstream results in a decay of the jet turbulence, allowing the outer-recirculation region to regain its coherence and hence the spacing of the vortex cores begins to reduce. Interestingly, once the convective mechanism fully recovers, the approacelocity of the vortices is independent of the initial jet momentum coefficient. Momentum flux was another parameter that was varied. Results revealed that the greater the strength of the jet, the more turbulence that was introduced into the flow which consequently had a larger effect on the merging process. hat is either more diffusion of the vortices or greater disruption to the outer-recirculation region. Similar trends were produced for all combinations of vortex circulation ratio, that is =, > and <. Overall it appears the data obtained on jet interactions with co-rotating vortices could be useful to alter the merging in the near wake for real aircraft. his is especially true for take-off when the jet flux from the engine is relatively large. Acknowledgment his research has been performed with the support from European Commission 6 th framework programme project, undamental Research on Aircraft Wake Phenomena (AR-Wake).

12 References Rossow, V.J., "Lift-generated vortex wakes of subsonic transport aircraft," Progress in Aerospace Sciences, Vol 35, No. 6, 999, pp Meunier, P., Le Dizes, S., and Leweke,., "Physics of vortex merging," Comptes Rendus Physique, Vol 6, No. 4-5, 25, pp Chen, A.L., Jacob, J.D., and Savas, O., "Dynamics of corotating vortex pairs in the wakes of flapped airfoils," Journal of luid Mechanics, Vol 382, 999, pp Meunier, P. and Leweke,., "hree-dimensional instability during vortex merging," Physics of luids, Vol 3, No., 2, pp Cerretelli, C. and Williamson, C.H.K., "he physical mechanism for vortex merging," Journal of luid Mechanics, Vol 475, 23, pp Leweke,., Meunier, P., Laporte,., and Darracq, D., "Controlled interaction of co-rotating vortices," 3rd ONERADLR Aerospace Symposium, No. paper S2-3., 2. 7 Griffiths, R.W. and Hopefinger, E.J., "Coalescing of geostrophic vortices," Journal of luid Mechanics, Vol 78, 987, pp Meunier, P., Ehrenstein, U., Leweke,., and Rossi, M., "A merging criterion for two-dimensional co-rotating vortices," Physics of luids, Vol 4, No. 8, 22, pp Crow, S.C., "Stability theory for a pair of trailing vortices," Vol 8, No. 2, 97, pp Leweke,. and Williamson, C.H.K., "Cooperative elliptic instability of a vortex pair," Journal of luid Mechanics, Vol 36, 998, pp Jimenez, J., "Stability of a pair of co-rotating vortices," Physics of luids, Vol 8, No., 975, pp Paoli, R. and Garnier,., "Interaction of exhaust jets and aircraft wake vortices: small-scale dynamics and potential microphysical-chemical transformations," Comptes Rendus Physique, Vol 6, No. 4-5, 25, pp Batchelor, G.K., "Axial flow in trailing line vortices," Journal of luid Mechanics, Vol 2, No. Part 4, 964, pp Paoli, R., Laporte,., Cuenot, B., and Poinsot,., "Dynamics and mixing in jet/vortex interactions," Physics of luids, Vol 5, No. 7, 23, pp Michalke, A. and Hermann, G., "On the inviscid instability of a circular jet with external flow," Journal of luid Mechanics, Vol 4, 982, pp Wang,.Y., Proot, M.M.J., Charbonnier, J.-M., and Sforza, P.M., "Near-field interaction of a jet with leading-edge vortices," Journal of Aircraft, Vol 37, No. 5, 2, pp Wang,.Y. and Zaman, K.B.M.Q., "Aerodynamics of a jet in the vortex wake of a wing," AIAA Journal, Vol 4, No. 3, 22, pp Margaris, P., Marles, D., and Gursul, I., "Experiments on interaction of a jet with a trailing vortex," AIAA Paper AIAA-27-23, 45th Aerospace Science Meeting and Exhibition, January 27, Reno, NV. 9 Dritschel, D.G., "Strain-induced vortex stripping," Mathematical aspects of vortex dynamics; Proceedings of the Workshop, Leesburg, VA, (A ), 989, pp

13 Wing-tip vortex generator lap-edge vortex generator ip vortex h s lap vortex U j Water level U _ c y z x igure. Schematic of generic wings and jet nozzle model Laser Sheet (Cross-flow plane) Digital Camera - PIV - low visualization (digital video) Experimental Rig - 2 cambered wings - Jet nozzle structure Laser Unit - PIV (Nd:YAG) - low visualization (Argon Ion) z y x U igure 2. Experimental setup in water tunnel 3

14 = =.25 a) x/c = 4 f) x/c = 4 x/c = 8 g) x/c = 8 c) x/c = 2 h) x/c = 2 igure 3. low visualization for equal strength co-rotating vortices ( = tip vortex, = flap vortex), /c =.75, /c =.6. Left column =, right column =.25. Schematic illustrates the experimental setup (configuration I). Continues over page. 4

15 d) x/c = 6 i) x/c = 6 e) x/c = 24 j) x/c = 24 igure 3. low visualization for equal strength co-rotating vortices ( = tip vortex, = flap vortex), /c =.75, /c =.6. Left column =, right column =.25. Schematic illustrates the experimental setup (configuration I). See previous page 5

16 = =.25 a) x/c = 4 f) x/c = 4 x/c = 8 g) x/c = 8 c) x/c = 2 h) x/c = 2 igure 4. low visualization for equal strength co-rotating vortices ( = tip vortex, = flap vortex), /c =.75, /c =.6. Left column =, right column =.25. Schematic illustrates the experimental setup (configuration II). Continues over page. 6

17 d) x/c = 6 i) x/c = 6 e) x/c = 24 j) x/c = 24 igure 4. low visualization for equal strength co-rotating vortices ( = tip vortex, = flap vortex), /c =.75, /c =.6. Left column =, right column =.25. Schematic illustrates the experimental setup (configuration II). See previous page 7

18 a) ωc U d) c) e) igure 5. Normalized instantaneous vorticity at x/c = 4, /c =.75 and /c =.6. a) Reference case (no nozzle in flow), Jet configuration I, =, c) Jet configuration I, =., d) Jet configuration II, =, e) Jet configuration II, =.. 8

19 a) U std U (%) e) f) c) g) igure 6. urbulence intensity for equal strength co-rotating vortices and jet configuration I, /c =.75 and /c =.6. (left column - =, right column - =.). a) x/c = 4, x/c = 8, c) x/c = 2, d) x/c = 6, e) x/c = 4, f) x/c = 8, g) x/c = 2, h) x/c = 6. Continues over page. 9

20 d) h) igure 6. urbulence intensity for equal strength co-rotating vortices and jet configuration I, /c =.75 and /c =.6. (left column - =, right column - =.). a) x/c = 4, x/c = 8, c) x/c = 2, d) x/c = 6, e) x/c = 4, f) x/c = 8, g) x/c = 2, h) x/c = 6. See previous page. 2

21 a) U std U (%) e) f) c) g) igure 7. urbulence intensity for equal strength co-rotating vortices and jet configuration II, /c =.75 and /c =.6. (left column - =, right column - =.). a) x/c = 4, x/c = 8, c) x/c = 2, d) x/c = 6, e) x/c = 4, f) x/c = 8, g) x/c = 2, h) x/c = 6. Continues over page. 2

22 d) h) igure 7. urbulence intensity for equal strength co-rotating vortices and jet configuration II, /c =.75 and /c =.6. (left column - =, right column - =.). a) x/c = 4, x/c = 8, c) x/c = 2, d) x/c = 6, e) x/c = 4, f) x/c = 8, g) x/c = 2, h) x/c = 6. See previous page. 22

23 .2.8 lap vortex a) ip vortex d) c) e) igure 8. Normalized vorticity for equal strength co-rotating vortices at x/c = 6, /c =.75 and /c =.6. a) Reference case (no nozzle in flow), =, c) =.25, d) =.5, e) =.. Minimum contour level ωc/u =.5 with.25 intervals. Schematic illustrates the experimental setup (configuration I). 23

24 .2.8 ip vortex a) lap vortex d) c) e) igure 9. Normalized vorticity for equal strength co-rotating vortices at x/c = 8, /c =.75 and /c =.6. a) Reference case (no nozzle in flow), =, c) =.25, d) =.5, e) =.. Minimum contour level ωc/u =.5 with.5 intervals. Schematic illustrates the experimental setup (configuration II). 24

25 7 Reference Case = =.25 =.5 =. 6 lap Vortex ip Vortex 5 ωc/u Distance from centre of vortex pair / c igure. Normalized vorticity profile througortex cores in igure 8. Equal strength co-rotating vortices for x/c = 6, /c =.75 and /c =.6 with the jet in configuration I. a) 2 Reference Case (ime-averaged) Reference Case (Instantaneous) /c =.6 (ime-averaged) /c =.6 (Instantaneous) 2 Reference Case (ime-averaged) Reference Case (Instantaneous) /c =.6 (ime-averaged) /c =.6 Instantaneous) 8 8 ω max c/u 6 ω max c/u igure. ime-averaged and mean instantaneous maximum vorticity values in the vortex core as a function of momentum coefficient for x/c =6, /c =.75 and /c =.6 with the jet in configuration I. a) lap vortex, ip vortex. 25

26 .2 lap vortex lap ip a) ip vortex d) c) e) igure 2. Instantaneous peak vorticity locations for equal strength co-rotating vortices at x/c =6, /c =.75 and /c =.6 with the jet in configuration I (see schematic). Error bars represent the standard deviation of positions about the time-averaged centre location. a) Reference case (no nozzle in flow), =, c) =.25, d) =.5, e) =

27 45 a) θ Reference Case = =.25 =.5 = x/c h.2 Reference Case = =.25 =.5 =. θ.8 h/ x/c igure 3. Downstream development for equal strength co-rotating vortices for /c =.75 with the jet in configuration I (see schematic). a) ime-averaged rotation angle, ime-averaged vortex separation. 27

28 45 a) θ 2 5 Reference Case = =.25 =.5 = x/c h.2 Reference Case = =.25 =.5 =. θ.8 h/ x/c igure 4. Downstream development for equal strength co-rotating vortices for /c =.75 with the jet in configuration II (see schematic). a) ime-averaged rotation angle, ime-averaged vortex separation. 28

29 a) U std U (%) igure 5. urbulence contours for equal strength co-rotating vortices overlaid with time-averaged streamlines in a rotating frame at x/c = 4, /c =.75 and /c =.6 with the jet in configuration I (see schematic). a) =, =.5 29

30 a) U std U (%) igure 6. urbulence contours for equal strength co-rotating vortices overlaid with time-averaged streamlines in a rotating frame at x/c = 4, /c =.75 and /c =.6 with the jet in configuration II (see schematic). a) =, =.5 3

31 a) x/c = 4 c) x/c = 4 x/c = 6 d) x/c = 6 igure 7. low visualization for equal strength co-rotating vortices ( = tip vortex, = flap vortex), /c =., /c =.6 and =.25. Schematic above columns indicate experimental setup (left column = configuration I, right column = configuration II). Continues over page. 3

32 e) x/c = 4 f) x/c = 6 igure 7. low visualization for equal strength co-rotating vortices ( = tip vortex, = flap vortex), /c =., /c =.6 and =.25. Schematic above column indicates experimental setup (configuration III). See previous page. 32