PHYSICS OF FLUIDS 26, 046101 (2014)

Vortex dynamics studies in supersonic flow: Mergingof co-rotating streamwise vortices

L. Maddalena,a) F. Vergine,b) and M. Crisantic)

Department of Mechanical and Aerospace Engineering, University of Texas at Arlington,Arlington, Texas 76019, USA

(Received 4 November 2013; accepted 31 March 2014; published online 14 April 2014)

For air-breathing propulsion systems intended for flight at very high Mach numbers,combustion is carried out at supersonic velocities and the process is mixing limited.Substantial increase in mixing rates can be obtained by fuel injection strategies cen-tered on generating selected modes of supersonic, streamwise vortex interactions.Despite the recognized importance, and potential of the role of streamwise vorticesfor supersonic mixing enhancement, only few fundamental studies on their dynam-ics and interactions have been conducted, leaving the field largely unexplored. Areduced order model that allows the dynamics of complex, interacting, supersonicvortical structures to be investigated, is presented in this work. The prediction of theevolution of mutually interacting streamwise vortices represents an enabling elementfor the initiation of an effective, systematic experimental study of selected cases ofinterest, and is an important step toward the design of new fuel injection strategiesfor supersonic combustors. The case presented in this work is centered on a mergingprocess of co-rotating vortices, and the subsequent evolution of a system composedof two counter-rotating vortex pairs. This interaction was studied, initially, with theproposed model, and was chosen for the peculiarity of the resulting morphology of thevorticity field. These results were used to design an experimental investigation withthe intent to target the same specific complex flow physics. The experiment revealedthe same peculiar features encountered in the simulation. C© 2014 AIP PublishingLLC. [http://dx.doi.org/10.1063/1.4871022]

I. INTRODUCTION

Streamwise supersonic vortices, along with their interactions, are of particular interest fortheir potential to enhance fuel/air mixing in the combustion chamber of hypersonic air-breathingpropulsion systems. Because of the high speed, the residence time of the flow within the combustor isof the order of 1ms and the process is mixing limited. Mixing enhancement with streamwise vorticalstructures is achieved by means of the synergistic action of both additional turbulence introducedin the flowfield and increased strain rates at the interface between the reactants.1, 2 Streamwisevortices can be produced by a jet issued into a cross stream,3–5 a comprehensive review of which hasbeen presented by Schetz,6 by the evolution of a particular distribution of baroclinically depositedvorticity,7 or by employing physical devices such as vortex generators. Vorticity generation oncontoured devices is mainly due to the so-called cross-stream shear:8 a Counter-rotating VortexPair (CVP) is shed from the trailing edge of a ramp, promoting the entrainment of the surroundingflow. Regardless of the specific generation mechanism, both subsonic and supersonic vortices arecharacterized by their mutual interaction capability, which is responsible for the variation of theirspatial displacement in the flowfield and the modification of the morphology of a fuel plume issuing

a)maddalena@uta.edub)fabrizio.vergine@mavs.uta.educ)matthew.crisanti@mavs.uta.edu

1070-6631/2014/26(4)/046101/17/$30.00 C©2014 AIP Publishing LLC26, 046101-1

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-2 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

from an injection device. However, despite the recognized importance of the role of streamwisevortices in the evolution of reacting and non-reacting supersonic mixing flows, only few fundamentalstudies on their dynamics and interactions have been conducted.9

One important mechanism of vorticity generation results from the interaction between variabledensity and pressure fields. In their original work on shock enhanced hypersonic mixing, Marble,Hendricks, and Zukoski10 proposed the possibility of generating streamwise vorticity utilizing thedensity gradient at the interface between air and hydrogen fuel interacting with the pressure gradientcreated by an oblique shock. Specifically, Marble, Hendricks, and Zukoski10 considered the caseof a cylindrical stream of hydrogen flowing parallel with a supersonic airstream and impingingon a weak oblique shock. In the aforementioned work it was suggested that, because the cross-plane velocities introduced by the shock interaction are small compared to the free-stream velocity,the steady interaction between the weak shock and the light gas jet immersed in the co-flowingsupersonic air stream is analogous to a two-dimensional time-dependent interaction between a weaknormal shock and an initially circular region filled with the light gas embedded in air. Shock tubeexperiments were conducted primarily in the GALCIT 17-in. Shock Tunnel by Marble et al.7 andwere aimed at studying the effects of the passage of a shock through a laminar circular columnof helium. The experiments utilized planar laser-induced fluorescence (PLIF) in which helium wasseeded with a small amount of biacetyl tracer. The time sequence PLIF image data showed thatthe vorticity deposited by the baroclinic torque due to the misalignment of pressure and densitygradients at the edges of the light-gas column evolved into a CVP which notably increased themixing rate. The analysis of the two-dimensional temporal evolution of the considered case ofbaroclinically deposited vorticity on the jet periphery showed that this analogous flow captured thedevelopment and the distortion caused by the resulting self-induced vortical flow, and illustratedthe basic phenomenon observed in the series of shock tube experiments. The properties of turbulentmixing in a Richtmyer-Meshkov unstable fluid layer have been recently studied since then by manyauthors.11–13

In an effort to apply this mechanism to a practical injection concept, Marble et al.7 proposed aseries of contoured compression-expansion ramps through which helium was injected at Mach 1.7into a parallel Mach 6 airflow. This geometry was intended to baroclinically introduce vorticity inthe flow due to the interaction between the oblique shock, located at the base of the ramps, with theinjectant. In the works of Waitz, Marble, and Zukoski,8, 14 the concept was extensively studied bothexperimentally and numerically. Among other outcomes, these efforts showed that axial vorticitywas produced by shock impingement, but it was also clear that the vorticity produced by the cross-stream shear was of the same order of magnitude, hindering the chance to recognize the relativecontribution of each phenomenon. Later, Waitz, Marble, and Zukoski14 and Marble15 proposed anupdated design of the injection device increasing by a factor of three the spacing of the rampscompared to the initial concept7 as it was noticed that the boundary layer from the compressionramps into the troughs weakened the compression shock at the base, compromising the performance.In essence, from a vortex dynamics perspective, this new configuration prevented any interactionamong the multiple vortical structures shed from the injector and resulting from the roll-up of thevorticity, which, on the other hand, is one of the scopes of the present investigation.

Waitz et al.1 thoroughly analyzed the subsonic flow downstream of lobed mixers, and addition-ally employed a two-dimensional unsteady approach to describe an example of streamwise vorticesevolving in a Mach 2 flow by solving the incompressible, two-dimensional Navier-Stokes equations.The adopted approach was justified by arguing that for the lobed mixers shapes investigated, cross-stream Mach numbers are subsonic for low-supersonic axial Mach numbers, and the magnitude andevolution of the streamwise circulation are unchanged compared to low speed cases. Research wasalso devoted to the numerical investigation of the flowfield originating from the vortices shed fromalternating compression ramps and expansion troughs at Mach 6, considered as two-dimensional andunsteady.7, 14 By leveraging Marble’s proposed analogy,7 Yang, Kubota, and Zukoski16 numericallysimulated families of two-dimensional, unsteady shock-induced vortical flows consisting of one ormore regions of light gas surrounded by heavy gas and processed by a normal shock wave. In thatwork, mixing was characterized by an asymptotic stretching rate. Although the results were defi-nitely able to capture important aspects of the morphology associated with the distortion and mixing

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-3 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

of the light gas due to the reorganization of the baroclinically deposited vorticity, the hyperbolicnature of the supersonic flow equations was not taken into account.

This work describes a reduced order model – implemented in a code named VorTx – suitable forthe prediction and analysis of the dynamics and interaction of complex configurations of streamwisevorticity patches in supersonic flows (not necessarily completely organized into coherent vorticalstructures), taking into account the implications of the existence of domains of influence, dictated bythe Mach number, outside of which interactions are not possible. The potential of this model to targetsystematic studies of supersonic vortex interactions is presented here by focusing the investigationon a specifically selected merging process. The experimental investigation, intended to reproducethe specific complex case analyzed with VorTx, did reveal the expected morphology, and alsohighlighted some similarities with the physics of subsonic vortex merging, extensively describedin the works of Cerretelli and Williamson17 and Meunier, Dizes, and Leweke.18 The challenge inthe prediction of the complex physics of this phenomenon in high speed flows makes it a suitableshowcase to validate the concepts developed. As will be shown, the use of the proposed methodenables a whole new approach in the analysis and the understanding of the interactions among evenmore complex systems of supersonic vortices.

II. MODEL

In this section a reduced-order model capable of describing the relevant dynamics of an inter-acting system of streamwise, supersonic, vortical structures is discussed. The assumptions made andtheir implications are the subject of the next paragraphs in which the slender body approximation,the streamwise supersonic vortex filament model, and the construction of the finite-scale streamwisevortices characteristic of the flows to be investigated are discussed. With this model, the flowfieldcan be computed once the Mach number of the flow in which the vortices are shed, the convec-tive velocity, the initial relative position of the vortices, and an estimation of the circulation of thelarge-scale structures are known.

A. Slender body approximation

In their work on shock-enhanced hypersonic mixing, Marble, Hendricks, and Zukoski10 sug-gested that the steady interaction between a weak shock and a light gas jet immersed in a co-flowingsupersonic air stream is analogous to a two-dimensional time-dependent interaction between a weakshock and an initially circular region filled with the light gas embedded in air. The analysis of thetwo-dimensional temporal evolution of the baroclinically deposited vorticity on the jet peripheryshowed that this analog flow captures the development and the distortion caused by the result-ing self-induced vortical flow and illustrates the basic phenomenon observed in a series of shocktube experiments. The works of Yang, Kubota, and Zukoski,16 Waitz, Marble, and Zukoski,8 andDrummond et al.19 corroborate the usefulness of this analogy as a qualitative tool for the illustrationof the basic phenomenon of shock-induced vortical flow. Marble15 indicated that the base of theaforementioned analogy is that the scales of the motions associated with the cross-plane velocitiesestablished by the vorticity dynamics are small in comparison with the freestream velocity. Thisdifference in scale allows the adoption of a slender body approximation.

The hypersonic equivalence principle dictates that the steady hypersonic flow over a slenderbody is equivalent to an unsteady flow in one less space dimension. The transformation that relatesthe third dimension x, and the time t, is given by x = Uc · t, where Uc is the convective velocity.The experiments shown by Marble et al.7 and Waitz, Marble, and Zukoski14 were conducted atMach 6. However, experiments conducted by Neice and Ehret20 on the pressure distributions overogive cylinders show that the hypersonic similarities, based on the hypersonic small-disturbanceequations, also hold at supersonic Mach numbers.

In this work, we have adopted the slender body approximation for the analysis of the complexinteraction of multiple supersonic vortices generated by specific vortex generators in a shock-freedomain while, therefore, neglecting the baroclinic contribution to the vorticity as studied in Marble’scanonical case.7 The experimental results corroborate the 2D unsteady flow simulations. When, as in

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-4 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 1. (a) Schematic of a horseshoe vortex in supersonic flow; (b) schematic of the interaction of two vortex filaments: theinteraction zone begins when the cores of each filament (dashed lines) enter in the domain of influence of each other.

the cases presented here, vortices are the dominant evolutionary elements of the flow, the slendernessbecomes a condition on the ratio between the in-plane and off-plane velocities. In the simplest caseof a single vortex with tangential velocity uθ and circulation �, the assumption requires that thisratio be much smaller than unity. The in-plane components scale as uθ ∝ �/l, thus the conditionbecomes �/Ucl � 1, where l is the scale of the vortex core. In the case of a complex interaction,typical of vortex merging and amalgamation processes, the maximum in-plane velocity must beconsidered in order to assess the effective slenderness of the resulting structure. Additionally, threedimensional effects introduced by the presence of spanwise coherent structures must be negligiblefor the previous assumptions to hold. This condition establishes that the flow is essentially dominatedby the streamwise vortex dynamics. Therefore, the validity of the model is limited to regions of theflow in which the spanwise structures, if present, have a circulation which is small compared to thatof the streamwise vortices, and in which the convective velocity is sufficiently large. For example,in the wake created by an intrusive injection strategy, these conditions may be achieved at somedistance from the injection point.

B. Supersonic vortex model

For the high Reynolds numbers typical of the supersonic flows of interest, and the time scalesassociated with the processes considered here, an inviscid, non-diffusive formulation is considered.Although this simplification will suppress some features of the actual process, it does reproduce, asit will be clearly shown later, peculiar features associated with the morphological evolution of theplume of a passive scalar introduced in the vortical flow and subjected to the action of the large-scalestirring structures.

A vortex model consistent with the inviscid description and the assumption that the small-disturbance theory can be applied is the one that follows from supersonic lifting line theory. Thestreamwise vortices of a supersonic lifting line can influence only the domain defined by the Machcones that arise from the point of their formation. Closed-form relations for calculating the inducedvelocity field of the lifting line are obtained by computing the spatial derivatives of the lifting linepotential in supersonic flow, which is written in Eq. (1) for trailing vortices lying on the (x, y) plane,21

where x is the streamwise direction as shown in the schematic in Fig. 1(a).

� = �

2π

[tan−1 x(y − 1)

z√

�− tan−1 x(y + 1)

z√

�

], (1)

where

� = x2 − (M2 − 1)[(y − 1)2 + z2

]. (2)

The surface represented by � = 0 defines the Mach cone surrounding the streamwise vortex filamentsand is also the boundary of influence of each filament. The potential is other than zero only withinthe Mach cones, while it is zero in the remaining portion of the space. The two velocity components,v(x, y, z) and w(x, y, z) representing the flow in a plane perpendicular to the streamwise vortex in

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-5 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

a single generic Mach cone of a counterclockwise-spinning vortex evolving along the x axis andstarting at (0, ys, zs) are shown in Eqs. (3) and (4):

v(x, y, z) = �

2π

x(z − zs)[(z − zs)2 + (y − ys)2

]√�

, (3)

w(x, y, z) = − �

2π

x(y − ys)[� − (M2 − 1)(z − zs)2

][(z − zs)2� + (y − ys)2x2

] √�

. (4)

These velocity components become infinite at the cone’s surface and tend to the induced velocitiesobtained by a vortex filament in incompressible flow (i.e., the Biot-Savart law), for values of thedownstream coordinate x that tend to infinity. When several vortices are considered, the ith vortexinduces a velocity, V̄i = (vi , wi ), only in the portion of the (y, z) plane enclosed within the boundariesof its Mach cone. As a consequence, it is not possible for two (or more) vortical structures to interactwhen they are outside of their respective Mach cones. The mutually induced velocities on eachvortex can be calculated as the superposition of the effects of the other N − 1 vortices in thesystem (V̄i = ∑N−1

j=1 V̄ j , with i �= j), accounting for their relative position, circulation, and Machcone aperture. To obtain a closed system of equations for the translational motion of the vortices,Helmholtz’s result that the vortex lines are material lines is used. Hence, the point vortex equation onthe unbounded plane for the generic vortex ith can be written as dr̄i/dt = V̄i , where r̄i is the positionvector. The singularity of the point vortex is removed by assigning a finite-size core to the vortexfilaments. Large-scale vortices are constructed by means of a given initial circulation distribution ofa number of vortex filaments arranged in a coherent structure of a chosen dimension. A Gaussiandistribution of vorticity is used to resemble that of a Burgers vortex.22, 23

III. SELECTED VORTEX INTERACTION

Due to its vectorial nature, vorticity can be re-oriented and re-distributed by certain processes,suggesting the possibility to control the evolution of large-scale structures in the flow through theappropriate manipulation of these processes: one of them is the merging of co-rotating vortices.

One of the difficulties associated with the study of complex vortex interactions, and probablyone of the reasons for this class of flows to be relatively unexplored in supersonic regime, is thechallenge (both experimental and numerical) represented by the targeting of interaction modes ofinterest without recurring to iterative processes based on varying all the key variables (vortices size,circulation, relative position, Mach number, convective velocity, etc.) which would lead to large testmatrices that could make the investigation impractical.

The case presented in this section is for the merging process and subsequent evolution of co-rotating vortices in a system composed of two CVP’s. This interaction was studied, initially, withthe model described in Sec. II and was chosen for the peculiarity of the resulting morphology of thevorticity field and the plume. These results were used to design an experimental investigation withthe intent of reproducing the same specific complex flow physics. The experiment revealed the samefeatures encountered in the simulation.

A. VorTx simulations

The model described in Sec. II has been implemented in a code called VorTx. Due to the reducedorder nature of the underlying model, the code can be used to quickly build and run simulationsof many classes of flowfield of interest. Elementary vortical structures of prescribed values ofcirculation and dimension are constructed utilizing a number of vortex filaments with an appropriatespatial distribution and an equivalent total circulation. To ensure that the time required to performa simulation is low (<5 min) and the resulting datasets are of manageable size, the simulations aregenerally performed with <10 000 filaments. The flowfield is then computed by calculating theresulting induced velocity within the specific domain of influence.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-6 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

Ramp-based vortex generators have been considered in these investigations due to the advantageoffered by the possibility of estimating a priori the circulation of the vortices being shed using theexpression � ∝ U∞sin(αe)h, where � is the circulation, U∞ is the freestream velocity, αe isthe expansion angle, and h is the height of the ramp.8 This relation can be used to calculate anapproximate value for the circulation pertaining to the vortices shed from expansion ramps of thistype. However, for the purpose of obtaining a more accurate value to use during the design stageof experiments involving more complex vortical systems, an experiment with a single ramp wasperformed to characterize the actual strength of the resulting CVP.24 During this initial investigation,it was also found that the central positions of the cores of the vortices did not coincide exactlywith the corners of the ramp. It was found that a good estimation, for the numerical simulations,was to consider the vortices as being shed at 2/3 of the ramp’s height. Sidewash was not found tosignificantly affect the displacement of the vortices relative to the sides of the ramp. Finally, the radiiof the vortex cores were found to scale with the height of the ramp (i.e., l ≡ h). The magnitude ofthe circulation of each vortex was determined to be approximately 1.6 m2/s. This value was usedas a reference for all the numerical investigations performed with VorTx.

A series of simulations were conducted to explore the evolution of interacting supersonicstreamwise vortices generated by a two-ramp system. Although the code was capable of managingan arbitrary number of interacting vortices, it was decided to begin with a systematic analysisof a system composed of only two CVP’s in order to gradually increase the complexity of theinvestigation. From the beginning, this analysis revealed that selected modes of vortex interactioncould be identified for specific combinations of relative position, strength and size of the interactingCVP’s.

The complex interactions as predicted by the code needed to be experimentally verified.For this reason, the case analyzed in Sects IV–VI is for a selected merging process of co-rotating

vortices within two CVP’s of opposite sign. This interaction mode was chosen, among several, forthe peculiarity of the morphology of the resulting flowfield. To the best of the authors’ knowledge,similar results have never been reported in literature. For this reason, this case also represented achallenging scenario for the experimental verification of the results predicted by VorTx (see Sec. V).With reference to the schematic depicted in Fig. 3(b), this merging mode was identified with VorTxfor a system composed of four vortices arranged in two CVP’s. The computations were carried outwith a mutual overlap of 7 mm between the counter-rotating vortex pairs. The magnitude of thecirculation assigned to each vortex in the system was 1.6 m2/s, while the dimension of the corewas expected to scale with the height of the ramps h = 5.8 mm. In building the simulation, thecirculation was divided among approximately 1300 vortex filaments with a Gaussian distribution ofvorticity imposed in each vortex as an initial condition. The structures then evolved under the effectof the resulting velocity field.

The outcome of the simulation is shown in Fig. 2, in which the vorticity contour plots arepresented at different downstream sections together with the 3D evolution of the interaction. As itcan be seen, the code predicts that merging of the two inner patches of vorticity is attained within 32ramp heights from the injection plane (i.e., 32h or approximately 19 cm). It is possible to note thatthe two internal co-rotating structures evolve from an incipient merging state to the amalgamationof their vorticity at station 32h, where the vorticity peaks are no longer discernible. Based on thepredictions, the central area of the plume undergoes a peculiar evolution of its geometric features:starting with a bulge (yellow dotted ellipse in Fig. 2) oriented with an offset with respect to theline connecting the vorticity minima (i.e., the centroids of the merging vortices) both at 10h and16h, to an elongated, Z-shaped plume at 32h, which reached approximately 40 mm of extent alongthe z axis. It will be later shown that this misalignment could be explained by studying the flowin a reference frame which is rotating with the angular velocity of the merger. Another feature isthe different angular velocity associated with the external structures with respect to the internalstructures with important effects on the spatial redistribution of vorticity and potential effects onmixing augmentation (not addressed in this model) due to generation of high strain rates. To simulatethe distortion produced by the resulting vortex dynamics, the evolution of three lines of tracers isconsidered. The red and black lines in Fig. 2 of these tracers mark areas which are initially placedat the center plane and the approximate borders of an ideal injectant plume, respectively.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-7 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 2. VorTx simulations of the merging process at stations (a) 10h (58 mm); (b) 16h (92.8 mm); (c) 32h (185.6 mm)downstream of the injection point. Red line: center plane of the plume; black lines: boundaries of the plume. (d) 3D evolutionof the streamwise vorticity up to 48h.

It is noteworthy to mention that the resulting induced velocities of the supersonic vortex filamentswill tend to the Biot-Savart result when the downstream distance tends to infinity and when the regionof interest is close to the axis of the vortex. For the case presented here, the hyperbolic nature ofthe interaction does impact the resulting vortex dynamics because the aperture of the Mach conesdeparting from each vortex selectively allows the interaction of the closest structures. Specifically,if we consider the external vortical structures (color coded in orange in Fig. 2), they are definitelysingularly interacting with the merger but only partially interacting between them (i.e., the radius oftheir Mach cones slightly exceeds 25 mm at station 10h). Even in the event of complete inclusionof the vortices within each other’s cone of influence, the conditions for the solution to reduce to theBiot-Savart law are not achieved.

IV. EXPERIMENTAL SETUP

An experimental investigation was conducted in order to verify the predictive capabilities of theanalytical model.

All the experiments shown in this work were conducted in the supersonic wind tunnel of theAerodynamics Research Center (ARC) at the University of Texas at Arlington and were aimedat verifying the merging scenario predicted by VorTx. The tunnel is a blow-down type equippedwith a 15.2 × 11.4 × 76 cm3 test section and a variable geometry nozzle, which was configuredfor a nominal operation at Mach 2.5 for this experimental campaign. Three optical access points– two windows along the sidewalls and one on the top plate – provide a full view of the probed

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-8 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 3. (a) Strut injector; (b) front view schematic of the ramp configuration investigated; (c) rendering of the wind-tunneltest section and the spanwise S-PIV setup; (d) instantaneous image of the streamwise plume.

flowfield (see Fig. 3(c)). The nominal stagnation conditions (plenum pressure: p0, f = 610 kPa;total temperature: T0, f = 294 K) were maintained within 5% of their nominal values and allowedsteady run times of approximately 12 s each. The free-stream Reynolds number per unit length was6.04 × 107m−1.

A strut-type injector (Fig. 3(a)) was used to generate the flow of interest. Its body was mounted inthe center plane of the test section spanning its entire width; for further details on the injection system,the reader is encouraged to refer to the work by Vergine and Maddalena.24 The injection slit (101.6× 0.5 mm2) is included in the trailing edge, and was designed to produce a two-dimensional shearlayer, shown in Fig. 3(d), where an instantaneous image of the streamwise flowfield as visualized bythe laser-illuminated TiO2 particles is presented. Earlier measurements of the spanwise vortices inthe plume revealed that their strength is one order of magnitude smaller than that of the streamwisestructures which, therefore, dominate the flow of interest.24 The strut injector is intended to serveas a modular platform which provides the ability to inspect multiple ramp configurations in order tostudy the evolution and the dynamics of vortical systems pre-determined through studies performedwith VorTx. The injection configuration ensured a shock-free area bounded by the spanwise stationsat 58 mm and 185.6 mm downstream of the injection point, as verified by means of shadowgraphmeasurements (see Fig. 4).

The arrangement pertaining to the case considered here is schematically shown in the detailof Fig. 3(b) and is intended to reproduce the interaction of the two CVP’s analyzed numerically inSec. III A: two 18 mm-wide and 5.8 mm-tall expansion ramps were positioned on either side ofa strut injector and overlapped 7 mm. The streamwise extension of the ramps is 32.8 mm. Theposition of the injection slit in the experiments presented is made to coincide with the z = 0 axisused in the simulations.

Stereoscopic Particle Image Velocimetry (S-PIV) was chosen as the primary flow-measurementtechnique and its setup is shown in Fig. 3(c). The S-PIV system consists of a double-pulsed NewWave Research Solo PIV 120 Nd:YAG laser generating a 532 nm wavelength beam and two 12 bitLaVision Imager Intense CCD cameras (1376 × 1040 px2, with a pixel pitch matching the pixelsize of 6.45 μm) equipped with 50 mm lenses mounted on Scheimpflug adapters. The LaVisionDaVis 7.1 software was used for both controlling the laser-camera system and for performing the

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-9 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 4. Shadowgraph of the flow downstream of the strut injector.

post-processing of the data. The laser optics were adjusted to target a sheet thickness of 2 mmat the measurement plane. Seeding of titanium dioxide nano-particles (TiO2, nominal diameter20 nm, cluster diameter 0.25 μm) took place both from the plenum of the supersonic tunnel and theinjection slit (101.6 × 0.5 mm2) included in the trailing edge of the strut for the PIV experimentspresented.

Three spanwise stations were surveyed in the selected shock-free area, located at stations 10h,16h, and 32h downstream of the injection point. Helium injection was subsonic and the mass flowrate kept constant at 0.64 g/s. For the plume evolution studies presented in Sec. V, a mixture of heliumand acetone was delivered exclusively from the slit. The mean flowfields were obtained by collectingapproximately 300–400 uncorrelated image pairs per station with an acquisition frequency of 5 Hzand two-pass calculations were conducted on decreasing interrogation areas size from 256 × 256 px2

to 32 × 32 px2 and 50% window overlap, which proved effective in limiting the number of spuriousvectors. The resolution and the grid size obtained for all the cases are approximately 1.86 mm and0.93 mm, respectively. The interrogation areas and grids were considered sufficient for probing thevortical structures, as their radii were expected to scale with the height of the expansion rampsmounted on the strut (i.e., 5.8 mm). Based on the a priori sizing of the vortices, their circulationwas estimated on the order of 1 m2/s, a datum which was later confirmed by the experimentalresults: this suggested good tracking performance of the TiO2 particles.25 The maximum expectedin-plane displacement was 4px using a dt = 1.2 μs resulting in a related off-plane displacementof 0.6 mm, which is approximately 30% of the chosen laser sheet thickness (i.e., 2 mm). In allthe experiments, the cameras were placed in an angular displacement configuration with viewingangles of approximately 35◦. Considering a magnification factor of 0.11 (typically obtained in theexperiments conducted), the expected particle image diameter was approximately 1.8 times the pixelpitch for f # = 8 (i.e., the f-number used in the experiments) and is therefore suitable for avoidingthe occurrence of peak locking and minimize the displacement estimation error of the three-pointGaussian peak-fit used in the vector calculations.26–28

V. EXPERIMENTAL RESULTS

A. Acetone plume visualization

Preliminary tests were conducted by seeding the injected helium with acetone in order to verifythe predictions of the reduced order model on a qualitative basis. The image data are generated bycapturing the light scattered by the acetone illuminated with the coherent laser beam at 532 nm.Images were corrected for optical distortions and camera perspective. The average images werecalculated over the usable instantaneous images from one single run and obtained by subtracting theaverage background image, captured in quiescent air prior to the experiment. The images in Fig. 5depict the instantaneous and average plumes obtained at stations 10h, 16h, and 32h (approximately

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-10 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 5. Plume shape downstream of the injection point: (a) 10h instantaneous; (b) 10h average; (c) 16h instantaneous;(d) 16h average; (e) 32h instantaneous; (f) 32h average.

58 mm, 93 mm, and 186 mm downstream of the injection point, respectively). The average acetoneplume captured at station 10h shows a horizontally oriented rectangular lobe at the center of theimage. Although the survey was conducted at this early stage of its development, the plume appearsgreatly distorted when compared to the base case of a shear layer in the absence of ramps, thethickness of which can be inferred from the borders of the images to be approximately 5 mm. At16h and 32h the plume assumes the Z-shaped profile already noted in the computer simulations.From the horizontal position at the injection point, the plume is seen to have reoriented to a verticalposition during its development downstream with a noticeable increase of spreading along thez axis. The vertical extent of the modified segment of the plume can be seen to have reachedapproximately 50 mm (i.e., around 20% more than the prediction of the code), which is almost 67%more than its base width along y (i.e., 30 mm), indicating that it experienced stretching during theevolution.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-11 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 6. Superposition of the average in-plane velocity vector field and streamwise vorticity with the plume images down-stream of the injection point: (a) 10h; (b) 16h; (c) 32h.

B. PIV results

The results of the stereoscopic PIV surveys are presented in Fig. 6 where the in-plane velocityand the streamwise vorticity contour plots have been superimposed onto the average plume. Althoughthe total number of instantaneous flowfields collected for the 10h case was 420, in Fig. 6 it waschosen to show the average vorticity as calculated over 175 pairs only; the reason is that the averagingof the flowfields can cause the loss of important information such as the position of the centroids(i.e., the vorticity peaks) in the merger when averaged over several separate runs of the tunnel. Thetypical low-frequency oscillation of the cores of the vortices can, in fact, affect the average of thepeak streamwise vorticity which would consequently be smeared across a wider area than in reality.The vortices were found to be completely merged at 16h and 32h, therefore, the average flowfieldscalculated with the full number of collected image pairs (i.e., 474 and 317 images, respectively) areshown. The contour plots in Fig. 6 show an interesting scenario: the shape of the plume at station10h is not due to the inclination of the central vorticity patch. Rather, the angle between the majoraxis of the merger and the horizontally oriented plume is 26.6◦. This is an indication that the plumewas rotating, moving downstream with a certain delay with respect to the merger, at least up tothat station. Two small areas of accumulation of positive vorticity are also recognizable on the sidesof the merger and appear to correspond to the location of the most peripheral edges of the centralbulge of the plume. The presence of the patches as well as the particular topology of the plumewill be further investigated by studying the flow in the reference frame of the elongated mergerin Sec. VI. The analysis of the images obtained at 16h and 32h and included in Fig. 6, suggeststhat the plume rotates approximately in phase with the merger in this fraction of the test window.The outcomes of this scenario are a highly increased spreading and a notable stretching of theplume.

As can be inferred from the surveys, the streamwise axis of the merger remains approximatelyaligned with the streamwise direction (i.e., perpendicular to the imaged plane) in the average,

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-12 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

whereas the external structures move around it in an orbiting manner. For this reason, the evaluationof the circulation decay was carried out for the clockwise component only. The clockwise circulationwas evaluated across the entire imaged area of the test cases and was found to decay only slightly,reaching at station 32h a value which was 18% lower than that calculated at 10h (i.e., −3.1 m2/s).Therefore, the related vortex Reynolds number (i.e., Rev = |�| /ν) of the isolated structures waskept approximately constant at 1.6 × 105. The growth of the vortex cores, defined as an averagedimension of an ideal diameter, d, passing through the vorticity peak up to the points of maximumtangential velocity, was found to increase approximately 22% at station 32h (i.e., d = 10.5 mm)from its initial value at station 10h (i.e., d = 8.3 mm). These findings allow the inference that forthe time scales associated with the processes considered here turbulent diffusion did not signifi-cantly affect the dynamics of the vortical structures, capturing the morphological evolution of theplume.

Compared to the experimental case shown in Fig. 6, the results of the simulation performed inVorTx (see Fig. 2) show a delay in the evolution of the structures between stations 10h and 16h.The reason for this is that the calculations are conducted considering a constant convective velocity(approximately 500 m/s) while in the actual flow it is relatively low in the vicinity of the injector andthen asymptotically approaches the free-stream speed downstream.24 The late evolution is almostmatched downstream for the combined effect of the convective velocity of the structures, which inthis area approaches 500 m/s, and the slight diffusion which the actual merging vortices undergowhich inevitably lowers the auto-induced velocity in the elongated patch.

VI. DATA ANALYSIS: VORTEX-PLUME INTERACTIONS

The importance and the implications inherent in the peculiar morphology of the plume en-countered at station 10h are not to be underestimated. The distortion of the interfacial area (bothinstantaneous and average) between the plume and the surrounding air is one of the driving mecha-nisms of the vortex-enhanced mixing. To the best of the authors’ knowledge, the reported morphologyhas never been analyzed before in any vortex merging studies in supersonic flow: the reason for thisis that vortex merging experiments have been principally conducted in non-mixing flows, making itimpossible to recognize particular flow features. The agreement between the simulations conductedwith VorTx and the experimental surveys corroborates a fundamental feature of the flow of interest:the flowfields can be studied as if it were two-dimensional and unsteady. For this reason, the analysisof the spanwise flowfields was expected to unveil most of its important features. A possible under-standing of the combined dynamics of the plume and vorticity patches can be attained by studyingthe flowfield in the reference frame which is rotating with the merger. In this case the rotationspeed of the axis connecting the vorticity maxima (i.e., the major axis of the merger) is chosen.Figures 7(a) and 7(b) present the streamlines of the in-plane flow in the absolute (laboratory) ref-erence frame for stations 10h and 16h. As it can be inferred by an inspection of the image data, noclear explanation can be given to the morphology of the plume by inspecting the streamlines pattern.The flow paths in the absolute reference frame can, in fact, be misleading in the interpretation.Previous studies conducted in incompressible flow17, 18 recognized that vorticity tails in a subsonicmerging process form at the point where the vorticity patches, in a system consisting of two co-rotating vortices, overcome the streamlines passing through the stagnation point generated alongthe line connecting their centroids (i.e., separatrices). In a reference frame which rotates with thesame angular velocity as the merger, two so-called ghost vortices are created: their opposite rotationgives an explanation for the mechanism of vorticity transport outside of the merger which ultimatelygenerates the typical vorticity tails at the edges of the organized structure. An analogous approachhas been used in this investigation, but the attention was focused on the effects that the ghost vorticeshave on the resulting shape of the plume, as this is an aspect which has a direct consequence onmixing.

In order to define a rotating reference frame, two pieces of information are needed: the positionof the center of rotation and the angular velocity of the merger. As for the first datum, the centerof rotation is chosen as coincident with the center of mass of the vorticity in the merger. Althoughthe calculation of the exact angular velocity would require the knowledge of the rate of change of

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-13 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 7. Superposition of the average in-plane streamlines in the absolute – (a) 10h and (b) 16h – and rotating – (c) 10h and(d) 16h – reference frames and the corresponding plume.

the angle of the major axis of the merger (i.e., θm), the information of its convective velocity andthe angle of the axis at two spanwise stations can be used to produce an estimation of this value.For this purpose, a constant convective velocity and a linear variation of θm between the stationswas assumed. In this way, Uc being the mean convective velocity between the available stations, theangular velocity can be calculated as: �∝ Uc(θm/x). Therefore, the angular velocity of the mergerat 16h was found to be |�|16h

∼= 1.0 × 104 rad/s, as Uc = 439.5 m/s and θm/x ∼= −24.4 rad/mbased on the change of angle of the aforementioned axis between 10h and 16h. A different rationalewas followed for the station 10h. In this case the angular velocity was evaluated as the solid bodyrotation of two inviscid structures spinning around one another and placed at a distance chosen tobe the average of the initial overlap of the ramps (i.e., 7 mm) and the distance between the cores asmeasured in the PIV survey (i.e., 4.23 mm) with an average circulation of 1.53 m2/s. Following theequation: � = �/πb2

i , where bi is the separation distance of the vortices, the angular velocity forthis case was |�|10h

∼= 1.5 × 104 rad/s.Figures 7(c) and 7(d) show the streamlines in the reference frame of the merger superimposed

on the average plume of the two stations considered, obtained by subtracting the solid body rotation

FIG. 8. Superposition of plume images downstream of the injection point and separatrix streamlines in the rotating referenceframe of the merger: (a) 10h; (b) 16h.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-14 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 9. Plot of the normalized angular velocities of the merger calculated at the streamwise stations 10h, 13h, 16h, 20h, and32h downstream of the injection point.

from the original velocity field. In this rotating frame it is possible to recognize a recirculating flow,suggesting that the plume’s morphology is a consequence of the entrainment of fluid within theseghost vortices. In Fig. 8 the separatrix streamlines of the ghost vortices are shown. As can be seenthe two streamlines transport fluid towards and away from the center of the system, respectively:the plume, however, is displaced along the separatrix which is responsible for the transport from thecenter of the merger to peripheral areas.

Figure 9 shows a plot of the change of angular velocity of the merger calculated at differentstreamwise stations, specifically at 10h, 13h, 16h, 20h, and 32h, and normalized with respect to itsmaximum value at station 10h. To obtain the plot, additional experiments have been performed tomore accurately estimate the aforementioned quantity. As can be seen, the angular velocity reaches anearly constant value after station 20h, which can be considered as the location from which the flowin the streamwise direction reaches a steady state, thus explaining the higher degree of matchingbetween the numerical and experimental results at station 32h.

VII. ADDITIONAL CASES

Additional cases have been investigated in order to assess the capabilities of VorTx to predict theevolution of the plume and the vorticity patches in other complex vortical flows. Some preliminaryresults are presented here. Figure 10(a) shows the schematic of a three-ramp configuration on thestrut injector presented in Sec. IV. As can be seen in Figs. 10(b) and 10(c), the simulation conductedwith VorTx captures with accuracy the features of the average plume experimentally obtained in theMach 2.5 freestream flow of interest. In this particular interaction the vortical structures from thebottom ramps were expected to merge with the two shed from the top ramp.

A case of imposed vortex dynamics has also been considered under the effect of heat release.That work29 showed the evolution of the hydrogen plume issuing from a thin slit at the base of afour-ramp pylon injector (see the schematic of the ramp disposition in Fig. 11(a)) as surveyed by

FIG. 10. (a) Ramp configuration on the strut injector; (b) VorTx simulation of the plume; (c) average particle-seeded plumeexperimentally obtained in cold flow at a downstream station.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-15 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

FIG. 11. (a) Ramp configuration on the pylon injector; (b) VorTx simulation of the plume; (c) nondimensional concentrationof OH radicals in the instantaneous plume obtained in a reacting flow at a downstream station; (d) evolution of the streamwisevortices shed from the ramps on the pylon injector.

means of OH Planar Laser Induced Fluorescence (OH-PLIF) in a Mach 2.4 high enthalpy flow. Theinjector was specifically designed using VorTx, prior to the experimental campaign. As it can beseen in Fig. 11(b), the simulated plume qualitatively resembles the instantaneous distribution of OHradicals (Fig. 11(c)). In that work, the consistency and the repeatability of the plume’s morphology,revealed by the instantaneous OH-PLIF in several uncorrelated instantaneous images throughout theentire surveyed area, confirmed the coherency of the dominant structures produced by the deviceand predicted by VorTx. For the simulation presented in Figs. 11(b) and 11(d), the velocities inducedby the mirror images of the vortices were also computed in order to take into account the effects ofthe proximity of the wall on the vortex dynamics. Figure 11(d) shows the three-dimensional patternof the streamwise vortices. The vorticity plot was created using the lambda-2 criterion to recognizeand mark the surfaces of vortical structures, while the fill-color indicates the vorticity magnitudealong each surface.

While the inspection of the OH-PLIF results shows a plume composed of two distinct lobes(Figure 11(c)) with no additional information, the results of the numerical simulation reveal that theCVP’s generated from the ramps evolved towards a configuration in which two distinct quadrupletsof streamwise vortices are formed providing the appearance of the two lobes.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-16 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

VIII. CONCLUSIONS

The detailed description of a reduced order model, implemented in a code named VorTx,to be used for predicting and analyzing the dynamics of complex interacting vortical systems insupersonic flow has been presented. The foundations of the model are a slender body approximation,the streamwise supersonic vortex filament model, and the construction of the finite-scale streamwisevortices. The slender body approximation for the analysis of the interaction among supersonicvortices reduces a steady three-dimensional flow to a 2D unsteady evolution, allowing for a highlyreduced computational cost. The supersonic lifting line theory is used to take into account thehyperbolic nature of the supersonic flow equations: the interaction among the vortices is, in fact,confined within the correspondent domain of influence of the structures. The finite scale vortices arebuilt with a given initial Gaussian distribution of a chosen number of vortex filaments.

An application of the code for a merging process of co-rotating vortices, and subsequentevolution of a system composed of two CVPs is analyzed. The selected interaction was chosen forthe absolute peculiarity of the resulting morphology of the vorticity field revealed by the simulations.These results were used to design an experimental investigation with the intent to reproduce thesame specific, complex, flow physics. The merging process was experimentally targeted by properlyplacing two expansion ramps on a strut injector in a Mach 2.5 cold flow and the resulting flowfieldwas documented by means of acetone-tracer based plume visualization and Stereoscopic ParticleImage Velocimetry. Although the simplifications adopted for the model inevitably suppress somefeatures of the actual process, the experiment confirmed the same characteristics encountered in thesimulation.

ACKNOWLEDGMENTS

This research is sponsored in part by the NASA Langley Research Center through the NASAResearch Announcement Grant No. NNX12AG46A with Dr. Tomasz G. Drozda as the TechnicalMonitor.

1 I. A. Waitz, Y. J. Qiu, T. A. Manning, A. K. S. Fung, J. K. Elliot, J. M. Kerwin, J. K. Krasnodebski, M. N. O’Sullivan,D. E. Tew, E. M. Greitzer, F. E. Marble, C. S. Tan, and T. G. Tillman, “Enhanced mixing with streamwise vorticity,” Prog.Aerosp. Sci. 33, 323–351 (1997).

2 F. E. Marble, “Growth of a diffusion flame in the field of a vortex,” Recent Advances in the Aerospace Science (PlenumPress, 1985), pp. 395–413.

3 J. F. Keffer and W. D. Baines, “The round turbulent jet in a cross-wind,” J. Fluid Mech. 15, 481–496 (1963).4 J. F. Campbell and J. A. Schetz, “Analysis of the injection of a heated turbulent jet into a cross flow,” Technical Report

No. R-413 (NASA, 1973).5 F. Billig and J. A. Schetz, “Analysis of penetration and mixing of gas jets in supersonic cross flow,” AIAA Paper 92-5061,

1992.6 J. A. Schetz, Injection and Mixing in Turbulent Flow, Progress in Astronautics and Aeronautics (American Institute of

Aeronautics and Astronautics, New York, 1980), Vol. 68, pp. 145–164.7 F. E. Marble, E. E. Zukoski, J. W. Jacobs, G. J. Hendricks, and I. A. Waitz, “Shock enhancement and control of hypersonic

mixing and combustion,” AIAA Paper 90-1981, 1990.8 I. A. Waitz, F. E. Marble, and E. E. Zukoski, “Vorticity generation by contoured wall injectors,” AIAA Paper 92-3550,

1992.9 L. Maddalena, “Investigation of injectors for scramjet engines,” Ph.D. thesis (Virginia Polytechnic Institute and State

University, 2007).10 F. E. Marble, G. J. Hendricks, and E. E. Zukovski, “Progress toward shock enhancement of supersonic combustion

processes,” AIAA Paper 87-1880, 1987.11 S. Kumar, G. Orlicz, C. Tomkins, C. Goodenough, and K. Prestridge, “Stretching of material lines in shock-accelerated

gaseous flows,” Phys. Fluids 17, 082107 (2005).12 A. A. Gowardhan, J. R. Ristorcelli, and F. Grinstein, “The bipolar behavior of the Richtmyer-Meshkov instability,” Phys.

Fluids 23, 071701 (2011).13 B. J. Balakumar, G. C. Orlicz, J. R. Ristorcelli, S. Balasubramanian, K. P. Prestridge, and C. D. Tomkins, “Turbulent mixing

in a Richtmyer-Meshkov fluid layer after reshock: velocity and density statistics,” J. Fluid Mech. 696, 67–93 (2012).14 I. A. Waitz, F. E. Marble, and E. E. Zukoski, “Investigation of a contoured wall injector for hypervelocity mixing

augmentation,” AIAA J. 31, 1014–1021 (1993).15 F. E. Marble, “Gasdynamic enhancement of nonpremixed combustion,” Int. Symp. Combust. 25, 1–12 (1994).16 J. Yang, T. Kubota, and E. E. Zukoski, “Applications of shock-induced mixing to supersonic combustion,” AIAA J. 31,

854–862 (1993).17 C. Cerretelli and C. H. K. Williamson, “The physical mechanism for vortex merging,” J. Fluid Mech. 475, 41–77 (2003).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51

046101-17 Maddalena, Vergine, and Crisanti Phys. Fluids 26, 046101 (2014)

18 P. Meunier, S. Le Dizes, and T. Leweke, “Physics of vortex merging,” C. R. Phys. 6, 431–450 (2005).19 J. P. Drummond, M. H. Carpenter, D. W. Riggins, and M. S. Adams, “Mixing enhancement in a supersonic combustor,”

AIAA Paper 89-2794, 1989.20 S. E. Neice and D. M. Ehret, “Similarity laws for slender bodies of revolution in hypersonic flows,” J. Aeronaut. Sci. 18,

527–530 (1951).21 A. Ferri, Elements of Aerodynamics of Supersonic Flows (The MacMillan Company, 1949), pp. 350–359.22 M. K. Smart, I. M. Kalkhoran, and S. Popovic, “Some aspects of streamwise vortex behavior during oblique shock

wave/vortex interaction,” Shock Waves 8, 243–255 (1998).23 M. Klaas, W. Schroder, and W. Althaus, “Experimental investigation of slender streamwise vortices and oblique shock-

vortex interaction,” AIAA Paper 2005-4652, 2005.24 F. Vergine and L. Maddalena, “Evolution of large-scale structures generated by a strut injector in a Mach 2.5 flow,” AIAA

Paper 2012-0332, 2012.25 F. Vergine, M. Crisanti, and L. Maddalena, “Investigation of the merging process and dynamics of streamwise vortices

generated by a flow-mixing device in a Mach 2.5 flow,” AIAA Paper 2013-0699, 2013.26 R. J. Adrian and J. Westerweel, Particle Image Velocimetry (Cambridge University Press, 2011).27 M. Raffel, C. Willert, S. Wereley, and J. Kompenhans, in Particle Image Velocimetry: A Practical Guide (Springer-Verlag,

Berlin/Heidelberg/New York, 2007).28 J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8, 1379–1392 (1997).29 F. Vergine, L. Maddalena, V. Miller, and M. Gamba, “Supersonic combustion and flame holding characteristics of pylon

injected hydrogen in a Mach 2.4 high enthalpy flow,” AIAA Paper 2012-0333, 2012.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

66.169.175.227 On: Wed, 16 Apr 2014 03:37:51