PIV/Dual-plane-PIV/OH-PLIF Measurements

AIAA SciTech Forum 8–12 January 2018, Kissimmee, Florida 2018 AIAA Aerospace Sciences Meeting

10.2514/6.2018-0153

Complete Determination of the Velocity Gradient Tensor Upstream of the Flame Front with High-speed TomoPIV/Dual-plane-PIV/OH-PLIF Measurements Tongxun Yi1, Christopher Fugger1, Naibo Jiang2, Josef Felver1, Mikhail Slipchenko1, and Sukesh Roy3 Spectral Energies, LLC, Dayton, OH 45431, USA

Downloaded by UNIVERSITY OF CINCINNATI on February 5, 2018 | http://arc.aiaa.org | DOI: 10.2514/6.2018-0153

Travis Smith4, Jamie Lim4, Matthew Sirignano9, Benjamin Emerson5, and Tim Liewen6 School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 31308, USA Benjamin Halls7 and James Gord8 Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, OH 45433, USA

Accurate prediction of the flame stretch necessitates knowledge of the nine-component velocity-gradient tensor upstream of the flame front. However, stereo-PIV/PLIF, which has been commonly used in turbulent combustion research, only resolves the six in-plane velocity gradients. As a first step toward volumetrically- and temporally-resolved, i.e. 4D, characterization of turbulent combustion, we propose to completely determine the ninecomponent velocity-gradient tensor with simultaneous, high-speed, tomographic-PIV/OHPLIF measurements and simultaneous, high-speed, dual-plane stereo-PIV/OH-PLIF measurements. The high-speed Tomo-PIV/OH-PLIF technique is demonstrated on a turbulent, transverse, non-premixed reacting jet, and the high-speed dual-plane stereoPIV/OH-PLIF technique is demonstrated on a turbulent, swirling, reacting jet. Depending on the orientation of vortices, the magnitude of the leading eigenvalue (‖𝑨‖𝟐 ) for the 𝟑 × 𝟑 velocity-gradient matrix can be substantially larger than that for the 𝟐 × 𝟑 velocity-gradient matrix based on stereo-PIV measurements, strongly suggesting the importance of fully resolving the nine-component velocity-gradient tensor upstream of the flame front.

I. Nomenclature

V

A AT

= the velocity gradient tensor

AS

⃑𝑆 = ( = the 2  3 velocity gradient tensor 𝐴𝑆 = ∇𝑉

A2

⃑𝑇 = ( = the 3  3 velocity gradient tensor 𝐴 𝑇 = ∇𝑉

𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤

;

𝜕𝑥 𝜕𝑥 𝜕𝑥 𝜕𝑦 𝜕𝑦 𝜕𝑦 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑥

𝜕𝑥 𝜕𝑥

;

𝜕𝑦

𝜕𝑦 𝜕𝑦

;

𝜕𝑧 𝜕𝑧 𝜕𝑧

)

)

= the large eigenvalue of the matrix 𝐴𝐴𝑇

1

Research Engineer, 5100 Springfield St., Suite 301, Dayton, OH 45431, AIAA Member Senior Research Engineer, 5100 Springfield St., Suite 301, AIAA Associate Fellow 3 Senior Research Scientist & CEO, 5100 Springfield St., Suite 301, AIAA Associate Fellow 4 Graduate students, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30318 5 Research Engineer, School of Aerospace Engineering, Georgia Institute of Technology, AIAA Member 6 Professor, School of Aerospace Engineering, Georgia Institute of Technology, AIAA Fellow 7 Research Engineer, AFRL, WPAFB, AIAA Member 8 Principal Research Chemist, AFRL, WPAFB, AIAA Fellow 2

1

Copyright © 2018 by Tongxun Yi, Christopher Fugger, Naibo Jiang, Josef Felver, Mikhail Slipchenko, Sukesh Roy, Travis Smith, Jamie Lim, Matthew Sirignano, Benjamin Emerson, Tim Liewen, Benjamin Halls, an Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

II. Introduction

T

HE flame stretch, i.e., the fractional rate of change of the flame surface area due to strain and curvature effects, is a key concept for turbulent combustion within the flamelet regimes [1–3]. A flame stretch modifies the transport of species and heat into the reaction zone, thus changing the chemical reaction rates, the chemical equilibrium, and the flame speed. Following the denotations in Ref. 2, the flame stretch k can be written as,

k  n f n f : V   V  Sd   n f ,

(1)

n f refers to the flame normal, V is the velocity vector, V  u, v, w , and S d denotes the flame

where


displacement speed. The first term on the RHS of Eq. (1) is the strain rate normal to the flame front, the second term denotes the volumetric expansion due to heat release, and the last term refers to the flame stretch due to the flame

 V is appreciable only at the flame front. Clearly, accurate determination of the flame stretch requires knowledge of the flame orientation n f , the flame curvature   n f , the nine-component curvature. The flow divergence

velocity-gradient tensor

V , the gas dilation  V , and the flame displacement speed S d .

Stereoscopic PIV measurements only allow determination of the six in-plane velocity-gradient components, i.e., 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤 ⃑ ∇𝑉𝑆 = ( ; ). As a first step toward accurate determination of the flame stretch, we propose to 𝜕𝑥

𝜕𝑥 𝜕𝑥

𝜕𝑦

𝜕𝑦 𝜕𝑦

⃑ 𝑇 = (𝜕𝑢 completely resolve the nine-component velocity gradient tensor ∇𝑉 𝜕𝑥

𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑥 𝜕𝑥

;

𝜕𝑦

𝜕𝑦 𝜕𝑦

;

𝜕𝑧 𝜕𝑧 𝜕𝑧

) with two

strategies, namely tomographic PIV (Tomo-PIV) and polarization-based, dual-plane stereo-PIV measurements. Tomo-PIV measurements yield a volumetric distribution of velocity from which the nine-component velocity-gradient tensor can be readily computed [4][5]. Dual-plane stereo-PIV measurements provide velocity distribution on two parallel planes, thus enabling computation of the nine-component velocity-gradient tensor [6][7].

III. High-speed Tomo-PIV/OH-PLIF Measurements of a Transverse Reacting Jet A. Experimental Setup High-speed Tomo-PIV measurements synchronized with OH-PLIF imaging are conducted on a turbulent, transverse, reacting propane jet issued into a hot (~ 1350 K), vitiated, oxidizing crossflow. The jet momentum flux ratio, and

J   jV j2 0V02 , is 41, where  0

V0

and

and

j

denote the density of the crossflow and the fuel jet, respectively,

V j denote the velocity of the crossflow and the fuel jet, respectively. Figure 1(a) is a contour plot of the

mean transverse velocity from which one can identify the bending fuel jet downstream of fuel injection. The exit center of the fuel nozzle is at ( x, y, z )  (0,0,0) . Figure 1(b) shows one instantaneous flame image which overlaps the planar velocity (U, V) at the Z=0 plane. The transverse velocity along the bending fuel jet is much higher than that in the crossflow. A detailed description of the reaction zones of this transverse reacting jet, including the autoignition kernels, flame kernels, and flame fragments, is provide in Ref. [8].

2

Fig.1 (a) The mean transverse velocity V of the transverse reacting fuel jet, and (b) an instantaneous flame image overlapping the planar velocity (U, V) at the plane Z=0.


B. Optical Setup Figure 2 shows the optical setup for high-speed, burst-mode Tomo-PIV measurements synchronized with OHPLIF imaging which overlaps LOS flame emissions. High-speed tomographic PIV measurements are enabled with a flash-lamp-pumped, quasi-continuous, burst-mode (QCBM) laser operating at 10 kHz. The high-speed QCBM laser is described in [9]. The QCBM laser produces a double-pulse train at 532 nm with a pulse separation of 40 µs. The 532-nm laser beam from the QCBM laser is expanded from a diameter of 6 mm to 25 mm, collimated with a 4:1 telescope, and then expanded with a negative cylindrical lens (focal length: -200 mm). The expanded 532-nm laser beam enters the test section through a square slit (20x30 mm2) on the top wall of the rectangular channel. The centerplane of 20-mm-wide laser beam, i.e., Z=0, bisects the exit of the fuel nozzle. Particle images are taken with four strategically-placed, high-speed CMOS cameras (Photron SA-Z) featured with interference filters around 532 nm. Both the crossflow and the fuel jet are seeded with TiO 2 particles (nominal diameter: ~ 0.5 – 1 μm). The Stokes number, i.e., the ratio of the particle relaxation time and the sampling period, is 0.02. Thus, seeding particles are capable of faithful flow-tracking up to the Nyquist frequency of 5 kHz. High-speed OH-PLIF imaging is enabled with a diode-pumped, solid-state (DPSS) dye laser which is synchronized with the PIV laser. Interested readers may refer to Ref. 8 for image interpretation.

Fig. 2 The optical setup for high-speed, burst-mode Tomo-PIV measurements synchronized with OH-PLIF imaging overlapping LOS flame emissions for a transverse reacting propane jet in a hot, vitiated, oxidizing crossflow. C. Procedures of Tomographic Processing Major steps of tomographic processing include 2D particle-image preprocessing, Tomo-PIV particle calibration, volumetric reconstruction of particles, and 3D cross-correlation. An iterative subtraction procedure is used to minimize the background noise, light reflections from cameras and lenses, and images of particle agglomerates on windows. The particle displacement within an interrogation window is obtained with 3D cross-correlation of the reconstructed particles at two exposures with a separation of 40 μs. Vectors are obtained with an ultimate interrogation window of 64x64x64 pixels with 75% overlap. The vector spacing is 1.8 mm. By assuming a cross-correlation displacement error of 0.1 pixels, the velocity error is estimated to be 0.3 m/s. Following Rehm & Clemens [10] and assuming the characteristic length of velocity variations as the correlation window size, the error in the velocity gradient is estimated to be 40 s-1. D. Results D.1 The Counter-rotating Vortex Pair With Tomo-PIV measurements of the volumetric velocity, the nine-component velocity gradient tensor can be readily determined with the central-difference scheme. The counter-rotating vortex pair (CVP), a major quasi-static vortical structure in transverse jets, originates shortly downstream of the jet exit featured with vorticity aligned with

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the jet trajectory [11][12]. Figure 3 shows the iso-surfaces of the mean axial vorticity at

x  1000

s-1 (Fig. 3(a)),

600 s-1 (Fig. 3(b)), and 300 s-1 (Fig. 3(c)), respectively. The mean axial vorticity is obtained by averaging 98


snapshots. The two-lobbed vortical structures on both sides of the bending jet are the CVP. The CVP extends well beyond the Tomo-PIV measurement domain in the spanwise direction. From Fig. 3(d), one can see that the peak axial vorticity consistently decreases downstream of x / d  16 , and the CVP center gradually lifts up in the transverse direction.

Fig. 3. Mean axial vorticity

x .

(a) The iso-surface at 𝝎𝒙 = ±𝟏𝟎𝟎𝟎 s-1, (b) the iso-surface at 𝝎𝒙 = ±6𝟎𝟎 s-1,

(c) the iso-surface at 𝝎𝒙 = ±3𝟎𝟎 s-1, and (d) the slice-plot of

x

in the streamwise direction.

D.2 The Toroidal Jet Column Wake Vortices The toroidal jet column wake vortices are shed alternatively from the lateral sides of the transverse jet with one end on the boundary layer and the other end onto the jet. It has been observed that the toroidal jet column wake vortices draw the flame surface toward the UV laser plane, thus forming bright spots at the UV laser plane [8]. Figure 4 shows iso-surfaces of the transverse vorticity  y and one of its major components w x from which one can identify the toroidal jet column wake vortices.

Fig. 4 (a) The instantaneous transverse vorticity

 y , and (b) the instantaneous velocity gradient w x .

D.1.3. The Strain Rate Tomographic PIV enables complete determination of the nine-component velocity-gradient tensor, i.e., 𝐴 𝑇 = ⃑ 𝑇 = (𝜕𝑢 𝜕𝑣 𝜕𝑤 ; 𝜕𝑢 𝜕𝑣 𝜕𝑤 ; 𝜕𝑢 𝜕𝑣 𝜕𝑤); however, stereo-PIV only allows determination of the six in-plane ∇𝑉 𝜕𝑥

𝜕𝑥 𝜕𝑥

𝜕𝑦

𝜕𝑦 𝜕𝑦

𝜕𝑧 𝜕𝑧 𝜕𝑧 𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤

⃑𝑠 = (𝜕𝑢 velocity gradients, 𝐴𝑠 = ∇𝑉 𝜕𝑥

𝜕𝑥 𝜕𝑥

;

𝜕𝑦

𝜕𝑦 𝜕𝑦

). In Fig. 5, five vortical structures with a large ratio of

‖𝐴 𝑇 ‖2 ⁄‖𝐴𝑆 ‖2 are identified, numbered, and enclosed with circles. These vortical structures are mainly aligned in the

4

out-of-plane direction, and their interactions with a flame front cannot be characterized and quantified with stereoPIV/OH-PLIF measurements.


(a)

(b)

(c)

Fig. 5 The matrix norm ‖𝑨‖𝟐 of a velocity snapshot at Z = 0.07. (a) ‖𝑨𝑻 ‖𝟐 , (b) ‖𝑨𝑺 ‖𝟐 , and (c) ‖𝑨𝑻 ‖𝟐 ⁄‖𝑨𝑺 ‖𝟐 .

IV. High-speed Dual-plane Stereo-PIV/OH-PLIF Measurements of a Turbulent Swirling Jet A. Experimental Setup Figure 6 shows the optically accessible, turbulent, premixed, swirling combustor at GaTech. The swirling jet is essentially unconfined as the jet exit diameter accounts for only 6% in the Z direction and 3% in the X direction within the rig. Results shown here are for the nominal velocity of 25 m/s at the nozzle exit at the equivalence ratio of 0.85. The pulse separation for DP-Stereo-PIV measurements is 15 μs.

(a) Fig. 6 (a) The swirling combustion rig (a), and (b) the coordinate system.

(b)

B. The Optical Setup Figure 7 shows the optical setup. The vertically-polarized, 532-nm laser beam from the QCBM laser is split into two beams with orthogonal polarization using a half-wave plate and a polarizing cube prism. The two beams are recombined at a common point with a thin-film polarizer, and the combined beams pass through an optical train with a 4:1 telescope and sheet-forming lenses. A negative cylindrical lens (f = -200 mm) expands the beams vertically. The 4:1 telescope consists of a spherical positive lens (f = 200 mm) and a spherical negative lens (f = - 50 mm) lens, which reduces the beam width from 7–8 mm down to 1.7 mm beam. The two oppositely-polarized PIV planes are separated at 2 mm, corresponding to the Taylor scale, and variations in separation across the 100-mm FOV are less than 3%, which has been verified with a beam profiler. The doublet pulses are generated at 10 kHz, and 164 pairs of images are acquired every 12 seconds. Mie-scattering images are taken with four high-speed CMOS cameras (Photron SA-Z) at 20 kHz with full resolution (1024x1024 pixels) in the frame-straddling mode. Each camera is equipped with a Scheimfplug adapter, a Nikon 50 mm f/2.8 camera lens, and a 532-nm interference filer with FWHM of 9 nm. Dualplane PIV measurements are repeated 10 times (i.e. with ten partitions) at each working condition, and each partition contains 164 frame-straddled pairs of Mie-scattering signals. In total, we have 1640 velocity vectors at each working condition. Calibration is done with a LaVision dot target (106-10), and self-calibration is performed thereafter to account for the misalignment between the laser beams and the dot target. The OH-PLIF system consists of a highspeed DPSS Nd:YAG laser and a tunable Sirah Credo dye laser. The UV output from the dye laser was tuned to the Q1(9) transition of OH in the (1,0) vibrational band of the A2Σ+–X2Π system near 283.94 nm. The present paper

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focuses on velocity measurements and determination of the velocity-gradient tensor instead of flame imaging, thus details of flame interpretation are skipped.

Fig. 7 Optical setup for high-speed, burst-mode, polarization-based, dual-plane stereo-PIV/OH-PLIF measurements. C. Data Processing Target calibration, self-calibration, and vector processing are performed with David 8.1.6 software. Background subtraction of each Mie-scattering image is done with a 32x32 pixel sliding kernel, and the particle intensity is normalized with a 6x6 sliding kernel. Vectors are computed with a multi-pass correlation-based algorithm with a decreasing window size from 48x48 (75% overlap) to 24x24 (50% overlap), resulting in vector spacing of 1.3 mm. A special procedure has been developed to overlap the coordinate systems on the two stereo-PIV planes by taking advantage of the fiducial marks (a triangle and a square) on both sides of the LaVision dot target (106-10). The overlapping of coordinate systems is done after self-calibration instead of target calibration. To facilitate the computation of the out-of-plane velocity gradients, velocity on the grids on the stereo-PIV plane (i.e., Plane 2) on the side of Camera 3 and 4 are interpolated onto the grids on the stereo-PIV plane (i.e., Plane 1) on the side of Camera 1 and 2. D. Results D.1. Velocity on Both Planes Figure 8 shows a velocity snapshot on the two PIV planes. Four similar, large-scale, flow structures have been identified on both PIV planes and marked by indexed circles or elliptic circles. The planar velocity (U and V) and the out-of-plane velocity (W) within indexed circles or elliptic circles have similar magnitude and share the same direction.

Fig. 8 A snapshot of velocity on the two PIV planes. (a) Velocity on Plane 1, and (b) velocity on Plane 2. Velocity unit: m/s. The planar velocity is shown in vectors and the out-of-plane velocity is shown as scalars. 6

D.2. The Velocity Gradients on Both Planes


Figure 9 shows a snapshot of the 15 velocity gradients. Similar large flow structures on both PIV planes are identified and marked with circles or elliptical circles. These large flow structures are spiraling counter-clockwise upstream toward the swirler exit.

(a)

(b)

(d)

(e)

7

(c)

(f)

(g) (h) (i) Fig. 9 A snapshot of velocity gradients on both PIV planes for swirling reacting flows at 𝜱=0.85. a) 𝑼𝒙 , b) 𝑼𝒚 , c) 𝑽𝒙 , d) 𝑽𝒚 , e) 𝑾𝒙 , f) 𝑾𝒚 , g) 𝑼𝒛 , h) 𝑽𝒛 , and i) 𝑾𝒛 . Unit of velocity: m/s; unit of velocity gradients: 1/s. D.3. The Matrix Norm ‖𝑨‖𝟐 Figure 10 shows the matrix norm ‖𝐴𝑠 ‖2 for the six in-plane velocity gradients on Plane 1 and the matrix norm ⃑𝑠 = (𝜕𝑢 𝜕𝑣 𝜕𝑤 ; 𝜕𝑢 𝜕𝑣 𝜕𝑤 ) and ‖𝐴𝐷𝑃 ‖2 based on the nine-component velocity-gradient tensor. Note that 𝐴𝑠 = ∇𝑉 𝐴𝐷𝑃

⃑ 𝐷𝑃 = (𝜕𝑢 = ∇𝑉 𝜕𝑥

𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑢 𝜕𝑣 𝜕𝑤 𝜕𝑥 𝜕𝑥

;

𝜕𝑦

𝜕𝑦 𝜕𝑦

;

𝜕𝑧 𝜕𝑧 𝜕𝑧

𝜕𝑥

𝜕𝑥 𝜕𝑥

𝜕𝑦

𝜕𝑦 𝜕𝑦

). The ratio ‖𝐴𝐷𝑃 ‖2 ⁄‖𝐴𝑠 ‖2 is larger than 3 in a major portion of the


measurement domain, strongly suggesting the importance of the out-of-plane motion and the out-of-plane velocity gradients in turbulent swirling combustion.

Fig. 10 The matrix norm ‖𝑨‖𝟐 of a velocity snapshot for dual-plane stereo-PIV measurements. (a) ‖𝑨𝒔 ‖𝟐 , (b) ‖𝑨𝑫𝑷 ‖𝟐 , and (c) ‖𝑨𝑫𝑷 ‖𝟐 ⁄‖𝑨𝑺 ‖𝟐 .

V. Conclusions Flow structures with velocity gradients in the out-of-plane direction and their interactions with a flame front cannot be detected with stereo-PIV/OH-PLIF measurements. As an ongoing effort to fully characterize turbulent combustion, two high-speed laser-diagnostic strategies capable of spatially- and temporally-resolving the nine-component velocitygradient tensor are demonstrated, namely high-speed Tomo-PIV/OH-PLIF measurements and dual-plane stereoPIV/OH-PLIF measurements. High-speed, bust-mode Tomo-PIV/OH-PLIF measurements have been conducted on a transverse reacting propane jet in hot, vitiated crossflows; high-speed, burst-mode DP-stereo-PIV/OH-PLIF measurements have been conducted on a turbulent, premixed, swirling, reacting jet. Preliminary analyses reveal the critical importance of fully-resolving the nine-component velocity-gradient tensor and the three vortical components in characterization and understanding of turbulent combustion.

VI. Acknowledgments This work was funded, in part, by the Air Force Research Laboratory under Contract Nos. FA8650-15-D-2518 and by the Air Force Office of Scientific Research (AFOSR) (Dr. Enrique Parra, Program Officer, 15RQCOR202; and Dr. Chiping Li, Program Officer, 14RQ06COR). This manuscript has been cleared for public release by the Air Force Research Laboratory (No. 88ABW-2017-5832).

VII. References [1] Law, C. K., “Dynamics of Stretched Flames,” Proc. Combust. Inst., Vol. 22, No.1, 1988, pp. 1381–1402. doi: 10.1016/S0082-0784(89)80149-3 [2] Candel, S. M. and Poinsot, T. J., “Flame Stretch and the Balance Equation for the Flame Area,” Combust. Sci. Technol., Vol. 186, 1990, pp. 1041–1074. doi: 10.1080/00102209008951608 [3] Peters, N., Turbulent Combustion, Cambridge University Press, Cambridge, 2000. [4] Scarano, F., “Tomographic PIV: Principles and Practice,” Meas. Sci. Technol., Vol. 24, No.1, 2013, pp. 012001.

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doi: 10.1088/0957-0233/24/1/012001 [5] Elsinga, G. E., Scarano, F., Wieneke, B., and van Oudheusden, B. W., “Tomographic particle image velocimetry,” Experiments in Fluids, Vol. 41, No. 6, 2006, pp. 933–947. doi: 10.1007/s00348-006-0212-z [6] Ganapathisubramani, B., Longmire, E. K., Marusic, I., and Pothos, S., “Dual-plane PIV technique to determine the complete velocity gradient tensor in a turbulent boundary layer,” Experiments in Fluids, Vol. 39, 2005, pp. 222–231. doi: 10.1007/s00348-005-1019-z [7] Hu, H., Saga, T., Kobayashi, T., Taniguchi, N., and Yasuki, M., “Dual-plane stereoscopic particle image velocimetry: system set-up and its application on a lobed jet mixing flow,” Experiments in Fluids, Vol. 31, No.3, 2001, pp. 277–293. doi: 10.1007_s003480100283 [8] Yi, T., Halls, B. R., Jiang, N., Felver, J., Sirignano, M., Emerson, B. L., Lieuwen, T. C., Gord, J. R., and Roy, S., “Autoigitioncontrolled Flame Initiation and Flame Stabilization in a Reacting Jet in Crossflow,” submitted to Combustion Symposium 2018. [9] Slipchenko, M. N., Miller, J. D., Roy, S., Meyer, T. R., Mance, J. G., and Gord, J. R., “100 kHz, 100 ms, 400 J Burst-mode Laser with Dual-wavelength Diode-pumped Amplifiers,” Optics Letters, Vol. 39, No. 16, 2014, pp. 4735–4738. doi: 10.1364/OL.39.004735 [10] Rehm, J. E. and Clemens, N. T., “The Association of Scalar Dissipation Rate Layers and OH Zones with Strain, Vorticity, and 2-D Dilatation Fields in Turbulent Nonpremixed Jets and Jet Flames,” AIAA 99-0676, 1999. [11] Schlegel, F., Wee, D., Marzouk, Y. M., and Ghoniem, A. F., “Contribution of the Wall Boundary Layer to the Formation of the Counter-rotating Vortex Pair in Transverse Jets,” J. Fluid Mech., Vol. 676, 2011, pp. 461–490. doi: 10.1017/jfm.2011.59 [12] Karagozian, A. R., “Transverse Jets and their Control,” Prog. Energy Combust. Sci., Vol. 36, 2010, 531–553. doi: 10.1016/j.pecs.2010.01.001

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