AIAA Paper Accepted for: 42nd AIAA Aerospace Sciences Meeting and ExhibitLocation and Dates: Reno, NV, 5-8 January 2004Prepared for AIAA Session: Fluid DynamicsSession Topic: Aero-Optics

AIAA 2004-0473

Aerooptical Interactions in Turbulent Compressible Separated

Shear Layers and the Interfacial-Fluid-Thickness Approach

Roberto C. Aguirre †, Jennifer C. Nathman † , and Haris J. Catrakis ‡

Aeronautics and Fluid Dynamics LaboratoriesUniversity of California, Irvine, CA 92697

Abstract

The interfacial-fluid-thickness (IFT) approach is extended to investigate the structure of high-gradient regions of the density field and their effect on the aberrations of optical wavefrontsin turbulent compressible separated shear layers. A new aerooptics facility was designed andbuilt to allow simultaneous imaging of the density field and the flow-generated optical wave-front distortions. This novel facility consists of a main Aerooptics Pressure Vessel that has aninside diameter of 4 feet, an internal height of 8 feet, and it can be pressurized up to 20 atm.Benchmark testing of the new Aerooptics Pressure Vessel Facility enabled the simultaneousmeasurement of density-field images and optical-wavefront images from a turbulent separatedshear layer at low-compressibility (Mc ∼ 0.15) and medium-compressibility (Mc ∼ 0.47) condi-tions. The variations in interfacial fluid thickness or inverse of the local density gradient wereextracted from the density-field images in order to examine their direct effect on the propaga-tion of optical wavefronts. One of the major benefits of using the IFT approach is being able toidentify spatially isolated high-gradient networks corresponding to locally-thin interfaces, whichwere observed to dominate the large-scale aerooptical distortions on the basis of direct correla-tion between the measured optical wavefront distortions and the instantaneous flow structure.The high-gradient networks of the density field, and their effect on the optical wavefront distor-tions, are compared to the shear-layer mixing-field counterparts. The IFT approach suggestsa new way to model the flow-generated aerooptical distortions at large Reynolds numbers forincompressible, low-, medium-, and high-compressibility flow conditions.

1. Introduction

The aerooptical interactions in turbulent com-pressible flows remain an important issue inboth applied and fundamental studies (e.g.Jumper & Fitzgerald 2001 [1] and referencestherein). Of particular interest are separatedflows in which the flow geometry lends itselfto controlled laboratory experiments wherethe results and implications are applicable to

external flow dynamics of fast-moving plat-forms. It can be expected that the aeroopti-cal phenomena may depend on the Reynoldsnumber and the level of compressibility, andboth of these effects are combined in deter-mining the behavior of the interactions be-tween the fluid flow and the optical wavefronts(e.g. Dimotakis et. al. 2001 [2], Hugo 2001

†Graduate Student, Member AIAA.‡Asst Professor, Member AIAA. Corresp. Author. Tel: (949) 378-7781. E-mail: catrakis@uci.edu

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42nd AIAA Aerospace Sciences Meeting and Exhibit5 - 8 January 2004, Reno, Nevada

AIAA 2004-473

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

[3]). This complicates the efforts to arrive ata simple mechanism that captures most of theaerooptical interactions.

A physically-based approach to investigatethe fluid-optical interactions is to identify therefractive fluid interfaces. The behavior ofthese interfaces can provide a means to un-derstand and describe the dominant contri-butions to the optical wavefront distortions.It has been demonstrated for incompress-ible high-Reynolds-number dual-stream shearlayers between optically-different gases, thatthe outer fluid interfaces provide the domi-nant contributions to the aerooptical distor-tions (Dimotakis et. al. 2001 [2]). An ap-proach to relate organized large-scale pres-sure variations in weakly-compressible shearlayers has been demonstrated to capture thelarge-scale aerooptical distortions (Jumper &Fitzgerald 2001 [1]). Further increasing thecompressibility conditions beyond the weakly-compressible regime can be expected to de-mand a different approach since the organi-zation of the large-scale structure in shearlayers has been observed to exhibit differentbehavior at high-compressibility compared toits weakly-compressible and incompressiblecounterparts (Clemens & Mungal 1995 [4]).

In previous work by Catrakis & Aguirre(AIAA Paper 2002-2269 [5]), optical wave-fronts propagating through high-Reynolds-number incompressible flows were examinedat the small scales in terms of a wavefront-anisotropy parameter. The interfacial-fluid-thickness (IFT) approach was introduced inrecent work by Aguirre, Ruiz-Plancarte, &Catrakis (AIAA Paper 2003-0642 [6]), wherethe thickness of refractive fluid interfaces wasproposed as one of the key physical quan-tities in aerooptical interactions. Most re-cently, the IFT approach was applied to low-compressibility and medium-compressibilitymixing shear layers where the structure of thehigh-gradient networks and the variability ofthe thickness of fluid interfaces were exam-ined by Aguirre, Ruiz-Plancarte, & Catrakis(AIAA Paper 2003-3609 [7]).

In the present work, the interfacial-fluid-thickness (IFT) approach is extended for thecase of the density field. A new AeroopticsPressure Vessel Facility was commissioned tosimultaneously image the density field andthe flow-generated optical wavefront distor-tions. In §2 the new facility is described aswell as the laser-induced digital imaging tech-nique. The application of the IFT approachis demonstrated on density interfaces and theeffect of locally-thin density interfaces on theoptical wavefront distortions is quantified in§3. The structure of the density interfacesand their contributions to the optical-pathlength is also compared to their mixed-fluidinterfaces counterpart. In §4, implicationsof the present results are discussed includingan outline of the new aerooptics IFT mod-eling approach applicable to turbulent sepa-rated shear layers at low-, medium-, and high-compressibility flow conditions.

2. Description of the Aeroop-tics Pressure Vessel Facility

A new Aerooptics Facility was designed andbuilt to allow simultaneous imaging of thedensity field and the flow-generated opticalwavefront distortions. The new facility con-sists of a main pressure vessel that has a 4-foot diameter, 8-foot internal height, and itcan be pressurized to 20 atm, as shown in fig-ure 1. The variable pressure capability allowsfor elevated test-section pressures which en-hances the measurable aerooptical effect andthe signal-to-noise ratio of the flow and wave-front imaging at high Reynolds numbers andhigh convective Mach numbers.

The Aerooptics Pressure Vessel houses thetest-section and the flow tunnel internals canbe modified to accommodate different flow ge-ometries, e.g. dual-stream shear-layer, single-stream shear-layer. In the present study, theflow tunnel is configured to generate a single-stream shear-layer with a splitter-plate test-section exit height of 3 inches and a span of12 inches. The current configuration allowsfor a comprehensive study of a separated flow

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Figure 1: Left: The Aerooptics Pressure Vessel at UC Irvine designed for simultaneousimaging of the flow field and the optical wavefront distortions. The facility can generateaerooptical flows at large Reynolds numbers Re ∼ 106 − 108 and over a wide range ofcompressibilities 0.15 <∼ Mc

<∼ 1.0. The quick-release door provides access to the interiorand the shear-layer tunnel. Right: Schematic of the separated shear-layer tunnel andtest section, in the subsonic configuration, housed in the aerooptics vessel.

of practical relevance for aerooptics wherethe effects of Mach number, Reynolds num-ber, and density-ratio may be isolated. High-Reynolds number (Re ∼ 106 − 108) and high-Mach number (Mc ∼ 1.0) flows are attain-able with the current single-stream shear-layer configuration.

The facility enables the simultaneous imagingof the density field and the optical wavefrontsthrough five 10-inch diameter quartz windows

which allow optical access to the interior ofthe vessel. A new density-field imaging tech-nique was developed where laser-induced flu-orescence of acetone, seeded in the flow in acalibrated way to remove additional mixingeffects, provided direct measurements of thedensity field. A new wavefront sensor wasdeveloped to directly measure the of opticalwavefronts using a 1,024 microlens array toprovide high spatial resolution of the distor-tions generated by the density field.

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Figure 2: Left: Schematic of the Aerooptics Laboratory at UC Irvine in the simultaneousflow-/beam-imaging configuration. A pulsed laser beam shaped into a vertical laser sheetis directed through the shear-layer test section and imaged directly onto a high-resolution1,024-microlens Shack-Hartmann wavefront sensor. Simultaneously, a high-resolutiondigital camera images the acetone fluorescence which yields the density field by a newcalibrated-seeding technique. Right: Example of the IFT approach to identify the high-gradient interfaces, shown using previously-recorded mixing-field images [8].

Figure 3: Demonstration of the large-scale aerooptical distortions captured, at high com-pressibility, using the high-gradient interfaces (Catrakis & Aguirre 2003 [8]).

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The simultaneous measurements of the den-sity field and of the optical wavefronts providea unique opportunity to apply and evaluatethe interfacial-fluid-thickness approach as de-scribed in the next section.

3. Description and appli-cation of the interfacial-fluid-thickness (IFT) approach

A useful physical point of view in estab-lishing the relation between the flow struc-ture and the resulting aerooptical distortionsis to consider the variations in the thick-ness of the refractive fluid interfaces. InCatrakis & Aguirre (2003 [8]), the interfacial-fluid-thickness (IFT) approach was intro-duced and applied to mixed-fluid interfacesattained from dual-stream shear layers. Theoptical-path-length (OPL) integral was writ-ten in terms of the variations of the interfacialthickness, hn, along the propagation path, as

Λ(x, t) ≡∫ray

n(s, t) hn | sec θ| |dn| , (1)

where θ quantifies the local interfacial inclina-tion and is defined as the angle between the lo-cal optical-ray propagation direction and therefractive-index gradient. Knowledge of thevariability in hn and θ, and their connectionto the flow dynamics, can be expected to helpdetermine the relation between the aeroopti-cal distortions and the interfacial structure.

The use of the IFT approach was pre-viously demonstrated on turbulent highly-compressible mixed-fluid interfaces. The newdensity-field imaging technique enabled thedirect measurement of density interfaces. Thestructure of high-gradient networks observedin the mixing layers is compared to the locally-thin density interfaces. This density field canbe used to compute the interfacial-thicknessfield in the same manner as it was computedfrom the index-of-refraction field shown in fig-ure 2 (right). These high-gradient interfacesare organized in networks present in the in-terior and near the outer boundaries of theshear layer for high-compressibility flows. The

effect of compressibility on the high-gradientdensity networks is one of the objectives ofthe current study. The structure of these net-works is compared to the their mixed-fluid in-terfaces counterparts. This is a way to sepa-rate the contributions of turbulent mixing ofdissimilar gases from the compressibility ef-fects on the distortions of optical wavefronts.

Using the IFT approach suggests a new wayto model aerooptical distortions in highly-compressible turbulent flows. The locationof the high-gradient interfaces and the valueof the gradient across these interfaces can beexpected to be enough to capture the dom-inant contributions that generate the large-scale aerooptical distortions. The proposedmodeling approach offers a large reduction inthe amount of flow information needed to cap-ture the large-scale aerooptical distortions athigh compressibility.

4. Conclusions

In the present work, the interfacial-fluid-thickness approach was extended to density-field data at low-compressibility (Mc ∼ 0.15)and medium compressibility (Mc ∼ 0.47).A new Aerooptics Pressure Vessel Facilitywas validated by demonstrating its capabil-ities to allow simultaneous imaging of thedensity field and the flow-generated optical-wavefront distortions. Direct imaging ofthe density interfaces was made possibleusing a laser-induced fluorescence density-field digital-imaging technique. Direct mea-surements of the distorted wavefronts wererecorded using a custom wavefront sensorwhich consists of 1,024 microlenses in orderto allow high-resolution results. Direct cor-relation between the structure of the flowand the flow-generated optical-wavefront dis-tortions provided a way to investigate com-pressibility effects on the flow structure andthe behavior of the optical wavefronts. TheIFT approach provided a way to separatethe effect of turbulent mixing from the com-pressibility effect on the index-of-refractionfield. The current observations indicate that

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isolated high-gradient regions dominate thelarge-scale aerooptical distortions and this ispractically important because it shows theutility of the IFT approach to model aeroop-tical interactions in separated shear layers atlarge Reynolds numbers for low-, medium-, aswell as high-compressibility flow conditions.

Acknowledgements

This work is supported by the Air Force Of-fice of Scientific Research (Dr. T. Beutner,Program Manager) and by the National Sci-ence Foundation (Prof. M. Plesniak, ProgramDirector).

References

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[3] R. J. Hugo. Mechanical and optical turbu-lence relationships in free shear flows. InAIAA 32nd Plasmadynamics and Lasers

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[4] N. T. Clemens and M. G. Mungal. Large-scale structure and entrainment in the su-personic mixing layer. J. Fluid Mech.,284:171–216, 1995.

[5] H. J. Catrakis and R. C. Aguirre. Inner-scale structure of turbulence-degraded op-tical wavefronts. In AIAA 33rd Plasma-dynamics and Lasers Conference, AIAA2002-2269, Maui, HI, 2002.

[6] R. C. Aguirre, J. Ruiz-Plancarte, andH. J. Catrakis. Physical thickness of tur-bulent fluid interfaces: structure, vari-ability, and applications to aerooptics.In AIAA 41st Aerospace Sciences Meet-ing and Exhibit, AIAA 2003-0642, Reno,Nevada, 2003.

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