Roberto C. Aguirre, ∗ Jennifer C. Nathman, ∗ Philip J. Garcia, ∗ and Haris J. Catrakis †
Aeronautics and Fluid Dynamics Laboratories, Mechanical and Aerospace EngineeringHenry Samueli School of Engineering, University of California, Irvine, CA 92697
A combined experimental/computational technique useful for aero-optics is developedwith emphasis on the interfacial-fluid-thickness approach. The proposed technique is use-ful both for low-energy and high-energy laser applications. The experiments enable flowimaging and beam measurements at large Reynolds numbers and the computations, com-bined with the experiments, permit the study of aero-optical interactions at both lowand high laser energies. Experimentally, the method consists of using laser-induced fluo-rescence for the refractive-field imaging and Hartmann sensing for the optical-wavefrontmeasurements. In the UC Irvine pressurized single-stream wind tunnel, acetone vaporcan be seeded in the ambient air or in the high-speed air, or in both. This is usefulto compare density-effects due to compressibility alone and mixing-effects due to dis-similar gases. A custom-built high-resolution Hartmann wavefront sensor is developedthat is useful to measure the propagated wavefronts simultaneously the refractive in-terfaces. Computationally, an optical beam solver is developed based on the eikonalequation with a marching algorithm in order to simulate the propagation of the opticalwavefronts through the refractive-index field. The computations are combined with theexperiments by employing the flow images as the refractive field, for the low-energy-lasercase. For high-energy laser pulsed beam propagation, the eikonal equation is coupled withan absorption law to modify both the refractive field and the wavefront profile. This ap-proach, which combines flow imaging with geometrical-optics computations, is especiallyuseful for the study of near-field aero-optical distortions in separated flows, as would begenerated by high-maneuverability aircraft, whereas far-field beam propagation requiresFourier optics.
Introduction
THE variability of the index-of-refraction field inturbulent flows remains a highly sought after phe-
nomena for understanding, predicting, and control-ling aero-optical interactions (Jumper & Fitzgerald1
and references therein). The optical distortions im-posed by variable-index-of-refraction turbulent flowson a propagated wavefront have severe implicationson many aero-optical systems such as laser communi-cations, imaging, and directed-energy (e.g. Andrews,Phillips, & Hopen2; Gilbert & Otten3; Kyrazis4). Inorder to develop techniques for the prediction and con-trol of aero-optical phenomena in turbulent flows, animproved understanding is needed of turbulent-index-of-refraction field properties such as the complexityof the instantaneous structure of turbulent refractivefluid interfaces across which the wavefront aberrationsoccur.
Turbulent flows which become separated provide thelargest optical aberrations, in the absence of shockwaves, and the distorting mechanism(s) may be in
∗Graduate Student, AIAA Member†Assistant Professor, AIAA Member, Corresponding Author,
part due to scalar mixing of dissimilar gases and/orin part due to velocity fluctuations and flow curva-ture effects. It is possible for more than one distortingmechanism to operate simultaneously and dependingon the flow conditions the dominant aero-optical aber-rations may be described in terms of the large scaleBrown-Roshko coherent structures, density-well re-gions, instantaneous large-scale boundaries of mixedfluid interfaces, focusing/defocusing lenses, and/or theinterfacial thickness of turbulent flows (e.g. Truman &Lee5; Dimotakis, Catrakis, & Fourguette6; Fitzgerald& Jumper7; Trolinger & Rose8; Catrakis & Aguirre9).
In the present work, a combined experimen-tal/computational technique useful for aero-opticsis developed with emphasis on the interfacial-fluid-thickness approach. The proposed technique is usefulboth for low-energy and high-energy laser applications.Experimentally, the method consists of using laser-induced fluorescence for the refractive-field imagingand Hartmann sensing for the optical-wavefront mea-surements. This is useful to compare density-effectsdue to compressibility alone and mixing-effects due todissimilar gases. A custom-built high-resolution Hart-mann wavefront sensor is developed and described.Computationally, an optical beam solver is developedbased on the eikonal equation in order to simulate
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American Institute of Aeronautics and Astronautics Paper 2005–1080
43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada
the propagation of the optical wavefronts through therefractive-index field. The computations are combinedwith the experiments by employing the flow imagesas the refractive field, for the low-energy-laser case,and coupling the eikonal equation with an absorptionlaw to modify both the refractive field and the wave-front profile, for high-energy laser pulsed beam prop-agation. This approach, which combines flow imag-ing with geometrical-optics computations, is especiallyuseful for the study of near-field aero-optical distor-tions in separated flows, as would be generated byhigh-maneuverability aircraft, whereas far-field beampropagation requires Fourier optics.
The pressurized flow facility housed in the Aeronau-tics and Fluid Dynamics Laboratories at UC Irvineis especially designed to enable high-resolution aero-optical measurements. The facility consists of an airreservoir that is located upstream and can be pressur-ized up to 3000 psig in order to provide the necessarydriving pressure. The main aero-optics vessel can bepressurized up to 325-psig and is physically 4-ft. indiameter by 9-ft. tall, which provides an enclosed en-vironment to study large-scale separated flows. Asshown in figure 1, the air reservoir is connected tothe main aero-optics vessel via 6-in diameter piping inorder to meet the demands of the high-mass flow rateof large-scale flows. The facility is operated in a blow-down manner with a range in run time duration of 1-30 seconds depending on the flow geometry and size ofthe configured test-section.
Fig. 1 Picture of the main pressure vessel in theaero-optics pressurized flow facility at UC Irvine.
The elevated pressures provide three advantagesfor aero-optics research: higher resolution and signal-
to-noise-ratio flow/beam images; larger Reynoldsnumbers applicable to flight conditions; Mach- andReynolds-number effects that can be identified sepa-rately. The facility can generate flow conditions witha freestream Mach number, or flight Mach number,spanning subsonic and supersonic values in the rangeM ∼ 0.3 − 2.5, i.e. at convective Mach numberMc ∼ 0.15 − 1.0. The large test section and elevatedpressures provide Reynolds numbers up to Re ∼ 108,based on the visual thickness, or Re ∼ 400× 106 m−1.The main aero-optics vessel enables access to the in-terior via a 2-ft. diameter quick-release door that ishydraulically operated. This grants flexibility to thedesign of experiments by enabling the configuration ofvarious flow geometries, while also allowing for test-section modifications before each experiment. Opticalaccess to the interior is made possible through five10-in. diameter windows made of quartz material toenable a sufficiently large view needed for whole-fieldmeasurements of the test section.
Single-Stream Shear Layer Geometry
The single-stream shear layer is an example of a sep-arated flow, which has the largest growth rate of shearlayers. Although reduced growth rates are desirablefrom the point of view of reducing aero-optical distor-tions, the large growth rate of the single-stream shearlayer is a favorable flow feature for high-resolution di-rect whole-field measurements of turbulent refractivefluid interfaces. Figure 2 shows a schematic of thesingle-stream shear-layer tunnel in its subsonic config-uration. The single-stream shear-layer tunnel includesa flow management section, which contains honeycomband mesh screens to straighten the flow, followed bya contoured converging nozzle for the subsonic case.The test-section consists of an adjustable guidewall, a90-degree-corner entrainment wall, and two sidewalls.Because of the large internal size of the pressure ves-sel, ample entrainment is naturally provided for thegrowth of the shear layer.
Fig. 2 Single-stream shear-layer schematic shownin a subsonic configuration.
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Flow-/Beam-Imaging Technique
In order to utilize laser-induced fluorescence of ace-tone vapor to conduct high-resolution imaging of therefractive-index field, a suitable seeding method is de-sirable. The typical way to seed air with acetone vaporis to employ atomizing nozzles, but these create ace-tone droplets in addition to the vapor. A differentapproach is to employ bubblers or vaporizers whichavoid the generation of acetone droplets. We have con-ducted experiments with a custom acetone bubbler asshown in figure 3, at pressures up to 80 psig, in orderto investigate the extent to which the acetone vaporcan be generated and excited by a UV laser with asufficient fluorescence signal. We utilized a frequency-quadrupled Nd:YAG laser operating at 266 nm, whichis an appropriate wavelength to excite the acetonevapor. The laser was operated at ∼ 100 mJ/pulseand shaped into a laser sheet which was propagatedthrough the pressure vessel and the test section.
Air
Air
Acetone Vapor
+ Air
Acetone Bath
Fig. 3 Schematic of acetone bubbling technique.
The acetone-bubbling technique was able to providesufficiently-high acetone vapor concentration for fluo-rescence along the entire laser-sheet propagation pathin the interior of the vessel. This propagation pathis 4 feet for the present flow facility. Visible fluores-cence, in the blue part of the spectrum, was observedthroughout the laser-sheet propagation path which iscrucial in order to do flow imaging in a large-scaleflow facility such as the present one. One key ad-vantage of this approach is that experiments can beconducted at subsonic as well as supersonic flow con-ditions, in the single-stream shear layer, with seedingin the ambient air rather than in the high-speed air.An acetone vaporizer is also desirable, as an alternativeto the bubbler, which is shown in figure 4 and providesmore flexibility in terms of refining the acetone seeding
level. Figure 5 shows the custom Hartmann wavefrontsensor which is a one-dimensional sensor with a linearCCD array. The array currently has ∼ 3, 000 pixelswhich can be increased to ∼ 8, 000 − 12, 000 pixelsin the future. This provides a method to conducthigh-resolution direct wavefront sensing, in one spa-tial dimension, which matches the high-resolution flowimaging technique for the spatially-two-dimensionallaser sheet.
SENSORS FOR MASS FLOW AND PRESSURE
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Fig. 5 Schematic of high-resolution Hartmannwavefront sensor.
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Computational Aero-Optics Combinedwith the Experimental Technique
In computational aero-optics, as in computationalfluid dynamics, there are currently limitations re-garding the Reynolds numbers that are achievableeven with massively-parallel computers. Prior com-putational work in aero-optics includes large-eddy-simulation (LES) approaches, or other flow-modelingmethods, and direct-numerical-simulation (DNS) tech-niques. Examples of previous work include the studiesof: Elghobashi & Wassel10; Tsai & Christiansen11;Truman & Lee5; Childs12; Yahel13; Jones & Bender14;Mani, Wang, & Moin15; Tromeur, Garnier, Saguat, &Basdevant.16 Computational aero-optics can offer keyadvantages compared to experimental aero-optics, asfor example in the context of high-energy-laser beampropagation. However, the computations are limitedto moderate Reynolds numbers unless subgrid-scalemodeling is employed. In comparison, experimentsat large Reynolds numbers with finite-resolution flowimaging provide essentially large-eddy experimentalsimulations without subgrid-scale modeling. In thepresent work, we combine the experimental and com-putational approaches in order to retain the large-Reynolds-number capability of the experiments whileincluding the unique advantages of computations. Weconfine our discussion to the near-field aero-optical dis-tortions for which geometrical optics provides a usefulapproximation,14 whereas far-field optical beam prop-agation requires Fourier optics.
Low-Energy-Laser Computational Method
For low-energy-laser applications, we consider theeikonal equation for the optical path length:
|∇OPL| = n , (1)
which can be rearranged in a computational contextso that it can be treated by marching schemes as:
∂ OPL∂z
=
√√√√n2 −
[(∂ OPL
∂x
)2
+(
∂ OPL∂y
)2]
.
(2)Here n(x, y, z, t) denotes as usual the refractive-indexfield and z is the main propagation direction of thelaser beam.
In the present combined computa-tional/experimental approach, the refractive-indexfield can be input to the eikonal equation from thelarge-Reynolds-number flow imaging experiments thatrely on the acetone fluorescence technique in the pre-vious section. With an initial or boundary conditionfor the shape of the optical wavefront, the eikonalequation can be solved by standard finite-differenceschemes or other methods such as level-set methods.17
The present approach is useful also because it canbe employed to compare the wavefront propagation
and distortion effects with the full eikonal equationas opposed to the approximations sometimes used inwhich light-ray bending is neglected.9,18
High-Energy-Laser Computational Method
For high-energy-laser beam propagation, one musttake into account the modification of the refractive-index field due to absorption of laser energy by thefluid. This can be investigated, in the combined com-putational/experimental approach, by coupling theeikonal equation with an absorption model. In gen-eral, such as for continuous high-energy-laser beampropagation, the full coupling will be required usingthe time-dependent energy equation. However, forpulsed beam propagation at a repetition rate lowerthan the turbulent advection time scales, where ef-fectively a frozen-flow analogy can be employed, theenergy equation can be simplified. An example of thistype of coupling for the latter case is as follows. Theeikonal equation:
|∇OPL| = n , (3)
can be coupled with a beam-absorption model such asthe Beer-Lambert law,
∂I
∂z= −α
ρ
ρrefI , (4)
and with the energy equation simplified as,
ρ Cp∂T
∂t= α I , (5)
integrated over a short time interval corresponding tothe propagation of the laser pulse. This model pro-vides a closed set of coupled equations since:
n = 1 + βρ
ρref. (6)
Here α is the absorption coefficient and β is theGladstone-Dale constant.
Interfacial-Fluid-Thickness Approach
The above approach also offers a means to exam-ine in detail the Interfacial-Fluid-Thickness (IFT) ap-proach.9 The local thickness of the refractive fluidinterfaces can be identified, for both the low-energyand high-energy laser cases, and the spatial variabilityof the interfacial thickness can be examined. This canbe helpful to identify the dominant contributions tothe beam distortions. The present combined approachoffers a way to include high-resolution large-Reynolds-number measurements of the refractive-index field intoa computational geometrical-optics method. The com-putational component enables a comparison of thebeam-propagation behavior between the full eikonalequation and lower-order approximations such as theweak aero-optical regime model where ray bending isignored.9,18
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American Institute of Aeronautics and Astronautics Paper 2005–1080
useful for aero-optics has been developed, with empha-sis on the interfacial-fluid-thickness approach, which isuseful both for low-energy and high-energy laser ap-plications. The experimental technique enables flowimaging and beam measurements at large Reynoldsnumbers. The computations, combined with the ex-periments, permit the study of aero-optical interac-tions at both low and high laser energies. Exper-imentally, laser-induced fluorescence is used for therefractive-field imaging and Hartmann sensing is usedfor the optical-wavefront measurements. In the pres-surized single-stream wind tunnel, acetone vapor isseeded in the ambient air or in the high-speed air,or in both, in order to compare density-effects dueto compressibility alone and mixing-effects due to dis-similar gases. A custom-built high-resolution Hart-mann wavefront sensor is developed that is usefulto measure the propagated wavefronts simultaneouslythe refractive interfaces. Computationally, an opticalbeam solver is developed based on the eikonal equa-tion with a marching algorithm in order to simulatethe propagation of the optical wavefronts through therefractive-index field. The computations are combinedwith the experiments by employing the flow imagesas the refractive field, for the low-energy-laser case.For high-energy laser pulsed beam propagation, theeikonal equation is coupled with an absorption lawto modify both the refractive field and the wavefrontprofile. This approach, which combines flow imag-ing with geometrical-optics computations, is especiallyuseful for the study of near-field aero-optical distor-tions in separated flows, as would be generated byhigh-maneuverability aircraft, whereas far-field beampropagation requires Fourier optics.
AcknowledgementsThis work is supported by the Air Force Office of
Scientific Research (Dr. Thomas Beutner, ProgramManager) and is part of a program on aero-optical in-teractions in turbulent flows.
References1Jumper, E. J. and Fitzgerald, E. J., “Recent advances in
aero-optics,” Prog. Aerospace Sci., Vol. 37, 2001, pp. 299–339.2Andrews, L. C., Phillips, R. L., and Hopen, C. Y., Laser
beam scintillation with applications, SPIE Optical EngineeringPress, 2001.
3Gilbert, K. G. and Otten, L. J., “Aero-optical phenomena,”Progress in Astronautics and Aeronautics, Vol. 80, AmericanInstitute of Aeronautics and Astronautics, 1982.
4Kyrazis, D., “Optical degradation by turbulent free shearlayers,” Optical Diagnostics in Fluid and Thermal Flow , editedby S. S. Cha and J. D. Trolinger, Orlando, Florida, 1993, pp.170–181.
5Truman, C. R. and Lee, M. J., “Effects of organized tur-bulence structures on the phase distortion in a coherent opticalbeam propagating through a turbulent shear flow,” Phys. FluidsA, Vol. 2, 1990, pp. 851–857.
6Dimotakis, P. E., Catrakis, H. J., and Fourguette, D.C. L., “Flow structure and optical beam propagation in high-Reynolds-number gas-phase shear layers and jets,” J. FluidMech., Vol. 433, 2001, pp. 105–134.
7Fitzgerald, E. J. and Jumper, E. J., “The optical distortionmechanism in a nearly incompressible, free shear layer,” J. FluidMech., 2004, to appear.
8Trolinger, J. D. and Rose, W. C., “Technique for simu-lating and evaluating aero-optical effects in optical systems,”AIAA 42nd Aerospace Sciences Meeting and Exhibit, AIAA2004-0471 , Reno, Nevada, 2004.
9Catrakis, H. J. and Aguirre, R. C., “New interfacial-fluid-thickness approach in aero-optics with applications to compress-ible turbulence,” AIAA J., 2004, in press.
10Elghobashi, S. E. and Wassel, A. T., “The effect of turbu-lent heat transfer on the propagation of an optical beam acrosssupersonic boundary/shear layers,” Intl J. Heat Mass Transfer ,Vol. 23, 1980, pp. 1229–1241.
11Tsai, Y.-P. and Christiansen, W. H., “Two-DimensionalNumerical Simulation of Shear Layer Optics,” AIAA J., Vol. 28,1990, pp. 2092.
12Childs, R. E., “Prediction and control of aero-optical dis-tortion using large-eddy simulations,” AIAA 1993-2670 , 1993.
13Yahel, R. Z., “Turbulence effects on high energy laser beampropagation in the atmosphere,” Appl. Opt., Vol. 29, 1990,pp. 3088–3095.
14Jones, M. and Bender, E. E., “CFD-based computer sim-ulation of optical turbulence through aircraft flowfields andwakes,” AIAA 32rd Plasmadynamics and Lasers Conference,AIAA 2001-2798 , Anaheim, CA, 2001.
15Mani, A., Wang, M., and Moin, P., “Computation of op-tical beam propagation through numerically simulated turbu-lence,” Bull. Am. Phys. Soc., 2003.
16Tromeur, E., Garnier, E., Sagaut, P., and Basdevant, C.,“Large eddy simulations of aero-optical effects in a turbulentboundary layer,” J. Turbulence, Vol. 4, No. 5, 2003, pp. 1–22.
17Kim, S., “An O(N) level set method for eikonal equations,”Unpublished.
18Aguirre, R. C. and Catrakis, H. J., “Aero-optical wave-fronts and scale-local characterization in large-Reynolds-numbercompressible turbulence,” AIAA J., 2004, in press.
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