Aero-Optic Calculations of A Spherical Turret at Transonic ... · Transonic Flow Eran Arad*, Mickey Weidenfeld Aeronautical Systems, RAFAEL Ltd,Haifa ISRAEL 3102102 Flow over a at-window

Aero-Optic Calculations of A Spherical Turret at

Transonic Flow

Eran Arad*, Mickey Weidenfeld�

Aeronautical Systems, RAFAEL Ltd,Haifa ISRAEL 3102102

Flow over a flat-window spherical turret at transonic flow conditions is simulated. Anadvanced LES method is used for flow simulation. Optical wavefront distortions are real-ized through imaging on an otherwise diffraction limited system. Visual and quantitativerepresentations of the distorted signal are evaluated through the systems’ PSF and MTFfunctions. Simulation results were validated against well established experiment databaseof cylinder-hemisphere turret at subsonic flow. At Mach number 0.81, a backward lookingconfiguration faces similar yet amplified wake induced distortions than those produced insubsonic regime. Noteworthy are the forward-looking window results, where an incidentplanar wavefront propagates through supersonic region and a buffeting shockwave, resultingin a double-image. Shockwave buffeting occurs also beyond the shear layer, in backward-looking configurations, inducing further optical distortions. Analysis of these phenomenatogether with preliminary evaluation of control technique, designed to mitigate the signaldegradation, are reported in the current paper.

Nomenclature

D Hemisphere diameterf Focal lengthk Turbulent kinetic energyMach Mach numberMTF Modulation transfer functionn Index of refraction (defined in equation 1)OPD Optical Path Difference (defined in equation 4)OPL Optical Path Length (defined in equation 3 )PSF Point Spread FunctionReD Reynolds number based on hemisphere diameterU∞ Free-stream velocityW Optical window diameterx,y,z Ordinates in main-flow direction, wall-normal and lateral direction, accordinglyλ Light wave length

∆y+ Wall-nondimensional mesh size ∆y+ = ∆ywU∞ν

ρ Flow densityρSL Reference flow density at sea level

I. Introduction

The use of accurate airborne optical systems has become abundant in the last decade, with constantlyrising challenges of resolution and range. A severe obstacle in the development of these systems is the

close range aero-optical phenomenon. The requirement for a large field-of-regard imposes the use of bluff-body turrets. The flow field over such bluff bodies at flight is turbulent and complex and may cause severeoptical aberrations at even low subsonic Mach numbers, as shown by Gorodeyv et al.1 Density fluctuations in

*Head, CFD Group�Senior Research Engineer

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American Institute of Aeronautics and Astronautics

turbulent regions scale with Mach2.2 At transonic flow regime, the high level of density oscillations directlygenerates significant fluctuations in the index of refraction, leading to deformed wavefronts and images. Thecombination of very unsteady separated shear layers and vortices creates a sizable challenge for predictivetools. Mani2,3 and Mathews et al.4,5 have shown the inadequacy of industry-standard RANS methods inthe prediction of aero-optical aberrations, asserting Large Eddy Simulation (LES) as the minimum level forreliable aero-optic prediction.

Mathews et al.4,5 reported on successful reconstructions of aero-optical aberrations, using advancedcompressible LES method, over a large range of Reynolds number. They focused their attention mainly onlow Mach subsonic flow. While low-Mach flow regime poses significant challenges, transonic regime introducesadditional compressibility effects that raises the bar of the computational challenge even higher: In additionto the turbulent shear layers, one has to handle now supersonic sub-regions with definitely different densities(compared with the surroundings subsonic flow) and shock waves with very strong density gradients thatexhibit also buffeting behavior.6

Whereas most of the works cited here consider the propagation problem of a planar wavefront originatingat the window to the far-field, we are primarily interested in the imaging problem of a far-field object on anideal optical system. The far-field-originated planar wavefront is deformed solely by the flow-field and furthertransformed onto the focal plane of an ideal circular aperture lens by the use of Fraunhoffer formulation.18

Suppression of the flow activity (be it shear layers or shockwave buffeting) may decrease the aero-opticalinteraction and thus enhance optical performance. Design of turrets in a manner that avoids both shearlayers and supersonic enclosed region is the obvious venue. However such major redesign may be marked outas it hampers other operational requirements. A possible bypass is the use of minor geometry modificationstogether with application of active-flow-control (AFC) devise. Arad et al7 and Schatzman et al8 have shownthat properly applied, AFC devices can impose major modifications of the flow field, using minute amountsof energy. The current effort is a preliminary attempt to verify control authority, aiming at mitigation ofthe signal degradation.

II. Configuration and Flow Conditions

A spherical turret with flat circular window is considered. Window diameter is W = 0.5D (where D isthe sphere diameter). It is subjected to a free-stream with Mach = 0.81 and ReD = 2.74M (based on

turret diameter D). Figure (1) presents a schematic sketch of the problem in which an elevation angle of−10o is considered, featuring a backward-looking setup. An incident planar wave-front propagating throughthe turbulent wake towards the window, exhibits deformations owing to the wake density fluctuations.

Figure 1. Spherical turret with flat window tilted backward by 10◦

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The configuration of the validation case is a cylinder-hemisphere. Measurements were reported in manypublications of Notre-Dame University. The hemisphere-on-cylinder turret configuration is a platform ofparticular interest1,19–21 and therefore suited for validation purposes of aero-optical numerical simulation.This group has actually performed also LES simulations for these configurations4,5 using the same code9

that is used in the current effort, reporting good agreement with measurements. Since the current simulationapproach was well validated already, we just repeat part of the simulations mentioned above, to assure thatwe are indeed in line with the published results.

The case of a flat window turret, matching Goerdeyev’s20 was simulated: A 12in diameter hemisphereon top of a 4in length cylinder extruding from the wind tunnel floor. The turret was equipped with a 5.4indiameter window at a fixed elevation angle of 30 degrees and various azimuthal angles. The measurementswere taken at a Reynolds number of around ReD = 2.3M, based on sphere’s diameter D, and for differentMach numbers ranging from 0.3 to 0.5. The present computation was conducted at a reduced Reynoldsnumber regime of ReD = 0.45M, Mach=0.35, and azimuthal angle of 110°. The window to sphere diameterratio is 0.375 compared with the experiment’s 0.45. Porter et al.21 have shown that optical data taken fromairborne experiment on a similar turret with a 0.33 window-to-sphere diameter ratio, compared well (fig. 14)with the tunnel’s data obtained for a ratio of 0.45. Furthermore, it is generally excepted that flow inducedoptical aberrations features only a high order dependence on Reynolds number for sufficiently high Reynoldsregime.2,22 These observations support using reduced Reynolds number in order to alleviate computationalcost.

III. Computational Method

A. Flow Simulation

Flow simulation was performed using compressible, unstructured-mesh Large Eddy Simulation (LES),developed by Cascade Technologies Inc. CharLES9 is a fully explicit solver, using a third order Runge-

Kutta formulation in time and a low-dissipative finite-volume scheme in space. A blending method thatcombines non-dissipative central flux with a dissipative upwind flux is used, providing computational stabilityin regions of low mesh quality. The numerical dissipation due to the use of upwind scheme is minimized sincethe upwind flux is applied only in limited regions, depending on the local quality of the mesh. The solver issecond-order accurate in space. The Vreman subgrid-scale (SGS) model10 is used to represent sub-grid scalestructures. As the cases under consideration have high Reynolds numbers, a wall model11 was applied. Thecurrent transonic flow conditions over a bluff body lead to the development of supersonic confined regionsand shockwaves, as can be observed in figure 10. For localized shockwave modeling, a fully unstructured2nd-order ENO method is used12 and HLLC approximate Riemann13 solver is applied to compute the flux.An hybrid switch detects the shocks and activates the shock-appropriate scheme14,15 .

Solution domain length is 85D in streamwise direction (D is the sphere diameter) while the sphere islocated at the first quadrant. The width and height of solution domain is 14D. The computational meshcomposes about 10 million cells. Originally hexahedral cells, then refined locally by CharLES,9 addingprismatic cells. Wall resolution was about ∆y+ = O(1) on the window and O(10) on the sphere. Thelateral near-wall mesh size was about ten times larger. Sponge layer was set downstream, beyond x=20D.Fully upwind layers with a thickness of 7D at the inlet, 20D at the outlet and 10D radially were employedto prevent the reflection of outgoing waves back into the domain. Total inflow conditions were set at theinflow and free-flow conditions were set on the other external boundaries. About 2 million time steps wereperformed, covering about 20 flow-through times.

B. Optical Calculations

The index of refraction, n, depends on the density field through the Gladston-Dale formula

n = 1 +Gρ, (1)

where G is the Gladstone-Dale constant which slightly varies with the wavelength of light and mediumproperties. For wavelengths λ ∈ (1µm, 10µm) through air it obtains the value G = 2.21 × 10−4 [m3/Kg].16

Electromagnetic radiation through turbulent medium is governed by the Maxwell equations and the com-pressible Navier-Stokes equations. It is common practice in aero-optic applications, to assume that theoptical wave propagates through a ”frozen” flow-field, owing to the different problems timescales. Under

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such and other dimensional considerations17, the Maxwell system of equations reduces to a single scalar waveproblem. Applying the paraxial assumption, the solution of the wave equation is a phase distorted signal,where the distortion is accumulated along the path of propagation:

U(x, y, z) = U(x, y, 0) exp

[−ik

∫ z

0

n(x, y, z1)dz1

]. (2)

The integral in (2) is known as the optical path length (OPL):16

OPL(x, y, t) =

∫ b

a

n(x, y, s)ds, (3)

where wave-front distortions are quantified by the optical path difference (OPD) which is the variation ofOPL about its mean value,16

OPD(x, y, t) = OPL(x, y, t)− 〈OPL(x, y, t)〉. (4)

The angle brackets denote spatial averaging over the aperture. The index of refraction values are obtainedover the fluid computational volume, then interpolated onto an optical volume comprised of a single uniformCartesian mesh such as presented in figure (2(a)) with a dimension of 0.3D in the z-direction normal tothe aperture. Figure (2(b)) presents refraction index contours interpolated over the optical grid. The OPD

(a) Optical box schematics (b) Instantaneous index of refraction

Figure 2. Optical Box

functions were henceforth used as inputs to the optical solver, facilitated by the Fraunhoffer integral18:

U(x′, y′, t) =eikfei

k2f (x′2+y′2)

iλf

∫∫W

P (ξ, η) e−i2πλf (x′ξ+y′η)e−i

2πOPD(ξ,η,t)λ dξdη (5)

The integration is performed over the optical window. U is the optical signal, x’,y’ map the focal plane,k = 2π

λ is the wavenumber, f is the focal length, ξ, η map the aperture and P (ξ, η) is the aperture function.The image on the focal plane is visualized by the Point-Spread Function (PSF) and system performanceis quantified via it’s counterpart Modulation Transfer Function (MTF). The former represents the signalintensity distribution on the aperture and the latter is the relative power of the different wave-numberscomprising the signal.

IV. Results

A. Hemisphere on Cylinder Turret With A Flat Window

For validation, the computational mesh contains about 7M hexagonal cells with ∆y+ = 0.6 (wall normaldirection) for the turret and window. Some visualization of the computational flow field is provided

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in figure 3: The instantaneous pressure distribution on the turret surface in figure 3(a), and contours ofvelocity magnitude on a cross-cut in the flow field in figure 3(b). The massive separation over the windowis clearly visible. Instantaneous OPD contours over the optical window are presented in figure 4: Current

(a) Instantaneous pressure distribution (Pa) (b) Velocity contours in a cross-cut. Blue: 0 ; Red; 272m/sec

Figure 3. Instantaneous flow parameters for an hemisphere-on-cylinder turret. Flow from left to right

results (figure 4(a)) were scaled by ρ/ρSLMach2D (where ρSL = 1.229Kg/m3 is sea-level density, definedby Gordeyev et al1) to match the experiments flow conditions and the measurements of Gordeyev et al1

(figure 4(b)). The OPD variation across the window in both cases is in the range OPD ∈ (±0.1,±0.2)µm.Any similarities are coincidental owing to the instantaneous nature of the separation zone at different timeinstances. The values obtained from measurements1 and present computations for the OPD functions onthe aperture were OPDRMS = 0.0653 [µm], and 0.043 [µm], correspondingly. The OPDRMS was computedafter removal of tip, tilt, spatial averaging and time averaged OPD4. Instantaneous pressure fluctuations

(a) Instantaneous OPD: Current results (Mach=0.37) (b) Instantaneous OPD: Experiment1

Figure 4. Optical aberrations over the window, for an hemisphere-on-cylinder turret. OPD contours in µm

were recorded at three different locations denoted by probes #3, #5, and #6 as specified in figure (5) andcompared with measurements of a conformal window turret from Gordeyev.1 Despite the differences in theconfiguration, the fluctuating field appears to be in a very good agreement.

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#6 #3

#5

#5

#6#3

#3

#5,#6

Figure 5. Pressure spectra on the turret surface; comparison with experiments.1 Computation: Black ;Experiment : Red

B. Spherical Turret: Base Flow

1. Backward Facing Window

The most spectacular feature of flow over a sphere is the thick oscillatory wake. In the case of backwardfacing window the optical path goes through this wake and one can expect significant reduction in wave

front quality. Visualization of the flow field is presented in figure 6. Strong oscillations in velocity magnitudecan be observed in figure 6(a). The rate of dilatation, which is defined as ∇ · ~u represents the deviationfrom incompressible flow, and thus serves as an indicative tool to identify density variations. As presentedin figure 6(b), large dilatation gradients characterize the separated shear layer over the window. Indeed,

(a) Velocity magnitude; 0: Blue ; 340m/sec: brown (b) Dilatation

Figure 6. Flow visualization on a cross-cut, for 10o backward facing window

the instantaneous density distribution (figure 7(a)) and the turbulence energy contours (figure 7(b)) display

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sizable activity over the optical window, implying on significant induced optical aberrations. As expected,

(a) Instantaneous density Kg/m3 (b) Turbulence energy

Figure 7. Contours of flow parameters on a cross-cut, for 10o backward facing window

the instantaneous OPD distribution over the window (figure 8(a) is pretty noisy, with OPDrms = 0.6µm. Ifwe consider light with wavelength of λ = 1.5µm, using focal length f = O(10W ) then the non-dimensionaloptical distortion becomes rather large:2πOPDRMS

λ = 2.5. Some secondary images can be observed in thePSF (figure 8(b)), mainly in flow-wise (X) direction. The output for the optical designer is the Modulation

(a) Instantaneous OPD [m] (b) Instantaneous PSF

Figure 8. Optical aberrations over the window, for 10o backward facing window

Transfer Function (MTF). As shown in figure 9, significant losses can be observed, mainly in the X direction(figure 9(a)).

2. Forward Facing Window

Pointing the window forward, away from the noisy wake, one may expect a significant improvementin performance. However, when the turret cruises at transonic flow regime, the flow expands into a

super-sonic flow region followed by a standing (slightly buffeting) shockwave. For the current Mach number

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(a) MTF-X (b) MTF-Y

Figure 9. Modulation Transfer Function (MTF) for λ = 1.5µm at long exposure (3.2ms), for 10° backwardfacing window. Blue curve represents ideal diffraction limited optics.

(Mach=0.81), the shock-wave is located in the center of the window, as shown in figure 10(a). The pictureof dilatation contours (figure 10(b)) shows one implication of this phenomenon: Strong gradients of densityjust over the window. However, the super-sonic region creates another disturbance: two distinct density

(a) Time-averaged Mach number (b) Instantaneous dilatation

Figure 10. Flow contours on a cross-cut , for a 10° forward facing window

(and refraction index) regions on the two sides of the shockwave. The resulting abrupt variation in lightpropagation speed invokes a step-function distribution of the OPD function 12(a). The strong gradient inthe signal’s wavefront, effectively splitting the lens into two, creates a double-object-image as displayed inthe PSF plot of figure 12(b). This steady-lensing effect is the primary source of aberrations in the forward-looking configuration. A second order distortion mechanism takes place in the form of shock buffeting, welldisplayed in figure 11(b). However, both the shock-buffeting and the shock-induced separated layer appearto play only a secondary role in this case.

The position of the super-sonic region and shock-wave in the center of the window have a catastrophiceffect on the OPD distribution, as shown in figure 12(a): The lens is actually split to two distinctly differentparts. The step-like phase distortion in the streamwise direction, illustrated by the OPD function, result indouble-image emergence in the same direction. as can be observed in the PSF obtained for a wavelengthof λ = 1.5µm (figure 12(b). Substantial aberrations can be clearly observed in the Modulation TransferFunction (figure 13). Furthermore, here again exists a significant difference between the MTF in the Xdirection (figure 13(a)) and the lateral Y-direction (figure 13(b)).

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(a) ρ (b) ρ′ρ′

Figure 11. Contours of density ([Kg/m3]) on a cross-cut for a 10° forward facing window

(a) Instantaneous OPD [m] (b) Instantaneous PSF

Figure 12. Optical aberrations over the window , for a 10° forward facing window

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(a) MTF-X (b) MTF-Y

Figure 13. Modulation Transfer Function (MTF) for λ = 1.5µm at long exposure (3.2ms) , for a 10° forwardfacing window

C. Spherical Turret: Performance Enhancement

The analysis that was presented above, for two spherical turret settings, clearly shows that the currentconfiguration, which performs considerably well at low Mach regimes, suffers from significant optical

performance degradation at transonic flow regime. Two flow mechanisms were identified as the source ofthe optical aberrations: separated shear layer over the window, and a supersonic enclosed region followedby a shockwave. The former characterizes primarily backward looking configurations, while the latter ispredominant at forward-looking settings, though it may show up on different configurations as well. At mid-tilt angles the two phenomena sometimes unite. The whole set of flow-induced aberrations can be efficientlyavoided by a substantial redesign of the turret. However, the present effort is constrained by a requirementof using only minor modifications of the original geometry. An attempt to enhance the performance shouldbe focused on these two mechanisms. The separation of the shear layer may be triggered either by the spherecurvature, reaching a point where the flow can no longer follow the surface, or by the sharp discontinuitybetween the sphere surface and the flat window. At small backward-tilt angles the interaction with the flatwindow edges induces the separation. A fillet that connects the window and the surrounding sphere surfacecan decrease the curvature discontinuity and attenuate the size of the shear layer. However, the smaller radiusof the fillet might invoke higher level of acceleration and increase the size of the super-sonic region. To avoidthat, additional design tool is needed: A low-velocity jet was applied, to reduce the local acceleration. Thesections above dealt with large elevation angles of the window (±10o) introducing substantial flow-inducedaberrations. The preliminary attempt to control the flow is focused on milder conditions, at an elevationangle of -2° (backward, relative to the downward vertical axis). The suggested modifications are preliminary,mainly aimed at proving control authority. Further development are required to make them practical.

1. Design Modification and AFC

The design modification consists of pushing the optical window towards the sphere center by about 4% ofthe turret diameter (D). A thin (of 0.001D width) slot was extruded, conformal to the optical window

and located 0.085D above the original window. A smooth fillet was matched between the slot and translatedwindow edges. The suggested configuration is presented in figure 14. The jet velocity was set verticallydownwards. It was found that a constant velocity magnitude of 0.24U∞ was sufficient to introduce a changein the flow structure which is reflected in the optical performance. It should be clearly stated that detailedoptimization of jet direction and magnitude has not been performed yet.

2. Results of Design Manipulation

The base flow, at tilt angle of -2° (backward, relative to downward pointing normal) is composed of a shearlayer and an enclosed supersonic region, both over the optical window. The flow structure can be clearly

observed in the contours of time averaged flow parameters (Mach number and turbulence) over flow-fieldcross-cut, presented in figure 15. Both the shear layer and supersonic regions, observed in figure 15(a) leavetheir imprint on the density field as seen in figure 16. In particular, strong density oscillations were recorded

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Figure 14. Design modification and AFC jet

(a) Mach number (b) Turbulence energy

Figure 15. Time averaged flow field parameters on on a cross-cut, with backward facing window

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both at the shear layer and at the shockwave regions (figure 16(b)). Introducing only fillet redesign had very

(a) ρ (b) ρ′ρ′

Figure 16. Flow density [Kg/m3] on a cross-cut (averaged and oscillations RMS), with backward facing window

insignificant effect on the flow field and optical aberrations (actually slightly worse than the base flow dueto higher acceleration over the smaller curvature radius of the fillet). Once the AFC jet was applied overthe modified configuration, though the shear layer and supersonic region were not extinguished, they stillwere significantly reduced, as shown in figure 17. While the shear layer is slightly reduced, the supersonicregion is nearly totally smoothed out (figure 17(a)). This effect is clearly reflected in the turbulence energyspread-out (figure 17(b)): The high value region in the shear layer is significantly smaller and beyond theshear layer, turbulence energy is rather small, with no imprint of the shockwave which could be observedin the base flow (figure 15(b)). The influence of the above listed effects on the density field is paramount

(a) Mach number (b) Turbulence energy

Figure 17. Flow field parameters on on a cross-cut for the modified configuration with AFC on

for the optical performance. Comparing the density distribution with AFC on (figure 18) and the base-flowdensity distribution (figure 16) shows significant differences. The time-averaged density distribution displaysonly minor difference (figure 16(a) versus figure 18(a)): smaller low density region in the AFC-applied case.

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However, the density oscillatory field (figure 16(b) versus figure 18(b)) exhibit much more dramatic effect: Alayer with very high activity over the optical window was replaced by a thinner layer with smaller amplitudeof density oscillations. This favorable manipulation of the flow field is expected to have a positive influenceover the optical performance. Using the practice described above, the Modulation Transfer Function was

(a) ρ (b) ρ′ρ′

Figure 18. Flow density ([Kg/m3]) on a cross-cut (averaged and oscillations RMS), with AFC jet on

computed for the base-flow and the manipulated flow cases. Over a long exposure, the limiting values ofMTFX and MTFY are plotted in figure 19. In the X (flow-wise) direction, the application of AFC producedthinner distribution of MTF functions (figure 19(a)). The effect on MTFY was performance improvementfor most of the wavenumbers (figure 19(b)).

0 10 20 300

0.2

0.4

0.6

0.8

1

cycle/mm

MT

F(k

x)

afc low

afc high

Diff Lim

Base low

Base high

(a) MTFX

0 10 20 300

0.2

0.4

0.6

0.8

1

cycle/mm

MT

F(k

y)

afc low

afc high

Diff Lim

Base low

Base high

(b) MTFY

Figure 19. Effect of AFC jet on long exposure optical performance

It should be noted that this improvement was obtained by using the AFC at preliminary setup, justas a proof of control authority. Further detailed refinements are required. The current results provide apositive outlook on the ability to obtain significant performance enhancement even at a design that operatesin conditions that are far beyond its comfort zone.

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V. Concluding Remarks

Analysis of aero-optical aberrations based on compressible Large-Eddy-Simulation (LES) appears tobe an effective tool for the design of airborne turrets. First, for an hemisphere-on-cylinder turret,

satisfactory agreement between wind tunnel measurements and corresponding computations was obtained.On this ground, further investigations of a spherical turret were made possible. At transonic speed, somehowsurprising aberrations were revealed. Unattended, they might hinder the performance of an optical turretat flight.

The analysis which was performed in the current study clearly demonstrates that at transonic flow regime,a spherical turret with a flat optical window is out of its comfort zone. At backward pointing elevation anglesof the optical window, a thick and very active shear layer develops over the optical window. This shear layer isassociated with significant density oscillations which introduce a prominent level of aberrations of the opticalsignal, blurring any image. At forward looking setting, due to acceleration along the sphere curvature, anenclosed supersonic region develops on the window, followed by a shockwave. This region of very low densityrenders a double-image in the streamwise direction on the focal plane of an ideal optical system and isvery uncongenial to the quality of the optical signal. At moderate backward-looking angles, the near-fieldis characterized by a shockwave and shear layer. However, at these rear-elevation angles, minor designmodification combined with application of simple AFC technique, can significantly mitigate the destructiveeffect of flow induced aberrations. Preliminary non-optimized application of such an approach was appliedin the current study. It goes without saying that any practical application requires detailed redesign of thismanipulation. However, the success of the current effort raises hope that this approach might enable properuse of spherical turret at transonic flow regions with large performance envelop.

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Aero-Optic Calculations of A Spherical Turret at Transonic ... · Transonic Flow Eran Arad*, Mickey Weidenfeld Aeronautical Systems, RAFAEL Ltd,Haifa ISRAEL 3102102 Flow over a at-window

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