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WILLIAM J. TROPF, MICHAEL E. THOMAS, TERRY J. HARRIS, and STEVEN A. LUTZ

PERFORMANCE OF OPTICAL SENSORS IN HYPERSONIC

Hypersonic flight through the atmosphere presents unique environmental conditions that significantly affect the performance of a vehicular optical sensor. Knowledge of high-speed optical conditions and of the resulting effects on sensor performance is important in the design of optical instruments used in space shuttles, high-speed , and guided missiles. This article reports on recent work to quantify the transmissive and radiative effects of conlplex flow and heated windows caused by in order to predict sensor performance and investigate the effect of film cooling of windows.

INTRODUCTION Basic flow features that affect optical performance in Generally, the detector size is matched to the optical reso­ supersonic flight are illustrated in Fig. 1. The outermost lution; therefore, a loss of resolution because of blurring effect is the sharp density gradient at the in or defocusing results in decreased signal and reduced an­ front of the optical window. The density gradient refracts gular accuracy. Conversely, an oversized detector reduces optical rays and acts as a lens. Shocks from other parts capabilities in recognition, angle measurement, and clut­ of the forward vehicle body will also refract optical rays ter rejection, and increases noise. Therefore, a knowledge and may interact with the window shock to form a com­ of the optical effects of hypersonic flight will avoid sen­ plex optical path. Gas behind the shock is highly com­ sor performance degradation. pressed and heated. Density variations in this compressed Boresight error can affect performance in several ways. flow create refractive index variations and act as a Boresight fluctuations (caused by turbulence, shock in­ gradient-index lens. teraction, or coolant mixing) can blur images, cause er­ A second effect of compressed flow is aerodynamic rors in data transmission, and induce angle noise in heating of the window itself. The window trackers. Changes in boresight caused by body motion greatly affects the density in the . If the (e.g., changing shock structure or window distortion) ap­ window temperature or stress-causing thermal gradients pear as position errors or tracking rate errors that ad­ (thermal shock) become excessively high, a fllm-cooling versely affect sensors used for guidance and navigation. gas can be injected directly into the boundary layer to Radiation from the compressed gases and aerodynam­ give thermal protection. Such cooling further complicates ically heated window heats interior components and can flow and heat-transfer conditions. The principal optical increase sensor noise. Heating of interior components effects are resolution (blur and defocus), boresight error, leads to re-radiation and increased background noise. and radiation from gases and windows, which can sig­ Temperature-sensitive components suffer degradation as nificantly alter sensor performance. a result of overheating, thermal expansion, increased fric­ High resolution is desirable for detection (including tion, or changes in operation. Highly sensitive infrared clutter rejection), tracking accuracy, and recognition. photodiodes, whose noise performance is limited by the

Free-stream conditions

Figure 1-Hypersonic flow around Nose shock '-.... an optical window. High-speed flight produces a complex optical environ­ ment, including refraction and radi­ ation from the gases and the aero­ dynamically heated window. Upstream boundary layer

Optical sensor Compressed gas (refraction and emission)

370 Johns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) background radiation, will experience increased noise. Symbols Multiplexed photodiodes, whose dynamic ranges are limit­ ed by the multiplex process, can be saturated when the absorption coefficient background radiation is high enough, precluding mea­ {3 constant in Gladstone-Dale relationship surements of any kind. o boundary layer thickness; vibrational mode width An integrated, interdisciplinary approach (including flu­ emissivity; dielectric constant id dynamics, , optics, and material science shock angle input) is necessary to understand, model, and measure absolute viscosity the effect of high-speed flight on optical sensors. This ar­ v wave number ticle discusses optical effects of hypersonic flight and P density reports on analytical and experimental advances (funded T transmittance as APL Independent Research and Development) that W frequency, in rad/ s quantify these effects and their impact on sensor perfor­ summation over index n mance. The work performed includes prediction and mea­ linear coefficient of gas index with P / RT surement of the refractive effects of hypersonic flow, quadratic coefficient of gas index with P/RT analysis of fIlm cooling (and experiments that are heat capacity (constant ) planned), absorption and index measurements of gases, shock standoff distance and both theoretical and experimental optical characteri­ coolant effectiveness zation of materials at high . spectral radiance FLOW AROUND OPTICAL WINDOWS gas constant IN HYPERSONIC FLIGHT m coolant-to-edge mass flux ratio Aerodynamic bodies flying through the atmosphere rh mass flow rate (of coolant) per unit width compress air at the leading edges, resulting in n index of refraction (real part) and temperatures that are higher than ambient condi­ P pressure tions. At supersonic speeds, the disturbed air lies behind Re a shock or density discontinuity. As speed increases, the R radius (of blunt nose) strength of the shock (i.e., the pressure rise across the r single-surface reflectivity shock) and the temperature behind the shock increase T temperature (absolute); 1'* is reduced temperature rapidly. Increasing speed also causes the shocks to bend (dimensionless) more sharply and lie closer to the body. By the time thickness hypersonic speed (speeds greater than Mach 5) is ob­ s (coolant) slot height tained, air temperature behind the shock is very high, u (coolant) velocity and surfaces (e.g., optical windows) experience high heat­ x distance along flow direction ing rates caused by viscous friction in the flow bound­ y distance normal to flow ary layer. High-temperature gases surrounding the sensor may radiate significantly and are high in density; hence they Subscripts have increased refractive power. For air, the refractive aw adiabatic wall index (n) is defined by the Gladstone-Dale relationship bl boundary layer (a simplification of the Lorentz-Lorenz equation) given c coolant by (see the table of symbols) e edge (of boundary layer) conditions en entrained quantity from edge of boundary layer n - 1 = {3p (1) 00 free-stream conditions; high frequency n index for summation where {3 is a wavelength-dependent constant and p is the o stagnation conditions; fundamental frequency mass density of the air. Reference 1 gives the values of p constant pressure {3 for wavelengths from 0.2 to 10 J.tm; for wavelengths s slot longer than 1 J.tm, {3 has a nearly constant value of 2.2 x length 3 x 10 - 4 m /kg. Under some conditions, the simple 2 condition behind shock Gladstone-Dale formula is insufficient, and higher or­ A function of wavelength der terms must be considered. This case will be discussed further in the section on coolant gas properties. Hypersonic flow is conveniently characterized in terms of density ratios referenced to free-stream (unperturbed viscid flow theory, in which viscosity, thermal conduc­ air) conditions. Referring to Fig. 1, there are density tion, and mass diffusion are neglected. Boundary layer changes associated with shock waves, expansion waves, theory augments inviscid results to describe the behavior shear layers produced by shock interactions, and the of flow in shear and surface boundary layers. Density boundary layer surrounding the body. Shock and expan­ profiles associated with the flow field effects identified sion waves are adequately described using supersonic in- in Fig. 1 are discussed further below. fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) 371 Tropf et al. - Performance of Optical Sensors in Hypersonic Flight

Shock and Expansion Waves 1.0~----.------.----.-----r--"""""'" A shock is a discontinuity in a supersonic flow. Fluid

(air) crossing a stationary shock rises abruptly in pres­ '+­ 0.8 o sure and decreases in velocity. In air, the density down­ Q) -Cl) ClQ. stream from the shock, P2, referenced to the free-stream "tJ_ ~...:; 0.6 density, P' and Mach number, M, is expressed as C'C ... >Q) ...... - C'C>

(J) 2 ~ ~ 0.4 6(M sin "tJ C'C (2) -"tJ ~c P (M sin (J) 2 + 5 ' .- :::J 1) regions in the Boundary Layer Flow flow field. The governing equations are mathematically Flow behavior in shear and surface boundary layers elliptical in the subsonic region and hyperbolic in the su­ can be described using boundary layer flow equations. personic region. Time-dependent numerical techniques are Boundary layer theory differs from shock and expansion used to determine flow fields surrounding blunt bodies. wave theory in that viscosity, thermal conductivity, and Inviscid flow results of Fig. 3 were calculated using Mac­ mass diffusion effects dominate flow behavior. A com­ Cormack's predictor-corrector algorithm. The density mon assumption used for surface (wall) boundary layers gradient from shock to blunt-body surface depends on is constant pressure across the layer. Combining the gas the density change behind the shock and the shock stand­ equation of state (e.g., law) and the constant­ off distance. An empirical formula for the shock stand­ pressure assumption allows determination of the density off distance, do, at the tip of a conical body with a profIle from the temperature solution. Density profIles spherical nose is of a fully developed, turbulent, compressible, Mach 5 boundary layer over a flat plate are shown in Fig. 2. These do / R = 0.143 e[3.24/~1 , (3) profIles are determined from the Crocco-Busemann tem­ perature solution2 for two limiting conditions: (1) adia­ where R is the nose radius. 3 This equation shows the batic wall (no heat transfer to the wall) and (2) cold wall shock standoff distance decreasing with Mach number. (maximum heat transfer) conditions. The cold-wall den­ Figure 4 shows a typical blunt-body refractive index sity approaches infinity at the wall, creating a sharp den­ result along the stagnation streamline of a hemispheri­ sity gradient. The adiabatic-wall density ratio (referenced cal blunt body (see Fig. 3). Density results, calculated to the density at the edge of the boundary layer) has a from thin-layer Navier-Stokes equations, are combined value of 0.182 at the wall. with the Gladstone-Dale Law to determine the index of Shear layers are also characterized by boundary layer refraction for two cases: cold wall and hot wall (after theory. The same basic equations for wall boundary lay­ 15 s of ). These results are typical ers apply. Boundary conditions and the shear layer mix- of those used in the optical analysis described below.

372 fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) Tropf et at. - Performance of Optical Sensors in Hypersonic Flight

0.002 ,------,-----.----.r----,-----.-:f/-r- ...... ---,-----, (a) Hot window

I c: Body x' Q) Subsonic flow ~ 0.001 region Q) Boundary > ''::; layer Flow u ~ direction ---l~ 't 0:

Stagnation / O~--~--~----~--~--~~r~--~--~~ streamline 0.002.---...,.---,---,--,----...-t'/-t----,---,------, Cold window Boundary layer

I 80 80 c: x' Q) ~ 0.001 1 60 60 c:. Q) > ------.... ''::; ...... 8 u co I:: - 't o 40 40 0: 8 ~ Q. 1 2 1.2 1 . is: :c Distance (mm) 1.0 1.0 Figure 4-The refractive index along the stagnation streamline 0 10 20 30 40 50 60 of a 7.1-cm-diameter hemisphere at Mach 6. Note the scale Body angle (deg) change that exaggerates the depth of the boundary layer. Op­ tical effects of the boundary layer are small because of its small Figure 3-The flow field surrounding a hemispherical blunt body size. at Mach 6. (a) shows the subsonic and supersonic regions be­ hind the shock and identifies the stagnation streamline. (b) gives inviscid flow temperature and density (references to free-stream conditions), shock angle, and shock distance from the body (references to body radius). transfer of hypersonic flight. The facility, part of the Propulsion Research Laboratory, is being instrumented to give a unique optical testing capability in high-speed flow.7 One capability of the facility is the production Shock Wave Impingement on Blunt-Body Flows of shock interference using a movable shock-generating The impingement of a forward shock (from the nose probe. The test setup is shown in Fig. 5a. The hyper­ of a vehicle) on a blunt-body shock wave can create sonic free jet emerges from the and surrounds several possible interference flow fields. These interfer­ the test article mounted on a sting. A movable shock ence patterns are characterized by Edney. 4 The most generator is lowered into the hypersonic flow from the severe heating condition results when the shock interac­ top of the test cabin. The shock generator consists of tion occurs in front of the subsonic region (see Fig. 3). a rod with a wedge-shaped end. When the end is low­ If the impinging shock strength and free-stream Mach ered into the flow, a second shock is created ahead of number are sufficiently high, an embedded supersonic the test article. As the wedge is lowered, this second jet (toward the surface) can be created. The jet region, shock interacts with the blunt-body shock surrounding bounded by shear layers, has a reported width of 3 0 of the test article. Shadowgraphs are used to observe the body surface arc.4-6 Peak heating values of approxi­ shock structure. Figures 5b, 5c, and 5d show the shock mately 16 and 10 times the undisturbed stagnation point interaction with a hemispherical window. Figure 5b value for a spherical body5 and for a cylinder, 6 respec­ shows the blunt-body shock alone, Fig. 5c shows one tively, have been reported. This intense heating will cre­ type of shock interaction that creates a shear layer across ate severe local thermal gradients that cause optical the test article body, and Fig. 5d shows the interaction degradation because of thermal expansion and refrac­ that occurs when a supersonic jet impinges on the test tive index change. If heating rates become excessive, ac­ article surface. The last two cases create severe refrac­ tive cooling may be necessary to ensure survival or to tive disturbances and very high aerodynamic heating. maintain the window at acceptable temperatures. The sapphire dome shown here survived this transient APL has a test facility capable of simulating the flow shock impingement condition. Optical measurements conditions (speed, temperature, and pressure) and heat made with the setup are discussed below. fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) 373 Tropf et al. - Performance of Optical Sensors in Hypersonic Flight

Expansion wave at joint

Nozz le Movab le shock generator

Hyperson ic f low __ Diffuser Shadowgra ph area

Test ca:1L-_____S_t_in_g __-'1

(a) Test setup (b) Shadowgraph without shock impingement

(c) Shear layer impingement (d) Supersonic jet impingement

Figure 5-Shadowgraphs of shock wave impingement on a sapphire hemispherical window at Mach 5. (a) A sketch of the shock generator and resulting shadowgraphs of (b) the blunt-body shock alone, (c) shock interaction with shear layer impingement, and (d) shock interaction with supersonic jet impingement.

Air Temperature, Flow-Field Radiation, infrared-active gases of the atmosphere. Figure 6 shows and Aerodynamic Heating the calculated spectral radiance from the stagnation re­ gion of a hemisphere in Mach 6 flight at an altitude of Air compressed in front of a body in hypersonic flight 24.4 km. Significant radiation (an order of magnitude experiences a sharp rise in temperature. For example, greater than earth scene thermal emission) emanates the static temperature increase behind a normal shock from the 2300 cm - I band of carbon dioxide and the (T2 ) in air is 3700 cm - I band of water, despite the very low emis­ sivity of this short segment of gas. Note that the radia­ T21Too = (7 M~ - 1) (M~ + 5)/36 M~ . (4) tion in these two bands exceeds that of a nominal 300 K scene background. Much greater radiation will result The temperature T2 approximates the static tempera­ from lower altitude flight because of increased ambient ture behind the normal portion of a blunt body shock. pressure and, at very low altitudes, significantly higher Although the thickness of the compressed layer is small water vapor concentration. Gases injected into the (0.157 times the radius of a hemispherical nose at Mach boundary layer as a film coolant (see below) may also 6; Eq. 3), temperature and pressure are high enough to be a source of significant infrared radiation. produce significant radiation. The blunt-body aerodynamic heating rate is propor­ The principal radiation in the compressed gas comes tional to the velocity gradient at the edge of the bound­ from carbon dioxide and water, which are the primary ary layer and the enthalpy difference between the stagna-

374 f ohns Hopkins APL Technical Digest, Volume 8, Number 4 (1 987) Tropf et at. - Performance of Optical Sensors in Hypersonic Flight Aero-Optical Computations Initial work has focused on hemispherical windows (domes) that give good optical performance over a large Carbon dioxide optical field of view. Such windows are commonly used for missile optical guidance systems, and they have the advantage of an axisymmetric flow field for ease of fluid dynamic and optical calculation. Density results from fluid flow calculations are con­ verted to the refractive index using Eq. 1, the Gladstone­ Dale relationship (a typical example is shown in Fig. 4). Table 1 lists the flight conditions used in this optical per­ formance study. The variable index of refraction of air in front of the dome is then modeled as a series of thin lens elements, each with a power-series description of the two-dimensional (radial and axial) gradient index, for ex­ act ray tracing. In addition to flow-field effects, optical effects of the deformation of the window caused by aero­ dynamic heating were evaluated using a heat transfer code 10-9~-----L~------L--L---~--~~~ to determine window temperature and a finite-element 2000 2500 3000 3500 4000 stress code to determine the window shape after heating. Wave number, v (cm-1) Optical calculations are compared with the diffraction­ limited performance of a sensor operating at 4/Lm. Us­ Figure 6-Radiance of gases along the stagnation streamline ing a 3.0-cm-diameter optical system behind a 3.5-cm of a 7.1-cm-diameter hemisphere at Mach 6 flight at an altitude radius, 0.25-cm-thick dome, the most significant effect of 24.4 km. Calculated radiance (brightness) of high-temperature is a slight focus shift that increases geometric blur to a gases behind the normal shock of a hemisphere exceeds that of a nominal 300 K background. level still smaller than a 4-/Lm-wavelength diffraction­ limited spot size (as represented by the Airy radius). Fig­ ure 7 shows typical results. The blur caused by focus tion and wall conditions. The enthalpy, H, and temper­ shift can be easily removed by refocusing to obtain op­ ature are related by timum performance. Wavefront maps show no more than a one-quarter wavelength distortion (at 4-/Lm wave­

dH = Cp dT, (5) length) across the exit pupil. Boresight shifts are very small, the largest being about 0.01 mrad. where Cp is the specific heat at constant pressure. Stag­ Results from optical resolution studies of the flow over nation temperature is given by hemispherical windows (including shock wave, compress­ ed flow behind the shock, and the boundary layer) show ToIT:;o = 1 + 0.2 M~ . (6) very small changes in resolution and boresight for an in­ frared system operating at 4 /Lm. Since the reference Airy Stagnation heating is highest when the wall is cold and radius is proportional to wavelength over the aperture di­ decreases as the wall temperature asymptotically ap­ ameter, ultimate angular resolution of a visible wavelength proaches equilibrium temperature. As a window heats, sensor (of the same aperture) is much smaller than that it becomes an additional radiation source that can ex­ of an infrared system, and flow-induced blurring will ceed that of the background scene or the compressed dominate resolution. gas behind the shock.

AERO-OPTICAL EFFECTS Table 1-Flight conditions used for aero-optical computations. OF HYPERSONIC FLOW The aero-optical effects of hypersonic flow are deter­ Flight Condition mined by using the results of flow density calculations Speed Altitude as the input to optical ray-trace codes that determine Case (Mach) (km) Window Attachment blurring and boresight error. This work has concentrat­ ed on calculating and understanding the optical effects of simpler flight conditions in order to gain an appreci­ 1 4.0 0.3 None (free expansion) ation of the magnitude of the optical effects, to develop 2 5.0 15.2 None (free expansion) computational techniques, and to guide development and 3 6.5 30.5 None (free expansion) evaluation of equipment that will be used to measure op­ 4 5.0 15.2 Rigid (constrained ex- tical effects under simulated high-speed flight conditions. pansion) Optical effects of complicated flow structures and highly 5 5.0 15.2 ring (par­ transient events (such as shock-wave impingement on a tially constrained side-mounted sensor) are best determined experimentally. expansion) fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) 375 Tropf et al . - Perf ormance of Optical Sensors in Hypersonic Flight

Diffraction limit Airy radius (4-J-tm wavelength) 0.4

Case 1 & Case 1 L Case 2 • Case 2 • • Case 3 X Cas e 3 0.14 ::0 0.3 • Case 4 ~ Case 5 =0 0.12 E • V> ~ :::J ";0.10 No focus shift "0 ..,.., __ ---e---.. } ~

.... ~ :::J OJ C co oR. ~ 0.1 Airy rad ius (4-J-tm wavelength)

Reference geometric spot size

O~----~ ______-L ______L- ____-L ____ ~ 0 o 10 20 30 40 50 O· 10 20 30 40 50 Look angle (deg) Look angle (deg)

Figure 7-Resolution of a small optical system in several flight Figure 8-Resolution of a small optical system after aerody­ conditions. The shock, compressed gases, and boundary layer namic heating of the window. The nonuniform aerodynamic surrounding a cold hemispherical window in high-speed flight heating of a hemispherical window after 15 s exposure to several cause some blurring that can be corrected by a focus shift. In flight conditions shows a significant thermal distortion of the the infrared, the focus change is smaller than the diffraction­ window. In the infrared, this distortion is up to twice the diffrac­ limited spot size (Airy radius). tion limit.

Thermal expansion of a hemispherical window has a significantly larger effect on optical performance. Aero­ 1.5 IR dome dynamic heating produces a significant temperature gra­ I Collection optics dient around the window that translates into a distortion 5~.~1'"""8-1--f-t~ 13.~cm diaml in shape through thermal expansion. Figure 8 shows the resulting resolution as a function of look angle (i.e., the 1.0 ~ angle from the stagnation line) for several conditions af­ 2.54 ter 15 s of heating. Further examination of optical performance shows sig­ ~ 0.5 (Pupil coordinates) E nificant deviation of optical rays across the aperture and shows that the deviation increases as the size of the aper­ ture increases. This effect is shown in Fig. 9, where larg­ er apertures are presented as pupil coordinates greater C1l than unity. A typical wavefront map (Fig. 10) shows 0> c much larger thermal expansion distortion (at 4 JLm) across « -0.5 the pupil compared with that caused by hypersonic flow • Case 1 alone. Boresight errors caused by dome distortion are also • Case 2 larger, with a peak value as high as 0.5 rnrad. & Case 3 Combined effects of the flow-field and dome thermal -1.0 expansion distortions show that, as expected, expansion • Case 4 )( Case 5 dominates and determines both resolution and boresight error. -1 .5 Vehicle nose-shock refraction on a side-mounted opti­ 0 2 cal system was evaluated as an independent effect. (Note Pupil coordinate that the flow field surrounding a vehicle will affect the Figure 9-0ptical ray deviation in heated windows as a func­ flow surrounding an optical window, hence the effects tion of pupil coordinate. The deviation of individual rays shows are not completely independent.) A conical shock is as­ that the on-axis blurring is principally caused by marginal rays. If the collecting aperture is increased, blurring will be much sumed (Eq. 2), although this representation is strictly true greater. only for conical forebodies with no angle of attack. A 15° forebody half-angle is used to determine shock The conical shock surface introduces a significant parameters. amount of asymmetry to the calculation of optical per-

376 fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) Tropf et al. - Performance of Optical Sensors in Hypersonic Flight Wavefront map Case 1

0.5

e ~ 1.0 +-' L C'l 'Vi oOJ OJ .& Case 1 1.5 • Case 2 • Case 3

Figure 10-Wavefront map showing the distortion of a heated 2.0 ___---'- ___---'- ___-'-- __---'- ___--' window. The optical path difference across the pupil, in one­ o 10 20 30 40 50 quarter wavelengths at 4 I-tm , is shown for a hemispherical win­ dow exposed for 15 s at Mach-4, 30-m-altitude flight conditions Look angle (deg) and a 45 ° look angle. A similar map for a cold dome shows a Figure 11-Boresight error from a conical nose shock off a 15 ° maximum one-quarter-wavelength optical path difference. (half-angle) forebody. The bow shock in front of a side-mounted optical sensor can experience a significant boresight error. formance. In one plane, the conical shock has no curva­ ture (hence, no focusing power); in the other plane, it Mo = 6.5, alt = 30.48 km has curvature that varies along the shock. The difference 10° angle of attack in the two planes will cause astigmatism in the image, al­ though for the flight conditions examined, the astigmat­ ic asymmetry is quite small. A more significant nose-shock effect is boresight error, which can be as high as 2 rnrad when looking directly forward (Fig. 11). An angle of attack in the plane of a side-mounted win­ dow will cause significant changes to the optical effects. On the windward side, there will be a significant increase in air density and heat transfer, and, if the angle of at­ tack is significantly great, impingement of the nose shock on the sensor window. On the leeward side, the bound­ ary layer of the vehicle body enlarges and can begin to cover the seeker aperture. Figure 12 schematically shows these effects in the form of crossflow density contours at a typical sensor location. One of the important factors in high-altitude guided (homing) flight is the coupling of body motion (angle of attack) into apparent inertial line-of-sight through vari­ able boresight errors. A nose-mounted, hemispherical win­ dow, while having small flow-induced, look-angIe-de­ pendent boresight errors, has no angle-of-attack coupling, Figure 12-Crossflow density contours showing the effect of angle of attack on the flow field surrounding side-mounted op­ since the flow moves with body angle changes. All other tical sensors. forms of boresight error (including those from non­ hemispherical windows, from dome expansion, or from side-mounted windows behind a nose shock) have bore­ order of 0.0014 rnrad per degree angle of attack for Mach sight error slopes that couple angle-of-attack motion into 6 flight at sea level (and falling with altitude as a func­ apparent line-of-sight rate. Since side-mounted sensors ex­ tion of atmospheric density). perience the largest flow-induced boresight error, an es­ timate of coupling was made using the change in boresight Aero-Optical Testing error of central rays as a function of body angle of at­ The optical effects of shock wave impingement are dif­ tack. This coupling was found to be very small, on the ficult to predict. Preliminary experiments have been con- f ohns Hopkins A PL Technical Digest, Volume 8, Number 4 (1987) 377 Tropf et at. - Performance of Optical Sensors in Hypersonic Flight ducted at the Propulsion Research Laboratory to measure shows the image centroid as calculated from the detec­ optical effects of shock wave impingement on a hemi­ tor output for both pre-test (no flow) and test condi­ spherical window. A fIxed-angle optical system observes tions. A transient perturbation is seen on all detector a collimated target with an optical system and linear de­ channels as the model reaches position. The pre-test mea­ tector array. This target is projected into the test system surement clearly shows a ringing (vibration) as the model Oocated behind a hemispherical window at 45 0 from the is brought to rest. The ringing is masked by noise dur­ flow direction). Once the test model is inserted into the ing the test that is likely caused by interaction of the hypersonic flow and the target signal is detected, a shock hypersonic jet with still air in the test cabin or perhaps generator probe is lowered to sweep a shock across the by vibration from the force of the flow. After the tran­ hemispherical window, simulating the passage of a vehi­ sients of inserting the model diminish, the shock-gener­ cle nose shock across a side-mounted window during a ating wedge is lowered and the shock - shock interaction maneuver. Figure 5 shows shadowgraphs of the shock. traverses the window of the test system. The time of the A diagram of the test setup and a photograph of the op­ shock interaction is marked on Fig. 14. No significant tical test hardware are shown in Fig. 13. increase in angle noise or centroid shift was noted in this A typical aero-optical test result is shown in Fig. 14. particular case, although a few possible (minor) effects At time zero, the model is inserted into the hypersonic are noted by arrows on Fig. 14. Further work is under flow stream. As the model reaches its final position in way to improve the accuracy of these measurements in the stream, a linear array of detectors begins to mea­ preparation for a comprehensive optical test program. sure the signal from a collimated infrared target pro­ jected into the test cabin. The detector field of view is ACTIVE COOLING OF OPTICAL WINDOWS 0.5 mrad and the center-to-center spacing is 1 mrad. As flight speeds increase and the thermal environment Changes in signal strength or distribution across the ar­ becomes severe, active thermal protection of windows ray indicate optical perturbations (in this case caused by becomes necessary. The optical performance of the win­ shock interaction; see Fig. 5). Outputs from the four dow is degraded by changes in optical power caused by principal receiving detectors (channels 3 through 6) are thermal expansion and refractive index change, the op­ shown in the lower portion of Fig. 14. The top portion tical transmission is reduced by increased absorption, and the sensor performance is degraded by higher radiation levels. The structural integrity of the window may be in Collimated jeopardy in severe thermal environments. These prob­ infrared target\ lems associated with the thermal environment can be radiation

~Testcabin No flow data 6 "0 .g 5 c u 4 3 "-Diffuser ~Jet L..-----r--~ 6 .g"0 5 c Test setup U 4 Steering mirror 3

I I I I I I I Test data .l& J 6 --- t Qi c •.....-..L. -. ~ ~ c 5 1 co .!: U J ~ 4 -- 1 J

,1 .i L array 3 1 (in mount) o 2 3 4 5 6 7 8 Test time (s) electronics Figure 14-Measurement of optical spot's position during shock interaction in hypersonic flow. The upper portion shows the measured target centroid in (a) no-flow and (b) hypersonic flow conditions. The lower portion (c) shows the output of the in­ Figure 13-Sensor used to measure optical effects of hyper­ dividual detector channels during flow. Arrows mark possible sonic flow. shock interaction optical effects.

378 fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) Tropf et al. - Performance of Optical Sensors in Hypersonic Flight mitigated by maintaining the window material at accept­ To predict the extent of the surface protected by the able temperatures with active, tangential slot cooling. On coolant gas, the coolant mass flow rate is given by the other hand, optical effects caused by injecting cool­ ant into the boundary layer are greater than those of (10) the uncooled boundary layer. and the boundary layer mass flow rate 7 by Tangential Slot Cooling on Flat Plates Tangential slot cooling injects a coolant gas along the (11) window surface and parallel to the external stream. A schematic of the process is shown in Fig. 15. The win­ where the boundary layer thickness, 0, is given by the dow temperature is maintained at the coolant gas tem­ incompressible-gas relationship perature as long as the mixing layer does not reach the window surface. When the mixing layer attaches to the o/X = 0.37(Re); 115 , (12) surface, the surface will heat. Design of a satisfactory cooling system requires an accurate estimate of the cool­ and where (Re)x is the Reynolds number, which is equal ant flow rate required to protect the window surface. to X(Pu)e/lle. Determination of the cooling rate requirements of the A dimensionless expression for the cooled surface tangential slot is based on a control volume approach. length can be derived by substituting Eqs. 10 to 12 into The conservation of energy (total enthalpy form) for Eq. 9 with E c = 1. This approach assumes that the steady-state, adiabatic wall conditions is coolant gas and edge of the boundary layer have equal pressure. Performing the substitutions gives an expres­ sion for the ratio of the protected surface length to the slot height: where the boundary layer energy (rh bI H aw ) is the sum 0.25 (13) of the coolant energy (rhcH e ) and the energy entrained 4.1 m[ (Re)s Ilc /lle1 from the edge of the boundary layer (rh enHe ). Here rh where Xc is the protected surface length; s is the slot represents the mass flow rate per unit width. Conserva­ height; m is the coolant-to-edge mass flux ratio, tion of mass is given by (pu)c/(pu)e; (Re)s is the slot Reynolds number, (pu)cs/ Ilc; and Ilc,e is the absolute viscosity at coolant (8) and edge conditions, respectively. This control volume boundary layer approach breaks Solving for the entrained mass flow rate in Eq. 8 and down for m > 1.5. Equation 13 allows one to estimate substituting into Eq. 7 yields the following expression for the coolant flow required for specified slot height, s ; the coolant effectiveness, Ec ' protected surface length, xc ; coolant temperature; and boundary layer edge conditions. Equation 13 then al­ lows calculation of the coolant mass flux, and the cool­ ant mass flow rate is determined from Eq. 10. Unity coolant effectiveness implies zero entrainment from the external boundary layer. In that case (Ec = 1), the Tangential Slot Cooling coolant gas insulates the window from the hot external of Inclined Surfaces and Blunt Bodies stream. Zero cooling effectiveness (Ec = 0) implies that the coolant does not protect the surface at all. This con­ Cooling of supersonic inclined surfaces is similar to the trol volume approach is consistent with previous analy­ flat-plate analysis described above. An added benefit of ses. 8,9 mass injection over an inclined surface is the control of boundary-layer separation. The pressure rise associated with the inclined surface may be sufficient to cause the / Velocity profile upstream boundary layer to separate, as shown in Fig. 16. The recirculating, separated flow region creates ther­ (pu)e __V ~~3: h--~ ~--~-- 1 mal and possibly optical problems. High heat transfer oc­ Surface r curs where the shear layer attaches to the inclined surface. boundary 8 Mass (coolant) injection can reduce or eliminate the sepa­ layer J rated flow region. Slot S A blunt optical window has high heating at the stag­ nation point. It may be necessary to cool that region to ensure survival and maintain acceptable optical perfor­ ~~~~~~--~~----~~--~x mance. A similar control-volume boundary layer ap­ Coolant boundary layer I proach can be used to define the region of high cooling --Cooling length x _ Optical I C Window efficiency. This approach will differ from the flat-plate analysis because a different expression for the boundary­ Figure 15-Sketch of tangential slot cooling along a window surface. This figure defines terms used to describe active sur­ layer mass-flow rate is used. Little experimental data are face cooling. available for the blunt-body case. f ohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) 379 Tropf et al. - Performance of Optical Sensors in Hypersonic Flight

Reattachment Table 2-lndex of refraction parameters (A = 0.6328 Ilm). shock A B Separation Gas (em 3 /mole) (em6/mole2) T* shock Flow direction. He 0.78 =9 =0 N 2 6.90 14 =0 Ar 6.66 95 =0 CO2 10.2 1674 3.12 SF6 17.5 1702 4.20

Note: The unit cm3/ mole is a reciprocal molar density.

Figure 16-Boundary layer separation from a compression sur­ efficient coolants from a mass standpoint, while those face. Side-mounted windows may cause flow separation, which with high molecular weights are volume efficient. can be controlled by active cooling. Index of refraction measurements were made with a laser interferometer operating at 0.633 J-tm and a high­ temperature, high-pressure gas cell. Measurements were made as a function of pressure and temperature and were fitted to an equation of the form

n - 1 = A (P/RT) + B(P/RT) 2

x exp[T* (295/T - 1)] , (14)

where the parameters A, B, and V are experimentally determined. Note that this equation is a higher order form of the Gladstone-Dale relationship of Eq. 1, with density in a number-per-unit-volume form (PIRT). The pressure-squared term in the refractive index is entirely attributable to nonideal gas behavior. Depending on the size of the virial coefficients and the strength of collision­ induced absorption, the quadratic term may be impor­ tant. Table 2 gives the index parameters for the gases. Figure 17-Window configuration for multiple-pane cooling be­ CO and SF have significant quadratic terms. ing developed at APL. 2 6 A Fourier-transform spectrometer and the same high­ temperature, high-pressure gas cell were used to measure Figure 17 shows a cooled window concept being de­ transmittance in the 1800 to 5000 cm - I spectral range. veloped under APL's Independent Research and Devel­ Measurements were made of the significantly absorbing opment program. This configuration, using several win­ gases-nitrogen, carbon dioxide, and sulfur hexafluo­ dow panes, is also readily adapted to side-mounted sen­ ride-as well as water vapor. Pressures to 6.9 x 106 Pa sors. Coolant passes along the top and side, if the win­ and temperatures to 690 K were used to determine the dows are slotted. Gas exits the slots and separates the win­ pressure- and temperature-dependence of transmission dow from the high-temperature boundary layer, thus (and, therefore, emission). maintaining a cool surface. Slot dimensions were sized Figure 18, an example of transmission measurements, using a slightly modified form of Eq. 13. A test model shows pressure-dependent room-temperature spectra of is being constructed with testing of the cooling effective­ carbon dioxide. The zero absorption level of each spec­ ness and optical characteristics expected by the end of the trum is offset in order of increasing pressure. Each ab­ year. sorption band is identified by number (1 to 11): bands 1, 2, 5, 8, 9, 10, and 11 are fundamental bands; 3 and Optical Properties of Coolant Gases 4 are hot bands; and 6 and 7 are collision-induced bands. Several gases have been proposed as fluids for fIlm The fundamental and collision-induced bands decrease in cooling of optical windows, including helium, argon, strength with temperature while the hot bands will grow. nitrogen, carbon dioxide, and sulfur hexafluoride. Trans­ Carbon dioxide is an undesirable gas in the spectral re­ mission and refractive index measurements of the gases gion from 2000 to 2600 cm - 1 because of high absorp­ 6 were made at high pressure (up to 6.9 X 10 Pa) and tion and emission. It is also generally undesirable as a temperature (up to 775 K). The data were taken to de­ coolant because of its high index of refraction compared termine the coolant gas with the best optical properties. with air (image scintillation is caused by mixing of gases In general, gases with low molecular weights are the most of different indexes).

380 fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) Tropf et at. - Performance of Optical Sensors in Hypersonic Flight

11 0.20 2 I I 10 HYPERSONIC WINDOW MATERIALS = I CO spectra PC02 ~ 2 Materials considered for hypersonic optical windows 'I 0.16 ~ V35.58 Pa T=294K I are selected on the basis of high-temperature stability, E t.l thermal shock resistance, and good optical properties. P C02 = ~ 0.12 ~ Oxides and nitrides satisfy these criteria. The four mea­ V20.41 Pa 'u 5 sured materials-ALON, sapphire, spinel, and yttria­ !£ 9 OJ PCO = 2 are commercially available in high-quality optical form. 8 0.08 -1 P C02 = c 5 All are clear and colorless, although thicker samples of o 6.8 Pa V 10 Pa '';:::; polycrystalline materials may appear slightly cloudy be­ Q. 3 \. 0.04 ~6 ~ 7 ,d :; J cause of scatter. All have good infrared transmission to £ ~) \.. --~ \. ..c 4 J at least 4 j.tm.

Johns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) 381 Tropf et at. - Performance of Optical Sensors in Hypersonic Flight high-strength windows capable of withstanding both high have been developed to maintain good spectrometer temperatures and extreme thermal stress of the rapid aero­ source stability and to reduce the time between sample dynamic heating of hypersonic flight. measurements, thus improving experimental accuracy. The required absorption accuracy needed to predict sen­ Window Optical Property Measurements sor performance is typically 20070. Figure 19 shows typi­ The most significant optical property of a window at cal measurements and model results (discussed below). high temperature is its emission. Since the window can­ These values can be used to estimate the normal emis­ not be thermally insulated by conventional techniques, sivity, f A' in terms of the thickness and single-surface the total window radiation governs the heat transfer into reflectivity, r: the interior of the sensor and affects the ultimate win­ CX f dow temperature via radiant heat transfer. For high­ fA = (l - r) (l - e- ) • (16) sensitivity infrared sensors, the amount of window radi­ ation within the sensor spectral bandpass governs sys­ The normal-incidence, single-surface reflectivity is ap­ tem noise and possibly dynamic range. Temperature also proximated by (n - 1)2/ (n + 1)2. Further absorption changes the optical thickness of windows both by ex­ data, including single-frequency laser measurements, are pansion and by index change. As noted above, the non­ reported in Ref. 10. uniform thermal expansion of hemispherical windows The temperature-dependent refractive index (n) has significantly affected optical resolution. Changes in op­ been measured using an automated fringe-counting la- tical index are expected to have an effect of similar mag­ nitude. Optical materials considered for hypersonic windows Yttria are transparent from the ultraviolet through the near­ -- Multiphonon absorption model infrared. Table 3 summarizes properties of typical win­ • FTS data, T = 295 K } GTE dow materials. The short-wavelength absorption is caused • FTS data, T = 775 K by electronic transitions and the infrared absorption cut­ • FTS data, T = 295 K Raytheon off results from lattice vibrations and their high harmonics 103.-----.-----.-----.-----.-----.---~ (called multiphonon processes). These optical materials I" have a fundamental lattice frequency, wo, in the far in­ E frared and are typically transparent above 3wo. The mul­ 2 tiphonon absorption edge shifts to higher frequencies with ~ ..... 100 c increasing temperature. It is therefore necessary to char­ Q) '13 acterize the material absorption (and, therefore, emission) i: Q) as a function of temperature. 0 Transmission spectra of two different sample thick­ u .§ 10-3 T = 2000 K nesses are measured at room temperature using a Fourier­ C. transform spectrometer. The ratio of transmittances o ..cU) (72/71) and difference in thickness ((2 - (1) of the sam­

Table 3-0ptical properties of durable, high-temperature ceramics.

Index of Refraction, * Melting Room Temperature dn/dT Temperature Transparent Region** 1 Material n (K- ) (K) (cm - I )

ALON 1.79 7.5 x 10-6 2415 2100 - (4O,000)? Sapphire 1.765 6.1 x 10 - 6 2315 2000 - 55,000 Spinel 1.715 7.4 x 10 - 6 2410 1875 - 50,000 Yttria 1.925 -1.6 x 10 - 6 2695 1400 - (50,000)?

*Index of refraction at 0.6328 J-Lm * * Room-temperature absorption coefficient exceeds 1 cm - I

382 fohns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) Tropf et al. - Performance of Optical Sensors in Hypersonic Flight ser interferometer operating at 0.6328 /Lm. The sample and is placed in one leg of the interferometer and heated in a vacuum cell. Once the sample temperature reaches (18) equilibrium, the change in optical path length can be de­ termined to one-quarter wavelength. Refractive index change can then be determined if the thermal expansion where EO and Eoo are the dielectric constants at low and coefficient is known. Values of the derivative of index optical frequencies, respectively. Combining the deter­ with temperature (dnl d1) derived from these measure­ mined transverse (v n ) and longitudinal optical modes ments are given in Table 3. (Eq.18), the Lyddane-Sachs-Teller relationship 12 and Reflection measurements in the spectral region of the reflectance data parameters of Eq. 16 can be determined. fundamental (one-phonon) lattice vibrations are made The complex refractive index is the square root of the to deduce optical constants for estimating total hemi­ complex dielectric constant. Results from sapphire were spherical absorption (emission). These data are used in compared with published model parameters to evaluate a model to determine the complex refractive index, as the method. The model was then applied to ALON, described below. spinel, and yttria. Figure 20 shows the ALON room­ temperature refractive index derived using this method. Modeling Properties of Optical Windows Optical index data can be used to estimate total hemi­ Several models have been developed to aid in deter­ spherical and total direction emissivity of optical win­ mining optical properties to extend measurements be­ dows for radiative transfer estimates. yond the measured region. The principal models are a quantum-mechanical multiphonon model and a classi­ SUMMARY AND CONCLUSIONS cal single-phonon model. The high pressure, temperature, and radiation of The multiphonon model lO determines the absorption hypersonic flow and heat transfer to sensor windows al­ coefficient from spectral measurements made at two or ter the performance of a sensor experiencing this environ- more temperatures. The model uses a Morse potential that leads to an exact solution to the Schrodinger equa­ tion. The phonon distribution function is determined by 4 an asymptotic solution of the central-limit theorem. Statistical parameters of the phonon distribution func­ c .;::;0 tion are determined from sapphire data. Those para­ u meters are then scaled to each material by its maximum ~ 3 ~ - Reflectance measurements longitudinal optical-mode frequency, as determined from '+- 0 the reflectance spectrum. Dissociation energy and scal­ X Q) ing parameters are determined from transmission mea­ "0 2 .~ surements. The model represents the absorption coef­ a ficient as a function of frequency and temperature and t: co can be used to interpolate and extrapolate the intrinsic Q.

384 Johns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) Tropf et al. - Performance of Optical Sensors in Hypersonic Flight

THE AUTHORS

WILLIAM 1. TROPF was born in TERRY 1. HARRIS graduated in Chicago in 1947. He received a B.S. 1982 from the University of Colora­ degree from the College of William do with a B.S. degree in engineer­ and Mary (1968) and a Ph.D. de­ ing physics. He is a member of the gree from the University of Virginia Electro-Optical Systems Group, where (1973), both in physics. He is now where he specializes in geometric the supervisor of the Electro-Optical optics, lens and optical system de­ Systems Group in APL's Fleet Sys­ sign, and ray-trace analysis. He is tems Department. Dr. Tropf has a member of the Society of Photo­ been engaged in the development Optical Instrumentation Engineers. and testing of advanced missile Mr. Harris has designed optical sys­ guidance systems since joining APL tems for ground and space instru­ in 1977. His activities have encom­ ments, as well as the optics for tar­ passed both radar and infrared sen­ get projection systems and optical sors, including atmospheric, target, measurements in hypersonic flow. and background modeling; signal He also conducted the aero-optical processing for clutter suppression; analysis reported in the article in this and material properties. He has worked on hypersonic optical sensor issue. He is now designing the optical system for a solar vector mag­ development and test since 1981 . netograph instrument.

MICHAEL E. THOMAS's biography can be found on p. 369.

STEVEN A. LUTZ was born in 1953 in Harrisburg, Pa. He attend­ ed West Virginia University, receiv­ ing a Ph.D. degree in mechanical and aerospace engineering in 1984. His dissertation research dealt with the sampling efficiency of gas-solid aspiration probes for highly turbu­ lent flow streams. While at West Virginia, he taught undergraduate thermodynamics. Dr. Lutz worked from 1983 to 1985 for the Depart­ ment of Energy, where he analyzed and designed optical access ports for laser diagnostic instrumentation of coal conversion systems. Since 1985, he has been a member of APL's Aeronautics Department. His interests include aerodynamic heating, supersonic and hypersonic turbulent boundary layer flows, and nonin­ trusive instrumentation for high-speed testing.

Johns Hopkins APL Technical Digest, Volume 8, Number 4 (1987) 385