_p' ll' AIAA-2002-0743 CARS Thermometry in a Supersonic Combustor for CFD Code Validation A.D. Cutler, The George Washington University, Hampton, VA P.M. Danehy NASA Langley Research Center, Hampton, VA R.R. Springer, The George Washington University, Hampton, VA R. DeLoach, D.P. Capriotti NASA Langley Research Center, Hampton, VA 40th AIAA AerospaceSciences Meeting & Exhibit 14-17 January 2002 / Reno, NV Forpermissiontocopy or republish, contact the copyright owner namedonthe first page. ForAIAA-held copyright, writeto AIAA,Permissions Department, 1801Alexander Bell Drive, Suite500, Reston, VA20191-4344. AIAA-2002-0743 CARS THERMOMETRY IN A SUPERSONIC COMBUSTOR FOR CFD CODE VALIDATION A. D. Cutler*, P. M. Danehy:, R. R. Springer :!:.R. DeLoach _,D. P. Capriotti _I NASA Langley Research Center. Hampton, VA 23681 Abstract x. y, z position coordinates in right-handed system, An experiment has been conducted to acquire data see Fig. 2 (m) for the validation of computational fluid dynamics (CFD) a, thermal diffusivity of wall (m2/s) codes used in the design of supersonic combustors. The rr standard deviation primary measurement technique is coherent anti-Stokes Raman spectroscopy (CARS), although surface pressures Introduction and temperatures have also been acquired. Modern- Computational fluid dynamics (CFD) codes are design-of-experiment techniques have been used to extensively employed in the design of high-speed air maximize the quality of the data set (for the given level of breathing engines. CFD analysis based on the Reynolds effort) and minimize systematic errors. The combustor averaged Navier-Stokes equations uses models tbr the consists of a diverging duct with single downstream- turbulent fluxes that employ many ad hoc assumptions and angled wall injector. Nominal entrance Mach number is 2 empirically determined coefficients. Typically, these and enthalpy nominally corresponds to Mach 7 flight. models cannot be applied with confidence to a class of Temperature maps are obtained a! several planes in the flow tor which they have not been validated. This flow for two cases: in one case the combustor is piloted by experiment is one of several adopted by a working group injecting fuel upstream of the main injector, the second is of the NAT() Research and Technology Organization not. Boundary conditions and uncertainties are adequately (RTO) as a test case lot their CFD development and characterized. Accurate CFD calculation of the flow will validation activity. Another is a study of supersonic ultimately require accurate modeling of the chemical coaxial jets without combustion _. Calculations of the kinetics and turbulence-chemistry interactions as well as coaxial jet and the present geometry using the SPARK accurate modeling of the turbulent mixing. code-", performed in conjunction with the RT() activity, have been presented 3. Nomenclature The experiment is designed to provide a relatively CN2 concentration of nitrogen simple case for CFD codes involving supersonic injection, k_ thermal conductivity of wall (W/InK) mixing and combustion in aduct. The model geometry is n number of samples simple and large regions of subsonic/recirculating flow p number of parameters arc avoided. Care is taken to define the geometry and q heal flux (W/m 2) model inlet conditions. The enthalpy of the test gas (hot t time (s) air "simulant") is nominally equivalent to Macb 7 flight. It T temperature (K) was believed, on the basis of calculations performed (e.g., *Associate Professor, The George Washington University, MS335.Senior Member AIAA -;"Research Scienlist, Instrumenlalion Systems l)evelopmen! Branch.MS236. Member AIAA :i:Graduate Research Scholar Assistant, TheGeorge Washingtun Universily. Current address, IJ,_ckheed-Mar/in NE&SS -Marine Systems. Member AIAA §Senior Research Scientist, lnstrumention Systems I)evelopmenI Branch. MS236. Member AIAA Research Engineer, Hypersonic Airbreathing Propulsion Branch, MS 168. Note: The inclusion of equipmem brand names inIbis paper isforinfimnalional purposes only andshould not be interpreted asanendorsemenl of these products bythe authors, NASA or the USGovernmenl. Copyright ©2002 bythe American Institule of Aeronautics and Asmmautics, Inc.No copyright is asserted inthe United States under Title 17,U.S. Code. The US. Government hasaroyalty-free license toexercise allrights under the copyright claimed herein forGovernmental purposes. All other rights are reserved bythe copyright owner, American Institute of Aeronautics and Astronautics 1 AIAA-2002-0743 Ref. 2), that this would produce mixing-limited flow, that test the combustor of a supersonic combustion ramjet is to say, one for which chemical reaction to equilibrium (SCRAM JET) engine by directly connecting thc facility proceeds at a much greater rate than mixing. It later nozzle exit to the entrance of the combustor. This facility proved that this was not the case, is typically used in fundamental combustor research. The primary experimental technique employed is coherent anti-Stokes Raman spectroscopy, known by o2 its acronym CARS. An introduction to CARS is given by Eckbreth _, and an application of CARS to supersonic combustors is given by Smith et al.5.The species probed is molecular nitrogen and the quantity measured is temperature, although. If assumptions are made as to the relative proportions of the other major chemical species, composition can also be estimated. Composition data are not reported herein. CARS, like other optical techniques, does not significantly alter the flow being studied. Intrusive probes, such as Pitot, total temperature, hot-wire, etc., are not used due to access liner difficulty and high heat flux in the combustor, and water in because they may alter the flow. Also, CARS has Figure 1DCSCTF heater and nozzle. several advantages over other optical methods. It is The test conditions are nominally representative of relatively mature and well understood. Signal levels are Mach 7 flight. Gas flow rates to the heater are: relatively high. The signal is in the form of a coherent 0.915_+0.008 kg/s air, 0.0284_+0.0006 kffs hydrogen, and (laser) beam, and can be collected through relatively small 0.30(0,20.005 kg/s oxygen. The heater stagnation pressure windows. Consequently, incoherent (non-CARS) is 0.765_+0.008 MPa. All uncertainties presented in this interference can be rejected by spatial filtering. paper are based on the 95% probability limits (1.98 times Application of a complicated technique like CARS the standard deviation). The above uncertainties are due to inhigh-speed engine environments is not routine. Since it the random run-to-run variations and do not include a is a pointwise (rather than planar) technique, building a +3% uncertainty in the mass flow rate measurements. "picture" of the internal temperature field of the Heater and nozzle exit conditions are estimated from combustor requires hundreds of facility runs, which is cxpensive. Thus, modern-design-of-experiments (MDOE) the flow rates, heater pressure, and nozzle minimum and exit areas using one-dimensional (ID) analysis 7.The flow techniques are used to minimize the quantity of data exiting the heater into the nozzle is assumed to be in required to meet the goals of this work. Due to the complexity of the experiment and the fact that, at the thermodynamic equilibrium, but has unknown enthalpy outset, the effects of important variables (including due to heat lost to the structure and cooling water. The enthalpy is guessed and the area of the sonic throat facility operation, model and instrumentation variables, computed by ID analysis assuming isentropic flow inthe etc.) are not fully understood, there are likely to be significant uncontrolled variables. MDOE techniques are nozzle. The enthalpy is then iterated until the computed used to minimize systematic errors associated with these. area at the sonic throat equals the geometrical minimum area of the nozzle. Nozzle exit conditions arc computed from the geometrical exit area. The composition at the Flow Facility nozzle throat and exit could be evaluated at frozen (at The experiment is conducted in NASA Langley's heater values) or equilibrium conditions. All significant Direct-Connect Supersonic Combustion Test Facility minor species are included. Calculations assuming (DCSCTF) _.Hot air simulant, known as vitiated air, is equilibrium and frozen composition differ in minor produced in the "'heater", shown in Fig. i. Oxygen and air species concentration, but not significantly in major are premixed and then hydrogen is burned in the oxygen- species, temperature or pressurc. The nominal calculated enriched air. Flow rates are selected so that the mass conditions, and uncertainties due to mass flow rate fraction of oxygen in the vitiated air is the same as that of measurement error and run-to-run variations in heater standard air. The high pressure, vitiated air isaccelerated conditions are: heater stagnation temperature 1827+75 K. through a water-cooled convergent-divergent nozzle, exit temperature 1187+60 K, exit pressure 100+1.5 kPa, before entering the test model. The facility isdesigned to exit Mach number 1.989_+0.005. Errors arising in the American Institute of Aeronautics and Astronautics 2 AIAA-2002-0743 calculatiodnue to the assumption of ID flow (the effects 87.88 mm. Five small pilot fuel injector holes are located of non-uniform composition, boundary layers, etc.) are not ahead of the step. and the main fuel injector islocated just considered. downstream of the start of the 3: divergence. The A study of the flow quality at the exit of the facility injection angle is 30° to the opposite wall. The injector nozzle was previously conducted _.A Pitot probe rake was nozzle is designed by the method of characteristics to employed to map the exit Pitot pressure and additionally produce Mach 2.5, 1D flow at the injector exit. Hydrogen the flowfield at the exit of the nozzle was visualized. injection is provided at a pressure of 2.12-+0.07 MPa, Silane (Sill0 was added to the heater hydrogen and temperature of 302+4 K, and equivalence ratio of burned to form silica particles in the heater. The particles 0.99_+0.04. On some runs, additional hydrogen injection is were illuminated by a pulsed laser-sheet and imaged with provided by the 5 pilot injectors at the same nominal a CCD camera. Results were compared to CFD temperature and atotal equivalence ratio of0.148 _+0.008. calculations of the nozzle flow. The flow at the nozzle exit The pilots are turned on and off at the same time as the was not completely ID, but the computed Pitot pressure main tuel injector. distribution agreed well with measurement. The flow The duct is uncooled: however, the wall thickness of appeared well mixed. the copper duct is greater than 32 mm and the carbon steel The test model is shown in Fig. 2: flow direction is duct is 19ram. Thus, given the good thermal conductivity from left to right, The model consists of two main sections of these materials, it ispossible tooperate the facility with of duct: the copper upstream section and the carbon steel the model fueled for run times in excess of 20 s (and downstream section, Stainless steel flanges and carbon unfueled for much greater times). With atmospheric gaskets separate the sections from each other and the temperature air flowing in the model between runs, runs nozzle. Proceeding from left to right, there is a constant could be repeated every 10-15 minutes. area segment, a small outward step at the top wall, a The model is equipped with 7 slots to allow the second short constant area segment followed byaconstant CARS beams to penetrate the duct, of which slots 1,3, 5. 3° divergence of the top wall. The span is constant at 6, 7, depicted in Fig. 2(a), are used in (a) this study. The slots are in pairs, one on each side of the duct, 4,8 mm wide, No .... S.S Flange ,. C. gasket zzJe /.- H2 .. _ _pq ,_,,,_ Tovacuum . extending the full height of the duct. _" ./ Copperblock _ ......... When not in use the slots are plugged _..".....F_ :..1_' ,:_-- _ _ 6 2" flush to the wall. Windows covering the slots are mounted at the end of short rectangular tubes, at the Brewster Heater _26;6.C. " 7-_".0 • - angle to minimize reflections (Fig. 3). ................ t234,2L--- The window tubes are ventilated with a constant flow of electrically heated (- 400 K)dry air to prevent condensation (b) of water on the windows. The CARS beams tocus can thus be translated the full span and height of the duct without damaging the windows. The model is instrumented with 19.2_ both pressure taps and wall I temperature probes. The details of this X " _ " / 43.64 3° .... i , , instrumentation are different in the upstream and downstream duct s .,,aZoo sections. Thirty-five static pressure taps are located in the copper duct, consisting of 0.80 mm diameter Dimensionsinmm square-edged holes. Taps are located on the bottom wall, at the centerline, Figure 2 Test model: (a) nozzle, copper and steel duct sections, (b) detail and on the top wall at : = -36.3 mm (z in vicinity of fuel injector and pilots. ismeasured from the horizontal center American Institute of Aeronautics and Astronautics 3 AIAA-2002-0743 line).Forty-ninsetaticpressurteapsarelocatedinthe matching the Raman shift of nitrogen. steedluct,consisting of 1.6 mm diameter square-edged Figure 3 shows a schematic of the remaining holes. Taps are located at top and bottom wall centerlines, components of the CARS system, The second 532 nm and sidewall midpoints. Pressures are measured with an beam is split into two parallel, roughly equal intensity accuracy of _+0,6 kPa by a Pressure Systems Inc. beams. The dye beam is expanded in a bcam expander electronically scanned pressure-measuring system. (B). Dye and 532 nm beams arc combined at a dichroic Six spring-loaded, bayonet, ribbon, K-type mirror (C) and are relayed via a periscope to a spherical thcrmocouples from Nanmac Corp. are located in 6.35 (focusing) lens (SL) of focal length 0.41 m. All three mm diameter blind holes inthe copper block. The bottom beams cross at their focal points: the total point of the dye of these holes is square and the wall thickness (to the duct beam is made coincident with the focal point of the 532 interior surface) is2.8 mm. The thermocouple junction is nm beams by adjusting the beam expander. Beams are located at the bottom of the hole at the center. This phase matched in a vertical planar BOXCARS diameter and wall thickness are chosen, based on a configuration 3. multidimensional heat transfer analysis, so that the At the lens, the lull (to -10% of peak) diameter of thermocouple would measure the unperturbed duct surface the 532 nm beams is~ '8.5 mm, and the beams are 18mm temperature. While the temperature at the bottom of the apart. The full diameter of the dye is - 1I ram, At the hole is less than local duct surface temperature, the effect tk_cus, the diameters are respectively - 0.12 mm and - of the hole, which alters the conduction path, is to raise 0.15 mm, yielding ageometrical beam intersection length the local duct surface temperature, and these effects of 5.4 mm. The length of the measurement volume is olivet. Six "eroding" K-type thermocouples from Nanmac measured by translating the CARS measurement volume Corp., 7.9 mm diameter and incorporating a carbon-steel through a thin planar jet of nitrogen, surrounded by a sheath, are located in the carbon-steel duct. The coflowing jet of helium. The length over which CARS thermocouple junction for these probes is located flush to signal is recorded is ~ 4.5 mm and the full width hall" the duct flow surface. Over timc, the juncti_,_n isremoved maximum (FWHM) of the signal distribution is ~ 2.25 by the hot flow, but can be regenerated using sandpaper. mm. The measurement w)lume length is selected (by Since the probe material is predominantly carbon-steel, selecting the spacing of the beams on the lens) as a the same as the duct, this probe also measures the compromise between the desire to have high spatial unperturbed duct surface temperature. resolution and high signal power. The following beam energy levels per pulse are obtained at the focusing lens: CARS Technique -`85 mJ for each of the green, from 12mJ to 24 mJ tbr the Optical System dye. The CARS system uses an unseeded Spectra-Physics The beams (including the CARS signal beam) are DCR-4 pulsed Nd:YAG laser frequency doubled to 532 relayed via a second spherical (collimating) Ions and a nm. The nominal power is 550 mJ per pulse in the green, second periscope back to the optical bench. The repetition rate is 10 Hz, and nominal line width is less overlapping CARS and 532 nm beams are separated ina than Icm j. Beams arc horizontally or "p" polarized with splitter (S). The splitter consists of two 100 mm long dichroic mirrors that reflect -99.5% of the incident CARS respect to the plane of the optical system. A broadband dye laser isemployed inthe system. This laser consists of signal while reflecting only -20% of the 532 rim, an oscillator cavity, lormed between a total reflecting transmitting the rest, The CARS and 532 nm beams entcr mirror and a 30e,_ rellector, and a single amplifier stage. the splitter at 45°tothe mirrors and undergo six back-and- Two identical dye cells are uscd, one inthe oscillator and forth reflections. The beam is then directed through one the amplifier, through which flows rhodamine 640 in additional filters as needed to reiect residual 532 nm or methanol. Alter separating the 532 nm from residual 1064 for CARS signal attenuation. It enters a polarizer that nm with dichroic mirrors, the 532 nm beam is split. One allows only p-polarized light to pass (not a critical beam with 45% of the total power isused to pump the dye component since itisfound that the signal is already well laser, split 22% to the oscillator and 7'8% to an amplifier. polarized). It is then focuscd by a pair of cylindrical Pump beams are loosely focused on the dye cell, nearly lenses (CL) and enters a I m monochrometer with 1200 parallel to the dye laser beam. Cell windows are at the groove/mm grating via an aperture (E). An EG&G PAR Brewster angle to minimize rellcctions and ensure the dye model 1420 intensified, linear, self-scanned silicon laser is "p" polarized. Thc wavelength iscentered between photodiode array detector (IPDA) is mounted at the exit 605 nm and 606 nm by adjusting the dye concentration, plane of the detector. The detector consists of 1024 American Institute of Aeronautics and Astronautics 4 AIAA-2002-0743 elements2..5mmhighby25umwide,ofwhichthe initialized prior to data acquisition. When data is to be centra5l98elemenatsreusedT.hecylindricalelnseasre acquired, a control pulse is sent to the IPDA and adjustetdoproducaehorizontafolcusatthedetector translation stage controller, which then execute (maximizinimgagesharpnesasn)dalooseverticafol cus preprogrammed sequences. The IPDA scans at 30 Hz: (toensurethedetectoprrovideas linearresponsteo scans 1,4, 7 etc. are clearing scans and are not saved. sI•gnal 9). An optical splitter (X) is located in front of the scans 2, 5, 8,etc. are prescans, and scans 3,6, 9. etc. are detector _. The splitter creates a secondm'y signal on the data scans, coincident with the laser pulse• After detector, identical to the primary but offset by 290 pixels completion of acquisition, resultant IPDA data is and of 6.1c_ the intensity. When the intensity of the transferred to the PC. Two types of acquisition are primary signal exceeds the dynamic range of the detector. employed. In the first, data is acquired at a single point in the secondary signal is used for analysis. space. [n the second, data is acquired while either the The two top prisms of the periscope are mounted on vertical or the horizontal stages ,'ue in constant velocity stepping motor driven vertical translation stages. The two motion. bottom prisms and the vertical translation stages are CARS data are acquired inthe supersonic combustor mounted on similar horizontal stages. By translating the during multiple sets of test runs. During a set of runs vertical and/or horizontal stages in tandem (maintaining (which might last as long as 5hours/, access to the model alignment) the measurement volume could be moved in and optical system is prohibited for safety reasons. Test the vand/or zdirection. It is important that the beams are runs consisted of approximately 5 s during which the heater is operating but no fuel is He-Ne injected in the model, tbllowed by from II s to 20 sduring which fuel is injected. CARS data is acquired over a period 2 s shorter than the period of fuel injection. Immediately after arun, 10sof data isacquired with the system operating as hot'ore, the dye laser beam B = Beam expander blocked by a remotely operated flag, C = Combining mirror These "'background" scans measure SL = Spherical lens non-CARS interferences such as S = Signal separator scattered laser light. Dye laser spectra F = Filter P = Polarizer are acquired simultaneously with each CL= Cylindrical lens data run by sampling with a fiber optic E=Entranceaperture probe coupled to an Instaspec _/,im X=Splitter spectrometer with a CCD detector, controlled by a sepm'ate PC Photodiode Array Just before and just after a set of _onochrometer test runs, "'reference" CARS spectra are acquired in alow speed jet of"PC- Figure 3CARS system: beam combining optics, interaction and signal Duster" refrigerant gas. Since this jet detection optics. contained no nitrogen, and is of constant CARS susceptibility, the parallel to the direction of motion of the translation stage. spectra reflect the spectral variation in dye laser power. A reference, low-power helium-neon laser (tte-Ne) beam Additionally, spectra are acquired with room temperature isdirected through the periscopes, parallel tothe direction air flowing in the duct. of motion of both sets of stages, and through the center of The test facility poses problems in relation to the the spherical lenses. The Nd:YAG and dye laser beams operation of the CARS system. The effect of acoustic and are periodically realigned by ensuring that they intersect structural vibration is not significant. However. large the He-Ne beam at their tbcus. temperature swings are common since the room inwhich CARS data acquisition is under the control of a the apparatus operated is continuously ventilated with personal computer (PC). The PC provides a continuous external atmospheric air: additionally significant heat is sequence of pulses to trigger the laser and synchronize the radiated from the model. Thermal expansion effects onthe iPDA. The IPDA and translation stage controllers are American Institute of Aeronautics and Astronautics 5 AIAA-2002-0743 mechaniccaolmponenotsftheopticasl ystemarenot 1t" sufficientotrequireremotaedjustmen(atsdequastiegnal 09]- CN2 = 028 T levelsaretypicallymaintainefdor severahlours). 0.8 500 K Howevetrh.ermaelxpansionssignificantclyhangdeye / 1000 K o7 / lasecrentewravelengatnhdpower. 1500 K 06 ' / , - - 2000 K ! 2500 K Data Reduction 00.45' /_ ,,' CARS data are analyzed on a separate workstation. Prescans are subtracted from data scans. Background scans (after subtraction of prescans) are averaged and subtracted fi'om data scans. Both primary eto 01 .... -- - -.._ --- 0 0 _ I , , + I , , I , and secondary (produced by the splitter) CARS signal are contained within the data scan, Ifthe primary issaturated, the secondary is selected tot' analysis. Data scans are divided by the reference spectrum to remove the effect of - O,_[,o_,.°.+..t...-.---"Jl the dye laser spectral power distribution, and normalized to unit area (primary or secondary). Data are compared to 0.5 ], _ _ . --- -- _ a library of similarly normalized theoretical spectra to /; ! determine the temperature and nitrogen concentration. The pixel location of the start of the theoretical spectra is 03 _ . allowed to float +10 pixels from anominal position in0.3 0J2 \ pixel increments. The combination of temperature, 01 concentration, and pixel location that produces the least 0 _225i0 , _ 230I0 , I , 23150 J mean square deviation between theory and data is Raman shift, crn-1 selected. Figure 4 Theoretical CARS spectra Theoretical CARS spectra are generated using the The peak of the reference CARS spectrum shifts program CARSFT _. The combustion gases are assumed significantly during a set of runs. This shift can be to be a mixture of nitrogen and non-resonant buffet" gas, attributed largely to a shift in the dye laser wavelength. both having non-resonant susceptibility of 8.5×10 ts However, there are other factors. Thermal effects on cm/erg. The nominal static pressure is assumed to be I mechanical components of the optical system, beam atmosphere. Infact, as may be seen in Fig. 7. the pressure steering by the hot gases inthe duct, and even translation at the CARS planes is as much as 20 kPa below and 35 of the periscope stages all can change the position of the kPa above. The error introduced by this assumption is CARS beam t'ocus at the entrance slit to the estimated by calculating theoretical spectra over a range monochrometer, and hence the position of the spectra on of pressures and temperatures and fitting to them the detector. Two techniques are employed to correct for assuming 1atmosphere pressure. The difference between this problem. The first is toallow the pixel location of the fit and true temperatures (fit minus true) isabout 25 K per start of the theoretical CARS spectra to float in the fitting 10kPadifference from 1atmosphere tbr Fs near 2000 K. process, as described. The second is to estimate the The Exponential Gap Model tbr collisional narrowing of reference spectrum fiom the run data itsel/: The technique the Raman line shape is used: a Voigt model was also is inspired by the observation that the directly measured tried and tbund to make little difference tbr the test dye-laser spectra could be accurately fit to a Gaussian conditions. A 532 nm laser line width of I cm -_ is function. assumed: spectra are not sensitive to 532 nm laser line The procedure is illustrated in Fig. 5. The first step width for the test conditions. An experimentally is to analyze the data from agiven run using the reference determined instrument probe function is used. spectrum obtained with the refi'igerant gas at the end of a Temperatures from 150 K to 3000 K in increments of 25 set of runs. For a particular laser pulse, spectrum A is the K. and 29 non-uniformly spaced concentrations of best-fit theoretical CARS spectrum, B is the measured nitrogen are used in the library. Typical spectra at several CARS spectrum (prior to normalization by the reference temperatures and concentrations are shown in Fig. 4 spectrum), and C, the ratio of Bto A, isan estimate of the giving an indication of the sensitivity of the spectra to reference spectrum for this particulm" shot. All such these variables estimates for a given run are averaged, and then fit to a American Institute of Aeronautics and Astronautics 6 AIAA-2002-0743 and the measured temperature compared to a A: CARStheory calculation based on measured flow rates and il equilibrium chemistry (including minor species). The mean temperatures for several 10 s (100 laser pulse) tuns are shown in Fig. 6. The Ii !l equivalence ratio is accurate to within +--3%. 8 =CARSdata Included in the data are runs at an equivalence ! ratio of one. in which the total laser power is varied from 200 mJ to 550 mJ. Also included 20(3 .%0 400 500 600 cue data in which, through the use of different neutral density tilters, the signal in the primary C=B/A is saturated, forcing use of the secondary in analysis. No trends are tbund with either of these __------_i, .,.... , ,"','7---..._..._, variables, indicating that the nitrogen specttum 30C 40(3 500 _30 is not saturated by high laser powers and thatthe splitter device works well. The average of all the D=fitofGaussiantomeanofC data points at an equivalence ratio one is 2360 K, compared to the theoretical value of 2380 K. Standard deviations of the tuns are shown. The 200 3CO 400 _, bOO j'_# _ \ trend with increasing laser power is to lower standard deviations owing to increased signal- FitCARStheorytoBID to-noise ratios. The standard deviation of the !p !/ /' \ Region of _t ,• H2/S(9) individual (single laser pulse) measurements at Region of fit ,_, an equivalence ratio of one about the overall 400 500 600 average is approximately 100 K. Thus, 100 K 14 I,i may be taken as a conservative estimate of the { t,; standard deviation inherent in the CARS ..... F_ Data instrument. i , i i i . , | | . | | 2o0 2X?O .2(30 4013 500 eO_ p_xel Figure 5 CARS data analysis 175 Gaussian function tor amplitude, center and width. The 150 region of fit is indicated in the figure, and excludes a 125:_ region around the bandhead of nitrogen (which was very noisy), and the region to the left of pixel 275 (potentially 100 E affected by masking from the optical splitter). As a 75 practical matter, it is necessary to exclude fl'om the 50 average individual spectra for which good fits to theory Mean T could not be obtained. Acceptable averages for fitting :_, RMS T - Calculation 25 could be found for ahnost allruns. The Gaussian fit. D. is then used as the reference spectrum for normalization of o_ 1I , , , 2I 3I 40 all data tbr the given run. The figure shows data from a equivalence ratio Figure 6 Comparison of theory and data in an laser pulse after normalization, and the best fit theoretical adiabatic flame spectrum. This procedure istypically iterated twice, with the latest best-fit theoretical spectrum used to determine The measurements agreed satisfactorily with an improved reference spectrum. calculation at an equivalence ratio less than or equal to The techniques used for acquisition and analysis of one. However, for hydrogen rich flames, the measured CARS data in the supersonic combustor are tested in a temperature is, on average, nearly 150 K high. It is "'Hencken'" adiabatic, flat-flame burner burning hydrogen suspected that this is a problem with the way the CARS in air. Equivalence ratio (ratio of hydrogen rate to spectra are modeled in the presence of excess hydrogen, stoichiometric hydrogen rate for given air flow) is varied rather than with the experiment. For example, the American Institute of Aeronautics and Astronautics 7 AIAA-2002-0743 hydrogen S(10) rotational linc is located at a Raman shift spatial coordinates. This would defend against artificial of 2267.5 cm -_ (compare Fig. 4)t-'. Hydrogen is not asymmetries that might otherwise occur. For these specifically included in calculating the spectral libraries. reasons, spatial set-points are set in random order in this However, comparison of measured spectra with calculated experiment. spectra that include the line suggest that its presence isnot alone sufficient to explain the discrepancy observed. This Response Surface Methods problem is being investigated, but tbr now it isaccepted Response surface methods are applied in this study, that measured temperature may be -150 K high in in which the spatial dependence of temperature is hydrogen rich regions. represented ineach of a number of planes in a supersonic combustor duct by a mathematical function of the spatial Modem Design of Experiments coordinates. This method has the potential fi_rproviding a Randomization very compact representation of the temperature When repeated measurements or "replicates" made distribution, by replacing a potentially large volume of within a relatively short interval of time are more alike individual measurements with a relatively small set of than otherwise identical replicates acquired over alonger numerical coefficients that can be used to adequately time period, the observations are not independent. This predict the temperature for any combination of spatial condition iscommon inreal experiments, and iscaused by coordinates within the range examined in the experiment. often unrecognized sources of systematic variation that The method has the additional virtue that it provides persist over time, such as instrumentation drift, estimates of thc response variable (temperature) for temperature effects, operator fatigue and learning effects. combinations of the independent variables (coordinates) Sample means and variances estimated under such that are not physically set in the experiment. conditions are biased by generally non-reproducible Because the response models are based on functions of the systematic variation, which render the experimental data afflicted with uncertainty, predictions experimental results difficult to duplicate and of dubious made with these models will likewise feature some degree value for confirming the predictions of computational of uncertainty. The specific uncertainty associated with models. Standard references on experiment design treat any one model prediction depends on the variance in the this phenomenon in detail, t3'ta'15 response data used to develop the model, the number and Fisher 16recognized that independent observations location of points from which the model is fitted, the occur less frequently in nature than generally assumed, nature of the model itself (number and form of individual and proposed the simple act of randomizing the set-point model terms), and the specific coordinate location for levels of independent variables as an effective way to which the prediction is to be made. However, Box and ensure independence in case nature neglected to do so in Draper 17show that the average variance across points used somc inopportune phase of an experiment. For example, if to lit the model is simply poZ/n, where p is the number of a horizontal scan of temperature is planned for several parameters in the model, nisthe number of points used to uniformly spaced locations across an operational fit the model, and o"is the standard deviation of those supersonic combustor model. Fisher would recommend data. that the spatial coordinates be selected in random order An inverse relationship between data volume and rather than systematically. If the spatial coordinates are inference error risk characterizes all experimental selected in a monotonically increasing sequence, starting investigations. In this case, lor agiven functional tbrm of on the left side of the supersonic combustor duct and the model (which determines p), and a given measurement proceeding systematically toward the right side, tor environment (which determines o-), the average model example, wall-heating effects could cause measurements prediction uncertainty can be driven to arbitrarily low madc on the right side of the duct to be biased high levels by selecting a large enough volume of data, n. relative to measurements made on the left. This would Conversely, by establishing in advance the levels of impose an artificial asymmetry on the spatial dependence uncertainly that are acceptable, the volume of data of temperature across the duct. However. if the spatial necessary to achieve stated precision goals can be coordinates are selected in random order, some of the computed. This is useful in the design of an experiment, measurements made on the left would occur earlier and because it can reveal in advance when insufficient some would occur later, and similarly tbr the right sidc, resources are available to acquire data in a volume ensuring that the effect of all time-varying systematic necessary to achieve minimum precision requirements, errors (not just wall effects) would then be independent of and it can also prevent the acquisition of substantially American Institute of Aeronautics and Astronautics 8