Laser Velocimetry. Biasing Errors and Corrections. von Karman Institute for Fluid Dynamics. Lecture Series

Transcription

1 von Karman Insttute for Flud Dynamcs Lecture Seres Laser Velocmetry June 1-14, 1991 Basng Errors and Correctons James F. Meyers NASA - Langley Research Center Hampton, Vrgna, USA

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3 Basng Errors and Correctons by James F. Meyers NASA - Langley Research Center Hampton, Vrgna Unted States Introducton The nablty to perfectly measure a physcal process can be attrbuted to the lack of precson and accuracy of the measurng devce and the affect of external nfluences on the overall accuracy of the measurement. Early nstrumentaton systems suffered from such poor precson that external nfluences were generally gnored. The advent of analog-to-dgtal converters helped the precson by reducng the sources of varablty error nherent n analog systems to just the sensor. The converters however, added new problems by measurng a process only at dscrete tmes requrng statstcal estmates of that process, thus contnuous trackng was no longer possble. Wth the ncreased precson, external nfluences now became mportant, especally the added nfluence of dgtal samplng. Mathematcans tell us there s no nfluence on the measurement statstcs f the samplng s ndependent of the physcal process. Thus one may obtan qualty measurements by unformly samplng a process because the dgtal clock typcally used to drve analog-to-dgtal converters s ndependent of the process beng sampled. The mathematcans further tell us that unform samplng s not requred, any clock wth ndependent statstcs wll do, e.g., random walk, Gaussan, Posson, etc. Durng the advent of laser velocmetry, analog measurement technques such as spectrum analyzers and frequency lock loops were used to measure the near contnuous sgnals obtaned from water flows. The dgtal frequency tracker was developed by usng an analog-to-dgtal converter to sample the output from the frequency dscrmnator n a frequency lock loop. The ncreased control of the feedback loop by dgtal crcuts operatng on dgtal sgnals ncreased measurement precson and even reduced the requrement of near contnuous nput sgnals. The next logcal step was to remove the frequency lock loop and drectly dgtze the ndvdual sgnal burst obtaned from a sngle partcle passng through the laser velocmeter sample volume. Extensve studes of partcle passage statstcs ndcated that ther arrvals obeyed Posson statstcs regardless of the average rate.

4 Rememberng that the mathematcans stated that Posson statstcs were an ndependent samplng process, researchers placed ther laser velocmeters n ar flows and reduced ther seedng rates to tolerable levels wth full confdence that ths new method was the panacea of measurement technques. In 1973 McLaughln and Tederman, reference 1, of Oklahoma State Unversty notced that ther mean velocty measurements of a turbulent boundary layer were consstently hgher than theory predcted. Seekng to determne the cause of ths dscrepancy, they reasoned that a unformly seeded volume would yeld a greater number of partcle passages per unt tme through the sample volume as the velocty ncreased. Snce the number of measurements of the hgher veloctes n the turbulent flow would be greater than the number from lower veloctes, the statstcal velocty mean would be weghted toward the hgher veloctes. Applyng a weghtng functon of nverse velocty to the statstcal calculatons, ther measurements agreed much closer to theory. Now convnced that mathematcans should be barred from the real world, researchers began to apply the nverse velocty correcton to all laser velocmetry data. It wasn t long before correcton schemes were beng developed faster than researchers could dgest them. Technques such as two-dmensonal weghtng, true velocty magntude weghtng, resdence tme weghtng, and tme averagng were beng developed as the true correcton scheme, reference. The only unversally accepted truth was that all laser velocmeter data were n error and needed correctng. Look Agan, Somethng s Not Rght In 198 Meyers and Wlknson, reference 3, from NASA - Langley Research Center were tasked to prove that the laser velocmeter could be used to make turbulence ntensty measurements of flow felds wth acceptable accuracy. The test was conducted n the jet from a fully developed turbulent ppe flow usng an orthogonal three component laser velocmeter, fgure 1, wth a hot wre placed mm downstream of the sample volume to serve as the measurement standard, fgure. The hot wre was calbrated n a partcle laden, low turbulent jet placed just above the ppe flow, fgure 3. The velocty of the calbraton jet was adjusted, under computer control, to obtan the hot wre calbraton wth the laser velocmeter provdng the mean velocty measurements at each velocty staton. The seedng partcles n both the calbraton jet and the ppe flow jet were.5 mcron polystyrene mcrospheres to nsure partcle trackng fdelty n the flow felds. The hot wre output was

5 dgtzed wth each measurement converted to velocty through a splne ft calbraton curve wth the resultng ensemble statstcally analyzed. The 15 m/sec flow was seeded suffcently to yeld an average data rate of, samples per second. True velocty vector measurements made by the three component laser velocmeter operatng n full concdence ndcated an on-axs flow wth small angular scatter untl the entraned regon was reached where the flow devated slghtly outward and the scatter ncreased to approxmately ±1 degrees. The local turbulence ntensty at ths pont was n excess of 3 percent. Thus the flow was one dmensonal through the operatng envelope of the hot wre. Wth the test condtons well defned, comparatve testng began. Radal scans were made at several downstream locatons from the ext of the jet. The local turbulence ntensty values compared well wthn the core regon of the jet, but devated greatly n the entraned regon, e.g., fgure 4. The measured data were processed usng standard statstcal calculatons: σ U = = N u ( u U) Attemptng to mprove the comparatve measurements, the onedmensonal weghtng factor proposed by McLaughln and Tederman: where σ U = = A N A u A A ( u U) = 1 u was appled to the laser velocmeter data, fgure 5. Curously, the comparsons wthn the core became worse whle the comparsons n the entraned regons mproved. Ths trend remaned consstent at all scan postons downstream from the ext of the ppe flow. A (1) () (3) (4) 3

6 Rememberng that McLaughln and Tederman stated that a unformly seeded flow wll yeld a greater number of partcle passages per unt tme through the measurement volume as velocty ncreases, basng should have been present. Snce the partcles were added 66 ppe dameters upstream of the jet, full mxng should yeld the necessary unform spatal dstrbuton wthn the fully developed turbulent flow, but the correcton does not work. In the entraned regon, the porton of the flow from the ppe contans many partcles whle the entraned flow has few partcles. The seedng n ths regon s far from unform, yet the correcton appears to work. The hypothess that hgh velocty ncreases the data rate whle lower veloctes decrease the data rate mples a correlaton between velocty and data rate. Ths correlaton can be verfed by calculatng the standard correlaton coeffcent between any two processes: U u R r C = < >< > σ σ u r (5) where U s the statstcal mean velocty from the selected measurement ensemble and u s the th velocty durng the shortest perod of tme consdered to be ndependent from other tmes. Ths perod of tme s referred to as the Taylor tme mcroscale and s the tme that the flow takes to change one standard devaton: T λ = σ dv < > dt v 1 (6) The brackets, < >, denote the expected value of the enclosed expresson. There s an mplct assumpton that statonary systems are beng dscussed so that no dstncton s made between tme averagng and ensemble averagng. The parameter u s the flow root mean square varaton. The Taylor mcroscale has also been descrbed as the tme scale over whch there s no sgnfcant change n the energy of an eddy. The varable R n equaton (5) s defned as the statstcal mean data rate durng the acquston of the selected measurement ensemble and r s the data rate durng the th flow mcroscale. The smultaneous measurement of velocty wth the hot wre provded the data necessary to determne the Taylor tme mcroscale for each measurement ensemble n the radal scan. The velocty tme hstory obtaned wth the laser velocmeter was dvded nto Taylor tme mcroscales and the nstantaneous veloctes and rates calculated. Applyng these values to equaton (5) and normalzng by the standard devatons of velocty, u, 4

7 and data rate, r, the correlaton coeffcents were determned. The resultng coeffcents, plotted n fgure 6, ndcate an ndependent samplng process n the center of the flow snce the coeffcents are near zero, and a dependence n the entraned regon snce the coeffcents are greater than zero. Therefore the measurements wthn the core of the flow are ndeed ndependent and the statstcs should not be corrected whereas the measurements wthn the entraned flow are not ndependent and ther statstcs should be modfed. Ths explans the behavor of the data comparsons. Whle the results from these calculatons ndcate ndependence n the core regon, the logcal strength of the hypothess s hard to gnore. Plottng the ncremental correlaton coeffcents versus the dfference between the nstantaneous data rate and the average data rate durng the correspondng Taylor tme mcroscale results n the scatter pattern shown n fgure 7. A correlaton between velocty and data rate would result n a data groupng along a 45-degree lne. A porton of the velocty and data rate tme hstory for a seres of mcroscales, also shown n fgure 7, do not exhbt any pattern. Expandng the tme hstory, fgure 8, reveals a few mcroscales where velocty and data rate have the same trends, however the remanng mcroscales have opposng trends. The nvestgaton clearly llustrates that the smple correcton schemes prevously proposed are not applcable because they are based on the general assumpton of unform spatal seedng. The nvestgaton shows that ths assumpton s not generally vald and even when t s, the samplng may stll be ndependent and thus the data do not requre correcton. The correctng scheme must determne, based only on the measurement ensemble beng processed, f correcton s necessary, and f so, how much s requred. The frst approach to be based only on the ensemble characterstcs was the sample and hold processng technque developed by Dmotaks, reference 4, (backward step algorthm) and Edwards and Jensen, reference 5, (forward step algorthm). Ths technque develops a contnuous velocty tme hstory by holdng a velocty measurement untl the next velocty measurement s made n the manner of a sample and hold crcut. Ths technque can be mplemented by ether usng nterarrval tme, t, as a weghtng factor: U = u t t (7) 5

8 σ = ( ) u U t + 1 t + 1 (8) or unformly samplng of the tme hstory at an arbtrary rate to develop the flow statstcs. By unformly samplng the tme hstory, the partcle arrval statstcs are nullfed and the resultng measurement statstcs are correct. Usng ths technque to process the jet flow data mproves the comparatve measurements n both the core and entraned regons as shown n fgure 9. Stevenson, Thompson, and Roesler, reference 6, approxmate the sample and hold method by usng a hgh partcle densty n the flow, coupled wth a hgh-speed burst counter wth a long reset tme to obtan a saturated detector. Snce ths approach obtans a velocty measurement every tme the burst counter s ready to acqure one, a unform and thus unbased samplng of the flow feld s obtaned. Unfortunately the data rates requred to obtan a saturated detector are prohbtvely hgh to be useful n normal wnd tunnel applcatons. Even the sample and hold method should have a data rate greater than 1 measurements per Taylor tme mcroscale to fully descrbe the velocty tme hstory. Snce the requred data rate s dependent on the Taylor tme mcroscale at each pont n the flow, a method needs to be developed to estmate the mcroscale ether durng data acquston or from the acqured data ensemble. If t s assumed that the flow velocty remans near a gven value durng the Taylor tme mcroscale, a method for estmatng that tme mcroscale can be developed as follows: Dvde the velocty range of the selected data ensemble nto ten velocty bns and overlay these bns on the velocty tme hstory, fgure 1. Based on the assumpton, velocty measurements made wthn the mcroscale wll reman n the same velocty bn, whereas measurements n successve mcroscales probably wll be n other bns. Thus an estmate of the flow correlaton tme may be obtaned by calculatng the average resdence tme for the flow velocty to reman wthn a bn. Testng ths technque usng the data from the turbulent jet ndcated that the average resdence tmes were approxmately -percent of the Taylor tme mcroscales obtaned from the hot wre. The requred data rate can now be determned for the sample and hold technque based only on the measurement ensemble. The velocty : data rate correlaton coeffcent can be determned by usng the average resdence tme to establsh the nstantaneous velocty and data rate, fgure 11. 6

9 Calculaton of Independent Statstcs Instead of adjustng the partcle generator to obtan suffcent data rates to use the sample and hold method, t may be easer to use the Taylor tme mcroscale and the knowledge that measurements n successve mcroscales are ndependent to develop a new technque to nsure statstcal ndependence of the data. A sngle velocty measurement wthn a correlaton tme should represent the flow velocty durng that tme and addtonal measurements gve an ndcaton of the partcle arrval rate statstcs for that velocty. Thus a second nterrogaton of the velocty tme hstory can yeld ensembles of ndependent velocty measurements, and partcle arrval rates as a functon of flow velocty. The method developed by Edwards and Meyers, reference 7, s based on two suppostons: (1) The velocty feld s coherent durng the Taylor tme mcroscale followng a measurement and thus addtonal measurements occurrng durng ths tme yeld no further nformaton. () The number of addtonal measurements yeld an ndcaton of the probablty of occurrence of that measured velocty. The method s mplemented by establshng two hstograms, the normal velocty hstogram of measured veloctes and the occurrence hstogram contanng the number of addtonal measurements durng the Taylor tme mcroscale followng each measured velocty. The frst measurement n the velocty tme hstory shown n fgure 1 s located n bn 6 wth two addtonal measurements wthn the followng mcroscale. Thus the count n bn 6 of the velocty hstogram s ncremented by one and the count n bn 6 n the occurrence hstogram s ncremented by two. The frst measurement followng the mcroscale s also n bn 6 wth three addtonal measurements followng. Bn 6 n the velocty hstogram s agan ncremented and bn 6 n the occurrence hstogram s ncremented by three. Ths procedure contnues through the entre tme hstory. The acqured data for ths example were obtaned on the centerlne of the jet wth the resultng raw data hstogram shown n fgure 13. Followng data nterrogaton, the resultng hstogram of measured veloctes obtaned from the measurement ensemble s shown n fgure 14. The velocty hstogram s then used to normalze the occurrence hstogram yeldng the average number of measurements n the mcroscale followng the measured velocty as a functon of velocty, fgure 15. The fgure shows the normalzed occurrence hstogram to be approxmately flat ndcatng no velocty s favored n the samplng process over the others. Therefore t s expected that the correlaton coeffcent between velocty and data rate wll be low, as was found to be the case, fgure 6. If the hypothess by McLaughln and Tederman was correct, the normalzed occurrence hstogram would approxmate a ramp functon wth the hghest value located at the hghest velocty. 7

10 The fnal step n the data processng scenaro s to dvde the normalzed occurrence hstogram nto the measured velocty hstogram to yeld a normalzed velocty hstogram wth all samplng bases removed, fgure 16, and to perform the desred statstcs on the resultng dstrbuton. A second example ensemble obtaned near the edge of the jet s presented to llustrate the procedure wth measurements of a hghly turbulent flow feld. The raw data hstogram, normalzed occurrence hstogram, and normalzed velocty hstogram are shown n fgures 17, 18, and 19 respectvely. The normalzed occurrence hstogram s bascally flat wth a small rse toward hgher veloctes ndcatng a small velocty bas. Ths s verfed by a velocty : data rate correlaton coeffcent of.9 obtaned for ths ensemble. The results of processng the ppe flow measurements usng ths technque are shown n fgure. The ensung comparson wth the hot wre data s superor to the other technques employed. Vortex Flow Above a 75 o Delta Wng Now that the presence of velocty bas can be determned usng the velocty : data rate correlaton and a procedure has been developed to obtan an ndependent data set from a velocty measurement ensemble, t s approprate to study a more complcated flow feld than the turbulent ppe flow jet. The flow selected was the leadng edge vortex flow feld above a 75 o delta wng, reference 8. The selecton s approprate snce ths fundamental flow s utlzed n many hgh performance arcraft desgns to ncrease the flght performance envelope. A leadng edge vortex par contans a great deal of energy whch, f carefully controlled, can provde sgnfcant lft on an arcraft. However, f a vortex s dsturbed t wll burst, dsspatng ts energy n a random manner resultng n a sudden loss of lft. Ths problem s of specal concern for arcraft stablty when only one vortex of a coupled par bursts, resultng n sudden substantal rollng moments beng appled to the arcraft. The model s a 75 o swept delta wng wth a.35 meter span and sharp leadng edges (1 o bevel on the lower surface wth the upper surface flat). A.5 o angle of attack yelds a stable vortex flow above the model. An ncrease to 4. o causes the vortex flow to burst over the model. The tunnel speed s adjusted to obtan a chord Reynolds number of 1. mllon for both condtons. The nvestgatons were conducted n a plane orthogonal to the surface of the model at an x/l =.7. The flow above the delta wng at an angle of attack of.5 o conssts of two stable leadng edge vortces. A laser lght sheet vsualzaton of these vortces s shown n fgure 1. The three component mean velocty 8

11 measurements obtaned wth the laser velocmeter at.5 o angle of attack are shown n fgure. It s noted that the streamwse component ncreases to twce free stream velocty wthn the core of the vortex. The vortex flow s very stable whch should yeld long Taylor tme mcroscales n the core regon. The contour map of the estmated mcroscales s shown n fgure 3 and ndeed the core regons are very dstnctve wth ther long mcroscales. Contours of the velocty : data rate correlaton, shown n fgure 4, have no dscernble pattern nor are the coeffcents large enough to ndcate sgnfcant velocty bas. If the angle of attack s ncreased to 4. o, the vortces burst. The velocty measurements shown n fgure 5 ndcate that the streamwse component reverses whle the crculaton velocty remans ntact. Ths unstable flow would be expected to have short Taylor tme mcroscales. The estmates, shown n fgure 6, support ths expectaton wth no evdence of any flow structure. Agan the contours of the velocty : data rate correlaton, shown n fgure 7, have small coeffcents ndcatng no dscernble velocty bas, although a mnor pattern does appear to be present. Shear Flow Feld Downstream of a Backward Facng Step When makng a comparatve nvestgaton between varous technques, the relatve mert of each s best determned by applyng them to the same flow feld. A classc flow used by several researchers to determne the capablty of a velocty bas correcton technque s the flow downstream of a backward facng step. Adams and Eaton, reference 9, tested the tme average approach (smlar to the sample-and-hold method) whle Stevenson, Thompson, and Roesler, reference 6, tested the use of a saturated detector. Snce these nvestgatons ndcated the presence of velocty bas, a backward facng step was constructed, reference 1. The flow feld was nterrogated wth a three component laser velocmeter. The data was processed usng standard statstcs and the hstogram method developed by Edwards and Meyers. One and three component versons of the McLaughln and Tederman correcton scheme were used as a reference. The backward facng step faclty, llustrated n fgure 8 and shown n fgure 9, s a sucton faclty wth ar beng pulled through a sngle screen and honeycomb followed by four addtonal screens down a flat secton 16 step heghts long to a step expanson of :1 and an aspect rato of 1:1. The nlet flow had a free stream velocty of 4.5 m/s and a turbulence ntensty, measured by a hot wre of 1. percent. The Reynolds number was 65 based on the momentum thckness of the boundary layer at the step. The Reynolds number based on step heght 9

12 was, and the dsplacement thckness of the boundary layer at the step was.35 step heght. Polystyrene partcles,.8 mcrons n dameter, were njected va atomzaton of a 5:5 mxture of ethanol and water n the ar beng pulled nto the faclty. Osclloscope observatons of the sgnal bursts ndcated only monodsperse partcles were passng through the measurement volume. The laser velocmeter, shown n fgure 9, was a four component system usng a sngle Argon on laser. The 488. nm lne was selected and nput to fber optcs and transmtted to a sngle component system located just downstream of the fnal screen. Ths fxed system measured the velocty along the centerlne of the faclty and provded the reference free stream velocty and data rate measurements and baselne partcle arrval statstcs. The remanng three components usng the nm, nm, and nm lnes comprsed the measurement system. The measurement system, llustrated n fgure 3, used orthogonal transmsson optcs rotated 45 degrees to obtan drect three component measurements through a sngle wndow. A sngle optcal recever, usng chromatc flterng for component separaton, located perpendcular to the faclty collects the scattered lght. The focal length was.5 m wth f-8.5 collectng optcs yeldng a sphercal sample volume 1 mcrons n dameter. Hgh-speed burst counters processed the sgnals from the three measurement components. A LVABI data acquston system, reference 11, acqures the dgtal measurements from the three counters and passes the data ensembles to a mncomputer for fnal data processng and storage. The free stream component s processed by a burst counter n free run mode wth drect nput to the mcrocomputer used to montor the faclty parameters. The free stream results are passed to the mncomputer upon demand when the measurement ensembles are obtaned. A detaled vertcal traverse was conducted three step heghts downstream of the step. The velocty scan was made wth the three laser velocmeter components n full concdence and the velocty vector of each partcle determned. Ths provded the velocty vector magntudes requred for the three-dmensonal correcton. As shown n fgure 31, the determnaton of the mean velocty profle usng the basc statstcs and the hstogram method track closely. The one-dmensonal correcton caused the veloctes to devate consderably behnd the step whereas the three-dmensonal correcton moved the veloctes closer to the basc statstcs. The standard devatons of velocty normalzed by the free stream velocty accentuates the dfferences between the basc statstcs and the McLaughln and Tederman correctons, fgure 3. Snce the hstogram method contnues to track the basc statstcs, the correlaton coeffcent between velocty and data rate s expected to be small. The velocty : data rate correlaton coeffcent, plotted n 1

13 fgure 33, s ndeed small wth the maxmum magntude of.16 whereas the coeffcent for the ppe flow data, fgure 6, was up to a value of.3. However, the trend of the data s nterestng. The correlaton ncreases to a peak n the free shear layer where the heavly seeded hgh speed flow s mxng wth the lghtly seeded recrculatng flow. The correlaton then decreases to a negatve peak n the shear regon between the recrculaton and the boundary layer ndcatng the slower boundary layer contans the greater number of partcles. The flow Taylor tme mcroscale, plotted n fgure 34, s constant above the step then makes a smooth transton to a value three tmes longer behnd the step. A marked ncrease n correlaton tme s then seen wthn the boundary layer behnd the step. An overall vew of the flow feld was made by measurng the veloctes over a.5-nch grd from 1-nch upstream to 4-nches downstream of the step. The laser velocmeter was run n nonconcdence mode to ncrease the data rate especally n the separated regon behnd the step. The basc statstcs, the hstogram method, and the 1-dmensonal bas correcton results are shown for the mean velocty n fgures respectvely and fgures 38-4 respectvely for the standard devatons normalzed by the local mean velocty. Agan the basc statstcs and the hstogram method have comparable results whereas the 1-dmensonal bas corrected data devates consderably from them, especally behnd the step. The velocty : data rate correlaton coeffcent map s shown n fgure 41. If the correlaton coeffcents nne nches downstream of the step are compared to the correspondng data n fgure 33, one notces major dfferences between the two data sets. Apparently the recrculaton zone has ganed sgnfcant numbers of partcles, reversng the prevous trends. A repeat of the vertcal scan whch yelded the data for fgure 33, was performed wth the same nstrumentaton settngs used for the flow feld mappng. A comparson of these two scans n fgure 4 show smlar results above the step, however the trends behnd the step have opposte phases. Ths ndcates that the heavest partcle concentraton was wthn the recrculaton zone. In realty ths apparent change n the partcle dstrbuton s attrbuted to nstrumentaton settngs. Durng the frst scan, the reset tme was adjusted from the normal 75 µsec to 3 µsec when the measurement volume was n the recrculaton regon. Durng the flow feld mappng, the reset tme was held at 75 µsec for all measurement locatons. When the mean velocty slowed n the shear regons, the short reset tme allowed the hgh-speed burst counters to obtan two or more measurements from the same Bragg-shfted sgnal burst. These extra measurements had no effect on the resultng velocty statstcs because the correlaton was so low, however they dd cause the 18 degree phase shft n the correlaton data. These results clearly 11

14 show the senstvty of the velocty : data rate correlaton to changes n the experment, ncludng the nstrumentaton. Summary The dependence of laser velocmeter measurement rate on flow velocty was frst descrbed by McLaughln and Tederman n They proposed that the dependency was a drect result of the flud mechancs n the flow. In 1983, Edwards and Jensen nvestgated the possblty that the dependency was statstcal and not drectly coupled to flow velocty. Ths possblty was strengthened n 1984 by Edwards and Meyers when revewng the data obtaned earler by Meyers and Wlknson whch smultaneously acqured three component laser velocmeter and hot wre data. Usng the standard equaton to determne the correlaton between two parameters, ths data proved that the ensemble was an ndependent samplng of the flow velocty feld n the jet extng from a fully developed turbulent ppe, a flow fully satsfyng the assumpton made by McLaughln and Tederman. Further nvestgatons outlned n ths lecture have shown that any dependence s purely statstcal, and s nonstatonary both spatally and temporally. The only patterns found were n mxng regons where two flows of dfferent veloctes contanng dfferent partcle denstes nteract. Examples of these mxng regons nclude the entraned flow at the edge of a jet, and the strong shear regon above a separaton zone. The man conclusons to be drawn are that the tmes between successve partcle arrvals should be routnely measured and the calculaton of the velocty : data rate correlaton coeffcent should be performed to determne f a dependency exsts. If none s present, accept the data ensemble as an ndependent sample of the flow. If a dependency s found, the data should be modfed to obtan an ndependent sample. Unversal correctng procedures should never be appled because ther underlyng assumptons are not vald. References 1. McLaughln, D. K.; and Tederman, W. G., Jr.: Basng Correcton for Indvdual Realzaton of Laser Anemometer Measurements n Turbulent Flow. The Physcs of Fluds, 16, 1, pp. 8-88, Edwards, R. V., edtor: Report of the Specal Panel on Statstcal Partcle Bas Problems n Laser Anemometry. J. Flud. Engr., vol. 19, pp , June

15 3. Meyers, J. F.; and Wlknson, S. P.: A Comparson of Turbulence Intensty Measurements Usng A Laser Velocmeter and A Hot Wre In A Low Speed Jet Flow. Proceedngs of the Internatonal Symposum on Applcatons of Laser-Doppler Anemometry to Flud Mechancs, Lsbon, Portugal, paper 17.4, June 5-7, Dmotaks, P. E.: Sngle Scatterng Partcle Laser Doppler Measurements of Turbulence. Applcatons of Non-Intrusve Instrumentaton to Flud Flow Measurement, AGARD CP-193, Edwards, R. V.; and Jensen, A. S.: Partcle Samplng Statstcs n Laser Anemometers: Sample-and-Hold Systems and Saturable Systems. J. Flud Mech., vol. 133, pp , Stevenson, W. H.; Thompson, H. D.; and Roesler, T. C.: Drect Measurement of Laser Velocmeter Bas Errors n a Turbulent Flow. AIAA Journal,, pp , Edwards, R. V.; and Meyers, J. F.: An Overvew of Partcle Samplng Bas. Proceedngs from the Second Internatonal Symposum on Applcatons of Laser Anemometry to Flud Mechancs, Lsbon, Portugal, paper.1, Meyers, J. F.; and Hepner, T. E.: Measurement of Leadng Edge Vortces from a Delta Wng Usng a Three Component Laser Velocmeter. AIAA 15th Aerodynamc Testng Conference, San Dego, CA, paper AIAA-88-4, May 18-, Adams, E. W.; and Eaton, J. K.: An LDA Study of the Backward- Facng Step Flow, Includng the Effects of Velocty Bas. Proceedngs of the Internatonal Symposum on Laser Anemometry, Wnter Annual Meetng of the Amercan Socety of Mechancal Engneers, Mam Beach, FL, FED-Vol. 33, November 17-, 1985, pp Meyers, J. F.; Kjelgaard, S. O.; and Hepner, T. E.: Investgaton of Partcle Samplng Bas n the Shear Flow Feld Downstream of a Backward Facng Step. Proceedngs of the Ffth Internatonal Symposum on Applcatons of Laser Technques to Flud Mechancs, Lsbon, Portugal, paper 9.1, July 9-1, Cavone, A. A.; Sterlna, P. S.; Clemmons, J. I., Jr.; and Meyers, J. F.: A Hgh Speed Buffer for LV Data Acquston. Proceedngs of the 1th Internatonal Congress on Instrumentaton n Aerospace 13

16 Smulaton Facltes, College of Wllam and Mary, Wllamsburg, VA, pp , Fgure 1.- Orthogonal three component laser velocmeter and the 5. cm dameter ppe. 14

17 Fgure.- Relatve postons of the three component laser velocmeter measurement volume and the hot wre n the jet extng from a fully developed turbulent ppe flow. Fgure 3.- Vew of the 5. cm dameter ppe and the low turbulence hot wre calbraton jet faclty. 15

18 Turbulence ntensty, percent Dfferental, percent Hot Wre Laser Velocmeter Radal locaton, cm Radal locaton, cm Fgure 4.- Comparson of laser velocmeter and hot wre turbulence ntensty measurements along a radal scan 1 cm downstream from the ppe ext. Turbulence ntensty, percent Dfferental, percent Hot Wre Laser Velocmeter Radal locaton, cm Radal locaton, cm Fgure 5.- Comparson of corrected (McLaughln and Tedermann) laser velocmeter and hot wre turbulence ntensty measurements along a radal scan 1 cm downstream from the ppe ext. 16

19 Turbulence ntensty, percent Velocty:Rate Correlaton Hot Wre Laser Velocmeter Radal locaton, cm Radal locaton, cm Fgure 6.- Velocty : data rate correlaton coeffcents along a radal scan 1 cm downstream from the ppe ext. Incremental Velocty:Rate Correlaton Devaton from Mean v - V r - R r - R Tme, msec Fgure 7.- Examnaton of ncremental veloctes and data rates from the laser velocmeter measurement ensemble obtaned along the centerlne of the ppe, flow 1 cm downstream from the ppe ext. 17

20 v - r - V R Devaton from Mean 1 3 Tme, msec Fgure 8.- Detaled examnaton of ncremental veloctes and data rates from the laser velocmeter measurement ensemble as a functon of tme. Turbulence ntensty, percent Dfferental, percent Hot Wre Laser Velocmeter Radal locaton, cm Radal locaton, cm Fgure 9.- Comparson of corrected (sample and hold processng) laser velocmeter and hot wre turbulence ntensty measurements along a radal scan 1 cm downstream from the ppe ext. 18

21 Velocty, m/sec Tme, msec Fgure 1.- Measured velocty tme hstory of the measurement ensemble obtaned along the centerlne of the ppe flow, 1 cm downstream from the ppe ext used to estmate the Taylor tme mcroscale of the ensemble Velocty, m/sec Tme, msec Fgure 11.- Dvson of the velocty tme hstory of the measurement ensemble obtaned along the centerlne of the ppe flow, 1 cm downstream from the ppe ext nto Taylor tme mcroscales to obtan the statstcs requred to calculate the velocty : data rate correlaton coeffcent. 19

22 Velocty, m/sec Tme, msec Fgure 1.- Determnaton of ndependent measurement samples from the velocty tme hstory of the measurement ensemble obtaned along the centerlne of the ppe flow, 1 cm downstream from the ppe ext. 4 Number of measurements Velocty, m/sec Fgure 13.- Hstogram of velocty measurements obtaned along the centerlne of the ppe flow, 1 cm downstream from the ppe ext.

23 3 5 Number of measurements Velocty bns Fgure 14.- Hstogram of measured (frst velocty measurement wthn a Taylor tme mcroscale) veloctes obtaned along the centerlne of the ppe flow, 1 cm downstream from the ppe ext. 4 Number of occurrences Velocty bns Fgure 15.- Occurrence hstogram of addtonal measurements followng the frst velocty measurement wthn a Taylor tme mcroscale obtaned along the centerlne of the ppe flow, 1 cm downstream from the ppe ext. 1

24 Number of measurements Velocty bns Fgure 16.- Hstogram of ndependent veloctes obtaned along the centerlne of the ppe flow, 1 cm downstream from the ppe ext. 1 Number of measurements Velocty, m/sec Fgure 17.- Hstogram of velocty measurements obtaned at the edge of the ppe flow jet, 1 cm downstream from the ppe ext.

25 4 Number of occurrences Velocty bns Fgure 18.- Occurrence hstogram of addtonal measurements followng the frst velocty measurement wthn a Taylor tme mcroscale obtaned at the edge of the ppe flow jet, 1 cm downstream from the ppe ext. 15 Number of measurements Velocty bns Fgure 19.- Hstogram of ndependent veloctes obtaned at the edge of the ppe flow jet, 1 cm downstream from the ppe ext. 3

26 Turbulence ntensty, percent Dfferental, percent 8 Hot Wre Laser Velocmeter Radal locaton, cm Radal locaton, cm Fgure.- Comparson of corrected (hstogram processng - Edwards and Meyers) laser velocmeter and hot wre turbulence ntensty measurements along a radal scan 1 cm downstream from the ppe ext. Fgure 1.- Laser lght sheet vsualzaton of the leadng edge vortex flow feld above a 75 4 o delta wng at.5 o angle of attack at an x/l =.7.

27 1 Heght, cm Span, cm Freestream Normalzed U-component mean Fgure.- Three component velocty measurements of the leadng edge vortex flow feld above a 75 o delta wng at.5 o angle of attack at an x/l =.7. 1 Heght, cm Span, cm Integral tme scale, U-component, sec Fgure 3.- Estmated Taylor tme mcroscales of the leadng edge vortex flow feld above a 75 o delta wng at.5 o angle of attack at an x/l =.7. 5

28 1 Heght, cm Span, cm U-component: data rate correlaton Fgure 4.- U-component velocty : data rate correlaton coeffcents of the leadng edge vortex flow feld above a 75 o delta wng at.5 o angle of attack at an x/l =.7. 1 Heght, cm Span, cm Freestream Normalzed U-component mean, m/sec Fgure 5.- Three component velocty measurements of the leadng edge vortex flow feld above a 75 o delta wng at 4. o angle of attack at an x/l =.7. 6

29 1 Heght, cm Span, cm Integral tme scale, U-component, sec Fgure 6.- Estmated Taylor tme mcroscales of the leadng edge vortex flow feld above a 75 o delta wng at 4. o angle of attack at an x/l =.7. 1 Heght, cm Span, cm U-component: data rate correlaton Fgure 7.- U-component velocty : data rate correlaton coeffcents of the leadng edge vortex flow feld above a 75 o delta wng at 4. o angle of attack at an x/l =.7. 7

30 } Screens Flow 3" 6" Honeycomb 48" 48" Fgure 8.- Axal cross secton of the backward facng step apparatus. Fgure 9.- The backward facng step apparatus and the four component laser velocmeter system nstalled on the traversng mechansm. 8

31 Fgure 3.- Schematc of the three component laser velocmeter measurement system. 3 1 Basc statstcs Hstogram method 1-dmensonal correcton 3-dmensonal correcton Heght, n Normalzed mean velocty Fgure 31.- Mean velocty measurements normalzed by the free stream velocty upstream of the step along a vertcal traverse, three step heghts downstream of the backward facng step. 9

32 3 1 Basc statstcs Hstogram method 1-dmensonal correcton 3-dmensonal correcton Heght, n Normalzed standard devaton Fgure 3.- Standard devatons of velocty normalzed by the free stream velocty upstream of the step along a vertcal traverse, three step heghts downstream of the backward facng step. 3 1 Heght, n Velocty : Data rate correlaton Fgure 33.- Velocty : data rate correlaton coeffcents along a vertcal traverse, three step heghts downstream of the backward facng step. 3

33 3 1 Heght, n Flow correlaton tme, sec Fgure 34.- Estmated Taylor tme mcroscales along a vertcal traverse, three step heghts downstream of the backward facng step. 3 1 Heght, n Axal dstance, n Normalzed U-component mean Fgure 35.- Mean velocty flow feld map about the backward facng step usng basc statstcal data processng. 31

34 3 1 Heght, n Axal dstance, n Normalzed U-component mean Fgure 36.- Mean velocty flow feld map about the backward facng step usng the hstogram method of data processng developed by Edwards and Meyers. 3 1 Heght, n Axal dstance, n Normalzed U-component mean Fgure 37.- Mean velocty flow feld map about the backward facng step wth the basc statstcal data corrected usng the classc 1-dmensonal velocty bas correcton technque developed by McLaughln and Tedermann. 3

35 3 1 Heght, n Axal dstance, n Normalzed U-component standard devaton Fgure 38.- Flow feld map of standard devaton of velocty normalzed by the local mean velocty about the backward facng step usng basc statstcal data processng. 3 1 Heght, n Axal dstance, n Normalzed U-component standard devaton Fgure 39.- Flow feld map of standard devaton of velocty normalzed by the local mean velocty about the backward facng step usng the hstogram method of data processng developed by Edwards and Meyers. 33

36 3 1 Heght, n Axal dstance, n Normalzed U-component standard devaton Fgure 4.- Flow feld map of standard devaton of velocty normalzed by the local mean velocty about the backward facng step wth the basc statstcal data corrected usng the classc 1-dmensonal velocty bas correcton technque developed by McLaughln and Tedermann. 3 1 Heght, n Axal dstance, n Velocty : data rate correlaton Fgure 41.- Map of the velocty : data rate correlaton coeffcents about the backward facng step. 34

37 3 1 Long reset tme behnd step Short reset tme behnd step Heght, n Velocty : Data rate correlaton Fgure 4.- Comparson of velocty : data rate correlaton coeffcents along a vertcal traverse three step heghts downstream of the backward facng step. 35