Increasing Accuracy in Super-Resolution PIV

Transcription

1 Theunissen R. *, Stitou A. + ; Riethmulle M.L. * * Von Kaman Institute fo Fluid Dynamics 7, Chaussée de Wateloo 164 Rhode-Saint-Genèse BELGIUM af.theunissen@vki.ac.be; iethmulle@vki.ac.be + Cuently at Univesity of Cambidge Insect Flight Goup - Mico Ai Vehicle Poject Downing Steet - Cambidge CB3 EJ UK as73@hemes.cam.ac.uk ABSTRACT In the development of new measuement techniques, inceasing the esolution has always been one of the main goals. Fo the moment, coss-coelation algoithms such as PIV, ae limited by the size of the inteogation aeas. Algoithms of hybid PIV-PTV pocessing, so called Supe Resolution methods, ae about to be matue and have shown an incease in the spatial esponse. The pesent wok is addessing the accuacy issue of such methods. An appoach that coelates individual paticle images is developed and it is efeed as the IPC method. It aims at impoving the efficiency compaed to the classical appoach using estimatos of the successive paticle locations. Examples of application in votical flows ae pesented aiming at discussing the ability to chaacteize coheent stuctues. Ideal cases of votices ae simulated with synthetic images. This wok pesents also measuements of the flow field behind a backwad facing step at low Re (Re h 5) pefomed in a low speed wind tunnel (U 3.75 m/s, hcm, expansion atio1.). Votical stuctues ae extacted and esults obtained fom the two appoaches (coelation PIV, hybid PIV-PTV) ae compaed. 1. INTRODUCTION Votical tubulent stuctues ae playing an impotant ole in many industial and aeonautical inteests. As an example, the eduction in stength of wingtip votices is cuently investigated by many instances (Scaano et al., ). This type of eseach equies a pope chaacteization of flow stuctues. Instantaneous whole field velocity measuements ae valuable because they povide infomation that allows an altenative intepetation with espect to the classical Reynolds decomposition. The concept of coheent stuctues has been intoduced and has tuned out to be an inteesting appoach fo investigating unsteady and tubulent flow fields (Hussein, 1986). Indeed a statistical analysis cannot explain the entie phenomenon and give only a limited view of the physics. Recently, diffeent tools wee developed aiming at chaacteizing these votices, such as wavelet analysis (Scham and Riethmulle, 1) and a patten ecognition method (Scaano, ) among othes. These methods highlight the need of whole field measuement techniques. Paticle Image Velocimety is such a whole field measuement technique. A thin lase sheet enlightens a section of the flow field, which is sufficiently seeded with taces. A CCD camea then Theunissen, R.; Stitou, A.; Riethmulle, M.L. (5). In Recent Developments in Non-Intusive Measuement Technology fo Militay Application on Model- and Full-Scale Vehicles (pp ). Meeting Poceedings RTO-MP-AVT-14, Pape. Neuilly-su-Seine, Fance: RTO. Available fom: RTO-MP-AVT-14-1

2 Repot Documentation Page Fom Appoved OMB No Public epoting buden fo the collection of infomation is estimated to aveage 1 hou pe esponse, including the time fo eviewing instuctions, seaching existing data souces, gatheing and maintaining the data needed, and completing and eviewing the collection of infomation. Send comments egading this buden estimate o any othe aspect of this collection of infomation, including suggestions fo educing this buden, to Washington Headquates Sevices, Diectoate fo Infomation Opeations and Repots, 115 Jeffeson Davis Highway, Suite 14, Alington VA -43. Respondents should be awae that notwithstanding any othe povision of law, no peson shall be subject to a penalty fo failing to comply with a collection of infomation if it does not display a cuently valid OMB contol numbe. 1. REPORT DATE 1 APR 5. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Von Kaman Institute fo Fluid Dynamics 7, Chaussée de Wateloo 164 Rhode-Saint-Genèse BELGIUM 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 1. SPONSOR/MONITOR S ACRONYM(S) 1. DISTRIBUTION/AVAILABILITY STATEMENT Appoved fo public elease, distibution unlimited 13. SUPPLEMENTARY NOTES See also ADM ABSTRACT 15. SUBJECT TERMS 11. SPONSOR/MONITOR S REPORT NUMBER(S) 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified 18. NUMBER OF PAGES 18 19a. NAME OF RESPONSIBLE PERSON Standad Fom 98 (Rev. 8-98) Pescibed by ANSI Std Z39-18

3 ecods the eflections of these taces. In geneal, two snapshots sepaated by time steps in the ode of 1 to 1µs, ae divided into smalle ectangula windows, called coelation windows o inteogation aeas. Fo each inteogation aea, the intensities in both fames ae coss-coelated fom which an ensemble aveaged displacement is obtained. Note that it is also possible to ecod two sequential snapshots onto one fame; double-exposue single fame (Rehm and Clemens, 1999). In that case displacements ae obtained though auto-coelation. Howeve, the focus of this aticle will lie on the fist type of coelation as it is nowadays moe common. An extensive liteatue suvey can be made in which authos popose a ange of impovements in the coelation algoithms to incease its accuacy. To name two, sub-pixel window offset and iteative window defomation (Scaano and Riethmulle, 1999) have shown to be the most ewading and pomising. In ode fo the coelation peak to be distinct fom the suounding noise peaks, a minimum numbe of image pais must emain within the inteogation windows, typically about 1 paticle pais (Westeweel, 1997). These two opeations incease the coelation signal by minimizing the numbe of paticles which disappea fom the inteogation aea duing the time step t, due to lage in-plane tanslations o velocity gadients and out-of-plane motion (Keane and Adian 199, Huang et al. 1993, Cowen and Monismith 1997). The spatial esolution of the velocity measuements is a citical issue because many post-pocessing tools need that the flow stuctues ae sufficiently sampled in ode to identify them but also to chaacteize them coectly. Fo coss-coelation PIV, the spatial esolution is detemined by the size of the inteogation windows (Weeley and Meinhat, 1). Despite all pogess, the spatial esolution is limited by the numbe of paticle images captued in the inteogation aeas (Keane and Adian, 199) and hence invesely popotional to the coelation window size (Scaano and Riethmulle, ). This estiction lead to the development of Paticle Tacking Velocimety, in which the displacement of individual paticles is detemined. PTV pocesses stat with identifying the paticles. Pixels ae classified as paticles if thei intensity lies above a cetain theshold (Kiitsis 1989, Stitou and Riethmulle 1, Cowen and Monismith 1997) o when the intensity distibution esembles a Gaussian shape (Takehaa and Etoh, 1999). A cucial step in PTV is the coect paiing of paticles between the fames. This caused that PTV was oiginally only suitable fo flows with a low seeding density. Flow stuctues wee hence pooly sampled. Keane et al. (1995) intoduced the concept of Hybid PIV-PTV algoithms o supe-esolution PIV (SRPIV). A supeesolution algoithm has been developed at the VKI (Stitou and Riethmulle, 1). The idea is that one fist pefoms PIV on the ecoded images. Using the obtained displacement field and taking into account only paticles inside a cetain seach aea (centeed on the pedicted position), one naows down the numbe of possible patnes and educes the numbe of false measuements. As such, one maintains the typical PIV seeding and geatly enhances the spatial esolution (Figue 1). Figue 1: Pinciple of Hybid PIV/PTV algoithms. Both paticle detection and paiing lie beyond the scope of this aticle. We addess in the following discussion the accuacy issue supposing that the paticle images ae associated in a coect way. Logically, the displacement between two paticles is epesented by the vecto connecting the paticle centes. The simplest appoach to find these centes seems to be the centoid method (Guezennec and - RTO-MP-AVT-14

4 Kiitsis 199, Udea et al. 1996) in which the cente of mass of the aea illuminated by a paticle spot is looked fo. A vaiant consists in weighing evey point with its intensity value. The method is vey sensitive to the theshold that selects which pixels ae accounted fo. Since the paticle image distibution can be modelized by a Gaussian cuve (Adian and Yao, 1983), thee-points intepolation was applied (Wenet et al. 1993, Cowen and Monismith 1997, Zimme 1). Two-dimensional least squae fitting has the advantages to use moe points and is to be in theoy less sensitive to the imaging noise (Udea et al. 1996, Maxen et al., Takehaa et al. 1999). These methods lead to a system of non-linea equations that need to be solved with an iteative numeical algoithm. The pocess is in geneal stated using paametes fom a simple cente estimato such as the centoid method. Maxen et al. () epoted in thei wok that this method pesents an impotant dawback since it inceases the computation time by a facto 1. Udea et al. (1996) compaed pefomances of diffeent localization methods and concluded that paticle cente estimatos not only show a andom eo due to noise but also a systematic eo that is caused by the pixel discetization and depends on the sub-pixel position. Maxen et al. () concluded that thee is no majo advantage of the least-squae fitting ove the 3-points Gaussian estimato but they consideed isolated paticles. Both woks find an optimum size of aound 4 pixels. In geneal the Gaussian intepolation pefoms well even though two-dimensional fitting could get some impovement especially when paticle images ovelap at intemediate and high concentation. Nevetheless, the PIV community agees (Stanislas et al., 3) on the fact that the accuacy of the measuement of PTV is pesently lowe than using coelation techniques. Indeed, this advantage is to be cedited to the statistical natue of the coelation that opeates on seveal taces at the same moment in an inteogation aea and, then, by incopoating the souces of eos, aveages it. The souces of eo ae mainly due to the impefect optics, to the digitization pocess and the inheent noise. Anothe souce is the ovelapping of individual paticle image. In this aticle an appoach will be pesented that coelates individual paticles images and is efeed to as the IPC method. It aims at impoving the efficiency compaed to the classical appoach using the estimation of the successive paticle locations.. PRINCIPLE OF INDIVIDUAL PARTICLE CORRELATION The poposed method aims at ovecoming the afoe mentioned limitations of the centoid-seach schemes and at impoving the pefomances compaed to the classical Gaussian fit method. The poposed featue is integated at the end of the pocess of a hybid PIV-PTV method. The paticle images ae identified on the two successive ecodings. A fist guess of the velocity map is evaluated using a coelation PIV method. Using this pedicto field the paticles ae associated individually aftewads. The poposed idea in the pesent wok is to coelate individual paticle images instead of making the effot to localize them individually (Figue ). The inteest is then to take advantage of the aveaging effect of the coelation opeation. This appoach will be efeed as Individual Paticle Coelation (IPC). Figue : Pinciples of Individual Paticle Coelation. The pocessing is fist initiated by the individual tacking of the taces and then finalized with a statistical appoach. The method is applied in the same fashion than any classical PIV iteative method. RTO-MP-AVT-14-3

5 Stating fom an initial position estimated with a fitting appoach, windows ae coelated in a digital way and the elative displacement is detemined. Then, the windows ae shifted accoding to the pevious patial measuement and the pocess is iteated seveal times. It is also possible to poceed in the same way as advanced PIV algoithms, by moving the two windows aound a cental point to obtain a second ode accuate discetization of the flow field (Weeley and Meinhat, 1). Since sub-pixel displacement of the windows is adopted, a e-sampling of the images is equied. The scheme used is simila to the one used by Scaano and Riethmulle (). It consists on a development of Sinc functions (Hall, 1979). Each window is centeed aound one complete paticle instead of cuts of paticle images as what is happening in the iteative coelation method as illustated on Figue 3. In coelation PIV, moe and moe taces ae lying on the bode duing the efinement of the inteogation aeas. Theefoe, when a gadient of velocity is encounteed, the signal-to-noise atio of the coelation deceases because, in this case, the paticles on the bode ae likely to move out of the coelated templates and do not contibute positively. The eduction of the windows size is theefoe limited. On the contay, in the IPC appoach the souce of infomation is always centeed inside the inteogation aea. Figue 3: Compaison of the inteogation aea obtained espectively with the IPC method and by a PIV iteative coelation pocess. The coelation function is implemented using the following nomalized fomula: C I1,I ( x, y) [ I1 (x, y) µ I (x, y) ]. [ I (x x, y y) (x x, y y) ] µ I + + σ I1 (x, y). σ I (x + x, y + y) (1) The value µ 1 and σ I ae espectively the mean and the standad deviation of the intensity of the templates. One advantage of using a nomalized vesion of the coelation function is that it is possible to quantify the degee of matching between the two image samples. The function is computed in the spatial domain instead of using an FFT-based appoach. Indeed, since the inteogation aeas scale with the paticle diamete, one has to deal with small windows. Theefoe a diect coelation implementation offes a moe efficient computational time. In ealistic situations, seveal souces of touble can be listed: the impefection and the pixelisation of the imaging system, the limited pefomances of image e-intepolato, the ovelap of paticle images. Example of successful measuements and non-successful ones ae showed in Figue 4. Convegence occus afte less than 1 iteations (Figue 4a). It was obseved that the iteative pocess of coelation does not convege in evey situation (Figue 4b). The eason is the pesence of othe paticle image in the neighbouhood. To pevent this situation, a check is pefomed at each iteation to ensue that the coection is at the sub-pixel level. If not, this pocess is abandoned and the Gaussian fitting is consideed again. - 4 RTO-MP-AVT-14

6 (a) Figue 4: Implementation of the IPC method. (a) Conveging case. (b) Diveging case. (b) 3. ASSESSMENT OF INDIVIDUAL PARTICLE CORRELATION 3.1 Assessment of the Accuacy: Unifom Displacement Field An assessment of the IPC method is poposed by means of synthetic images of efeence velocity fields (Figue 6). Synthetic images of by pixels wee geneated. Paticles ae unifomly displaced in both diections ( x y1.5 pixels). This value was chosen because it is the one fo which the highest andom eo is expected (Scaano and Riethmulle, ). Consevative conclusions can hence be made. The esults ae compaed to the efeence PIV method, named WIDIM. The dimension of the coelation aea of the IPC method and WIDIM was vaied and fo each case a seies of images was pocessed ensuing a sufficient numbe of samples to calculate the dispesion of the andom eo (aound 1 vectos). The evolution of the RMS eo of the displacement at a efeence case with a concentation C p.1pat/pix and souce density N S.9 is displayed in Figue 6a. The souce density (Eq. ) is elated to the atio between the spacing of the taces λ p and the paticle image diamete D p (Adian and Yao, 1983). It is an indicato of the paticle image ovelap. C 3 D z o numbe of paticles D p N π S D p C p D p D p 4 image aea M o λ p () A high value of N S means a high concentation and vice vesa. The SRPIV stategy stats by pocessing the images with standad PIV. Afte all window efinements, PIV stops at a coelation window of 16 by 16 pixels. Afte this, the PTV pocess kicks in and futhe efines the pocess to tack individual paticle images. The SPRIV stategy povides in those conditions an infomation spacing (vecto spacing) of 4.3 pixels. The WIDIM pefomances seem not to be affected by the inteogation aea dimension. Compaed to the Gaussian fit, the IPC method pefoms bette poviding the window size aound the paticle is at least the size of the paticle image itself. Fo a coelation aea of 5 by 5 pixels, the impovement is of 4%. When inceasing the window size, the eo is deceasing till it eaches the same ode of magnitude than the given PIV algoithm. This is a statistical effect since the numbe of pixels involved in the coelation is popotional with the squae of the window size. Nevetheless, fo this paticle diamete (3 pixels) and the adopted windows size (5 pixels), the spatial esolution of the IPC (4. pixels) has still to be taded with the accuacy of the PIV. A situation with a bette esolved imaging senso is simulated (Figue 5). One can also imagine using slightly defocused ecodings to incease the size of the images of the taces. The effect of the discetization of the image is pesented in Figue 6. In the case of bette sampling, the souce density (N S ) and then the ovelap facto is kept at the same level as the efeence case even though the concentation expessed in paticle/pixels is lowe. The Gaussian algoithm is impoved because the discetization is RTO-MP-AVT-14-5

7 bette. In the IPC pocess, the selected windows size is 7 pixels since the diamete of the paticle images is 6 pixels. In that case, the accuacy of the IPC is compaable with the PIV one. The advantage is that the spatial esolution scales with the spacing of the paticles (7.9 pixels) and not with the window size as with coelation PIV (each paticle gets a vecto). Fo a unifom displacement field, the dimension of the inteogation aea of a coelation PIV algoithm can be highly educed but fo ealistic flows containing gadients thee is a limitation due to the in-plane loss of pais (Keane and Adian, 1993). Figue 5: Effect of the image sampling D p,1 <D p, - C p,1 >C p, - (λ p /D p ) 1 (λ p /D p ). (a) Figue 6: RMS eo obtained with the IPC method, the Gaussian fit and coelation PIV fo diffeent window-sizes (a) Refeence case (b) Effect of bette image sampling. (b) Figue 7: Systematic eo in function of the applied sub-pixel displacement. The chaacteization of the pefomances in tem of systematic eo is also pefomed by means of synthetic images. A database of images with unifom displacement of seveal amplitudes is constituted and pocessed. 16 by 16 pixels windows size whee consideed fo WIDIM as pocessing paamete fo a efeence. Figue 6 shows that the esults ae not in this case significantly influenced by the windows size. It is also easonable paametes fo a eal pocessing. The mean of the measuement eo in function of the sub-pixel pat of the applied displacement is displayed on Figue 7. The pixelization intoduces a peiodical behaviou of the eo with a peiodicity of 1 pixel. This peiodical behaviou is esponsible fo - 6 RTO-MP-AVT-14

8 the so-called pixel-locking. Looking to the sign of the systematic eo, it is clea that the measuements ae biased to the closest intege value. The SRPIV teatment with a Gaussian fit is giving the highest eo. Switching to IPC mode emoves it almost completely. It is also obseved that this method shows an even lowe eo compaed to the coelation PIV algoithm. 3. Assessment of the Spatial Response: Sinusoidal Displacement Field The pocessing of a one-dimensional sinusoidal displacement field is an appopiate test case to examine the spatial esponse. The equations of the field ae: Π x A.sin.y λ y (3) The amplitude A is set to pixels and the wavelength λ is vaied fom 1 pixels to 1 pixels. The lage wavelength coesponds to a low spatial fequency. The geneated synthetic images ae pocessed using the SRPIV stategy combined with the Gaussian fit appoach and the IPC method. A stuctued vecto field is obtained by using the AGW method (Agui and Jimenez, 1987) to edistibute the data. Results ae compaed to the efeence PIV algoithm WIDIM (Scaano and Riethmulle, ). Inteogation aeas of 1 by 1 pixels ae coelated with an ovelap facto of 75%. This velocity field is also used as a pedicto fo the tacking pocess. As depicted in Figue 8, a sinusoidal function is then fitted with the measuements to define the measued amplitude A m. Figue 8: Methodology of the post-pocessing of the data. The spatial modulation of the diffeent techniques is defined as A m /A. The plot on Figue 9 epesents the modulation in function of the imposed wavelength λ. The diamete of the paticle images is 3 pixels and seveal values of concentation ae applied. The esults do not show significant effect of the concentation in paticles. Fo all pocessing method, the small wavelengths ae moe attenuated than the lage ones. It is obseved that the two vaiants of the SRPIV method pefom the same way. Compaing to the coelation algoithm, two modes can be obseved. Submitted to lage wavelength, the esponse of SRPIV is bette wheeas at small wavelength the opposite behaviou is obseved. The switch between these two modes happens at a wavelength of aound 37.5 pixels. It occus at the same value fo the consideed ange of concentation. It is expected that SRPIV pefoms at least the same way as PIV. A bilinea scheme is used to intepolate the PIV velocity pedicto towads the scatteed paticle positions and its effect is suspected. It is indeed expected that this intepolato is always undeestimating. Theefoe the algoithm is looking fo a paticle match in the wong egion since the pedicted position is not coect enough. This loss of paticles pai is inceased if one uses a coase PIV pedicto fo high spatial fequencies. The effect the velocity pedicto is examined on the Figue 1. The modulation of SRPIV is compaed fo two diffeent PIV pedictos. The fist one uses window size of 1 by 1 pix and 4 by 4 pix fo the second one. It is clea that, with the coase velocity pedicto, the modulation facto of the SRPIV method is lowe than in the efeence case. RTO-MP-AVT-14-7

9 Figue 9: Modulation facto of an imposed sinusoidal velocity field (D p 3 pixels). Figue 1: Effect of the velocity pedicto on the modulation facto of the SRPIV method. 4. CHARACTERIZATION OF VORTICAL STRUCTURES Votical flows ae pesent in numeous eal flows of inteest. They ae of geat industial impotance and specifically fo the aeospace industy. Stong wingtip votices behind commecial aiplanes limit the time sepaation between aicafts, which will without doubt lead to seious economic dawbacks. Reduction of this time inteval equies a pofound undestanding of these wingtip votices and hence accuate measuements. The voticity is pobably one of the most impotant paametes. The votex shedding is also a dominant featue in combustion chambes. The chaacteization of the eddies would be valuable fo the impovement of the design. Moe geneally, tubulent flows ae mainly dominated by the pesence of oganized coheent stuctues (Hussein, 1986). We popose in this section to compae the ability of hybid PIV-PTV to measue the chaacteistics of votices and to compae it to the efeence coelation PIV algoithm. Synthetic images of vitual votices ae valuable to assess the intinsic pefomances. 4.1 Imposed Velocity Field The influence of the paticle image diamete, concentation, votex adius and gadient is investigated. Fo each case, 1 images ae used. The synthetic geneated votices wee based on the Oseen-votex model, which is given in pola coodinates in the equation below: - 8 RTO-MP-AVT-14

10 RTO-MP-AVT-14-9 π Γ σ θ u e 1 u u z (4) Fom the elation above, the out-of-plane voticity component and the gadient can be calculated: ( ) ( ) ( ) ( ) max z max z z u u e 1 e u e u 1 πσ Γ ω ω ω σ + π Γ πσ Γ ω σ σ σ θ (5) Note that the maximum voticity equals two times the gadient in the cente of the votex. The gadient can be appoximated as a linea function poviding the adial distance is small enough. 4. Methodology Diffeent size of the inteogation aeas ae used duing the PIV pocessing. Indeed, since the concentation of paticles will be vaied, the dimension of these windows has adapted at each case to keep a easonable value of the coelation level. Concening the SRPIV technique, the unstuctued velocity field is edistibuted towad a egula gid (Agui and Jimenez, 1987) in ode to allow computing the voticity map. The deivative of the velocity ae computed using a cental diffeence scheme: y j 1, i j 1, i x j 1, i j 1, i z h u u h v v y u x v + + ω (6) To compae the ability to chaacteize votical flows between the diffeent image analysis appoaches, a fitting is pefomed though the diffeent data in ode to extact the maximum measued voticity (ω m ) and the dimensions (σ m ) of the imposed votex as illustated in Figue 11. Figue 11: Chaacteization of votices data pocessing methodology. 4.3 Measued Velocity Field The measued velocity field is discussed consideing a efeence case: Size of the paticle image D p 3pixels Seeding concentation C p.1 pat/pix Votex with σ 5 pixels and ω. pix/pix with a maximum imposed displacement of 3.3 pixels

11 The influence of the vaiation of the paametes is addessed in the next section. Velocity maps ae obtained and plotted in Figue 1. The cicle epesents the coe of the imposed votex. The coelationbased PIV is pefomed using windows of 1 by 1 pixels ovelapped by a facto of 75%, giving a vecto evey 3 pixels. The SRPIV povided a data evey 4.4 pixels. Since the size of the paticle spot is 3 pixels, an inteogation aea of 5 by 5 pixels is adopted fo the IPC method. All PTV fields ae edistibuted towads a egula gid of 5 pixels to compute deivatives. Although coelation based PIV etuns moe vectos, one must keep in mind that because of the lage ovelap, the vectos ae not uncoelated, which can lead to eoneous velocity/voticity data. A voticity map is plotted in Figue 13 fo all consideed pocessing method. The highe scatteing of the deivative quantity eveals the lowe level of accuacy of PTV techniques espect to the coelation appoach. Pofiles ae extacted and pesented on Figue 14. All the velocity measuements ae in ageement with the imposed votex. The pofiles of voticity confim the obsevation made on Figue 13 that the PTV measuements ae dispesed aound a tend that follows the eal flow. It is to be noted that the andom eo level seems to be simila fo the two vaiants of the PTV pocessing. Figue 1: Velocity map obtained fo a synthetic votex. The eos of the measuement using each method can be highlighted by establishing a cumulative histogam. The moe the cuve is on the left side of the gaph the moe accuate is the technique. Figue 15a demonstates that the IPC method is able to povide moe accuate measuement than the Gaussian fit appoach in PTV. The advantage of coelation-based PIV is also confimed. The situation is diffeent when consideing the edistibution of the unstuctued PTV field towads a egula gid. The limited bandwidth of e-intepolato methods intoduces some smoothing that can be valuable. The consequence is that the level of eo is deceased as showed in Figue 15b. The disadvantage of the Gaussian fit in PTV is smeaed out and the pefomances become simila to the IPC ones. In that case, it is also obseved that the - 1 RTO-MP-AVT-14

12 IPC method pefoms in a vey simila way to the PIV algoithm in tem of accuacy, keeping the advantage of the highe spatial esolution of the PTV. PIV 1 by 1 pixels (75% ovelap) SRPIV IPC 5 by 5 pixels SRPIV Gaussian fit Figue 13: Voticity map fo all consideed pocessing appoaches. Figue 14: Velocity and voticity pofiles though the cente of the votex (solid lines epesent the imposed vecto, coss-hais epesent each consideed technique). Figue 15: Cumulative histogam of eo of measuement of the velocity. 4.4 Compaison in the Chaacteization of Votices The chaacteization of votices by the diffeent consideed methods is pesented in Figue 16 fo the voticity and in Figue 17 fo the detemination of the size of the imposed votex. On each sub-gaph, a RTO-MP-AVT-14-11

13 paamete is vaied keeping the othe ones constant. Table 1 summaizes the diffeent cases. The successive consideed vaiables ae the imposed voticity (ω ), the concentation in seeding (C p ), the diamete of the paticle spot (D p ) and the size of the imposed votex (σ ). a b c d ω (pix/pix) vaied... C p (pat.pix ).1 vaied.1.1 D p (pix) 3 3 vaied 3 σ (pix) vaied Table 1: Chaacteization of votices paametes of the synthetic images. The modulation of the imposed voticity (ω m /ω ) is investigated on the uppe pat of Figue 16. The imposed voticity, the concentation and the diamete of paticles size do not have a significant influence since the modulation emains almost constant fo the consideed ange of paametes. The cuve coesponding to the two vaiants of SRPIV method ae almost supeimposed. The pefomances ae the same even though the IPC is intinsically moe accuate. It stesses again the fact that the edistibution step to a stuctued gid helps educing the andom eo. As expected, going fom a window size of 4 by 4 pixels to 1 by 1 pixels impoves the spatial esponse of the pocessing by a coelation-based PIV algoithm. The SRPIV method pesents an impovement espect to the PIV esults that can each 4% fo the consideing set of paametes. The value of the ecoveed voticity is highe than 9%. This indicates a limited modulation of the voticity. Nevetheless, when vaying the size of the imposed votex, the elative impovement of spatial esponse of the PTV is evolving. Fo instance, it anges fom 6% when σ is pixels to less than a pecent when σ is 8 pixels. Moe ove, fo a vey small stuctue (σ pix), the ecoveed voticity can dop to 91% fo the SRPIV and 85% fo the PIV. Figue 16: Chaacteization of votices measuement of the voticity. The elative eo made on the measuement of the voticity can be estimated fom the value RMS(ω m )/ω. This quantity is plotted on the lowe pat of Figue 16. In all cases, the eo is less that 1.5% and the diffeences between the methods ae not significant and ae lowe than a.5%. The PIV algoithm povides less scatteed measuement since the plotted quantity is systematically lowe. On - 1 RTO-MP-AVT-14

14 anothe hand the IPC method is slightly moe eliable than the Gaussian fit appoach. Neithe the concentation in seeding of the paticle diamete is affecting significantly the esults. Nevetheless an optimum value between 3 and 4 pixels is ecommended. The assessment of the measuement of the votex size is poposed in Figue 17. The measued size (σ m ) nomalized by the size (σ ) of the imposed votex is plotted vesus the consideed paametes. In geneal, the measued votex is systematically oveestimated because (σ m /σ ) is always lage than 1. The imposed voticity, the concentation and the diamete of paticles size do not have a significant influence since the measued size emains almost constant fo the consideed ange of paametes. PTV is oveestimating by about 1% wheeas PIV with an optimized inteogation window does by %. As expected, a lage inteogation aea (4 by 4 pixels ) is smoothing the field and one get a lage votex. Concening the eo on the votex diamete, the obsevations ae stictly simila to the one made fo the eo of the measuement of the imposed voticity. The esults ae poposed in the lowe pat of the Figue 17 fo infomation. Figue 17: Chaacteization of votices measuement of the size of the coe of the votex. 5. APPLICATION TO THE TURBULENT FLOW PAST A BFS The tubulent flow ove a backwad facing step (BFS) is a common test case adopted in expeimental fluid dynamics as well in the CFD field. Although the geomety is simple and the location of the detachment point is stable, the flow field pesents complex featues. Measuements ae taken in the plane of symmety of the test section. 5.1 Expeimental Conditions A low speed wind tunnel with a coss-section of by cm is opeated with a centifugal fan. The contaction atio of the wind tunnel is 6. A splitte plate allows using half of the total section and the RTO-MP-AVT-14-13

15 flow is blown into a channel with a section of 1 by cm. The backwad facing step geomety is ceated by an expansion of the main channel. The step height h is cm with an expansion atio ER of 1.. The flow conditions (U o 3.75m/s,ν m /s, hcm) at ambient tempeatue ensue a step-height-based Re h aound 5. A tubulent bounday laye is tigged using a sand pape and it develops along the channel. The chaacteistics of the bounday laye ae measued by Scaano and Riethmulle (1999). The bounday laye thickness δ is 1.h with a maximum tubulence intensity level (Ti bl ) of 11% inside the bounday laye and 5% in the fee steam (Ti fs ). A smoke geneato is used to seed the flow. Infomation about the expeimental conditions is summaized in Table and illustated on Figue 18. The illumination souce is a double pulsed Nd:Yag lase. It delives mj at each pulse fo a woking fequency of 1 Hz. A classical aangement is implemented to ceate a light sheet. The beam is fist expanded with a cylindical lens. A second spheical conveging lens allows getting a plane with a thickness that is less than 1mm. Then the illumination plane is folded with a pism to each the egion of inteest. Geomety Wind tunnel Bounday laye Flow conditions h H L Section U δ Ti bl Ti fs ER Re h 1 76 x % cm cm cm cm m/s h % % - - Table : BFS flow conditions Figue 18: BFS configuation. The analysed field is ecoded by a cooled CCD camea (PCO Sensicam) with a quantization in 1- bits and with a esolution of 18 by 14 pixels. The egion of inteest coveed 18 by 64 pixels. The captued egion spead ove 4h downsteam the step. Fo this configuation, the maximum fequency of acquisition is 5.71Hz. Since the lase is opeated at 1 Hz, the camea is gabbing one pai of pulses ove two at 5Hz. The maximum displacement of the paticles on the images is set to 8 pixels and it is obtained with a lase pulse sepaation of 165µs. 5. Data Pocessing Concening the pocessing of the ecodings by coelation, a compomise between spatial esolution and the numbe of validated vecto is obtained by using a coelation window of 4x4 pixels and an ovelap of 5%. In that case, less than 1% of vectos ae flagged as eoneous. The tacking method associated with the IPC appoach is able to povide a vecto evey 4.6 pixels that ae edistibuted towads a egula gid with a pitch of 5 pixels. Coheent stuctues ae identified in the velocity field obtained by the PIV pocessing accoding to the wavelet analysis method poposed by Scham and Riethmulle (1). In the identified egions, a Gaussian fit of the voticity is pefomed with the same methodology than duing the investigation of the synthetic images RTO-MP-AVT-14

16 5.3 Chaacteization of the Identified Coheent Stuctues Figue 19 pesents the esults in tem of voticity measuement. The histogams of measued voticity ae established fo the two pocessing methods that ae consideed hee. The voticity is nomalized with the step height and the fee steam velocity. The most pobable value of (ω m.h/u ) fo the SRPIV is 6 wheeas fo the PIV it is 5. In that case, SRPIV is measuing highe value of the peak voticity. Figue pesents the esults in tem of votex sizing whee, the measued size is nomalized by the step height. These histogams show that the size of the votices that is measued by PIV is lage. The most pobable value fo SRPIV is.1h and fo PIV it is.115. These esults ae coheent with the conclusions made on the synthetic images analysis: the modulation of the SRPIV is lowe than PIV and the oveestimation of the votex size done by SRPIV is lowe than PIV. Nevetheless, moe samples will be needed to have an accuate evaluation of the impovement. Figue 19: Application to the flow past a BFS histogam of the nomalized measued voticity. Figue : Application to the flow past a BFS histogam of the nomalized measued votex-size. 6. CONCLUSIONS It is always tempting to implement hybid PIV-PTV method to impove the spatial esolution of coelation appoaches. The accuacy of such method is addessed. A method based on the coelation of individual paticle images (IPC) is poposed to impove the accuacy of classical Gaussian fit. A chaacteization was done on synthetic images. It showed that, fo lage paticle images, the accuacy of the IPC is compaable with the PIV one. In that case, the advantage of PTV is that the spatial esolution scales with the spacing of the paticles and not with the window size. Synthetic images of a sinusoidal velocity field allowed evaluating the spatial esponse. An impovement of a few pecents is obtained fo the lowe pat of the spectum. It was noticed that this behaviou is inveted fom a cetain imposed spatial fequency. The influence of the intepolato of the PIV pedicto field is suspected. Indeed, this velocity field is intepolated towads the location of the tace using a simple bilinea scheme. This issue deseves theefoe futhe wok in ode to compae the potential benefit of highe ode intepolato. RTO-MP-AVT-14-15

17 The application of hybid PIV-PTV method to chaacteization of votices is pesented. The assessment on synthetic flow fields evealed that the effect of the edistibution of the scatteed PTV vecto map to a egula gid is not negligible. By using an AGW scheme, the eo is deceased by smoothing the andom eo. It allows the SRPIV associated to the Gaussian fit method to each an eo level that is compaable to the IPC appoach. In the consideed cases, the IPC stategy showed to be able to each the accuacy of a pue coelation algoithm. A geneal impovement of the modulation of the measued voticity, that is % in aveage but can ange up to 4%, is obseved. Concening the sizing of a given votex, the impovement ange fom less than 1% and eaches 1% depending on the imposed stuctues size. The tend of these obsevations can be noticed when applying the techniques to the flow ove a BFS. Nevetheless, the analysis of moe samples will be needed to have an accuate evaluation of the impovement. 7. REFERENCES [1] Adian R.J., Yao C.S. (1983), Development of pulsed velocimety fo measuement of fluid flow, Poceedings of the 8 th Symposium on tubulence, Rolla (USA), pp [] Agui J.C., Jimenez J. (1987), On the pefomance of paticle tacking, Jounal of Fluid Mechanics, 185, pp [3] Cowen E.A., Monismith S.G. (1997), A hybid digital paticle tacking velocimety technique, Expeiments in Fluids,, pp [4] Guezennec Y.G., Kiitsis N. (199), Statistical investigation of eos in paticle image velocimety, Expeiments in Fluids, 1, pp [5] Hall E.L. (1979), Compute image pocessing and ecognition, Ed. Academic Pess, New Yok. [6] Huang H.T., Fielde H.E, Wang J.J., (1993), Limitation and impovement of PIV Pat I: Limitation of conventional techniques due to defomation of paticle image pattens, Expeiments in Fluids, 15, pp [7] Hussain K.M.F. (1986), Coheent stuctues and tubulence, Jounal of Fluid Mechanics, 173, pp.33. [8] Keane R.D., Adian R.J. (199), Optimisation of paticle image velocimetes, pat 1: double pulsed systems, Measuement Science Technology, 1, pp [9] Keane R.D., Adian R.J. (1993), Theoy of coss-coelation analysis of PIV images, Flow Visualization and Image Analysis, Kluwe Academic Publishes, Edito: Nieuwstadt F.T.M., pp.1-5. [1] Keane R.D., Adian R.J., Zhang Y., (1995), Supe-esolution paticle imaging velocimety, Measuement Science Technology, 6, pp [11] Kiitsis N., (1989), Statistical investigation of eos in Paticle Image Velocimety, M.Sc. Thesis, Ohio State Univesity. [1] Maxen M., Sullivan P.E., Loewen M.R., Jähne B. (), Compaison of Gaussian paticle cente estimatos and the achievable measuement density fo paticle tacking velocimety, Expeiments in Fluids, 9, pp RTO-MP-AVT-14

18 [13] Rehm J.E., Clemens N.T., (1999), An impoved method fo enhancing the esolution of conventional double-exposue single-fame paticle image velocimety, Expeiments in Fluids, 6, pp [14] Scaano F., Benocci C., Riethmulle M.L., (1999), Patten ecognition analysis of the tubulent flow past a backwad facing step, Physics of Fluids, Vol 11, N 1, pp [15] Scaano F., Riethmulle M.L. (1999), Iteative multigid appoach in PIV image pocessing with discete window offset, Expeiments in Fluids, 6-6, [16] Scaano F., Riethmulle M.L. (), Advances in iteative multigid PIV image pocessing, Expeiments in Fluids, 9-S1, [17] Scaano F., (), Review aticle: Iteative image defomation methods in PIV, Measuement Science and Technology, 13, pp.r1-r9. [18] Scham C., Riethmulle M.L., 1, Votex ing evolution in an impulsively stated jet using digital PIV and continuous wavelet analysis, Measuement Science and Technology, Vol 1, N 9, pp [19] Stanislas M., Okamoto K., Kähle C. (3), Main esults of the Fist intenational PIV Challenge, submitted to Measuement Science Technology. [] Stitou A., Riethmulle M.L. (1), Extension of PIV to supe-esolution using PTV, Measuement Science Technology, 1, pp [1] Stitou A., Theunissen R., Riethmulle M.L. (3), Advances in hybid PIV-PTV techniques and application to votical flows, Poceedings of the EUROPIV Wokshop on PIV, Zaagoza (Spain), Mach 31-Apil 1. [] Takehaa K., Etoh T. (1999), A study on paticle identification in PTV- paticle mask coelation method, Jounal of Visualization, 1, [3] Takehaa K., Adian R.J., Etoh G.T., Chistensen K.T. (), A Kalman tacke fo supeesolution PIV, Expeiments in Fluids, 9-S1, [4] Udea D.D., Byanston-coss P.J., Lee W.K., Funes-Gallanzi M. (1996), Two sub-pixel pocessing algoithms fo high accuacy paticle cente estimation in low seeding density paticle image velocimety, Optics and Lase Technology, 8-5, [5] Weeley S.T., Meinhat C.D., (1), Second-ode accuate paticle image velocimety, Expeiments in Fluids, 31, pp [6] Wenet M.P., Pline A. (1993), Paticle displacement tacking technique and Came-Rao lowe bound eo in centoid estimates fom CCD imagey, Expeiments in Fluids, 15, [7] Westeweel J., (1997), Fundamentals of digital paticle image velocimety, Measuement Science Technology, 8, pp [8] Zimme L., Buchlin J.-M., Riethmulle M.L. (1999), Paticle Tacking Velocimety and Sizing: Application to liquid spays, Poceedings of the Intenational Wokshop on Paticle Image Velocimety, Santa-Babaa (USA), Sept RTO-MP-AVT-14-17

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