Statistical Characterization of Helium-Filled Soap Bubbles Tracing Fidelity for PIV

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(1)Delft University of Technology. Statistical Characterization of Helium-Filled Soap Bubbles Tracing Fidelity for PIV Morias, Koen; Caridi, Giuseppe Carlo Alp; Sciacchitano, Andrea; Scarano, Fulvio. Publication date 2016 Document Version Final published version Published in Proceedings of the 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics. Citation (APA) Morias, K., Caridi, G. C. A., Sciacchitano, A., & Scarano, F. (2016). Statistical Characterization of HeliumFilled Soap Bubbles Tracing Fidelity for PIV. In Proceedings of the 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics Lisbon, Portugal: Springer. Important note To cite this publication, please use the final published version (if applicable). Please check the document version above.. Copyright Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim.. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10..

(2) PROCEEDINGS OF THE. 18th INTERNATIONAL. SYMPOSIUM ON APPLICATION OF LASER AND IMAGING. TECHNIQUES TO FLUID MECHANICS.

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(4) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . . . !

(5) 1)014-%5-75)22)%4-(-0(4)% '-%'',-6%017.8-1 '%4%01 )261*)4152%')0+-0))4-0+).*6"0-8)45-691*!)',01.1+9).*6!,))6,)4.%0(5 144)5210()06%76,14 +'%4-(-67().*60. . %4+)5'%.)#64%'-0+*-().-69).-7/*-..)(51%2&7&&.)5. !! The p resent w ork follow s a p reviou s stu d y on the aerod ynam ic characterization of heliu m -filled soap bubbles (H FSBs) for large-scale PIV m easu rem ents. H FSBs w ere fou nd to yield , on average, a tim e resp onse of abou t 10Ps. H ow ever, the resp onse of each ind ivid u al tracer remained to be ascertained , w hich is the top ic of the p resent stu d y. The velocity of the bu bbles in the stagnation region ahead of a circu lar cylind er is evalu ated by the PTV techniqu e. The resu lts are com p ared w ith m icro-size fog d rop lets taken as reference. The tracking error of ind ivid u al trajectories is assessed by statistical analysis of the relative slip betw een the bu bble and the airflow . The instantaneou s p article relaxation tim e is retrieved from the ratio betw een slip velocity and local acceleration . Ad d itional inform ation on the bu bble instantaneou s p rop erties is taken by inferring the d iam eter from the d istance betw een the glare p oints. The resu lts are d iscu ssed and related to the d ifferences observed in the bu bbling and jetting regim es for bu bble p rod u ction. Finally, the H FSBs relative d ensity to the air is estim ated u sing a m od ified Stokes d rag law .. 1. Introduction Since the introd uction. of Tom ographic Particle Im age Velocim etry (Tom o-PIV), the. m easurem ent volum e has been recognized as a m ajor bottleneck d ue to the lim itation of laser pulse energy and the constraints on im aging d epth of focus (Scarano 2013). The use of lasers w ith pulse energy up to 1 J has m arginally increased the volum e w ith respect to the first experim ent cond ucted by Elsinga et al. (2006), w here the velocity w as m easured in a d om ain of 3.53.50.7 cm 3. Instead , experim ents in w ater flow s could be cond u cted at significant larger size by using large neutrally buoyant tracers. The little energy scattered by m icro-size tracers can be consid ered as the m ain lim itation preventing the upscale of Tom o-PIV and its d eployment for ind ustrial aerod ynam ics. The use of sub-m illim eter helium -filled soap bubbles (H FSBs) as tracer particles has show n to overcom e this lim itation. With a d iam eter (300-500 µm ) tw o ord ers of m agnitud e larger than the conventional seed ing particles, the am ount of scattered light enables the m easurem ent over a m easurem ent volum e several ord ers of m agnitud e larger (Carid i et al. 2015)..

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(7) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . The first analysis on the tracking fid elity of HFSBs w as perform ed by Kerho and Bragg (1994) in the stagnation region of a N ACA0012 airfoil. Bubbles w ith d iam eter varying betw een 1 and 5 m m w ere used . H ow ever, the use of a device filtering heavier bubbles caused the average d ensity of bubbles to becom e slightly lighter -than-air causing a m arked d eparture from the stream lines of the airflow . The conclusion w as that H FSBs d id not qualify for quantitative m easurem ents in aerod ynam ics. Bosbach et al. (2009) introd uced a novel bubble generator d eveloped by the Germ an Aerospace Center (DLR) capable of prod u cing bu bbles of 0.2 to 0.6 m m w ith a high production rate (50,000 bubbles/ s). Planar PIV m easurem ents on the m ixed 2. convective flow in a full scale airplane cabin m ock -u p (measurem ent d om ain of 7 m ) d em onstrated their effectiveness as flow tracers. A large-scale tom ographic application is reported by Kuhn et al. (2011) ad d ressing the three-d im ensional flow field in a rectangular 3 convective cell over a volum e of 754516.5 cm .. The tracing fid elity of these bubbles has been stud ied recently by Scarano et al. (2015). The bubbles velocity in the stagnation region of a cylind er w as com p ared w ith that of m icro-size d roplets, taken as reference for the airflow . H FSBs can be prod uced approaching neutral buoyancy and exhibiting a m ean relaxation tim e of about 10 Ps. Furtherm ore, the authors. d em onstrated the potential to em ploy these tracers for large-scale tim e-resolved tomographic PIV w ith a m easurem ent in a volum e of 202012 cm 3 in the w ake of a cylind er of 4.5 cm . Later, Carid i et al. (2015) d eveloped a d ed icated seed ing system to increase the concentration of tracers for large-scale experim ents in w ind tunnels reaching a m easurement volum e of 16,000 cm . The use of H FSBs for large-scale experim ents is also d ocum ented in the w ork of Schneid ers et al. (2015) w ho used the bubbles to reconstruct the instantaneous flow pressure in the w ake of a cylind er-flat plate by tim e-resolved Tom o-PIV measurem ents. Som e questions rem ain open concerning the aerod ynamic behaviour of H FSBs. First, Scarano et al. (2015) report only the ensem ble average relaxation tim e of the HFSBs. It is not know n to w hat extent ind ivid ual bubbles d epart from the m ean. This aspect is of prim ary im portance to valid ate the use of H FSBs for velocity fluctuations and turbulent statistics. Furtherm ore, the results reported on the tracing behaviour of the bubbles rely on the hypothesis of Stokes flow theory, w hich is only valid at Reynold s num ber w ell below unity. The latter is d efined as:. . U u u P. (1). w here up and dp and are the particle velocity and d iam eter, respectively. The sym bol uf refers to the flow velocity. The d ifference betw een particle velocity and fluid velocity is referred to as slip velocity. Density and d ynam ic viscosity of the fluid are expressed by ȡf and µf, respectively. When.

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(9) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . the specific d ensity of a bubble ߩҧ (ratio of bubble d ensity over fluid d ensity) d eviates from unity. and the d iam eter increases, a finite slip velocity arises and the assu m ption Re p<<1 m ay no longer be valid . In this cond ition, the bubble m otion relative to the air is not in the Stokes flow regim e and the equation of motion read s as (Mei, 1996):. u S U . SP ) .

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(11). u. u S U . (2). In Equation (2), gravity force, ad d ed -m ass force, tim e-history force and Magnus force have been neglected . The term on the left-hand sid e is the particle inertia. The right-hand sid e contains the quasi-stead y d rag force and the pressure force. The term s are expressed in function of particle rad ius a. The tem poral d erivative D/ Dt is expressed follow ing a fluid elem ent, w hereas d / d t is consid ered along the particle path. Th e quasi-stead y d rag force d iffers from the viscous Stokes d rag by an em pirical correction factor ݊(Re p)1, w hich accounts for the finite particle Reynold s num ber. An overview of the available correction factors and their accuracy is given by Clift et al. (1978). The present w ork aim s at characterizing statistically the tracing fid elity of H FSBs in PIV experim ents. The tracing capability of the bubbles is stud ied consid ering the statistical d istribution of the bubbles’ d iam eter, slip velocity, relaxation tim e and d ensity. The analysis w ill account not only for the viscous Stokes d rag, but also for quasi-stead y d rag at finite Re p. The contribution of the latter w ill be evaluated in the slip velocity and particle response tim e. An experim ent is perform ed at a spatial resolution such to d eterm ine sim ultaneously the bubbles trajectory and their d iam eter. Based on the relaxation tim e, the stud y w ill d eterm ine the tracing fid elity expected from ind ivid ual bu bbles and its d epend ence upon the bubble generation regim e. 2. Experimental Setup The experim ent is cond ucted in the W-tunnel, an open-jet open-return facility of the Aerod ynam ics Laboratories of TU Delft. The tunnel has a test section of 4040 cm w ith a free stream turbulence level of approxim ately 0.5% at 20 m / s. The m od el is a circular cylind er w ith a d iam eter of 40 m m . A sp litter plate, w ith a length of 7 cylind er d iam eters and a thickness of 2 m m , is attached to the aft of the cylind er preventing the von Kárm án vortex shed d ing and the resulting fluctuations of the stagnation point. Experim ents are cond ucted at freestream velocity V =20 m / s. The stagnation region in front of the cylind er.

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(13) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . features an irrotational, stead y, tw o-d im ensional, incom pressible flow , w hich can be accurately m od elled w ith potential flow theory. Figure 1-right illustrates the experim ental setup . The im aging system consists of a Photron Fast Cam SA1 cam era (CMOS, 1,0241,024 pixels, 12bit, pixel pitch 20 µm ). The cam era is equip ped w ith a 105 m m N ikkor objective w ith aperture settings of f/ 5.6 (for m easurem ents w ith fog d roplets) and f/ 16 (for m easurem ents w ith H FSBs). The sensor is cropped to 704336 pixels. The field of view is 3.411.63 cm , yield ing an optical m agnification of 0.41. The illum ination is provid ed by a Quantronix Darw in -Duo N d :YLF laser w ith nom inal pulse energy of 225 m J at 1 kH z. The reference velocity field is obtained by PIV m easurem ents w ith m icro-size fog d roplets, generated by a SAFEX Tw in Fog sm oke generator (med ian particle d iam eter of 1 µm ). A set of 3,000 d ouble-fram e im ages is acquired at a frequency of 250 H z w ith a t im e separation of 38 µs. Im age pre-processing and cross-correlation are perform ed w ith LaVision Davis 8.2. The final interrogation w ind ow size is 1616 pixels and the overlap is 75%. This results in a vector pitch of approxim ately 0.2 m m. For the H FSBs m easurem ents, 20,000 single-fram e im ages are acquired at an acquisition frequency of 20,000 H z. The experim ental setup follow s that used for the fog m easurem ents. A single LaVision bubble generator (prod uction rate of 50,000 bu bbles/ s) is installed in the settling cham ber of the w ind tunnel in sid e a N ACA0012 airfoil (chord length of 12 cm ) to m inim ize the aerod ynam ic intrusiveness of the seed ing probe (Figure 1-left). The bubble d iam eter and d ensity is controlled by varying the pressure of the bubble fluid solution (BFS) m ixture, helium and air flow through the supply unit of the bubble generator. For a d etailed d escription of the w orking principle of the bubble generator, the read er is referred to Bosbach et al. (2009)..

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(17) . Fig. 1 Exp erim ental setu p . Left: bu bble generator in settling cham ber. Right: test section..

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(19) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . 3. Methodology 3.1 V elocity and A cceleration Velocity and acceleration m easurem ents of the H FSBs are carried out using the Particle Tracking Velocim etry (PTV) technique. The particle-tracking algorithm is based on that of Malik et al. (1993). Sub-pixel accuracy is applied by fitting a Gaussian intensity through the intensity peaks of the im age particles. The position of the tracer along its trajectory is regularized fitting the m easured values w ith a third ord er polynom ial. Each fit m akes use of seventeen consecutive im ages. The first tim e-d erivative of the polynom ial yield s the velocity and the second tim e d erivative gives the Lagrangian acceleration at the particle location . The reference flow velocity is obtained via a cross-correlation of the PIV im ages obtained w ith fog droplets as tracers. A com parison of the velocity and acceleration along the stagnation line is perform ed , w here the fluid and the tracers therein und ergo one-d im ensional d eceleration. For the H FSBs, the m ean velocity and acceleration of all the bubbles are computed by averaging the instantaneous values w ithin a box of 24 p ixels height (sym m etric around the stagnation stream line) an d 15 pixels stream w ise length. The reference velocity from fog d roplets is interpolated to the bubble position and averaged w ithin the sam e control volum e as that used for H FSBs. The Lagrangian acceleration of the flow is d efined as:. u . wu u u w. w here the first term of the right-hand sid e is zero d ue to the stead y flow field . Thus, the. Lagrangian acceleration can be evaluated solely by the convective term u u . The velocity grad ient in Equation (3) is obtained w ith a second ord er central finite d ifference schem e. 3.2 Bubble Diameter Each bubble is visible through tw o glare points (van d e H ulst and Wang, 1992). In the present experim ent the view ing axis is perpend icular to the illum ination d irection. Therefore, the relation betw een the bubble d iam eter dp and the d istance betw een the im age of the glare points dG read s as:. dp. 2dG . 3.3 Tracing Fidelity The particle relaxation tim e Ĳp can be com puted as:.

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(21) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . . Wp. up u f u u. . When the assum ption of Stokes flow regime d oes not hold strictly, the relaxation tim e is no longer a constant, but it varies in the flow field d epend ing on the local acceleration and associated slip velocity. An expression of the relaxation tim e that includ es an em pirical d rag correction factor is given below . The correction factor used in this w ork is the one by Schiller and N aum ann (1933), w hich expand s the range of valid ity to Re p < 800:. Wp. d p2 U p U f. 18. Pf. 1 ) Re p

(22). The above expressions are true und er the assum ption that the fluid acceleration equals the particle acceleration and that gravity and history force can be neglected . 3.4 Bubble density The bubble d ensity is retrieved by solving Equation (6) for ȡp. The bubble d iam eter is m easured as d escribed in section 3.2. The slip velocity and thus the p article Reynold s num ber is d eterm ined by calculating the d ifference betw een the bubble velocity and the reference velocity field (section 3.1). The particle relaxation tim e is m easured as given in Equation (5). Finally, the d ensity of the surround ing fluid air is calculated using the perfect gas law (pressure and tem perature w ere record ed d uring the laboratory experiments). 4. Bubble formation regimes The generation process of H FSBs has d irect effects on PIV m easurem ents w here the bubbles are used as tracers. As d iscu ssed by Melling (1997), d iam eter and d ensity of the seed ing particles d efine their tracking capabilities. As a consequence, tracers w ith m onod isperse d istribution in size and d ensity are preferable for m ore accurate m easurem ent s. H FSBs are generated w ith an orifice-type nozzle, as d escribed by Bosbach et al. (2009). The d esign of the present nozzle w as d eveloped in ord er to prod uce bubbles in a so-called co-flow configuration, also com m only used for air bubble prod uction in w ater flow s (Sevilla et al. 2005a). Sevilla et al. (2005b) and Gañán-Calvo et al. (2006) d iscu ssed the im portance of the velocity ratio betw een the co-flow ing fluid s for a stable and continuou s bubble prod uction. Tw o d ifferent form ation regim es w ere id entified : bubbling and jetting. The latter is characterized by a long cylind rical ligam ent of the d iscrete phase that breaks up far from the exit of the generator. This.

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(24) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . resu lts in an aperiod ic and polyd isperse bubble prod uction. Conversely, the bubbling regim e features a fairly periodic and stable form ation of the bubbles at the exit of the nozzle. In the present w ork, the H FSB generator show s sim ilar w orking regim es to those m entioned above. The d etails of H FSB form ation at the exit of the nozzle are inspected w ith high-speed shad ow graphy at 90 kH z, w ith continuous illum ination. The results in Figure 2 illustrate an exam ple of the stable bubbling regim e w ith rather m onod isperse size d istribution (Figure 2a). The visualizations also reveal the form ation of sm all d roplets at the m om ent of d etachm ent, either insid e or outsid e the bubble. Although irrelevant for the bubble d iam eter, this phenom enon m ay affect the d ispersion of bubble w eight. In the observed bubbling regim e, H FSBs are ejected w ith a velocity of 20 m/ s and w ith an average separation d istance of 440 µm betw een each other; hence, the prod uction rate is estim ated to be approxim ately 50,000 bubbles per second . When the bubble generator operates in the jetting regim e, a quasi-cylind rical interface of BFS protrud es from the exit of the nozzle. It w as observed that the cylind rical film is affected by large scale flu ctuations and occasionally breaks up into bubbles far from the orifice. The resulting bubbles are characterized by a broad er d istribution in d iam eter, as illustrated in Figure 2b.. Fig. 2 H igh sp eed visu alization of H FSB p rod u ction in bu bbling (a) and jetting regim e (b).. 5. Experimental Results N eutrally buoyant helium -filled soap bu bbles are generated suppling flow rates of q bfs=4.78 m l/ h, q H e=4.83 l/ h and q sa=115.30 l/ h, w here bfs, He and sa ind icate bubble fluid solution, helium and second ary air, respectively. The heavier-than-air bubbles are generated w ith air instead of H elium insid e the bubbles. The m ean velocity and acceleration profiles of neutrally buoyant and heavier-than-air bubbles on the stagnation stream line at a freestream velocity of 20 m / s are illustrated in Figure 3. The results are show n w ith the reference d ata obtained by PIV m easurem ents w ith fog d roplets. The uncertainty is illustrated w ith error bars that represent the stand ard d eviations of the m easurem ents. Figure 3 show s that the m ean velocity and acceleration profile of the neutrally buoyant bubbles are in agreem ent w ith those of the fog m easurem ents. The heavier-than-air bubbles profile exhibits the expected offset, ind icating a d elayed response to the d ecelerating flow and confirm ing the observations of Scarano et al. (2015). This d elay is also clearly visible in the acceleration profile, w here heavier-than-air bubbles exhibit low er acceleration for x/ D < -0.7..

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(26) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . . Fig. 3 Mean velocity (left) and acceleration (r ight) p rofiles on the stagnation stream line ahead the cylind er.. . Largely heavier-than-air (air-filled ) soap bubbles are consid ered first, having a specific d ensity of about 1.3. The slip velocity and relaxation tim e of these bubbles are show ed in Figure 4. Since the bubble velocity and acceleration are d eterm ined by m eans of PTV, they feature low m easurem ent uncertainty. Rand om m easurem ent errors on the bubble position are strongly red uced by fitting a third -ord er polynom ial through the series of seventeen d ata points. The reference velocity field is com puted as the tim e-average of 3,000 instantaneous uncorrelated velocity field s. The turbulence intensity of the w ind tunnel is m easured to be 0.5% at a freestream velocity of 20 m / s. Since the bubble record ings and the fog d roplet m easurem ents are not m ad e sim ultaneously, velocity d ifferences up to ±0.1 m / s can occur that are not d ue the aerod ynam ic behaviour of the bu bbles, but solely to the freestream turbulence intensity. This uncertainty in the slip velocity calculation is ind icated by black d ashed lines in Figure 4. The light-blue d ots represent ind ivid ual bubble record ings, w hile the red line is the m ean of all record ings and the error bars ind icate one stand ard d eviation of the d istribution..

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(28) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . . Fig. 4 Slip velocity (left) and relaxation tim e (right) of ind ivid u al bu bbles on the stagnation line of the cylind er for heavier-than-air air-filled soap bu bbles. Black d ashed lines ind icate the u ncertainty d u e to the freestream tu rbu lence intensity.. . In the range x/ D=[-1.1 -0.7], the acceleration approximately doubles (see Figure 3-right). Since the correction factor Ȱ d epend s on the particle Reynold s num ber less than linearly (Schiller and. N eum ann, 1933), the relaxation tim e can be assum ed constant for sm all variations of the slip. velocity. Assum ing a constant relaxation tim e Wp , also the slip velocity is expected to d ouble. The results of Figure 4-left show an approxim ately linear increase of the slip velocity. While the m ean value of u slip d oubles in the consid ered x/ D range, the stand ard d eviation instead has a sm aller increase. This result is ascribed to the slight overestim ation of the slip velocity d ue to the effect of freestream turbulence. This effect is larger aw ay from the cylind er (x/ D < -0.9), w here the slip velocity is expected to be low er. For the sam e reason , the stand ard d eviation of the relaxation tim e is probably overestim ated w hen com puted far aw ay from the cylind er (see Figure 4-right). The results are further analysed in the interval x/ D=[-0.75 -0.65], w here the flow d eceleration is the strongest, resu lting in the largest slip velocity and the low est relative influence of freestream turbulence intensity. H ere the average slip velocity is approxim ately 0.7 m / s w ith a stand ard d eviation of 0.26 m / s, giving a m ean relaxation tim e of approxim ately 98 ȝs w ith a stand ard d eviation of 38 ȝs. This ind icates the poor tracing fid elity of air-filled soap bubbles and further confirm s the need of H elium as filling gas to counterbalance the w eight of the soap film . The slip velocity and relaxation tim e of nearly neutrally buoyant HFSBs are analysed in Figure 5. Those bubbles have a specific d ensity of about 0.97..

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(30) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . . Fig. 5 Slip velocity (left) and relaxation tim e (right) of ind ivid u al bu bbles on the stagnation line of the cylind er for neu trally bu oyant heliu m -filled soap bu bbles. Black d ashed lines ind icate the u ncertainty d u e to the freestream tu rbu lence intensity.. The m ean slip velocity is approxim ately zero for x/ D < -0.9 and slightly increases approaching the cylind er. The uncertainty d ue to the turbulence intensity is again ind icated w ith black d ashed lines. The m agnitud e of the slip velocity and the uncertainty d ue to the turbulence intensity are of the sam e ord er . For the sam e reason as before, the results are analysed in the interval x/ D=[-0.75 -0.65]. The m ean slip velocity is around 0.05 m / s w ith a stand ard d eviation of 0.25 m / s, yield ing a m ean relaxation tim e of less than 10 ȝs, w ith a m ore significant stand ard d eviation of approxim ately 40 ȝs. The relaxation tim e in Figure 5-right is m ultiplied by the sign of the slip velocity. As a result, lighter than air H FSBs exhibit a negative response. Com bining the latter inform ation w ith the measurem ent of the bubble d iam eter , it is possible to d eterm ine the bubble d ensity from the d efinition of the relaxation tim e (see Section 3.4). As d epicted in Figure 6-left, the statistical d istribution of the m easured bubble d iam eter is approxim ately Gaussian . The average bubble d iam eter is 370 µm . This correspond s to an average glare point d istance of 7.7 pixels. The stand ard d eviation of the d istribution is 16 µm or 0.33 pixels. Therefore the d istribution is m onod isperse, ind icating that the nozzle operates in the bubbling regim e and prod uces bubbles w ithin 5% variations in d iam eter. The uncertainty of the bubble d iam eter is d eterm ined by d ivid ing the stand ard d eviation of the d iam eters of all the record ings of each bubble by the square root of the num ber of record ings of that bubble. The histogram of the d iam eter m easurem ent uncertainty in Figure 6-right approxim ates a Poisson d istribution w ith its p eak at 2.6 µm or 0.054 pixels. H ence, the m easurem ent uncertainty is less than 1 % of the bubble d iam eter. As a result, the m easured 5% v ariation in d iam eter show ed in Figure 6-left is d ue to a bubble prod uction process that is not perfectly repeatable.. .

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(32) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . . Fig. 6 H FSB d iam eter statistics. Left: d iam eter d istribu tion. Right: d iam eter u ncertainty.. Know ing the relaxation tim e and the bubble d iam eter, the bubble d ensity can be d eterm ined . The d ensity is calculated for each bu bble ind ivid ually, w ith its ow n relaxation tim e and d iam eter. Figure 7 illustrates the bubble d ensity of each bubble along the stagnation line of the cylind er. In the interval x/ D=[-0.75 -0.65] the m ean d ensity value of the H FSBs is found to be 1.18 kg/ m and the stand ard d eviation is m easured to be 0.16 kg/ m . The d ensity of air in the laboratory w as 1.213 kg/ m , giving a specific d ensity ߩҧ = 0.97 ± 0.13. 3. . Fig. 7 Bu bble d ensity of ind ivid u al bu bbles on the stagnation line of the cylind er for neu trally bu oyant heliu m -filled soap bu bbles.. The sam e approach is applied to helium -filled soap bubbles and air-filled soap bu bbles (AFSBs) w ith d ifferent supply flow rates. The results are sum marised in Table 1. From the first three com binations a higher ratio q bfs/ q H e (i.e. m ore soap per unit volum e helium ) increases the d ensity.

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(34) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . of the bubble. A higher q bfs also seem s to have a stabilizing effect on the d ispersion in bubble d iam eter for a constant flow rate of air. This is visualised in Figure 8-left, w here an increase of q bfs results in a low er spread of the bubbles’ d iam eter . At q sa=163 l/ h (H FSB 4 and AFSB 7), an unstable bubble prod uction is reported , w hich is ascribed to the jetting regim e. The bubble d iam eter d istribution at this cond ition is rather broad and non -Gaussian, as illu strated in Figure 8-right for H FSB 4. As a resu lt, the statistical values of bu bble d iam eter and d ensity exhibit a relatively large stand ard d eviation .. . Fig. 8 The influ ence of the q bfs on the bu bble d iam eter statistics (left) and an exam p le of the u nstable bu bble p rod u ction for H FSB 4 (right).. From the d iam eter observations in H FSB 1 and 2, it is fou n d that the volum e flow rate of H elium has a m inor effect on the d iam eter. A higher H elium flow rate w ill slightly increases the bubble d iam eter. In case of stable prod uction, a higher volum e flow rate of the second ary airflow in the nozzle ind uces sm aller bubbles, w hile a low er volum e flow rate m akes the bubbles bigger. This is confirm ed by the d iam eter observations of H FSB 5 and H FSB 4, although the latter has an unstable prod uction. Consequently, the prod uction rate of the bu bbles d epend s on the flow rate of air. Table. 1 Diam eter, relaxation tim e and d ensity statistics for d ifferent helium -filled soap bu bbles. N ame H FSB 1 H FSB 2 H FSB 3 H FSB 4 H SFB 5 AFSB 6 AFSB 7 AFSB 8. q He [l/h]. q bfs [ml/h]. q sa [l/h]. 4.78 4.14 4.78 4.78 4.78 5.23 5.23 3.79. 4.83 5.73 3.35 4.83 4.83 4.83 4.83 4.83. 115.30 115.30 115.30 162.57 77.49 115.30 162.57 77.49. D iameter [ȝm] Mean ȝ SD ı 370.7 16.0 359.3 9.8 373.5 25.1 302.9 62.0 542.6 54.0 437.2 23.7 365.3 72.4 549.3 11.3. Relaxation time ୳౩ౢ౟౦ ߬୮ ή [ȝs] ห୳౩ౢ౟౦ ห. Mean ȝ -6.8 12.8 -44.4 -24.6 -39.6 98.1 87.7 193.0. SD ı 38.9 39.3 33.7 32.5 51.5 37.3 38.4 42.2. ഥ [-] D ensity ratio ࣋ Mean ȝ SD ı 0.974 0.131 1.044 0.141 0.844 0.129 0.931 0.191 0.915 0.123 1.304 0.148 1.320 0.237 1.532 0.164.

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(36) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . 5. Conclusion This w ork presents a statistical characterization of the tracing fid elity of H FSBs for PIV experim ents. H igh-speed visualization s id entify tw o d ifferent operating regim es of the bubble generator. In the bubbling regim e, H FSBs are prod uced in a stable w ay and the bubbles’ properties are rather m onod ispersed . Conversely, the jetting regim e is u nstable w ith a broad d istribution of the bubble d iam eter . The latter is measured ind epend ently from the d istance of the glare points of ind ivid ual bubbles. The relaxation tim e w as calculated experim entally for the bubbles along the stagnation line of a cylind er. Through m easurem ents of the relaxation tim e and the bubbles’ d iam eter, the d ensity of H FSBs w as com p uted . Both stable and u nstable prod uction regim es w ere d etected in the results. When the bubble generators operate in a stable prod uction regim e, variations of the bubble d iam eter below 5% are observed . For neutrally buoyant bubbles, the m ean value of the relaxation tim e is of the ord er of 10 µs, w hich agrees w ell w ith the previous results of Scarano et al. (2015). H ow ever, even in these cond itions, the stand ard d eviation of the relaxation tim e exceed s 30 µs. When the bubbles’ prod uction regim e is unstable, the stand ard d eviation of the bubble d iam eter and relaxation tim e can be as high as 70 µm and 50 µs, respectively. These results ind icate that the current bubble prod uction system s yield H FSBs allow ing accurate m easurem ents of the tim e-averaged velocity field . Conversely, caution should be taken concerning the accuracy of the instantaneous and fluctuating flow properties, w hich are d irectly linked to the spread of the relaxation tim e of ind ivid ual bubbles and strongly d epend s upon the tim e scales of the specific flow that is in vestigated . Acknow ledgement Jan Schneid ers is acknow led ged for supporting the particle tracking velocim etry analysis. LaVision Gm bH is kind ly acknow led ged for provid ing the H FSB generation system . Bibliography Bosbach J, Kühn M, Wagner C (2009) Large scale particle image velocim etry w ith helium filled soap bu bbles. Exp Fluid s 14: 2719-2737 Carid i GCA, Ragni D, Sciacchitano A, Scarano F (2015) A seed ing system for large -scale tom ographic PIV in aerod ynam ics. P 11th Int Sym p PIV, 14-16 Septem ber, Santa Barbara, USA Clift R, Grace JR, Weber ME (1978) Bubbles, d rops and particles. Acad em ic Press, N ew York, USA.

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(38) 6,06)40%6-10%. 9/215-7/106,)22.-'%6-101*%5)4%0(/%+-0+!)',0-37)561.7-()',%0-'5࣭ :!"࣭"$ – . Elsinga G, Scarano F, Wieneke B, van Oud heusd en B (2006) Tom ographic particle im age velocim etry. Exp Fluid s 41:933-947 Gañán-Calvo AM, H errad a MA, Garstecki P (2006) Bubbling in unbound ed coflow ing liquid s. Phys Rev Lett 96(12):124504 Kerho M, Bragg M (1994) N eutrally buoyant bubbles u sed as flow tracers in air. Exp Fluid s 16:393-400 Kuhn M, Ehrenfried K, Bosbach J, Wagner C (2011) Large-scale tom ographic particle im age velocim etry using helium -filled soap bubbles. Exp Fluid s 50:929-948 Malik N , Dracos T, Papantoniou D (1993) Particle tracking velocim etry in three d im ensional flow s. Exp Fluid s 15:279-294 Mei R (1996) Velocity fid elity of flow tracer particles. Exp Fluid s 22:1-13. Melling A (1997) Tracer particles and seed ing for particle im age velocim etry. Meas Sci Technol 8(12):1406. Scarano F (2013) Tom ographic PIV: principles and practice. Meas Sci Technol 24(1):012001. Scarano F, Ghaem i S, Carid i GCA, Bosbach J, Dierksheid e U (2015) On the use of helium filled soap bubbles for large-scale tom ographic PIV in w ind tu nnel experim ents. Exp Fluid s 56:42. Schiller L, N aum ann A (1933) Über d ie gund legend en. Berechungen bei d er. Schw erkraftaufbereitung. Zeitsch Ver Dtsch Ing 77:318-320 Schneid ers JFG, Carid i GCA, Sciacchitano A, Scarano F (2015) Instantaneous pressure m easurem ents from large-scale tom o-PTV w ith H FSB tracers past a surface-m ounted finite cylind er. P AIAA Scitech Conf 2016, 4-8 January 2016, San Diego, California, USA Sevilla A, Gord illo JM, Martinez-Bazan, C (2005a) Bubble form ation in a coflow ing air w ater stream . J Fluid Mech 530:181-196 Sevilla A, Gord illo JM, Martínez-Bazán C (2005b) Transition from bubbling to jetting in a coaxial air–w ater jet. Phys Fluid s 17(1):018105 van d e H ulst H , Wang R (1992) Glare points. Appl Opt 30:4755-4763.

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