Evaporating droplets tracking by holographic high speed video in turbulent flow
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1 Evaporating roplets tracking by holographic high spee vieo in turbulent flow Loïc Méès 1*, Thibaut Tronchin 1, Nathalie Grosjean 1, Jean-Louis Marié 1 an Corinne Fournier 1: Laboratoire e Mécanique es Fluies et 'Acoustique, UMR CNRS 5509, Ecole Centrale e Lyon, Université e Lyon, France : Laboratoire Hubert Curien, UMR CNRS 5516, Université Jean Monnet, Université e Lyon, France * Corresponent author: loic.mees@ec-lyon.fr Keywors: Holography, Inverse Problem, Droplet Evaporation, Turbulent flow ABSTRACT The evaporation rate of iethyl ether roplets ispersing in a Homogeneous an isotropic (HI) turbulence is measure by following roplets along their trajectory. Measurements are performe at ambient temperature an pressure by using in-line igital holography. The holograms of roplets are recore with a single high-spee camera (3kHz) an reconstructe with an inverse problems approach (IPA). IPA provies a measurement of roplet size an location accurate enough to follow the ynamic of the roplets in 3 imensions as well as their instantaneous evaporation rate though their size evolution. In aition, the thermal-vapor concentration wakes eveloping aroun the roplets are visible on holograms. It is foun that these wakes when reconstructe using a classical back light propagation metho are aligne with the relative Lagrangian velocity seen by the roplets at each time. The relative velocity can be calculate from the roplets equation of motion an the positions an iameter measure by holography an IPA processing, when the orientation of the wake is inepenently euce from the phase retrieval of the vapor wake. Droplets trajectories an time evolution of iameter an relative velocity are presente. In a number of cases, the evaporation rate of the roplets changes along the trajectory an eviates from that calculate with a stanar film moel, showing that turbulence may influence significantly the evaporation process. 1. Introuction In many practical situations roplets vaporize in turbulent flow. It is then of primary importance to know whether or not turbulence influences evaporation (Birouk an Gokalp 006; Reveillon an Demoulin 007). The most physically relevant approach to investigate this question is to aopt a Lagrangian point of view an measure the phase change of the roplet by following its iameter evolution along its trajectory. This is the objective that we aim to achieve with the experiments presente here. Diethyl Ether roplets are release in a homogeneous isotropic an strong turbulence prouce by synthetic jets as escribe in (Goepfert et al 010). One interest of this situation is that the parameters of the turbulence are well controlle. The Lagrangian tracking metho that has been chosen is in-line igital holography associate with an Inverse
2 Problem Approach (IPA). This approach provies the highly accurate measurement of roplet size an position require for both roplet tracking an evaporation rate measurement at a relatively large istance. The paper is organize as follow. After this introuction, section gives a short escription of the holographic setup. The hologram processing is escribe in section 3. Holograms are first processe using an inverse problem approach (IPA) to etect the roplet an to measure their 3D position an iameter. A secon reconstruction process, base on a stanar back light propagation metho is then apply to the resiual images to reconstruct the wake of vapor aroun the roplets. Results obtaine on a sample of roplets trajectories are presente an iscusse in section 4, where measure evaporation rates are compare to those euce from a simple evaporation/conensation moel. Section 5 is a conclusion.. Holographic setup Fig.1 provies a schematic of the optical set-up. It consists of a iverging beam illuminating the measurement volume an a CMOS sensor of a high spee camera (V611 phantom, 180x800 pixel of 0µm). The measurement volume is locate at the intersection of synthetic jets generate by six woofers (only four are presente in the figure for convenience) resulting in a homogeneous an isotropic turbulence (HIT) in the whole measurement volume. This measurement volume is etermine by the source point (focal point of the laser) CMOS sensor istance an size (5.6x16.0 mm ) an limite in z irection to superimpose with the volume where HIT is ensure. Its imensions are approximately 16x10x50 mm 3. The mean flow velocity, the turbulence fluctuations an the integral length scale of the HIT are of the orer of 0.03 ms -1, 0.8 ms -1 an 49 mm respectively. The ivergence of the beam leas to a magnification ratio m of the holograms which epens on the roplet z coorinate following zs m( z) = z z + z Where s ( ) zs is the istance between the CMOS sensor an the light source S, z0 the istance between the CMOS sensor an the center O of the measurement volume an the coorinate system. The magnification factor has been euce from calibration by using a linear scale glass reticle (Emuns Optics, 6 5), following the same proceure as in Marié et al (014). In the present configuration, the magnification ratio is about for z=0 an it varies between 1.51 an 1.58 in the measurement volume, corresponing to z s = 1778 mm an z = 66.5mm 0 0. The roplets are generate by a piezoelectric MJ-AT-01 MicroFab Technologies jetting evice, equippe with a 60 "m orifice iameter glass capillary. Unlike in Chareyron et al (01); Marié et al (014) where the rop on eman moe was use, it is operate in continuous roplet jet-
3 moe. The ether jet create at the capillary exit by a syringe pump is isrupte an elivers roplets of approximately 1.8 times the orifice iameter (Lee 003), that is about 110 "m, with an initial velocity of the orer of m.s. Injection parameters are ajuste to allow a sufficient 1 number of roplets enters the measurement volume. The injector positioning is critical as the roplets must enter the volume before completely evaporating, the injector shoul not be to close to the volume an moify the turbulence properties an the roplets must be trappe in the HIT volume. Fig.1 Experimental set-up. 3. Hologram processing Time sequences (vieos) of roplets holograms are recore uner the conitions escribe above at 3kHz. For each run, a backgroun correction is applie, the backgroun image being calculate by averaging on the whole sequence. Fig. shows an example of roplets hologram after the backgroun correction. Droplets holograms consist of circular fringes resulting from interferences between the roplet iffraction pattern an the reference beam which is the illuminating beam it-self in the in-line configuration here consiere. A wake, attache to the hologram is also clearly visible in Fig, for the roplet near the image center in particular. It results from the vapor wake ue to evaporation an the associate refractive inex graient in the gas phase surrouning the roplet as iscusse in Méès et al (013). The wake will be
4 18th International Symposium on the Application of Laser an Imaging Techniques to Flui Mechanics LISBON PORTUGAL JULY 4 7, 016 consiere later, it can be first ignore (Seifi et al, 013) to estimate roplet position an iameter using an inverse problem approach (IPA). This proceure is base on the minimization of the ifference between the recore hologram an a moel hologram, base on Fraunhoffer iffraction of an opaque isk. The IPA metho is escribe in Soulez et al (007a) an Soulez et al (007b) an has been successfully applie in Chareyron et al (01), Seifi et al (013) an Marié et al (014). The Fraunhoffer iffraction moel is accurate enough in such a configuration (at large istance) to escribe a roplet hologram (without wake), using if necessary a mask in the center part of the hologram where the wake influence is larger. IPA was preferre to a stanar back light propagation proceure to extract the coorinates x,y,z an the iameter of the roplets because the moel hologram intrinsically takes into account truncation an low spatial resolution of the sensor which are significant sources of error an low accuracy measurements. The accuracy expecte for 60 "m iameter water roplets ispersing in the turbulence uner the same operating conitions as here, has typically be estimate to less than 1 "m on iameter, 3 "m (about one tenth of pixel size) on the transverse positions (parallel to the sensor) an about 60 "m (one iameter) on epth z (Chareyron et al 01). Fig Droplets hologram after backgroun correction. The minimization proceure applie to the hologram of fig. leas to an estimation of (x,y,z) coorinates an iameter of a first roplet, that is locate about the center of the image. Then, the corresponing best fit moel hologram can be subtracte from the image to obtain a resiual image as shown in fig 3. After the subtraction, IPA algorithm can be applie again to etect the next roplet an so on.
5 18th International Symposium on the Application of Laser an Imaging Techniques to Flui Mechanics LISBON PORTUGAL JULY 4 7, 016 In this paper, the resiual image is further process to extract information on the vapor wake aroun the roplets. We assume that gray scale variations aroun the roplet in the resiual image of Fig 3 (near the image center) is only ue to the vapor wake generate by the roplet evaporation. In other wors, we assume purely aitive contributions of the roplet an the vapor to the hologram an we assume that the IPA proceure has provie the exact parameter (x, y,z, ) escribing the roplet alone. The wake image of the resiual image is then consiere as a phase object hologram an it is phase retrieve using a stanar back light propagation metho to obtain the image shown in Fig 4. The istance z of reconstruction is that obtaine by IPA. Note also that a threshol has been applie to fig 4 to remove the twin image noise associate to stanar reconstruction methos. This phase retrieval image provies information on the vapor wake, an its evolution in time when consiering a whole sequence of holograms. To be more specific, the retrieve phase epens on the D projection along irection of the refractive inex fiel which epens itself on vapor concentration an temperature. As the roplets trajectories an the flow characteristics are 3D, the extraction of quantitative information on vapor wake is not a small matter. However, the D orientation of the wake projection in the (x,y) plane is easy extracte from the image, proviing a D information on relative velocity, the gas flow velocity viewe by the roplet. Fig 3 Resiual image. Hologram of fig after best fit moel subtraction. Sequences of hologram were thus processe following ifferent step as follow: Backgroun correction of each image of the sequence. IPA measurement of (x,y,z,) for each roplet an image an magnification ratio application.
6 Trajectory reconstruction from (x,y,z,) results (using a nearest-neighbor criteria) IPA resiual image sequence construction for each roplet trajectory. Phase retrieval in the roplet plan from IPA resiual images. Extraction of the D wake orientation along the trajectory. Fig 4 Phase retrieval image, calculate from the resiual image presente in fig. 3 by using a stanar back light propagation metho. 4. Results an iscussion The main objective of this work is to etermine whether or not turbulence influences roplets evaporation. Up to now, a few trajectories have been recore an processe following the proceure escribe above. Fig 5 shows the evolution of two typical roplets iameter along there trajectories. The square of iameter evolution with time is compare to that calculate with the simple evaporation/conensation moel valiate in case of free falling Ether roplets. The moel is that escribe in Marié et al (014). It takes into account the conensation water from humi air at the roplet surface whose influence cannot be neglecte. The inputs are the initial size an velocity of the roplet euce from the first images IPA processing, the initial roplet temperature, an ambient temperature an humiity rate. Humiity rate an room temperature are measure for each run. In this experiment the initial roplet temperature is unknown but it can be set arbitrarily, as the system converge to an equilibrium state after a few time step. In the presente results, the simulation is run once a time with an arbitrary value to etermine an equilibrium temperature use in a secon run. Another ifference between the present
7 simulations an those presente in Marié et al (014) is that the relative velocity is not constant as for free falling. But the Lagrangian relative velocity is euce from the IPA measurements (x,y,z,) versus time an the roplet equation of motion. It requires that the main forces acting on the roplets reuce to the gravity an rag force, in which case their motion is escribe by an equation of the form (see for instance Michaelies (006)) u t 1 3C Re = γ 4γ ( ) u u ( u u ) D 1 g + (1) where γ is the ensity ratio ρ l / ρg between liqui an gas, u the roplet velocity, u the gas velocity an Re the Reynols number base on the roplet iameter an the relative velocity ur = u u. This form is justifie because the roplets are heavier than the gas, have a size comparable to the Kolmogorov length scale (0.15 mm) an o not interact uring evaporation, since their concentration is low. The Diethyl Ether roplets having a Reynols number typically in the range 0 Re 10 the rag coefficient is estimate by the correlation propose by Clift for this case (Clift et al 1978) C D 4 α ( ) = ( 1+ βre ) Re () Re where β = an α = The unknown Lagrangian relative velocity norm u r is then inferre by solving the equation obtaine by summing the square of the projections of equation (1) along the three irections of the holographic set-up τ α ( u + ( u! g) +u ) = u ( 1 + βre )! (3)! x y z r Where τ 18 = ρl / µ g an notation u! i stans for the erivative of u i. In practice, τ, u! x, u! an y u! z are calculate at each time step from the reconstructe trajectory an the measure iameter. Once u r is etermine, Re is known an the three components of the relative velocity can be reaily euce from the 3 projections of equation (1). Fig 5 it can be seen that the simulate time evolutions, incluing the calculate relative velocity remain very close to the law which preict a linear evolution of iameter square with time. The experimental result is also very close to this law for roplet 1 but not for roplet. More generally, such behavior is observe for about one thir of the trajectory recore an processe until now. Droplet oes not evaporate regularly with strong variations of the evaporation rate.
8 Fig 5 Two typical examples of roplet iameter evolution (iameter square versus time in black) extracte from IPA processing of high spee hologram sequences. Droplet 1 show a similar behavior as observe in free falling conition an agree with the simple evaporation/conensation roplet. Droplet evaporation rate is clearly influence by the surrouning turbulent flow. Fig 6 shows a sample of holograms an phase retrieval images extracte from roplet trajectory. The (x,y) projection of the calculate relative velocity (green arrow) an wake orientation (white ashe line) are compare, showing a very goo agreement. However, the wake oes not realign instantaneously with the relative velocity, but with a certain time elay that correspons to the response time of the wake to changes in irection. This appears in Fig. 7 where the time evolution of the angles of θwxy the wake axis an of θ urxy the urxy irection in the (x,y) plane for roplet are plotte. linearly to θ urxy variations as τ w can be estimate assuming that θ wxy respons θ urxy t θ = urxy θ τ w wxy (4) In this example, τ w = 0.4 ms is the relaxation that ensure the best match between between eq.(4) an the phase retrieve wake angle. The goo accorance between the two angles is similar for all the teste trajectories with relaxation time τ w varying between 0.3 an 1.0 ms.
9 Fig 6 Images sample corresponing to roplet trajectory. In gray (column 1 an 3): roplet hologram recore on the CMOS after backgroun correction; the black line is the trajectory of the roplet in the x y plane; the yellow arrow is the velocity of the roplet (uxy), the green one is the x y Lagrangian relative velocity (urxy) calculate from the moel. In black (column an 4): the phase retrieve wake, magnifie an centere on the roplet, with the same two velocities; the white otte line materializes the axis of the wake; the two blue arrows point out the vapor releases.
10 This eviences that roplets positions an iameter measurements an resulting velocities are accurate enough to reprouce well the trajectory an the overall consistency of measurements, incluing IPA an phase retrieval processing. The question of the mechanisms responsible for the evaporation rates fluctuations is still open. These fluctuations are often associate with suen variations of the relative velocity, in amplitue an orientation but no clear epenence as been ientifie yet. It can be note however that rapi ecreasing in roplets iameter are generally precee by a plateau, a short time uring which evaporation slow own or nearly stoppe. These events seem to coincie with suen vapor releases clearly visible in fig. 6 at time t=17 an 4 ms. These observations suggest that evaporation rate fluctuations coul be relate to vapor accumulation aroun the roplets an suen sweeping win but further investigations are efinitely require. Fig 7 Comparison between the Lagrangian relative velocity urxy an the phase retrieve wake orientation in (x,y) plan. 5. Conclusion Digital In-line holography was use to perform a Lagrangian tracking of roplets evaporating in an homogeneous an isotropic turbulence. An inverse problem approach was use to reach the accuracy require by such a stuy, proviing 3D trajectories an iameter estimation versus time. In aition, the wake of vapor aroun the roplets was reconstructe using a stanar
11 back light propagation metho. This vapor wake orientation is foun to be in very goo agreement with the relative velocity, calculate from the IPA measurements an the roplets equation of motion, emonstrating the overall coherency of the proceure. Comparison of the measure iameter evolution with a simple evaporation/conensation moel, previously valiate on free falling configuration shows that the evaporation rate of roplets may be affecte by the turbulent flow. In numerous cases (not all) the evaporation rate was no more constant as it was in laminar conition. Strong fluctuations of this rate were observe an it seems that they are connecte with fast variations of the relative velocity, in magnitue an orientation. However, further investigations an a larger amount of statistics are require to assess this assumption, to quantify the influence of turbulence on evaporation an to clearly explain the involving mechanisms. Acknowlegements This work was partially fune by the French National Research Agency (ANR) uner grants AMO-COPS (ANR-13-BS ) an TEC (ANR-1-BS ). References Birouk M, Gökalp I (006) Current status of roplet evaporation in turbulent flows. Prog Energ Combust Sci 3(4): Chareyron D, Marié JL, Fournier C, Gire J, Grosjean N, Denis L, Lance M, Méès L (01) Testing an in-line igital holography "inverse metho" for the Lagrangian tracking of evaporating roplets in homogeneous nearly isotropic turbulence. New J Phys 14, Clift R, Grace JR, Weber ME (1978) Bubbles, Drops an Particles. Acaemic Press Marié J L, Grojean N, Méès L, Seifi M, Fournier C, Barbier B an Lance M (014), Lagrangian measurements of the fast evaporation of falling Diethyl Ether roplets using in-line igital holography an a high-spee camera, submitte to Experiments in Fluis. Méès L, Grosjean N, Chareyron D, Marié JL, Seifi M, Fournier C (013) Evaporating roplet hologram simulation for igital in-line holography setup with ivergent beam. J Opt Soc Am A 30(10): Michaelies E (006) Particles, bubbles an rops: Their Motion, Heat an Mass Transfer. Worl Scientific. Reveillon J, Demoulin FX (007) Effects of the preferential segregation of roplets on evaporation an turbulent mixing. J Flui Mech 583:73 30 Seifi M, Fournier C, Grosjean N, Méès L, Marié JL, Denis L (013) Accurate 3D tracking an size measurement of evaporating roplets using an in-line igital holography an inverse problems reconstruction approach. Opt Express 1(3), DOI: /OE Soulez F, Denis L, Fournier C, Thiébaut E, Goepfert C (007a) Inverse-problem approach for particle igital holography: accurate location base on local optimization. J Opt Soc Am A 4(4):
12 Soulez F, Denis L, Thiébaut E, Fournier C, Goepfert C (007b) Inverse problem approach in particle igital holography: outof-fiel particle etection mae possible. J Opt Soc Am A 4(1):
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