SPLASHING OF WATER DROPLETS ON A TILTED FLOWING LIQUID FILM

Transcription

1 DIPSI Workshop 0 on Droplet Impat Phenomena & Spray Investigation May 7, 0, Bergamo, Italy SPLASHING OF WATER DROPLETS ON A TILTED FLOWING LIQUID FILM He Zhao, Romain Eault, Carlos Alberto Dorao, Svend Tollak Munkejord Department of Energy and Proess Engineering, Norwegian University of Siene and Tehnology (NTNU), Kolbjørn Hejes vei B, 749 Trondheim, Norway SINTEF Energy Researh, Sem Sælands vei, 7465 Trondheim, Norway ABSTRACT An experimental investigation of water droplets impinging with a liquid film of water flowing on a 0 -tilted aluminium board was arried out. The effets of impinging droplet size, veloity and liquid film parameters on splashing were both qualitatively and quantitatively studied and disussed. The evolution of a non-symmetri rown was haraterized by investigating the normalized rown height and a non-symmetry fator versus the normalized time, and the breakup of seondary droplets was found influential to the rown evolution. An inrease of film veloity and depth redued the rown height, but it does not affet the non-symmetry fator until the rown started to ollapse. Threshold of splashing was investigated, and it was found that the threshold an be well desribed by the model reported in Ref. [4]. INTRODUCTION Droplet impating on a surfae was studied sine the end of 9 th entury [], and there has been a substantial progress in understanding the droplet impat phenomena in the last two deades [] owing to the development in the tehnology of high speed amera. Distinguishing different flow regimes was one of the most important purposes due to its ontribution to the ontrol of different proesses suh as fuel injetion, inkjet printing, phase separation et. Suh works were related with both high energy impingement orresponding to splashing and jetting and low energy impingement orresponding to bouning on either a dry surfae [3][0] or a liquid-overed surfaes [4][5][8][9]. Another highlighted purpose was to study the evolution proess of the droplet impat for establishing models, and suh work an also be found for droplets impinging on a dry surfae [] and a liquid-overed surfae impat [6]. One aspet in ommon for most of the droplet impat studies was that the targets on whih droplets impated were immobile, but in some industrial proesses this is less likely to be true. One example is annular flow, in whih droplets are torn off from and deposit to a flowing liquid film dynamially suh as shown in Figure. Annular flow models without onsidering the dynamis of the dispersed phase fail in desribing the parameters suh as pressure drop, film thikness and heat transfer. This is also the ase for other proesses where a flowing liquid film and droplets interat with eah other. In order to make robust models, one shall understand further the interations between droplets and a flowing liquid film. Studies of droplets impating with a flowing liquid film are, however, found to be inadequate. Initial attempts are made in Ref. [][3][4], of all whih the impat onditions are nearly Figure Sketh of annular-mist flow. normal (tilted angle less than 0, with a horizontal surfae defined as 0 ). Ref. [][3] foused on studying the relationship between the size of the rater formed by the impat of the droplet and the dependene of the total volume of seondary drops on the thikness and veloity of the liquid layer, and the slope of the tray. Ref. [4] foused on the transitions of flow regimes, and the ritial ber numbers for haraterizing the regime-transitions seem to be independent on both the film thikness and veloity reported in the artile. It is thus desired to investigate the impat of droplets on a flowing liquid film with more tilted angles and veloities as to investigate the effets of non-symmetrial impat and liquid film parameters on splashing evolution and transition.

2 EXPERIMENTAL METHODS AND PARAMETERS Experimental apparatus Experimental apparatus and methods are to be desribed in this setion. A sketh of the experimental apparatus is shown in Table shows the film parameters, in whih the measured quantities are flow rate ( Q ), thikness ( ), surfae veloity ( V s ), and the alulated quantities are mean veloity ( V m ) and the film Reynolds number ( Re f ) shown by Eq. () and Eq. (). Q V () m W 4 Q Re f () W Table Liquid film flow rate ( Q, m 3 /s) and orresponding liquid film thikness (, mm), surfae veloity ( V s, m/s), mean veloity ( V m, m/s) and Reynolds number ( Re f ). Figure Sketh of experimental apparatus. Figure. A ollimated LED was served as a light soure. A Phantom V9 digital amera operated at 55 fps (in most of the aquisitions) with a resolution of pixels was employed for apturing the droplet-film interations. A 0 -tilted aluminum board was plaed inside a test ell, and a shallow hannel, in whih a liquid film flowed, was made of one pair of aluminum foil bands. The hannel width was 5.5 mm, and depth was deided by the thikness of the aluminum foil, whih was about 0. mm. A liquid pump irulated water for generating a flowing liquid film. Droplet was generated from a dropper, a needle of gauge 33 (Hamilton). Droplet releasing height was varied in order to have different impinging veloities. Measurement methods and parameters Droplet diameter and veloity were measured from the aptured videos. Diameter was evaluated by using the ross-setional area of the droplet, and veloity was alulated by using the displaement and time interval. The relative unertainties for both the diameter and veloity measurements were approximately 3%. Four flow rates,.8 0-6, , , m 3 /s were used. Liquid film thikness was evaluated by omparing the image differene with and without a liquid film. The relative unertainty of the thikness was dependent on the flow rate, and the lowest and highest flow rates ( and m 3 /s) orresponds to an unertainty about 0%, while the other two flow rates ( , m 3 /s) orresponds to an relative unertainty about 5%. Surfae veloity of the liquid film was measured by traking polybutylene beads ( mm), whih were set in the upstream of the flow. The relaxation time of the beads ( r ) was less than 5 ms, whih was about 0 times shorter than the time taken for the beads travelling from the released point to the amera fous, and thus, the beads an follow the flow well. The relative unertainty of the surfae veloity for the two lower flow rates (.8 0-6, m 3 /s) was about 5%, and was approximately % for the other two flow rates ( , m 3 /s). NO. Q V s V m Re f where Q, and W are flow rate, thikness and hannel width 3 shown by, where 000 kg/m and 0.89 mpa s are density and visosity of water at 5 C. EXPERIMENTAL OBSERVATIONS In this setion, we first show typial observations for the non-splashing regime, whih is next to the regime of splashing. Seondly, splashing regime is shown, and the effets of droplet parameters, i.e. diameter and veloity, as well as the effets from the liquid film on splashing are desribed. Non-splashing For droplet-pool interations, the non-splashing regimes an be jetting, oalesene, bouning and partial oalesene. Jetting, whih is adjaent to splashing and haraterized by the entral jet formation (sometimes breakup) [5][4], is of interest here. Figure 3 shows the typial non-splashing. t = 0 ms ms.5936 ms ms.7490 ms ms ms ms Figure 3 The non-splashing regime adjaent to splashing. Droplet parameters: diameter.0 mm, impinging veloity.8 m/s. Film parameters: angle 0, thikness 0.55 mm, surfae veloity 0.37 m/s (other parameters see Table ). Figure 3 shows that a non-symmetri wave is formed at t = ms. Due to the fat that the tangential (T) veloity of the droplet ( m/s ) is higher than the film veloity (0.37 m/s), the droplet has a relative motion towards downstream, along the tangential diretion, of the liquid film, and thus a higher

3 wave (in the normal diretion and relative to the undisturbed film surfae thereinafter) an be expeted and seen at the downstream side of the impat point. At t = ms, the leading edge of the wave develops to about the maximum height. A primary entral jet is initially seen at t =.7490 ms, and it reahes its maximum height at approximately t = ms. Different from the entral jet formation with a normal impat, where the entral jet appears at the impat point, the entral jet formed here moves away from the impat point, and it appears at downstream of the impinging point. This owes to the oblique impat ondition and the liquid film motion. Another remarkable differene between the entral jet formation here and that from droplet-pool interations is that the primary jet does not disintegrate into seondary droplets. Ref. [6][7] reported no entral jet formation for splashing on thin films (dimensionless film thikness / D less than 0.5, where D is diameter of droplet), and Ref. [7] proposed the reasons. Crown breaking led to energy loss.. No avity ollapse. With thiker films ( approx. 0.3~0.6) presented in this investigation, the primary jet is observed without breaking up. suggest that ability of fousing the reeding wave as to form and break up the entral jet here is weaker than in the ase of droplet-pool interation due to two reasons:. Shallow film - unlike the impat on a pool, where an undisturbed rater is formed and ollapses naturally, the rater formation is interrupted by an unyielding surfae, and the wave expands radially, whih redues the mass fousing during reeding.. Non-symmetri wave - the tilted surfae and film movement form a non-symmetri wave, with whih the ability of fousing the reeding mass is weaker than with a more symmetri wave. Splashing with different impinging veloities In this part, the effet of the impinging veloity on splashing is to be examined with fixed film parameters and a fixed impinging droplet size. Figure 4 and Figure 5 show the impats with the same droplet diameter (.0 mm) and film parameters (angle 0, thikness 0.55 mm, surfae veloity 0.37 m/s, other parameters see Table ) but with different impinging veloities. Comparing the first row of Figure 4 with Figure 5, one an readily see the differenes that an inreased veloity makes more released seondary droplets from the rown breakup and also higher evoked rown height. It an also be seen that the released seondary droplets in Figure 5 have greater veloity omponents in the normal diretion than the two released seondary droplets shown in Figure 4. Figure 4 shows that the maximum rown height (of the leading edge thereinafter) is reahed at around t = ms, and in Figure 5, the maximum rown height is reahed at t = ~ ms, whih is - frames delayed ompared to the lower veloity ase. This is beause that all the seondary droplets in Figure 4 are formed at a time-point (t = ms, defined as single-stage breakup), whih should be noted that this is not the exat moment due to the non-ontinuity of the piture-taking but shall be haraterized by a ertain frame in a video, while in Figure 5, seondary droplets are released at multiple time-points (t = ,.5936 and ms, defined as multi-stage breakup). The multi-stage breakup leads to the postponement of reahing the maximum rown height. Figure 4 also shows that a primary entral jet is initially seen at approximately t = ms and reahes its maximum height at about t = 9.35ms, and this time is dramatially longer than the jetting ase shown in Figure 3 (at t = ms). Therefore, time required for reahing the maximum jetting height is prolonged in the splashing ase perhaps due to the breakup of seondary droplets. Splashing with different impinging drop sizes In this setion, we shall examine the effets of varying droplet size on splashing with fixed film parameters the same as in the above setion and a fixed impinging veloity at 3.9 m/s. Figure 5 will be referred as the splashing with a larger droplet diameter (.0 mm), and Figure 6 shows a splashing with a lower droplet diameter (.6 mm). t = 0 ms ms.5936 ms ms t = 0 ms ms.5936 ms ms ms ms ms 9.35 ms Figure 4 Splashing with impinging droplet diameter.0 mm, veloity 3.4 m/s. t = 0 ms ms.5936 ms.3904 ms ms ms ms ms Figure 5 Splashing with impinging droplet diameter.0 mm veloity 3.9 m/s..554 ms.95 ms.7490 ms ms Figure 6 Splashing with impinging droplet diameter.6 mm and veloity 3.9 m/s. It is obvious that a smaller droplet leads to the single-stage breakup of rown with less seondary droplets generation. The time for reahing the maximum rown height is at about t = ms, whih is earlier than that in the splashing with multi-stage breakup in Figure 5. Splashing with different film parameters Effets of film parameters on splashing will be illustrated in this setion, and Figure 5 will be employed to show the splashing with a liquid film flowing at a lower flow rate (thikness 0.55 and surfae veloity 0.37 m/s). Figure 7 shows a splashing with the same impinging droplet diameter and veloity as those listed in Figure 5 but on a film with a higher flow rate (thikness.0 and surfae veloity 0.6 m/s).

4 multi-stage breakup.5 t = 0 ms ms.9685 ms ms Figure 7 Splashing with film number 4: angle 0, thikness.0 mm, surfae veloity 0.6 m/s (other parameters see Table ), droplet diameter and veloity are the same as those listed in Figure 5. Figure 7 shows that the rown height is lower than that shown in Figure 5. Another notieable differene is that the leading edge of the rown is more strethed towards the tangential diretion as shown by the filaments at t = and.9685 ms. The time required to reah the maximum rown height is at about t = ms, whih is slightly delayed but not largely different from that in Figure 5, as both of the splashing ases experiene multi-stage breakup. EXPERIMENTAL ANALYSIS Quantitative analysis of the impat evolutions In this setion, we shall analyze the rown height evolution of splashing. The normalized height of the leading edge of the rown ( H ) and the non-symmetry fator of the rown ( S ) as shown in Figure 8 are studied with the normalized time ( t ), H H D (3) H S H (4) tv n t D (5) where t and Vn are elapsed time and normal omponent of impinging veloity. Figure 9 shows the rown development for splashing on a flowing liquid film (angle 0, thikness 0.55 mm, surfae veloity 0.37 m/s, other parameters see Table ). H D=.0 mm, V=3.4 m/s D=.6 mm, V=3.9 m/s D=.6 mm, V=3.9 m/s D=.6 mm, V=3.9 m/s D=.0 mm, V=3.9 m/s (multi-stage breakup) D=.0 mm, V=3.4 m/s D=.0 mm, V=3.4 m/s D=.0 mm, V=3.9 m/s (multi-stage breakup) t Figure 9 Crown evolution of splashing on a flowing liquid film (No. in Table ): effet of multi-stage breakup. Figure 9 shows that rown evolutions with single-stage breakup follow nearly the same path, while the rown evolutions with multi-stage breakup deviate from that path at the moment that multi-stage breakup is formed. Due to the multi-stage breakup, a delayed maximum rown height is obtained. It an also be noted that the earlier multi-stage breakup tends to maintain the rown height at maximum, while the rown height drops faster in the ase with the later multi-stage breakup during the ollapse of rown. Figure 0 illustrates the non-symmetry fator during the rown evolutions. As an be seen from the figure, this fator is maintained at about S while the rown height is growing (approx. for t 0 ), and it inreases fast as the rown starts to ollapse. It reveals that the leading edge and trailing edge grow with a similar sale, while the trailing edge ollapses with a larger sale. Figure shows the rown evolution for splashing on a flowing liquid film with a higher flow rate (angle 0, thikness.0 mm, surfae veloity 0.6 m/s, other parameters see Table ), and the data shown in Figure 9 is plotted with grey olour. It is obvious that the inrease of liquid film veloity and depth leads to a lower rown height formation. Multi-stage breakup is also observed, and it behaves in the similar way whih makes the evolutionary urves of rown height deviate from the splashing with single-stage breakup D=.6 mm V=3.9 m/s D=.6 mm V=3.9 m/s D=.6 mm V=3.9 m/s D=.0 mm, V=3.9 m/s (multi-stage breakup) 3 S t Figure 8 Sketh of splashing heights of leading edge ( H ) and trailing edge ( H ). Figure 0 Non-symmetry fator of splashing on a flowing liquid film (No. in Table ).

5 .5 multi-stage breakup (6) for the ritial ber number ( ), whih distinguishes splashing and non-splashing (6) 0.4 Oh H D=.0 mm V=3.9 m/s (multi-stage breakup) D=.0 mm V=3.9 m/s (multi-stage breakup) D=.5 mm V=3.7 m/s D=.6 mm V=3.8 m/s t Figure Crown height evolution of splashing on a flowing liquid film (No. 4 in Table ), and grey symbols present the rown height evolution shown in Figure 9. Figure shows the non-symmetry fator for splashing on a flowing liquid film (angle 0, thikness.0 mm, surfae veloity 0.6 m/s, other parameters see Table ), and the data shown in Figure 0 is plotted in grey olour. Little differene is seen between the non-symmetry fators of splashing on the two films during the rown height inrease (approx. for t 0 ), while the non-symmetry fator for the flowing film with a higher veloity and depth tends to ontinually stay at around S during the ollapse of rown. S D=.0 mm V=3.9 m/s (multi-stage breakup) D=.0 mm V=3.9 m/s (multi-stage breakup) D=.5 mm V=3.7 m/s D=.6 mm V=3.8 m/s t In the present investigation, the impat of droplets on to a 0 -tilted board was lose to the normal impat ondition regarding the omparison between the normal vetor and the omposite vetor of the impinging ber number. With a 0 -tilted board, the ratio between the normal vetor ( n, ) and the omposite vetor ( ) of the ritial ber number is as follows. sin (7) n, Thus, if the motion of the liquid film is assumed to be not influential under the quasi-normal impat ondition, the ritial ber number for a 0 -tilted board should be lose to the ritial ber number predited for a horizontal film-overed surfae in Ref. [4]. Figure 3 shows the ber number against the dimensionless thikness of the flowing liquid film. For omparison, the ritial ber number alulated using model (6) is plotted in the figure. Figure 3 shows that the threshold of splashing and jetting for droplets impinging with a 0 -tilted board is, in general, well haraterized by model (6). In fat, the threshold fits better the alulated value for 0.5, and the experimental thresholds beome to be overestimated by the model as dimensionless thikness inreases. This agrees well with Ref. [4], in whih the agreement between the model and experimental results is better for 0.3 than for 0.5, where the alulated threshold starts to be overestimated. Thus, the assumption is true that the effets of the liquid film motion on the threshold of splashing are not obviously seen for droplets impinging with a tilted flowing liquid film with a quasi-normal impat ondition suh as the 0 board inlination in the present study Splashing Jetting Coalesene Splashing Jetting Coalesene Figure Non-symmetry fator of splashing on a flowing liquid film (No. 4 in Table ), and grey symbols present the non-symmetry fator shown in Figure 0. Splashing threshold In the analysis of the threshold between splashing and jetting, only the data of splashing and jetting is of interest. The Ohnesorge number ( Oh /( D), 7 mn/m denotes the surfae tension of water) range in the present investigation is Oh [0.003, ], and the dimensionless thikness is [0.,0.9]. Both of the parameters were omparable with the experiments of water in Ref. [4], whih presented a model mm Splashing Jetting Coalesene mm mm Splashing Jetting Coalesene mm Figure 3 ber number ( ) versus dimensionless thikness ( ) with omparison to the ritial ber number ( ) alulated using model (6).

6 CONCLUDING REMARKS An experimental investigation of water droplets impinging with a liquid film of water flowing on a 0 -tilted board was made with the fous on splashing evolution and threshold. The investigation showed that, for a given liquid film, an inrease in either droplet diameter or veloity resulted in more seondary droplets from rown breakup. The rown evolutions with single-stage breakup followed a similar path, while those with multi-stage breakup deviated from this path with higher rown heights and delays in reahing the maximum rown heights. An inrease in the film veloity and depth led to lower rown height. The non-symmetri rown was haraterized by a non-symmetry fator S, whih was steady ( S ) during the rown growing and inreased during the rown ollapse for a thin and slow-flowing film (NO. in Table ). With a thiker and faster-flowing film (NO. 4 in Table ), this fator tended to maintain stable ( S ) throughout both the rown growing and ollapse. The impat ondition in this investigation was quasi-normal, and little differene in the splashing threshold from the normal impat was notied as the ritial ber numbers an be well haraterized by using the model (6) presented in Ref. [4]. However, the threshold model beame less robust as the normalized film thikness is above 0.5. ACKNOWLEDGMENT This publiation is based on results from the researh projet Enabling low emission LNG systems, performed under the Petromaks program. The authors aknowledge the projet partners; Statoil and GDF SUEZ, and the Researh Counil of Norway (9306/S60) for support. NOMENCLATURE Symbol Quantity SI Unit Film thikness m Dimensionless film thikness Visosity of water Pa s Density of water kg/m 3 Surfae tension of water N/m r Relaxation time s D Droplet diameter m H Crown height, leading edge m H Dimensionless rown height, leading edge H Crown height, trailing edge m Oh Ohnesorge number Q Flow rate m 3 /s Re f Film Reynolds number S Non-symmetry fator t Elapsed time s t Dimensionless time V Impinging veloity m/s V Film veloity m/s f V m Mean veloity of film m/s V Normal omponent of m/s n impinging veloity V s Surfae veloity of film m/s W Width of hannel m ber number Critial ber number Normal omponent of ritial n, ber number REFERENCES [] A.M. Worthington, On the Forms Assumed by Drops of Liquids Falling Vertially on a Horizontal Plate, Pro. R. So. Lond., vol. 5, pp. 6-7, 876. [] A.L. Yarin, Drop Impat Dynamis: Splashing, Spreading, Reeding, Bouning, Annu. Rev. Fluid Meh., vol. 38, pp. 59-9, 006. [3] C. Mundo, M. Sommerfeld and C. Tropea, Droplet-Wall Collisions: Experimental Studies of the Deformation and Breakup Proess, Int. J. Multiphase Flow, vol. (), 5-73, 995. [4] G.E. Cossali, A. Coghe and M. Marengo, The Impat of a Single Drop on a tted Solid Surfae, Exp. Fluids, vol., pp , 997. [5] H. Zhao, A. Brunsvold and S.T. Munkejord, Investigation of Droplets Impinging on a Deep Pool: Transition from Coalesene to Jetting, Exp. Fluids, vol. 50 (3), pp , 0. [6] A. Bisighini, G.E. Cossali, C.Tropea and I.V. Roisman, Crater Evolution after the Impat of a Drop onto a Semi-infinite Liquid Target, Phys. Rev. E, vol. 8 (3), pp , 00. [7] F. Blanhette and T.P. Bigioni, Partial Coalesene of Drops at Liquid, Nat. Phys., vol., pp , 006. [8] K.L. Pan and C.K. Law, Dynamis of Droplet-Film Collision, J. Fluid Meh., vol. 587, pp. -, 007. [9] H. Zhao, A. Brunsvold and S.T. Munkejord, Transition between Coalesene and Bouning of Droplets on a Deep Liquid Pool, Int. J. Multiphase Flow, 0, Aepted. [0] D. Bartolo, F. Bouamrirene, É. Verneuil, A. Buguin, P. Silberzan and S. Moulinet, Bouning or Stiky Droplets: Impalement Transitions on Superhydrophobi Miropatterned Surfaes, Europhy. Lett., vol. 74 (), pp. 99, 006. [] Š. Šikalo and E.N. Ganića, Phenomena of Droplet Surfae Interations, Exp. Therm. Fluid Si., vol. 3 (), pp. 97-0, 006. [] V.G. Sister, O.A. Eliseeva, and A.K. Lednev, Study of the Features of Impat Reation of a Droplet with a Liquid Surfae, Chem. Pet. Eng., vol. 45 (5-6), pp. 7-74, 009. [3] V.G. Sister, O.A. Eliseeva, and A.K. Lednev, Formation of Seondary Drops upon Collision of a Drop with a Liquid Surfae, Chem. Pet. Eng., vol. 45 (7-8), pp , 009. [4] S.K. Alghoul, C.N. Eastwik and D.B. Hann, Normal Droplet Impat on Horizontal Moving Films: an Investigation of Impat Behaviour and Regimes, Exp. Fluids, vol. 50 (5), pp , 0. [5] S.K. Alghoul, C.N. Eastwik and D.B. Hann, Normal Droplet Impat on Horizontal Moving Films: an

7 Investigation of Impat Behaviour and Regimes, Exp. Fluids, vol. 50 (5), pp , 0. [6] D.A. iss and A.L. Yarin, Single Drop Impat onto Liquid Films: Nek Distortion, Jetting, Tiny Bubble Entrainment, and Crown Formation, J. Fluid Meh., vol. 385, pp. 9-54, 999. [7] A.B. Wang and C.C. Chen, Splashing Impat of a Single Drop onto Very Thin Liquid Films, Phys. Fluids, vol. (9), pp , 000.

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