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Secondary atomisation produced by single drop vertical impacts onto heated surfaces
Experimental Thermal and Fluid Science 29 (2005) 937–946 www.elsevier.com/locate/etfs
Secondary atomisation produced by single drop vertical impacts onto heated surfaces G.E. Cossali *, M. Marengo, M. Santini Universita` di Bergamo, Facolta` di Ingegneria, viale Marconi 5, 24044 Dalmine (BG), Italy Received 30 August 2004; received in revised form 10 November 2004; accepted 7 December 2004
Abstract The paper reports an experimental analysis of the secondary atomisation produced by the impact of a single drop on a solid heated surface. Different wall temperatures were used to study different boiling regimes. The size of secondary drops produced by the impact was measured by two techniques, namely the phase Doppler anemometry (PDA) and the image analysis technique (IAT); this allowed to extend the measurable size range from 5.5 lm up to few mm. Two impacting walls with different surface roughness were used to show the effect of this parameter on different atomisation regimes. The liquid viscosity was also varied in a limited range by using water–glycerol mixtures. Image analysis allowed also to define the details of the morphology of drop spreading and break-up. 2005 Elsevier Inc. All rights reserved. Keywords: Two-phase flows; Nucleate boiling; Leidenfrost regime; Drop impact; Phase Doppler anemometry; Image analysis
1. Introduction The impact of liquid drops onto solid heated surfaces is a phenomenon linked to many industrial applications, such as the hot coating of surfaces, the metal surface cooling in the steel industry and in the nuclear power plants, the direct fuel injection in diesel and gasoline engines and in many other technological processes where it is useful to achieve a local and rapid thermal control. When the surface temperature is higher than the liquid saturation temperature, the phase transition caused by the intense heat transfer from the solid wall to the spreading liquid radically modifies the impact dynamics, comparing to the isothermal case [1]. The explosions of the vapour bubbles at the liquid–air interface of the spreading lamella originates a secondary atomisation. The impact velocity, the surface temperature, the impact
*
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0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.12.003
angle, the surface tension and the viscosity of the liquid and the surface wettability [2], effusivity [3,4] and roughness [5] are the main parameters influencing the process and many research works are already available in the open literature. During the very first phase (s = tV0/d0 < 1) the drop temperature is almost constant [6,7], while the surface temperature is rapidly cooled to the interface temperature (determined by the liquid and wall effusivities). When the liquid–wall contact area increases, the heat transfer becomes relevant and a nucleate boiling process takes place, with the generation of bubbles and secondary droplets [8]. Varying the surface temperature, different atomisation regimes are observed [8], mainly related to different boiling regimes that are governed by the wall temperature and the liquid Nukiyama (TN) and Leidenfrost (TL) temperatures. When the wall temperature is below the TN, the lamella spreading process shows a peculiar behaviour: even for low Weber numbers, there is a strong contraction of the lamella after spreading, with production of secondary droplets [9,10]. Akao et al. [11,12] found different
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Nomenclature Ca D, d d32 d10 La Ra Rz R S SMD T t V We
Capillary number (Vl/r) drop diameter Sauter mean diameter (also SMD) arithmetic mean diameter Laplace number (dqr/l2) arithmetical mean roughness 10-point mean roughness rough surface smooth surface Sauter mean diameter (also d32) temperature time impact velocity Weber number (dqV2/r)
critical Weber numbers for three regimes (deposition, ejection of few droplets after rebounding and ‘‘secondary atomisation’’) using different liquids, different drop diameters and a coated copper surface. When the wall temperature is increased, the lamella may break-up in liquid ligaments and, under certain conditions, the liquid bulk on the surfaces tends to break-up and/or rebound [8]. When the surface temperature is above the Leidenfrost temperature, the formation of a vapour film during the liquid spreading lead to a rather different impact morphology, and Wachters and Westerling [10] were the first to describe quantitatively the secondary atomisation regimes. The Leidenfrost temperature has a phenomenological definition and it depends also on the dynamics parameters, such as the impact velocity and angle [13]. Resuming, many literature papers, most at low Weber impacts (for example, see also [14–16]) and few at ‘‘moderate’’ Weber number (We < 300) give as outcomes the phenomenon morphology, the impact regimes, the spreading evolution, the maximum spreading radius, the evaporation time and the surface temperature profile and evolution. The aim of this paper is to study the boiling induced secondary atomisation produced by drop impacting normally to heated surfaces at moderate Weber numbers (250 < We < 660). Besides a detailed qualitative description of the various impact regimes, the work is addressed to obtain further new information about the secondary drop diameter distributions resolved in time and space. The next section describes the experimental set-up and the measuring techniques, then the experimental results are reported and discussed, considering particularly the effects of surface roughness, liquid viscosity and primary drop size on the different atomisation regimes. The last section summarises the main results.
z
distance from the wall (vertical direction)
Greek symbols l liquid viscosity q liquid density r liquid surface tension s dimensionless time Subscripts L Leidenfrost N Nukiyama sat saturation w wall 0 primary drop
2. Experimental set-up Distilled water and water–glycerine mixture drops were let to fall by gravity onto an aluminium alloy (AlMg3) circular disc, electrically heated from below. Wall temperatures larger than 330 C can be reached and maintained by PC-based PID controller. A thermocouple positioned under the centre of the impacting wall supplies the feedback needed by the heater controller. Needles were used as drop generators, the internal diameters ranged from 0.16 mm to 2 mm, and they were connected through flexible pipes to a small, pressurised tank containing the working liquid. The impacting frequency was controlled by a throttling device and was low enough to assure a true single drop impact, (no overlapping and no fouling from previous drop impact were assured and the initial wall temperature was re-obtained after each impact). The drop generator produced drops with diameters ranging between 1.8 and 4.6 mm while the drop impact velocity could range between 1 m/s and about 6 m/s. A CCD camera (Colour PCO SensiCam, 1280 · 1024 pixels) with a long distance microscope objective (Navitar, 12X) was used to acquire the images of the impact. The CCD acquisition and illumination systems were driven by a triggering system made by an He–Ne laser (1 mW power) imaged onto a photodiode. The falling drop crossing the laser beam gave the trigger pulse, a delay was then added to account for the drop travel time from the laser beam to the impact wall; the correct delay was evaluated from the images acquired during the setup procedure. A continuous back illumination system was used and, to get the correct time resolution, acquisition times from 5 ls to 20 ls were used. A commercial image analysis code (Image-Pro Plus) was used and home built routines were developed for measuring
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secondary drop size, roundness, etc. The size range that can be measured by this image analysis technique (IAT) is from 40 lm to few millimetres. As a second sizing technique a DANTEC PDA (phase Doppler anemometer) was used to measure simultaneously the secondary drop velocity (the component normal to the wall) and size. A purposely-built computer code was used to design the optical set-up, in order to minimise the effect of the lack of knowledge of secondary droplets refracting index, as the liquid temperature of ejected secondary droplets is unknown. The PDA size range, with the chosen configuration, was between 5.5 lm and 250 lm, thus partially overlapping the IAT size range. This allowed reconstructing the entire drop size distribution (hereinafter called p.d.f.) from 5.5 lm to few millimetres by means of a proper postprocessing. Acquisition of measurements from many subsequent drop impacts allowed to obtain statistically significant samples. The PDA triggering system was the same described above. In this case it was not possible to observe directly the drop impact, the delay between the trigger pulse and the actual drop impact time was then calculated from the impact velocity and the distance of the laser beam from the wall, then the absolute accuracy in defining the time after impact was about 1 ms. The accuracy in defining the surface temperature was evaluated to be better than 2 K, keeping into account the wall temperature variation due to the heat transfer caused by subsequent impact of drops. The IAT technique used to measure the secondary droplet size have an absolute accuracy better than 25 lm (with the optical configuration used in this work). The accuracy in measuring the primary drop size was better than 3%. The impacting velocity was measured from multiple exposed images and its accuracy was better than 3%.
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Table 1 Arithmetical mean roughness (Ra) and 10-point mean roughness (Rz) of the surfaces used for the experiments Surface
Rz (lm)
Ra (lm)
S R
1.6 14.5
0.205 2.844
primary drop size was varied. Capillary number (Ca = Vl/r) and Laplace number (dqr/l2) will be used to represent the impact conditions in non-dimensional form (as they can be interpreted as drop non-dimensional velocity and size), however also the corresponding Weber number (We = q dV2/r = La Ca2) will be explicitly given throughout the paper. Non-dimensional time defined as s = tV/d will be used. 3.1. Morphology of the impact The morphological structure of the liquid lamella after drop impact is analysed and the main results are discussed here. The effect of temperature will be analysed as well as the effect of changing liquid viscosity and surface roughness. 3.1.1. Boiling regimes Fig. 1(a) shows the comparison of the impact outcomes at different wall temperatures (We = 247). The comparison to the picture taken with Tw = 70 C (below saturation temperature) shows that for these impacting conditions the secondary atomisation is due only to thermal (boiling) effects as inertia effects are not strong enough to produce secondary atomisation. At least two main regimes of boiling were detected, depending on the wall temperature, which can be related to different regimes of secondary atomisation. When the wall temperature is above the saturation temperature of the impacting liquid but well below the Leidenfrost temperature (TL, that depends on many parameters such as
3. Results and discussion This section is devoted to show the characteristics (both qualitative and quantitative) of the secondary atomisation produced by the impact of a single liquid drop onto a hot surface. The dynamical impact conditions were chosen in order to avoid the secondary atomisation when the surface temperature (Tw) was below the liquid boiling temperature (Tsat) to assure that the observed secondary atomisation was solely an effect of the heat transfer process. The surface temperature is the value measured prior the drop impact; care was taken to assure that the same temperature was recovered after each impact. Two different surface roughness were analysed (see Table 1) to show possible effects of this parameter on secondary atomisation. Liquid viscosity was changed by using different water–glycerine mixtures and also
Fig. 1. Effect of wall temperature (70 C, 150 C, 260 C) on the impact morphology for two different fluids: impact onto rougher surface (R) at s = 13; pure water: Ca = 0.0431, La = 133,000, We = 247; water-glycerine 8.8% mass mixture: Ca = 0.0447, La = 136,000, We = 272.
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the surface roughness, the impact angle, etc. [9,13]) bubble boiling takes place. A wall temperature of 150 C (well below the pool boiling value of the Leidenfrost temperature for water under steady conditions, TL,p 220 C) was chosen to represent this regime. In this case bubbles, produced by the heat transfer from the wall, grow and rupture the liquid lamella, producing a plethora of small secondary drops (Fig. 1). When instead the wall temperature is above the Leidenfrost temperature (Tw > TL) the film boiling regime is reached. A wall temperature of 260 C (well above the nominal Leidenfrost temperature) was chosen to represent this regime. In this case, the wall temperature is sufficiently high to generate a vapour film almost immediately after impact, that may finally levitate the liquid from the wall (see Fig. 1a) and the diminished liquid–wall contact is responsible of the smaller number of secondary drops. It is necessary to stress that the present definition of the Leidenfrost temperature is not linked with an actual measurement of the minimum heat flux from the wall, but is purely morphological. The value of 260 C is therefore to be intended only for the present experiment and for the considered parameter ranges. Moreover, for the case at 260 C (film boiling regime) the formation and break-up of a sort of central jet (the sequences in Figs. 2 and 3 show better the effect) is observed, its generation starting just at the beginning of the spreading phenomenon (s = 3 and s = 4). Chaves et al. [17] suggested as a possible mechanism for droplet formation under bubble boiling regime, the break-up of thin jets caused by the explosion of vapour bubbles through the liquid lamella. Fig. 4 shows an enlargement of some pictures evidencing a phenomenon in some way analogous to that suggested by Chaves et al. [17], that may be one of the main causes of the secondary atomisation under this regime. But the ‘‘pagoda-like’’ bubbles are not visible in previous works and need a further theoretical explanation. Another important difference between the two regimes is the character-
Fig. 2. Effect of liquid viscosity on the impact morphology: impact onto rougher surface (R) at 150 C; pure water: Ca = 0.0431, La = 133,000, We = 247; water-glycerine 8.8% mass mixture: Ca = 0.0447, La = 136,000, We = 272.
Fig. 3. Effect of liquid viscosity on the impact morphology for two different fluids: impact onto rougher surface (R) at 260 C; pure water: Ca = 0.0431, La = 133,000, We = 247; water-glycerine 8.8% mass mixture: Ca = 0.0447, La = 136,000, We = 272.
istic times at which the secondary atomisation starts. In bubble boiling regime (Tw = 150 C) the formation of first secondary droplets starts few milliseconds after impact (Fig. 2) whereas the secondary drop production starts immediately after impact for film boiling (Tw = 260 C) regime (Fig. 3). Also the secondary drop direction is affected by the wall temperature: for bubble boiling the secondary drop direction is always mainly vertical, whereas for film boiling there is also an ejection in radial direction during the very first impacting period. Finally, for the film boiling regime, the presence of a vapour film produces the levitation of relatively large droplets coming from the break-up of the film layer (Fig. 3). 3.1.2. Effect of surface roughness To study the effect of surface roughness on the secondary atomisation mechanism, experiments were run using two different surface roughness (Table 1) for both boiling regimes and with the same impacting conditions.
Fig. 4. Vapour bubble bursts at the liquid/air interface. Formation of ‘‘pagoda-like’’ bubbles (notice the liquid jet on top of the bubbles).
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For the bubble boiling regime (Tw = 150 C, Fig. 5) the difference is mainly on spreading that appears faster for the larger surface roughness and atomisation appears earlier. For film boiling (Tw = 260 C, Fig. 6) no clear central jet is observed for the smoother surface impact (although the phenomenon is not fully deterministic), and a larger secondary droplet production (quite similar to the bubble boiling droplet production) is observed during the early stage. 3.1.3. Effect of liquid viscosity The influence of viscosity was studied by comparing the results obtained with water to those obtained using different water–glycerol mixtures. In particular, the use of a solution of glycerol in water (8.8% in mass) allowed, by using proper values of the impact velocity and diameter, to maintain the non-dimensional impacting conditions in term of Ca, La and We numbers almost equal (with a maximum difference of 4%) to those used in the previously described experiments. For bubble boiling regime the time at which the secondary atomisation starts is influenced by the liquid viscosity: for the water–glycerol solution the secondary atomisation starts later than for pure water (Fig. 2) and this effect must be due only to the increase of viscosity, since all the other Fig. 6. Time evolution of water drop impact onto smooth (S) and rough (R) surfaces at 260 C; pure water: Ca = 0.0431, La = 133,000, We = 247.
important parameters (the heat of vaporisation, the liquid conductivity and the specific heat) are practically unvaried. A possible explanation may rely on the fact that an increase of liquid viscosity may decrease the local Reynolds number, then decreasing the convective heat transfer from wall to liquid and depressing vaporisation. For the film boiling regime the central jet disappears when viscosity is increased, the higher viscous dissipation of kinetic energy may be responsible for this effect. 3.2. Quantitative image analysis and PDA measurements
Fig. 5. Time evolution of water drop impacts onto smooth (S) and rough (R) surfaces at 150 C; pure water: Ca = 0.0431, La = 133,000, We = 247.
From images similar to those reported above the size of the secondary droplets was evaluated after proper image conditioning and analysis by means of ad hoc built routines. The spatial accuracy of the acquisition set-up and the image analysis technique allowed measuring only droplets larger than about 40 lm. Important parameters, such as the minimum (dmin) and maximum (dmax) diameter of the drop (for a deformed droplet dmin 5 dmax), the size of the rectangle enclosing each droplet, etc., were also measured and post-processing procedures were set-up to reject droplets having large aspect ratios. A statistical analysis allowed to discover
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that values of the aspect ratio dmax/dmin larger than 2 were mainly due to uncertainty on the measured size of the smallest droplets, then measurements with dmax/dmin > 2 were rejected during the post-processing procedures. To enlarge the measured size range toward smaller sizes, the PDA system was set up and the experiments were repeated performing droplet diameter measurements at three different distances (2, 4 and 9 mm) above the drop impact point in a square region of 6 mm side size (Fig. 7). The chosen PDA set-up allowed to measure drop size in the diameter range of 5.5– 250 lm together with the vertical (normal to the wall) velocity component. A further post-processing was developed to obtain a sort of ‘‘extended p.d.f.’’ using data coming from both techniques. The diameter p.d.f. was evaluated from the results from both techniques, covering two partially overlapping size ranges: 5.5–250 lm (PDA) and 40 lm–few mm (IAT). The two techniques are statistically different because the PDA gives a instantaneous, local measurement, while the IAT is determining the measure of the drops located at a given time (and produced up to that time) in the measurement box over the impacted plate, i.e. ‘‘integrating’’ in space and time the diameter p.d.f. Therefore, before comparing the IAT probability distribution at the time t0, the PDA measurements were integrated in time up to t0. As a correct space integration of the PDA p.d.f. was not possible to perform (due to the limited number of measurement locations), a uniform drop counting was assumed all over the measurement region. This assumption is partially confirmed from the IAT measurements that show an almost uniform drop number distribution (in the range 40 lm to few millimetres) over the PDA measurement region. Finally, a scaling of the IAT p.d.f. and of the integrated PDA p.d.f. was performed by equating
Fig. 7. PDA measurement positions above the heated plate.
(through a least square method) the count values where the two size ranges overlap, obtaining a sort of ‘‘extended’’ p.d.f. (see also Fig. 8). The dependence of drop size on {x, y} coordinates was found to be neglectful for both size ranges (5.5– 250 lm by PDA and 40 lm–few mm for IAT) and also the normal velocity, in the region analysed by the PDA, was almost independent of the location in the {x, y} plane. 3.2.1. Boiling regimes and effect of surface roughness As the two boiling regimes were found to be morphologically very different, in this section they will be analysed separately. (a) Bubble boiling regime. The drop data rate (which is related to the mass flow rate through the PDA measurement volume) was found to depend strongly on time during a first period of about 40 ms after drop impact, while later a milder dependence is observed (Fig. 9). This is linked to the first phase of the nucleate boiling when a large number of small bubbles are produced and burst when the liquid/air interface is reached. The values of the mean diameter (d10) reported in Fig. 10 were obtained by PDA measurements (range: 5.5– 250 lm) as it was not practically suitable to acquire a sufficient number of pictures on a such long time interval. d10 is slightly dependent on time after drop impact but is independent of the distance from the wall. The effect of roughness does not appear to be significant and also the differences between curves relative to different wall distances should not be considered significant (the magnitude of diameter rms in each time slot may reach values as large as 100% of mean values, due to the difficulty to get larger data samples as the data rate was very small). The average velocity depends on the distance from the wall (Fig. 11), clearly due to the action of the drag on the ejected droplets (as gravity effects are neglectful
Fig. 8. Example of an extended p.d.f.: superposition of the Image Analysis Technique p.d.f. and the time-integrated PDA p.d.f. (rough surface, T = 150 C, t = 24 ms, Ca = 0.0431, La = 133,000, We = 247).
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Fig. 10. Time evolution of the secondary drop mean diameter measured by the phase Doppler anemometer at different locations above the rough and smooth heated surfaces (Ca = 0.0431, La = 133,000, We = 247).
Fig. 9. Time evolution of the secondary drop number measured by the phase Doppler anemometer at different locations above the smooth (a) and rough (b) heated surfaces (Ca = 0.0431, La = 133,000, We = 247).
on those distances), and decreases with time. No velocity size correlation appears to exist. This further analysis confirms that, for this regime, also the extended size distributions do not depend on the distance from the wall. It was interesting to notice that, although the mean diameter evaluated on the PDA data alone is quite close to that evaluated on the extended distribution (discrepancy about 10%), the Sauter mean diameter (d32), as expected, is strongly different, because the bigger drops detected by IAT play an important role in increasing d32. Table 2 reports the results: the d10 obtained with the smooth surface is comparable to that obtained with the rough surface, whereas the Sauter mean diameter (d32) is smaller (about 25%). The quantitative analysis shows that the secondary atomisation characteristics do appear to be influenced by wall roughness in the bubble boiling regime. (b) Film boiling regime. PDA measurements in this regime were quite time consuming, as the number of small secondary drops is small for this regime. Just after the impact, a burst of secondary drop production is observed (Fig. 12). A possible explanation of this phe-
Fig. 11. Time evolution of the secondary drop mean velocity measured by the phase Doppler anemometer at different locations above the smooth (a) and rough (b) surfaces at T = 150 C (Ca = 0.0431, La = 133,000, We = 247).
nomenon is related to the existence of a sort of transient bubble boiling regime, although no other experimental evidence exists, to the authorsÕ knowledge. Then the vapour film, formed by the fast phase transition, levitates the liquid from the surface thus inhibiting bubble formation and the subsequent break-up. The mentioned initial
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Table 2 Comparison among the mean diameters obtained by extended p.d.f. S: Rz = 1.6 lm d10 150 C 260 C d32 150 C 260 C
25.58 35.64 86.5 221.7
R: Rz = 14.5 lm 25.3 46.32 105.3 274.1
Table 3 Liquid properties of pure water and the glycerine/water mixtures % wt. glycerine/water
Viscosity (kg/m s)
Density (kg/m3)
Surface tension (kg/s2)
0 8.8 50 60
1.076 · 103 1.243 · 103 4.958 · 103 9.239 · 103
996.2 1019.5 1128.5 1154.9
7.370 · 102 7.087 · 102 6.545 · 102 6.517 · 102
Table 4 Impact conditions for the experiments with different liquid viscosities
Fig. 12. Time evolution of the secondary drop number measured by the phase Doppler anemometer at different locations above the rougher (R) heated surface for the film boiling regime (Ca = 0.0431, La = 133,000, We = 247, T = 260 C).
burst is also observed by the image acquisition (Fig. 6). The IAT analysis shows that the number of drops produced is about one-tenth than that observed under the same conditions for bubble boiling regime, whereas the size distributions (and the extended ones too) are very similar. The secondary drop diameters (both d10 and d32) are larger than for the bubble boiling regime, as it was suggested by the qualitative analysis of the images above reported (Table 2). Moreover, for the film boiling regime the rougher surface produces larger droplets. The other characteristics, like the data rate evolution and the size evolution, do not seem very much affected by the surface roughness in this boiling regime. As a general remark, the secondary atomisation is much less efficient under the film boiling regime, as the overall mean diameter is much larger than that found in bubble boiling, with a small influence of the surface roughness. 3.2.2. Effect of liquid viscosity The effect of liquid viscosity on the size of secondary droplets was investigated for both boiling regimes. To change significantly the viscosity, four water– glycerine mixtures were used, and Table 3 reports the values of the mass concentration and physical properties. As it was practically impossible to maintain com-
% wt. glycerine/water
Viscosity (kg/m s)
Diameter (mm)
Velocity (m/s)
0 8.8 50 60
1.076 · 103 1.243 · 103 4.958 · 103 9.239 · 103
2.11 2.91 1.99 1.99
2.94 2.55 3.01 3.2
plete similarity between all experiments while varying significantly the viscosity (only with the first two liquids, namely pure water and 8.8% glycerine–water mixture, the same Ca and La numbers could be maintained, see Fig. 1), it was decided to keep at least Ca equal for the two experiments with the larger viscosities (55% and 60% glycerine concentration, Ca = 0.375), but to a value different than that obtained with the other two mixtures (Ca = 0.044). In this way the impact velocity for the experiments with the four liquids were quite close to each other (see Table 4, the largest difference is about 20% of the average value), and this parameter is expected not to have a large effect on secondary atomisation under conditions where the phenomenon is mainly driven by the wall-drop heat transfer. Only measurements with IAT were performed since the need of cleaning the wall after the impact of few drops, to eliminate the residuals of glycerine, caused the duration of the experiments to be impracticably long. Fig. 13 reports the mean value of d32 (in the IAT measuring range) as a function of liquid viscosity for both
Fig. 13. Effect of the liquid viscosity on the secondary droplet SMD for two different surface temperatures (rough surface, see Table 4 for the experimental conditions).
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levitation and the increase of viscosity may reduce the spreading, thus keeping the lamella thickness larger and yielding larger droplets after break-up. 3.3. Effect of primary drop size
Fig. 14. Effect of the primary drop diameter d0 on the secondary droplet SMD evolution (rough surface, bubble boiling regime, Ca = 0.044, distilled water).
boiling regimes (Rz = 14.5 lm). It is interesting to observe that for the bubble boiling regime the effect of large variation of viscosity is much less important than for the film boiling regime. This may be due to the fact that the average size in film boiling regime is mainly determined by the break up of the liquid lamella after
The dependence of the secondary drop size on the primary one is an argument of capital importance as it is often postulated a linear scaling between them [18]. A first experiment to study this possibility was then designed: three drops of different size were made to impact on the same surface under the same impacting conditions in terms of Capillary number (Ca ¼ 0:045) and the secondary drop size was measured through the IAT technique. Fig. 14 reports the secondary drop size for the three sizes showing that the influence of the primary drop size on the secondary ones exists and Fig. 15(a), reporting the average drop size evaluated over all the drops produced during the firsts 25 ms after impact, shows that secondary drop size depends linearly on the primary drop size but it cannot be considered proportional to it, as shown in Fig. 15(b). As it may be expected, the primary drop size is not the sole parameter determining the size of secondary droplets, but its influence should be considered significant.
4. Conclusions Two different regimes of atomisation were investigated by varying the wall temperature: (1) a bubble boiling regime, for wall temperature larger than saturation temperature and lower than Leidenfrost temperature, characterised by large production of secondary drops of small size mainly directed along the normal to the wall; (2) a film boiling regime, for wall temperature larger than Leidenfrost temperature, characterised by a lower number of secondary drop production of a larger size on the average and a trajectory initially directed almost tangentially to the wall.
Fig. 15. Effect of the primary drop diameter d0 on the Sauter mean diameter (a) and on the scaled SMD (b) time averaged value (bubble boiling regime, Ca = 0.044, distilled water).
Many morphological differences were found between the two regimes: the formation of a central jet and the levitation of the liquid lamella with subsequent disruption in larger drops (for film boiling regime) and a larger number of small secondary drops (for the bubble boiling regime), are the most evident. Two non-intrusive measurement techniques, a phase Doppler anemometer and an Image Analysis Technique based on CCD Camera acquisition, were used simultaneously to obtain quantitative information about the secondary droplet characteristics in two different diameter ranges. A statistical technique allowed the estimation of an extended p.d.f., capable to characterise the
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secondary droplet diameter from 5.5 lm to few millimetres. From the performed measurements the following could be obtained: (a) the effect of roughness appears to be secondary but not negligible, particularly for the film boiling regime: the decrease of surface roughness changes the morphology (disappearing of the central jet) and increases slightly the mean drop diameters; (b) the increase of liquid viscosity increases considerably the secondary drop size for the film boiling regime, whereas it seems not significant for the bubble boiling regime. A first experiment shows that secondary drop size depend linearly on the primary drop size but it cannot be scaled by it.
Acknowledgments The work was partially financed by European Project DWDIE (5th Framework program) and by the National Program PRIN2000. The authors would like to thanks Prof. Cam Tropea and Prof. Paolo Tartarini for the useful discussions and information and Dr. J. Watanabe for the work during data acquisition.
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[3] T. Loulou, J.-P. Bardon, First stages of metallic drop cooling after its impact on a substrate, Revue Generale de Thermique 36 (9) (1997) 682–689. [4] M. Seki, H. Kawamura, K. Sanokawa, Transient temperature profile of a hot wall due to an impinging liquid droplet, ASME J. Heat Transfer 100 (1978) 167–169. [5] J.D. Bernardin, C.J. Stebbins, I. Mudawar, Effects of surface roughness on water droplet impact history and heat transfer regimes, Int. J. Heat Mass Transfer 40 (1) (1996) 73–88. [6] M. Pasandideh-Fard, S.D. Aziz, S. Chandra, J. Mostaghimi, Cooling effectiveness of a water drop impinging on a hot surface, Int. J. Heat Fluid Flow 22 (2) (2001) 201–210. [7] W.M. Healy, J.G. Hartley, S.I. Abdel-Khalik, On the validity of the adiabatic spreading assumption in droplet impact cooling, Int. J. Heat Mass Transfer 44 (20) (2001) 3869–3881. [8] J.D. Bernardin, C.J. Stebbins, I. Mudawar, Mapping of impact and heat transfer regimes of water drops impinging on a polished surface, Int. J. Heat Mass Transfer 40 (2) (1997) 247–267. [9] J.D. Naber, P.V. Farrell, Hydrodynamics of droplet impingement on a heated surface, SAE 930919, 1993, pp. 1–16. [10] L.H.J. Wachters, N.A.J. Westerling, The heat transfer from a hot wall impinging water drops in the spheroidal state, Chem. Eng. Sci. 21 (1966) 1047–1056. [11] K. Araki, A. Moriyama, Deformation behaviour of a liquid droplet impinging on a hot metal surface, ICLASS 1982, 1982, pp. 389–396. [12] F. Akao, K. Araki, S. Mori, A. Moriyama, Deformation of a liquid droplet impinging onto hot metal surface, Trans. ISIJ (1980) 20. [13] S. Yao, K.Y. Cai, The dynamics and Leidenfrost temperature of drops impacting on a hot surface at small angles, Exp. Thermal Fluid Sci. 1 (1988) 363–371. [14] M. Di Marzo, P. Tartarini, Y. Liao, D. Evans, H. Baum, Evaporative cooling due to a gently deposited droplet, Int. J. Heat Mass Transfer 36 (17) (1993) 4133–4139. [15] M. Di Marzo, P. Tartarini, Y. Liao, D. Evans, H. Baum, Dropwise evaporative cooling, ASME HTD 166 (1991) 51–58. [16] S. Chandra, C.T. Avedisian, On the collision of a droplet with a solid surface, Proc. Royal Soc. London, 42 (1991) 13–41. [17] H. Chaves, A.M. Kubitzek, F. Obermeier, Dynamic processes occurring during the spreading of thin liquid films produced by drop impact on hot walls, Heat Fluid Flows 20 (1999) 470–476. [18] G.E. Cossali, M. Marengo, M. Santini, Single drop empirical models for spray impact on solid walls: a review, Atomisation and Spray Journal, AT/EU/043, accepted for publication.
Secondary atomisation produced by single drop vertical impacts onto heated surfaces G.E. Cossali *, M. Marengo, M. Santini Universita` di Bergamo, Facolta` di Ingegneria, viale Marconi 5, 24044 Dalmine (BG), Italy Received 30 August 2004; received in revised form 10 November 2004; accepted 7 December 2004
Abstract The paper reports an experimental analysis of the secondary atomisation produced by the impact of a single drop on a solid heated surface. Different wall temperatures were used to study different boiling regimes. The size of secondary drops produced by the impact was measured by two techniques, namely the phase Doppler anemometry (PDA) and the image analysis technique (IAT); this allowed to extend the measurable size range from 5.5 lm up to few mm. Two impacting walls with different surface roughness were used to show the effect of this parameter on different atomisation regimes. The liquid viscosity was also varied in a limited range by using water–glycerol mixtures. Image analysis allowed also to define the details of the morphology of drop spreading and break-up. 2005 Elsevier Inc. All rights reserved. Keywords: Two-phase flows; Nucleate boiling; Leidenfrost regime; Drop impact; Phase Doppler anemometry; Image analysis
1. Introduction The impact of liquid drops onto solid heated surfaces is a phenomenon linked to many industrial applications, such as the hot coating of surfaces, the metal surface cooling in the steel industry and in the nuclear power plants, the direct fuel injection in diesel and gasoline engines and in many other technological processes where it is useful to achieve a local and rapid thermal control. When the surface temperature is higher than the liquid saturation temperature, the phase transition caused by the intense heat transfer from the solid wall to the spreading liquid radically modifies the impact dynamics, comparing to the isothermal case [1]. The explosions of the vapour bubbles at the liquid–air interface of the spreading lamella originates a secondary atomisation. The impact velocity, the surface temperature, the impact
*
Corresponding author. Tel.: +39 0352052309; fax: +39 035562779. E-mail address: [email protected] (G.E. Cossali).
0894-1777/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.12.003
angle, the surface tension and the viscosity of the liquid and the surface wettability [2], effusivity [3,4] and roughness [5] are the main parameters influencing the process and many research works are already available in the open literature. During the very first phase (s = tV0/d0 < 1) the drop temperature is almost constant [6,7], while the surface temperature is rapidly cooled to the interface temperature (determined by the liquid and wall effusivities). When the liquid–wall contact area increases, the heat transfer becomes relevant and a nucleate boiling process takes place, with the generation of bubbles and secondary droplets [8]. Varying the surface temperature, different atomisation regimes are observed [8], mainly related to different boiling regimes that are governed by the wall temperature and the liquid Nukiyama (TN) and Leidenfrost (TL) temperatures. When the wall temperature is below the TN, the lamella spreading process shows a peculiar behaviour: even for low Weber numbers, there is a strong contraction of the lamella after spreading, with production of secondary droplets [9,10]. Akao et al. [11,12] found different
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Nomenclature Ca D, d d32 d10 La Ra Rz R S SMD T t V We
Capillary number (Vl/r) drop diameter Sauter mean diameter (also SMD) arithmetic mean diameter Laplace number (dqr/l2) arithmetical mean roughness 10-point mean roughness rough surface smooth surface Sauter mean diameter (also d32) temperature time impact velocity Weber number (dqV2/r)
critical Weber numbers for three regimes (deposition, ejection of few droplets after rebounding and ‘‘secondary atomisation’’) using different liquids, different drop diameters and a coated copper surface. When the wall temperature is increased, the lamella may break-up in liquid ligaments and, under certain conditions, the liquid bulk on the surfaces tends to break-up and/or rebound [8]. When the surface temperature is above the Leidenfrost temperature, the formation of a vapour film during the liquid spreading lead to a rather different impact morphology, and Wachters and Westerling [10] were the first to describe quantitatively the secondary atomisation regimes. The Leidenfrost temperature has a phenomenological definition and it depends also on the dynamics parameters, such as the impact velocity and angle [13]. Resuming, many literature papers, most at low Weber impacts (for example, see also [14–16]) and few at ‘‘moderate’’ Weber number (We < 300) give as outcomes the phenomenon morphology, the impact regimes, the spreading evolution, the maximum spreading radius, the evaporation time and the surface temperature profile and evolution. The aim of this paper is to study the boiling induced secondary atomisation produced by drop impacting normally to heated surfaces at moderate Weber numbers (250 < We < 660). Besides a detailed qualitative description of the various impact regimes, the work is addressed to obtain further new information about the secondary drop diameter distributions resolved in time and space. The next section describes the experimental set-up and the measuring techniques, then the experimental results are reported and discussed, considering particularly the effects of surface roughness, liquid viscosity and primary drop size on the different atomisation regimes. The last section summarises the main results.
z
distance from the wall (vertical direction)
Greek symbols l liquid viscosity q liquid density r liquid surface tension s dimensionless time Subscripts L Leidenfrost N Nukiyama sat saturation w wall 0 primary drop
2. Experimental set-up Distilled water and water–glycerine mixture drops were let to fall by gravity onto an aluminium alloy (AlMg3) circular disc, electrically heated from below. Wall temperatures larger than 330 C can be reached and maintained by PC-based PID controller. A thermocouple positioned under the centre of the impacting wall supplies the feedback needed by the heater controller. Needles were used as drop generators, the internal diameters ranged from 0.16 mm to 2 mm, and they were connected through flexible pipes to a small, pressurised tank containing the working liquid. The impacting frequency was controlled by a throttling device and was low enough to assure a true single drop impact, (no overlapping and no fouling from previous drop impact were assured and the initial wall temperature was re-obtained after each impact). The drop generator produced drops with diameters ranging between 1.8 and 4.6 mm while the drop impact velocity could range between 1 m/s and about 6 m/s. A CCD camera (Colour PCO SensiCam, 1280 · 1024 pixels) with a long distance microscope objective (Navitar, 12X) was used to acquire the images of the impact. The CCD acquisition and illumination systems were driven by a triggering system made by an He–Ne laser (1 mW power) imaged onto a photodiode. The falling drop crossing the laser beam gave the trigger pulse, a delay was then added to account for the drop travel time from the laser beam to the impact wall; the correct delay was evaluated from the images acquired during the setup procedure. A continuous back illumination system was used and, to get the correct time resolution, acquisition times from 5 ls to 20 ls were used. A commercial image analysis code (Image-Pro Plus) was used and home built routines were developed for measuring
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secondary drop size, roundness, etc. The size range that can be measured by this image analysis technique (IAT) is from 40 lm to few millimetres. As a second sizing technique a DANTEC PDA (phase Doppler anemometer) was used to measure simultaneously the secondary drop velocity (the component normal to the wall) and size. A purposely-built computer code was used to design the optical set-up, in order to minimise the effect of the lack of knowledge of secondary droplets refracting index, as the liquid temperature of ejected secondary droplets is unknown. The PDA size range, with the chosen configuration, was between 5.5 lm and 250 lm, thus partially overlapping the IAT size range. This allowed reconstructing the entire drop size distribution (hereinafter called p.d.f.) from 5.5 lm to few millimetres by means of a proper postprocessing. Acquisition of measurements from many subsequent drop impacts allowed to obtain statistically significant samples. The PDA triggering system was the same described above. In this case it was not possible to observe directly the drop impact, the delay between the trigger pulse and the actual drop impact time was then calculated from the impact velocity and the distance of the laser beam from the wall, then the absolute accuracy in defining the time after impact was about 1 ms. The accuracy in defining the surface temperature was evaluated to be better than 2 K, keeping into account the wall temperature variation due to the heat transfer caused by subsequent impact of drops. The IAT technique used to measure the secondary droplet size have an absolute accuracy better than 25 lm (with the optical configuration used in this work). The accuracy in measuring the primary drop size was better than 3%. The impacting velocity was measured from multiple exposed images and its accuracy was better than 3%.
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Table 1 Arithmetical mean roughness (Ra) and 10-point mean roughness (Rz) of the surfaces used for the experiments Surface
Rz (lm)
Ra (lm)
S R
1.6 14.5
0.205 2.844
primary drop size was varied. Capillary number (Ca = Vl/r) and Laplace number (dqr/l2) will be used to represent the impact conditions in non-dimensional form (as they can be interpreted as drop non-dimensional velocity and size), however also the corresponding Weber number (We = q dV2/r = La Ca2) will be explicitly given throughout the paper. Non-dimensional time defined as s = tV/d will be used. 3.1. Morphology of the impact The morphological structure of the liquid lamella after drop impact is analysed and the main results are discussed here. The effect of temperature will be analysed as well as the effect of changing liquid viscosity and surface roughness. 3.1.1. Boiling regimes Fig. 1(a) shows the comparison of the impact outcomes at different wall temperatures (We = 247). The comparison to the picture taken with Tw = 70 C (below saturation temperature) shows that for these impacting conditions the secondary atomisation is due only to thermal (boiling) effects as inertia effects are not strong enough to produce secondary atomisation. At least two main regimes of boiling were detected, depending on the wall temperature, which can be related to different regimes of secondary atomisation. When the wall temperature is above the saturation temperature of the impacting liquid but well below the Leidenfrost temperature (TL, that depends on many parameters such as
3. Results and discussion This section is devoted to show the characteristics (both qualitative and quantitative) of the secondary atomisation produced by the impact of a single liquid drop onto a hot surface. The dynamical impact conditions were chosen in order to avoid the secondary atomisation when the surface temperature (Tw) was below the liquid boiling temperature (Tsat) to assure that the observed secondary atomisation was solely an effect of the heat transfer process. The surface temperature is the value measured prior the drop impact; care was taken to assure that the same temperature was recovered after each impact. Two different surface roughness were analysed (see Table 1) to show possible effects of this parameter on secondary atomisation. Liquid viscosity was changed by using different water–glycerine mixtures and also
Fig. 1. Effect of wall temperature (70 C, 150 C, 260 C) on the impact morphology for two different fluids: impact onto rougher surface (R) at s = 13; pure water: Ca = 0.0431, La = 133,000, We = 247; water-glycerine 8.8% mass mixture: Ca = 0.0447, La = 136,000, We = 272.
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the surface roughness, the impact angle, etc. [9,13]) bubble boiling takes place. A wall temperature of 150 C (well below the pool boiling value of the Leidenfrost temperature for water under steady conditions, TL,p 220 C) was chosen to represent this regime. In this case bubbles, produced by the heat transfer from the wall, grow and rupture the liquid lamella, producing a plethora of small secondary drops (Fig. 1). When instead the wall temperature is above the Leidenfrost temperature (Tw > TL) the film boiling regime is reached. A wall temperature of 260 C (well above the nominal Leidenfrost temperature) was chosen to represent this regime. In this case, the wall temperature is sufficiently high to generate a vapour film almost immediately after impact, that may finally levitate the liquid from the wall (see Fig. 1a) and the diminished liquid–wall contact is responsible of the smaller number of secondary drops. It is necessary to stress that the present definition of the Leidenfrost temperature is not linked with an actual measurement of the minimum heat flux from the wall, but is purely morphological. The value of 260 C is therefore to be intended only for the present experiment and for the considered parameter ranges. Moreover, for the case at 260 C (film boiling regime) the formation and break-up of a sort of central jet (the sequences in Figs. 2 and 3 show better the effect) is observed, its generation starting just at the beginning of the spreading phenomenon (s = 3 and s = 4). Chaves et al. [17] suggested as a possible mechanism for droplet formation under bubble boiling regime, the break-up of thin jets caused by the explosion of vapour bubbles through the liquid lamella. Fig. 4 shows an enlargement of some pictures evidencing a phenomenon in some way analogous to that suggested by Chaves et al. [17], that may be one of the main causes of the secondary atomisation under this regime. But the ‘‘pagoda-like’’ bubbles are not visible in previous works and need a further theoretical explanation. Another important difference between the two regimes is the character-
Fig. 2. Effect of liquid viscosity on the impact morphology: impact onto rougher surface (R) at 150 C; pure water: Ca = 0.0431, La = 133,000, We = 247; water-glycerine 8.8% mass mixture: Ca = 0.0447, La = 136,000, We = 272.
Fig. 3. Effect of liquid viscosity on the impact morphology for two different fluids: impact onto rougher surface (R) at 260 C; pure water: Ca = 0.0431, La = 133,000, We = 247; water-glycerine 8.8% mass mixture: Ca = 0.0447, La = 136,000, We = 272.
istic times at which the secondary atomisation starts. In bubble boiling regime (Tw = 150 C) the formation of first secondary droplets starts few milliseconds after impact (Fig. 2) whereas the secondary drop production starts immediately after impact for film boiling (Tw = 260 C) regime (Fig. 3). Also the secondary drop direction is affected by the wall temperature: for bubble boiling the secondary drop direction is always mainly vertical, whereas for film boiling there is also an ejection in radial direction during the very first impacting period. Finally, for the film boiling regime, the presence of a vapour film produces the levitation of relatively large droplets coming from the break-up of the film layer (Fig. 3). 3.1.2. Effect of surface roughness To study the effect of surface roughness on the secondary atomisation mechanism, experiments were run using two different surface roughness (Table 1) for both boiling regimes and with the same impacting conditions.
Fig. 4. Vapour bubble bursts at the liquid/air interface. Formation of ‘‘pagoda-like’’ bubbles (notice the liquid jet on top of the bubbles).
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For the bubble boiling regime (Tw = 150 C, Fig. 5) the difference is mainly on spreading that appears faster for the larger surface roughness and atomisation appears earlier. For film boiling (Tw = 260 C, Fig. 6) no clear central jet is observed for the smoother surface impact (although the phenomenon is not fully deterministic), and a larger secondary droplet production (quite similar to the bubble boiling droplet production) is observed during the early stage. 3.1.3. Effect of liquid viscosity The influence of viscosity was studied by comparing the results obtained with water to those obtained using different water–glycerol mixtures. In particular, the use of a solution of glycerol in water (8.8% in mass) allowed, by using proper values of the impact velocity and diameter, to maintain the non-dimensional impacting conditions in term of Ca, La and We numbers almost equal (with a maximum difference of 4%) to those used in the previously described experiments. For bubble boiling regime the time at which the secondary atomisation starts is influenced by the liquid viscosity: for the water–glycerol solution the secondary atomisation starts later than for pure water (Fig. 2) and this effect must be due only to the increase of viscosity, since all the other Fig. 6. Time evolution of water drop impact onto smooth (S) and rough (R) surfaces at 260 C; pure water: Ca = 0.0431, La = 133,000, We = 247.
important parameters (the heat of vaporisation, the liquid conductivity and the specific heat) are practically unvaried. A possible explanation may rely on the fact that an increase of liquid viscosity may decrease the local Reynolds number, then decreasing the convective heat transfer from wall to liquid and depressing vaporisation. For the film boiling regime the central jet disappears when viscosity is increased, the higher viscous dissipation of kinetic energy may be responsible for this effect. 3.2. Quantitative image analysis and PDA measurements
Fig. 5. Time evolution of water drop impacts onto smooth (S) and rough (R) surfaces at 150 C; pure water: Ca = 0.0431, La = 133,000, We = 247.
From images similar to those reported above the size of the secondary droplets was evaluated after proper image conditioning and analysis by means of ad hoc built routines. The spatial accuracy of the acquisition set-up and the image analysis technique allowed measuring only droplets larger than about 40 lm. Important parameters, such as the minimum (dmin) and maximum (dmax) diameter of the drop (for a deformed droplet dmin 5 dmax), the size of the rectangle enclosing each droplet, etc., were also measured and post-processing procedures were set-up to reject droplets having large aspect ratios. A statistical analysis allowed to discover
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that values of the aspect ratio dmax/dmin larger than 2 were mainly due to uncertainty on the measured size of the smallest droplets, then measurements with dmax/dmin > 2 were rejected during the post-processing procedures. To enlarge the measured size range toward smaller sizes, the PDA system was set up and the experiments were repeated performing droplet diameter measurements at three different distances (2, 4 and 9 mm) above the drop impact point in a square region of 6 mm side size (Fig. 7). The chosen PDA set-up allowed to measure drop size in the diameter range of 5.5– 250 lm together with the vertical (normal to the wall) velocity component. A further post-processing was developed to obtain a sort of ‘‘extended p.d.f.’’ using data coming from both techniques. The diameter p.d.f. was evaluated from the results from both techniques, covering two partially overlapping size ranges: 5.5–250 lm (PDA) and 40 lm–few mm (IAT). The two techniques are statistically different because the PDA gives a instantaneous, local measurement, while the IAT is determining the measure of the drops located at a given time (and produced up to that time) in the measurement box over the impacted plate, i.e. ‘‘integrating’’ in space and time the diameter p.d.f. Therefore, before comparing the IAT probability distribution at the time t0, the PDA measurements were integrated in time up to t0. As a correct space integration of the PDA p.d.f. was not possible to perform (due to the limited number of measurement locations), a uniform drop counting was assumed all over the measurement region. This assumption is partially confirmed from the IAT measurements that show an almost uniform drop number distribution (in the range 40 lm to few millimetres) over the PDA measurement region. Finally, a scaling of the IAT p.d.f. and of the integrated PDA p.d.f. was performed by equating
Fig. 7. PDA measurement positions above the heated plate.
(through a least square method) the count values where the two size ranges overlap, obtaining a sort of ‘‘extended’’ p.d.f. (see also Fig. 8). The dependence of drop size on {x, y} coordinates was found to be neglectful for both size ranges (5.5– 250 lm by PDA and 40 lm–few mm for IAT) and also the normal velocity, in the region analysed by the PDA, was almost independent of the location in the {x, y} plane. 3.2.1. Boiling regimes and effect of surface roughness As the two boiling regimes were found to be morphologically very different, in this section they will be analysed separately. (a) Bubble boiling regime. The drop data rate (which is related to the mass flow rate through the PDA measurement volume) was found to depend strongly on time during a first period of about 40 ms after drop impact, while later a milder dependence is observed (Fig. 9). This is linked to the first phase of the nucleate boiling when a large number of small bubbles are produced and burst when the liquid/air interface is reached. The values of the mean diameter (d10) reported in Fig. 10 were obtained by PDA measurements (range: 5.5– 250 lm) as it was not practically suitable to acquire a sufficient number of pictures on a such long time interval. d10 is slightly dependent on time after drop impact but is independent of the distance from the wall. The effect of roughness does not appear to be significant and also the differences between curves relative to different wall distances should not be considered significant (the magnitude of diameter rms in each time slot may reach values as large as 100% of mean values, due to the difficulty to get larger data samples as the data rate was very small). The average velocity depends on the distance from the wall (Fig. 11), clearly due to the action of the drag on the ejected droplets (as gravity effects are neglectful
Fig. 8. Example of an extended p.d.f.: superposition of the Image Analysis Technique p.d.f. and the time-integrated PDA p.d.f. (rough surface, T = 150 C, t = 24 ms, Ca = 0.0431, La = 133,000, We = 247).
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Fig. 10. Time evolution of the secondary drop mean diameter measured by the phase Doppler anemometer at different locations above the rough and smooth heated surfaces (Ca = 0.0431, La = 133,000, We = 247).
Fig. 9. Time evolution of the secondary drop number measured by the phase Doppler anemometer at different locations above the smooth (a) and rough (b) heated surfaces (Ca = 0.0431, La = 133,000, We = 247).
on those distances), and decreases with time. No velocity size correlation appears to exist. This further analysis confirms that, for this regime, also the extended size distributions do not depend on the distance from the wall. It was interesting to notice that, although the mean diameter evaluated on the PDA data alone is quite close to that evaluated on the extended distribution (discrepancy about 10%), the Sauter mean diameter (d32), as expected, is strongly different, because the bigger drops detected by IAT play an important role in increasing d32. Table 2 reports the results: the d10 obtained with the smooth surface is comparable to that obtained with the rough surface, whereas the Sauter mean diameter (d32) is smaller (about 25%). The quantitative analysis shows that the secondary atomisation characteristics do appear to be influenced by wall roughness in the bubble boiling regime. (b) Film boiling regime. PDA measurements in this regime were quite time consuming, as the number of small secondary drops is small for this regime. Just after the impact, a burst of secondary drop production is observed (Fig. 12). A possible explanation of this phe-
Fig. 11. Time evolution of the secondary drop mean velocity measured by the phase Doppler anemometer at different locations above the smooth (a) and rough (b) surfaces at T = 150 C (Ca = 0.0431, La = 133,000, We = 247).
nomenon is related to the existence of a sort of transient bubble boiling regime, although no other experimental evidence exists, to the authorsÕ knowledge. Then the vapour film, formed by the fast phase transition, levitates the liquid from the surface thus inhibiting bubble formation and the subsequent break-up. The mentioned initial
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Table 2 Comparison among the mean diameters obtained by extended p.d.f. S: Rz = 1.6 lm d10 150 C 260 C d32 150 C 260 C
25.58 35.64 86.5 221.7
R: Rz = 14.5 lm 25.3 46.32 105.3 274.1
Table 3 Liquid properties of pure water and the glycerine/water mixtures % wt. glycerine/water
Viscosity (kg/m s)
Density (kg/m3)
Surface tension (kg/s2)
0 8.8 50 60
1.076 · 103 1.243 · 103 4.958 · 103 9.239 · 103
996.2 1019.5 1128.5 1154.9
7.370 · 102 7.087 · 102 6.545 · 102 6.517 · 102
Table 4 Impact conditions for the experiments with different liquid viscosities
Fig. 12. Time evolution of the secondary drop number measured by the phase Doppler anemometer at different locations above the rougher (R) heated surface for the film boiling regime (Ca = 0.0431, La = 133,000, We = 247, T = 260 C).
burst is also observed by the image acquisition (Fig. 6). The IAT analysis shows that the number of drops produced is about one-tenth than that observed under the same conditions for bubble boiling regime, whereas the size distributions (and the extended ones too) are very similar. The secondary drop diameters (both d10 and d32) are larger than for the bubble boiling regime, as it was suggested by the qualitative analysis of the images above reported (Table 2). Moreover, for the film boiling regime the rougher surface produces larger droplets. The other characteristics, like the data rate evolution and the size evolution, do not seem very much affected by the surface roughness in this boiling regime. As a general remark, the secondary atomisation is much less efficient under the film boiling regime, as the overall mean diameter is much larger than that found in bubble boiling, with a small influence of the surface roughness. 3.2.2. Effect of liquid viscosity The effect of liquid viscosity on the size of secondary droplets was investigated for both boiling regimes. To change significantly the viscosity, four water– glycerine mixtures were used, and Table 3 reports the values of the mass concentration and physical properties. As it was practically impossible to maintain com-
% wt. glycerine/water
Viscosity (kg/m s)
Diameter (mm)
Velocity (m/s)
0 8.8 50 60
1.076 · 103 1.243 · 103 4.958 · 103 9.239 · 103
2.11 2.91 1.99 1.99
2.94 2.55 3.01 3.2
plete similarity between all experiments while varying significantly the viscosity (only with the first two liquids, namely pure water and 8.8% glycerine–water mixture, the same Ca and La numbers could be maintained, see Fig. 1), it was decided to keep at least Ca equal for the two experiments with the larger viscosities (55% and 60% glycerine concentration, Ca = 0.375), but to a value different than that obtained with the other two mixtures (Ca = 0.044). In this way the impact velocity for the experiments with the four liquids were quite close to each other (see Table 4, the largest difference is about 20% of the average value), and this parameter is expected not to have a large effect on secondary atomisation under conditions where the phenomenon is mainly driven by the wall-drop heat transfer. Only measurements with IAT were performed since the need of cleaning the wall after the impact of few drops, to eliminate the residuals of glycerine, caused the duration of the experiments to be impracticably long. Fig. 13 reports the mean value of d32 (in the IAT measuring range) as a function of liquid viscosity for both
Fig. 13. Effect of the liquid viscosity on the secondary droplet SMD for two different surface temperatures (rough surface, see Table 4 for the experimental conditions).
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levitation and the increase of viscosity may reduce the spreading, thus keeping the lamella thickness larger and yielding larger droplets after break-up. 3.3. Effect of primary drop size
Fig. 14. Effect of the primary drop diameter d0 on the secondary droplet SMD evolution (rough surface, bubble boiling regime, Ca = 0.044, distilled water).
boiling regimes (Rz = 14.5 lm). It is interesting to observe that for the bubble boiling regime the effect of large variation of viscosity is much less important than for the film boiling regime. This may be due to the fact that the average size in film boiling regime is mainly determined by the break up of the liquid lamella after
The dependence of the secondary drop size on the primary one is an argument of capital importance as it is often postulated a linear scaling between them [18]. A first experiment to study this possibility was then designed: three drops of different size were made to impact on the same surface under the same impacting conditions in terms of Capillary number (Ca ¼ 0:045) and the secondary drop size was measured through the IAT technique. Fig. 14 reports the secondary drop size for the three sizes showing that the influence of the primary drop size on the secondary ones exists and Fig. 15(a), reporting the average drop size evaluated over all the drops produced during the firsts 25 ms after impact, shows that secondary drop size depends linearly on the primary drop size but it cannot be considered proportional to it, as shown in Fig. 15(b). As it may be expected, the primary drop size is not the sole parameter determining the size of secondary droplets, but its influence should be considered significant.
4. Conclusions Two different regimes of atomisation were investigated by varying the wall temperature: (1) a bubble boiling regime, for wall temperature larger than saturation temperature and lower than Leidenfrost temperature, characterised by large production of secondary drops of small size mainly directed along the normal to the wall; (2) a film boiling regime, for wall temperature larger than Leidenfrost temperature, characterised by a lower number of secondary drop production of a larger size on the average and a trajectory initially directed almost tangentially to the wall.
Fig. 15. Effect of the primary drop diameter d0 on the Sauter mean diameter (a) and on the scaled SMD (b) time averaged value (bubble boiling regime, Ca = 0.044, distilled water).
Many morphological differences were found between the two regimes: the formation of a central jet and the levitation of the liquid lamella with subsequent disruption in larger drops (for film boiling regime) and a larger number of small secondary drops (for the bubble boiling regime), are the most evident. Two non-intrusive measurement techniques, a phase Doppler anemometer and an Image Analysis Technique based on CCD Camera acquisition, were used simultaneously to obtain quantitative information about the secondary droplet characteristics in two different diameter ranges. A statistical technique allowed the estimation of an extended p.d.f., capable to characterise the
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secondary droplet diameter from 5.5 lm to few millimetres. From the performed measurements the following could be obtained: (a) the effect of roughness appears to be secondary but not negligible, particularly for the film boiling regime: the decrease of surface roughness changes the morphology (disappearing of the central jet) and increases slightly the mean drop diameters; (b) the increase of liquid viscosity increases considerably the secondary drop size for the film boiling regime, whereas it seems not significant for the bubble boiling regime. A first experiment shows that secondary drop size depend linearly on the primary drop size but it cannot be scaled by it.
Acknowledgments The work was partially financed by European Project DWDIE (5th Framework program) and by the National Program PRIN2000. The authors would like to thanks Prof. Cam Tropea and Prof. Paolo Tartarini for the useful discussions and information and Dr. J. Watanabe for the work during data acquisition.
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