Experimental analysis of the behavior of the droplets of high viscous fluids

impacting on a flat heated surface

A AMORESANO, V.NIOLA, F.LANGELLA Mechanical and Energetic Department

Naples University “Federico II” Via Claudio 21 80125

ITALY viola@unina.it http://www.dime.it

Abstract: - A lot of study speak about the behavior of water droplets, fuel droplets with particular references to burning and combustion processes, agricultural applications, heat transfer from heat surfaces. In this paper the behavior of droplets of high viscous fluid is analyzed to approach a new field of the application of the spray technology. In the last years, the development reached by propellers in terms of improvement of service and efficiency showed the problem of lubrication systems. A kinematics couples reaching high friction conditions, call for new solutions which allow the improvement of lubrication process[5], increasing transmission efficiency and lifetime of transmission. The aim of the present study is to develop a new system of lubrication where one or more injectors atomize lubricant previously filtered and send it in little drops on the surface of the transmission elements. Key-Words: - Forced lubrication, Droplets coalescence, Experimental 1 Introduction In the last years the study about droplet behavior has been a renewed interest. Some results carried out from these studies analyze very well the mechanisms of the breakup of a droplet in a spray jet or during the impact on a hot surface or wet surface, roughness surface and so on. Others studies analyze , instead, [1] the interactions between two or more droplets when atomized in a liquid jet or analyze the shape changing due to high Re number. In other words the studies about the dynamics laws governing the physic of the droplets (interaction, break up, ecc…) are strongly alive to day.. The proposed technology should allow to solve all those errors which happen by applying the traditional lubrication systems. Lubrication is no more realized through messy movement of the oil inside the carter by means of 'shaking', but by using nozzles action which sprays on the kinematics couples the right quantity of oil as well as stated trajectory and speeds thus between the contact surfaces there is always the designed quantity of lubricant and there is the possibility to optimize the lubrication regime. Because of a system working, it is necessary that the drops of the spray jet, once the kinematics surfaces are reached, could share coalesce in a very short time to form then an uninterrupted film of lubricating. In this paper has given a description of some tests on the drop coalescence phenomenon and 'sharing' for a lubricating oil in order to collect data useful for next study on geometrical and fluid-dynamic parameters of the spray system. Some base concepts are shown on physical phenomena which happen during spray lubrication process as atomization, drop-surfaces impact and 'sharing'.

2 Lubrication Spray Fundamentally this system is represented as pressurized circuit where oil, which is taken away from a small basin by means of pump, passes through a filtering system and it reaches the injectors; these ones atomize the oil so the generated droplets will impact on the coupling surfaces

continuing then on a crop small basin. This technology try to solve the inconvenient that we find in the traditional lubrication system. In fact, in the lubrication spray system the oil when it arrives on the surface, coming back from a process of filtering, without impurity. Another advantage of this solution is the speed working without lack. In fact, since the wheels are not dipped into the basin they are not submitted to a pasty endurance, there is not problem linked to the reduction of performance, and

Fig. 1. Layout of spray lubrication system

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there is no any problem concerning the oil emulsioning and consequentially heat production. To achieve a good lubrication it is necessary to tweak fluid-dynamic settings of[1] the spray jet, as the distribution of the diameters of the drops, the geometry of the above mentioned jet, the quantity of lubricator, the frequency of the injector, the speed of drops impact. The optimization of all these factors are the aim of the study about this new technology. Also if the spray represents a consolidate technology and it is supported by a good theory and experimental base, the results found in literature [3] supply a partial help to the studies of our interest. While in the common spray applications the main purpose is to obtain a nuke force, in order to accelerate chemical/physical processes produce onto the interface between two different phases, in the lubrication spray the primary purpose is to induce the atomized jet drops, once reached the surface to lubricate, to coalesce as soon as possible in order to create a perpetual process. Noticeably the lubrication spray process is the result of the following three phases:

• lubricant atomization • interaction of the jet with the surface

(impact drop-surface) • interaction between drops of the jet on the

surface (coalescence) A particular attention is set for the last two points, because the lubricant atomization process already has a wide bibliography. Phenomena of impact and coalescence are experimentally analyzed in this work 3 Experimental Activity The study concerned the phenomena of drop impact and coalescence. As already introduced in the previous chapter, proper lubricator is due to a continuous lubricant process between the surfaces during their relative motion; the purpose of this research is checking if at the temperature of functioning exist the conditions to obtain a complete coalescence of the lubricant drops injected under spray form. A high speed camera was used for observing the dynamical phenomena of coalescence. The experimental apparatus used for this study is schematically shown in Fig. 3.It is composed of

following system: Heated plate simulating the job surface of a car change temperature regulation

• Falling-drops • Illumination plate • Acquisition temperature plate

• Acquisition imagine

3.1 Drop impact study for highly viscous fluid

To optimization of lubrication spray process goes through the optimization of each step above mentioned. Each of them is characterized by a specific phenomenology. The test carry out the study of the impact of a single drop in order to analyze the behavior of a single drop impinging on a hot surface Experimental proves were made using a lubricant for transmission EP type, whose characteristics are as follows:

Mark: EUROLUBE Type: eplus 5 SAE 80W/90 API GL5

3.2 Drop expansion time

The time of the droplets expansion has been observed to analyze the influence of the surface temperature and the impact speed forward the expansion of the drop. Three test each one with a full value of the height of the crash of drop has been evaluated , to register the time of enlargement for the three different value, of plate temperature. The speed impact has been banded at three different height between plate and system of drops.

Fig.3 Setup facility

Fig. 2 Gear box lubricated by spray

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The height has been chosen for checking the growing sensibility of drops after their impact. The heights choose for the test are 15, 40 and 70 cm, corresponding ( 2v gh= , value of impact speed) 1.7, 2.8 and 3.7 m/s respectively. For each value of droplet velocity and on the basis of the characteristics of fluid, the following values of Weber number were carried out (ρ = 877,7 kg/m3, σ = 26 mN/m, Dmean = 3 mm) • We = 301 • We = 804 • We = 1407

3.2 Droplet Impact The impact of the oil droplet on the surface is without rebound[4] and splashing this behavior is

due to the viscosity. The droplet after the impact increases its area. When the drop tries to growth it lose the circular form, but it tends to flow towards a

preferential direction imposed by the set-up of the surface. The tests show the drop is longer and it signs up a new form like an oval and the accounting mount up between x and z axes. The phenomenon has been observed on a temporal scale of 3 seconds, starting from the instant of impact, which is the starting point With a distance ejector-plate equal to 15, 40 and 70 cm, and it

corresponding to impact speed of the drops equal to 1.7, 2.8 and 3.7m/s, respectively, setting for each height the temperature of the plate at 80, 95 and 110°C. In each test, independently from the height of fall, i.e. from the speed of impact, the increasing of

Fig. 4 We vs height of

Fig. 6 Droplet area after the impact for different wall temperature at 40 cm of the height

Fig.7 Droplet area after the impact for different wall temperature at 70

cm of the height distance Fig.5 Droplet area after the impact for different wall temperature at 15 cm of

the height distance

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temperature of the surface favors the phenomenon of the drop expansion The effect of the temperature

is evident especially in the last stint of the observation interval (i.e., for long period of time). This happens because the thermal trials are not instant trials, as a consequence, the drop reacts to the thermal effect caused by the plate after a certain interval of time. In order to evaluate the effect of the impact speed[18] on the expansion it has been useful to operate a comparison of test performed for different heights of fall with reference to the several temperature of plate. Observing the diagrams below where the droplet impact is characterized by the Weber number it show that the speed of impact influences both the dimension of the drop in the instant of impact, and the extension speed of the same drop for each temperature of the plate.

4 COALESCENCE OF TWO DROPS

The coalescence with the formation of a liquid bridge among two drops growing up to reach the same drops, so at a certain point they don't result more noticeable. The process seems to be regulated by many parameters[5]. The purpose of this research is to identify the most meaningful of them and to characterize quantitatively their influence on the phenomenon. The search is focused on the parameters related to the surface of impact. It is concerning the injectors and the kinematic parameters of the drops. In particular the influence of the following parameters was analyzed: • Temperature of the surface

• Impact speed of drops • Distance between injectors • Diameter of the drops • Surface not wrinkled 4.1 Coalescence analysis (injectors distance equal to 8mm)

The first parameter to be analyzed is the speed of impact of the drops. It has indirectly been regulated varying the distance of nozzle-surface. Such distances are the same used for the tests on the single drop. It regards the value of temperature, settled at 80°C. (i.e. typical temperature of lubrication process). The distance between the injector and the hot plate has been initially chosen equal to 8 mm. Such value represents the least value obtainable in this phase of analysis of the parameters. At smaller distances the phenomenon of the coalescence happens with very fast dynamics, so it is results difficult to appreciate the influence of the other parameters during the trial. The two nozzles have been set, with reference to the surface, along the direction of roughness of the plate. This favours the formation of the liquid bridge between the two drops Fig 9 , the expansion happens strongly along the direction connecting the two ones. The characteristic

dimension used for the quantitative study of the coalescence is the thickness of the liquid bridge formed between two drops. Time of observation of

Fig. 8 Increment percentage of droplet area, for various Weber number and

wall temperature at 80°C

t = 0

t = 0.2 s

g.Fig. 9 Liquid bridge formation

Fig. 10 Characteristic dimensions of the liquid bridge

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phenomenon has been selected equal to 1.5 s beginning from the instant of first ligament that forms the bridge. The fig. 10 shows[2] the behaviour of the phenomenon of coalescence obtained varying the heights of fall of the drops. The diagrams have been drawn by acquiring the images from the by camera CCD at speed of 1000 frams/s and recording the phenomenon from the impact up to the complete coalescence of the drops. In this way it has been possible to analyze the growth and therefore the time of formation and disappearance of the bridge between the two drops. The correctness of the instants of beginning formation of the bridge and its disappearance has been achieved through the image processing which allowed the cleaning of the frames and therefore the correct extraction of the contours. Then from the elaboration of the images ( i.e Fig. 9)s it has been possible to draw the characteristic dimension of the bridge to the different instants of time. From the following graph Fig 10) it is deduced as the law of variation of the characteristic dimension of the in operation bridge of the time both of the type:

( ) 5,0tkd = [3]

( ) 5,0tkd =

Representing the thickness of the bridge vs. the square root of the time the results is a straight . Interpolating the points with a linear function a coefficient of correlation is obtained equal to 0.99 for all the diagrams. The curve of tendency, that allows to draw the constant k, underlines that such constant assumes different values in the three cases and precisely: • distance injector-plate 15cm; k=2.502

• distance injector -plate 40cm; k=2.47 • distance injector -plate 70cm; k=2.17

5 CONCLUSIONS

To vary the speed of impact a direct proportionality has been found between the thickness of the liquid bridge and the square root of the time as follows

tδ ∝ The result is in accordance with the available results in literature [3]. Different test conditions and different characteristics of fluid employed (i.e., water and oil) set the absolute time of coalescence is different; it is nevertheless remarkable the fact that the law of variation preserves the same form. Increasing the speed of impact the constant of proportionality decreases. This result is a further confirmation of as high speed of impact negatively influences the time of widening and therefore of the coalescence.

This also happens with a distance between the nozzles equal to 10 mm. The diagrams in fig. 11 and 12 represent the values of the thickness of the bridge between the drops vs. the square root of the time for different values of the number of Weber. Besides from the analysis of different test it is deduced that the growing law of the liquid bridge is also valid for the lubricant employed and therefore for highly viscous fluid. In fact in all the test it was found the following relationship

d=k(t)0.5 The increasing of the distance between the

Fig. 11

Fig.10

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nozzles, with equal speed of impact of the

drops, determines a reduction of coefficient k, Diagrams in fig 13, 14,15 show, for several value of the speed of impact, a comparative behaviour of the temporal evolution of the liquid bridge with the reference to the two

values of the distance between the nozzles. It is

important to underline that, the increasing of the distance between the injectors, influence the dynamics of growth of the liquid bridge, and also increases the beginning of the bridge formation , because each drop tend to expand greater before

coming in contact with the nearest one. In order to have a rapid coalescence and therefore the quickly formation of a continuous film of lubricant. It is important that the droplets will have high velocity and their impact have to be closer between them

REFERENCES

[1] Bernard J. Hamrock, Fundamentals of Fluid Film Lubrication, NASA Reference Publication 1255 1991 [2] Dirk G. A. L. Aarts, Henk N.W. Lekkerkerker, Hua Guo, Gerard H. Wegdam, Daniel Bonn, Hydrodynamics of Droplet Coalescence, PhysRevLett.95.164503. [3] Mingming Wua, Thomas Cubaud and Chih-Ming Ho, Scaling law in liquid drop coalescence driven by surface tension, American Institute of Physics, 2004, DOI: 10.1063/1.1756928. [4] L. Duchemin, J. Eggers, C. Josserand. Inviscid coalescence of drops, J. Fluid Mech. 487 , 167 (2003). [5] J. Eggers, Theory of drop formation Phys. Fluids 7, 941 (1995) [6] J. Eggers, Breakup and coalescence of free-surface flow , S. Yip, Editor, Springer 2005. [7] Koch, Donald L., Bach, Gloria A., Gopinath, Arvind, The transition between coalescence and bouncing of low Weber number aerosol droplets, American Physical Society, 2000.

Fig.13

Fig.14

Fig.15

Fig.12

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