Paper ID ICLASS EXPERIMENTS ON BREAKUP OF WATER-IN-DIESEL COMPOUND JETS

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1 ICLASS-2006 Aug.27-Sept.1, 2006, Kyoto, Japan Paper ID ICLASS EXPERIMENTS ON BREAKUP OF WATER-IN-DIESEL COMPOUND JETS Sheng-Lin Chiu 1, Rong-Horng Chen 2, Jen-Yung Pu 1 and Ta-Hui Lin 1,* 1 Department of Mechanical Engineering, National Cheng Kung University, Taiwan, R.O.C., thlin@mail.ncku.edu.tw 2 Department of Mechanical Engineering, Southern Taiwan University of Technology, Taiwan, R.O.C. ABSTRACT The experimental investigation on the disintegrating behavior of a single diesel oil jet and a water-in-diesel jet, which consists of the core jet, a water jet, surrounded by a sheath of the shell jet, a diesel oil jet, was conducted. These two kinds of liquid jet will break up into distinct modes under different conditions. For the single diesel oil jet, four modes of the breakup type were observed and the dimensionless wavelength / D is the main controlling parameter. For the water-in-diesel compound jet, the core-to-shell mass ratio and the dimensionless wavelength / D play important roles to the breakup behavior. For a core-to-shell mass ratio less than 0.5, five breakup modes were observed at varied dimensionless wavelength / D in our experiments. For lower water-to-diesel mass ratio, the shell jet dominates the breakup behavior mainly and the range forming the stable compound drop stream is wider than the range for the stable pure diesel drop stream. That both the single diesel oil jet and the water-in-diesel compound jet break up randomly for / D 3 in good agreement with Rayleigh s analysis. has been found to be Keywords: drops, liquid jets, compound jets, breakup 1. INTRODUCTION to the size of the jet radius. During the last decade, research in this field intensified The phenomena of capillary instability of liquid jets and drop formation have been of interest to scientists and engineers for more than a century. The physical properties of liquid jets play a significant role in many industrial applications such as spray cooling, spray drying, and the spinning of synthetic fibers and so on. The prominent predecessor, Rayleigh [1], who made a theoretical work on the instability of liquid jets, gave some fundamental concepts to successors. With the assumption of an inviscid liquid and neglecting the effects of surrounding air, Rayleigh inferred that only axisymmetrical surface disturbances with wavelengths greater than the circumference of the jet would grow, i.e. the breakup would occur when the amplitude of these disturbances would grow because of their application in ink-jet printing. The understanding of jet breakup process is crucial to the control and elimination of the satellite-drop, which causes malfunctions of the printer. Due to the linear approach presented by Rayleigh failed to predict the formation of satellite-drop, which has been recognized as a nonlinear behavior, several theoretical studies considering nonlinear effects on jet instability were made by Yuen [2], Rutland and Jameson [3], Nayfeh [4]and LaFrance [5]. Donnelly and Glaberson [6] conducted typical experiments on the capillary instability of a liquid jet. They made a direct measurement of the growth rate of the disturbances and the complete dispersion curve has been investigated. The effects of the viscosity on the stability

2 have also been examined, but the formation of the satellite drop has not been considered. One of the experimental studies on the nonlinear effects of jet instability was that of Goedde and Yuen [7]. They found that the first break-up point to form a separated ligament always occurs on the downstream end of the ligament. This observation was contradicted by Pimbley and Lee [8], who investigated experimentally on the behavior and formation of satellite drops in a liquid jet. Pimbley and Lee found that satellite separation from a main drop can occur on the fore side of the drop first, on the aft side first, or on both ends simultaneously. Also, they observed that the satellite drop may merge forward or backward with the adjacent main drop. The research literature on the experimental investigations on the satellite-drop behavior and the nonlinear perturbation analyses of the jet up to 1979 has been surveyed and discussed in Bogy [9]. Later, Vassallo and Ashgriz [10] using water as a working fluid performed an experiment on the satellite-drop formation and merging in liquid jet breakup. They grouped the jet breakup into several distinct regions depending on the disturbance wavelength and the undisturbed jet diameter and discovered a new type of satellite merge, which is referred to as the reflexive merging satellite. The discussion mentioned above focuses mainly on a single liquid jet. In 1983, Hertz and Hermanrud [11] developed a liquid-in-liquid compound jet, which consists of the central primary jet surrounded by a sheath of secondary fluid for application in ink-jet printer. They described the mechanism of the compound jet quantitatively and found that the compound jet exhibited three different types of instabilities under varied jet velocity. After Hertz and Hermanrud [11], many theoretical and numerical researches on the liquid compound jet were presented [12-15]. The understanding is, however, insufficient on the breakup of the liquid compound jet. In the present work, a method differing from that of Hertz and Hermanrud [11] was utilized to produce a liquid-in-liquid compound jet and a periodic excitation was performed on the jet for breakup. It is the purpose of this paper to compare qualitatively the hydrodynamics of a liquid-in-liquid compound jet to a single liquid jet and seek parameters which control the breakup processes of a liquid-in-liquid compound jet. 2. EXPERIMENTAL APPARATUS AND CONTROLLING PARAMETERS As shown in Figure 1, the experimental apparatus comprised a liquid jet generation system, which included a nozzle, two liquid reservoirs, a pulse generator and a voltage amplifier; and a visualization system, which included a digital video camera, a monitor, a stroboscope and a digital oscilloscope. Two types of nozzle, i.e. a glass nozzle of 0.4mm inner diameter for generation of the single diesel oil jet and a concentric nozzle for generation of the water-in-diesel compound jet, were used. The concentric nozzle comprises a dental needle of 0.17 mm inner diameter placed inside a glass tube of 0.47 inner diameter, as shown in the enlarged picture in Figure 1. The core liquid, water, of the water-in-diesel compound jet was issued through the dental needle from the water reservoir and the shell liquid, diesel, through the glass tube from the diesel reservoir. For easy tracking of the liquid, the core water jet was dyed red. The exits of nozzles were polished smoothly. All jets emanate vertically downwards from nozzles into the ambient gas. Figure 1. Experimental apparatus

3 A piezo-electric plate driven by a signal generator and amplifier gave the jet a periodic excitation to induce the jet breakup. The amplified amplitude of the periodic excitation was kept at a constant value (about 40 voltages). According to previous researchers [8-10], the amplitude of the periodic excitation would change the formation mechanism of the satellite drop. In the present study, the effects of the excitation amplitude on the breakup behavior of liquid jets were not discussed. A digital video camera, a monitor and a stroboscope were used as the visualization means for the observation and recording of the breakup processes. The stroboscope was aligned towards the video camera and operates in a mode of short delay with respect to the pulse signal of the function generator to obtain slow motion of the breakup event. For monitoring the frequency and shape of exciting signal after the amplification, a digital oscilloscope was used. A dimensionless wavelength / D was chosen to be the controlling parameter for describing the characteristics of the breakup of the jet, where λis the wavelength of the disturbance and D is the undisturbed jet diameter [10]. 3. RESULTS AND DISCUSSIONS At first, the experimental observations on the breakup processes of diesel oil jets due to external excitation were conducted. The properties of the working fluids are shown in Table 1.During the performance of experiment, we kept the flow rate of the diesel oil constant and modulated the frequency of the excitation acting on the jet monotonously by every 10 Hz. Several different types of the jet breakup were observed in our experiments, as shown in Figure 2. We further classified the breakup types into four modes as follows: Mode I: random breakup; Mode II: uniform drops; Mode III: single-satellite; Mode IV: train of varied drops. For Mode I, the jet does not break for a long distance from the exit of the nozzle. No regular breakup type of the jet was observed. Based on Rayleigh s linear theory, the input excitations do not grow for wavelengths less than the circumference of the jet; therefore, the ambient disturbances Table 1. Properties of the working fluids Fluids Water Diesel 3 3 Density 998 kg / m 817 kg / m Surface tension coefficient N/m at 25 C N/m at 25 C Dynamic viscosity 1.005cp at 20 C 3.16cp at 20 C Figure 2. Breakup modes of a single diesel oil jet. dominate the jet breakup process. For Mode II, a stable stream of diesel oil drop is formed. Obviously, the input excitations grow fast enough so that the jet breaks up into uniform sized drops. The drop size became larger as the excitation frequency decreases. Then, a tiny drop called a satellite drop pinches off from the tip of the liquid bridge in the downstream end and this mode is named Mode III. Although Pimbley and Lee [8] showed that the satellite drop can separate from the fore side of the main drop first, on the aft side first, or on both ends simultaneously, the satellite drop usually forms in the downstream end of the liquid jet in the present study. This was because we conducted the experiment with constant amplitude. By decreasing the excitation frequency further, the liquid bridge became thicker gradually. More than one satellite drop started to form and Mode IV was reached. For Mode IV, a train of irregular sized drops was formed in one wavelength. The number of the irregular sized drops increases as the excitation frequency decreases. Vassallo and Ashgriz [10]

have observed the similar phenomena and called this a long-wavelength Rayleigh breakup. Figure 3 shows the measured data for a single diesel oil jet with different flow rates.

4 have observed the similar phenomena and called this a long-wavelength Rayleigh breakup. Figure 3 shows the measured data for a single diesel oil jet with different flow rates. All four jets of different flow rate exhibited the same tendency of breakup processes. For / D 3, Mode I occurs. This result agrees with the predictions of Rayleigh s analysis. Mode II, the mode for stable stream of drops, occurs in the range of 3 / D 4.2, as shown in the gray area in the Figure 3. For / D 4.2, the satellite drops formed between two main drops. One satellite drop formed in the range of 4.2 / D 8 and more than one satellite drop, i.e., a train of irregular sized drop formed in the range of / D 8. As expected, the dimensionless wavelength / D is the main controlling parameter for the breakup of the single liquid jet. run of the experiments and the averaged values were used. We grouped the breakup of the water-in-diesel compound jet into five modes as shown in Figure 4. They were as follows; Mode I: random breakup, Mode II: uniform single-core compound drop, Mode III: shell-liquid satellite or compound satellite, Mode IV: train of varied drops, and Mode V: uniform multi-core compound drop.. Figure 4. Breakup modes of a water-in-diesel compound jet. For Mode I, the input excitations do not grow and no regular pattern of drop formation occurs. The core liquid, water, breaks up into drops because of higher surface tension even though the shell liquid, diesel oil, is still in the shape of Figure 3. Wavelength dependence of the breakup mode of a single diesel oil jet Now we pay our attention to the breakup of a liquid compound jet. In this study, the water-in-diesel compound jet consisting of a shell fluid, diesel, and a core fluid, water. We define the water-to-diesel mass ratio as m / m, where m and m W D are the mass flow rates of water and diesel oil, respectively. The flow rates of water and diesel oil were measured by graduated cylinder before and after each W D a jet. For Mode II, the compound jet breaks up into stable compound drops, i.e., one water drop is encased by one diesel drop. For Mode III, one of two types of satellite, namely, a pure diesel satellite or a compound satellite is formed. A pure diesel satellite and a compound satellite are shown in the left column and the right column in the Figure 4, respectively. Both of them contain one satellite drop between two main drops. For Mode IV, a train of irregular sized drops are formed in one wavelength and these drops include pure diesel drops or compound drops. For Mode V,

5 because the breakup times of the core and the shell are different, a compound drop containing more than one core drop is formed. With respect to the current experiment, there are three things worthy to be noted. Firstly, because the core liquid momentum is not sufficiently large, a continuous core jet without the shell jet cannot be formed. Actually, the core liquid is drawn out by the shell jet and looks like a jet. Secondly, because of the higher surface tension, the core liquid always breaks up earlier than the shell jet. Thirdly, due to the impossibility of keeping the flow field perfectly axisymmetric, the core liquid trends to clings to the side of the shell jet. Figure 5 shows the dependence on wavelength for the different breakup mode of a water-in-diesel compound jet. We found that the breakup mechanism of the compound jet is similar to the single jet for a low water-to-diesel mass ratio, namely, 0.25.In other words, the interaction between the core liquid and the shell liquid is weak, and the shell liquid dominates the breakup behavior. For 0.25, the stable compound drop stream form in the range of 3 / D 6. On the other hand, the stable drop stream occurs in the range of 3 / D 4.2 for a single jet as shown in the figure for 0. Therefore, the range for the formation of drop of a water-in-diesel compound jet is wider than that of a single diesel oil jet. A concept of Vassallo and Ashgriz [10] is helpful for us to understand the causes. Consider the water-in-diesel compound liquid column shown in Figure 6. The liquid bridge which is formed between two main drops will first break on the downstream side. Then, if the upstream side of the liquid bridge separates from the main drop, a satellite forms. This process is associated with the pressure imbalance in the liquid bridge. In Figure 6 the pressure on the free end of the liquid bridge is larger than that on the attached end by is the liquid surface tension and / R,where R is the radius of curvature. This pressure difference will push the free end toward the attached end and result in preventing the formation of the satellite drop. The pressure difference is proportion to the radius of the jet inversely. Therefore, it becomes more difficult for the formation of the satellite drop for a smaller jet. To the water-in-diesel compound liquid jet, the core jet breaks into spherical drop prior to the shell jet; hence the radius of the liquid bridge reduces dramatically for the elimination of the space occupied originally by core jet. This process suppresses the formation of satellite drops. From Figure 5, we found that the larger the is, the more noticeable the tendency is. Figure 5. Wavelength dependence of the breakup mode of a For 0.25 water-in-diesel compound jet., i.e., increasing the core liquid, the interactions between the core jet and the shell jet become stronger. The shell liquid does not dominate the break up behavior any more. The breakup modes differ from those of the single jet. The range for the formation of stable water-in-diesel compound drops is wider further, and even form in two discrete section. It is noted that for 0.5, the water-in-diesel compound jet cannot be broken for / D 3, regardless of the value of. Therefore, for a water-in-diesel compound jet, Rayleigh s analysis that only axisymmetrical surface disturbances with wavelengths greater than the circumference of the jet would grow is still suitable.

6 Taiwan, R.O.C. under the contract NSC E REFERENCES 1. Rayleigh, Lord. Theory of Sound, Vol. 2, Figure 6. The pressure difference of a compound jet. 4. CONCLUSIONS A traditional glass nozzle and a concentric nozzle was utilized to produce a single diesel oil jet and a water-in-diesel compound jet, respectively. The sine wave excitation with constant amplitude act on the jet for breakup. By using a digital video camera, a monitor and a stroboscope as the visualization means for the observation and recording of the breakup processes, we compared the breakup mechanism of the water-in-diesel compound jet to that of the single diesel oil jet. Based on the experimental investigations, some conclusions have been made as follows: 3 (1) For mass flow rate less than g / sec, four modes of the breakup were observed for single diesel oil jets. The stable drops form in the range of 3 / D 4.2. (2) The breakup type of the water-in-diesel compound jet was grouped into five modes for 0.5. The surface tension of the core or shell liquid has effects on the breakup mechanism. (3) For lower, namely 0.25, the shell liquid of the water-in-diesel compound jet dominates the breakup behavior mainly. The range for the formation of drop of a water-in-diesel compound jet is in 3 / D 6 and wider than that of a single diesel oil jet. (4) Regardless of the type of the jet, i.e., a single diesel oil jet or a water-in-diesel compound jet, no regular breakup mode was observed for / D 3. This result is in good agreement with the prediction of Rayleigh. 5. ACKNOWLEDGEMENT 2. Yuen, M. C., Non-liner capillary instability of a liquid jet, J. Fluid Mech. Vol. 33, p.151, Rutland, D. F. and Jameson, G.. J. Theoretical prediction of the sizes of drops formed in the breakup of capillary jets, Chem. Eng. Sci., Vol. 25, p.1689, Nayfeh, A. H., Non-liner instability of a liquid jet, Phys. Fluids, Vol. 13, p.841, LaFrance, P., Non-liner breakup of a laminar liquid jet, Phys. Fluids, Vol. 18, p.428, Goedde, E. F. and Yuen, M. C., Experiments on liquid jet instability, J. Fluids Mech., Vol. 40, p.495, Donnelly, R. J. and Glaberson, W., Experiments on the capillary instability of a liquid jet, Proc. R. Soc. Lond. A, Vol. 290, p.547, Pimbley, W. T. and Lee, H. C., Satellite droplet formation in a liquid jet, IBM J. Res. Dev., Vol. 21, p.21, Bogy, D. B., Drop formation in a circular liquid jet, Ann. Rev. Fluid Mech., Vol. 11, p.207, Vassallo, P. and N. Ashigriz, Satellite formation and merging in liquid jet, Proc. R. Soc. Lond. A, Vol. 433, p.269, Hertz, H. and Hermanrud, B., A liquid compound jet, J. Fluids Mech., Vol. 131, p.271, Sanz, A. and Meseguer, J., One-dimensional linear analysis of the compound jet, J. Fluids Mech., Vol. 159, p.55, Radev, S. and Gospodinov, P., Numerical treatment of the steady flow of a liquid compound jet, Int. J. Multiphase Flow, Vol. 12, p. 997, Radev, S. and Tchavdarov, B., Linear capillary instability of compound jets, Int. J. Multiphase Flow, Vol. 14, p.67, Tchavdarov, B. M., Minev, P. D. and Radev, S., Comput. Methods Appl. Mech. Engrg., Vol. 118, p.121, This work was supported by Notional Science Council,

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