Non-Newtonian Secondary Atomization in the Bag and Multimode Break up Regimes

Transcription

1 ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, May 2015 Non-Newtonian Secondary Atomization in the Bag and Multimode Break up Regimes J. Rocha* and Paul E. Sojka M.J. Zucrow Laboratories School of Mechanical Engineering Purdue University West Lafayette, IN USA Abstract Secondary atomization of shear thinning non-newtonian liquids in the bag and multimode breakup regime was studied. Rheology for these fluids was controlled by varying amounts of Ashland s Carboxymethylcellulose (CMC-7MF or CMC-7HF) polymers, and deionized water. Three solutions having various cross model parameters were formulated. Secondary atomization was achieved using a continuous jet setup. For videos, a Vision Research Phantom v7.1 high speed camera was utilized to collect images at more than 4500 fps, which typically yielded more than 100 frames for each breakup event. Post processing was performed using in-house written MATLAB code. The max cross stream dimension at initiation time was obtained and compared to literature. Also, at the bag breakup event, max rim diameter, max bag length, and vertical displacements were acquired. The maximum cross stream dimension was found to be practically liquid invariant, while bag breakup times, vertical displacements, and transition Weber numbers were found to have liquid viscosity dependencies. Also, transition effects from bag to bag-n-stamen were identified in relation to max bag length and max rim diameter. *Corresponding author: Rocha0@purdue.edu

2 Introduction and Literature Review When large enough relative velocities exist between a liquid drop and the surrounding gas phase, the drop will deform and fragment into smaller drops. This process is known as secondary atomization. Some typical applications include pharmaceutical sprays, diesel injectors, and air assisted fuel atomizers in gas turbines [1]. There exists various modes to which drops disintegrate. Generally, the nomenclature given to modes of breakup are oscillatory deformation, bag breakup, multimode breakup, and shear breakup [2]. Each mode has its own characteristic deformation stages. In example, bag breakup involves a sphere deforming into an ellipsoid, bag growth, bag break up, and rim break up [3]. Furthermore, there are various experimental methods used to produce these breakup modes. The most popular are shock tube, continuous jet and drop towers [4]. A remarkable development found uniquely to continuous jet methods is the dual bag breakup mode which is considered within multimode breakup. This mode consist of a second bag developing after the first bag breakup [5]. Usually, for Newtonian liquids, the mode of breakup for a given relative velocity can be predicted using two non-dimensional parameters [2]. These parameters are Weber number (We), We = ρ 2 gu reld0 (1) σ l Which is the ratio of aerodynamic forces to restorative forces. While Oh number, Oh = μ l ρ l σ l d 0 (2) Considers the effect of liquid viscosity [1]. In these equations, ρ g and ρ l are the gas and liquid densities, u rel is the initial relative velocity between the gas and the liquid drop, d o is the initial drop diameter, σ l is the liquid surface tension, and μ l is the liquid phase viscosity. Further challenges become apparent when we begin to consider secondary atomization with non-newtonian liquids. These liquids involve a changing viscosity with shear rate and time of applied shear. Experimentally, the shear thinning (or pseudo plastic) liquids [6] and time dependent (or thixotropic) liquids [7] make studying the non-newtonian liquids a feasible option due to their viscosity reducing behavior as shear is increased. In contrast, a shear thickening (or dilatant) liquid would be more difficult to produce fragmentation and as a result is a less viable option to study experimentally. A few useful applications for non-newtonian liquids include aerospace propellants, bio-fuels, firefighting liquids, thermal barrier coatings, water gel explosives, paints, and many more [8]. Since the viscosity of non-newtonian liquids does vary with shear rate, then a model is required to determine the effective viscosity at a given shear. A popular model used for shear thinning liquids is the cross model, μ eff = μ + μ 0 μ 1+ γ n (3) Here, μ eff is the effective viscosity, μ 0 is the viscosity at zero shear, μ is the viscosity at infinite shear, n and α are curve fitted constants. However, α 1 n represents the characteristic shear at which the viscosity of the system is the mean of the two limiting values μ 0 and μ [9]. Despite the variable viscosity, the breakup modes are qualitatively similar to that found for Newtonian breakup. In regimes above multimode breakup, the only qualitative difference found between the two types of liquids is persistent ligaments [6-8, 10-15]. Within the bag regimes, is increased bag growth, ears extruding on the rim, and the tenacious ligaments [6, 7, and 14]. In literature, there is some experimental data including fragmented drop sizes [8, 10, 13], breakup times [6, 7, 11, 12, 14], maximum cross stream dimension [6, 7, 15], and drag coefficients [15]. However, what makes this data much scarcer is that the data from above articles is obtained at various regimes, Non-Newtonian liquids (viscoelastic, shear thickening, and shear thinning) and experimental methods. The process of secondary atomization is complex. Laser-Induced Fluorescence (LIF) is a photography method which uses emitted light within the liquid mass at wavelengths distinct from those of the laser. LIF allows in-depth visualization of surface structures. This method emphasizes just how complex and transient the break up process is [13, 15]. It is mentioned due to its visually enlightening nature on the complexities of breakup that cannot be seen with shadowgraph. Literature provides trends which seem to apply for all/most relative velocities. For instance, adding less than 2.0% of various soluble polymers/additives has been found to inhibit breakup and therefore requires higher relative velocities to reach the same breakup mode and create fragments [6, 7, 10, 11, 14]. This may be due to the higher effective viscosity produced by adding polymers. A few authors has shown that for a wide range of We numbers there is a correlation of We number required to initiate a particular breakup mode with increasing Oh number [6, 7, 15]. These plots are qualitatively similar to those found for Newtonian liquids [2]. What s more, at lower air velocities, the effects of additives becomes more pronounced [10, 14, 6]. Thus, adding polymers may be useful if a specific breakup regime is desired at higher relative velocities. However, there are other consequences to adding polymers. Many soluble additives tend to increase the fragmented drop sizes significantly, as much as 1.5 orders

3 larger [10, 16]. This is a consequence of ligaments being formed instead of drops within the various stages of breakup. In respect to these ligaments, increasing viscosity as much as 25 times, without polymers, does not have a significant effect on creating ligaments instead of drops [10, 11]. However, in literature many data points are obtained from manual measurements. This involves not only errors from pixelated shadow graphs but human error. Not many authors have attempted to apply a program to extract data. As a result of applying such a method, human error can be eliminated and allow for more revelations in differences between liquids or a lack there of. Furthermore, there is still not much data in literature which compares dimensional measurements of non-newton liquids in order to reveal relationships. This study attempts to remove human error involved in data extraction using a MATLAB code and obtain some dimensional information for Non-Newtonian liquid comparison. Solution and its Properties The polymers used in this study is ASHLAND s PH Sodium Carboxymethylcellulose (CMC) 7MF and 7HF. The solutions are 0.8%CMC-7MF, 1.4%CMC-7MF, and 0.5%CMC-7HF. The percent s are by mass dissolved in de-ionized (DI) water. These liquids are effectively inelastic (shear thinning) [17]. Thus, the viscosity decreases as shear rate increases. In the designations 7MF and 7HF, the 7 represents the degree on substitution (D.S.) which is short for 0.7 and a D.S. greater than 0.4 is water soluble. The H and M represent high and medium viscosity grades which is produced by the molecular weights of 750kDa and 250 kda. The F in the acronyms stands for food grade. The solutions were created through stirring using magnetic stirrers and masses weighed using Ohaus-Pioneer PA1502 Mass Balance with a readability of 0.01g. The surface tension was obtained using CSC Scientific s DuNouy Tensiometer with a reproducibility of 5E-5 N/m. Furthermore, the instrument required using a correction factor [18]. The systematic method was validated using water, alcohol, and glycerin. Errors were found to be less than 1% for the two former and less than 3% error for glycerin, from known values at laboratory conditions (20⁰C and 101 kpa). The viscosity vs. shear rate was acquired using TA instruments AR-G2 Rheometer and a 60 mm cone peltier plate geometry. To ensure systematically accurate results, mixtures of 75% Glycerin / 25% DI-water, 80% Glycerin / 20% DI-Water, and 85% Glycerin / 15% DI-Water were tested. All the values were compared to those in literature and found to have less than 1.5% errors [19]. The viscosity of these inelastic liquids was found using equation (3). Since infinite shear data is not available, the infinite shear viscosity was estimated as the viscosity of the base Newtonian solution, DI-Water, at laboratory conditions. The other parameters were obtained from averaging at least 3 flow sweep measurements between 1000 s 1 and 0.1s 1. The shear values below 0.6 s 1 were neglected since repeatability diminishes drastically at these lower shear rates. All the liquids, parameters, and liquid properties are listed in table 1. For visualization of accuracy between data and fitted curve, the averaged data is plotted with the cross model shown in figure 1. Error bars were not plotted on this graph because even with 2 standard deviations the errors bars were minimal and only caused clutter in the plots. Furthermore, the effective viscosity was estimated by applying an analogy to which viscosity is defined. Viscosity is historically defined through a visualization of a liquid between one stationary and one moving plate. The shear rate is the velocity of the moving plate divided by the distance between plates. Thus, for a drop, the shear rate may be approximated as the relative velocity over the drop radius. The velocity goes the free stream velocity near the edge of the drop and becomes zero at the windward stagnation point. Thus, equation 4 would be used in equation 3 to determine the effective viscosity. The effective viscosity varies with increasing velocity and is shown in figure 2. Additionally, it seems that higher molecular weighted polymers in liquids (0.5% CMC-7HF) have a higher effective zero shear viscosity yet have a larger shear thinning behavior as observed in figure 1. Thus, it seems relevant to state that at low shear rates, the higher molecular weighted polymers would have higher viscosities yet at higher shears degrade much quicker and could in fact drop below the lower molecular weighted polymers. What s more, the shear rates estimated in this study are far greater than what is needed for polymer chain degradation. γ = u rel r 0 (4) Experimental Apparatus A continuous jet setup was used for these experiments and utilized a clear acrylic air nozzle which was designed for uniform exit velocity. Between the 15 cm inlet and 2.54 cm outlet a polycarbonate honeycomb structure was imbedded to prevent large scale eddies and a fine wire mesh to produce small turbulence which dissipates before the nozzle exit is reached. The compressed air is supplied from a 300p.s.i. supply tank and is controlled using a needle valve. The flow rate is monitored using a Micro Motion F-series Coriolis flow meter where readings were correlated to exit velocity for this particular system using LDA and PIV [20]. Drops were generated using a compressed tank that was filled with the liquid of interest and supplied to a 25 gauge needle (inner

4 Liquid μ 0 (Pa s) μ (Pa s) n(-) α (sec n ) α 1 n (sec 1 ) ρ l (( kg m 3) σ l ( N m ) 0.8% CMC-7MF % CMC-7MF % CMC-7HF diameter of 0.26 mm). The needle was placed 10 cm above the nozzle exit and 10 mm downstream of it. A schematic of the setup is shown in figure 3 [6]. The lighting was produced by a Kratos 1000 W Xe arc lamp which was then expanded and diffused. High speed images were taken using Vision Research s Phantom v7.1 high speed camera to collect images at more than 4500 fps. To obtain dimensional data from these images, a clear calibration sheet was used and later correlated to pixels in the drop images. Table 1. Cross curve fitted parameters. Figure 3. System Schematic Figure 1. Experimental and Cross curve fitted viscosity vs. shear rate. The open symbols represent the data and the solid/filled symbols are from the curve fit. MATLAB Code and Methods To obtain temporal data and the specific data points discussed in this study, a semi-automatic MATLAB code was written. The basic treatment of images was noise removal, contrasting, converting to a black and white image and obtaining data from matrix operations and numerical analysis. A significant point that was considered was whether the center of mass was being correctly obtained during data extraction. When the density of drop is uniform (no bag is formed), the projected area centroid is approximately equal to the mass centroid. However, once the drop begins to form into a bag, most of the mass remains on the rim of the drop as can be seen in figure 6. Thus, once the bag emerges, using the rim axis as the mass centroid is a reasonable assumption for obtaining displacement, velocity, and acceleration. Sample calculations revealed this to be true. Time zero was found using a geometrical argument. When the drop deforms by 10% of its original projected area (figure 4), then time zero is the frame prior to that point. 10% is chosen because there is always noise in any system yet 10% deformation is significant enough to not be mistaken with noise. It is obvious from figure 4 that the drop is still nearly spherical at this point and has a small indentation in the bottom left corner. The relative velocity is in the direction given by the arrow. Figure 2. Estimated effective viscosity.

5 Figure 4. Typical image when 10% deformation is reached. Time zero would begin at a frame prior to this. In this study, initiation time is defined as the time difference between time zero and when the stream direction length (or horizontal length) becomes a minimum (figure 5) which is of similar definition in literature. Furthermore, the purpose of this time is to indicate when analytical and computational methods must switch from a sphere deforming into an ellipsoidal shape to a bag emerging from the same ellipsoid, with respect to the bag modes of breakup. Furthermore, the choice of this method is valid because any growth past the minimum is essentially the bag growing. Figure 5. Typical image of minimum stream direction length. Relative velocity indicated by arrow. The bag breakup time is defined here as the time it takes from time zero to when the bag first bursts (figure 6). It should be noted that there may be 2 bags which developed during breakup and therefore has 2 bag break up times. Figure 6. Typical image of when the bag first bursts. To ensure that data is being obtained correctly over time, the code created pop up figure windows for each step and each frame in the movie so the user can visually inspect the data being obtained frame by frame as data is collected (figure 7). All points and lengths being obtained were plotted onto the original frame of the drop and all figures were zoomed onto the deforming drop. Figure 7. Two sample frames used for visual inspection during data extraction. Results and Discussions For this study, the regimes of focus are bag breakup, bag-n-stamen, and the transition between them. This involves 14 < We < 37 or alternatively 18 < u rel < 29. Additionally, the Mach number for these experiments was always less than 0.2 so the air can be treated as incompressible. In the figures presented here, the graphs are color and shape coded. The color red identifies the bag breakup regime, green is transition, and blue is bag- N-stamen breakup. The shapes identify the liquids, solid squares for 0.8%CMC-7MF, solid triangle for 1.4% CMC-7MF, and solid X for 0.5%CMC-7HF. The first relation considered is known to literature as the maximum cross stream dimension (d c /d 0 ) at initiation time (figure 8). The plot shows that d c /d 0 is similar for all liquids considered. As can be seen, the liquid closest to Newtonian (0.8% CMC-7MF) follows the curve prediction from literature more accurately. However, those deviating further from Newtonian (1.4% CMC-7MF and 0.5%CMC-7HF) seem to have slightly lower values than the Newtonian predictions. Furthermore, using the estimated effective viscosity (figure 2), all liquids considered have an Oh < 0.1 which is the conditional requirement for the predicted curve. Therefore, the prediction curve is still reasonably accurate for the tested non-newtonian liquids under these conditions. Furthermore, this plot also reveals that continuous jet and shock tube experiments have similar results for these particular measurements. Also, it should be noted that there is no distinct transitioning effect as the breakup regime transitions from bag breakup to stamen breakup. There is only a seemingly steady increase of (d c /d 0 ).

6 We 0.8%CMC 7MF transition < We 0.5%CMC 7HF transition < We 1.4%CMC 7MF transition Therefore, the same relative trend for bag breakup time and transition We follow the same tendency as would be expected if the effective viscosities followed, μ 0.8%CMC 7MF eff < μ 0.5%CMC 7HF eff < μ 1.4%CMC 7MF eff Figure 8. Maximum Cross stream dimension at initiation time. While figure 8 depicts little variation between values there are indeed distinct differences between the liquids. Figure 9 is one example. It can definitely be stated from this plot that the time it takes for the bag to break is not constant and decreases with We. This is due to increased shearing and pressure build up within the bag as the relative velocity increases. Also, there is no apparent effect from transitioning from bag breakup to bag-n- stamen breakup and the time required for breakup drops by almost a factor 3 over the range tested. What s more, the relative time for each liquid s bag to break has the following relationship, T 0.8%CMC 7MF bag < T 0.5%CMC 7HF bag < T 1.4%CMC 7MF bag Figure 9. Time when bag first erupts. Additionally, looking at the green symbols in figure 9, it shows us that the transition We differs for each liquid with the following relationship, It should also be noted that the effective viscosity being estimated (figure 2) would not predict the relative behavior of figure 9, except for the 1.4% CMC-7MF. The higher effective viscosity throughout the breakup stages would increase the time to reach the bag rupturing and would increase the We for onset of bag-n-stamen breakup. The reason the effective viscosity estimation may not support the findings is due to the estimation being made with the initial relative velocity. As the drop enters the flow, it accelerates and the dimensions vary, so the actual effective viscosity is likely to change. Furthermore, the 0.5% CMC-7HF and 0.8% CMC- 7MF estimated effective viscosities are very close to one another as seen in figure 2. Also, the 0.5% CMC-7HF has a highly shear thinning behavior and highest zero shear viscosity which can be seen in figure 1. Thus, over the course of break up as the relative velocity decreases, it is quite possible that the effective viscosity actually increases for the 0.5% CMC-7HF and therefore inhibits breakup which would explain figure 9. Thus, there may be a necessity to estimate an average shear over the breakup time considered or use a smaller shear estimation. What s more, the cross parameters alone do not predict the behavior described yet the viscosity in figure 1 at a shear between 100 and 1000 s 1 would predict this outcome. Finally, perhaps another effective viscosity equation, besides equation 3, with less parameters, yet predicts the viscosity accurately may assist in predicting outcomes of the breakup phenomenon. As relative velocity is increased, the time it takes for the bag to erupt decreases as stated above. As a consequence, the drop can be expected to displace a smaller distance from the point where the drop enters the flow to the point where the bag breaks, as shown in figure 10. In this plot, zero represents the point where the drop enters the flow (figure 4) and negative values are given to the drop centroid as it drops vertically. The liquid cross stream displacements are also distinct and are related as, y 0.8%CMC 7MF bag > y 0.5%CMC 7HF bag > y 1.4%CMC 7MF bag This relationship is more prevalent at the higher We numbers tested. Generally, the less negative (or more

7 positive) the centroid of the drop has fallen is due to the bag breaking sooner. Another possible contributing factor is during entrance into the flow, the drop has some upward forces as it traverses the boundary layer. This effect would increase as higher We numbers are reached and would slow the drops velocity which would ultimately reduce the amount being displaced. Additionally, figure 10 shows that at the lowest weber numbers tested, the drop moves approximately 6 diameter lengths vertically downward before the bag erupts. Also, at the higher We tested, the drops will displace as little as 2 diameter lengths. These results bring into question the use of stationary needle height (figure 3). If the drop s vertical displacement before break up is decreasing and this trend continues then at much higher We numbers the drop will ultimately breakup within the boundary layer of the continuous jet or at least be significantly affected by boundary layer turbulence. This will ultimately lead to inconsistencies and could be responsible for differing data in literature. Moreover, it can be seen that the rim at most expands about 5 times the original diameter and at a minimum of about 2.5 times the original diameter. Here, differences between liquids is not obvious and all liquids tend to follow a similar trend. Figure 11. Non-dimensional cross stream dimension when bag breaks. Figure 10. Non-dimensional cross stream displacement when bag breaks Figures 8, 9, and 10 have shown either a steady increasing or decreasing with We with no transient effects from transitioning from bag breakup to bag and stamen breakup. In figure 11, it is evident that transition effects do exist for all liquids considered. Since the time for bag breakup is being reduced then the increase in rim diameter must be due to increased shearing caused by the higher relative velocities. Another contributing factor may be due to higher pressures being present within the bag which force the rim outward. The decline after the transition is due to the mass of the stamen increasing and reducing the available mass for the rim and bag. This combined with the time for the bag to break being reduced will cause the rim to expand less over that time interval. Similarly, in figure 12, near the transition region the bag length becomes a maximum. However, the peak bag length seems to be slightly skewed to the left in figure 12 compared to the maximum rim diameter in figure 11. The increase and decrease are of the same reasoning described for figure 11 but the skewing to the left to the left of the transition region is due to the small mass being formed on the bag in the transition region which reduces the available liquid for expanding. At higher We that small mass becomes larger and actually becomes the stamen. Besides that, from figure 12, it can be said that the drop expands at most about 9 diameters lengths and as little as 3 diameter lengths for the range and conditions tested. There doesn t seem to be any distinct difference between liquids except perhaps at higher We where the lengths are related by, L 0.8%CMC 7MF bag < L 0.5%CMC 7HF bag < L 1.4%CMC 7MF bag This distinct difference between the liquids may be attributed to the delayed We transition. Since for the same We, the higher viscosity liquid would inhibit breakup further and therefore likely to have a smaller stamen. Smaller stamen means there is more mass available for the bag and thus the 1.4%CMC-7MF has the largest bag relative the other liquids tested.

8 y Vertical displacement (mm) α Cross model constant (s n ) µ Viscosity (Pa s) σ Surface Tension ( N m ) ρ Density ( kg m 3 ) γ Shear Rate (s 1 ) Figure 12. Non-dimensional bag length when bag breaks. Conclusions The polymers tested were 0.8%CMC-7MF, 1.4% CMC-7MF, and 0.5%CMC-7HF put into solution with DI-Water. The range of experimental results is 14 < We < 37 or alternatively 18 < u rel < 29. It was found that regardless of the liquid, some characteristic dimensions have no distinct differences and are even approximately the same compared to Newtonian liquids. One such example, was as the maximum cross stream dimension where the trend proposed by Hsing and Faeth ([2]) still remains valid. There are distinct relative trends for non-newtonian liquids. The bag breakup time, bag-n-stamen transition We number and cross stream displacement when the bag breaks were found to follow the same predictable relative pattern if the effective viscosity for 1.4%CMC-7MF is greater than 0.5%CMC-7HF which is greater than 0.8%CMC-7MF. It is evident that there are also specific dimensions which demonstrate bag break up to bag-n-stamen transition effects such as rim diameter and bag length at the moment when the bag breaks. There still remains the necessity for a characteristic equation which can predict the relative behavior for all non-newtonian liquids and still predicts the viscosity accurately. Otherwise, a more appropriate effective viscosity estimation with physical meaning so relative behaviors can be determined is needed. Nomenclature d Diameter (mm) L Length of Bag (mm) n Cross model index constant (-) Oh Ohnesorge number (-) r Radius (mm) T Time (ms) u Air velocity (mm/ms) We Weber number (-) Subscripts 0 Initial rel Initial Relative l Liquid eff Effective g Gas bag Refers to bag developed during breakup rim Referes to rim developed during breakup Acknowledgements This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No.DGE Further thanks goes to Dr. Sojka for his diligent guidance, Dr. Daniel Guildenbecher, Dr. Celienid Lopez Rivera, Dr. Sharon E. Snyder, and Dr. Varun Kulkarni whose similar works at Zucrow Labs has given invaluable guidance. Also, Neil Rodriguez s assistance in writing this document. Disclaimer Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation. References References should be indicated in the text by full sized numbers enclosed within square brackets. Use different formats for journals [1], books [2], symposium proceedings [3], and internal reports [4], as illustrated in the examples below. 1. Flock, A. K., Guildenbecher, D. R., Chen, J., Sojka, P. E., & Bauer, H. J. (2012). Experimental statistics of droplet trajectory and air flow during aerodynamic fragmentation of liquid drops. International Journal of Multiphase Flow, 47, Hsiang, L. P., & Faeth, G. M. (1995). Drop deformation and breakup due to shock wave and steady disturbances. International Journal of Multiphase Flow,21(4), Dai, Z., & Faeth, G. M. (2001). Temporal properties of secondary drop breakup in the multimode breakup regime. International Journal of Multiphase Flow,27(2), Guildenbecher, D. R., Lopez-Rivera, C., & Sojka, P. E. (2009). Secondary atomization. Experiments in Fluids, 46(3),

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