Breakup morphology of inelastic drops at high Weber numbers

Transcription

1 ILASS Americas 28th Annual Conference on Liquid Atomization and Spray Systems, Dearborn, MI, May 2016 Breakup morphology of inelastic drops at high Weber numbers Varun Kulkarni *, N.S. Rodrigues, and Paul E. Sojka School of Mechanical Engineering West Lafayette, IN 47906, USA Abstract We report breakup morphology of inelastic non-newtonian drops exposed to a co-flowing air stream at high air jet velocities. Power-law solutions were prepared by mixing one of two grades of CMC (sodium carboxymethylcellulose) with DI-water. Breakup morphology is reported in terms of Weber number, We based on the air density, a, and Ohnesorge number, Oh, based on the zero shear rate viscosity. We present results for the sheet thinning and catastrophic breakup regimes, which correspond to We beyond those at which bag-and-stamen breakup is seen. For the sheet thinning case the morphology is very similar to its Newtonian counterpart. For the catastrophic case, however, we observed the formation of a thin sheet which rolls up from it edges before collapsing onto itself and eventually disintegrating into smaller fragments. These topological changes are strongly dependent on the ratio Oh/ We. In contrast, the dependence on power law index, n, however, was not found to be strong for the range of n tested. * Corresponding author: vk @gmail.com

2 Introduction Sprays are ubiquitous in everyday life and contain an ensemble of various sized drops. These distributions are pivotal in determining the efficacy of devices or conditions producing these sprays [1]. For instance, with pesticide sprays we wish to avoid spray drift and thus don t want drops below a certain size. The goas for automobile engines is quite different, where a finer spray would lead to more efficient combustion. In addition, applications such as paint sprays require a more mono-dispersed drop size distribution. Obviously, there is a need to understand the factors governing these drop size distributions in various scenarios. These factors may be broadly categorized as, (i) the geometry of the spray-producing device, (ii) transport properties of the liquid being atomized and, (iii) the environment in which the liquid atomization takes place. Amongst these, (i) and (ii) have been extensively studied so in this work we focused on analyzing the effect of viscosity for an inelastic non- Newtonian fluid. From a practical standpoint these shear rate dependent viscosity characteristics are introduced by performance enhancing additives like nitromethane or, n-butane in fuels such as gasoline. The use of gelled propellants displaying strong non-newtonian characteristics are also employed in rocket engines for achieving greater thrust [2]. These reasons serve as the motivation for the study of non-newtonian liquid fuel atomization. Atomization of bulk fluid into smaller fragments occurs in stages [3]. The first of these is called primary atomization wherein the liquid fuel jet or sheet disintegrates into drops. Subsequent fragmentation of these drops is termed secondary atomization. Factors (i), (ii) and (iii) play an important role during primary and secondary atomization. In the current study we investigate the effects of shear rate dependent viscous behavior for secondary atomization. The non-newtonian behavior considered here is not viscoelastic, nor is there a yield stress so ther rheology follows the Carreau model [2] n Here µ 0 and µ are the zero and infinite shear rate viscosities, λ is the characteristic time equal to the reciprocal of the shear rate (γ ) at which shear thinning begins and also may be interpreted as the fluid response time to a change in imposed shear rate, (n 1) is the powerlaw slope of the viscosity at high shear rates. The product λγ is sometimes referred to as the Carreau number, Cu, which is used to characterize shear thinning behavior. Dimensionless parameters typically governing the atomization process for Newtonian drops are We and (1) 2 Oh. Another relevant parameter in such studies is Re. However, since we are concerned with the disruptive aerodynamic forces of the surrounding air, restorative surface tension force and dissipative viscous force within the liquid, a dimensionless quantity analogous to Re emerges; it is Oh/ We, which reduces to 1/Re if we include l in the definition of We. In this study we use µ 0 in the expression for Oh. Five regimes are observed for Newtonian drops, depending on Oh and We. Similar breakup morphologies are observed for inelastic non-newtonian drops as well [1]: vibrational, bag, bag-and-stamen, sheet thinning and catastrophic. Most of the secondary breakup research to date has focused on viscoelastic or Newtonian drops or at lower We for inelastic drops [4-11], with almost no literature available for the sheet thinning or catastrophic modes. These regimes are particularly important as they represent typical atomization conditions for fuels in automobile engines, for instance. To help fill this knowledge bap, the present investigation provides insight into the morphology of drop deformation and breakup in these regimes and notes differences from breakup of Newtonian drops under similar aerodynamic loadings. Additionally, the transition boundaries beyond which these breakup patterns may be observed are reported in terms of We and Oh. Rheological testing and test conditions The three non-newtonian liquids used in this work were formulated using CMC-7HF (700 kda) and CMC- 7MF (200 kda) and DI-water in concentrations of 0.5 wt.-% CMC-7HF, 0.8 wt.-% CMC-7HF, and 1.4 wt.-% CMC-7MF. Their rheological character was measured using: a rotational rheometer operated in controlled-rate mode with a cone-and-plate configuration (60 mm, angle) at strain rates of 0.01 < γ < 100 1/s; and a capillary rheometer having an 0.66 mm capillary die for measurements at strain rates of 1,000 < γ < 10,000 1/s. Rotational rheometer data points were considered to be valid if three consecutive measurements lay within ±5%; sweep up and sweep down tests revealed no thixotropy. The Weissenberg-Rabinowitsh correction factor was applied to capillary rheometer measurements [12]. Further details can be found in [2]. The measured rheologies are presented in Figures 1, 2, and 3. Drop strain rates were calculated to be between 1400 and /s, which are within the range covered by the two rheometers. The Bird-Carreau rheological model was used because it can accurately model the Newtonian plateau observed at very low strain rates and the strong shear-thinning behavior at increased strain rates. Although a Newtonian plateau at high strain rates was not experimentally observed, µ

3 was set to the viscosity of the base liquid (water) per [13]. Table 1 includes rheological parameters for all three solutions. Note that for DI-water, the Bird- Carreau parameters are taken to be µ 0 = µ = Pas, n = 1, and λ = 0 s. The surface tension of all three CMC solutions was determined using a du Noüy ring tensiometer. Values for the 0.8 wt.-% CMC-7MF (σ = ± N/m) and 0.5 wt.-% CMC-7HF (σ = ± N/m) solutions were close to the literature value of water (σ = N/m). One standard deviation from a sample size of ten was used as the measurement uncertainty. Table 2 lists all experimental conditions in terms of Oh, We and We/Oh. Uncertainties were calculated in the standard manner using the Kline and McClinctock method [2,4]. Experimental methods and setup Figure 4 shows the experimental arrangement used to study the fragmentation processes. The main components are a needle, which serves as a drop generator, connected to a syringe pump which forces fluid to the needle through a polystyrene hose. The drops fall into the continuous jet that is produced by a specially designed air nozzle connected to a ~700 kpa (100 psi) air supply. Jet turbulence velocity fluctuations are within 3% of the mean and the velocity profile is nearly flat for most of its width. Drops produced by the needle are approximately 2.5 mm in diameter, with the exact diameter depending on the solution surface tension and viscosity. Images were captured using a Vision Research Phantom v7 camera coupled to a 105 mm focal length lens that provide the necessary magnification. A 1000 W Xenon arc lamp (Kratos model LH151N) produced the required background illumination, which was followed by a plano-convex and optical diffuser so as to provide more uniform illumination. Images were recorded at 4700 fps with an exposure time of 100 s and resolution of pixels. This was adequate to capture the drop breakup dynamics. Results and Discussion The sheet thinning and catastrophic breakup patterns were observed. They are analyzed for inelastic shear thinning non Newtonian drops. Regime boundaries ranged from 30 We 50 for sheet thinning breakup and 50 We 70 for catastrophic breakup. As Figure 5 shows, they are relatively unaffected by n for the range considered during this 3 study, although a slight variation is seen for the range of Oh considered. Sheet thinning breakup is ascribed to Rayleigh- Taylor (R-T) instabilities. Figure 6 shows the different stages: (i) the initial spherical drop, (ii) the periphery of the drop separating out from the core because aerodynamic loading is becoming more important, and then (iii) the core flattening as it is gradually subjected to R- T destabilization. In the final stage we see complete fragmentation of the drop and long ligaments are formed. The long ligaments further destabilize owing to interactions with the surrounding air, and eventually lead to an ensemble of drops. This behavior is consistent with that observed for Newtonian drops [1], except for the effects of shear thinning. The process for determining R-T instability wavelength is shown by the blue arrows in Figure 7. The maximum unstable wavelength for sheet thinning breakup, st, non-dimensionalized by the initial drop diameter, D 0, is seen to vary exponentially with Oh/ We in Figure 9. The dependence on n, which is a measure of the shear thinning behavior, is not apparent. It may lead to an increase in st /D 0 at a given Oh/ We, further study is needed for verification. Fragmentation is sudden in the catastrophic regime due to the higher aerodynamic loads imposed on the drops. As Figure 8 shows, the breakup processes proceed much the same as for sheet-thinning breakup through (iii). However, after this point the drop does not destabilize due to R-T instability, but is instead rapidly flattened into a sheet having a thin central region and thick rim. The rim retracts due to surface tension, rolls up, and then disintegrates into fragments. The collapse time, col is chosen to quantity this process. Figure 10 presents the dependence of collapse time non-dimensionalized by the characteristic time ( = D 0 l /U a ) for a liquid sheet in catastrophic breakup versus Oh/ We for different values of n. The collapse time increase with increasing Oh/ We is consistent with the assumption that viscosity lengthens breakup of liquid films and filaments. The dependence of this quantity on n is not clear from the limited observation made, however one may surmise that the collapse time increases with increasing n for a given Oh/ We. Summary and Conclusions This study determines the effects of high We on the secondary atomization of the inelastic shear thinning drops. For the sheet thinning regime, 30 We 50, the behavior was similar to that of Newtonian drops except for shear thinning viscous effects in the non-newtonian case. In the catastrophic regime, 50 We 70, a liquid sheet not seen in Newtonian drops was formed, rolled up into itself, then fragmented. The instability wave-

4 length and sheet collapse time for these regimes was quantified and their dependence on Oh/ We established. Nomenclature a density of air kg m 3 l density of the liquid kg m 3 surface tension between air and liquid inter face m 1 l dynamic viscosity of liquid drop [Pa s] D 0 initial diameter of the undeformed drop [m] st instability wavelength in the sheet thinning regime [m] characteristic breakup time in secondary atomization [ms] col collapse time for the liquid sheet [ms] U mean air jet velocity [m/s] 11. Theofanous, T.G., Aerobreakup of Newtonian and viscoelastic liquids, Annual Review of Fluid Mechanics 43: , Morrison, Faith A. Understanding rheology, Oxford University Press, USA, Madlener, K. and H.K. Ciezki, Estimation of Flow Properties of Gelled Fuels with Regard to Propulsion Systems, Journal of Propulsion and Power 28.1: , References 1. Guildenbecher, D.R., C. López-Rivera and P.E. Sojka, "Secondary atomization," Experiments in Fluids 46.3: , Rodrigues, N.S. Impinging jet spray formation using non-newtonian liquids, MSME thesis, Purdue University, Lefebvre, A.H., Atomization and Sprays, McGraw- Hill, p. 130, Kulkarni, V. and P.E. Sojka. Bag breakup of low viscosity drops in the presence of a continuous air jet, Physics of Fluids 26.7: , Kulkarni, V. An analytical and experimental study of secondary atomization of vibrational and bag breakup modes, PhD dissertation, Purdue University, Kulkarni, V., D.R. Guildenbecher and P.E. Sojka, Secondary Atomization of Newtonian Liquids in the Bag Breakup Regime: Comparison of Model Predictions to Experimental Data, 12th ICLASS, Heidelberg, Germany, Lopez Rivera, C., Secondary breakup of inelastic non-newtonian liquid drops, PhD dissertation, Purdue University, Zhao, H., H.F Liu, J.L. Xu and W.F. Li, Secondary breakup of coal water slurry drops, Physics of Fluids 23.11: , Joseph, D.D., G.S. Beavers and T. Funada, Rayleigh Taylor instability of viscoelastic drops at high Weber numbers, Journal of Fluid Mechanics 453: , Joseph, D.D., J. Belanger and G.S. Beavers, Breakup of a liquid drop suddenly exposed to a high-speed airstream, International Journal of Multiphase Flow 25.6: ,

5 ILASS Americas 28th Annual Conference on Liquid Atomization and Spray Systems, Dearborn, MI, May 2016 Table 1. Bird-Carreau rheological parameters. Parameter 0.5 wt. - % CMC -7HF 0.8 wt. - % CMC -7MF 1.4 wt. - % CMC- 7MF µ 0 [Pa-s] ± ± ± µ [Pa-s] n [-] ± ± ± λ [s] ± ± ± Table 2. Test conditions in terms of dimensionless parameters. Uncertainty in Oh = ± 0.004, We = ± 2, We/Oh = ± 2.5 Dimensionless number Sheet thinning Catastrophic Oh We We/Oh Figure 1. Viscosity versus strain rate of 0.5 wt.-% CMC-7HF.

6 Figure 2. Viscosity versus strain rate of 0.8 wt.-% CMC-7MF. Figure 3. Viscosity versus strain rate of 1.4 wt.-% CMC-7MF. 6

7 Fig 4: Experimental setup for the study of the drop fragmentation process. Figure 5: Regime boundaries for sheet thinning and catastrophic breakup based on the We and Oh. Three We are presented in the plot for a given Oh. Each Oh corresponds to a particular n, the flow behavior index. 7

8 Figure 6. Breakup morphology for sheet thinning breakup and catastrophic breakup modes for the 0.5% CMC and D.I. water solution and We = 33 and 55. Time difference, t between successive images, (i), (ii), (iii), (iv) and (v) and (vi) for both types of breakup is roughly 2 ms. The changes in morphology of the drop are captured from its initial spherical shape to its final fragmented state. (i) (ii) (iii) (iv) (v) Sheet thinning breakup (i) (ii) (iii) (iv) 3 mm (v) Catastrophic breakup (vi) 8

9 Figure 7. The formation and evolution of the liquid sheet in the catastrophic breakup regime for 0.8 % CMC and D.I. water solution at We = 45. Time difference, t between successive images is roughly 2 ms. The red dotted circle shows the initial liquid sheet and the red arrows in subsequent images shows the retraction of the edges of the liquid sheet until their final collapse in the last frame. Rim Thin central region 3 mm Figure 8. Rayleigh-Taylor instability as observed in the breakup of 1.4 % CMC and D.I. water solution at We = 40 in the sheet thinning regime. Time difference, t between successive is roughly 3 ms. The blue arrows indicate the crests and troughs corresponding to the Rayleigh-Taylor instability wavelength. Blue arrows: Rayleigh-Taylor instability wavelength st 3 mm 9

10 Figure 9. Variation of non-dimensional Rayleigh-Taylor instability wavelength with Oh/ We for different values of power law index, n. Uncertainty in measurements vary between 4 8%. Figure 10: Variation of collapse time for liquid sheet in catastrophic breakup with Oh/ We for different values of power law index, n. Uncertainty in measurements vary between %. 10

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