High Fidelity Simulation of the Impact of Density Ratio on Liquid Jet in Crossflow Atomization

Transcription

1 ILASS Americas 28th Annual Conference on Liquid Atomization and Spray Systems, Dearborn, MI, May 2016 High Fidelity Simulation of the Impact of Density Ratio on Liquid Jet in Crossflow Atomization Xiaoyi Li *, and Marios C. Soteriou United Technologies Research Center East Hartford, CT 06108, USA Abstract Atomization of liquid fuel jets by cross-flowing air is critical to the performance of many aerospace combustors. Recent advances in numerical methods and increases in computational power have enabled the first principle, high fidelity simulation of this phenomenon. In the recent past we demonstrated for the first time such simulations that were comprehensively validated against experimental data obtained at ambient conditions. At combustor operating conditions, however, both temperature and pressure are significantly elevated. In this work we perform a computational study of the impact of reduced liquid-gas density ratio due to increased air density associated with operating pressure elevation on the atomization physics. A previously validated ambient condition case is used as the baseline for comparison with three cases with decreasing density ratios. The density ratio is independently varied by adjusting the gas density and velocity together so that the momentum flux ratio and Weber number are maintained constant. Results indicate a significant modification of the atomization process at lower density ratios. Although the global-scale jet penetration and trajectory are not significantly modified by the conditions, both the process of liquid breakup and the degree of atomization are altered. The trends in the degree of atomization represented by the liquid volume to area ratio extracted from in the simulation results agree with the observations from a recent experiment at elevated pressure conditions. Further effort is still required to understand the detailed physical mechanisms for atomization at different density ratios. * Corresponding author: lixy2@utrc.utc.com

2 ILASS Americas 28th Annual Conference on Liquid Atomization and Spray Systems, Dearborn, MI, May 2016 Introduction Liquid Jet atomization In a Crossflow (LJIC) using aerodynamic forcing is a critical process occurring in the liquid fuel injection step during the operation of aircraft engine combustors. The increasingly strong requirements and regulations on improving the aeroengine combustor efficiency and reducing pollutant emissions have driven the increases in the combustor inlet pressure and temperature for an enhanced liquid fuel evaporation rate and fuel-air mixing. Since the fuel/air properties are highly sensitive to the operating pressure and temperature, e.g. the air density being strongly dependent on the pressure, the sensitivity of the atomization process to the operating conditions is strong. Thus understanding and optimizing LJIC in such elevated conditions has become an important subject in the liquid atomization research. In the current study we focus on the dependence of atomization process on the liquid-gas density ratio altered by pressure conditions. Traditional liquid atomization research has relied on experimental approaches that were mostly constrained to ambient pressure conditions due to the complexity and high cost of experiments at elevated conditions. Global features such as liquid jet trajectory and penetration and far-field spray distribution were measured and reported using a variety of empirical correlations [1-6]. A number of detailed experiments focusing on near-field atomization details [7-11] shed some light towards understanding the fundamental multiphase breakup mechanisms, despite the fact that whether we could extrapolate these understandings to assess LJIC at elevated pressure condition is still questionable. Results from only a few high pressure experiments of LJIC were reported in the literature [12-15]. Becker and Hassa [12] studied the breakup of kerosene jet in crossflow with pressure up to 15 bar. They explored the impact of pressure on liquid atomization regime, jet penetration and lateral dispersion, and droplet size distribution. However, the effects of elevated pressure were lumped into the effects of increased air momentum flux or Weber number as a result of an increase in air density. In fact, the density ratio and the Weber number are two controlling parameters that can be independently varied, with the effects of the former being rarely studied and the impact of the latter being relatively well understood from the ambient condition work. The observed changes in high pressure atomization in terms of a reduction in jet penetration and reduced sensitivity of droplet sizes to Weber number variations [12] can be explained by the shift into a higher Weber numbers shear breakup regime. And such physical link has been established during the ambient condition investigations. In Bellofiore et al. [14], a large number of flow conditions at 10 bar and 20 bar were tested, allowing the extraction of the density ratio effects independent of the Weber number. The impact of pressure on spray trajectory, plume width and coverage area was reported, yet the large degree of data scattering causes difficulty in extracting the detailed impact of density ratio, as pointed out by Herrmann et al. [16]. In a recent LJIC experiment by Song et al. [15], the air pressure was elevated from 2.07 to 9.65 bar, and the impact of density ratio was independently investigated by comparing data at fixed momentum flux ratio and Weber number. Jet breakup regime and mean droplet size downstream were shown to have a strong dependency on the density ratio while the dependence of penetration/trajectory on density ratio seemed to be weak. At very high pressure, the reduced liquid-gas density ratio may become comparable to the density ratio existing in many Gaseous Jets In Crossflow (GJIC) applications. The physics of GJIC has been extensively studied [17-20] in terms of a complex set of interacting vortex system. While the knowledge developed from GJIC studies may be borrowed for understanding the large scale vortical flow structures in LJIC at high pressure, the multiphase breakup phenomena unique to LJIC have to be understood by accounting for the phase separation caused by the presence of surface tension. Due to the complex multiphase multiscale physics involved in the liquid atomization process, traditional modelling approaches have encountered severe difficulties in capturing the impact of operating conditions. The applicability of the phenomenological models [21, 22] calibrated at ambient condition is questionable when the operating conditions are elevated. High fidelity simulation of liquid atomization [23-28] has emerged to provide a very promising path for detailed investigations of the impact of operating conditions without reliance on the experimental calibration due to its firstprinciple nature. Yet because of the challenges of overcoming the numerical instabilities that typically occur when the liquid/gas density contrast is high, a number of high-fidelity simulations of LJIC have been conducted at reduced density ratios only [25, 29], which happened to reflect the scenarios at elevated pressure conditions. Numerical study of the impact of density ratio on LJIC atomization was initiated by Herrmann and coworkers [16] considering two density ratios r ρ =10 and r ρ =100, both lower than the typical liquid-gas density ratios at ambient condition. Reducing density ratio was found to cause the decrease of liquid core penetration together with an increased bending and transverse spreading. It also increases the column wavelength and the mean droplet size [30]. The decrease in density ratio also leads to an increase in the normalized crossflow droplet velocity and a decrease in the normalized transverse droplet velocity, due to the increase in the relative Stokes number controlled by size. However, in addition to the limit on the density ratio set by the numerical instability challenges, in Herrmann s work [16, 30], the

3 variation of density ratio was configured by altering the liquid density, not exactly the same as an air density change, which is the dominant response of pressure change. To which degree such configurations represent the high pressure condition needs further verification. Recently, simulations of high density-ratio LJIC at ambient condition have been performed by our team and successfully validated against near-field experiment [8] in terms of detailed column features and droplet formation [28, 31]. The solver with enhanced interface tracking capabilities allows stable simulations at density ratios covering a broader range of pressure conditions, thus enables a comprehensive study of the impact of density ratio changes associated with operating pressure variations. In this work, we present the results from three LJIC simulation cases with increasing air density reflecting the trends with pressure increases. For the current investigation, all other impacts of pressure are ignored. The cases were set up based upon a previously validated ambient condition case. The density ratio was independently varied while the momentum flux ratio and the Weber number were fixed to be constants. Previous ambient condition simulation case was used as the baseline for investigating the impact of decreasing density ratio. In the following, previously adopted formulation and numerical methods are briefly highlighted. The computational configurations of LJIC with varying density ratios are described. The impact of density ratio on the qualitative feature and quantitative degree of atomization is presented. Finally, summary and conclusions are provided. Computational Approach A. Formulation and Numerical Methods It is assumed that the fluid properties for each phase are spatially invariant at the specified operating conditions and the two-phase flow of liquid and gas is incompressible and can be represented by a single fluid formulation. Under these assumptions the governing mass and momentum conservation equations are: u 0. (1) u 1 uu ( pi 2D) H, (2) t where p is the fluid dynamic pressure, the density, the viscosity, I the identity tensor, D the deviatoric strain rate tensor, the constant interfacial tension, the local curvature and H the Heaviside function defined as 1 0 (liquid) H ( ). (3) 0 0 (gas) Here is a function that identifies the interface location. The density and viscosity are correspondingly defined as H H L G 1 LH G 1 H. (4) The motion of interface follows u 0. (5) t Since the numerical methods adopted in this paper have been comprehensively described in our previous work [26, 28, 32], only a brief highlight is provided here for the completeness of the paper. Our computational approach uses the Coupled Level-Set and Volume Of Fluid (CLSVOF) method [33] to capture the liquid-gas interface. The method capitalizes on the advantages of both the accurate geometric interface representation in level set method and the volume-preserving properties in volume of fluid method. The Eulerian CLSVOF interface tracking method is implemented under the framework of a block structured adaptive mesh refinement (AMR) [33, 34], and also coupled with a Lagrangian droplet transformation and tracking approach to capture the smallest spherical droplets with significant cost-saving benefits, especially when the jet column and dense spray region occupy only a small part of the domain. The Eulerian to Lagrangian transformation follows the algorithms similar to the implementation by Herrmann [35] and a number of criteria (e.g. size, sphericity and diluteness criteria) are required to be met before the transformation occurs [26, 36]. The flow solver features a two-fluid advection approach [33, 37] to avoid artificial smearing of velocity field across the interface, which causes poorly resolved gas velocity gradient leading to solver divergence at high density ratios. The pressure projection equation is solved using a Multi-Grid Preconditioned Conjugate Gradient method (MGPCG). The method is augmented by a ghost fluid (GF) treatment for pressure jump conditions to achieve stable and fast pressure solution. Such a suite of sharp interface treatments mitigate the problem of solver divergence that typically occurs at high density ratios. B. Computational Setup In our previous work [28], the computational approach was validated against near-field experimental measurements [8] for a non-turbulent water jet in steady crossflow of air at the ambient condition. The inlet flow turbulence was experimentally suppressed to focus the study on liquid atomization due to aerodynamic forces. And correspondingly plug-flow profiles were set for both the liquid and gas inlets in the simulations. In this work, we inherit the same computational configuration

4 and use one of the validated ambient cases as the baseline for investigating the impact of density ratio. The two-phase flow and breakup are controlled by the competition between surface tension and aerodynamic flow forces at the liquid-gas interface, and can be characterized by a density ratio r ρ =ρ l /ρ g, a momentum flux ratio q=ρ l U 2 2 l / ρ g U g and gas Weber number We=ρ g U 2 g d 0 /σ. The other two independent nondimensional parameters are the liquid Reynolds number Re l = ρ l U l d 0 /µ l, and viscosity ratio r μ = μ l /µ g. In this study, the system is maintained at ambient temperature and the liquid evaporation is not considered. We focus on the effects of density ratio and fix other fluid properties. The fixed fluid properties and flow parameters are listed in Table 1. The density ratio is varied by adjusting the air density. Here we make a low Mach number assumption, and the impact of fluid dynamic pressure on the change of air density is assumed small and neglected. The air density affects multiple nondimensional numbers and here we fix the momentum flux ratio at q=88.2, and Weber number at We=160, the same as in one of the ambient condition cases [28]. We select the case at this Weber number as the baseline due to the predominantly high Weber number condition in aircraft engine applications. The parameters allowed to vary are listed in Table 2. Case 1 is the baseline case. As the air density increases from 1.2 to kg/m 3, the density ratio decreases from to 1.7. To maintain a constant gaseous momentum flux, the gas inlet velocity is decreased from to 4.9 m/s. The gaseous Reynolds numbers are relatively large and the effects of viscosity are assumed to be secondary for all the cases. Since the gas inlet turbulence is excluded in the simulations, the smallest relevant flows scales are generated at the liquid-gas interface by multiphase flow instabilities. In the simulations, the coordinate system has the x- axis in the crossflow direction and the z-axis in the direction of liquid injection. The computational domain is a box of 3.0 cm 2.0 cm 3.0 cm. The jet orifice is located at a coordinate of (0.2, 1.0, 0.0) with a diameter of d 0 =0.8 mm. Impermeable no-slip boundary conditions are imposed at the z = 0 plane, except at the jet orifice where a liquid velocity inlet condition is imposed. Gas velocity inflow is imposed at the inlet boundary located at x = 0 cm. Outflow boundary conditions are imposed on the remaining boundary planes. Three levels of AMR are used in the simulations to refine the grid near the liquid-gas interface. The use of AMR greatly improves the affordability of the simulations. The finest grid size is set to be x = 39 µm. Smaller-scale events such as liquid pinch-off do occur in reality, however, we postulate here that the smallerscale physics has little impact on the larger-scale flow. Previous validations [28] have shown that when the grid resolution is smaller than the ligament or droplet size observed in the experiment [8], the simulation can resolve physics down to the experimentally measured scales and the under-resolved flow and pinch-off physics do not have a significant impact on the atomization features of interest at the measurement scales. Since it has been reported that decreasing density-ratio at higher pressure tends to increase the mean droplet size [15, 30], the grid size as required by the baseline high density ratio case is deemed to be sufficient for capturing the atomization processes in other lower density ratio cases. The time stepping for all the simulations is defined by two criteria: CFL criterion and surface tension criterion [33] 1 x 1 l 32 t min, x i, j n u. (7) For all the cases, the jet reaches full penetration within 1.2 non-dimensional flow-through time τ flow = max(l x / U g, L z /U l ). Data are collected over another flow-through time afterwards to provide reasonable flow and interface statistics. Computational Results A. Qualitative atomization features In Fig. 1, the qualitative LJIC atomization features at different density ratios are illustrated using liquid surface images rendered in three orthogonal views. Results from the previously validated ambient condition case [28] are shown in the first column of images as the baseline for comparison. As the jets penetrate into the crossflow, they bend towards the direction of the crossflow stream. The degree of bending in the initial stage before column fracture points does not seem to be very sensitive to the change of density ratio (Fig. 1(a)-(d)) due to the same momentum flux ratios imposed for all the cases. It is consistent with a similar degree of blockage across all the cases as inferred by the similar degree of column flattening in the transverse direction (Fig. 1(e)-(h)). It has been shown in the ambient condition LJIC study that the gaseous Weber number controls the multiphase instability/breakup, and the breakup process can be categorized by several breakup regimes such as bag, multi-mode and shear breakup. Although the Weber number is held constant for all the cases in this work, significant changes in the liquid breakup details as a result of density ratio variations are observed. As the density ratio decreases, the characteristics of the instabilities developed on the column surface is altered significantly. The amplitude of column waves increases with decreasing density ratio and the onset location for column breakup is shifted towards the injection point at lower density ratios (Fig. 1(e)-(h)). The column waves are also observed to change their characteristics from appearing only on the windward surface at high density ratio (Fig. 1(a)) [28] to being present on the whole cir-

5 cumference of the liquid column at low density ratio (Fig. 1(d)). This can also be observed in the comparison of jet column shape for different conditions in Fig. 2. As the density ratio decreases, the circumferential instability becomes stronger and disturbances start at a height closer to the injection orifice. The surface stripping of droplets at the transverse edge of the column surface as observed in the high density ratio case does not seem to occur for the very low density ratio scenario (Fig. 1(d)(h) and Fig. 2(m)-(p)). Although the development of column waves is delayed in the higher density ratio cases, the liquid secondary breakup proceeds at a faster rate so that the size of droplets formed after column fracture points is small (Fig. 1(a)-(d), (i)-(l)). Based on side-view experimental shadowgraph images, Song et al. [15] observed an increase in surface wavelength and wave amplitude as the pressure was increased from 2.07 bar to 9.65 bar while the momentum flux ratio and Weber number were kept constant at q=10 and We=500. The simulations by Herrmann et al. [16] also showed an increase in surface wavelength with the decrease in density ratio. Such observed trends qualitatively agree with the simulation results shown in Fig. 1(a) to (c). Based on such observations, Song et al. [15] also suggest that the critical Weber number for transitioning the breakup regimes is shifted to higher values at higher pressure (or lower density ratio) conditions, e.g. at the same Weber number, a high density ratio jet may experience shear breakup while a low density ratio jet may experience multi-mode or bag breakup. The simulation results shown in Fig. 1, however, suggest that more complex instability transitioning may occur as the density ratio is varied, e.g. the onset location of surface breakup approaches the injection orifice as the density ratio decreases. B. Spray plume boundary and degree of atomization The boundaries for the spray plume were quantitatively extracted from the simulation data and plotted in Fig. 3. The boundaries were defined as the minimum and maximum locations of liquid surfaces (including both Eulerian surface and Lagrangian droplets representation) for each x-bin. The bin size was set to be 0.2 mm. Too small bin size leads to large oscillations of data due to the limited number of samples while too large bin size fails to capture the detailed boundary evolution. The data extracted over 20 snapshots for each case are averaged and plotted in Fig. 3. Although the detailed breakup process changes with conditions, both the z and y plume boundaries shown in Fig. 3(a) and (b) display very little sensitivity to the variation of density ratio. While the simulation by Herrmann et al. [16] reported a noticeable increase in the near-field core penetration with increasing density ratio, the experimentally observed spray trajectories identified by the maximum Mie-scattering intensity did not show significant dependence on the density ratio [15] and momentum flux ratio has been confirmed to be the most dominant factor in determining spray penetration. The data in Fig. 3 quantitatively confirm that the changes in breakup processes at different density ratios mainly cause local differences in liquid structures that may alter the spray boundaries in a minor way (Fig. 3(a) and (b)), and the overall spray penetration and spread are largely dictated by the global momentum balance independent of the density ratio changes in the current study. A common way to quantify the degree by which density ratio influences atomization is to measure or extract the size of droplets after jet primary breakup. As in our previous simulation work, the droplet data become readily available after the Lagrangian droplet transformation is introduced as shown in Fig. 4(a). The transformation approach using pre-defined size and sphericity criteria works well for the ambient condition case. The liquid is atomized to such a large degree that all the droplets can meet the criteria and be transformed into the Lagrangian phase before they leave the simulation domain. However, for the low density ratio case shown in Fig. 4(c) and (d), the atomization characteristics are different, and large and highly deformed ligaments/blobs may survive longer and persist beyond the simulation domain. As shown in Fig. 4(a)-(d), using the same transformation criteria, an increasing proportion of liquid remain in the Eulerian phase as the density ratio decreases. This presents a difficulty in accurately extracting the droplet size distribution only based on the Lagrangian phase data. To characterize the averaged degree of atomization in the above complex low density ratio scenario, we compute an averaged liquid volume to area ratio, which represents the effective size of the liquid structures. For the Eulerian phase, the surface area and volume are computed by numerical surface integration S and i x S 3 (based on divergence theorem). The i n i i calculation of the area and volume of the Lagrangian droplets is straightforward. The total volume and area for both the Eulerian and the Lagrangian phases are i Si i n i Si 3 V x d 6 (8) l A l i j 2 j j 3 j d (9) where i sums over all the Eulerian surface elements and j sums over all the Lagrangian droplets. The total volume, area and averaged volume to area ratio for all the liquid in the domain are compared in Fig. 5(a)-(c) for different density ratio conditions. The data represent values averaged over 20 snapshots for each case. The computed volume for all the liquid in the domain in i i

6 Fig. 5(a) shows a monotonic increase decreasing density ratio. The increasing accumulation of liquid in the domain (see Fig. 1) is due to the decreases in gas velocity to keep the gas momentum flux constant (see Table 2). The liquid surface area also shows a monotonic increase with decreasing density ratio in Fig. 5(b) and a monotonic trend in the total volume to area ratio cannot be identified in Fig. 5(c). Although the degree of atomization seems to be higher for the high density ratio case in terms of the size of the liquid structures downstream after column fracture point (see Fig. 1 and 4), the more intensive breakup of liquid column surface close to the injection point in the low density ratio case also contributes to an increase in the local volume to area ratio. As a result, the domain-averaged degree of atomization is comparable between cases with different density ratios. The spatial variations of the atomization degree are further investigated by computing the liquid volume and surface area for four equal-size bins at different x locations. The variations of bin liquid volume, area and volume to area ratio along the crossflow x-direction are compared in Fig. 5(d)-(f) for different conditions. As shown in Fig. 5(d), the bin volume for the high density ratio case decreases along the x-direction and finally reaches a saturation value. As the LJIC process reaches steady state, the liquid flow rate through each x plane reaches a constant value equal to the liquid injection flow rate. The decreases in the bin liquid volume in the crossflow direction can be explained by an increase in the averaged liquid x-velocity caused by the acceleration due to the crossflow. As the density ratio decreases, the crossflow velocity decreases and the bin liquid volume increases since the liquid flow rate is the same for all the conditions. It is interesting to observe a nonmonotonic change of bin liquid volume for the lower density ratio r ρ =16.9 case, which first decreases then increases. A more significant increase in bin liquid volume is observed for the r ρ =1.7 case. The cause of such bin volume increase requires further investigation. One possible explanation is that a larger proportion of liquid is trapped in the low speed wake zone in the low density ratio cases than in the high density ratio cases. In Fig. 5(e), the bin liquid surface area shows a monotonic decrease in the x-direction for all the conditions. The degree of atomization represented by the bin liquid volume to area ratio shows some interesting trends in Fig. 5(f). Near the injection orifice, the effective size of liquid structures is larger in the higher density ratio case since the early breakup on the column surface is weak for the high density ratio case and becomes progressively stronger as the density ratio decreases (see Fig. 1 and 4). The reverse trend is observed further downstream. In the high density ratio case, the high shear between liquid and gas due to the imposed high gas velocity drives the acceleration and the secondary breakup of liquid ligaments/blobs into smaller droplets. In the low density ratio case, even though the early stage breakup near the injection orifice is strong, the shear between liquid and gas is getting lower due to a lower gas velocity imposed. The variation of velocity magnitude on the Eulerian liquid surface at different conditions is shown in Fig. 6. Compared to the liquid injection velocity, which is held the same for all the cases, the surface velocity progressively increases downstream in the higher density ratio cases (Fig. 6(a)(b), but progressively decreases in the lower density ratio cases (Fig. 6(c)(d)). The transition between acceleration and deceleration occurs when the imposed liquid velocity being equal to the imposed gas velocity, i.e. U g =U l or q=r ρ, which happens in a condition between case 2 and 3 (see Table 2). Because of the progressively reduced shear in the lower density ratio cases, the surface tension may act to drive a recovery of elongated ligaments or deformed blobs into large spherical droplets without further breakup. This probably explains the increases in effective size or decreases in the degree of atomization in Fig. 5(f) for the lower density ratio case. Note that an increase of droplet size with decreasing density ratio was also reported in other simulation [30] and experiment work [15], although no clear physical explanation of the phenomena has been provided. Summary and Conclusions A computational investigation of the impact of density ratio variation associated with pressure change on the liquid jet atomization in a crossflow has been performed. The effects were independently studied by fixing the momentum flux ratio and Weber number to the values specified in a previously validated high density ratio simulation case at the ambient condition. Cases with three density ratios were simulated and compared with the baseline ambient condition case. The density ratio manifests its impact mostly in altering the breakup and atomization characteristics and does not show significant influences on the large scale spray penetration and spreading. A new approach was developed to generically characterize the degree of atomization when large and highly deformed liquid ligaments/blobs are present. The quantitative results point to an increase in droplet size or a decrease in the degree of atomization with decreasing density ratio, which qualitatively agrees with conclusions from the simulations by Herrmann [30] and the recent experimental observation by Song et al. [15]. The regions with the most intensive liquid breakup transition from column fracture point in the ambient high density ratio case to the point close to liquid injection in the low density ration case. More investigation is necessary to understand this transition and the change in physical mecha-

7 nisms of atomization due to density ratio change and this will be the subject of future work. Nomenclature A = Area d 0 = injector orifice diameter D = deviatoric strain rate tensor H = Heaviside function I = identity tensor L = length scale p = fluid dynamic pressure q = momentum flux ratio r μ = viscosity ratio r ρ = density ratio Re = Reynolds number t = time u = velocity U = imposed velocity V = volume We = Weber number x = coordinate x, = coordinate in direction of crossflow y, = coordinate orthogonal to x and z z, = coordinate in direction of liquid injection t = time step x = grid spacing Φ = phase indicator function κ = curvature = dynamic viscosity = density σ = surface tension τ = Non-dimensional time subscripts g = gas property l = liquid property min = minimum superscripts n = step n References 1. Wu, P.K., et al., Breakup Processes of Liquid Jets in Subsonic Crossflows. Journal of Propulsion and Power, (1): p Schetz, J.A. and A. Paddye, Penetration of a Liquid Jet in Subsonic Airstreams. AIAA Journal, (10): p Nguyen, T.T., and Karagozian, A. R., Liquid Fuel Jet in a Subsonic Crossflow. Journal of Propulsion Power, (1): p C. O. Iyogun, M.B., and N. Popplewell, Trajectory of water jet exposed to low subsonic crossflow. Atomization and Sprays, : p J. N. Stenzler, J.G.L., D. A. Santavicca, and W. Lee, Penentration of liquid jets in a crossflow. Atomization and Sprays, : p Q. Wang, U.M.M., C. T. Brown. and V. G. Mcdonell, Characterization of trajectory, break point, and break point dynamics of a plain liquid jet in a crossflow. Atomization and Sprays, (203-19). 7. Mazallon, J., Dai, Z., and Faeth, G. M., Primary Breakup of Nonturbulent Round Liquid Jets in Gas Crossflows. Atomization and Sprays, (3): p Sallam, K.A., Aalburg C. and Faeth, G. M., Breakup of Round Nonturbulent Liquid Jets in Gaseous Crossflow. AIAA Journal, (12): p David Sedarsky, M.P., Edouard Berrocal, Per Petterson, Joseph Zelina, James Gord, Mark Linne Model validation image data for breakup of a liquid jet in crossflow: part I. Experiments in Fluids, (2): p Mark A. Linnea, M.P., Edouard Berrocalb, David Sedarskyb, Ballistic imaging of liquid breakup processes in dense sprays. Proceedings of the Combustion Institute, (2): p Mark Linne, M.P., Tyler Hall, Terry Parker Ballistic imaging of the near field in a diesel spray. Experiments in Fluids (6): p Becker, J., and Hassa, C., Breakup and atomization of a kerosene jet in crossflow at elevated pressure. Atomization and Sprays, : p R. Ragucci, A.B., and A. Cavaliere, Trajectory and momentum coherence breakdown of a liquid jet in high-density air cross-flow. Atomization and Sprays, : p A. Bellofiore, A.C.a.R.R., Air density effect on the atomization of liquid jets in crossflow. Combustion Science and Technology, : p J. Song, C.C.C., and J. G. Lee, Liquid jets in subsonic air crossflow at elevated pressure. Journal of Engineering for Gas Turbines and Power-Transactions of the Asme, : p M. Herrmann, M.A., and M. Soteriou, The Impact of Density Ratio on the Liquid Core Dynamics of a Turbulent Liquid Jet Injected

8 into a Crossflow. ASME Journal of Engineering for Gas Turbines and Power, (6): p Karagozian, A.R., The jet in crossflow. Physics of Fluids, : p M'Closkey, R.T., King, J. M., Cortelezzi, L., and Karagozian, A. R., The actively controlled jet in crossflow. Journal of Fluid Mechanics, : p Karagozian, A.R., Transverse jets and their control. Progress in Energy and Combustion Science, : p Mahesh, K., The interaction of jets with crossflow. Annual Review of Fluid Mechanics, : p Reitz, R.D., Modeling atomization processes in high-pressure vaporizing sprays. Atomization and Sprays Technology, : p Madabhushi, R.K., A model for numerical simulation of breakup of a liquid jet in crossflow. Atomization and Sprays, (4): p Menard, T., S. Tanguy, and A. Berlemont, Coupling level set/vof/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet. International Journal of Multiphase Flow, (5): p Desjardins, O. and H. Pitsch, Detailed numerical investigation of turbulent atomization of liquid jets. Atomization and Sprays, (4): p Herrmann, M., Detailed Numerical Simulations of the Primary Atomization of a Turbulent Liquid Jet in Crossflow. ASME Journal of Engineering for Gas Turbines and Power, (6): p , Arienti, M., Li, X., Soteriou, M. C., Eckett, C. A., Sussman, M., Jensen, R. J., Coupled Level-Set/Volume-of-Fluid Method for Simulation of Injector Atomization. Journal of Propulsion and Power, (1): p Li, X., et al., High fidelity simulation of the spray generated by a realistic swirling flow injector, in Proceedings of ASME Turbo Expo : San Antonio, Texas. p. GT Li, X., and Soteriou, M. C. High-fidelity Simulation of High Density-Ratio Liquid Jet Atomization in Crossflow with Experimental Validation. in ILASS Americas 26th Annual Conference on Liquid Atomization and Spray Systems Portland, OR. 29. M. Behzad, N.A., and B. W. Karney, Surface breakup of a non-turbulent liquid jet injected into a high pressure gaseous crossflow. International Journal of Multiphase Flow, : p Herrmann, M. The Influence of Density Ratio on the Primary Atomization of a Turbulent Liquid Jet in Crossflow. in Proceedings of Combustion Institute Li, X., Soteriou, M.C., Prediction of High Density-Ratio Liquid Jet Atomization in Crossflow Using High Fidelity Simulations on HPC, in 50th AIAA Aerospace Sciences Meeting 2012: Nashville, Tennessee. p Li, X., and M.C. Soteriou, High-fidelity simulation of fuel atomization in a realistic swirling flow injector. Atomization and Sprays, (11): p Sussman, M., Smith, K. M., Hussaini, M.Y., Ohta, M., and Zhi-Wei, R., A sharp interface method for incompressible two-phase flows. Journal of computational physics, : p Almgren, A.S., et al., A conservative adaptive projection method for the variable density incompressible Navier Stokes equations. Journal of Computational Physics, : p Herrmann, M., A parallel Eulerian interface tracking/lagrangian point particle multi-scale coupling procedure. Journal of Computational Physics, (3): p Li, X., Arienti, M., Soteriou, M. C., and Sussman, M. M., Towards an Efficient, High- Fidelity Methodology for Liquid Jet Atomization Computations, in AIAA Aerospace Sciences Meeting2010: Orlando, FL. p. AIAA Sussman, M., A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. Journal of Computational Physics, (1): p

9 ρ l μ l μ g σ U l q We Re l Table 1. Fixed fluid properties and flow parameters (SI unit). Cases ρ g U g r ρ Re g Table 2. Fluid properties and flow parameters varying with operating pressure (SI unit). (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Figure 1. Instantaneous snapshots of liquid atomization at different conditions in different views. Density ratios for images from left to right are 845, 169, 16.9 and 1.7, respectively.

10 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) Figure 2. Comparison of jet column shape in several x-y plane cross-sections at different conditions. For images from left to right, z = , 0.001, , and m. For images from top to bottom, r ρ = 845, 169, 16.9 and 1.7.

11 (a) Figure 3. Comparison of spray plume boundaries at different conditions. (b)

12 (a) (b) (c) (d) Figure 4. Illustration of Eulerian to Lagrangian transformation at different conditions. (a) r ρ = 845, (b r ρ = 169, (c) r ρ = 16.9, and (d) r ρ = 1.7.

13 r ρ r ρ r ρ (a) (b) (c) (d) (e) (f) Figure 5. Comparison of liquid volume, area and volume-to-area ratio at different conditions.

14 (a) (b) (c) Figure 6. Velocity magnitude contour on the Eulerian liquid surface at different conditions. (a) r ρ = 845, (b) r ρ = 169, (c) r ρ = 16.9, and (d) r ρ = 1.7. (d)