High-fidelity Simulation of High Density-Ratio Liquid Jet Atomization in Crossflow with Experimental Validation

Liquid jet atomization in cross-flowing gas is a critical phenomenon in the fuel preparation process and controls combustor efficiency and emissions. Quantitative experimental studies of atomization have been rare due to limited optical access to the near-field dense spray region. High fidelity multiphase flow simulation has shown promise as an alternative approach for scrutinizing the complex physics involved. Computationally, it remains challenging to resolve the wide range of spatial and temporal scales involved and to properly account for the large variation of density across the liquid-gas interface. In this work, the Coupled Level Set and Volume Of Fluid (CLSVOF) approach is used to directly capture liquid-gas interface involving topological changes. The ghost fluid method is used to facilitate simulations at realistic fuel-air density ratio. Adaptive Mesh Refinement (AMR) and Lagrangian droplet models are used to efficiently resolve the multiple scales simultaneously. High performance computing is leveraged to manage the cost of the high resolution simulations which were performed using over 2000 processors at the Oakridge Leadership Computing Facility of the US Department of Energy. The equivalence between uniform resolution and AMR-based simulations is established by comparing surface instability and breakup. The significant cost advantages of using AMR are documented. The detailed simulation results at different Weber numbers are validated with experimental measurements of surface wavelength, breakup location and column trajectory. The size, velocity and mass rate of droplets formed along jet column are studied and also compared with experimental measurements. The effects of increasing Weber number on jet breakup and aerodynamic flow are discussed. * Corresponding author: [email protected] ILASS Americas 26th Annual Conference on Liquid Atomization and Spray Systems, Portland, OR, May 2014 Introduction Atomization of fuel jets in cross-flowing air to generate micron-size droplets is critical to the performance of combustors encountered in commercial and military aerospace applications, such as gas turbines, augmentors, scramjets and ramjets and rockets. Increased fuel area-to-volume ratio due to atomization significantly enhances the fuel evaporation rate, which contributes to better fuel-air mixing and subsequent combustion of fuels. While the magnitude of fuel-air ratio has an impact on engine efficiency and emissions, the spatiotemporal distribution of fuel vapor is strongly linked to dynamic stability. Therefore substantial demand exists for the quantitative understanding of liquid atomization in crossflow, as a first step in the optimization of combustion processes. From the breakup of centimeter-size liquid jet column to pinch-off of micron-size ligaments to form droplets, liquid primary atomization in a crossflowing gas manifests itself as a complex multiphysics multiscale phenomenon. Different dynamic forces due to gas flow, liquid inertia and surface tension compete with each other, controlling the various instabilities that tend to characterize multiphase flows. Near the liquid column, either Rayleigh-Taylor instability due to density difference, or Kelvin-Helmholtz instability due to aerodynamic shear, or the combination of both drives the large scale growth of surface waves and liquid breakup. On the other hand, capillary Plateau-Rayleigh instability due to surface tension plays a dominant role in the pinch-off of highly stretched thin ligaments when their size drops below a certain threshold. Different instability mechanisms selectively dominate the breakup process of jet column at different flow conditions, resulting in different breakup regimes including column breakup, bag breakup, multimode breakup and shear breakup [1, 2]. Various instabilities often occur simultaneously [3] at different spatial locations of the column. As a result, complicated location-specific liquid structures form which critically control the formation and spatial distribution of droplets. The transport and evaporation of these droplets controls the downstream fuel-air profile and hence the combustion process. Early experimental studies of primary atomization [4-7] focused on large-scale, integral and steady features such as penetration length or liquid column trajectory, mainly because of the limitations of optical techniques in resolving the spatiotemporal evolution of the near-field fast changing spray field. The situation is also complicated by the optical obstruction due to dense spray. Recently, several groups [1, 2, 8] started to use the pulsed shadowgraph technique to obtain more details of the evolution of liquid column. Despite the fact that most analyses are based on processing twodimensional images, near-field features such as wavelength of liquid surface waves, deformation of liquid column, onset of liquid breakup and deflected trajectory of liquid column were successfully extracted. The breakup of jet column was found similar to the wellstudied secondary breakup of drops due to shock wave disturbance [9, 10], and the data were summarized in a series of quantitative correlations [1, 2]. It is worth noting that most experimental studies were conducted at ambient conditions. Liquid properties (such as density, viscosity and surface tension) and therefore the breakup processes are highly dependent upon operating conditions (such as temperature and pressure) [11]. The extremely hostile high-temperature high-pressure environment in aerospace applications, however, makes experimental research prohibitively difficult and costly. Due to the fact that fundamental mechanisms of primary breakup and atomization remain largely unknown, phenomenological models have been developed to satisfy the needs in engineering applications. Mimicking jet atomization as “blobs” breaking up under harmonic oscillations and Kelvin-Helmholtz instability, two breakup models, the Taylor analogy breakup (TAB) [12, 13] and wave breakup models [14, 15] have been widely used in many engineering CFD computations based on Reynolds Averaged Navier-Stokes (RANS) formulation. A refined version of such models for liquid jet in cross flow has been developed by Madabhushi [16], taking into account special features such as drag, jet bending and flattening. The cost of the RANS based simulation is low and predictions of the model are reasonably good, despite the fact that experimental data must be available a priori for calibration. The applicability of the model in practical operating conditions is still questionable. With increasing computational power, it has become affordable in many engineering cases to use Large Eddy Simulations (LES) to capture important larger-scale dynamic features with smaller scale physics filtered out in the simulation and modeled separately. While success was achieved mostly when applying LES to dilute sprays [17], the recently developed LES models [18-20] also demonstrated their feasibility to capture dynamic interfacial flows near the jet column. However, the development of physically-sound subgrid models can be challenging as Herrmann and Gorokhovski [21, 22] pointed out that establishing subgrid models still requires fully resolved subscale interface geometry. Recently, direct numerical simulations based on interface tracking/capturing methods have shown promise in predicting detailed atomization without two-phase subscale models and experimental calibrations. Methods to directly track or capture the dynamic liquid-gas interface and its topological changes include level-set (LS) [23-27], volume-of-fluid (VOF) [28, 29] and front-tracking (FT) [30, 31], as well as their descendants, such as the refined level-set grid (RLSG) method [32], the Hybrid LSM & Mars (HLSM) method [33, 34], and the coupled level-set and volume-of-fluid (CLSVOF) method [35, 36]. Detailed atomization mechanisms including instability development and ligament/droplet formation [26, 34] have been explored. However, most simulation efforts have been focused on the case of straight jet injected into quiescent air mainly applicable to diesel engine applications. Because of the high cost of such simulations and lack of detailed experimental data, most numerical algorithms were verified in simple numerical tests and then directly applied to simulate complicated atomization cases at high Weber number and Reynolds number without experimental confirmation. One exception is the high fidelity simulation of liquid jet atomization in a realistic swirling flow injector [52], where the prediction of near-field sprays was compared with experimental data. In this work, we use a hybrid Eulerian-Lagrangian method [38] to investigate liquid jet atomization in crossflow. The computational approach combines the CLSVOF method to track/capture liquid-gas interface, and a Lagrangian droplet transformation/tracking approach [39] to capture small-scale physics using point particles and alleviate the needs of resolving flow inside droplets. The solver also features a Ghost of Fluid (GF) approach [40, 41] to allow sharp variation of properties across the interface, a Multi-Grid Preconditioned Conjugate Gradient (MGPCG) approach for robust and fast pressure solution, and an Adaptive Mesh Refinement (AMR) technique for liquid-gas interface to reduce grid count [42, 43]. The accuracy of CLSVOF method to capture interface evolutions in simplified geometric settings has been tested previously [35]. In this work, the solver is applied to predict the near-field liquid column in greater detail and compare with recent measurements [1] that employed pulsed shadowgraph techniques. It is noted that other numerical methods (e.g. RLSG) have also recently been applied in the high fidelity simulation of liquid jet atomization in crossflow [44] with improved algorithms for handling increased density ratio [45, 46]. However, to the knowledge of the authors, validation of such direct simulations for jet atomization in cross flow at realistic, high density ratio has not been attempted and therefore is the focus of current work. In the following, mathematical formulation and numerical implementation of the hybrid EulerianLagrangian approach are briefly described in section II. The algorithms for the Eulerian-to-Lagrangian transformation are briefly described and the details can be found in previous work [38]. In Section III, the presentation of results starts with a qualitative description of a typical jet in cross flow case at an intermediate Weber number. The effects of Weber number on near-field column deformation, surface instability, breakup, droplet formation and liquid-gas interactions are studied. The predictions are compared with correlations developed by Sallam et al[1]. The comparison of near-field data between uniform grid simulation and AMR simulations establishes the equivalence between the two configurations in capturing the surface instability and breakup. Finally, a summary is provided in Section IV.