Simulation and modeling of droplet formation in flash atomization of cryogenic rocket propellants

Abstract

A critical step for rocket engine operation in the vacuum of space is the efficient atomization, mixing and ignition of the liquid propellants. In the case of cryogenic fluids the atomization process is driven by flash boiling as the fluid exits the injectors. It is well known that the flash boiling process is caused by the nucleation of microscopic vapour bubbles in the superheated liquid that drive the jet expansion and an intense phase change process. This work investigates the primary breakup mechanisms at the micro-scale that are currently not well understood, due to limited empirical data. For this, direct numerical simulations (DNS) are performed using a multi-phase solver with interface capturing, providing a level of detail not previously achieved for this type of atomization process. The ab-initio methodology relies on first computing exact solutions for spherical bubble growth in superheated liquid, capturing compressibility and interface cooling effects. This reference data is then used to calibrate the fluid properties and vaporization rate on larger scale DNS that focus on the pure fluid-mechanical processes. These simulations are able to fully capture the hydrodynamic interactions between a large number of bubbles, as they grow, deform and coalesce, leading to the breakup of the liquid matrix into a spray of small droplets. The high level of resolution requires the use of high performance computing techniques with an in-house developed DNS solver. Significant effort was also invested in the development of an efficient post-processing algorithm that captures surface area of individual droplets in addition to their volume, thus avoiding limiting assumptions of droplet sphericity that are necessary in most experimental and theoretical modelling approaches. A series of test cases with regular bubble arrays demonstrates how, by varying the thermodynamic conditions and nuclei number density, various breakup mechanisms are observed resulting in distinct droplet patterns. These are systematically correlated to a range of Weber and Ohnesorge numbers, providing a predictive model for breakup classification and droplet size estimation. These breakup patterns extend beyond common assumptions and hypotheses previously suggested in the literature. Further DNS using randomized bubble clusters confirm the initial observations and provide statistical data on the spray composition. The results obtained include droplet size distributions and time-resolved evolution of total spray surface area, across a range of Weber numbers. A droplet size estimator is proposed, uncovering a minimum for the mean droplet size that is expected for each given level of local superheat, in spite of the nuclei number density being generally unknown. The DNS data is then used to calibrate and improve on this model, from which the expected area-weighted (Sauter) mean diameter of the spray can be inferred and interpolated for various cryogenic fluids. Similarly, a DNS-calibrated model for peak surface area generation rate is proposed. The models and data provided can be used for the development of sub-grid scale models for fluid simulations in engineering applications, namely source terms for surface area generation and liquid-vapour mass fractions or transported stochastic variables for droplet size. The DNS-calibrated models suggest that for relatively high fluid temperatures, or locally high levels of superheat, droplets can be formed in the sub-micron range and at equally small time scales, which are beyond the range accessible by common experimental methods. At more conservative levels of superheat, the method suggests droplets in the one to ten micron range, which is compatible with empirical evidence. This work complements experimental studies that are often limited to measurements of the global spray characteristics and lack insight into the conditions and processes in the dense regions of the spray or near the nozzle. The level of physical detail and accuracy of the DNS method is, however, still limited by computational constraints. Nonetheless, the findings of this work provide a clear path for further refinement of the technique, as well as suggestions for further investigations, both numerical and experimental.