NOx emission regulations have become more and more restrictive for Internal Combustion Engines vehicles, especially for road transport applications. To minimize emissions and comply with regulations, Selective Catalytic Reduction (SCR) systems are the most efficient deNOx technology thanks to the injection of a Urea-Water Solution (UWS). State-of-the-art Computational Fluid Dynamics (CFD) techniques employ Eulerian-Lagrangian frameworks to deal with the two phases of such problems. Still, the associated low velocities make using standard breakup models to generate initial drop size distributions difficult. Several studies end up needing experimentally characterized drop size distributions to initialize the CFD simulations or using expensive Eulerian-Eulerian simulations to obtain the outcomes of the primary breakup of the liquid jet. The Maximum Entropy Principle (MEP) allows generating a droplet size-velocity Probability Distribution Function (PDF) from initial injection conditions and injector characteristics while satisfying conservation equations. The most probable PDF curve is determined by the distribution that maximizes the entropy of the problem. A critical Weber number has been proposed to select which droplets will break up subsequently after the initial droplet break up. Validation is done against experimental results obtained by High-Resolution Laser Backlight Imaging. Comparable results have been found and realistic tendencies were achieved, decreasing the expected droplet size with increasing injection pressures. The proposed model could help introduce alternative breakup models for low-velocity applications without the need for prior droplet size knowledg

中文翻译：

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欧拉-拉格朗日喷雾初始化的最大熵原理模型

氮氧化物排放法规对内燃机车辆的限制越来越严格，特别是对于道路运输应用。为了最大限度地减少排放并遵守法规，选择性催化还原 (SCR) 系统通过注入尿素水溶液 (UWS) 成为最有效的脱氮技术。最先进的计算流体动力学 (CFD) 技术采用欧拉-拉格朗日框架来处理此类问题的两个阶段。尽管如此，相关的低速度使得使用标准破碎模型来生成初始液滴尺寸分布变得困难。一些研究最终需要通过实验表征液滴尺寸分布来初始化 CFD 模拟，或使用昂贵的欧拉-欧拉模拟来获得液体射流初级破碎的结果。最大熵原理 (MEP) 允许根据初始喷射条件和喷射器特性生成液滴尺寸-速度概率分布函数 (PDF)，同时满足守恒方程。最可能的 PDF 曲线由最大化问题熵的分布确定。提出了一个关键的韦伯数来选择在初始液滴破裂后哪些液滴将随后破裂。根据高分辨率激光背光成像获得的实验结果进行验证。已经发现了可比较的结果并实现了现实的趋势，随着喷射压力的增加，预期的液滴尺寸减小。所提出的模型可以帮助为低速应用引入替代的破碎模型，而无需事先了解液滴尺寸