Traveling and standing waves in liquid-vapor phase transitions and related problems

该方案研究了液体气溶胶中的相变波，包括一维行波和三维球对称驻波。这些波可以是亚音速、超音速或跨音速的; PI的目标是描述所有可能的波型，完成Fan、Lin和Wechselberger获得的部分列表。该建议还研究了一些相关问题：多孔介质中的相变和化学反应波、大边界区域中KPP型波的稳定性、简单行波串接描述的多波前波型以及计算行波的数值方法。本计划的主要目标是研究液体气溶胶、气体中细小液滴的悬浮、例如内燃机气缸的燃料喷射喷嘴中的汽油-空气混合物。 PI将研究锥形喷嘴中的蒸发波，作为汽油机喷嘴中燃料蒸发的模型。了解这种波的存在和稳定性的参数状态是重要的，并且可以帮助在点火之前实现良好混合的燃料和空气比，这反过来将有助于提高发动机的燃料效率并减少一氧化碳和碳氢化合物排放到环境中。 此外，PI还将研究在燃料电池和石油回收过程中应用的相变相关问题。

This proposal studies phase transition waves in liquid aerosols, including one-dimensional traveling waves and three-dimensional spherically symmetric standing waves. These waves can be subsonic, supersonic or transonic; the PI aims to characterize all possible wave patterns, completing a partial list obtained by Fan, Lin and Wechselberger. The proposal also studies some related problems: phase transition and chemical reaction waves in porous media, stability of KPP-type waves in large bounded domains, multi-front wave patterns described by a concatenation of simple traveling waves, and numerical methods for computing traveling waves.The main goal of this proposal is to study the liquid-vapor phase transition in liquid aerosols, suspensions of fine liquid droplets in a gas, such as the gasoline-air mixture in the fuel injection nozzle of a combustion engine cylinder. The PI will investigate evaporation waves in conical nozzles as models of evaporation of fuel in injection nozzles of gasoline engines. Understanding the parameter regime for the existence and stability of such waves is important, and can help achieve a well-mixed fuel and air ratio before ignition, which in turn will help improve the fuel efficiency of the engine and reduce emission of carbon monoxide and hydrocarbons into the environment. In addition, the PI will study some related problems on phase transition that have applications to fuel cell batteries and oil recovery processes.