Free Boundary Problems in Volatile Multi-fluid Flows

“挥发性多流体流动的自由边界问题”这一建议的中心是非平行轴对称逆流岩心-环流流态的基本描述。求解的数学方法包括连续性、纳维-斯托克斯方程和每种流体的能量方程的系统渐近化，以简化的演化方程来描述当管的半径远小于沿管轴的界面变化时的界面演化。该方程将包含粘度和密度分层的物理效应，表面力的轴向和方位角分量，剪切，惯性，浮力，热毛细，挥发性，潜热和热输送。在等温条件下，平行流动是可能的，并考虑平行流动解对大振幅孤立波不稳定的条件。实验中可以看到这种波。该建议的其余部分集中在非平行流动上，因为在挥发性情况下空间变化的解决方案不能平行，并且实验等温问题容易受到进口和出口扰动的不稳定性的影响。感兴趣的流动模式包括悬挂环空膜，其中重力通过核心流体中不利剪切、环空滴和段塞形成的存在而平衡。稳定性将通过直接数值模拟进化方程，在类似于实验中发现的条件下进行研究。在各种工程应用中，热量的传递是整个工程系统功能的限制因素，例如发电机，电子设备冷却阵列，锅炉管和液冷涡轮叶片。用于从底层应用中传输热量的系统使用多个流体层来增加热量传输速率。这些流体系统容易出现流体动力学不稳定性，这可能会大大降低传热性能，导致整个应用的崩溃。对这些不稳定性的理论和实验理解对于增强设计至关重要。提出的研究考虑了这些传热系统中常见流体排列的数学模型，作为更好地理解主要不稳定机制的范例。一旦很好地理解了这种机制，就有可能提高底层应用程序的性能。随着对肺部气道粘膜不稳定性的了解，进一步的应用在医学领域。了解这些不稳定是在什么身体条件下发生的，最终可以为一些呼吸系统疾病提供更好的医学治疗。

Abstract for "Free boundary problems in volatile multi-fluid flows" byB. S. TilleyThis proposal centers on the fundamental description of nonparallelaxisymmetric countercurrent core-annular flow regimes. The mathematicalmethods of solution consist of a systematic asymptotic reduction of thecontinuity, Navier-Stokes, and energy equations in each fluid to asimpler evolution equation that describes the interfacial evolutionwhen the radius of the tube is much smaller than the interfacialvariation along the tube's axis. This equation will contain thephysical effects of viscosity and density stratification, axial andazimuthal components of surface forces, shear, inertia, buoyancy,thermocapillarity, volatility, latent heat and thermal transport. Inthe isothermal situation, parallel flow is possible, conditions underwhich the parallel flow solution can be unstable to a large-amplitudesolitary wave will be considered. This wave is seen in experiment.The remainder of the proposal centers on nonparallel flows, since thespatially varying solutions in the volatile case cannot be parallel,and the isothermal problem experimentally is susceptible toinstabilities from inlet and outlet disturbances. The flow patternsthat are of interest include that hanging annular film, in whichgravity is balanced by the presence of an adverse shear in the corefluid, an annular drop, and slug formation. Stability will beinvestigated through direct numerical simulation of the evolutionequation under conditions similar to those found in experiment.In a variety of engineering applications, the transfer of heat is thelimiting factor of the functionality of the entire engineering system,such as electrical generators, electronic equipment cooling arrays,boiler tubes, and liquid-cooled turbine blades. The systems used totransport heat away from the underlying application use multiple fluidlayers to increase the rate of heat transport. These fluid systems areprone to hydrodynamic instabilities, which can greatly reduce theheat-transport properties, leading to a breakdown in the entireapplication. A theoretical and experimental understanding of theseinstabilities is critical to enhancements in design. The proposedresearch considers a mathematical model of a common fluid arrangementin these heat-transfer systems as a paradigm for a better understandingof the dominant instability mechanism. Once this mechanism is wellunderstood, it will be possible to enhance the performance of theunderlying application. Further applications are seen in the medicalfield, with the understanding of instabilities of the mucus covering ofthe airways in the lungs. Understanding under what physical conditionsthese instabilities occur can eventually lead to better medicaltreatments of some respiratory ailments.