Toward a Unified, Moment-Based Treatment of Multi-Variate, Interacting Population Balance Problems - Development/Incorporation of Realistic Rate Laws

摘要-0522944耶鲁大学一条有效模拟耦合、多相化学反应流的统一途径正在出现，这是耶鲁大学（在Grant NSF 998-0747下，于2005年1月31日完成）、布鲁克海文大学和爱荷华州州立大学最近进行的交互式研究的一个令人兴奋的结果。教授D.E. Rosner和D.T. Wu和R.麦格劳建议积极探索和发展这条道路，在目前的多研究者，多学科的长期计划。在一个非常广泛的各种重要的应用程序，现在必须反复处理相互作用，多变量群体（粒子，物种，漩涡，.）复杂性的增加。一种新的方法（解决这种“相互作用的种群平衡”问题）的前景不仅很有吸引力，甚至可能是势在必行的。本程序涉及基于正交的“矩”方法的扩展（即，经济地处理相互作用的多变量群体，并发展现实的速率定律，纳入这样的配方。在以前的工作“单一的”（通常是单变量）人口，许多见解是通过故意（过）简化速率定律（布朗凝聚，蒸汽生长/蒸发，烧结，热泳）到一般非线性积分偏微分方程称为“人口平衡”方程。然而，尽管该方程很复杂，并且需要在多维环境中沿着许多其他局部种群平衡原理来满足它，但是当前的工程要求，以及经常需要基于对种群而不是单个“颗粒”的实验室测量来推断有意义的物理化学参数，使得更精确的速率/传输定律的引入对于下一代工程预测至关重要（例如，知识价值：耶鲁大学和布鲁克海文国家实验室最近的合作研究已经揭示了一个强大的基于矩的“有远见的道路”，以理论/计算处理多变量群体（悬浮颗粒和/或蒸汽），这些群体不仅在它们之间相互作用，而且还与主流体相互作用。由于这样的问题现在在各种各样的工程应用中遇到（在本提案的背景部分中简要说明），本研究小组建议开发/应用这种统一的方法，同时为成核、凝结、从载液相生长和颗粒重构的每个参与过程引入更准确的速率定律（例如，烧结）。结果表明，尽管目前需要这样的扩展，其中几个已经开始在以前的耶鲁/NSF-CTS项目，令人惊讶的是，很少有人工作已被报道沿着这些广泛的路线。本研究团队的跨学科性质，他们的多变量高斯正交为基础的矩方法的初步成功，和前景，现在纳入更多的基本速率定律（在拟议的程序部分讨论）强烈主张追求这些想法furniture.Broader影响：本研究团队已经形成了一个“虚拟中心”，其中包括工业合作者。这些已经证实了作者的主张，即处理实际流动环境中相互作用的多变量群体的演变的能力将允许在许多类型的多相过程设备的设计中取得重大进展。大多数目前使用的方法，将人口平衡的方法是不太适合多变量，相互作用的人口扩展的利益在这里，或使用更现实的（非幂律）粒子速率定律。在研究水平上，对总体的测量往往比对单个粒子的测量更容易。在这种情况下，建议的方法/结果将是必不可少的，以推断更有意义的物理化学参数需要在现实的工程环境中进行工程预测。此外，这项研究现在将使直接数值模拟的使用，以指导更复杂的湍流非预混合多相系统的建模。

ABSTRACT - 0522944Yale UniversityA unified path to the efficient simulation of coupled, multi-phase chemically reacting flows isemerging as an exciting result of recent interactive research at Yale (under Grant NSF 998-0747, completed 1/31/05), Brookhaven, and Iowa State University. Profs. D.E. Rosner and D.T. Wu and Dr. R. McGraw propose to aggressively explore and develop this path in the present multiinvestigator, multi-disciplinary long-range program. In a remarkably wide variety of important applications one now has to repetitively deal with interacting, multi-variate populations (particles, species, eddies,...) of increasing complexity. The prospect of a UNIFIED APPROACH (to such 'interacting population balance' problems) is not only quite attractive, it is probably even IMPERATIVE. The present program deals with the extension of quadrature-based 'moment' methods (i.e., QMOM) to economically deal with interacting multi-variate populations, and the development of realistic rate laws to incorporate into such formulations. In previous work on 'single' (usually univariate) populations, much insight was obtained by introducing deliberately (over-) simplified rate laws (for Brownian coagulation, vapor growth/evaporation, sintering, thermophoresis) into the generally nonlinear integro-partial differential equation called the 'population balance' equation . However, despite the complexity of this equation, and the need to satisfy it along with many other local population-balance principles in multi-dimensional environments, current engineering requirements, as well as the frequent need to infer meaningful physico-chemical parameters based on laboratory measurements on populations rather than individual 'particles', make the introduction of more accurate rate/transport laws essential for next-generation engineering predictions (e.g., particle synthesis reactor-separator design).Intellectual Merit: Recent collaborative research at Yale University and Brookhaven National Labs has revealed a powerful moment-based 'visionary path' to the theoretical/computational treatment of mult-variate populations (of suspended particles and/or vapors) which not only interact among themselves, but also interact with the host fluid. Because such problems are now being encountered in a wide variety of engineering applications (briefly illustrated in the Background Section of this proposal) the present research team recommends developing/applying this unified approach, at the same time incorporating more accurate rate laws for each of the participating processes of nucleation, coagulation, growth from the carrier fluid phase, and particle restructuring (eg., sintering). It is shown that, despite the present need for such extensions, several of which have been initiated in a previous Yale/NSF-CTS project, surprisingly little work by others has been reported along these broad lines. The interdisciplinary nature of the present research team, the initial successes of their multi-variate Gaussian quadrature-based moment methods, and the prospect of now incorporating more fundamentally-based rate laws (discussed in the Proposed Program Section) argues strongly for pursuing these ideas to fruition.Broader Impact: The present research team has formed a 'virtual center' which includes industrial collaborators. These have confirmed the authors' claim that the ability to deal with the evolution of interacting multi-variate populations in practical flow environments would allow significant strides in the design of many types of multi-phase process equipment. Most presently-used methods for incorporating a population-balance approach are not well-suited to the multi-variate, interacting population extensions of interest here, or to the use of more realistic (non-power-law) particle rate laws. At the research level, it is often possible to make measurements on populations more readily than on a single particle. In such cases the suggested methods/ results will be essential to infer more meaningful physicochemical parameters needed for making engineering predictions in realistic engineering environments. Additionally, this research will now enable the use of direct numerical simulations to guide the modeling of more complex turbulent non-pre-mixed multiphase systems.