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

摘要-0522944耶鲁大学作为耶鲁大学(根据Grant NSF 998-0747,2005年1月31日完成)、布鲁克海文和爱荷华州立大学最近交互研究的令人兴奋的结果，出现了一种有效模拟耦合、多相化学反应流动的统一方法。教授们。D.E.Rosner和D.T.Wu和R.McGraw博士建议在目前的多研究者、多学科的远程计划中积极探索和发展这条道路。在非常广泛的重要应用中，人们现在必须重复处理相互作用的多变量种群(粒子、物种、涡流等)。变得越来越复杂。(解决这种“相互作用的人口平衡”问题)统一方法的前景不仅相当诱人，甚至可能是势在必行的。本程序涉及基于求积的‘矩’方法(即QMOM)的扩展，以经济地处理相互作用的多变量总体，并开发实际的速率定律以纳入这些公式。在以前关于单一的(通常是单变量的)种群的工作中，通过有意地将(过度)简化的速率定律(对于布朗凝聚、水蒸气生长/蒸发、烧结、热渗透)引入被称为种群平衡方程的一般非线性积分-偏微分方程式中，获得了许多见解。然而，尽管该方程很复杂，并且需要与多维环境中的许多其他局部人口平衡原则一起满足它，但是当前的工程要求以及基于实验室测量的人口而不是个体的粒子来推断有意义的物理化学参数的频繁需要使得引入更准确的速率/传输定律对于下一代工程预测是必不可少的(例如，智能优点：耶鲁大学和布鲁克海文国家实验室最近的合作研究揭示了一条强大的基于瞬间的“富有想象力的途径”，用于理论/计算处理(悬浮颗粒和/或蒸气)多变量种群，这些种群不仅相互作用，而且与宿主流体相互作用。由于目前在各种工程应用中都会遇到这样的问题(在本提案的背景部分中作了简要说明)，本研究小组建议开发/应用这种统一的方法，同时为成核、凝聚、载体流体相的生长和颗粒结构(如烧结)的每个参与过程纳入更准确的速率定律。结果表明，尽管目前需要这样的扩展，其中几个是在以前的耶鲁/NSF-CTS项目中启动的，但令人惊讶的是，其他人在这些广泛的路线上所做的工作却很少。本研究团队的跨学科性质，其基于多变量高斯求积的矩方法的初步成功，以及现在纳入更多基于根本的速率定律的前景(在拟议的计划部分中讨论)，有力地证明了追求这些想法取得成果的必要性。广泛的影响：本研究团队已经形成了一个包括行业合作者的“虚拟中心”。这些都证实了作者的主张，即在实际流动环境中处理相互作用的多变量种群的演变的能力将使许多类型的多相工艺设备的设计取得重大进展。大多数目前使用的结合人口平衡方法的方法不太适合于这里感兴趣的多变量、相互作用的人口扩展，或者不适合使用更现实的(非幂定律)粒子速率定律。在研究层面上，对群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/结果对于推断在现实工程环境中进行工程预测所需的更有意义的物理化学参数至关重要。此外，这项研究现在将能够使用直接的数值模拟来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.