A unified path to the efficient simulation of coupled, multi-phase chemically reacting flows is emerging 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.
