Direct numerical simulations (DNS) are perhaps the biggest new development in studies of multiphase flows and such simulations are already starting to have a major impact. As their use has increased, it has become clear that in many situations the formation of small-scale features such as thin films or drops require excessive (and often unachievable) resolution. Here it is proposed to develop multi-scale direct numerical simulations to allow the inclusion of such small scale phenomenon in simulations where everything else is fully resolved. The proposed work has the following objectives:
The development of a general strategy to include multi-scale description of small-scale phenomenon in numerical simulations of the dynamics of multiphase flows. The approach is based on the observation that many small-scale features (films, threads, boundary layers, strained advection-diffusion reaction layers, very small drops and bubbles, and so on) have a relatively simple structure and can therefore be described relatively accurately by analytical or semi-analytical models that are evolved concurrently with the fully resolved larger-scale motion. The challenges include identifying when and where to use such a description, how to efficiently and accurately couple the small-scale description and the numerically resolved flow, and the development of efficient data structures to implement the different descriptions in a way that does not overwhelm developers of such codes.
The development of specific multi-scale descriptions for thin films and threads, mass transfer, and chemical reactions to describe under-resolved features in direct numerical simulations of multifluid and multiphase flows. The need for multi-scale approach in these situations arises both because very thin films and threads can form naturally in multiphase flows, and since there is usually a large discrepancy between the length and time scales of the fluid motion on the one hand and mass transfer and reactions on the other. This work, which can be divided into the modeling of small scale flow features (films and threads), thin boundary layers in mass transfer problems, and reaction layers, will build on ideas currently being developed for boiling and an approach originally developed some time ago in the context of modeling of diffusion gas flames, where we showed that we could capture reasonably complex chemical reactions using a surprisingly simple approximation strategy. The numerical methods will be made available through an online repository, along with a thorough documentation of the methodology and the use of the codes.
The intellectual merit of the proposed activity: While direct numerical simulations (DNS) of multiphase flows have already had major impact on our understanding of such flow, and many opportunities still exist for applications of currently existing methods, it is also clear that in many cases the range of scales is too large to handle within the same numerical approach, even using adaptive grid refinement. Small-scale features in multiphase flows do, however, often exhibit a relatively simple structure that can be captured analytically or semi-analytically. In the present work we propose to extend DNS to include such multi-scale descriptions. This will greatly extend the range of multiphase flows that can be studied using DNS. It will, in particular, allow us to consider reacting systems for a realistic range of governing parameters.
The broader impacts of the proposed activity: Multiphase flows are critical in energy conversion, material processing, the chemical industry, atmospheric processes, and living systems. Incremental improvement in the efficiency of such processes translates into billions of dollars in savings and new discoveries have the potential to transform whole industries. Computational studies will bring about both incremental and transformative changes in the management of multiphase systems. Enlarging the community of users by providing online codes and documentations will help make that happen. In addition to training graduate students and postdocs, this project will provide research opportunities for undergraduate students.
