The main objective of the proposed research is to determine the effect of a fundamental property of fluids, viz, the bulk viscosity, on flow separation. It will be shown that the classical theory of shock-induced separation will break down and require modification when the bulk viscosity is sufficiently large. The required modifications and limits on the classical and modified theory will be delineated. Both analytical (triple-deck) and numerical techniques will be employed.
It is suggested that four problems be solved. The first two form the core of the project and will establish the breakdown of the classical triple-deck theory for supersonic and transonic freestreams. This analytical work will also serve to establish the limitations and modifications to the classical theory. Numerical solutions of the lowerdeck equations are proposed which will complete the description of the viscous- inviscid interactions. A third task is proposed which will provide general numerical solutions to the exact Navier-Stokes equations for the shockboundary layer interaction in fluids having large bulk viscosity; this task will serve as an independent verification and extension of the analytical work. As a further illustration of the effect of large bulk viscosity on separation and loss, we will adapt our Navier-Stokes code to the problem of a shock-boundary layer interaction on curved walls and blade or wing configurations; this problem will ascertain the effect on large-scale separation. The final task is to determine the conditions under which the modified interaction theory developed in the first two problems can be applied to particle-laden gases, e.g., those arising in dusty, smoky, or foggy environments.
The proposed work will uncover new physical phenomena associated with a fundamental property of fluids, will stimulate further analytical, numerical and experimental work, and will help modernize the discussion of a fundamental aspect of fluid mechanics in courses, books, and research articles.
The proposed study will benefit society through direct applications of the research to problems of technological and medical interest. These include applications to non-fossil fuel power systems, many of which employ large bulk viscosity fluids as working fluids. The work proposed here will enable more efficient and economical exploitation of these sources thereby relieving the nation's dependence on fossil fuels. Because even humid and/or dusty air corresponds to large bulk viscosities, the proposed work will have an impact on the design of military aircraft and helicopters, particularly those operating in desert or ship-based environments. Further aerodynamic applications include planetary probes which must inevitably operate in atmospheres primarily comprised of large bulk viscosity fluids. We also expect that the proposed research will have mid- to long-term impact on the production of nano-particles which will result in better absorption and delivery of medications such as ibuprofen.
In the course of the research described here, we will train one doctoral student and will involve the participation of one undergraduate student per year. The proposed research will further advance the National Science Foundation's goal to enhance diversity in engineering. In order to ensure that these goals are met, we have allocated funds for travel to recruit at traditionally female and black colleges. Locally, we will aggressively recruit with the assistance of college-level programs such as our Center for the Enhancement of Engineering Diversity and the local chapter of the Society of Woman Engineers.
The results of the research will also be disseminated through publications in top journals in the field, conferences and web sites; in addition to assisting the senior researchers in technical matters, the undergraduates will participate in the generation of such web sites.
