This Faculty Early Career Development (CAREER) grant aims to make the design of fluid systems more intuitive, accessible, and inexpensive. Fluid systems, such as aircraft, biomedical pumps, or turbines, play a vital role in many sectors of the U.S. economy. Due to the complex physics of fluid flow, these systems are often difficult and costly to design. This presents a barrier to start-up companies seeking to develop products that involve such complex fluid flows. The complicated nature of fluid flows also poses a barrier in engineering education, where students often struggle to achieve intuition regarding fluid flows. To mitigate these barriers, this award envisions an immersive, virtual-reality design environment in which engineers can interact with aircraft or heart pumps in the same way artists interact with clay. A key requirement of this vision is the ability to provide engineers with instantaneous performance predictions as they shape their virtual designs. This award will help build the knowledge necessary for real-time prediction of complex fluid flows, thereby enabling the next generation of tools for immersive computer-aided design and engineering education.
Predicting the performance of fluid systems quickly and accurately for preliminary design remains a challenge due to the nonlinearity of the governing equations and the large cost of high-fidelity simulations. Reduced-order models provide a suitable alternative approach, since they have the potential to significantly reduce computational cost with only a small reduction in accuracy. The innovation explored in this award is to create reduced-order models that achieve high accuracy for boundary quantities that engineers are typically interested in, e.g., lift and drag, rather than high accuracy for the overall flow. Specifically, the research team will investigate adjoint-based basis functions to construct reduced-order models suitable for prediction of such boundary integrals. After using the reduced-order model to find a preliminary design, a numerical optimization based on a high-fidelity model can be applied to refine the design parameters. Here, numerical error estimation and control is especially important, because an optimization algorithm may exploit numerical errors rather than physics to optimize the quantity of interest. This research will explore the use of simultaneous geometry and mesh optimization as a means of addressing error control. Finally, after optimization, an engineer may need to explore the design space in order to meet qualitative constraints or consider tradeoffs. The research team will test the hypothesis that matrix-free spectral methods can re-parameterize and approximate the design space in such a way that engineers can make real-time changes without significantly impacting optimality and feasibility.
