Optimization in Complex Fluid Mechanics Problems Using the Surrogate Management Framework

Alison Marsden Postdoctoral Fellow Stanford University Stanford, CA As computational tools mature in accuracy and ability to handle complex phenomena, their impact on solving significant engineering problems will grow. Along with the increase in fidelity of numerical simulations comes a need for development of optimization tools. Optimization applied to fluid mechanics encompasses some of the most challenging aspects of both sub jects, often requir-ing advanced numerical methods for fluid mechanics simulations, combined with non-traditional optimization methods. This talk will focus on new methodologies for optimization of airfoil shapes to reduce trailing-edge noise in turbulent flow. We will then briefly discuss how these optimization tools are being transferred to the field of cardiovascular bioengineering, where they have potential to impact surgical design for both congenital and acquired cardiovascular disease. In optimization for aeroacoustics, or flow generated noise, time accurate computations such as large-eddy simulation (LES) are required to resolve the range of spatial and temporal flow scales relevant to noise generation. The large computational cost coupled with the difficulty in computing gradients of cost functions makes optimization using traditional methods particularly challenging. In this work, we have developed a methodology to optimize the shape of a hydrofoil trailing-edge in order to minimize the aerodynamic noise propagated to the far field. The optimization method applied in this problem is a tailored version of the surrogate management framework (SMF) (Booker et al., 1999). Several novel adaptations to this method have made it more suitable for the trailing- edge problem, particularly for constrained optimization. Optimization has been performed to suppress the laminar vortex-shedding noise from acous-tically compact airfoils as well as the broadband noise from turbulent flow over an acoustically non-compact airfoil. For optimization in turbulent flow, LES is used for source field computations. Several optimal shapes have been identified, which result in significant reduction of trailing-edge noise in both laminar and turbulent flow with reasonable computational cost. The results of this study demonstrate the successful coupling of shape optimization to a time-accurate turbulent flow calculation, and validate the use of a novel methods for constrained optimization. The SMF optimization method is currently being applied to optimize cardiovascular geometries that are representative of surgeries and diseased states. These problems share several challenges in common with the trailing-edge noise problem, particularly the importance of computing the unsteady flow field and a large computational cost. We will discuss how the tools that were developed for the trailing-edge problem can be effectively coupled to blood flow simulations in order to impact surgery design and improve understanding of cardiovascular disease. Finally, we will discuss future work in the area of optimization and simulation in cardiovascular medicine, including coronary artery bypass grafting, peripheral vascular disease, and the identification of principles of optimality in vessel branching patterns.

Location: Seaver Science Library (SSL) Rm 150

Audiences: Everyone Is Invited

Contact: April Mundy