The MICDE PhD Student Seminar Series showcases the research of students in the Ph.D. in Scientific Computing. These events are open to the public, but we request that all who plan to attend register in advance. If you have any questions, please email micde-phd@umich.edu.

Solving High Reynolds Number Flows on Cartesian Cut-cell Meshes using a Jacobian-Free Newton–Krylov Method

In this work, we developed a Newton–Krylov method for a second-order Cartesian cut cell Reynolds-averaged Navier–Stokes (RANS) solver, Viscous Aerodynamic Cartesian Cut cells (VACC), with the one equation Spalart–Allmaras (SA) turbulence model. The Newton–Krylov method uses pseudo-transient continuation and a point Jacobi preconditioner to accelerate convergence. Then various wall functions were compared on a finite flat plate and 2D bump cases. The SA analytical wall function was used as a baseline. An ordinary differential equation (ODE) wall function and wall-modeled RANS (WMRANS) approach were also implemented. Although these methods all showed promise, the interior viscous fluxes resulted in oscillatory pressures. These oscillations degraded the accuracy of all of the solutions.

Alex Kleb, Aerospace Engineering

Alex Kleb is a fifth year PhD candidate in the CFD Group and MDO lab in the Aerospace Engineering department.

Geometrically Nonlinear Methods for High-Fidelity MDO of Very-Flexible Aircraft

Over the past decade, advances in Multidisciplinary Design Optimization (MDO) have enabled the optimization of aircraft wings using high-fidelity simulations of their coupled aerodynamic and structural behavior. Using RANS CFD and detailed structural finite element wingbox models, the aerodynamic shape and internal structural sizing of a wing can be optimized concurrently to tailor the wing’s aeroelastic behavior and optimally trade-off drag and structural mass. This capability makes MDO a key enabling technology for the next generation of efficient high-aspect-ratio transport aircraft. However, as their aspect-ratios increase, these wings increasingly exhibit geometrically nonlinear behavior that cannot be correctly modeled by typical linear structural analysis methods. This work demonstrates the first simultaneous optimization of a wing’s aerodynamic shape and structural sizing using high-fidelity geometrically nonlinear models. Our methods are implemented in the open-source finite element library, TACS, and include a geometrically nonlinear shell element formulation, an efficient and robust nonlinear solver, and a constitutive model for stiffened shells. We demonstrate the ability to couple these nonlinear structural analysis tools to a high-fidelity RANS CFD solver using a geometrically nonlinear load and displacement transfer scheme. Finally, we use this capability to optimize a single-aisle commercial transport aircraft wing featuring 547 design variables and 1277 constraints.

Alasdair Christison Gray, Aerospace Engineering

Alasdair Christison Gray is a 5th year PhD student in the Aerospace Engineering department’s MDO Lab. His research focuses on applying high performance computing to the large scale design optimization of aircraft wings.