Numerical Methods for Coupled Aeropropulsive Design Optimization

Abstract

Unconventional propulsion systems are used in several innovative aircraft concepts to save energy. Airframe-propulsion integration presents new design challenges due to emerging technologies such as over-wing nacelle, boundary layer ingestion, and distributed electric propulsion. Therefore, coupled aeropropulsive design optimization is a promising field in which to investigate the trade-offs between aerodynamics and propulsion models. However, coupled aeropropulsive design optimization is a relatively new field compared to aerodynamic shape optimization and aerostructural optimization. There are still some challenges in this field that need to be addressed to perform more advanced and rapid aeropropulsive studies.

In this thesis, we first develop a separation sensor to eliminate separation in gradient-based optimization. Designers often want to avoid separation at off-design conditions regardless of the drag. Therefore, we first develop a separation constraint formulation for airfoil shape optimization. Following the airfoil optimization, we also developed a novel separation sensor that is suitable for 3-D problems and used in the over-wing nacelle (OWN) coupled aeropropulsive problem in this thesis.

Secondly, we develop solvers suitable for coupled systems that have saddle-point system in their Jacobian, which often results in powered boundary condition problems in coupled aeropropulsive design optimization. Simulation-based multiphysics or multidisciplinary models are fundamental building blocks of multidisciplinary design optimization frameworks that involve coupled models. Solving the coupled linear and nonlinear systems that arise from these models is challenging. One common challenge arises when the Jacobian matrices represent a saddle-point problem, where a block-diagonal corresponding to a discipline is non-invertible. These problems require a coupled solver algorithm such as Newton's method instead of the popular block Gauss-Seidel based methods because of this non-invertible block. However, implementing coupled solver methods is challenging, and they suffer from robustness issues. To address these challenges with saddle-point problems, we introduce nonlinear and linear Schur complement solvers suitable for CFD-based coupled system models. We implement the solvers in NASA's OpenMDAO framework and demonstrate their effectiveness with two analytic problems and computational fluid dynamics based saddle-point problems: aerodynamic shape optimization of a wing and coupled aeropropulsive design optimization of a podded propulsor.

Thirdly, we also develop a robust Newton solver to solve challenging pyCycle thermodynamic nonlinear problems. Solving a nonlinear system of algebraic equations is a challenging task. Newton's method is a widely used approach for solving nonlinear systems of equations. Despite providing quadratic convergence near the final solution, it may not always converge the nonlinear system when the initial solution is further away from the final solution. Therefore, we develop the multilevel preconditioned Newton method with learning capability (MPNL) solver to increase robustness and efficiency. We implement the MPNL solver in OpenMDAO.

Finally, we study the aeropropulsive benefits of the OWN configuration. The OWN configuration has the potential to improve on the conventional under-wing nacelle configuration by enabling higher bypass ratios and increasing noise shielding. To explore this potential, we perform coupled aeropropulsive design optimization to study the coupled analysis and the design trade-offs between aerodynamics and propulsion. We first perform single-point optimization to study the fundamental aeropropulsive benefits and trade-offs. In this study, we also perform multipoint optimizations to understand the importance of multipoint optimization in terms of aerodynamics and propulsion. These advancements in aeropropulsive optimization are critical to OWN configuration design and more sustainable aircraft.