Adjoint-Based Mesh Adaptation and Shape Optimization for Simulations with Propulsion

Abstract

We demonstrate a well-posed formulation of permeable boundary conditions and massflow-rate functionals for adjoint-based mesh refinement and shape optimization governed by the steady Euler equations. The boundary conditions are used to model propulsionsystem effects of inlets and nozzles. A two-shock diffuser with an analytic solution is used to verify the implementation. Numerical examples show that the adjoint solution is smooth at the boundary, indicating that the discretization is adjoint consistent when exit pressure is specified at subsonic outflow, and stagnation temperature and pressure at subsonic inflow. The results focus on improving simulation techniques for low-boom aircraft analysis and design. By including mass-flow-rate outputs, we obtain reliable estimates of engine flow rates concurrently with nearfield pressure signatures without increasing simulation cost. We also demonstrate the importance of mass-flow-rate constraints in shape optimization by examining trade-offs between maximizing performance of a shrouded supersonic nozzle and minimizing shocks in its nearfield.

Cartesian Mesh Simulations for the Third AIAA Sonic Boom Prediction Workshop

“…Initial meshing refinement and subsequent adaptation always subdivides cells isotropically. Improved propulsive boundary conditions [31] have been implemented with accompanying functionals for the adjoint problem [32]. We used Cart3D version 1.5.5.3 to perform our near-field CFD simulations for SBPW3.…”

Isotropic and anisotropic mesh adaptation for RANS simulations of a nacelle under crosswind conditions

“…For the former configurations, the limited literature focuses either on mesh adaptation for structured meshes (for example in (Vivarelli et al, 2021)) or isotropic adaptation for multi-element meshes (Wyman et al, 2020). For hybrid external/internal flows, publications focus on unstructured meshes with either limited anisotropy (Ordaz et al, 2017) or with immersed boundaries and octree mesh refinement (Nemec et al, 2019). It is interesting to note that the two different types of flows are practically never treated by the same research groups, with a clear separation of approaches and solvers that are either turbomachinery-oriented or better suited for external flows.…”