Airfoil Unsteady Aerodynamic Analysis Using a Galerkin Reduced-order Modeling Approach

Abstract

Computational fluid dynamics (CFD) based aerodynamic design has received increasing interest because the simulated high-fidelity flow fields can provide useful insights to guide the design. Aerodynamic design often requires considering unsteady flow processes such as vortex shedding and periodic oscillation. Conducting unsteady flow simulations is expensive because it needs to march the solution with a limited time step; this high cost has become the bottleneck of CFD-based design. To alleviate this issue, we develop an efficient Galerkin reduced-order modeling (ROM) approach to speed up the unsteady aerodynamic simulation. The benefit of using a ROM approach is that one can quickly predict any three-dimensional flow fields, such as pressure and velocity, compared with interpolation-based methods (e.g., kriging or neural networks). In this paper, we elaborate on the proposed ROM formulation and its detailed implementation in pisoFoam; a built-in unsteady flow solver in OpenFOAM. We use the cylinder and NACA0012 airfoil as the benchmarks and evaluate the performance of the proposed ROM method in terms of speed and accuracy. We observe significant speed ups from the ROM simulations. The run time ratios between CFD and ROM (including the calculation of basis vectors and projection matrices) are 9.5 and 12.9 for the cylinder and airfoil cases, respectively. The drag, lift, and velocity and pressure fields simulated by the ROM approach agree reasonably well with the full-order CFD references at various time instances. In particular, we demonstrate the capability of correctly predicting flow fields that are not sampled in the snapshot. The proposed ROM approach is intrusive and is in principle applicable to any airfoil geometries and flow conditions. Therefore, it has the potential to integrate into a design optimization process to speed up unsteady aerodynamic analysis.