Reduced order model of three-dimensional Euler equations using proper orthogonal decomposition basis

Abstract

This study seeks to validate the accuracy and the efficiency of the aerodynamic reduced order model (ROM). In doing this, snapshot data are generated from the full system analysis of a fighter wing problem. From an eigensystem analysis of these snapshots, the basis vector reproducing the behavior of the full system is obtained. The span length, sweep angle, dihedral angle, and spar and rib thickness representing the wing configuration are determined as the input variables. The constructed ROM is applied to the fighter wing problem while varying the input conditions for validation. Subsequently, a comparison of the reduced system with the full system confirmed that the aerodynamic performance is within 4% error and that the L 2 norms are 10 -6 order of the entire flow field. Therefore, the ROM is able to capture the variation of the aerodynamic performance with respect to the input variables. Though there are structural input variables which influence the aerodynamic performance indirectly, the ROM can reproduce the flow field of the full system. Additionally, even if the ROM incurs a high computational cost to generate snapshots, it can represent the behavior of the full system efficiently once the reduced order model is constructed.

Reduced-Order Model with an Artificial Neural Network for Aerostructural Design Optimization

“…Beran et al [6] implemented a full model, which couples twodimensional (2-D) Euler equations and the von Kármán equation, and constructed a limit-cycle oscillation ROM. Jun et al [7] investigated the accuracy and efficiency of POD for three-dimensional (3-D) Euler equations and predicted the variation in the aerodynamic performance with respect to structural variables from the aerostructure coupling analysis.…”

“…Aerostructural Analysis The Euler solver with unstructured grids [7,[17][18][19][20] and the stresshybrid four-node shell element originally developed by Aminpour [21] and Cho and Kim [22] are used in the aerostructural analysis. For the aerodynamic analysis, inviscid fluxes at the cell interfaces are computed by Roe's flux-difference splitting scheme.…”

“…Thus, the penalty term in rotational degrees of freedom proposed by Clio and Kim [22] is added to the element formulation. The details and validations of the aerodynamic analysis and structural analysis code are presented in [7] and in [22]. Figure 1 shows the overall procedure of the aerostructural analysis.…”

Modelling the flow conditions in the tunnel and its reduced model

“…The solution will be realized by analytical methods and numerical simulation [13]. As the modelled case is quite simple, a relatively "thin" mesh was applied for the numerical solution (Fig.…”