Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

Abstract

Abstract:A method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computational domain, including the boundary layer attached to the aircraft surface and the wake. Thus, the method is both robust and computationally efficient, which is checked considering the aerodynamic flow around a horizontal tail plane, in the transonic range 0.4 < Mach number < 0.8, -3° < angle of attack < 3°.

Aerodynamic database reconstruction via gappy high order singular value decomposition

“…Truncated HOSVD is illustrated in Figure 2.5, where both the RMS and maximum errors (denoted hereafter as RMSE and MaxE respectively), 14) are plotted vs. the retained number of modes, m + p + q, for both the dense and coarse toy model databases. The error bound EB defined in Eq.…”

“…For example, transient three dimensional flow can be analysed by performing POD analysis at timeand space-windows of the flow in order to separately study temporal phenomena or focus the analysis on sub-domains [7]. This technique is useful in a variety of contexts, such as database generation [8,9,10], derivation of reduced order models [11,12,13,14,15,16], compression [17,18], and image processing [19].…”

Reduced order modeling of some fluid flows of industrial interest

“…The genetic algorithm is generally more robust and able to search a significant part of the phase space. It can be fairly standard (emphasizing the robustness of the process); see Alonso et al (2009bAlonso et al ( , 2010Alonso et al ( , 2012, for the selection of the various tunable parameters of the genetic algorithm. Gradient-like methods are much faster but require a good initial guess, which can be provided using a continuation method in the parameter space.…”

Aerodynamic database error filtering via high order singular value decomposition

“…For instance the cleaning-HOSVD should be tried on databases exhibiting steep gradients such as the ones found in transonic wing tests. In general, the underlying mathematical methods developed by Sirovich are known to perform poorly in such conditions, especially experimental ones, as described in [12,16]. Certain improvement can be made to those underlying method however such modifications are beyond the scope of this Thesis and its line of research.…”

“…the degree of influence, it exploits redundancies among the two original dimensions, also called directions, and produces a lower dimensional approximation. SVD has many applications, for instance database generation [10,11,12], derivation of reduced order models [13,14,15,16,17,18], compression [19,20] and image processing [21]. Additionally, it has a natural basic ability to filter noise out [22] from two-dimensional databases (namely, matrices).…”