Subsonic Indicial Aerodynamics for Unsteady Loads Calculation via Numerical and Analytical<br /> Methods: a Preliminary Assessment

On Elliptical Wings in Subsonic Flow: Indicial Lift Generation via CFD Simulations -- with Parametric Analytical Approximations

“…Time-accurate schemes, physically consistent grid motion and deformation algorithms [11] have reached a good maturity level [16,17] and are implemented in the most popular CFD solvers developed for the aeronautical community; however, for the accurate simulation of both circulatory and non-circulatory portions of the flow response there is no established best practice yet. Thus, this work extends and improves the accuracy of previous studies by the authors concerning the derivation of indicial lift functions for thin wings in subsonic flow [13,48,49].…”

“…The computational domains are rectangular boxes and contain the left half-wing only (see Figure 2), taking of advantage of the problem symmetry. The size of the domains, 400 × 400 × 200 chords in x, z and y, has been fixed in order to prevent pressure waves generated by the interaction between flow perturbation and boundary conditions (i.e., "slip" on wet surfaces and "far-field" on free surfaces) from affecting the flow around the wing; additional details may be found in previous publications [8,13,48,49].…”

“…All grids are structured (H-H) and built with great attention to quality. Despite the use of Euler equations, the grid cells are stretched near the wing surface almost like a grid for the Navier-Stokes equations, with a cell size the order of 10 −5 chords; this is done to provide a higher accuracy in the reconstruction of the pressure gradients due to the wing motion as well as to minimise the numerical oscillations (a similar study based on conventional unstructured computational grids and conventional spacing did show substantial numerical oscillations [49]).…”

“…The cells spacing normal to the wing surface has been stretched more than in a conventional Euler grid, with cell height in the order of 10 −5 chords. In the course of previous studies [13,49], the authors have assessed the sensitivity of the results to the spatial resolution normal to the wing surface; a positive correlation between quality of CFD results (or absence of spurious numerical oscillations) and the stretching ratio normal to the surface has been consistently noticed. We believe that a finer grid in the vicinity of the wall may resolve in a more robust way the strong pressure gradients appearing in the impulsive part of the response, even if no boundary layer must be resolved.…”

“…Multidisciplinary design and optimisation (MDO) [1] benefits from robust and efficient methods for aeroelastic stability investigation and dynamic loads calculation [34]. To this end, indicial-admittance functions [36] may serve as very effective tools and reduced-order models (ROMs) for characterising unsteady airloads [19,47]; more detailed literature may be found in previous works [8,13,48,49].…”