13:30
Low/high order methods 1
Chair: Daniella Raveh
13:30
30 mins

A modular TSM solver for aeroelastic analysis and optimizations
Cedric Liauzun, Christophe Blondeau
Abstract: Several typical aeroelastic phenomena and instabilities, like flutter, induce periodic oscillations of the structure and of the aerodynamic forces. Numerical methods based on the harmonic balance technique or the Time Spectral Method (TSM) with a projection on the Fourier space has proven to be very efficient to predict the oscillatory phenomena by resolving the established regime without solving for the transient one. Such formulations lead however to critical numerical difficulties especially with a fine time sampling.
A modular parallel TSM solver is developed in order to perform aeroelastic analyses and optimizations of wings. This solver is in charge of performing all the operations regarding the time discretization and the time resolution. An interface with the CFD elsA solver extracts all the needed information related to space discretization. Such architecture allows the adaptation of the TSM solver to any CFD codes (structured/unstructured), and most of all allows assessing and developing easily new resolution algorithms to improve the robustness and the computational efficiency. The structural deformations are taken into account in the TSM problem by an ALE formulation of the fluid equations. The time resolution of the TSM problem is carried out using an Approximate Newton Krylov method. Particular attention is paid for the investigation on the methods to solve the linear systems resulting from the ANK approach, especially on their preconditioning. An adjoint formulation of the TSM approach is also developed in order to perform aeroelastic optimizations with dynamic objective functions. The adjoint solver is actually aimed at replacing the low fidelity gust load computation based on DLM in an aeroelastic sizing and optimization process.
This TSM solver is evaluated for inviscid flows in the cases of a 2D airfoil to which pitching motions are applied, of a 3D large aspect ratio wing (DLRF25) subjected to harmonic oscillations which shape is a structural eigen mode one, and subjected to gust loads. A last case concerns the gust response of a 2D airfoil with plunge and twist degrees of freedom.

14:00
30 mins

Comparison between computational and experimental nonstationary pressure distribution on a pitchoscilating wing
Bruno Regina, Eduardo Molina, Roberto Silva
Abstract: The objective of this work is to obtain CFD results for the dynamic response of a wing oscillating in pitch in a transonic regime using an opensource tool. The purpose is to verify and improve the correspondence with the experimental data as performed in the wind tunnel test for a wing model developed by Embraer. For this, in some analyzes it is proposed to impose a prescribed movement to the wing in the CFD simulations that models the bending observed in the scaled model throughout the tests as a rigid mesh movement in rolling direction. Prescribed motion parameters are extracted directly from the model’s structural deformation measurement data. In addition, simulations of a test case using the Benchmark Supercritical Wing (BSCW) are performed to investigate the impact of relevant variables in this type of analysis, such as time step and mesh refinement level. The time step was identified as the most influential parameter to approximate the simulation results to experimentally obtained data. The CFD results for the Embraer wing were able to capture the main behaviors of the magnitude
and phase of the nonstationary pressure coefficient on the wing, mainly for conditions of higher reduced frequencies, with an affordable computational cost.

14:30
30 mins

Aerodynamic analysis of aircraft wings using a coupled PMBL approach
Lipeng Zhu, Changchuan Xie, Yang Meng
Abstract: The objective of this paper is to develop an aerodynamic model suitable for aeroelastic analysis with low computational cost and sufficient fidelity. The physicsbased reduce order model is based on the unsteady inviscid Panel Method (PM), selected for its low computation time. Viscous effects are modeled with twodimensional unsteady highfidelity boundary layer calculations at various sections along the span and incorporated as an effective shape boundary condition correction inside the PM. The viscous sectional data are calculated with twodimensional differential boundary layer equations to allow viscous effects to be included for a more accurate maximum lift coefficient and spanload evaluations. These viscous corrections are coupled through a modified displacement thickness distribution coupling method for 2D boundary layer sectional data.
Predicting the flowfield by solutions based on inviscidflow theory is usually adequate as long as the viscous effects are negligible. A boundary layer that forms on the surface causes the irrotational flow outside it to be on a surface displaced into the fluid by a distance equal to the displacement thickness, which represents the deficiency of mass within the boundary layer. Thus, a new boundary for the inviscid flow, taking the boundarylayer effects into consideration, can be formed by adding to the body surface. The new surface is called the displacement surface and, if its deviation from the original surface is not negligible, the inviscid flow solutions can be improved by incorporating viscous effects into the inviscid flow equations. For a given wing geometry and freest ream flow conditions, the inviscid velocity distribution is first obtained with the threedimensional panel method, and the boundary layer equations are solved along the streamline.
The fidelity of the method is verified against 3D RANS flow solver solutions on a high aspect ratio wing. The overall results show impressive precision of the 3D PM/2D BL approach compared to 3D RANS solutions and in compute times in the order of minutes on a standard desktop computer. The steady and unsteady analysis results of NACA 0012 airfoil are shown as follows.

15:00
30 mins

RayleighRitz method with multibody dynamics for highly flexible structures
Leonardo Barros da Luz, Flávio CardosoRibeiro, Pedro Paglione
Abstract: Flexible structures are increasingly prevalent in the commercial aviation industry, and the use of highly flexible structures is a prominent trend for the future. When analyzing those structures, it is crucial to consider geometric nonlinearities caused by large displacements. This means that the modeling of the structures must incorporate nonlinear structural models, which can lead to a reasonable increase in computational costs. To tackle this challenge, a framework has been developed for static and dynamic analyses of highly flexible structures. It is based on a linear structural model, utilizing the RayleighRitz method, coupled with multibody dynamics. The geometric nonlinearities are modeled through rigid connections between multiple flexible bodies that form the final structure. Two different approaches have been used for the multibody dynamics. The former considers all degrees of freedom of each body and solves only the kinematics of the constraint to maintain the connections between the bodies, which resulted in an augmented system with Lagrange multipliers that can be used to reconstruct forces and moments of constraint. The latter utilizes only the independent degrees of freedom whilst reconstructing the dependent ones through the equations that define the constraints between the bodies, directly solving the constraints. The results obtained show that proposed framework accurately describes the dynamics of highly flexible structures and can be used to simulate structures with various types of connections, showcasing its versatility for other applications like simulations of morphing structures such as wings with folding wingtips.

