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1

Numerical Modelling of Static Aeroelastic Deformations of Slender Wing in Aerodynamic Design

Bugała Pamela, Sznajder Janusz, Sieradzki Adam

Transactions on Aerospace Research

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2023

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Nr 4 (273)

52--70

EN

The article presents the validation of two methods for analyzing the aerodynamic properties of the aircraft wing concerning aeroelastic effects. The first method is based on low-cost computational models (Euler-Bernoulli Beam Model and Vortex Lattice Method [VLM]). Its primary objective is to estimate the wing’s deformation early in the design stages and during the automatic optimization process. The second one is a method that uses solutions of unsteady Navier-Stokes equations (URANS). This method suits early design, particularly for unconventional designs or flight conditions exceeding low-fidelity method limits. The coupling of the flow and structural models was done by Radial Basis Functions implemented as a user-defined module in the ANSYS Fluent solver. The structural model has variants for linear and nonlinear wing deformations. Features enhancing applicability for real-life applications, such as the definition of deformable and nondeformable mesh zones with smooth transition between them, have been included in this method. A rectangular wing of a high-altitude long-endurance (HALE) aeroplane, built based on the NACA 0012 profile, was used to validate both methods. The resulting deflections and twists of the wing have been compared with reference data for the linear and nonlinear variants of the model.

2

Assessment of the role of structural nonlinearity in galloping energy harvesters

Sarbinowski Filip, Starosta Roman

Vibrations in Physical Systems

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2021

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Vol. 32, nr 2

art. no. 2021209

EN

The study compares different variants of aeroelastic energy harvesters due to the power they generate. For this purpose, models of devices with different stiffness characteristics were prepared: linear, nonlinear, with combined stiffness and bistable. Then, using the authorial procedure, analytical expressions that describe the power of each system were determined and the influence of individual parameters on this quantity was examined. By way of optimization, the system parameters have been selected in such a way that, regardless of the flow velocity, each of them generates the maximum possible power. Based on the results obtained in this way, the advisability of using a device with combined stiffness and bistable characteristics was rejected. Moreover, it was pointed out that the linear system would provide greater efficiency for lower flow velocities.

3

Vibrations and Stability of a Plate in Supersonic Flow Subjected to a Follower Force, and Having a Hinged External Support and a Resilient Attenuation Internal Support

Nowotarski I.

Problemy Mechatroniki : uzbrojenie, lotnictwo, inżynieria bezpieczeństwa

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2018

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Vol. 9, Nr 4 (34)

127--148

EN

The vibrations and stability of a plate having a finite length were considered in a flat supersonic flow, having adopted an assumption that one of the edges of the plate has a hinged support, and the other edge is free. Another support was located in an internal point of the plate and featured resilient attenuation properties. A compressive force, called the follower force, was applied within the plane of the plate in a direction tangent to the deformed surface of the plate. This way, a superficial system was forced in which two independent physical factors occurred and caused its self-excitation. Therefore the superficial system could be termed a ‘double self-excited system’. The solution of the equations of motion for the system was derived with a Laplace transformation. In the further part of the work, a numerical analysis was carried out for the conditions of the occurrence of self-excited vibrations in relation to the position of the internal support (the so-called plate overhang), the damping within the material of the plate and other parameters of the plate, including the resilient attenuation parameters of the internal support. For the adopted parameters, the results were tested for the calculations of the stability area limits and the instability of the system in plane γ1, σ. The forms of vibrations for a series of typical cases was determined.

PL

Rozpatrzono drgania i stateczność płyty o skończonej długości w płaskim przepływie naddźwiękowym przy założeniu, że jedna z krawędzi płyty jest przegubowo podparta, a druga jest swobodna. W wewnętrznym punkcie płyty znajduje się podpora o własnościach sprężysto-tłumiących. W płaszczyźnie płyty działa siła ściskająca, która jest siłą śledzącą i zachowuje kierunek styczny do odkształconej powierzchni płyty. Powstaje w ten sposób układ powierzchniowy, w którym występują dwa niezależne czynniki fizyczne będące przyczyną jego samowzbudności. Jest to więc układ, który można nazwać układem podwójnie samowzbudnym. Rozwiązanie równań ruchu otrzymano za pomocą przekształcenia Laplace’a. W dalszej części pracy przeprowadzono numeryczną analizę warunków występowania samowzbudnych drgań w zależności od położenia podpory wewnętrznej (tzw. przewieszenia płyty), tłumienia w materiale płyty oraz innych jej parametrów, w tym także parametrów sprężysto-tłumiących podpory. Dla przyjętych parametrów zbadano wyniki obliczeń granic obszarów stateczności i niestateczności rozpatrywanego układu na płaszczyźnie γ1, σ. i wyznaczono postacie drgań dla szeregu typowych przypadków.

4

Limit cycle oscillation prediction based on Finite Element-Modal approach

Ahmad K., Wu Z., Rahman H.

Archive of Mechanical Engineering

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2018

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Vol. LXV, nr 4

497--514

EN

The central theme of this work was to analyze high aspect ratio structure having structural nonlinearity in low subsonic flow and to model nonlinear stiffness by finite element-modal approach. Total stiffness of high aspect ratio wing can be decomposed to linear and nonlinear stiffnesses. Linear stiffness is modeled by its eigenvalues and eigenvectors, while nonlinear stiffness is calculated by the method of combined Finite Element-Modal approach. The nonlinear modal stiffness is calculated by defining nonlinear static load cases first. The nonlinear stiffness in the present work is modeled in two ways, i.e., based on bending modes only and based on bending and torsion modes both. Doublet lattice method (DLM) is used for dynamic analysis which accounts for the dependency of aerodynamic forces and moments on the frequency content of dynamic motion. Minimum state rational fraction approximation (RFA) of the aerodynamic influence coefficient (AIC) matrix is used to formulate full aeroelastic state-space time domain equation. Time domain dynamics analyses show that structure behavior becomes exponentially growing at speed above the flutter speed when linear stiffness is considered, however, Limit Cycle Oscillations (LCO) is observed when linear stiffness along with nonlinear stiffness, modeled by FE-Modal approach is considered. The amplitude of LCO increases with the increase in the speed. This method is based on cantilevered configuration. Nonlinear static tests are generated while wing root chord is fixed in all degrees of freedom and it needs modification if one requires considering full aircraft. It uses dedicated commercial finite element package in conjunction with commercial aeroelastic package making the method very attractive for quick nonlinear aeroelastic analysis. It is the extension of M.Y. Harmin and J.E. Cooper method in which they used the same equations of motion and modeled geometrical nonlinearity in bending modes only. In the current work, geometrical nonlinearities in bending and in torsion modes have been considered.

5

Numerical approach in aeroelasticity

Sloboda O., Korba P., Hovanec M., Pila J.

Zeszyty Naukowe. Transport / Politechnika Śląska

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2016

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z. 93

115--122

EN

Aircraft wing design processes should comprise specific analyses oriented towards aeroelasticity, which is one of the essential factors determining flight envelope boundaries. For such cases, static or dynamic aeroelastic phenomena can be simulated using CFD simulation software. ANSYS software offers the fluid structure interaction (FSI) method for solving this multiphysics problem.

6

Aeroelastic analysis of helicopter rotor using virtual blade model and equivalent beam model of a blade

Sieradzki A.

Journal of KONES

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2016

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Vol. 23, No. 1

297--304

EN

Modern helicopter rotor blades design requires taking into account complex aeroelastic phenomena. Sophisticated computational fluid dynamics and structural dynamics models, available on the market, coupled together enable such analysis with very high fidelity. However, the computational cost of this type of simulation is usually very high and for this reason, it cannot be used in interactive design process or optimization run. Complex Fluid Structure Interaction models are excellent tools for validation purposes, but the design process requires simpler models with lower computational cost and still relatively high accuracy and capabilities. The paper presents a new efficient methodology for calculating helicopter rotor loads, deformations and performance. It uses the well-known Navier-Stokes equations aerodynamic solver – ANSYS Fluent, and modified Virtual Blade Model (based on Blade Element Theory) for rotor flow calculation. This connection guarantees exceptional capabilities and fidelity in comparison with simulation time. The dedicated structural dynamics solver, based on equivalent beam model of a blade and Finite Difference Method, was developed and coupled with CFD part using User Defined Functions in Fluent software. The accuracy of created module was validated with wind tunnel tests data of IS-2 helicopter rotor model, performed in Institute of Aviation. The results of calculations were compared with experimental data for a hover state and a forward flight with three different flight velocities. The comparisons showed very good agreement of the data in most of the analysed cases and pointed out new research possibilities. The presented aeroelastic helicopter rotor model combines all advantages of using three-dimensional Navier-Stokes solver with relatively low computational costs and high accuracy, confirmed by wind tunnel tests. It could be used successfully in helicopter rotor blades design process.

7

Racjonalne modelowania żagla jako obiektu aerosprężystego

Pietrucha J. A., Skórski W. W.

Przegląd Mechaniczny

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2013

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nr 5

23--27

PL

W pracy przedstawiono przesłanki fenomenologiczno-symulacyjne prowadzące do budowy modelu żagla jako obiektu aerosprężystego. Po przeprowadzeniu krytyki modelu membrany w ujęciu liniowej teorii sprężystości zaproponowano stworzenie modelu żagla jako nieliniowej membrany sprężystej. Pokazano również, jak istotny jest charakter opływu wiatru wokół żagla i zastosowano do modelowania przepływu pole prędkości średnich wiatru, a w dalszej kolejności wskazano na konieczność stworzenia różniczkowego modelu pola wiatru.

EN

In this paper it was presented premises of fenomenological simulation, working conditions to the construction model of the sail as a aeroelasticity object. After the criticism of the membrane model in terms of the theory of linear elasticity the creation the sail as a non-linear spring diaphragm was proposed. It was also shown, how significant is the nature of the flow of the wind around the sail and a field of average wind speed was applied to the flow modeling. Subsequently, indicated the need to create a model of a differential field of the true and apparent wind.

8

Flutter analysis of IV standard configuration cascades, direct integration method

Rządkowski R., Kubitz L.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 3

333-341

EN

A three-dimensional nonlinear time-marching method and numerical analysis for aeroelastic behaviour of oscillating blade row has been presented. The approach is based on the solution of the coupled fluid-structure problem in which the aerodynamic and structural equations are integrated simultaneously in time. Thus providing the correct formulation of a coupled problem, as the interblade phase angle at which a stability (or instability) would occur, is a part of the solution.

9

Obliczenia aeroelastyczne samolotu

Posadzy P., Roszak R., Morzyński M.

Zeszyty Naukowe Politechniki Poznańskiej. Budowa Maszyn i Zarządzanie Produkcją

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2007

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Nr 6

119-126

PL

W pracy przedstawiono wyniki obliczeń aeroelastycznycb samolotu pasażerskiego dokonanych zużyciem autorskiego oprogramowania. Pokazano rezultaty badań dla przypadków stacjonarnego i niestacjonarnego w warunkach lotu na wysokości 10 500 m. Przedstawiono również mechanizm powstawania i rozprzestrzeniania się niszczących drgań nietłumionych, występujących w niekorzystnych warunkach.

EN

In this paper results of aeroelastic calculaiions arę presented. Computations has been prepared using own numerical tool. Results in case of steady and unsteady research at altitude 10 500 me-ters arę shown. Also, source of undamped vibrations is presented.

10

On some useful classical publications for teaching and studying aeroelasticity

Battoo R.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

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1998

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nr 8

59-64

EN

This document is meant primarily for readers, who may want to teach aeroelasticity for the first time or students, who may not be familiar with the field of aeroelasticity. The main objective of this paper is to point the nonexpert reader to some important texts and papers that have been published in the areas which embrace aeroelasticity, using which the reader may gain sufficient knowledge about the subject to make informed decisions. It is hoped that by drawing the readers attention to these salient papers the more interested readers will be able to increase their knowledge on many aspects related to aeroelasticity. This paper is not meant to be exhaustive, rather it is meant to be a preliminary exposition. This paper does not attempt to be an expert guide nor direct the reader to publications in a specific area. It does attempt to do is hopefully generate interest and illuminate related to the field of aeroelasticity which readers may find useful. A modest list of references is included, however it must be emphasized that there are a very extensive number of papers published each year, in all fields of aeroelasticity. Inclusion of all these would not be appropriate in a paper of this kind. Never-the more interested reader will find sufficient Information to utilize the given citations for locating material.

11

Stability derivatives cast in the frame of subsonic unsteady aerodynamics

Nowak M.

Engineering Transactions

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1998

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Vol. 46, iss. 1

45-72

EN

On the basis of numerical results and theoretical considerations, a general from of the (unsteady) linear, discretized aerodynamic operator in the Laplace- and in the time-domain, for two- and three-dimensional subsonic flow is proposed. It corresponds to the classical Theodorsen solution for an airfoil in incompressible flow. The model of aerodynamic derivatives uses a polynomial approximation to the transfer functions. There are identified terms, which are neglected in this approach: these are the deficiency function and, in the case of compressible fluid, also the term responsible for the initial pulse. These results clears the limitations and possible improvements of the aerodynamic derivatives model.