Search results for: aeroelastic

Authors: N. Manoj

Abstract:

The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.

Keywords: aeroelasticity, finite volume, geometric nonlinearity, limit cycle oscillations, strake

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Authors: Chandra Shekhar Prasad, Ludek Pesek Prasad

Abstract:

In the present day fan blade of aero engine, turboprop propellers, gas turbine or steam turbine low-pressure blades are getting bigger, lighter and thus, become more flexible. Therefore, flutter, forced blade response and vibration related failure of the high aspect ratio blade are of main concern for the designers, thus need to be address properly in order to achieve successful component design. At the preliminary design stage large number of design iteration is need to achieve the utter free safe design. Most of the numerical method used for aeroelastic analysis is based on field-based methods such as finite difference method, finite element method, finite volume method or coupled. These numerical schemes are used to solve the coupled fluid Flow-Structural equation based on full Naiver-Stokes (NS) along with structural mechanics’ equations. These type of schemes provides very accurate results if modeled properly, however, they are computationally very expensive and need large computing recourse along with good personal expertise. Therefore, it is not the first choice for aeroelastic analysis during preliminary design phase. A reduced order aeroelastic model (ROAM) with acceptable accuracy and fast execution is more demanded at this stage. Similar ROAM are being used by other researchers for aeroelastic and force response analysis of turbomachinery. In the present paper new medium fidelity ROAM is successfully developed and implemented in numerical tool to simulated the aeroelastic stability phenomena in turbomachinery and well as flexible wings. In the present, a hybrid flow solver based on 3D viscous-inviscid coupled 3D panel method (PM) and 3d discrete vortex particle method (DVM) is developed, viscous parameters are estimated using boundary layer(BL) approach. This method can simulate flow separation and is a good compromise between accuracy and speed compared to CFD. In the second phase of the research work, the flow solver (PM) will be coupled with ROM non-linear beam element method (BEM) based FEM structural solver (with multibody capabilities) to perform the complete aeroelastic simulation of a steam turbine bladed disk, propellers, fan blades, aircraft wing etc. The partitioned based coupling approach is used for fluid-structure interaction (FSI). The numerical results are compared with experimental data for different test cases and for the blade cascade test case, experimental data is obtained from in-house lab experiments at IT CAS. Furthermore, the results from the new aeroelastic model will be compared with classical CFD-CSD based aeroelastic models. The proposed methodology for the aeroelastic stability analysis of gas turbine or steam turbine blades, or propellers or fan blades will provide researchers and engineers a fast, cost-effective and efficient tool for aeroelastic (classical flutter) analysis for different design at preliminary design stage where large numbers of design iteration are required in short time frame.

Keywords: aeroelasticity, beam element method (BEM), discrete vortex particle method (DVM), classical flutter, fluid-structure interaction (FSI), panel method, reduce order aeroelastic model (ROAM), turbomachinery, viscous-inviscid coupling

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Authors: Laith K. Abbas, Xiaoting Rui, Pier Marzocca

Abstract:

Aerospace systems, generally speaking, are inherently nonlinear. These nonlinearities may modify the behavior of the system. However, nonlinearities in an aeroelastic system can be divided into structural and aerodynamic. Structural nonlinearities can be subdivided into distributed and concentrated ones. Distributed nonlinearities are spread over the whole structure representing the characteristic of materials and large motions. Concentrated nonlinearities act locally, representing loose of attachments, worn hinges of control surfaces, and the presence of external stores. The concentrated nonlinearities can be approximated by one of the classical structural nonlinearities, namely, cubic, free-play and hysteresis, or by a combination of these, for example, a free-play and a cubic one. Compressibility, aerodynamic heating, separated flows and turbulence effects are important aspects that result in nonlinear aerodynamic behavior. An issue related to the low-speed flutter and its catastrophic/benign character represented by Limit Cycle Oscillation (LCO) of all-movable fin, as well to their control is addressed in the present work. To the approach of this issue: (1) Quasi-Steady (QS) Theory and Computational Fluid Dynamics (CFD) of subsonic flow are implemented, (2) Flutter motion equations of a two-dimensional typical section with cubic nonlinear stiffness in the pitching direction and free play gap are established, (3) Uncoupled bending/torsion frequencies of the selected fin are computed using recently developed Transfer Matrix Method of Multibody System Dynamics (MSTMM), and (4) Time simulations are carried out to study the bifurcation behavior of the aeroelastic system. The main objective of this study is to investigate how the LCO and chaotic behavior are influenced by the coupled aeroelastic nonlinearities and intend to implement a control capability enabling one to control both the flutter boundary and its character. By this way, it may expand the operational envelop of the aerospace vehicle without failure.

Keywords: aeroelasticity, CFD, MSTMM, flutter, freeplay, fin

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Authors: Ketseas Dimitris

Abstract:

In this work, we investigate the effect of noise on a classical two-degree-of-freedom pitch-plunge aeroelastic system. The inlet velocity of the flow is modelled as a stochastically varying parameter by the Ornstein-Uhlenbeck (OU) stochastic process. The system is a 2D airfoil, and the elastic problem is simulated using linear springs. We study the manifestation of Limit Cycle Oscillations (LCO) that correspond to the varying fluid velocity under the dynamic stall regime. We aim to delve into the unexplored facets of the classical pitch-plunge aeroelastic system, seeking a comprehensive understanding of how parametric noise influences the occurrence of LCO and expands the boundaries of its known behavior.

Keywords: aerodynamics, aeroelasticity, computational fluid mechanics, stall flutter, stochastical processes, limit cycle oscillation

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Authors: Evgeniia V. Mekhonoshina, Vladimir Ya. Modorskii, Vasilii Yu. Petrov

Abstract:

At present, vibrations of rotors of gas transmittal unit evade sustainable forecasting. This paper describes elastic oscillation modes in resilient supports and rotor impellers modeled during computational experiments with regard to interference in the system of gas-dynamic flow and compressor rotor. Verification of aeroelastic approach was done on model problem of interaction between supersonic jet in shock tube with deformed plate. ANSYS 15.0 engineering analysis system was used as a modeling tool of numerical simulation in this paper. Finite volume method for gas dynamics and finite elements method for assessment of the strain stress state (SSS) components were used as research methods. Rotation speed and material’s elasticity modulus varied during calculations, and SSS components and gas-dynamic parameters in the dynamic system of gas-dynamic flow and compressor rotor were evaluated. The analysis of time dependence demonstrated that gas-dynamic parameters near the rotor blades oscillate at 200 Hz, and SSS parameters at the upper blade edge oscillate four times higher, i.e. with blade frequency. It has been detected that vibration amplitudes correction in the test points at magnetic bearings by aeroelasticity may correspond up to 50%, and about -π/4 for phases.

Keywords: Centrifugal compressor, aeroelasticity, interdisciplinary calculation, oscillation phase displacement, vibration, nonstationarity

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Authors: Magu Raam Prasaad R., Venkatramani Jagadish

Abstract:

Recent studies in the literature have shown that randomly fluctuating wind flows can give rise to a distinct regime of pre-flutter oscillations called intermittency. Intermittency is characterized by the presence of sporadic bursts of high amplitude oscillations interspersed amidst low-amplitude aperiodic fluctuations. The focus of this study is on investigating the energy harvesting potential of these intermittent oscillations. Available literature has by and large devoted its attention on extracting energy from flutter oscillations. The possibility of harvesting energy from pre-flutter regimes have remained largely unexplored. However, extracting energy from violent flutter oscillations can be severely detrimental to the structural integrity of airfoil structures. Consequently, investigating the relatively stable pre-flutter responses for energy extraction applications is of practical importance. The present study is devoted towards addressing these concerns. A pitch-plunge airfoil with cubic hardening nonlinearity in the plunge and pitch degree of freedom is considered. The input flow fluctuations are modelled using a sinusoidal term with randomly perturbed frequencies. An electromagnetic coupling is provided to the pitch-plunge equations, such that, energy from the wind induced vibrations of the structural response are extracted. With the mean flow speed as the bifurcation parameter, a fourth order Runge-Kutta based time marching algorithm is used to solve the governing aeroelastic equations with electro-magnetic coupling. The harnessed energy from the intermittency regime is presented and the results are discussed in comparison to that obtained from the flutter regime. The insights from this study could be useful in health monitoring of aeroelastic structures.

Keywords: aeroelasticity, energy harvesting, intermittency, randomly fluctuating flows

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Authors: Jiri Cecrdle

Abstract:

This paper describes the concept of the W-WING whirl flutter aeroelastic demonstrator. Whirl flutter is the specific case of flutter that accounts for the additional dynamic and aerodynamic influences of the engine rotating parts. The instability is driven by motion-induced unsteady aerodynamic propeller forces and moments acting in the propeller plane. Whirl flutter instability is a serious problem that may cause the unstable vibration of a propeller mounting, leading to the failure of an engine installation or an entire wing. The complicated physical principle of whirl flutter required the experimental validation of the analytically gained results. W-WING aeroelastic demonstrator has been designed and developed at Czech Aerospace Research Centre (VZLU) Prague, Czechia. The demonstrator represents the wing and engine of the twin turboprop commuter aircraft. Contrary to the most of past demonstrators, it includes a powered motor and thrusting propeller. It allows the changes of the main structural parameters influencing the whirl flutter stability characteristics. Propeller blades are adjustable at standstill. The demonstrator is instrumented by strain gauges, accelerometers, revolution-counting impulse sensor, sensor of airflow velocity, and the thrust measurement unit. Measurement is supported by the in house program providing the data storage and real-time depiction in the time domain as well as pre-processing into the form of the power spectral densities. The engine is linked with a servo-drive unit, which enables maintaining of the propeller revolutions (constant or controlled rate ramp) and monitoring of immediate revolutions and power. Furthermore, the program manages the aerodynamic excitation of the demonstrator by the aileron flapping (constant, sweep, impulse). Finally, it provides the safety guard to prevent any structural failure of the demonstrator hardware. In addition, LMS TestLab system is used for the measurement of the structure response and for the data assessment by means of the FFT- and OMA-based methods. The demonstrator is intended for the experimental investigations in the VZLU 3m-diameter low-speed wind tunnel. The measurement variant of the model is defined by the structural parameters: pitch and yaw attachment stiffness, pitch and yaw hinge stations, balance weight station, propeller type (duralumin or steel blades), and finally, angle of attack of the propeller blade 75% section (). The excitation is provided either by the airflow turbulence or by means of the aerodynamic excitation by the aileron flapping using a frequency harmonic sweep. The experimental results are planned to be utilized for validation of analytical methods and software tools in the frame of development of the new complex multi-blade twin-rotor propulsion system for the new generation regional aircraft. Experimental campaigns will include measurements of aerodynamic derivatives and measurements of stability boundaries for various configurations of the demonstrator.

Keywords: aeroelasticity, flutter, whirl flutter, W WING demonstrator

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Authors: Paul V. Thomas, Mostafa S. A. Elsayed, Denis Walch

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Airframe structural optimization at different design stages results in new mass and stiffness distributions which modify the critical design loads envelop. Determination of aircraft critical loads is an extensive analysis procedure which involves simulating the aircraft at thousands of load cases as defined in the certification requirements. It is computationally prohibitive to use a Global Finite Element Model (GFEM) for the load analysis, hence reduced order structural models are required which closely represent the dynamic characteristics of the GFEM. This paper presents the implementation of Component Mode Synthesis (CMS) method for the generation of high fidelity Reduced Order Model (ROM) of complex airframes. Here, sub-structuring technique is used to divide the complex higher order airframe dynamical system into a set of subsystems. Each subsystem is reduced to fewer degrees of freedom using matrix projection onto a carefully chosen reduced order basis subspace. The reduced structural matrices are assembled for all the subsystems through interface coupling and the dynamic response of the total system is solved. The CMS method is employed to develop the ROM of a Bombardier Aerospace business jet which is coupled with an aerodynamic model for dynamic aeroelasticity loads analysis under gust turbulence. Another set of dynamic aeroelastic loads is also generated employing a stick model of the same aircraft. Stick model is the reduced order modelling methodology commonly used in the aerospace industry based on stiffness generation by unitary loading application. The extracted aeroelastic loads from both models are compared against those generated employing the GFEM. Critical loads Modal participation factors and modal characteristics of the different ROMs are investigated and compared against those of the GFEM. Results obtained show that the ROM generated using Craig Bampton CMS reduction process has a superior dynamic characteristics compared to the stick model.

Keywords: component mode synthesis, craig bampton reduction method, dynamic aeroelasticity analysis, model order reduction

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Authors: Ranjan Banerjee, W. D. Gunawardana

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The free vibration and flutter analysis plays a major part in aircraft design which is indeed, a mandatory requirement. In particular, high aspect ratio transport airliner wings are prone to free vibration and flutter problems that must be addressed during the design process as demanded by the airworthiness authorities. The purpose of this paper is to carry out a detailed free vibration and flutter analysis for a wide range of high aspect ratio aircraft wings and generate design curves to provide useful visions and understandings of aircraft design from an aeroelastic perspective. In the initial stage of the investigation, the bending and torsional stiffnesses of a number of transport aircraft wings are looked at and critically examined to see whether it is possible to express the stiffness distributions in polynomial form, but in a sufficiently accurate manner. A similar attempt is made for mass and mass moment of inertia distributions of the wing. Once the choice of stiffness and mass distributions in polynomial form is made, the high aspect ratio wing is idealised by a series of bending-torsion coupled beams from a structural standpoint. Then the dynamic stiffness method is applied to compute the natural frequencies and mode shape of the wing. Next the wing is idealised aerodynamically and to this end, unsteady aerodynamic of Theodorsen type is employed to represent the harmonically oscillating wing. Following this step, a normal mode method through the use of generalised coordinates is applied to formulate the flutter problem. In essence, the generalised mass, stiffness and aerodynamic matrices are combined to obtain the flutter matrix which is subsequently solved in the complex domain to determine the flutter speed and flutter frequency. In the final stage of the investigation, an exhaustive parametric study is carried out by varying significant wing parameters to generate design curves which help to predict the free vibration and flutter behaviour of high aspect ratio transport aircraft wings in a generic manner. It is in the aeroelastic context of aircraft design where the results are expected to be most useful.

Keywords: high-aspect ratio wing, flutter, dynamic stiffness method, free vibration, aeroelasticity

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Authors: Thanasis K. Barlas, Helge A. Madsen

Abstract:

A novel Active Flap System (AFS) has been developed at DTU Wind Energy, as a result of a 3-year R\&D project following almost 10 years of innovative research in this field. The full-scale AFS comprises an active deformable trailing edge has been tested at the unique rotating test facility at the Risoe Campus of DTU Wind Energy in Denmark. The design and instrumentation of the wing section and the active flap system (AFS) are described. The general description and objectives of the rotating test rig at the Risoe campus of DTU are presented, as used for the aeroelastic testing of the AFS in the recently finalized INDUFLAP project. The general description and objectives are presented, along with an overview of sensors on the setup and the test cases. The post-processing of data is discussed and results of steady flap step and azimuth control flap cases are presented.

Keywords: morphing, adaptive, flap, smart blade, wind turbine

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Authors: Timothee Gidenne, Xia Pinqi

Abstract:

In this paper, an investigation of the use of carbon nanotubes (CNTs) reinforced polymer as an actuator for an active flutter suppression to counter the flutter phenomena is conducted. The goal of this analysis is to establish a link between the behavior of the control surface and the actuators to demonstrate the veracity of using such a suppression system for the aeronautical field. A preliminary binary flutter model using simplified unsteady aerodynamics is developed to study the behavior of the wing while reaching the flutter speed and when the control system suppresses the flutter phenomena. The Timoshenko beam theory for bilayer materials is used to match the response of the control surface with the CNTs reinforced polymer (CNRP) actuators. According to Timoshenko theory, results show a good and realistic response for such a purpose. Even if the results are still preliminary, they show evidence of the potential use of CNRP for control surface actuation for the small-scale and lightweight system.

Keywords: actuators, aeroelastic, aeroservoelasticity, carbon nanotubes, flutter, flutter suppression

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Authors: M. Saifudin Ahmed Atique, Santosh Paudyal, Caixia Yang

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In an aircraft, a great portion of energy is wasted due to its inflight structural vibration. Structural components vibrate due to aeroelastic instabilities, gust perturbations and engine rotation at very high rpm. Energy losses due to mechanical vibration can be utilized by harvesting energy from aircraft structure as electrical energy. This harvested energy can be stored in battery panels built into aircraft fuselage and can be used to power inflight auxiliary accessories i.e., lighting and entertainment systems. Moreover, this power can be used for wireless Structural Health Monitoring System (SHM) for aircraft and as an excellent replacement of aircraft Ground Power Unit (GPU)/Auxiliary Power Unit (APU) during passenger onboard time to power aircraft cabin accessories to reduce aircraft ground operation cost significantly. In this paper, we propose the design of a noble aircraft wing in which Piezoelectric panels placed under the composite skin of aircraft wing will generate electrical charges from any inflight aerodynamics or mechanical vibration and store it into battery to power auxiliary inflight systems/accessories as per requirement. Experimental results show that a well-engineered piezoelectric energy harvester based aircraft wing can produce adequate energy to support in-flight lighting and auxiliary cabin accessories.

Keywords: vibration energy, aircraft wing, piezoelectric material, inflight accessories

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Authors: Matza Gusto Andika, Malinda Sabrina, Syarie Fatunnisa

Abstract:

Aerodynamic and aeroelastics studies on the hanger bridge profile are important to analyze the aerodynamic phenomenon and Aeroelastics stability of hanger. Wind tunnel tests were conducted on a model of H-beam profile from hanger bridge. The purpose of this study is to investigate steady aerodynamic characteristics such as lift coefficient (Cl), drag coefficient (Cd), and moment coefficient (Cm) under the different angle of attack for preliminary prediction of aeroelastics stability problems. After investigation the steady aerodynamics characteristics from the model, dynamic testing is also conducted in wind tunnel to know the aeroelastics phenomenon which occurs at the H-beam hanger bridge profile. The studies show that the torsional vortex induced vibration occur when the wind speed is 7.32 m/s until 9.19 m/s with maximum amplitude occur when the wind speed is 8.41 m/s. The result of wind tunnel testing is matching to hanger vibration where occur in the field, so wind tunnel studies has successful to model the problem. In order that the H-beam profile is not good enough for the hanger bridge and need to be modified to minimize the Aeroelastics problem. The modification can be done with structure dynamics modification or aerodynamics modification.

Keywords: aerodynamics, aeroelastic, hanger bridge, h-beam profile, vortex induced vibration, wind tunnel

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Authors: Anwar U. Haque, Waqar Asrar, Ashraf Ali Omar, Erwin Sulaeman, Jaffer Sayed Mohamed Ali

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Due to the interference effects, the intrinsic aerodynamic parameters obtained from the individual component testing are always fundamentally different than those obtained for complete model testing. Consideration and limitation for such testing need to be taken into account in any design work related to the component buildup method. In this paper, the scaled model of a straight rectangular canard of a hybrid buoyant aircraft is tested at 50 m/s in IIUM-LSWT (Low-Speed Wind Tunnel). Model and its attachment with the balance are kept rigid to have results free from the aeroelastic distortion. Based on the velocity profile of the test section’s floor; the height of the model is kept equal to the corresponding boundary layer displacement. Balance measurements provide valuable but limited information of the overall aerodynamic behavior of the model. Zero lift coefficient is obtained at -2.2o and the corresponding drag coefficient was found to be less than that at zero angles of attack. As a part of the validation of low fidelity tool, the plot of lift coefficient plot was verified by the experimental data and except the value of zero lift coefficient, the overall trend has under-predicted the lift coefficient. Based on this comparative study, a correction factor of 1.36 is proposed for lift curve slope obtained from the panel method.

Keywords: wind tunnel testing, boundary layer displacement, lift curve slope, canard, aerodynamics

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Authors: Liliia N. Butymova, Vladimir Y. Modorsky, Nikolai A. Shevelev

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Prediction of vibration processes in gas transmittal units (GTU) is an urgent problem. Despite numerous scientific publications on the problem of vibrations in general, there are not enough works concerning FSI-modeling interaction processes between several deformable blades in gas-dynamic flow. Since it is very difficult to solve the problem in full scope, with all factors considered, a unidirectional dynamic coupled 1FSI model is suggested for use at the first stage, which would include, from symmetry considerations, two blades, which might be considered as the first stage of solving more general bidirectional problem. ANSYS CFX programmed multi-processor was chosen as a numerical computation tool. The problem was solved on PNRPU high-capacity computer complex. At the first stage of the study, blades were believed oscillating with the same frequency, although oscillation phases could be equal and could be different. At that non-stationary gas-dynamic forces distribution over the blades surfaces is calculated in run of simulation experiment. Oscillations in the “gas — structure” dynamic system are assumed to increase if the resultant of these gas-dynamic forces is in-phase with blade oscillation, and phase shift (φ=0). Provided these oscillation occur with phase shift, then oscillations might increase or decrease, depending on the phase shift value. The most important results are as follows: the angle of phase shift in inter-blade oscillation and the gas-dynamic force depends on the flow velocity, the specific inter-blade gap, and the shaft rotation speed; a phase shift in oscillation of adjacent blades does not always correspond to phase shift of gas-dynamic forces affecting the blades. Thus, it was discovered, that asynchronous oscillation of blades might cause either attenuation or intensification of oscillation. It was revealed that clocking effect might depend not only on the mutual circumferential displacement of blade rows and the gap between the blades, but also on the blade dynamic deformation nature.

Keywords: aeroelasticity, ANSYS CFX, oscillation, phase shift, clocking effect, vibrations

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Authors: Malcolm Dinovitzer, Calvin Miller, Adam Hacker, Gabriel Wong, Zach Annen, Padmassun Rajakareyar, Jordan Mulvihill, Mostafa S.A. ElSayed

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The research work presented in this paper is developed by the Blended Wing Body (BWB) Unmanned Aerial Vehicle (UAV) team, a fourth-year capstone project at Carleton University Department of Mechanical and Aerospace Engineering. Here, a clean sheet UAV with BWB configuration is designed and optimized using Multiscale Design Optimization (MSDO) approach employing lattice materials taking into consideration design for additive manufacturing constraints. The BWB-UAV is being developed with a mission profile designed for surveillance purposes with a minimum payload of 1000 grams. To demonstrate the design methodology, a single design loop of a sample rib from the airframe is shown in details. This includes presentation of the conceptual design, materials selection, experimental characterization and residual thermal stress distribution analysis of additively manufactured materials, manufacturing constraint identification, critical loads computations, stress analysis and design optimization. A dynamic turbulent critical load case was identified composed of a 1-g static maneuver with an incremental Power Spectral Density (PSD) gust which was used as a deterministic design load case for the design optimization. 2D flat plate Doublet Lattice Method (DLM) was used to simulate aerodynamics in the aeroelastic analysis. The aerodynamic results were verified versus a 3D CFD analysis applying Spalart-Allmaras and SST k-omega turbulence to the rigid UAV and vortex lattice method applied in the OpenVSP environment. Design optimization of a single rib was conducted using topology optimization as well as MSDO. Compared to a solid rib, weight savings of 36.44% and 59.65% were obtained for the topology optimization and the MSDO, respectively. These results suggest that MSDO is an acceptable alternative to topology optimization in weight critical applications while preserving the functional requirements.

Keywords: blended wing body, multiscale design optimization, additive manufacturing, unmanned aerial vehicle

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Authors: Chukwuka Justus Iwegbu, Monye Christopher Prayer

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Propeller aircraft engines, and more generally engines with a large rotating part (turboprops, high bypass ratio turbojets, etc.) are widely used in the industry and are subject to numerous developments in order to reduce their fuel consumption. In this context, unconventional architectures such as open rotors or distributed propulsion appear, and it is necessary to consider the influence of these systems on the aircraft's stability in flight. Indeed, the tendency to lengthen the blades and wings on which these propulsion devices are fixed increases their flexibility and accentuates the risk of whirl flutter. This phenomenon of aeroelastic instability is due to the precession movement of the axis of rotation of the propeller, which changes the angle of attack of the flow on the blades and creates unsteady aerodynamic forces and moments that can amplify the motion and make it unstable. The whirl flutter instability can ultimately lead to the destruction of the engine. We note the existence of a critical speed of the incident flow. If the flow velocity is lower than this value, the motion is damped and the system is stable, whereas beyond this value, the flow provides energy to the system (negative damping) and the motion becomes unstable. A simple model of whirl flutter is based on the work of Houbolt & Reed who proposed an analytical expression of the aerodynamic load on a rigid blade propeller whose axis orientation suffers small perturbations. Their work considered a propeller subjected to pitch and yaw movements, a flow undisturbed by the blades and a propeller not generating any thrust in the absence of precession. The unsteady aerodynamic forces were then obtained using the thin airfoil theory and the strip theory. In the present study, the unsteady aerodynamic loads are expressed for a general movement of the propeller (not only pitch and yaw). The acceleration and rotation of the flow by the propeller are modeled using a Blade Element Momentum Theory (BEMT) approach, which also enable to take into account the thrust generated by the blades. It appears that the thrust has a stabilizing effect. The aerodynamic model is further developed using Theodorsen theory. A reduced order model of the aerodynamic load is finally constructed in order to perform linear stability analysis.

Keywords: advancing, entrepreneurial, knowledge, industralization

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

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This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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