In order to eliminate or reduce vibration problems inturbomachines without a high increase in the complexity of thevibratory behavior, the adjacent airfoils around the wheel areoften mechanically connected together with lacing wires, tip orpart-span shrouds in a number of identical sectors. Although anaerodynamic stabilizing effect of tying airfoils together ingroups on the whole cascade is indicated by numerical andexperimental studies, for some operating conditions suchsectored vane cascade can still remain unstable. The goal of the present work is to investigate thepossibilities of a sectored vane cascade to undergoself-excited vibrations or flutter. The presented method forpredicting the aerodynamic response of a sectored vane cascadeis based on the aerodynamic work influence coefficientrepresentation of freestanding blade cascade. The sectored vaneanalysis assumes that the vibration frequency is the same forall blades in the sectored vane, while the vibration amplitudesand mode shapes can be different for each individual blade inthe sector. Additionally, the vibration frequency as well asthe amplitudes and mode shapes are supposed to be known. The aerodynamic analysis of freestanding blade cascade isperformed with twodimensional inviscid linearized flow model.As far as feasible the study is supported by non-linear flowmodel analysis as well as by performing comparisons againstavailable experimental data in order to minimize theuncertainties of the numerical modeling on the physicalconclusions of the study. As has been shown for the freestanding low-pressure turbineblade, the blade mode shape gives an important contributioninto the aerodynamic stability of the cascade. During thepreliminary design, it has been recommended to take intoaccount the mode shape as well rather than only reducedfrequency. In the present work further investigation using foursignificantly different turbine geometries makes these findingsmore general, independent from the low-pressure turbine bladegeometry. The investigation also continues towards a sectoredvane cascade. A parametrical analysis summarizing the effect ofthe reduced frequency and real sector mode shape is carried outfor a low-pressure sectored vane cascade for differentvibration amplitude distributions between the airfoils in thesector as well as different numbers of the airfoils in thesector. Critical (towards flutter) reduced frequency maps areprovided for torsion- and bending-dominated sectored vane modeshapes. Utilizing such maps at the early design stages helps toimprove the aerodynamic stability of low-pressure sectoredvanes. A special emphasis in the present work is put on theimportance for the chosen unsteady inviscid flow model to bewell-posed during numerical calculations. The necessity for thecorrect simulation of the far-field boundary conditions indefining the stability margin of the blade rows isdemonstrated. Existing and new-developed boundary conditionsare described. It is shown that the result of numerical flowcalculations is dependent more on the quality of boundaryconditions, and less on the physical extension of thecomputational domain. Keywords: Turbomachinery, Aerodynamics,Unsteady CFD, Design, Flutter, Low-Pressure Turbine, Blade ModeShape, Critical Reduced Frequency, Sectored Vane Mode Shape,Vibration Amplitude Distribution, Far-field 2D Non-ReflectingBoundary Conditions. omain. Keywords:Turbomachinery, Aerodynamics, Unsteady CFD,Design, Flutter, Low-Pressure Turbine, Blade Mode Shape,Critical Reduced Frequency, Sectored Vane Mode Shape, VibrationAmplitude Distribution, Far-field 2D Non-Reflecting BoundaryConditions.

<p>In order to eliminate or reduce vibration problems inturbomachines without a high increase in the complexity of thevibratory behavior, the adjacent airfoils around the wheel areoften mechanically connected together with lacing wires, tip orpart-span shrouds in a number of identical sectors. Although anaerodynamic stabilizing effect of tying airfoils together ingroups on the whole cascade is indicated by numerical andexperimental studies, for some operating conditions suchsectored vane cascade can still remain unstable.</p><p>The goal of the present work is to investigate thepossibilities of a sectored vane cascade to undergoself-excited vibrations or flutter. The presented method forpredicting the aerodynamic response of a sectored vane cascadeis based on the aerodynamic work influence coefficientrepresentation of freestanding blade cascade. The sectored vaneanalysis assumes that the vibration frequency is the same forall blades in the sectored vane, while the vibration amplitudesand mode shapes can be different for each individual blade inthe sector. Additionally, the vibration frequency as well asthe amplitudes and mode shapes are supposed to be known.</p><p>The aerodynamic analysis of freestanding blade cascade isperformed with twodimensional inviscid linearized flow model.As far as feasible the study is supported by non-linear flowmodel analysis as well as by performing comparisons againstavailable experimental data in order to minimize theuncertainties of the numerical modeling on the physicalconclusions of the study.</p><p>As has been shown for the freestanding low-pressure turbineblade, the blade mode shape gives an important contributioninto the aerodynamic stability of the cascade. During thepreliminary design, it has been recommended to take intoaccount the mode shape as well rather than only reducedfrequency. In the present work further investigation using foursignificantly different turbine geometries makes these findingsmore general, independent from the low-pressure turbine bladegeometry. The investigation also continues towards a sectoredvane cascade. A parametrical analysis summarizing the effect ofthe reduced frequency and real sector mode shape is carried outfor a low-pressure sectored vane cascade for differentvibration amplitude distributions between the airfoils in thesector as well as different numbers of the airfoils in thesector. Critical (towards flutter) reduced frequency maps areprovided for torsion- and bending-dominated sectored vane modeshapes. Utilizing such maps at the early design stages helps toimprove the aerodynamic stability of low-pressure sectoredvanes.</p><p>A special emphasis in the present work is put on theimportance for the chosen unsteady inviscid flow model to bewell-posed during numerical calculations. The necessity for thecorrect simulation of the far-field boundary conditions indefining the stability margin of the blade rows isdemonstrated. Existing and new-developed boundary conditionsare described. It is shown that the result of numerical flowcalculations is dependent more on the quality of boundaryconditions, and less on the physical extension of thecomputational domain. Keywords: Turbomachinery, Aerodynamics,Unsteady CFD, Design, Flutter, Low-Pressure Turbine, Blade ModeShape, Critical Reduced Frequency, Sectored Vane Mode Shape,Vibration Amplitude Distribution, Far-field 2D Non-ReflectingBoundary Conditions. omain.</p><p><b>Keywords:</b>Turbomachinery, Aerodynamics, Unsteady CFD,Design, Flutter, Low-Pressure Turbine, Blade Mode Shape,Critical Reduced Frequency, Sectored Vane Mode Shape, VibrationAmplitude Distribution, Far-field 2D Non-Reflecting BoundaryConditions.</p>

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Os recentes desenvolvimentos na tecnologia de sistema aeronáutico de geometria variável têm sido motivados principalmente pela necessidade de melhorar o desempenho de aeronaves. O conceito de Morphing Aircraft, por meio da variação da linha de arqueamento, representa uma alternativa para sistemas aeronáuticos mais eficientes. No entanto, para aeronaves de alto desempenho, projetos com estes novos conceitos podem gerar reações aeroelásticas adversas, o que representa uma questão importante e pode vir a limitar esses novos projetos. A compreensão adequada do comportamento aeroelástico devido à variação da linha de arqueamento, particularmente em regimes transônico, compreende uma questão importante. Este trabalho consiste num estudo preliminar das consequências aeroelásticas de um sistema aeronáutico de geometria variável. O objetivo desse trabalho é explorar as repostas aeroelásticas transônicas de um aerofólio com arqueamento variável no tempo. A metodologia para análise aeroelástica é baseada num modelo de seção típica. A integração no tempo do sistema aeroelástico é obtida pelo método de Runge-Kutta de quarta ordem. A representação do escoamento transônico não estacionário foi computada por um código CFD em um contexto de malhas não estruturadas com uma formulação dada pelas equações de Euler-2D. Esses resultados preliminares podem fornecer aos projetistas informações importantes sobre as respostas aeroelásticas de um sistema aeronáutico com variação da linha de arqueamento, permitindo estabelecer um quadro adequado para futuras investigações de controle aeroelástico de sistema aeronáutico de geometria variável. / Recent developments on aircraft variable geometry technologies have been mainly motivated by the need for improving the flight performance. The morphing wing concept, by means of variable camber, represents an alternative towards more efficient lifting surfaces. However, for higher performance aircraft, this technology may lead to designs that create unsteady loads, which may result in adverse aeroelastic responses, which represents an important and limiting issue. Proper understanding of the aeroelastic behavior, particularly in transonic flight regimes, due to variations in camber comprises an important matter. This work is a primary study of aeroelastic consequences of an real-time adaptive aircraft. The objective of this work is to investigate prescribed variations to airfoil camberline and their influence to the aeroelastic response in transonic flight regime. The methodology is based on computational simulations of typical section with unsteady transonic aerodynamics solved with a Computational Fluid Dynamics (CFD) code. The time integration of the aeroelastic system is obtained by Runge-Kutta fourth order. The unsteady transonic flow was computed by a CFD code based on the 2D-Euler equations with unstructured mesh. Prescribed camber variation of a symmetrical airfoil is transferred to the CFD mesh, and aeroelastic responses and loading is assessed. These preliminary results may provide the designers valuable information on the interaction between changes in camber during airfoil aeroelastic reactions, allowing establishing an adequate framework for further aeroelastic control investigations of morphing wings.

Os recentes desenvolvimentos na tecnologia de sistema aeronáutico de geometria variável têm sido motivados principalmente pela necessidade de melhorar o desempenho de aeronaves. O conceito de Morphing Aircraft, por meio da variação da linha de arqueamento, representa uma alternativa para sistemas aeronáuticos mais eficientes. No entanto, para aeronaves de alto desempenho, projetos com estes novos conceitos podem gerar reações aeroelásticas adversas, o que representa uma questão importante e pode vir a limitar esses novos projetos. A compreensão adequada do comportamento aeroelástico devido à variação da linha de arqueamento, particularmente em regimes transônico, compreende uma questão importante. Este trabalho consiste num estudo preliminar das consequências aeroelásticas de um sistema aeronáutico de geometria variável. O objetivo desse trabalho é explorar as repostas aeroelásticas transônicas de um aerofólio com arqueamento variável no tempo. A metodologia para análise aeroelástica é baseada num modelo de seção típica. A integração no tempo do sistema aeroelástico é obtida pelo método de Runge-Kutta de quarta ordem. A representação do escoamento transônico não estacionário foi computada por um código CFD em um contexto de malhas não estruturadas com uma formulação dada pelas equações de Euler-2D. Esses resultados preliminares podem fornecer aos projetistas informações importantes sobre as respostas aeroelásticas de um sistema aeronáutico com variação da linha de arqueamento, permitindo estabelecer um quadro adequado para futuras investigações de controle aeroelástico de sistema aeronáutico de geometria variável. / Recent developments on aircraft variable geometry technologies have been mainly motivated by the need for improving the flight performance. The morphing wing concept, by means of variable camber, represents an alternative towards more efficient lifting surfaces. However, for higher performance aircraft, this technology may lead to designs that create unsteady loads, which may result in adverse aeroelastic responses, which represents an important and limiting issue. Proper understanding of the aeroelastic behavior, particularly in transonic flight regimes, due to variations in camber comprises an important matter. This work is a primary study of aeroelastic consequences of an real-time adaptive aircraft. The objective of this work is to investigate prescribed variations to airfoil camberline and their influence to the aeroelastic response in transonic flight regime. The methodology is based on computational simulations of typical section with unsteady transonic aerodynamics solved with a Computational Fluid Dynamics (CFD) code. The time integration of the aeroelastic system is obtained by Runge-Kutta fourth order. The unsteady transonic flow was computed by a CFD code based on the 2D-Euler equations with unstructured mesh. Prescribed camber variation of a symmetrical airfoil is transferred to the CFD mesh, and aeroelastic responses and loading is assessed. These preliminary results may provide the designers valuable information on the interaction between changes in camber during airfoil aeroelastic reactions, allowing establishing an adequate framework for further aeroelastic control investigations of morphing wings.