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A laminar wing test case for the flutter behavior in transonic flow with free boundary layer transition is presented. The DLR-AE-L1 airfoil and wing are designed to serve as an aeroelastic testbed to develop a better understanding for the effect of boundary layer transition on flutter stability. Coupled CFD-CSM simulations are used to determine the flutter onset in a transitional and a fully turbulent flow. It is found that flutter occurs at lower stagnation pressures for the transitional flow, which is in accordance with earlier research on laminar airfoils.

Оцінка характеристик аеродинамічних поверхонь у трансзвуковому потоці повітря теоретичними методами залишається актуальною науковою проблемою, яку необхідно вирішувати при удосконаленні методів дослідження аеропружних характеристик надзвукових літаків та аерокосмічних систем на трансзвукових швидкостях польоту.Труднощі вирішення проблеми обумовлені необхідністю врахування впливу стиснення повітря на зміну характеристик аеродинамічних профілів надзвукових літаків у трансзвуковому діапазоні швидкостей польоту. У деяких працях вплив стиснення повітря на зміну характеристик аеродинамічних профілів враховується за допомогою різноманітних поправок. Але похибка оцінки коефіцієнту тиску місцевого надзвукового потоку на поверхні аеродинамічного профілю с урахуванням стиснення повітря за допомогою цих поправок може бути дуже великої навіть для інженерних наближених оцінок.Додаткові труднощі оцінювання характеристик аеродинамічних поверхонь надзвукових літаків на трансзвукових швидкостях польоту виникають при формуванні стрибків ущільнення на поверхні аеродинамічного профілю, вплив яких цими поправками не може бути визначений.У статті для оцінки характеристик аеродинамічних профілів надзвукових літаків на трансзвукових швидкостях польоту пропонується метод, який базується на сумісному аналізу рівнянь Бернуллі для стислого газу і закономірностей зміни параметрів надзвукового струму у течії Прандтля – Майера та дозволяє оцінювати величини зміни тиску місцевого надзвукового потоку на профілі аеродинамічної поверхні керування при виникненні трансзвукового флатеру з достатньої для інженерних оцінок точністю.З порівняння отриманих запропонованим методом величин зміни тиску місцевого надзвукового потоку на профілю аеродинамічної поверхні керування з результатами, отриманими під час льотних та лабораторних досліджень, зроблено висновок щодо можливості використання запропонованого методу для попередньої наближеної оцінки деяких характеристик трансзвукового флатеру аеродинамічних поверхонь керування надзвукових літаків та аерокосмічних систем., Estimation of aerodynamic surface characteristics in transonic airflow using theoretical methods remains an urgent scientific problem that needs to be addressed on the way of improvement of methods for investigating the aeroelastic characteristics of supersonic airplanes and aerospace systems at transonic flight speeds.Difficulties in solving the problem are due to the need to take into account the effect of air compression on the change in the characteristics of the aerodynamic profiles of supersonic airplanes in the transonic flight speed range. In some papers, the effect of air compression on changing the characteristics of the aerodynamic profiles is taken into account by various corrections. But the error in estimating the pressure coefficient of the local supersonic flow on the surface of an aerodynamic profile with the use of the air compression corrections can be very considerable, even for engineering approximate estimates.Additional difficulties in estimation of the characteristics of aerodynamic surfaces of supersonic airplanes at transonic flight speeds arise under formation of shock waves on the surface of an aerodynamic profile the impact of which cannot be determined by the abovementioned corrections.In the article, for estimation of the characteristics of aerodynamic profiles of supersonic airplanes at transonic flight speeds, the authors propose a method based on a joint analysis of the Bernoulli equations for compressed gas and the change patterns of the supersonic flow parameters of the Prandtl–Meyer expansion fan that make it possible to estimate, with sufficient engineering precision, the pressure change of a local supersonic flow on the aerodynamic control surface profile in case of transonic flutter.Comparing the values of changes in the pressure of the local supersonic flow on aerodynamic control surface profiles obtained by the proposed method with the results received during flight and laboratory studies, it is concluded that it is possible to use the proposed method for preliminary approximate estimation of some characteristics of transonic flutter of aerodynamic control surfaces of supersonic aircraft and aerospace systems.

An investigation has been made into the nonlinear aeroelastic behavior of an airfoil system with free-play nonlinear stiffness in transonic flow. Computational Fluid Dynamics (CFD) and Reduced Order Model (ROM) based on Euler and Navier-Stokes equations are implemented to calculate unsteady aerodynamic forces. Results show that the nonlinear aeroelastic system experiences various bifurcations with increasing Mach number. Regular subcritical bifurcations are observed in low Mach number region. Subsequently, complex Limit Cycle Oscillations (LCOs) and even non-periodic motions appear at specific airspeed regions. When the Mach number is increased above the freeze Mach number, regular subcritical bifurcations occur again. Comparisons with inviscid solutions are used to identify and elaborate the effect of viscosity with the help of aeroelastic analysis techniques, including root locus, Single Degree of Freedom (SDOF) flutter and aerodynamic influence coefficient (AIC). For low Mach numbers in the transonic regime, the viscosity has little effect on the linear flutter characteristic because of limited influence on AIC, but a remarkable impact on the nonlinear dynamic behavior due to the sensitivity of the nonlinear structure. As the Mach number increases, the viscosity becomes significantly important due to the existence of shock-boundary layer interaction. It affects the unstable mechanism of linear flutter, impacts the aerodynamic center and hence the snap-through phenomenon, influences the AIC and consequently the nonlinear aeroelastic response. When the Mach number is increased further, the shock wave dominates the air flow and the viscosity is of minor importance.

The aeroelastic behavior of wing models is nonlinear particularly in the transonic Speed range. The interaction between aerodynamic and structural forces can lead to the occurrence of Limit-Cycle Oscillations (LCOs). If in addition the wing model is flexible and backward swept, the kinematic coupling between bending and torsion makes the Situation even more complex. In the research project ‘‘Aerostabil’’ such a wing was investigated, which was equipped with pressure transducers in three sections and accelerometers. The experiments were performed in the adaptive test section of the transonic wind tunnel TWG in Göttingen. Already Dietz et al. (2003) have reported about experimental details and preliminary results. Based on these data Bendiksen (2008) studied numerically LCO-flutter behavior using a very similar, theoretical model (G-wing) and Stickan et al. (2014) used the original data as a LCO flutter test case. The influence of flexibility on the steady aerodynamics of the wing was described in Schewe & Mai (2018). In this paper now the flutter experiments with the same flexible model were analyzed systematically in the transonic range 0.84

Transonic flows, which are common in aeronautical and spatial propulsion systems, produce shock-waves over solid boundaries. When a shock-wave impacts the boundary layer, an adverse pressure gradient is generated and a thickening or even a separation of the boundary layer is induced. If the solid boundary vibrates, the shock-wave oscillates, interacts with the boundary layer and produce a fluctuation of the static pressure at the wall. This induces an exchange of energy between the fluid and the structure which can be stabilising or lead to an aeroelastic instability (flutter).The main objective of this PhD thesis is the modelling of the unsteady behaviour the simulation of the shock-wave/boundary layer interaction for fluid-structure interaction studies. To this end, simulations have been carried out to solve Reynolds-Averaged Navier-Stokes equations using two equations turbulence model. The method is validated thanks to experimental data obtained on a transonic nozzle dedicated to aeroelastic studies. This method is then use to increase the predictability of flutter events in turbomachinery.A time linearised frequency-domain method is applied to RANS equations. It is shown that the unsteady behaviour of the turbulent boundary-layer contributes to the fluctuating static pressure when the shock-wave boundary layer interaction is strong. Hence, the frozen turbulence assumption is not valid and the turbulence model must be derivated. Thus, the regularisation of the non derivable operators is proposed and applied on k-? Wilcox (2006) turbulence model.The unsteady behaviour of the shock-wave/boundary-layer interaction in a transonic nozzle is evaluated thanks to 2D numerical simulations and shows good agreement with experimental data. When varying the reduced frequency an aeroelastic instability is found, known as transonic flutter. An active control device generating backward travelling pressure waves is then designed and numerically validated.Finally, a methodology is proposed to understand the aerodynamic onsets of transonic flutter. To this end, a preliminary design of a high bypass ratio transonic fan has been carried out. This fan, named ECL5, is dedicated to experimental aerodynamic and aeroelastic studies. The methodology relies on 2D simulations of a tip blade passage and uses linearisation to analyse the contribution of local sources as a function of reduced frequency, nodal diameter and mode shape, Les écoulements transsoniques rencontrés dans le cadre de la propulsion aéronautique et spatiale sont associés à l'apparition d'ondes de choc. En impactant la couche limite se développant sur une paroi, un gradient de pression adverse est généré qui conduit à l'épaississement ou au décollement de la couche limite. Lors de la vibration de la structure, l'onde de choc oscille et interagit avec la couche limite, générant une fluctuation de la pression statique à la paroi. Il s'ensuit alors un échange d'énergie entre le fluide et la structure qui peut être stabilisant ou au contraire conduire à une instabilité aéroélastique (flottement). La modélisation de la réponse instationnaire de l'interaction onde de choc / couche limite pour l'étude des interactions fluide-structure est l'objet de ce travail de recherche. Il s'appuie sur la résolution des équations de Navier-Stokes moyennées (RANS) et la modélisation de la turbulence. Les méthodes et modèles utilisés ont été validés à partir de résultats expérimentaux issus d'une tuyère transsonique dédiée à l'étude des interactions fluide-structure. Ces travaux sont ensuite appliqués à l'amélioration de la prédiction du flottement en turbomachine. Une méthode linéarisée en temps permettant la résolution des équations RANS dans le domaine fréquentiel est utilisée. Nous confirmons l'importance de la dérivation du modèle de turbulence lors de la prédiction d'une interaction forte entre une onde de choc et une couche limite décollée. Une méthode de régularisation est présentée puis appliquée aux opérateurs non dérivables du modèle de turbulence k-! de Wilcox (2006). La prédiction de la réponse instationnaire de l'interaction onde de choc / couche limite dans une tuyère est évaluée à partir de simulations bidimensionnelles et présente un bon accord avec les données expérimentales. En évaluant l'influence de la fréquence réduite, une instabilité aéroélastique de type flottement transsonique est identifiée. Un dispositif de contrôle, reposant sur la génération d'ondes de pression rétrogrades à l'aval de la tuyère, est proposé puis validé numériquement. Enfin, une méthodologie est proposée pour comprendre les mécanismes aérodynamiques conduisant au flottement. Pour cela, il a été réalisé un dessin provisoire d'une soufflante transsonique à fort taux de dilution. Cette soufflante, l'ECL5, est destinée à l'étude expérimentale des instabilités aérodynamiques et aéroélastiques. La méthodologie proposée repose sur la simulation 2D d'une coupe de tête et met à profit la linéarisation pour analyser la contribution de sources locales en fonction de la fréquence réduite, du diamètre nodal et de la déformée modale

Transonic flows, which are common in aeronautical and spatial propulsion systems, produce shock-waves over solid boundaries. When a shock-wave impacts the boundary layer, an adverse pressure gradient is generated and a thickening or even a separation of the boundary layer is induced. If the solid boundary vibrates, the shock-wave oscillates and interacts with the boundary layer, leading to fluctuations of the static pressure at the wall. This induces an exchange of energy between the fluid and the structure which can be stabilising or lead to an aeroelastic instability (flutter).The main objective of this Ph.D. thesis is the modelling of the unsteady behaviour of the shock-wave / boundary layer interaction for fluid-structure interaction studies. To this end, simulations have been carried out to solve Reynolds-Averaged Navier-Stokes (RANS) equations using two equations turbulence model. The method is validated using experimental data obtained on a transonic nozzle dedicated to aeroelastic studies. This method is then used to improve the predictability of flutter events in turbomachinery.A time-linearised frequency-domain method is applied to RANS equations. It is shown that the unsteady behaviour of the turbulent boundary-layer contributes to the fluctuating static pressure when the shock-wave / boundary layer interaction is strong. Hence, the frozen turbulence assumption is not valid and the turbulence model must be derivated. Thus, the regularisation of the non derivable operators is proposed and applied on Wilcox (2006) k-ω turbulence model.The unsteady behaviour of the shock-wave / boundary layer interaction in a transonic nozzle is evaluated thanks to 2D numerical simulations and shows good agreement with experimental data. When varying the reduced frequency, an aeroelastic instability is found, known as transonic flutter. An active control device relying on backward travelling pressure waves is then designed and numerically validated.Finally, a methodology is proposed to understand the aerodynamic onsets of transonic flutter. To this end, a preliminary design of a high bypass ratio transonic fan has been carried out.This fan, named ECL5, is dedicated to experimental aerodynamic and aeroelastic studies. The methodology relies on 2D simulations of a tip blade passage and uses linearisation to analyse the contribution of local sources as a function of reduced frequency, nodal diameter and mode shape.; Les écoulements transsoniques rencontrés dans le cadre de la propulsion aéronautique et spatiale sont associés à l'apparition d'ondes de choc. En impactant la couche limite se développant sur une paroi, un gradient de pression adverse est généré qui conduit à l'épaississement ou au décollement de la couche limite. Lors de la vibration de la structure, l'onde de choc oscille et interagit avec la couche limite, générant une fluctuation de la pression statique à la paroi. Il s'ensuit alors un échange d'énergie entre le fluide et la structure qui peut être stabilisant ou au contraire conduire à une instabilité aéroélastique (flottement).La modélisation de la réponse instationnaire de l'interaction onde de choc / couche limite pour l'étude des interactions fluide-structure est l'objet de ce travail de recherche. Il s'appuie sur la résolution des équations de Navier-Stokes moyennées (RANS) et la modélisation de la turbulence. Les méthodes et modèles utilisés ont été validés à partir de résultats expérimentaux issus d'une tuyère transsonique dédiée à l'étude des interactions fluide-structure. Ces travaux sont ensuite appliqués à l'amélioration de la prédiction du flottement en turbomachine.Une méthode linéarisée en temps permettant la résolution des équations RANS dans le domaine fréquentiel est utilisée. Nous confirmons l'importance de la dérivation du modèle de turbulence lors de la prédiction d'une interaction forte entre une onde de choc et une couche limite décollée. Une méthode de régularisation est présentée puis appliquée aux opérateurs non dérivables du modèle de turbulence k-ω de Wilcox (2006).La prédiction de la réponse instationnaire de l'interaction onde de choc / couche limite dans une tuyère est évaluée à partir de simulations bidimensionnelles et présente un bon accord avec les données expérimentales. En évaluant l'influence de la fréquence réduite, une instabilité aéroélastique de type lottement transsonique est identifiée. Un dispositif de contrôle, reposant sur la génération d'ondes de pression rétrogrades à l'aval de la tuyère, est proposé puis validé numériquement.Enfin, une méthodologie est proposée pour comprendre les mécanismes aérodynamiques conduisant au flottement. Pour cela, il a été réalisé un dessin provisoire d'une soufflante transsonique à fort taux de dilution. Cette soufflante, l'ECL5, est destinée à l'étude expérimentale des instabilités aérodynamiques et aéroélastiques. La méthodologie proposée repose sur la simulation 2D d'une coupe de tête et met à profit la linéarisation pour analyser la contribution de sources locales en fonction de la fréquence réduite, du diamètre nodal et de la déformée modale.

One criterion that determines time stepping size in the implicit time integration method is given for accurate and effective transonic flutter simulations. Transonic flows over two-dimensional forced oscillating airfoils with several reduced frequencies are first investigated for constructing a criterion for selecting the time stepping size, and then two and three-dimensional transonic flutter simulations are performed for evaluating the criterion. Results for the forced oscillating airfoil indicate that unsteady aerodynamic forces converge in a constant value as the time stepping size decreases and the time stepping size required the convergence of unsteady aerodynamic force depends on the reduced frequency. From these results, it turns out that 4,000 integration steps during one cycle of airfoil oscillations are enough for the estimation of the unsteady aerodynamic forces at any reduced frequency. The time stepping size is automatically decided by setting 4,000 integration steps during one cycle of airfoil oscillations. Results for two and three-dimensional transonic flutter simulations show that flutter boundaries can be accurately and effectively calculated based on the criterion., 資料番号: AA0048469017, レポート番号: JAXA-SP-04-012

MHI activities on aeroelasticity and the associated fields are presented. MHI has conducted many types of aeroelastic analysis throughout the development of aircraft in the past decades. The transonic dip phenomenon is one of the most important items in the aeroelasticity field and cannot be analyzed by the linear aerodynamics tools commonly used in the aircraft design. The recent progress in the time-marching method that calculates the flow field around the airfoil in the time domain enables solving the transonic dip by the analysis. In this paper, two analysis examples using USTF3 developed at NAL are presented that studied the transonic flutter properties of the high-aspect-ratio transport wing and SST wing, both of which were done in the design phase at MHI., 資料番号: AA0047427014, レポート番号: JAXA-SP-03-002

In a design of the Non-powered Supersonic Experimental Airplane, three kinds of flutter modes were focused; aileron with one degree of freedom, a first bending mode of a main wing and a rocket fin first torsion mode coupled with control surface motion. Therefore three types of model for each flutter test were made and tested in wind tunnels, in order to confirm analytical results. The results of the tests are described in this paper., 資料番号: AA0047429004, レポート番号: JAXA-SP-03-004

This paper presents YSX transonic flutter study and Arrow wing flutter study as NATAS (transonic flutter Analysis code made in NAL) numerical simulation example. The objective of YSX transonic flutter study is to investigate flutter characteristics on WRI (Wing Root Insert) structure. The objective of Arrow wing flutter study is to investigate that reduction of Wash-Out tendency can improve Arrow wing flutter characteristics. In analytical results, reduction of Wash-Out tendency is effective method to improve Arrow wing flutter characteristics., 資料番号: AA0047427015, レポート番号: JAXA-SP-03-002

航空宇宙技術研究所 12-13 Jun. 1997 東京 日本, National Aerospace Laboratory 12-13 Jun. 1997 Tokyo Japan, 非定常空力ツールとして、通常のDLM(ダブレット格子法)コードに加えて、フルポテンシャルコード(USTF3)を用いて、超音速輸送機の典型的なアロー翼形態に関する遷音速フラッタ特性を研究した。DLMコードを用いた解析では、マッハ数0.95までは、剛性設計モデルの対称モードフラッタ(燃料満載条件時)は、逆対称モードフラッタよりも常にクリティカルで、一方、USTF3を用いた解析では、逆対称モードフラッタは遷音速ディップ現象によりマッハ1近傍で極小フラッタ速度をとり、マッハ数0.90以上では、対称モードフラッタよりもクリティカルになった。また、逆対称モードフラッタと対照的に、対称モードフラッタでは遷音速ディップ現象が起きないことも示した。, Transonic flutter characteristics of a typical arrow wing configuration of a supersonic transport have been studied by using the full potential code (USTF3) in addition to the usual DLM (Doublet Lattice Method) code as the unsteady aerodynamic tools. According to the analyzes using the DLM code, the symmetric mode flutter (for full fuel condition) of the stiffness designed model is always more critical than the anti-symmetric mode flutter for Mach numbers up to 0.95, while the analyzes by using the USTF3 say that the anti-symmetric mode flutter becomes more critical than the symmetric mode flutter for Mach numbers greater than 0.90 taking the minimum flutter velocity around Mach one due to the transonic dip phenomenon. It also has been shown that the symmetric mode flutter does not show the transonic-dip phenomenon in contrast to the anti-symmetric mode flutter., 資料番号: AA0001433016, レポート番号: NAL SP-37

航空宇宙技術研究所 6-7 JUN. 1996 東京 日本, National Aerospace Laboratory 6-7 JUN. 1996 Tokyo Japan, 空力弾性型CFD(数値流体力学)コードを開発し、曲げモードで振動するバイオコンベックス翼断面を持つ矩形翼、および第一曲げモードで振動する高アスペクト比(YXX)翼の風洞モデルまわりの非定常遷音速流れの数値シミュレーションに適用した。第一の6つのモードを考慮してYXX翼の遷音速フラッタについても同様に数値シミュレーションを実施した。構造方程式と組合わせたナビエ・ストークス(N-S)方程式に基づくコードを用いた。N-S方程式は空力格子上のYee-Harten TVD(Total Variation Diminishing)スキームを用いて積分し、構造方程式はWilsonθ法を用いて積分した。, An aeroelastic version of CFD (Computational Fluid Dynamics) code was developed and applied to numerical simulations of unsteady transonic flows around a rectangular wing with bioconvex airfoil section oscillating in bending mode and a wing tunnel model of a high aspect-ratio (YXX) wing which is also oscillating in first bending mode. A numerical simulation of transonic flutter of the YXX wing considering first six modes has been performed as well. The code is based on Navier-Stokes (N-S) equations coupled with the structural equations. The N-S equations are integrated by Yee-Harten TVD (Total Variation Diminishing) scheme on dynamic grid, while the structural side is integrated by Wilson theta method., 資料番号: AA0000685050, レポート番号: NAL SP-34

The initial and general transient temporal behaviours of flow induced vibrations were studied particularly with regard to the extent with which self-excited, flow-induced vibrations can be described by the Landau equation. Three different cases are studied experimentally, using bodies with generic shape. The first case represents a bluff body: resembling a simplified section of the Tacoma bridge, which has a single torsional degree of freedom. The second case is a two-dimensional airfoil in transonic flow having a heave and a torsional degree of freedom. The third case is an elastic half-wing model, also investigated in transonic flow. It is shown that in all three cases, beyond the critical point and at small initial amplitude the temporal development of the oscillations up to the limit cycle i.e. the envelope of the measured time functions, agrees with the corresponding curve, given by the solution of the Landau equation. For the Tacoma section and the airfoil the same agreement was demonstrated for initial amplitudes much larger than that of the limit cycle. In addition for both last cases the bifurcation behaviour was investigated and the Landau constants were determined. Finally an elementary physical explanation for the instability phenomenon was given.

Industrial flutter prediction for large transport aircraft requires numerical capabilities to predict unsteady aerodynamic forces induced by harmonic oscillations for the complete flight envelope including transonic and separated flow conditions, with shock boundary layer interaction and inverse shock motion. Adequate numerical methods have to model both flow physical and geometrical complexities in more detail than the standard DLM approach. The application of CFD methods results in a more or less time consuming task. On the other hand the aircraft development process, which leads to structural modifications with impact on the flutter behaviour, requires robust and accurate analyses for various stiffness and/or mass conditions in short iteration times. Thus the CFD calculation process should be decoupled from the structural analysis process. This can be achieved by application of aerodynamic reduced order models (ROM). A new method following this strategy is presented. It relies on a limited number of unsteady CFD computations forming the ROM data base, combined with an arbitrary number of Doublet Lattice computations. Thus compatibility with standard DLM based linear flutter prediction process is conserved. The quality of the new approach depends significantly on the choice and number of single CFD computations, as well as on mapping of these results to the DLM aerodynamic data structure. The validation of this approach is performed in a first step by comparing unsteady pressure distributions and generalised airloads for cases of the parameter space, which have not been included in the data base. In a second step the complete process validation requires a common aeroelastic reference test case of adequate complexity. A brief review of available windtunnel data for both unsteady aerodynamics and flutter outlines the shortcomings of these data, like missing measurements of a clear transonic dip significantly below Mach number one, and of inverse shock motions. A new common test configuration with a transonic dip flutter boundary in the Mach number range between 0.80 and 0.95 is proposed. The aircraft geometry from the Drag-Prediction Workshop 4 fulfils the above mentioned unsteady aerodynamic requirements. It is extended to a flutter model of a generic aircraft. The capability of this model is demonstrated by applying the above flutter process. An unsteady aerodynamic ROM is generated in the 3 dimensional parameter space of Mach number, reduced frequency and elastic mode shape. For selected points of this parameter space a sufficient number of unsteady RANS simulations is performed to display unsteady pressure distributions at Mach numbers between 0.6 and 0.90, and reduced frequencies up to 4. A constant lift coefficient of 0.50 has been chosen for all Mach numbers. DLR’s TAU code is applied for attached flow conditions in linear modus. The ROM is completed by performing this procedure for several so called synthetic modes, which are chosen properly to display all realistic structural modes (of the fixed aircraft geometry), without their detailed knowledge.

The Unsteady Adaptive Stochastic Finite Elements (UASFE) approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations. In this paper, it is shown that the underlying Adaptive Stochastic Finite Elements (ASFE) method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing (ED). It is also shown that themethod is total variation diminishing (TVD) for one randomparameter and for multiple random parameters for first degree Newton-Cotes quadrature. It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time. The twomethods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.

The Unsteady Adaptive Stochastic Finite Elements (UASFE) approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations. In this paper, it is shown that the underlying Adaptive Stochastic Finite Elements (ASFE) method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing (ED). It is also shown that themethod is total variation diminishing (TVD) for one randomparameter and for multiple random parameters for first degree Newton-Cotes quadrature. It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time. The twomethods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.

Aerodynamic simulations were performed in order to compute the unsteady load response of the NLR7301 airfoil for heave and pitch oscillations in the transonic range. The data were used to determine the aeroelastic flutter boundary of a rectangular two degree of freedom wing. On the one hand the DLR TAU code was used to solve the Reynolds averaged Navier-Stokes (RANS) equations applying the Spalart-Allmaras and κ-ω turbulence models. On the other hand computations were made with the DLR TDLM code, which solves the time linearised transonic small disturbance (TSD) equation. The settings were chosen according to experiments by Dietz et al. [1] in the Transonic Wind Tunnel Gottingen (TWG). The comparison between the computed and the experimental results showed that the simulation codes are capable of computing reliable results. Characteristic transonic aeroelastic phenomena were found. The appropriate modeling of viscous effects in transonic flow came out to be an indispensable condition.

Details of unsteady aerodynamics for a two dimensional NLR7301 airfoil with flap were numerically investigated by a Navier-Stokes code in the transonic regime. Unsteady aerodynamic coefficients such as lift and pitching moment show nonlinear aspects in a small amplitude range of forced excitation modes. The pressure distribution of the supersonic region on the upper surface is very sensitive to the incidence angle, which yields the nonlinearity of the unsteady aerodynamics in a small amplitude range of pitching motion. The behaviour of reattachment of the boundary layer behind the shock wave also affects the nonlinearity. Shock wave motions were also examined. Linearized lift and pitching moment coefficients for each amplitude were applied to the Eigenvalue analysis for the flutter boundary. Time domain flutter simulations were also carried out and the result showed that the amplitude of the limit cycle oscillation could be explained by the flutter boundary of the Eigenvalue analysis.

This paper presents flutter and forced oscillation experiments in a transonic wind tunnel. For an aeroelastic supercritical 2-D airfoil configuration we studied typical transonic phenomena in as pure a form as possible. Various manifestations of small-amplitude limit cycle oscillations were observed for different flow conditions as well as coexisting limit cycles. We demonstrated how very small control forces were sufficient to excite or suppress flutter oscillations. Limit cycle oscillations occurred under free and forced turbulent boundary layer transition in a perforated wall test-section. Flutter calculations based on experimental aerodynamic forces yield stability limits which show good agreement with directly measured experimental flutter values. The results indicate that flow separation at the trailing edge, and the interactions between the shock and the marginal region of separated flow beneath it, may be responsible for limiting the amplitude of the observed limit cycle oscillations.

1993年度から1996年度にかけて行った航空宇宙技術研究所(以下「航技研」)の遷音速フラッタ試験設備の改修における風洞システム設計に関する報告である。第1部、第2部および第3部で構成され、都合7章からなる。第1部は第1、2、3、4章から成る。改修前の旧設備の機能を概観し、新システムの機能設計について述べる。まず、第2章では、1959年に設計された同設備の旧システムの概要を記す。新システムの設計に際し、機能向上を考えるに当たり基本となる項目を考察する。第3章では、改修目的、計画と新システムに関する仕様を述べる。主たる目的は気流の低乱化対策と老朽化対策である。同システムの構造および形態を最大限に活かす方針で新システムに対する仕様を定めた。これらをまとめる。第4章では、第3章を受け新システムの機能設計についてまとめる。主に、本設備のユーザーの立場から見える機能および利便性に焦点をあてる。前章の概念設計に基づき新システムについての概要は本章に集約されている。第2部は第5章のみである。新システムの設計、および技術検討について述べる。第5章では、仕様に従い行った各部の基本設計および技術検討を記し、調圧弁の設計、高圧導管、集合胴、測定部、抽気室の流体力学および構造力学の立場からの技術検討および設計の概要を記す。第3部は、第6章、第7章および4つのAppendixから成る。本設備の計測システムについての概略を示した後にまとめを述べる。さらに新システム設計時の参考資料および本設備での圧力較正に関する資料を添付する。第6章では、計測システムについて記述する。今回の改修では、計測系は対象外であったが、本設備に関する報告としては欠かすことのできない項目である。第7章ではまとめとして将来のフラッタ試験計画について述べる。さらに、付録として、主に第5章の技術検討、設計に関わる事項の理解を助ける意味で「数値風洞モデル」、「高圧導管の圧力損失の推定」、本設備の制御系に採用した「フィードフォワード演算法」および「圧力自動較正要領」についての技術検討結果を添付する。本研究の結果、気流の低乱化および設備の老朽化対策を目的とした改修が実施され、機能面においても最新の風洞に匹敵する程の改善が加えられた。本研究の妥当性が実風洞試験においても証明される結果となった。本報告が、将来にわたり設備使用者にとって有益な資料になることを希望する。, This report describes renewal of the Transonic Flutter Testing Facility (Flutter Wind Tunnel) at NAL, conducted from FY1993 to FY1996. The report consists of three parts-seven chapters and four appendices. Chapters 1,2,3 and 4 are grouped together as PART 1. These chapters outline the performance of the previous as well as the new system. Chapter 2 provides an overview of the previous system constructed in 1959. The concept design of the new system was based on improvements to the basic design of the previous system. In Chapter 3, the purpose of the renewal and specifications and plans for the new system are shown. The major aims were to reduce the turbulence of flow in the tunnel and renewal of out-of-date hardware. The specifications given ensured that the previous wind tunnel structures and concept were retained where possible. The proposed specifications are summarized. Chapter 4 describes the design of the new system performance. Items involving performance and utility are viewed from the client's perspective. PART 2 corresponds to Chapter 5 and describes the design concept and technical investigations of various issues concerning the renewal design including the design of the pressure control valve, the high pressure tubes, the chambers, test section and plenum chamber. These components are considered not only from an aerodynamical but also from a structural dynamical perspective. PART 3 consists of Chapters 6,7 and four appendices, and Chapters 6 explains the measurement systems in the present facility. The measurement system for the tunnel is beyond the scope of the renewal project, but an overview is necessary and included in this report. Chapter 7 describes the flutter examination plan for the future as settling. The four appendices assist in understanding the design routines of the present wind tunnel. These are Appendix 1 Numerical Wind Tunnel Model; Appendix 2 Pressure loss in the high pressure tubes; Appendix 3 Method of feedforward control used in the new system, and Appendix 4 Calibration of pressure. The results of the work meant renovation of the flutter testing facility was made possible by improvements to flow quality and renewal of hardware to the extent that the new system performs as well as any modern wind tunnel in the world. It is hoped that this report will be of assistance to users and clients of the wind tunnel in the future., 資料番号: AA0045942000, レポート番号: NAL TR-1454

This paper reports about our experimental and numerical investigations of forced and self-sustained oscillations of a supercritical airfoil section in transonic flow. Heave and pitch motion were examined. The unsteady pressure distributions were recorded and for some cases compared with Navier-Stokes simulations; the agreement was good below the buffet limit. In addition, the results of direct flutter experiments and a calculation in the frequency were compared; the descending branch of the "Transonic Dip" could be reproduced well. Another important result was, that all transonic flutter cases ended in limit cycle oscillations.