Study of the Impact of Multi-Row Interaction on Flutter Analysis for a Representative LPT Geometry

A preliminary inviscid version of the NASA LeRC/Mississippi State University 3-D aeroelastic computational fluid dynamics code, TURBO-AE, is evaluated using operating conditions from three test cases from an AlliedSignal Engines (AE) advanced technology integrally bladed fan rotor. Two of the cases corresponded to conditions where high op-line flutter vibrations were observed, and the third case was flutter-free during testing. TURBO-AE steady (no blade vibration) computations were performed for each test case and a reasonable match was found with the steady 3-D viscous code DAWES. Following completion of the steady computations, TURBO-AE flutter (blade vibration) analyses were completed by harmonically oscillating the airfoil with mode shapes computed by the structural finite-element code ANSYS. Aerodynamic work per vibration cycle and modal damping was computed by TURBO-AE at 0° and 180° Inter Blade Phase Angles (IBPA). For IBPA = 0°, TURBO-AE predicted aerodynamic damping to be low but positive. Further, for IBPA = 180°, the TURBO-AE predictions indicate a very high level of aerodynamic damping. Flutter was observed on the rotor only for IBPA = 32.7°, and TURBO-AE analyses are in process for this condition. Unsteady pressure perturbation contour plots are presented to aid in the visualization of the TURBOAE flow solution. Results presented in this paper indicate that, although TURBO-AE still requires significant development, it is making the difficult transition from a research code to a flutter and forced-response prediction tool for the U.S. aeropropulsion community.

PurposeThe separation of energy conversion and propulsor is a promising aspect of hybrid-electric propulsion systems, allowing for increased installation efficiencies and setting the basis for distributed propulsion concepts. University of Stuttgart’s Institute of Aircraft Design has a long experience with electrically powered aircraft, starting with Icaré 2, a solar-powered glider flying, since 1996. Icaré 2 recently has been converted to a three-engine motor glider with two battery-powered wing-tip propellers, in addition to the solar-powered main electric motor. This adds propulsion redundancy and will allow analyzing yaw control concepts with differential thrust and the propeller-vortex interaction at the wing-tip. To ensure airworthiness for this design modification, new ground vibration tests (GVTs) and flutter calculations are required. The purpose of this paper is to lay out the atypical approach to test execution due to peculiarities of the Icaré 2 design such as an asymmetrical aileron control system, the long wing span with low frequencies of the first mode and elevated wing tips bending under gravity and thus affecting the accuracy of the wing torsion frequency measurements.Design/methodology/approachA flutter analysis based on GVT results is performed for the aircraft in basic configuration and with wing tip propulsors in pusher or tractor configuration. Apart from the measured resonant modes, the aircraft rigid body modes and the control surface mechanism modes are taken into consideration. The flutter calculations are made by a high-speed, low-cost software named JG2 based on the strip theory in aerodynamics and the V-g method of flutter problem solution.FindingsWith the chosen atypical approach to GVT the impact of the suspension on the test results was shown to be minimal. Flutter analysis has proven that the critical flutter speed of Icaré 2 is sufficiently high in all configurations.Practical implicationsThe atypical approach to GVT and subsequent flutter analysis have shown that the effects of wing-tip propulsors on aeroelasticity of the high aspect ratio configuration do not negatively affect flutter characteristics. This analysis can serve as a basis for an application for a permit to fly.Originality/valueThe presented methodology is valuable for the flutter assessment of aircraft configurations with atypical aeroelastic characteristics.

PurposeA low-cost but credible method of low-subsonic flutter analysis based on ground vibration test (GVT) results is presented. The purpose of this paper is a comparison of two methods of immediate flutter problem solution: JG2 – low cost software based on the strip theory in aerodynamics (STA) and V-g method of the flutter problem solution and ZAERO I commercial software with doublet lattice method (DLM) aerodynamic model and G method of the flutter problem solution. In both cases, the same sets of measured normal modes are used.Design/methodology/approachBefore flutter computation, resonant modes are supplied by some non-measurable but existing modes and processed using the author’s own procedure. For flutter computation, the modes are normalized using the aircraft mass model. The measured mode orthogonalization is possible. The flutter calculation made by means of both methods are performed for the MP-02 Czajka UL aircraft and the Virus SW 121 aircraft of LSA category.FindingsIn most cases, both compared flutter computation results are similar, especially in the case of high aspect wing flutter. The Czajka T-tail flutter analysis using JG2 software is more conservative than the one made by ZAERO, especially in the case of rudder flutter. The differences can be reduced if the proposed rudder effectiveness coefficients are introduced.Practical implicationsThe low-cost methods are attractive for flutter analysis of UL and light aircraft. The paper presents the scope of the low-cost JG2 method and its limitations.Originality/valueIn comparison with other works, the measured generalized masses are not used. Additionally, the rudder effectiveness reduction was implemented into the STA. However, Niedbal (1997) introduced corrections of control surface hinge moments, but the present work contains results in comparison with the outcome obtained by means of the more credible software.

Unstarted supersonic flutter in a cascade is characterized by the existence of a detached bow shock wave ahead of each airfoil. To study the influence of the bow shock wave on this flutter, analysis is performed on the corresponding flow field, with use of the semiactuator disk theory. We investigate oscillation in the bending mode with the interblade phase angle, considering the effect of reflection of the pressure wave and production of a vorticity wave and an entropy wave by the bow shock wave. The results show that the existence of detached bow shock waves greatly destabilizes bending oscillation, and the flutter boundary drastically extends to a high-frequency region.

In this paper, a flutter prediction method based on flutter margins is proposed for streamlined bridges whose aeroelastic behavior can be well approximated by a two‐degree‐of‐freedom (2‐DoF) flutter model. The method enables prediction of the flutter boundary by extrapolating a curve of flutter margin versus wind speed, constructed using flutter margins at several subcritical wind speeds. In addition, an ‐optimal flutter active control method based on measured receptances and flutter margins is proposed. It enables assignment of the flutter boundary to a prescribed wind speed value or range for each considered angle of attack (AoA), while simultaneously minimizing vibration responses at subcritical wind speeds, using a single controller with optimal control effort. Hence, the designed controller is robust to the variations of wind speed and AoA. The proposed flutter prediction and control methods require only a small number of systems’ modal parameters or open‐loop receptances at several subcritical wind speeds. The proposed flutter prediction method typically requires fewer system modal parameters than existing methods that track the variation of damping ratio against wind speed. The proposed flutter suppression method avoids some modeling errors associated with conventional system matrix‐based methods. The working of the proposed flutter prediction and control methods are validated using wind tunnel tests and CFD simulations, respectively.

Energy extraction from flow-induced oscillations based on piezoelectric structures has recently been tackled by several researchers. This paper presents a study of the dynamic behavior analysis and parametric characteristics of a galloping piezoelectric micro energy harvester (GPEH) applied to self-powered micro-electro-mechanical systems (MEMS). The mechanical performance of a piezoelectric micro energy harvester cantilever beam with two layers of elastic silicon and piezoelectric (PZT-5A) attached to a tip elliptical cylinder is numerically simulated. Using size-dependent beam formulation on the basis of the modified couple stress theory and Gauss’ law, the coupled electro-mechanical non-linear governing equations of the energy harvester are obtained. The mode summation and Galerkin methods are used to derive the extracted power from the system. The study also models the flow field effect on the beam oscillations via CFD simulation. The effect of elliptical cylinder mass, damping ratio, beam thickness, and load resistance on the dynamic behavior and harvested power of the system is studied. Findings reveal that increasing the normalized tip mass from 0 to 0.5 and 1 increases the output power density from 0.12 to 0.2 and 0.22, respectively, and the corresponding electrical load resistance of maximum power increases from 175 to 280 kΩ and 375 kΩ, respectively. An approximately linear relation between the elliptical cylinder mass and the load resistance is observed. By increasing/decreasing the cylinder mass, the required electrical load resistance for maximum output power proportionally changes. The damping analysis shows that a higher damping ratio increases the onset velocity of galloping and decreases the extracted power.

Bubble-induced turbulence in CFD simulation of bubble columns. Part I: Coupling of SIT and BIT

An integrated computational fluid dynamics (CFD) and computational structural dynamics (CSD) method is developed here for the calculation and analysis of wing flutter in the time domain. The CFD solver is based on an unsteady multi-grid finite-volume algorithm for the Euler/Navier—Stokes equations on a multi-block structured grid. The CSD solver adopts a linear multi-step method to integrate the aeroelastic governing equations expressed in the modal space. A grid deformation method employing a radial basis function approach is introduced here to generate a dynamically moving grid. The solving procedure of an aeroelastic system is implemented with a predictor—corrector scheme in the physical time. By extrapolating the aerodynamic force, the hybrid predictor—corrector scheme is introduced to save the flow calculation right before the correcting step. The coupled CFD—CSD method is used to simulate wing flutter problems in the time domain in order to predict the stability of an aeroelastic system, which, in this paper, is fulfilled by finding the flutter boundaries. The calculation of the Isogai wing finds an S-shaped flutter boundary, which has been predicted by other studies. The obtained flutter boundary of the AGARD 445.6 wing shows a distinct transonic dip, which agrees well with the experiment result. Computational efficiency and accuracy using two predictor—corrector algorithms and a strong coupling algorithm are also compared.

T HE importance of mode shapes is undeniable in contemporary flutter analyses. Not only are modes used to transform the governing equations from spatial to modal coordinates, but they are also used to transform flutter solution eigenvectors back to physical space to facilitate viewing of the critical flutter mechanism components. Mode shapes have even been used to gain insight into nonlinear aeroelastic behavior, such as limit cycle oscillations [1]. Mode shapes are so commonplace and easy to generate that their ability to overcome weaknesses inherent in flutter solution methods is not appreciated. In essence, modes are powerful tools that are not consistently exploited to their full potential. One cause for the underutilization of mode shapes could be the difficulty in quantitatively comparing them in an efficient manner with other modes. Quantitative comparison of modal frequencies is convenient, but a subjective assessment of the deflection mode shapes is the convention. Because of this subjectivity, the results of modal comparisons in this fashion could be regarded as less reliable or of limited utility. The situation is further impaired for complex or large models that are often cumbersome and sometimes obscure key shape features of interest. Anyone who has evaluated large quantities of flutter analyses is aware of the benefits of being able to compare mode shapes of different dynamical systems. Thesemode shapes can be indicative of energy-extraction and damping pathways within the structural system. They can provide insight into the similarity of predicted solution results, thereby reducing the number of critical analysis cases that may require flutter flight testing. They can also aid in the identification of critical flutter modes during flight testing, which is necessary for damping determination [2] and flutter margin [3,4] methods. Many methods are available to identify modes, but methods to explicitly compare one mode shape with another are not well documented in the literature. Themethods that are available formode shape comparisons are predominantly visual-based, such as 3-D still plots, animations, and node lines, although some work to extend these methods to quantitative approaches is available. Of particular interest to the flutter engineer is Maxwell’s work (as reported in [5]) to depict the wingtip deformation characteristics of the flutter mode shape and Northington’s [6] basis vector approach. There are also strain energy methods [7]. In short, it appears that many in-house methods for mode shape comparison likely exist, but they are only passed from generation to generation internally and are not disseminated widely to the engineering public. The development and dissemination of concise and distinctive mode shape description methodologies would allow the flutter engineering community to take better advantage of the inherent utility of mode shapes. Some applications that would become more practicable are sorting, tracking, and screening of modes for large quantities of analyses and using modes in alternative solution methodologies, such as artificial neural networks [8]. This Note describes a simple method in which curve-fit equations are used to depict the mode shapes of the wing. Some examples will be presented that compare the conventional 3-D still plots of the mode shape to the fitted curves as well as the coefficients of the curve-fit equations.

An experimental research study to determine the effectiveness of spoiler surfaces in suppressing flutter onset for a low-aspect-ratio, rectangular wing was conducted in the Langley Transonic Dynamics Tunnel (TDT). The wing model used in this flutter test consisted of a rigid wing mounted to the wind-tunnel wall by a flexible, rectangular beam. The flexible beam was connected to the wing root and cantilever mounted to the wind-tunnel wall. The wing had a 1.5 aspect ratio based on wing semispan and a NACA 64A010 airfoil shape. The spoiler surfaces consisted of thin, rectangular aluminum plates that were vertically mounted to the wing surface. The spoiler surface geometry and location on the wing surface were varied to determine the effects of these parameters on the classical flutter of the wing model. Subsonically, the experiment showed that spoiler surfaces increased the flutter dynamic pressure with each successive increase in spoiler height or width. This subsonic increase in flutter dynamic pressure was approximately 15 percent for the maximum height spoiler configuration and for the maximum width spoiler configuration. At transonic Mach numbers, the flutter dynamic pressure conditions were increased even more substantially than at subsonic Mach numbers for some of the smaller spoiler surfaces. But greater than a certain spoiler size (in terms of either height or width) the spoilers forced a torsional instability in the transonic regime that was highly Mach number dependent. This detrimental torsional instability was found at dynamic pressures well below the expected flutter conditions. Variations in the spanwise location of the spoiler surfaces on the wing showed little effect on flutter. Flutter analysis was conducted for the basic configuration (clean wing with all spoiler surface mass properties included). The analysis correlated well with the clean wing experimental flutter results.

Long-endurance, unmanned air vehicles (UAVs) usually employ high-aspect-ratio, flexible wings to reduce weight and power required to achieve extended flight operation. There are currently several advanced concept designs and prototypes that will sustain autonomous operations for months or even years. The increased wing flexibility can lead to large structural deflections for trimmed flight states. These large elastic deformations within the static equilibrium state of the vehicle can induce aeroelastic instabilities quite different from their rigid counterparts. Therefore, it is imperative to perform flutter analysis, which considers the trimmed, large amplitude deformed state as a reference condition. Considering the complexity of the system under investigation, the aeroelastic flutter analysis process usually includes an experimental test phase for verification purposes. In this respect, wind tunnel test models provide the opportunity to modify and calibrate theoretical models, through a process of model updating. This paper proposes the development of an experimental, aeroelastic, slender-wing model that can be designed using a scaling procedure. The model is based on a consistent, aeroelastic, beam-wise scheme, capable of simulating the unconventional aeroelastic behavior of flexible wings.

This paper presents a comprehensive investigation into the aeroelastic stability behavior of a transonic front blade in an industrial compressor when operating outside its normal range of service parameters. The evolution of the airfoil’s aeroelastic stability in the first flexural mode is studied as the front blade operation progresses towards choked flow conditions. First, linearized 3D flutter computations representing today’s industry standard are performed. The linearized calculations indicate a significant, shock-driven flutter risk at these off-design flow conditions. To further explore the aeroelastic behavior of the rotor and to find a viable solution toward flutter risk elimination, two parallel investigations are undertaken: (i) flow perturbation nonlinearity effects and potential presence of limit-cycle oscillation; and (ii) effects of blade mistuning and flutter mitigation potential of intentional mistuning, including its impact on forced response behavior. The nonlinear harmonic analyses show that the minimum aerodynamic damping increases rapidly and essentially linearly with blade oscillation amplitude beyond the linear regime. Thus, a state of safe limit-cycle oscillation is predicted for the fully tuned blade. Additionally, it is found that intentional, realizable blade frequency offsets in an alternating pattern efficiently stabilize the blade. Finally, it is verified that alternating mistuning has a beneficial effect versus the inevitable random mistuning also in the forced response.

SummaryIn a recent paper, a theory explaining the wake-induced flutter of smooth circular cylinders was developed and vindicated. It was shown that, for moderate spacing of the cylinders (where the aerodynamic coupling between the constituent motions is small), flutter could occur only when the natural frequency, in still air, of vertical oscillations exceeded that of the horizontal motions. The theory, however, took no account of the possibility of mechanical coupling between the constituent motions and, while the results from this theory were corroborated by wind-tunnel tests in which a statically uncoupled mechanical support system was used, no indications were given of the changes in aeroelastic behaviour which might accompany the introduction of simple coupling terms.In this paper, the class of cases wherein the mechanical support system for the leeward cylinder exhibits static coupling is studied using “undamped flutter theory”. It is demonstrated that the appearance of static coupling terms can lead to quite dramatic changes in the flutter characteristics, and that considerable care must be exercised in the design and operation of wind-tunnel dynamic models if meaningful results are to be obtained.An Appendix deals with the general problem of mechanical coupling, using the normal coordinates approach, and aspects of the problem which bear on the subconductor oscillation phenomenon experienced on “bundled” overhead power transmission lines are highlighted.

The prediction of aerodynamic blade forcing is a very important topic in turbomachinery design. Usually, the wake from the upstream blade row and the potential field from the downstream blade row are considered as the main causes for excitation, which in conjunction with relative rotation of neighboring blade rows, give rise to dynamic forcing of the blades. In addition to those two mechanisms, the so-called Tyler–Sofrin (or scattered or spinning) modes, which refer to the acoustic interaction with blade rows further up- or downstream, may have a significant impact on blade forcing. In particular, they lead to considerable blade-to-blade variations of the aerodynamic loading. In Part I of the paper, a study of these effects is performed on the basis of a quasi-three-dimensional multirow and multipassage compressor configuration. Part II of the paper proposes a method to analyze the interaction of the aerodynamic forcing asymmetries with the already well-studied effects of random mistuning stemming from blade-to-blade variations of structural properties. Based on a finite element (FE) model of a sector, the equations governing the dynamic behavior of the entire bladed disk can be efficiently derived using substructuring techniques. The disk substructure is assumed as cyclically symmetric, while the blades exhibit structural mistuning and linear aeroelastic coupling. In order to avoid the costly multistage analysis, the variation of the aerodynamic loading is treated as an epistemic uncertainty, leading to a stochastic description of the annular force pattern. The effects of structural mistuning and stochastic aerodynamic forcing are first studied separately and then in a combined manner for a blisk of a research compressor without and with aeroelastic coupling.

The prediction of aerodynamic blade forcing is a very important topic in turbomachinery design. Usually, the wake from the upstream blade row and the potential field from the downstream blade row are considered as the main causes for excitation, which in conjunction with relative rotation of neighboring blade rows, give rise to dynamic forcing of the blades. In addition to those two mechanisms so-called Tyler-Sofrin (or scattered or spinning) modes, which refer to the acoustic interaction with blade rows further up- or downstream, may have a significant impact on blade forcing. In particular, they lead to considerable blade-to-blade variations of the aerodynamic loading. In part 1 of the paper a study of these effects is performed on the basis of a quasi 3D multi-row and multi-passage compressor configuration. Part 2 of the paper proposes a method to analyze the interaction of the aerodynamic forcing asymmetries with the already well-studied effects of random mistuning stemming from blade-to-blade variations of structural properties. Based on a finite element model of a sector, the equations governing the dynamic behavior of the entire bladed disk can be efficiently derived using substructuring techniques. The disk substructure is assumed as cyclically symmetric, while the blades exhibit structural mistuning and linear aeroelastic coupling. In order to avoid the costly multi-stage analysis, the variation of the aerodynamic loading is treated as an epistemic uncertainty, leading to a stochastic description of the annular force pattern. The effects of structural mistuning and stochastic aerodynamic forcing are first studied separately and then in a combined manner for a blisk of a research compressor without and with aeroelastic coupling.