Chordwise spacing aerodynamic detuning for unstalled supersonic flutter stability enhancement

Unstalled supersonic flutter is a significant problem in the development of advanced gas turbines because it restricts the high speed operating range of the engine. A new approach to passive control of unstalled supersonic flutter is aerodynamic detuning, defined as designed passage-to-passage differences in the unsteady aerodynamics of a blade row. In this paper, a mathematical model is developed to predict the unstalled torsion mode stability of an aerodynamically detuned turbomachine rotor operating in a supersonic inlet flow field with a subsonic axial component, with the aerodynamic detuning accomplished by alternate chordwise spacing of adjacent rotor blades. The unsteady aerodynamic moments acting on the blading are calculated in terms of influence coefficients. The stability enhancement associated with this alternate chordwise aerodynamic detuning is demonstrated utilizing an unstable twelve bladed rotor based on Verdon's Cascade B flow geometry. This model and unstable baseline rotor configuration are then used to show that axial spacing detuning leads to greater flutter stability enhancement than does circumferential spacing aerodynamic detuning. Finally, the trade-offs between structural damping, alternate chordwise aerodynamic detuning, and alternate circumferential aerodynamic detuning are considered.     

Effects of hysteretic and aerodynamic damping on supersonic panel flutter of composite plates

The governing equation for the finite element analysis of the panel flutter of composite plates including structural damping is derived from Hamilton's principle. The first order shear deformable plate theory has been applied to structural modelling so as to obtain the finite element eigenvalue equation. The unsteady aerodynamic load in a supersonic flow is computed by using the linear piston theory. The critical dynamic pressures for composite plates have been calculated to investigate the effects of structural damping on flutter boundaries. The effects are dependent on fiber orientation because flutter mode can be weak or strong in the fiber orientation of composite plates. Structural damping plays an important role in flutter stability with low aerodynamic damping but would not affect the flutter boundary with high aerodynamic damping.     

The stability of simply supported tubes conveying a compressible fluid

This paper is concerned with establishing the conditions of static stability of a simply supported tube conveying a compressible fluid by application of Euler's method of equilibrium. Timoshenko beam theory is used to describe the tube motion whiler Euler's equations of motion govern the compressible flow through the tube. The eigenvalue problem associated with the linearized equations of motion first derived by Niordson is solved by using Muller's method. The effects on critical velocity of fluid sound speed, tube shear, and tube aspect ratio are parametrically studied. When the flow is subsonic, the aspect ratio increases the critical velocity predicted by the theory while increased aspect ratio decreases the critical velocity when the flow is supersonic. Reduced sound speed and tube shear modulus always reflect a reduced critical velocity for the onset of tube buckling or divergence instability.     

The art and science of flow control – case studies using flow visualization methods

Active flow control (AFC) has been the focus of significant research in the last decade. This is mainly due to the potentially substantial benefits it affords. AFC applications range from the subsonic to the supersonic (and beyond) regime for both internal and external flows. These applications are wide and varied, such as controlling flow transition and separation over various external components of the aircraft to active management of separation and flow distortion in engine components and over turbine and compressor blades. High-speed AFC applications include control of flow oscillations in cavity flows, supersonic jet screech, impinging jets, and jet-noise control. In this paper we review some of our recent applications of AFC through a number of case studies that illustrate the typical benefits as well as limitations of present AFC methods. The case studies include subsonic and supersonic canonical flowfields such as separation control over airfoils, control of supersonic cavity flows and impinging jets. In addition, properties of zero-net mass-flux (ZNMF) actuators are also discussed as they represent one of the most widely studied actuators used for AFC. In keeping with the theme of this special issue, the flowfield properties and their response to actuation are examined through the use of various qualitative and quantitative flow visualization methods, such as smoke, shadowgraph, schlieren, planar-laser scattering, and Particle image velocimetry (PIV). The results presented here clearly illustrate the merits of using flow visualization to gain significant insight into the flow and its response to AFC.     

Acoustic radiation from a simple structure in supersonic flow

It is well established that fluid flow can have significant effects on structural acoustic behavior, as is the fact that induced coupling between discrete modes of vibration becomes significant as flow velocity increases. To date, work in this area has been confined to subsonic flows, with the effects on sound radiation efficiency and sound power radiation quantified and compared for various subsonic flow speeds. The purpose of this work is to study the effects that supersonic flow has on these structural acoustic phenomena, along with an investigation of the uncoupled behavior of single modes in the transonic region. Theoretical development of the equations governing the vibration of a simply supported plate in an infinite baffle and an aerodynamic system that models a semi infinite flowing medium along with the method for coupling these systems is included. Computational results are presented illustrating the behavior of the uncoupled modes in the transonic region and the uncoupled and coupled effects on the structural response and sound power radiation as well as a study of the radiation efficiency of the coupled system.     

Active vibration suppression of multilayered plates integrated with piezoelectric fiber reinforced composites using an efficient finite element model

The active vibration suppression of hybrid composite and fiber metal laminate (FML) plates integrated with piezoelectric fiber reinforced composite (PFRC) sensors and actuators is studied for the first time, using an efficient and advanced layerwise plate theory. Unlike the conventional finite elements, the equipotential condition of electroded surfaces of sensors is satisfied exactly and conveniently using a novel concept of electric node. The effective electromechanical properties of the PFRC laminas are computed using a coupled three-dimensional iso-field micromechanical model. Numerical results are presented for both classical constant gain velocity feedback (CGVF) and optimal control strategies. The instability phenomena in CGVF control with conventionally collocated actuator-sensor pairs, and its remedy with a truly collocated arrangement are illustrated. The effect of segmentation of electrodes on the control response is studied. The segmentation of electrodes leads to a multi-input-multi-output (MIMO) configuration. The effects of piezoelectric fiber orientation, volume fraction and dielectric ratio of PFRC on the control response and the actuation/sensing authority are investigated for cantilever and simply supported plates.     

Aeroelastic flutter of a disk rotating in an unbounded acoustic medium

The linear aeroelastic stability of an unbaffled flexible disk rotating in an unbounded fluid is investigated by modeling the disk-fluid system as a rotating Kirchhoff plate coupled to the irrotational motions of a compressible inviscid fluid. A perturbed eigenvalue formulation is used to compute systematically the coupled system eigenvalues. Both a semi-analytical and a numerical method are employed to solve the fluid boundary value problem. The semi-analytical approach involves a perturbation series solution of the dual integral equations arising from the fluid boundary value problem. The numerical approach is a boundary element method based on the Hadamard finite part. Unlike previous works, it is found that a disk with zero material damping destabilizes immediately beyond its lowest critical speed. Upon the inclusion of small disk material damping, the flutter speeds become supercritical and increase with decreasing fluid density. The competing effects of radiation damping into the surrounding fluid and disk material damping control the onset of flutter at supercritical speed. The results are expected to be relevant for the design of rotating disk systems in data storage, turbomachinery and manufacturing applications.     

Nonlinear flutter analysis of stiffened composite panels in super-sonic flow

The flutter instability of stiffened composite panels subjected to aerodynamic forces in the supersonic flow is investigated. Based on Hamilton's principle,the aeroelastic model of the composite panel is established by using the von Karman large deflection plate theory,piston theory aerodynamics and the quasi-steady thermal stress theory. Then,using the finite element method along with Bogner-Fox-Schmit elements and three-dimensional beam elements,the nonlinear equations of motion are derived. The effect of...     

Simplified approach to the vibration analysis of elastic plates due to sonic boom

A theoretical study of the response of a flat plate to a sonic boom excitation is presented. For such a study, the problem of transient vibrations of elastic plates having clamped or simply supported boundary conditions under a pulse load in the shape of a capital N corresponding to a typical far-field sonic boom disturbance is discussed in a new fashion by using the concept of iso-amplitude contour lines on the surface of the plate. Series solutions consisting of products of eigenfunctions times functions of time are employed to analyse the motions. As an illustration of the technique, an elliptical plate subjected to a typical N wave arriving at normal incidence is chosen as a model because this involves a curvilinear boundary of a relatively simple shape, yet has no simple exact solution. Closed form solutions are obtained for both clamped as well as simply supported edges. The results have technical importance for the prediction of response of window panes and wall-panels to sonic boom. All details are explained by graphs.     

导弹超声速尾退分离干扰特性试验

超/高超声速尾退分离在防热、保形、隐身、多次投放、回收等方面具有明显优势,有望成为高超声速飞行器载荷投放的优选方案。由此面临一类新的多体分离问题:超/高超声速尾退分离问题（aft super/hypersonic ejection separation,ASES）。超/高超声速尾退分离问题本质上是带空腔底部流动与多体分离构成的耦合问题,具有流场结构复杂、气动非定常非线性非对称效应显著的特点。针对超声速尾退分离问题,采用网格测力和轨迹捕获（captive trajectory system,CTS）风洞试验方法探索了尾退分离干扰流场的结构,发现可根据流场结构和舵效变化分为低速-亚声速无激波、高亚声速-跨声速弱激波、超声速激波和准自由流弱干扰4种典型干扰特征,揭示了尾流场影响后不同区域的全弹气动特性和舵效特性以及控制律、攻角、高度和Mach数对分离位移和姿态的影响规律。相关结论将有助于增强对尾退分离问题的认识,对尾退分离技术的工程实践具有参考价值。      

Longitudinal,transverse, and torsional vibrations and stabilities of axially moving single-walled carbon nanotubes

Thanks to the brilliant mechanical properties of single-walled carbon nanotubes (SWCNTs), they are suggested as high speed nanoscale vehicles. To date, various aspects of vibrations of SWCNTs have been addressed; however, vibrations and instabilities of moving SWCNTs have not been thoroughly assessed. Herein, vibrational properties of an axially moving SWCNT with simply supported ends are studied using nonlocal Rayleigh beam theory. Employing assumed mode and Galerkin methods, the discrete governing equations pertinent to longitudinal, transverse, and torsional motions of the moving SWCNT are obtained. The resulting eigenvalue equations are then numerically solved. The speeds corresponding to the initiation of the instability within the moving nanostructure are calculated. The roles of the speed of the moving SWCNT, small-scale parameter, and aspect ratio on the characteristics of longitudinal, transverse, and torsional vibrations of axially moving SWCNTs are scrutinized. The obtained results show that the appearance of the small-scale parameter would result in the occurrence of both divergence and flutter instabilities at lower levels of the speed.     

Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm

This paper deals with the optimization of piezoelectric actuators and sensors locations for active vibration control. Two modified optimization criteria are used, ensuring good observability or controllability of the structure, and considering residual modes to limit the spillover effect. Two optimization variables are considered for each piezoelectric device: the location of its center and its orientation. Genetic algorithms are used to find the optimal configurations. Several simulations are presented for a simply supported plate.     

Experimental application of orthogonal eigenstructure control for structural vibration cancellation

Orthogonal eigenstructure control (OEC) is a novel feedback control that is applicable to linear systems. Orthogonal eigenstructure control can minimizes the trial and error by the controller designer. It finds orthogonal vectors to some targeted modes of the structure within the achievable eigenvector set. When the targeted modes are replaced with the orthogonal vectors, it results in a decoupled system or structure that leads to vibration isolation. In this article, experimental application of this control method for active vibration cancellation of a plate is presented. Piezoelectric actuators are used as control actuators and accelerometers are used as feedback sensors. Vibration cancellation in a plate due to 150 Hz sinusoidal disturbance and a wideband disturbance within the range 200-300 Hz are experimentally studied. Since OEC is a model-based control method, system identification techniques are used for estimating the state-space realization of the system model. The effect of tuning the control gain is studied to compensate for the inaccurate system identification or factors that cannot be identified easily but play a major role in vibration of a structure. A finite element model of a plate is considered and the effects of scaling the control gains are investigated. It is shown that there is an allowable region for tuning the control gain without loosing the stability. The result of this analysis is used in the experiment for adjusting the control gains.     

The buckling and frequency of flexural vibration of rectangular isotropic and orthotropic plates using Rayleigh's method

A simple approximate formula for the natural frequencies of flexural vibration of isotropic plates, originally developed by Warburton using characteristic beam functions in Rayleigh's method, is modified to apply to specially orthotropic plates and extended to include the effect of uniform, direct inplane forces. The initial buckling problem is treated simply by equating the frequency expression to zero. The approach permits the ready determination of reasonably accurate natural frequencies and/or buckling loads for a given plate involving any combination of free, simply supported or clamped edges, without requiring the aid of a sophisticated calculating device or a knowledge of plate, vibration or buckling theory. To illustrate the applicability and accuracy of the approach, numerical results for a number of specific plate problems are presented.     

Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

Theoretical and Experimental Investigations of the Flow Field for Asymmetric Dual-Flow Interrupter Nozzles

Experimental investigations have indicated that electrode vapor can have a significant negative effect in thermal interruption speed for the gas-blast circuit breakers. This electrode vapor contamination can be minimized by the use of asymmetric dual-flow nozzle configuration. A computer program was developed to design the nozzle and electrode geometries of the asymmetric dual-flow interrupter and to calculate both the subsonic and supersonic cold flow fields. The Variational Principle of the finite element method, together with a Newton-Raphson iterative scheme, was used to solve the continuity equation for compressible flow. The supersonic flow field in the conical nozzle was calculated by the one-dimensional flow relationship. Two asymmetric dual-flow nozzle models were constructed to investigate the effects of orifice opening and nozzle divergent angle. The cold flow experiments were conducted in the Rensselaer Polytechnic Institute (RPI) Transonic and Supersonic Wind Tunnel Laboratory. Various upstream-to-downstream nozzle pressure ratios were used to obtain the subsonic and supersonic experimental flow-field data. The experimental flow measurements were correlated with the calculated values to validate the computer program.     

Aerodynamic analysis of a supersonic cascade vibrating in a complex mode

An analysis is presented which has been used to predict the unsteady aerodynamic behavior of a finite supersonic cascade of airfoils forced in harmonic oscillation with airfoil-to-airfoil variations in amplitude. Theoretical predictions are compared with some recent experimental results² at a reduced frequency representative of actual fan or compressor flutter cases. The similarity of the experimental situation in the finite cascade to the flutter of a severely mistuned rotor is noted.     

An approximate theory for the sound radiated from a periodic line-supported plate

An approximate method is presented for estimating the sound power radiated by an infinite plate, supported elastically along parallel, equi-spaced lines and subjected to a simple pressure field convecting uniformly over the plate in a direction perpendicular to the supports. Suitable complex modes are assumed for the induced plate flexural wave motion, and an energy method is used to estimate the plate response and the radiated sound power. The effect on the plate response of the acoustic loading is taken into account. The influence of the convection velocity (which may be subsonic) and of certain plate parameters is investigated.     

Free vibration analysis for micro-structures used in MEMS considering surface effects

Based on state space method, a three-dimensional (3-D) approach is proposed to study the size-dependent dynamical properties of micro-structures considering surface effects. The structure is modeled as a laminate composed of a bulk bounded with upper and bottom surface layers, which are allowed to have different material properties from the bulk layer. On the basis of 3-D fundamental elasticity, the state equations, including the surface properties of the structure, can be established to analyze the size-dependent dynamic responses of the plate-like thin film structures used in MEMS. To show the feasibility of the proposed approach, a simply supported plate-like thin structure, including the surface layers, is considered. An algorithm strategy is proposed for the calculation of the state equations obtained to ensure that the numerical results can reveal the surface effects clearly even for extremely thin surface layers. Comparing with the two-dimensional plate theories based size-dependent models for the thin film structures in literature, the present 3-D approach is exact, which can provide benchmark results to assess the accuracy of various 2-D plate theories and numerical methods. Numerical tests prepared for the prediction of natural frequency are carried out to illustrate the surface effects. Some discussions and conclusions are presented based on the results of the numerical examples.