Transonic Flutter Research Articles

Transonic flutter computations for the NLR 7301 supercritical airfoil

A numerical investigation of the transonic steady-state aerodynamics and of the two-degree-of-freedom bending/torsion flutter characteristics of the NLR 7301 section is carried out using a time-domain method. An unsteady, two-dimensional, compressible, thin-layer Navier–Stokes flow-solver is coupled with a two-degree-of-freedom structural model. Fully turbulent flows are computed with algebraic or one-equation turbulence models. Furthermore, natural transition is modeled with a transition model. Computations of the steady transonic aerodynamic characteristics show good agreement with Schewe's experiment after a simplified accounting for wind-tunnel interference effects is used. The aeroelastic computations predict limit-cycle flutter in agreement with the experiment. The computed flutter frequency agrees closely with the experiment but the computed flutter amplitudes are an order of magnitude larger than the measured ones. This discrepancy is likely due to the omission of the full wind-tunnel interference effects in the computations.

K-1232 遷音速フラッタに対する非線形数学モデルの連続法による検討(J06-3 流体関連の騒音と振動(3))(J06 流体関連の騒音と振動)

K-1232 遷音速フラッタに対する非線形数学モデルの連続法による検討(J06-3 流体関連の騒音と振動(3))(J06 流体関連の騒音と振動)

Evaluation of Acoustic Flutter Suppression for Cascade in Transonic Flow

Flutter suppression via actively excited acoustic waves is a new idea proposed recently. The high flutter frequency (typically 50–500 Hz for a fan blade) and stringent space constraint make conventional mechanical type flutter suppression devices difficult to implement for turbomachines. Acoustic means arises as a new alternative which avoids the difficulties associated with the mechanical methods. The objective of this work is to evaluate numerically the transonic flutter suppression concept based on the application of sound waves to two-dimensional cascade configuration. This is performed using a high-resolution Euler code based on a dynamic mesh system. The concept has been tested to determine the effectiveness and limitations of this acoustic method. In a generic bending-torsion flutter study, trailing edge is found to be the optimal forcing location and the control gain phase is crucial for an effective suppression. The P&W fan rig cascade was used as the model to evaluate the acoustic flutter suppression technique. With an appropriate selection of the control logic the flutter margin can be enlarged. Analogous to what were concluded in the isolated airfoil study, for internal excitation, trailing-edge forcing was shown to be optimal since the trailing-edge receptivity still works as the dominant mechanism for generating the acoustically induced airloads.

Transonic Flutter Suppression Control Law Design and Wind-Tunnel Test Results

Fluttersuppressioncontrollawdesignandwind-tunneltestresultsintransonice owforaNACA0012wingmodel, under the benchmark active control technology program at NASA Langley Research Center, will be presented. Two control law design processes using classical and minimax techniques are described. Design considerations for improving the multivariable system robustness are outlined. The classical control law was digitally implemented and tested in the NASA Langley Transonic Dynamics Tunnel. In wind-tunnel tests in air and heavy gas medium, the closed-loop e utter dynamic pressure was increased by over 50% up to the wind-tunnel upper limit. The active e utter suppression system also provided signie cant robustness, relative to gain and phase perturbations, even in the presence of transonic shocks and e ow separation.

On Flowfield Periodicity in the NASA Transonic Flutter Cascade

A combined experimental and numerical program was carried out to improve the flow uniformity and periodicity in the NASA transonic flutter cascade. The objectives of the program were to improve the periodicity of the cascade and to resolve discrepancies between measured and computed flow incidence angles and exit pressures. Previous experimental data and some of the discrepancies with computations are discussed. In the present work surface pressure taps, boundary layer probes, shadowgraphs, and pressure-sensitive paints were used to measure the effects of boundary layer bleed and tailboard settings on flowfield periodicity. These measurements are described in detail. Two numerical methods were used to analyze the cascade. A multibody panel code was used to analyze the entire cascade and a quasi-three-dimensional viscous code was used to analyze the isolated blades. The codes are described and the results are compared to the measurements. The measurements and computations both showed that the operation of the cascade was heavily dependent on the endwall configuration. The endwalls were redesigned to approximate the midpassage streamlines predicted using the viscous code, and the measurements were repeated. The results of the program were that: (1) Boundary layer bleed does not improve the cascade flow periodicity. (2) Tunnel endwalls must be shaped like predicted cascade streamlines. (3) The actual flow incidence must be measured for each cascade configuration rather than using the tunnel geometry. (4) The redesigned cascade exhibits excellent periodicity over six of the nine blades.

Transonic-Aerodynamic-Influence-Coefficient Approach for Aeroelastic and MDO Applications

A developed transonic-aerodynamic-influence-coefficient (TAIC) method is proposed as an efficient tool for applications to flutter, aeroservoelasticity, and multidisciplinary design/analysis optimization. Several plausible procedures for AIC generation are described. The modal-based AIC procedure is formally established as a general AIC scheme applicable to all classes of computational fluid dynamics (CFD) methods. The present TAIC method integrates the previous transonic equivalent strip (TES) method with the modal AIC approach; its computer code ZTAIC has a similar input format to that of doublet lattice method (DLM) except with the additional steady pressure input. The versatility of ZTAIC is shown by two sets of cases studied: those cases with pressure input from measured data and those from CFD computation. Computed results of unsteady pressures and flutter points are presented for six wing planforms. In contrast to the usual CFD practice, the effective use of the modal AIC in ZTAIC is clearly demonstrated by the flutter calculations of the weakened and solid 445.6 wings, where the CPU time of a transonic flutter point using warm-started AIC is less than 1 min on a SUN SPARC20 workstation. Moreover, the AIC capability allows ZTAIC to be readily integrated with structural finite element method (FEM). Hence, it is most suitable to be adopted in a multidisciplinary design (MDO) environment such as ASTROS.

Improved determination of aeroelastic stability properties using a direct method

The ability to accurately predict transonic flutter boundaries is investigated using an enhanced direct computational method. Steady characteristic and unsteady approximate nonreflecting characteristic far-field boundary conditions are utilized to more accurately model the aerodynamic flow physics in a direct method. In order to accomplish this, the aerodynamic model is modified to lock the movement of the far-field grid points while allowing the airfoil surface points to move freely. This is accomplished by introducing a linear weighting function in the grid deformation model. The direct method is based on a discretization of the Euler equations and a coupled set of structural dynamics equations representative of a pitch-and-plunge airfoil with trailing edge flap. The coupled equations are expanded to specify a Hopf-bifurcation point, which defines an incipient flutter state. In addition, the direct continuation method is extended by an analytic computation of the path tangent vector for pseudo-arclength continuation (PAC). A flapped NACA 64A006 airfoil, executing pitch and plunge motion, is utilized to demonstrate the ability of the enhanced boundary conditions to accurately calculate flutter boundaries for reduced domain sizes. Both zero and nonzero angle of attack results are shown to highlight the improved accuracy of the boundary conditions. Each boundary condition modification resulted in analysis improvements, with the steady characteristic model demonstrating significant improvements in the nonlinear flow regime. For a 1° static pretwist, analysis at a freestream Mach number of 0.84, the enhanced model resulted in over a 75% decrease in the flutter speed error. In addition, flutter boundary solutions are presented which demonstrate the capability of the PAC model to compute variations in structural parameters. The airfoil-fluid mass ratio and structural damping parameters are varied for both subsonic and transonic flow conditions, with nonlinear effects observed for the transonic results.

Flutter Analysis of Cascades Using an Euler/Navier-Stokes Solution-Adaptive Approach

In this study, cascade flutter analyses for inviscid and viscous flows are presented. In the present timedomain approach, the structural model equations for each blade as a typical section having plunging and pitching degrees of freedom are integrated in time by the explicit four-stage Runge-Kutta scheme. A solution-adaptive finite volume method with globally/rigid-deformable dynamic mesh treatments is introduced to solve the two-dimensional Euler/Navier -Stokes equations. For viscous flows, the BaldwinLomax turbulence model and two transition formulations are adopted. By comparing with the related data in two inviscid transonic-cascade-flutter problems, the reliability and suitability of the present approach are confirmed. From the time histories of blade displacements and total energy in transonic-flutter calculations, it is observed that the viscous effect has a damping influence on the aeroelastic behavior. The instantaneous meshes and vorticity contours clearly indicate the shock/boundary-layer interaction, large vortex structure, and big plunging motion in the transonic flutter, subsonic stall flutter, and supersonic bending flutter, respectively. By using the fast Fourier transformation and modal identification techniques, the aeroelastic behaviors in the inviscid transonic and viscous transonic, subsonic stall, and supersonic bending flutter problems are further investigated.

Navier-Stokes computations on flexible advanced transport wings in transonic regime

Steady, unsteady, and aeroelastic computations are performed on an advanced transonic wing configuration. The flow is modeled by the Navier-Stokes equations, and structures for aeroelastic computations are modeled by the modal equations. The inadequacy of Euler equations and the importance of using the Navier-Stokes equations with a turbulence model is demonstrated for supercritical flows in the transonic regime. The effect of Mach number on steady pressure distributions is illustrated. Steady flow computations for transonic wings are compared with wind-tunnel data and also with equivalent conventional wings. Unsteady computations are made hi the context of demonstrating the use of the indicial approach for generating aerodynamic data for aeroelastic computations. By using the unsteady data generated by indicial responses, a computationally efficient approach of computing preliminary flutter boundaries is demonstrated. The effect of Mach number on the flutter boundary including the prediction of the transonic flutter speed dip is demonstrated. The flutter boundaries of transonic wings are compared with equivalent conventional wings. Characteristics of the flutter boundaries are correlated with aerodynamic flow characteristics.

Limit cycle phenomena in computational transonic aeroelasticity

Limit cycle behavior has been observed in past transonic flutter calculations by the authors, using a two degree of freedom typical section model coupled to an unsteady Euler equation solver. In this article, the structural nonlinearity of freeplay has been added to the typical section model, and its effects on the dynamic stability problem are assessed. In addition, limit cycle behavior in the swept wing model of Isogai is demonstrated and related to the observed presence of multiple flutter points in the transonic dip region

Engineering methods of evaluating the characteristics of transonic flutter of control surfaces

Engineering methods of evaluating the characteristics of flutter of control surfaces with consideration of their interaction with shock waves are proposed on the basis of analyzing the results of theoretical and experimental investigations of transonic flow past airfoils. A comparison of the values of the rudder hinge moments obtained by calculation and in flight experiments showed their satisfactory agreement.

Unsteady transonic two-dimensional Euler solutions using finite elements

A finite element solution of the unsteady Euler equations is presented, and demonstrated for two-dimensional airfoil configurations oscillating in transonic flows. Computations are performed by spatially discretizing the conservation equations using the Galerkin weighted residual method and then employing a multistage RungeKutta scheme to march forward in time. Triangular finite elements are employed in an unstructured O-mesh computational grid surrounding the airfoil. Grid points are fixed in space at the far-field boundary and are constrained to move with the airfoil surface to form the near-field boundary. A mesh deformation scheme has been developed to efficiently move interior points in a smooth fashion as the airfoil undergoes rigid-body pitch and plunge motion. Both steady and unsteady results are presented, and a comparison is made with solutions obtained using finite volume techniques. The effects of using either a lumped or consistent mass matrix were studied and are presented. Results show the finite element method provides an accurate solution for unsteady transonic flows about isolated airfoils. HE accurate determination of the unsteady flowfield surrounding an oscillating airfoil or wing in transonic flow is of paramount importance in the prediction of the flutter characteristics of the body. Transonic flutter remains an active research topic because of the continued interest by both the military and commercial sectors to operate in these flight regimes with vehicles that are ever lighter and, as a result, more flexible. Typically, analysis of fluid-structure interaction in flight vehicles involves describing the vehicle structure using finite elements, whereas finite difference methods are used to model the surrounding fluid. Coupling of the two dissimilar models then presents problems because of the disparity between the two solution techniques. Additional complexities arise because of phase mismatching between the fluid pressures and the displacements of the structure. It seems a natural progression to use finite element methods to describe the behavior of both the fluid and structure, thus bringing more commonality into the analysis of the two media. Early research efforts concentrated on using the transonic small-disturbance equation or the nonlinear full potential equation as the model for the gas dynamic behavior in transonic flows. Unfortunately, this idealization leads to errors when strong shocks are present because of their inability to account for the production of entropy and vorticity. To properly account for these effects within the framework of the conservation laws, the Euler equations must be used. These equations, although they neglect fluid viscosity, have become the standard when unsteady transonic solutions are desired. The absence of a viscosity representation is an important limitation of the present formulation and must be considered

Transonic flutter analysis using time-linearization aerodynamics

Introduction O VER the past decade there has been considerable progress in the development of numerical simulation techniques for unsteady transonic flow calculations. This activity was motivated by the need to supplement the expensive and time-consuming wind-tunnel investigations and flight tests with inexpensive, fast, and efficient computer simulation programs to accurately predict flutter boundaries and many other important aeroelastic phenomena in the transonic regime. Although the basic fluid motion in unsteady aerodynamics is governed by the Navier-Stokes (NS) equations, numerical simulations of the complete NS equations for general threedimensional flow problems are not yet sufficiently developed for flutter applications. Computational methods in threedimensional unsteady transonic flows concentrate mainly on the transonic small disturbance (TSD) equation or full potential (FP) equation. The major advantage of the simpler model using TSD or FP approach over those based on Euler and NS formulation is the large reduction in computational time and memory requirements. In Ref. 1, the TSD code UST3D was described. This code utilizes the time-linearization approach for solving the transonic small disturbance equation. It was demonstrated that the technique could be used with confidence for computations of three-dimensional unsteady transonic flows over an isolated thin wing. An improved version of the UST3D program was given in Ref. 2 and results from a validation study were presented. This transonic aerodynamics code was incorporated into the Institute for Aerospace Research (IAR) Flutter Analysis Program. This Note presents some results from an aerodynamic and flutter analysis of the AGARD 445.6 wing which was recommended by AGARD as a standard configuration for code validation.

Current status of computational methods for transonic unsteady aerodynamics and aeroelastic applications

The current status of computational methods for unsteady aerodynamics and aeroelasticity is reviewed. The key features of challenging aeroelastic applications are discussed in terms of the flowfield state—low-angle high speed flows and high-angle vortex-dominated flows. The critical role played by viscous effects in determining aeroelastic stability for conditions of incipient flow separation is stressed. The need for a variety of flow modeling tools, from linear formulations to implementations of the Navier-Stokes equations, is emphasized. Estimates of computer run-times for flutter calculations using several computational methods are given. Applications of these methods for unsteady aerodynamic and transonic flutter calculations for airfoils, wings and configurations are summarized. Finally, recommendations are made concerning future research directions.

Transonic flutter/divergence characteristics of aeroelastically tailored and non-tailored high-aspect-ratio forward-swept wings

In order to see whether the divergence phenomenon of a transport-type high-aspect-ratio forward-swept wing can be effectively eliminated by aeroelastic tailoring, experimental studies have been performed focusing attention especially on the transonic regime. The transonic flutter/divergence boundaries of the two wind tunnel models, one of which simulates the tailored full-scale wing and the other of which simulates the non-tailored one, have been determined. The tailored model has experienced flutter as predicted by the linear theory which employs the Doublet Lattice Method; i.e., the divergence phenomenon is suppressed by aeroelastic tailoring. The non-tailored model has experienced flutter, contrary to theoretical prediction, which is conjectured as “Shock Stall Flutter”, in which the shock-induced flow separation plays the dominant role. By comparing the nondimensional flutter boundaries of the two models, it is shown that, by aeroelastic tailoring, the transonic flutter characteristics of this particular wing can be improved about 60–80% over that of the non-tailored wing.

Structural non-linearity effects on flutter of a swept wing in transonic flows

The transonic flutter analysis of swept wings containing structural non-linearities is considered. Concentrated preload non-linearities are treated using asymptotic expansions which take into account the influence of the higher harmonics of the load-displacement expansion series. The generalized aerodynamic load matrix is obtained using pulse transfer function analysis. Transonic aerodynamic flows are modeled using the transonic small-disturbance equation which is solved by applying an approximate factorization finite-difference algorithm. The frequency domain solution of the aeroelastic equation is obtained through root-locus analysis. The effects of the magnitudes of the preload non-linearities on the flutter stability boundary of the system are studied.

Unsteady Aerodynamic Damping Measurement of Annular Turbine Cascade With High Deflection in Transonic Flow

Unsteady aerodynamic forces acting on oscillating blades of a transonic annular turbine cascade were investigated in both aerodynamic stable and unstable domains, using a Freon gas annular cascade test facility. In the facility, whole blades composing the cascade were oscillated in the torsional mode by a high-speed mechanical drive system. In the experiment, the reduced frequency K was changed from 0.056 to 0.915 with a range of outlet Mach number M2 from 0.68 to 1.39, and at a constant interblade phase angle. Unsteady aerodynamic moments obtained by two measuring methods agreed well. Through the moment data the phenomenon of unstalled transonic cascade flutter was clarified as well as the significance of K and M2 for the flutter. The variation of flutter occurrence with outlet flow velocity in the experiments showed a very good agreement with theoretical analysis.

Transonic flutter analysis of aerodynamic surfaces in the presence of structural nonlinearities

The influence of structural nonlinearities on the transonic aeroelastic behavior of a two-degree-of-freedom system consisting of an airfoil which is plunging and pitching is considered. The preload and freeplay nonlinearity in the spring model are treated using the asymptotic expansion method which takes into account the influence of the higher harmonics. The aerodynamic load vector is obtained by solving the unsteady transonic small-disturbance (TSD) equation using an alternating-direction implicit (ADI) finite-difference algorithm. The frequency domain solution of the aeroelastic equation is obtained using the U-g method, and the aeroelastic response is carried out by applying Newmark-β and Wilson-ϑ methods. A comparison is made between the results obtained from these two solutions. The effects of preload and freeplay magnitudes on the stability of the system and the corresponding reduced frequency and mass density ratio at neutrally stable response are studied.

Integrated approach for active coupling of structures and fluids

Strong coupling of structure and fluids is common in many engineering environments, particularly when the flow is nonlinear and very sensitive to structural motions. Such coupling can give rise to physically important phenomena, such as a dip in the transonic flutter boundary of a wing. The coupled phenomenon can be analyzed in closed form for simple cases that are defined by linear structural and fluid equations of motion. However, complex cases defined by nonlinear equations pose a more difficult task for solution. It is important to understand these nonlinear coupled problems, since they may lead to physically important new phenomena. Flow discontinuities, such as a shock wave, and structural discontinuities, such as a hinge line of a control surface of a wing, can magnify the coupled effects and give rise to new phenomena. To study such a strongly coupled phenomenon, an integrated approach is presented in this paper. The aerodynamic and structural equations of motion are simultaneously integrated by a time-accurate numerical scheme. The theoretical simulation is done using the time-accurate unsteady transonic aerodynamic equations coupled with modal structural equations of motion. As an example, the coupled effect of shock waves and hinge-line discontinuities are studied for aeroelastically flexible wings with active control surfaces. The simulation in this study is modeled in the time domain and can be extended to simulate accurately other systems where fluids and structures are strongly coupled.

Effects of modal symmetry on transonic aeroelastic characteristics of wing-body configurations

To study accurately the transonic aeroelastic characteristics, it is important to model the full aircraft configuration, including asymmetry. Recently, an accurate method of computing unsteady transonic flows on full-span wing-body configurations was developed using the transonic potential flow theory. In this work, the method is further developed to account for the aeroelasticity of full-span wing-body configurations. This is accomplished by simultaneously integrating the unsteady aerodynamic forces and modal structural equations of the wing-body configurations. To validate the method, aeroelastic computations are made for a wing-body configuration with a rectangular wing. The aeroelastic responses of this configuration are correlated with the responses of a similar isolated wing. The comparisons are favorable. Aeroelastic computations associated with symmetric and antisymmetric modes are also made to study the influence of modal asymmetry on responses. This new development is further illustrated by computing the aeroelastic characteristics of a typical fighter aircraft. The results from this study will be useful in accurately computing the transonic flutter boundaries of aircraft, including those associated with asymmetric modes.