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A computational aeroelastic method has been extended to evaluate the static and dynamic characteristics of flexible shell structures. The numerical method applied was the ENS3DAE solver, which permits evaluation of high-order aerodynamic and structure interactions. Modifications to the code to permit smooth transition of internal flowfield characteristics and deflections for shell structures have been developed and verified, The modified methodology has been tested on a problem of merit in the engine community, an axisymmetric engine liner that has exhibited dynamic instabilities. An investigation into the dynamic characteristics of the liner, including Butter, was carried out. The results were compared with experimental data and demonstrate the ability of the method to analyze shell flutter problems of this kind.

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Store-induced limit cycle oscillation of a rectangular wing with a tip store in transonic flow is simulated. Stability boundaries for this wing are computed for both clean and tip store configurations and behavior beyond the critical freestream velocity is examined at a Mach number of 0.92. The Euler equations are used to model the fluid dynamics and a modal approach is used to model the structural response. Solutions obtained with the Euler equations are compared with results obtained using linear and transonic small disturbance theories. All methods are shown to give similar predictions of the stability boundary in the lower transonic regime but differences develop as the Mach number approaches unity. The linear method fails to capture the rise in flutter speed beyond the flutter dip and is, of course, unable to capture limit cycle behavior. The Euler and transonic small disturbance theories show reasonable qualitative agreement in predicting both unbounded and bounded behavior across a wide range of Mach numbers. There are, however, notable quantitative differences between the Euler and transonic small disturbance theories in the limit cycle onset velocities and response amplitudes and frequencies. The results suggest that the transonic small disturbance theory is a practical alternative to the Euler and Navier-Stokes theories for predicting store-induced limit cycle behavior so long as the small disturbance assumption is valid.

Store-induced limit-cycle oscillation of a rectangular wing with tip store in transonic flow is simulated using a variety of mathematical models for the flowfield: transonic small-disturbance theory (with and without inclusion of store aerodynamics) and transonic small-disturbance theory with interactive boundary layer (without inclusion of store aerodynamics). For the conditions investigated, assuming inviscid flow, limit-cycle oscillations are observed to occur as a result of a weakly subcritical Hopf bifurcation and are obtained at speeds lower than those predicted 1) nonlinearly for clean-wing flutter and 2) linearly for wing/store flutter. The ability of transonic small-disturbance theory, to predict the occurrence and strength of this type of limit-cycle oscillation is compared for the different models. Differences in unmatched and matched aeroelastic analysis are described. Solutions computed for the clean rectangular wing are compared to those computed with the Euler equations for a case of static aeroelastic behavior and for a case of forced, rigid-wing oscillation at Mach 0.92.

This paper presents a simulation for high-fidelity aeroelastic analysis of rotating wings with camber-wise structural flexibility and embedded actuators. An unstructured Reynolds-Averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solver is coupled with a non-linear structural dynamics analysis. The CFD solution uses overset grids to combine the stationary and moving frames of reference. The structural for-mulation expands the conventional one-dimensional beam representation with additional degrees-of-freedom to capture plate-like cross-sectional deformations while allowing an arbitrary distribution of active and pas-sive materials in the cross section. Motion and forces on the non-coincident fluid and structural grids are transferred using a finite-element-based interpolation, along with a least-squares fit for extrapolations. Trim and convergence to periodic response are assisted by a low-order analysis that is also discussed. Finally, as an initial verification of the implementations, results from the low-order and CFD-based solutions are compared for a rigid-airfoil rotor in forward flight.

This paper presents an overview of a joint effort to evaluate computational aeroelasticity codes for loads and flutter. Computations are performed on realistic problems for static aeroelasticity, classic flutter, Limit Cycle Oscillations (LCO), and control surface buzz. The codes being evaluated involve a transonic small disturbance code with an interactive boundary layer method and two Euler/Navier-Stokes codes. To evaluate the accuracy of these codes, comparisons are made with available wind tunnel or flight test data. This paper presents the results/status of the following applications: static aeroelasticity - aeroelastic tailored wing, flutter - AV-8B-like wing and F-I5-like tail, LCO - B-1-like and B-2, and control surface buzz - NASP wind tunnel model and Global Hawk wing.

This paper presents an experimental study on the stability of a cantilevered cylindrical flexible (silicone rubber) shell, concentrically located within a rigid cylinder and subjected to air flow in either the annular region or inside the shell. Measurements were made of (i) the critical flow velocities of the shell for various (shell length)/radius and (annular gap)/radius ratios, and (ii) frequencies of oscillation of the shell at different subcritical flow velocities. In the case of annular flow, both divergence and flutter were observed, while only flutter was observed for internal flow. The experimental results were compared with those obtained with the two theoretical models previously developed by the authors; in the first, the unsteady shell-motion-induced fluid forces are evaluated by inviscid flow theory, while the steady ones by viscous flow theory (this model is called "Theory 1" for short); in the second, both are calculated by viscous flow theory, with the unsteady forces being obtained from a CFD solution of the linearized, unsteady Navier-Stokes equations (this model is termed "Theory 2"). Theory 1 agrees quantitatively reasonably well with experimental data for annular flow, both in terms of frequencies of oscillation and critical flow velocities, although experimental values of the critical flow velocities are somewhat lower than the theoretical ones; on the other hand, the critical flow velocities as predicted by Theory 2 were found to agree with experimental data far better, in fact extremely well. In case of internal flow, critical flow velocities predicted by Theory 1 are higher than experimental values, but still in fairly good agreement with them.

A new numerical (CFD-based) model is presented for the study of the effects of unsteady viscous forces on the stability of a cantilevered, flexible cylindrical shell concentrically located inside a rigid cylinder, with incompressible viscous flow in the annulus and with stagnant fluid within the shell. Flügge's modified equations are used to describe shell motions, taking into account the steady viscous forces due to flow pressurization and traction effects on the shell; these equations are subsequently solved by the finite difference method. The unsteady viscous forces exerted on the shell are determined from flow perturbations governed by the linearized, unsteady Navier-Stokes equations, which are solved using a recently developed, finite difference based, time-marching technique with artificial compressibility. It was found that the analytical results obtained for a particular set of system parameters are in excellent quantitative agreement with experiment, although the predicted type of instability is not always the same as that observed; the unsteady viscous effects tend to become reduced with diminishing annular gap width, provided that the gap is moderately small.

In this paper the dynamics and stability characteristics of coaxial cylindrical shells containing incompressible, viscous fluid flow are examined in contrast to previous studies where the fluid has been considered to be inviscid. Specifically, upstream pressurization of the flow (to overcome frictional pressure drop) and skin friction on the shell surfaces are taken into account, generating time-mean normal and tangential loading on the shells. The fluctuating fluid forces, coupled to shell vibration, are determined entirely by means of linearized potential flow theory and formulated with the aid of generalized-force Fourier-transform techniques. It is found that the effect of viscosity in the annular flow generally tends to destabilize the system, vis-a-vis inviscid flow, whereas viscous effects in the inner flow stabilize the system.

A computer analysis has been developed for calculating the steady (or unsteady) three-dimensional flowfield for engine installations. This algorithm, called ENS3D, can compute the engine installation flowfield for subsonic, transonic or supersonic free-stream speeds. The algorithm can solve either the Euler equations for inviscid flow, the thin-shear-layer Navier-Stokes equations for viscous flow, or the full Navier-Stokes equations for viscous flow. The flowfield solution is determined on a body-fitted numerically-generated computational grid. A fully-implicit alternating-direction-implicit method is employed for solution of the finite-difference equations. For viscous computations, a two-layer eddy-viscosity turbulence model is used to achieve mathematical closure. For the present application, the algorithm is applied to compute transport engine installation flowfields at subsonic and transonic free-stream speeds.

A theoretical study is presented of the dynamical behaviour of a cylindrical shell coaxially located in a rigid cylindrical pipe, with viscous and incompressible fluid flow in the inner shell and the annulus. The fluid forces consist of two parts: (i) steady viscous forces representing the effects of upstream pressurization of the flow (to overcome frictional pressure drop) and skin friction on the shell surface, which are determined by using turbulent fully developed flow theory; (ii) unsteady viscous forces which are derived by means of linearized Navier-Stokes equations. Shell motion is described by Flügge's shell equations, modified to take the initial loading due to the steady viscous forces into account. A travelling wave solution is used to formulate the dynamical fluid-structure interaction problem. The objective is to investigate the effects of unsteady viscous forces on the dynamical behaviour and stability of the system in the presence and absence of steady forces. Calculations have been conducted with a steel shell conveying water with different gap-to-radius ratios . First, the system is subjected to unsteady viscous forces only. The results are compared to those of inviscid theory. It is found that, for internal flow and annular flow for , the effects of viscosity on the stability of the system are insignificant; however, for the smaller gap ( these effects are more pronounced, rendering the system more stable. When both steady and unsteady viscous forces are applied, the results are quite different from the previous case. For annular flow, the system loses stability at much lower velocities for both gap systems. The loss of stability depends primarily on the steady viscous forces, at least for the parameters considered in the paper. The unsteady viscous forces affect only the frequencies of the system before it becomes unstable.

A new formula for the natural frequencies of circular cylindrical shells is presented for modes in which transverse deflections dominate. It is valid for all boundary conditions for which the roots of the analogous beam problem can be obtained. Good agreement with experimental data for a variety of boundary conditions is shown.

The flutter of a convergent axisymmetric shell subjected to internal flow and external, annular flow has been investigated experimentally. The tested shell is a small-scale dynamically similar model of a heat-shielding shell experiencing flutter problems. At the onset of the shell instability, the flow on both sides is in the compressible regime. The model tests have been successful in reproducing the shell flutter, pinpointing the excitation source, and in clarifying the effect of different design parameters on the instability limit.The shell instability is caused by the external, annular flow. The internal flow has a stabilizing effect. Increasing the rate of the internal flow or the width of the annular flow delays the onset of instability. Some qualitative tests on the effect of structural damping show that the shell loses stability by flutter if the structural damping is low. On the other hand, if the structural damping is sufficiently high, the shell loses stability by divergence. Finally, some counter-measures to solve the flutter problem are discussed.

This is a theoretical study of the stability of cantilevered coaxial cylindrical shells conveying incompressible fluid in the annular space in between and within the inner shell. The viscous effects of the mean flow are taken into account, but the perturbations of the equilibrium state on the basis of which stability is assessed is carried out by means of potential flow theory, thus neglecting unsteady viscous effects which might well become important for narrow annular flows. Shell displacements are described by Fliigge's equations of motion. Solution of the coupled fluid-structure equations is carried out by means of the Fourier Transform Method. Preliminary checks into various aspects of the solution are carried out, notably on the choice of the so-called “out-flow models”, which determine the downstream boundary conditions on the fluid flow beyond the free end, and on the numerical aspects of the solution; these give confidence in the solution method, which is then used to obtain results for the problem at hand.The main finding of this research is that stability is lost by flutter for internal flow, according to both the inviscid and viscous variants of the theory; for annular flow, however, whereas inviscid theory predicts loss of stability by flutter, viscous theory (with dissipative effects included) predicts that the shell loses stability by divergence and then, at appreciably higher flow, by flutter. Reduction of the annular gap generally destabilizes the system; while increased steady viscous effects slightly stabilize the system for internal flow, they strongly destabilize it for annular flow. Increasing the length of the shell destabilizes the system for both internal and annular flows. The presence of internal flow in addition to annular flow tends to stabilize the system vis a-vis the case of annular flow, but only at low flow velocities, having the opposite effect at higher flows; the same effects arise when the main flow is internal and an annular flow added to the system.

This paper presents a study of the effect of some of the system parameters on internaland andular-flow-induced instabilities of clamped-clamped or cantilevered cylindrical shells in coaxial conduits; the parameters considered are shell thickness, length of the shell, annular width, and relative directions of the inner and annular flows. Shell motions are described by Flügge's shell equations, and the unsteady fluid dynamic forces are evaluated by means of potential-flow theory. The time-averaged viscous loads on the shell due to flow pressurization and surface traction as well as internal damping of the shell material are also taken into account. Solutions are obtained with the aid of the Fourier transform technique.It is found that in both systems of clamped-clamped and cantilevered shells, where steel shells and water as the working fluid were used, a reduction in the annular width or in the shell thickness destabilizes the system, while a reduction in the length of the shell stabilizes it. Clamped-clamped and cantilevered coaxial shells lose stability at lower annular flow velocities when subjected concurrently to both internal and annular flows; this is more pronounced for counter- as opposed to co-current flows for clamped-clamped shells.

An analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach. The applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the matrix has been determined by quadrature of the equations, the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges. The method is applied to truncated conical shells with linearly, parabolically or exponentially varying thickness, and the effects of the semi-vertex angle, truncated length and varying thickness on the vibration are studied.

A procedure for computing the aeroelasticity of wings on parallel multiple-instruction, multiple-data (MIMD) computers is presented. In this procedure, fluids are modeled using Euler equations, and structures are modeled using modal or finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. In the present parallel procedure, each computational domain is scalable. A parallel integration scheme is used to compute aeroelastic responses by solving fluid and structural equations concurrently. The computational efficiency issues of parallel integration of both fluid and structural equations are investigated in detail. This approach, which reduces the total computational time by a factor of almost 2, is demonstrated for a typical aeroelastic wing by using various numbers of processors on the Intel iPSC/860.

The National Aero-Space Plane (NASP), or X-30, is a single-stage-to-orbit vehicle that is designed to takeoff and land on conventional runways. Research in aeroelasticity was conducted by NASA and the Wright Laboratory to support the design of a flight vehicle by the national contractor team. This research includes the development of new computational codes for predicting unsteady aerodynamic pressures. In addition, studies were conducted to determine the aerodynamic heating effects on vehicle aeroelasticity and to determine the effects of fuselage flexibility on the stability of the control systems. It also includes the testing of scale models to better understand the aeroelastic behavior of the X-30 and to obtain data for code validation and correlation. This paper presents an overview of the aeroelastic research which has been conducted to support the airframe design.

An aeroelastic analysis method, based on three-dimensional Navier-Stokes equation aerodynamics, has been applied to improve the performance of fighter wings operating at sustained maneuver flight conditions. The scheme reduces the trimmed pressure drag of wings performing high-g maneuvers through a simultaneous application of control surface deflection and aeroelastic twist. The aerodynamic and structural interactions are decoupled by assuming an aeroelastic twist mode shape and optimizing the aerodynamic performance based on this aeroelastic mode. The wing structural stiffness properties are then determined through an inverse scheme based on the aerodynamic loads and desired twist at the maneuver flight condition. The decoupled technique is verified by performing a fully coupled aeroelastic analysis using the maneuver flight conditions and the optimized structural stiffness distributions.

Flight Loads Prediction Meth-ods for Fighter Aircraft

- D M Schuster
- J Vadyak
- E Atta

Schuster, D. M., Vadyak, J., and Atta, E., " Flight Loads Prediction Meth-ods for Fighter Aircraft, " Wright Research and Development Center, WRDC-TR-89-3104, Dayton, OH, Nov. 1989.

Develop-ment of an Euler/Navier–Stokes Aeroelastic Method for Three-Dimensional Vehicles with MultipleFlexible Surfaces AIAA Paper 96-1400 Supersonic Jet Noise Reduc-tion from Single and Coaxial Rectangular Jets

- M J Smith
- D M Schuster
- L Huttsell
- B Buxton
- K K Ahuja
- J Manes
- K Massey

Smith, M. J., Schuster, D. M., Huttsell, L., and Buxton, B., " Develop-ment of an Euler/Navier–Stokes Aeroelastic Method for Three-Dimensional Vehicles with MultipleFlexible Surfaces, " AIAA Paper 96-1400,April 1996. 11 Ahuja, K. K., Manes, J., and Massey, K., " Supersonic Jet Noise Reduc-tion from Single and Coaxial Rectangular Jets, " Final Rept. NASA Grant NAG3-1066, NASA John H. Glenn Research Center at Lewis Field, Cleve-land, OH, Feb. 1992.

Simulation of Aircraft Component Floww elds Using a Three-Dimensional Navier–Stokes Algorithm

- J Vadyak
- M Smith
- D Schuster
- G Shrewsbury

Vadyak, J., Smith, M., Schuster, D., and Shrewsbury, G., " Simulation of Aircraft Component Floww elds Using a Three-Dimensional Navier–Stokes Algorithm, " Third International Symposium on Science and Engineering on Cray Supercomputers, Cray Research, Inc., Minneapolis, MN, Sept. 1987.