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At least 91 records · Page 5

Flutter analysis of a supersonic cascade in time domain using an ADI Euler solver

The aeroelastic stability of a two-dimensional cascade oscillating in supersonic axial flow is analyzed in the time domain. The aeroelastic model consists of a single degree of freedom typical section structural model for each blade of the cascade and an unsteady two-dimensional cascade aerodynamic model based on the Euler equations. The Euler equations are solved using a time accurate Alternating Direction Implicit (ADI) solution scheme. The aeroelastic equations are integrated in time. The effect of interblade phase angle is included in the aeroelastic analysis by an appropriate choice of initial and boundary conditions. Flutter predictions are obtained from the time response of a flat plate cascade in single degree of freedom pitching motion. The results correlate well with those obtained from a separate frequency domain flutter analysis for all values of interblade phase angles considered. Flutter results are then presented for cascades having airfoil sections representative of a supersonic throughflow fan. The validity of the time integration method for a cascade of airfoils at various interblade phase angles is demonstrated.

Reddy, T. S. R.↗

Nonlinear oscillations of a fluttering plate.

Two- and three-dimensional plates in high supersonic flow undergoing limit cycle oscillations analyzed, using aerodynamic theory and von Karman large deflection plate theory

PLATE THEORY↗

A Wind-Tunnel Investigation of the Stall-Flutter Characteristics of a Supersonic-Type Propeller at Positive and Negative Thrust

An investigation has been made utilizing a three-blade, 10-foot- diameter, supersonic-ty-pe propeller to determine propeller flutter characteristics. The particular flutter characteristics of interest were (1) the effect of stall flutter on a propeller operating in positive and negative thrust, (2) the effect of stall flutter on a propeller operating with the thrust axis inclined, and (3) the variation of vibratory blade shear stresses as the stall flutter boundary is penetrated and exceeded. Thrust and power measurements were made for all test conditions. Wake and inflow surveys were made when appropriate, to define the thrust and torque distributions and the magnitude of the inflow velocity. Stress measurements were made simultaneously to obtain the propeller flutter and bending response. It was found when operating both in the positive and negative thrust regions that, for most cases after the onset of flutter, the magnitude of the flutter stresses at first increased rapidly with section blade angle P, after which further increases in 0 resulted in only a moderate increase or a reduction in stress. Thrust-axis inclination up to the limit of the tests (angle of attack of 15 deg and dynamic pressure of 40 psf) appeared to have no effect on stall flutter. The stall flutter stresses were found to be directly associated with the section thrust characteristics of the blades. The onset of flutter was found to occur simultaneously with the divergence of the section thrust variation with blade angle from linearity for stations outboard of the blade 0.8-radius station. The maximum flutter stresses appeared to be a function of the maximum section thrust obtained at or in the vicinity of the blade 0.8-radius station. In an attempt to correlate two-dimensional airfoil data with three-dimensional data to predict the stall angle of attack (divergence of the section thrust) of the blade sections, it was found that no consistent correlation could be obtained. Also, a knowledge of the inflow conditions appeared to be insufficient to account for differences in airfoil characteristics between the two-dimensional and the three-dimensional cases.

Rogallo, Vernon L.↗

Finite element nonlinear panel flutter with arbitrary temperatures in supersonic flow

A finite element frequency domain method for predicting nonlinear flutter response of panels with temperature effects is presented. By using the principle of virtual work, the element nonlinear stiffness formulation for a panel under a combined thermal and aerodynamic loads is derived on the bases of von Karman's large deflection plate theory, the first-order piston theory aerodynamics and the quasi-steady thermal stress theory. The system equations of motion can be mathematically separated into two sets of equations and then solved in sequence. The first set of equations yields the panel thermal-aerodynamic equilibrium and the second set of equations of motion leads to the flutter limit-cycle oscillations. Stability and flutter boundaries can also be obtained from the two sets of system equations. Finite element large amplitude limit-cycle flutter results at different uniform temperatures are obtained for a simply supported square panel and are compared with existing Galerkin/time integration and other finite element solutions. Effects of nonuniform temperature distributions, panel length-to-width ratios, and boundary conditions on flutter responses of rectangular and triangular panels are presented.

Xue, David Y.↗

Wind tunnel investigation of supersonic wing-tail flutter

A flutter model, consisting of a wing, horizontal tail, and splitter plate/fuselage mechanism, was tested in a 4-foot transonic tunnel in the Mach number range 1.1 to 1.3. Two types of flutter were encountered during the testing: a wing-tail flutter bending-torsion flutter mode. The wing-tail flutter speed was found to be a minimum at M = 1.2 for the configuration tested. Recorded model test data were digitized for a power spectral density (PSD) analysis and Random Decrement (Randomdec) analysis. Comparisons between the frequency and damping obtained from the PSD plots and the Randomdec signatures agreed very well. A limited flutter analysis was conducted using a Mach box unsteady aerodynamics method which accounted for interference and airfoil thickness. Analytical comparisons with experimental flutter speeds agreed well. The analyses assuming zero thickness predicted flutter speeds higher than those measured, ranging from 1 percent at M = 1.12 to 8 percent at M = 1.28. With the airfoil thickness included, the correlation was improved such that predicted flutter speeds for all cases investigated were within 2 percent of experimental speeds.

Huttsell, L. J.↗

Experimental Investigation of Flutter of Buckled Curved Panels Having Longitudinal Stringers at Transonic and Supersonic Speeds

Panel-flutter tests have been made at transonic and supersonic speeds With particular reference to buckled curved panels with longitudinal stringers. Other panel configurations were also tested in an attempt to determine effects of skin thickness, curvature, stringers, buckling, pressure differential, and Mach number on the dynamic pressure necessary to start flutter. For buckled curved panels with longitudinal stringers, the dynamic pressure required to start flutter was increased by increasing the skin thickness and increasing the pressure differential across the panel. There was no apparent effect of Mach number variation from 1.3 to 2.0. None of the curved panels failed because of flutter although the dynamic pressure at the start of flutter was exceeded by a factor of 3 in many cases. curved panels and four flat panels failed because of flutter. The flat panels fluttered at lower dynamic pressures than the curved panels and four flat panels failed because of flutter.

Tuovila, W. J.↗

Flutter of laminated plates in supersonic flow

A solution procedure was developed using linear small deflection theory for the flutter of simply supported laminated plates. For such plates, the bending and extensional governing equations are coupled and have cross-stiffness terms which do not appear in classical plate theory. An extended Galerkin method is used to obtain approximate solutions to the governing equations, and the aerodynamic pressure loading used in the analysis is that given by linear piston theory with flow at arbitrary cross-flow angle. A limited parametric study was conducted for typical laminated composite plates. The calculations show that both the bending-extensional coupling and the cross-stiffness terms have a large destabilizing effect on flutter. Since classical plate theory does not consider bending-extensional coupling and cross stiffness terms, it usually gives inaccurate and nonconservative flutter boundaries for laminated plates.

Sawyer, J. W.↗

Flutter, Postflutter, and Control of a Supersonic Wing Section

A number of issues related to the flutter and postflutter of two-dimensional supersonic lifting surfaces are addressed. Among them there are the 1) investigation of the implications of the nonlinear unsteady aerodynamics and structural nonlinearities on the stable/unstable character of the limit cycle and 2) study of the implications of the incorporation of a control capability on both the flutter boundary and the postflutter behavior. To this end, a powerful methodology based on the Lyapunov first quantity is implemented. Such a treatment of the problem enables one to get a better understanding of the various factors involved in the nonlinear aeroelastic problem, including the stable and unstable limit cycle. In addition, it constitutes a first step toward a more general investigation of nonlinear aeroelastic phenomena of three-dimensional lifting surfaces.

Marzocca, Piergiovanni↗

Supersonic axial-flow fan flutter

Lane's (1957) analytical formulation of the unsteady pressure distribution on an oscillating two-dimensional flat plate cascade in supersonic axial flow has been developed into a computer code. This unsteady aerodynamic code has shown good agreement with other published data. This code has also been incorporated into an existing aeroelastic code to analyze the NASA Lewis supersonic through-flow fan design.

Ramsey, John K.↗

Thermoelastic damping and its effect on flutter of stressed panels situated in a supersonic airflow

The effects of material damping on flutter of stressed rectangular panels are studied within the context of linear thermoelasticity theory. The closed-form expression for the thermoelastic (material) damping coefficient is obtained as a function of frequency, panel temperature and dimensions, and material properties. The solution of the stability boundary value problem is obtained by use of a generalized Galerkin method in the cross stream direction which reduces the governing partial differential equations to a system of ordinary differential equations in the streamwise direction. These equations are then solved exactly. Numerical results are given for the thermoelastic damping coefficients and for the flutter speeds of partially and fully clamped panels subjected to midplane stress.

Shieh, R. C.↗