Comparison of theory and experiment for nonlinear flutter of loaded plates
Flutter analysis of plates with inplane boundary support flexibility exposed to transverse pressure loading or buckled by uniform thermal expansion
Dowell, E. H.↗
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Application to rotary wings of a simplified aerodynamic lifting surface theory for unsteady compressible flow
A general method of predicting airloads is applied to helicopter rotor blades on a full three-dimensional basis using the general theory developed for a rotor blade at the psi = pi/2 position where flutter is most likely to occur. Calculations of aerodynamic coefficients for use in flutter analysis are made for forward and hovering flight with low inflow. The results are compared with values given by two-dimensional strip theory for a rigid rotor hinged at its root. The comparisons indicate the inadequacies of strip theory for airload prediction. One important conclusion drawn from this study is that the curved wake has a substantial effect on the chordwise load distribution.
Rao, B. M.↗
Calculation of subsonic and supersonic steady and unsteady aerodynamic forces using velocity potential aerodynamic elements
Expressions for calculation of subsonic and supersonic, steady and unsteady aerodynamic forces are derived, using the concept of aerodynamic elements applied to the downwash velocity potential method. Aerodynamic elements can be of arbitrary out of plane polygon shape, although numerical calculations are restricted to rectangular elements, and to the steady state case in the supersonic examples. It is suggested that the use of conforming, in place of rectangular elements, would give better results. Agreement with results for subsonic oscillating T tails is fair, but results do not converge as the number of collocation points is increased. This appears to be due to the form of expression used in the calculations. The methods derived are expected to facilitate automated flutter analysis on the computer. In particular, the aerodynamic element concept is consistent with finite element methods already used for structural analysis. The method is universal for the complete Mach number range, and, finally, the calculations can be arranged so that they do not have to be repeated completely for every reduced frequency.
Haviland, J. K.↗
Some examples of unsteady transonic flows over airfoils
A finite difference flutter analysis is presented for the NACA 64A-410 airfoil at M equals 0.72, where the incidence is abruptly changed from 2 to 4 degrees. The effect of gust loads is studied, and the unsteady flow adjusting process is displayed. The semi-implicit procedure of Ballhaus and Lomax (1974) is used to solve the small disturbance transonic potential equation. The physical aspects of the results, rather than the numerical details, are emphasized.
Ballhaus, W. F.↗
On least squares approximations to indefinite problems of the mixed type
A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.
Fix, G. J.↗
An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.
Ehlers, F. E.↗
Unsteady Newton-Busemann flow theory. III - Frequency dependence and indicial response
Hui and Tobak applied the complete unsteady Newton-Busemann flow theory to the study of dynamic stability of oscillating aerofoils and bodies in revolution. The present article extends the results to general frequencies that may be applicable to flutter analysis. The results are likewise applied to the indicial response fluctuations in unsteady flow at very high Mach numbers. The study shows that for a group of body shapes in Newtonian flow (including the cone and wedge), the aerodynamic response to a step change in angle of attack or pitching velocity contains an initial-instant impulse followed by a rapid adjustment to the new steady-flow conditions. The impulse component is in effect an apparent mass term analogous to that which occurs initially in the aerodynamic indicial response at the zero Mach number limit.
Hui, W. H.↗
Dynamics and control of large space structures
An attempt is made to gather data useful to investigators in the fields of large space structure dynamics and control modeling, design and testing. Attention is given to structural dynamics and its relationship to such allied engineering fields as flutter analysis, as well as to problems in the prediction of atmospheric density at orbital altitude. The first challenge posed by large space structure control is the design of control systems with natural frequencies above several major structural frequencies. The establishment of a sufficiently accurate structural model, plant excitation, and shape maintenance, are noted to be additional problems.
Nurre, G. S.↗
Approximations to eigenvalues of modified general matrices
The reanalysis of non-self-adjoint dynamic models is computationally very expensive in design optimization applications. This paper describes several approximations that can be applied to eigenvalues of non-hermitian matrices to reduce that computational cost. Approximations based on eigenvalue derivatives, generalized Rayleigh quotient and the trace theorem are presented and their accuracy and computational cost are estimated. The accuracy and cost estimates are verified by applying the approximations to random matrices and matrices arising in flutter analysis of compressor blades. Recommendations are made for selection of the best approximation when the derivatives are available and when they are not. In particular, it is concluded that the quadratic approximation for eigenvalues should never be used as higher order approximations are always more accurate as well as more efficient.
Murthy, Durbha V.↗
A streamwise upwind algorithm for the Euler and Navier-Stokes equations applied to transonic flows
A new algorithm was developed for the Euler and Navier-Stokes equations that uses upwind differencing based on the streawise direction. This algorithm is time accurate and can be used in codes for calculating unsteady transonic flows over wings. Such codes can be used for the flutter analysis of wings. In this algorithm, the coordinate system is locally rotated to align with the streamwise direction. For differencing the convective terms in the streamwise direction, a new form of flux splitting is employed, in which the biasing depends on the local Mach number. In the plane perpendicular to the stream direction, the new flux splitting uses the condition of no flow in that local plane. By using a locally rotated coordinate system, the convective flux vector biasing depends on the total Mach number. Hence, the switching of the flux vector biasing occurs across shock waves and the proper domain of dependence is used in supersonic regions. For comparison, many other upwind methods switch differencing based on Mach number of shock waves in multidimensional flows. The formulas for the convective flux vector differencing do not contain any user specified parameters. So, the amount of numerical dissipation is automatically determined.
Goorjian, Peter M.↗
Evaluation of the constant pressure panel method (CPM) for unsteady air loads prediction
This paper evaluates the capability of the constant pressure panel method (CPM) code to predict unsteady aerodynamic pressures, lift and moment distributions, and generalized forces for general wing-body configurations in supersonic flow. Stability derivatives are computed and correlated for the X-29 and an Oblique Wing Research Aircraft, and a flutter analysis is carried out for a wing wind tunnel test example. Most results are shown to correlate well with test or published data. Although the emphasis of this paper is on evaluation, an improvement in the CPM code's handling of intersecting lifting surfaces is briefly discussed. An attractive feature of the CPM code is that it shares the basic data requirements and computational arrangements of the doublet lattice method. A unified code to predict unsteady subsonic or supersonic airloads is therefore possible.
Appa, Kari↗
Assessment Of Semi-Empirical Dynamic Stall Models For Turboprop Stall Calculations
Report presents comparison of stall-flutter responses obtained from three semiempirical dynamic stall models. Part of effort to develop models for stall-flutter analysis of highly loaded propellers (advanced turboprops). Available models of dynamic stall applied to simple structural models to study extent of validity and select appropriate model for application to advanced turboprops. Conclusion during study is operating environment of advanced turboprop favors conditions of light stall, in which loads induced by vortexes not severe.
Kaza, K. R. V.↗
Role of computational fluid dynamics in unsteady aerodynamics for aeroelasticity
In the last two decades there have been extensive developments in computational unsteady transonic aerodynamics. Such developments are essential since the transonic regime plays an important role in the design of modern aircraft. Therefore, there has been a large effort to develop computational tools with which to accurately perform flutter analysis at transonic speeds. In the area of Computational Fluid Dynamics (CFD), unsteady transonic aerodynamics are characterized by the feature of modeling the motion of shock waves over aerodynamic bodies, such as wings. This modeling requires the solution of nonlinear partial differential equations. Most advanced codes such as XTRAN3S use the transonic small perturbation equation. Currently, XTRAN3S is being used for generic research in unsteady aerodynamics and aeroelasticity of almost full aircraft configurations. Use of Euler/Navier Stokes equations for simple typical sections has just begun. A brief history of the development of CFD for aeroelastic applications is summarized. The development of unsteady transonic aerodynamics and aeroelasticity are also summarized.
Guruswamy, Guru P.↗
Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures
A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.
Weatherill, Warren H.↗
A streamwise upwind algorithm for the Euler and Navier-Stokes equations applied to transonic flows
A new algorithm was developed for the Euler and Navier-Stokes equations that uses upwind differencing based on the streamwise direction. This algorithm is time accurate and can be used in codes for calculating unsteady transonic flows over wings. Such codes can be used for the flutter analysis of wings. In this algorithm, the coordinate system is locally rotated to align with the streamwise direction. For differencing the convective terms in the streamwise direction, a new form of flux splitting is employed, in which the biasing depends on the local Mach number. In the plane perpendicular to the stream direction, the new flux splitting uses the condition of no flow in that local plane. By using a locally rotated coordinate system, the convective flux vector biasing depends on the total Mach number. Hence, the switching of the flux vector biasing occurs across shock waves and the proper domain of dependence is used in supersonic regions. For comparison, many other upwind methods switch differencing based on Mach number of shock wave in multidimensional flows. The formulas for the convective flux vector differencing do not contain any user specified parameters. So, the amount of numerical dissipation is automatically determined.
Goorjian, P. M.↗
Flow Visualization Study of a 1/48-Scale AFTI/F111 Model to Investigate Horizontal Tail Flow Disturbances
During flight testing of the AFTI/F111 aircraft, horizontal tail buffet was observed. Flutter analysis ruled out any aeroelastic instability, so a water-tunnel flow visualization study was conducted to investigate possible flow disturbances on the horizontal tail which might cause buffet. For this study, a 1/48-scale model was used. Four different wing cambers and one horizontal tail setting were tested between 0 and 20 deg angle of attack. These wing cambers corresponded to the following leading training edge deflections: 0/2, 10/10, 10/2, and 0/10. Flow visualization results in the form of still photographs are presented for each of the four wing cambers between 8 and 12 deg angle of attack. In general, the horizontal tail experiences flow disturbances which become more pronounced with angle of attack or wing trailing-edge deflection.
Bjarke, Lisa J.↗
FREPS - A forced response prediction system for turbomachinery blade rows
FREPS (Forced REsponse Predicition System) is a software system that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced dynamic stresses of turbomachinery blades to aerodynamic and mechanical excitations. The program performs flutter analysis also. The FREPS system uses a modal approach for aeroelastic analysis. The structural dynamic analysis is based on MSC/NASTRAN, the steady aerodynamic analysis is based on potential theory and the unsteady aerodynamic analysis is based on a linearization of the non-uniform potential mean flow. The capabilities of the program are described and illustrated by application to the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine.
Murthy, Durbha V.↗
Blasim: A computational tool to assess ice impact damage on engine blades
A portable computer called BLASIM was developed at NASA LeRC to assess ice impact damage on aircraft engine blades. In addition to ice impact analyses, the code also contains static, dynamic, resonance margin, and supersonic flutter analysis capabilities. Solid, hollow, superhybrid, and composite blades are supported. An optional preprocessor (input generator) was also developed to interactively generate input for BLASIM. The blade geometry can be defined using a series of airfoils at discrete input stations or by a finite element grid. The code employs a coarse, fixed finite element mesh containing triangular plate finite elements to minimize program execution time. Ice piece is modeled using an equivalent spherical objective that has a high velocity opposite that of the aircraft and parallel to the engine axis. For local impact damage assessment, the impact load is considered as a distributed force acting over a region around the impact point. The average radial strain of the finite elements along the leading edge is used as a measure of the local damage. To estimate damage at the blade root, the impact is treated as an impulse and a combined stress failure criteria is employed. Parametric studies of local and root ice impact damage, and post-impact dynamics are discussed for solid and composite blades.
Reddy, E. S.↗