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NASA NTRS1973

The application of general aerodynamic lifting surface elements to problems in unsteady transonic flow

A study was conducted to investigate the feasibility of using combined subsonic and supersonic linear theory as a means for solving unsteady transonic flow problems in an economical and yet realistic manner. With some modification, existing linear theory methods are combined into a single program and a simple algorithm is derived for determining interference between lifting surface elements of different Mach number. The method is applied to a wide variety of problems for which measured unsteady pressure distributions and Mach number distributions are available. By comparing theory and experiment, the transonic method solutions show a significant improvement over uniform flow solutions. It is concluded that with these refinements the method will provide a means for performing realistic transonic flutter and dynamic response analyses at costs which are compatible with current linear theory based solutions.

Cunningham, A. M., Jr.↗

NASA NTRS1974

Topics in structural dynamics: Nonlinear unsteady transonic flows and Monte Carlo methods in acoustics

The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.

Haviland, J. K.↗

NASA NTRS1978

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.↗

NASA NTRS1986

User's manual for XTRAN2L (version 1.2): A program for solving the general-frequency unsteady transonic small-disturbance equation

The development, use and operation of the XTRAN2L program that solves the two dimensional unsteady transonic small disturbance potential equation are described. The XTRAN2L program is used to calculate steady and unsteady transonic flow fields about airfoils and is capable of performing self contained transonic flutter calculations. Operation of the XTRAN2L code is described, and tables defining all input variables, including default values, are presented. Sample cases that use various program options are shown to illustrate operation of XTRAN2L. Computer listings containing input and selected output are included as an aid to the user.

Seidel, D. A.↗

NASA NTRS1988

Effects of symmetric and asymmetric modes on transonic aeroelastic characteristics of full-span wing-body configurations

To accurately study 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 asymmetric modes are also made to study the influence of modal asymmetry on responses. This new development is further illustrated by computing 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.

Guruswamy, Guru P.↗

NASA NTRS1989

AGARD standard aeroelastic configurations for dynamic response

Since emphasis is on the transonic speed range, special importance is placed on configurations for which available data are sufficient to define accurately a transonic flutter boundary. Only configurations with clean, smooth surfaces are considered suitable. Segmented models or models with surface-slope discontinuities are inappropriate. Excluded also, in general, are configurations and data sets that involve behavior that is uncertain or not well understood, uncertain model properties, or know sensitivities to small variations in model properties. In order to assess the suitability of configurations already tested and the associated data for designation as standard, a survey of AGARD member countries was conducted to seek candidates for the prospective set. The results of that survey are given and summarized along with the initial selection of a standard configuration.

Yates, E. Carson, Jr.↗

NASA NTRS1989

Computational aeroelasticity challenges and resources

In the past decade, there has been much activity in the development of computational methods for the analysis of unsteady transonic aerodynamics about airfoils and wings. Significant features are illustrated which must be addressed in the treatment of computational transonic unsteady aerodynamics. The flow regimes for an aircraft on a plot of lift coefficient vs. Mach number are indicated. The sequence of events occurring in air combat maneuvers are illustrated. And further features of transonic flutter are illustrated. Also illustrated are several types of aeroelastic response which were encountered and which offer challenges for computational methods. The four cases illustrate problem areas encountered near the boundaries of aircraft envelopes, as operating condition change from high speed, low angle conditions to lower speed, higher angle conditions.

Edwards, John W.↗

NASA NTRS1991

Aeroelastic modeling of the active flexible wing wind-tunnel model

The primary issues involved in the generation of linear, state-space equations of motion of a flexible wind tunnel model, the Active Flexible Wing (AFW), are discussed. The codes that were used and their inherent assumptions and limitations are also briefly discussed. The application of the CAP-TSD code to the AFW for determination of the model's transonic flutter boundary is included as well.

Silva, Walter A.↗

NASA NTRS2001

Use of Pressure Sensitive Paint for Diagnostics in Turbomachinery Flows With Shocks

The technology of pressure sensitive paint (PSP) is well established in external aerodynamics. In internal flows in narrow channels and in turbomachinery cascades, however, there are still unresolved problems. In particular, the internal flows with complex shock structures inside highly curved channels present a challenge. It is not always easy and straightforward to distinguish between true signals and "ghost" images due to multiple internal reflections in narrow channels. To address some of the problems, investigations were first carried out in a narrow supersonic channel of Mach number 2.5. A single wedge or a combination of two wedges were used to generate a complex shock wave structure in the flow. The experience gained in a small supersonic channel was used for surface pressure measurements on the stator vane of a supersonic throughflow fan. The experimental results for several fan operating conditions are shown in a concise form, including performance map points, midspan static tap pressure distributions, and vane suction side pressure fields. Finally, the PSP technique was used in the NASA transonic flutter cascade to compliment flow visualization data and to acquire backwall pressure fields to assess the cascade flow periodicity. A summary of shortcomings of the pressure sensitive paint technology for internal flow application and lessons learned are presented in the conclusion of the paper.

Lepicovsky, Jan↗

NASA NTRS2004

An Overview of Recent Developments in Computational Aeroelasticity

The motivation for Computational Aeroelasticity (CA) and the elements of one type of the analysis or simulation process are briefly reviewed. The need for streamlining and improving the overall process to reduce elapsed time and improve overall accuracy is discussed. Further effort is needed to establish the credibility of the methodology, obtain experience, and to incorporate the experience base to simplify the method for future use. Experience with the application of a variety of Computational Aeroelasticity programs is summarized for the transonic flutter of two wings, the AGARD 445.6 wing and a typical business jet wing. There is a compelling need for a broad range of additional flutter test cases for further comparisons. Some existing data sets that may offer CA challenges are presented.

Bennett, Robert M.↗

NASA NTRSDate not supplied

Investigation of Aerodynamic Matching Sensitivities for Conceptual Design

A methodology for aerodynamic matching was implemented in the Higher fidelity Conceptual Design and structural optimization (HCDstruct) tool to support transonic flutter simulations. The Enhanced Factor Correction Technique was implemented in HCDstruct to correct the Nastran doublet lattice method using data from corresponding computational fluid dynamics simulations. In this paper, sensitivities associated with this aerodynamic matching technique were investigated using HCDstruct and a Boeing 737-200-like aircraft configuration. Specifically, sensitivities of the aerodynamic matching method were investigated with respect to changes in flight conditions, such as changes in Mach number and angle of attack, and also in key design variables for the main wing, such as changes in aspect ratio and sweep angle. The variations in flight conditions and design parameters were mapped to estimated prediction error in sectional lift for the main wing, which helps to demonstrate the extent to which a user may expect a given aerodynamic correction matrix to provide suitable aerodynamic predictions for a realistic aircraft wing.

Jesse R. Quinlan↗

NASA NTRSDate not supplied

Investigation of Aerodynamic Matching Sensitivities for Conceptual Design

Jesse Ray Quinlan↗

NASA NTRSDate not supplied

Transonic Limit Cycle Oscillations of the Benchmark Supercritical Wing

This paper considers transonic flutter mechanisms of the Benchmark Supercritical Wing, a model under study in the Aeroelastic Prediction Workshop series. Flutter boundaries are mapped out across an angle of attack sweep at Mach 0.8, utilizing both time-domain and linearized frequency-domain solvers, manual meshes and adapted meshes, and various governing equations. With increased angle of attack, linearized and finite amplitude flutter predictions exhibit differences above 3◦ as the flow begins to separate; the latter predictions are found to be driven by subcritical limit cycle oscillations whose strength increases with angle of attack. Moderate perturbation values provide a stability boundary at 5◦ which matches the experimental data, but it is not clear how the experimental perturbation, from one test condition to the next, can be reasonably characterized.

Bret Stanford↗

NASA NTRS1974

Transonic single-mode flutter and buffet of a low aspect ratio wing having a subsonic airfoil shape

Transonic flutter and buffet results obtained from wind-tunnel tests of a low aspect ratio semispan wing model are presented. The tests were conducted to investigate potential transonic aeroelastic problems of vehicles having subsonic airfoil sections. The model employed NACA 00XX-64 airfoil sections in the streamwise direction and had a 14 deg leading edge sweep angle. Aspect ratio, and average thickness were 4.0, 0.35, and 8 percent, respectively. The model was tested at Mach numbers from 0.6 to 0.95 at angles of attack from 0 deg to 15 deg. Two zero lift flutter conditions were found that involved essentially single normal mode vibrations. With boundary layer trips on the model, flutter occurred in a narrow Mach number range centered at about Mach 0.90. The frequency and motion of this flutter were like that of the first normal mode vibration. With the trips removed flutter occurred at a slightly high Mach number but in a mode strongly resembling that of the second normal mode.

Erickson, L. L.↗

NASA NTRSDate not supplied

Flutter Analysis of the Transonic Truss-Braced Wing Aircraft Using Transonic Correction

This paper describes a flutter analysis method for the Transonic Truss-Braced Wing aircraft using a vortex lattice method coupled to an unsteady transonic correction method to account for unsteady aerodynamics in transonic flow. A steady-state vortex-lattice model of the Truss-Braced Wing aircraft is developed using vortex lattice code VSPAERO. A transonic and viscous flow correction method is implemented in the VSPAERO model to account for steady-state transonic and viscous flow effects using transonic small disturbance code TSFOIL coupled to an in-house integral boundary layer code. In addition, a wing-strut interference correction method is developed to account for the transonic interference aerodynamics in the strut juncture region using high-fidelity CFD code FUN3D. A structural dynamic finite-element model of the Truss-Braced Wing aircraft is developed using BEAM3D in-house finite-element code and is coupled to the VSPAERO. The BEAM3D model includes a geometric nonlinearity due to the tension in the strut which causes a deflection-dependent nonlinear stiffness. An unsteady transonic correction method is developed to better capture the unsteady aerodynamics in transonic flow. The unsteady transonic correction method makes use of the Theodorsen’s theory to account for the amplitude and phase shift of the unsteady lift coefficient in transonic flow. A preliminary flutter analysis of the Truss-Braced Wing aircraft is conduct to illustrate the unsteady transonic correction approach.

Nhan Nguyen↗

NASA NTRS1983

A three degree-of-freedom, typical section flutter analysis using harmonic transonic air forces

Typical section flutter solutions are obtained using generalized air forces calculated with OPTRAN2, a program based on the transonic small perturbation potential equation, which uses potentials from a nonlinear solution to the steady flow to obtain linear unsteady air forces. Flutter results are calculated with a conventional, linear V-g type solution. Results are presented for a NACA 64A010 airfoil oscillating in plunge and pitch, and with a quarter-chord control surface in the Mach number range of 0.80 to 0.90. The flutter boundary shows a significant 'transonic' bucket, together with changes in flutter mode as, with increasing Mach numbers, a shock appears on the airfoil and then moves aft. Single degree-of-freedom instabilities associated with both the pitch and the control surface motions are identified.

Weatherill, W. H.↗

NASA NTRS1985

An airfoil flutter model suspension system to accommodate large static transonic airloads

A pitch/plunge flutter model suspension system and associated two-dimensional MBB-A3 airfoil models is described. The system is designed for installation in the Langley 6-by-19-inch and 6-by-18-inch transonic blowdown wind tunnels to enable systematic study of the transonic flutter characteristics and static pressure distributions of supercritical airfoils at transonic Mach numbers. A compound spring suspension concept is introduced which simultaneously meets requirements for low plunge-mode stiffness, lightweight suspended model, and large steady lift due to angle of attack without the need for excessive static deflections of the plunge spring. The system features variable pitch and plunge frequencies, changeable airfoil rotation axes, and a self aligning control system to maintain a constant mean position of the model with changing airload.

Reed, W. H., III↗

NASA NTRS2000

Test Cases for Flutter of the Benchmark Models Rectangular Wings on the Pitch and Plunge Apparatus

The supercritical airfoil was chosen as a relatively modem airfoil for comparison. The BOO12 model was tested first. Three different types of flutter instability boundaries were encountered, a classical flutter boundary, a transonic stall flutter boundary at angle of attack, and a plunge instability near M = 0.9 and for zero angle of attack. This test was made in air and was Transonic Dynamics Tunnel (TDT) Test 468. The BSCW model (for Benchmark SuperCritical Wing) was tested next as TDT Test 470. It was tested using both with air and a heavy gas, R-12, as a test medium. The effect of a transition strip on flutter was evaluated in air. The B64AOlO model was subsequently tested as TDT Test 493. Some further analysis of the experimental data for the BOO12 wing is presented. Transonic calculations using the parameters for the BOO12 wing in a two-dimensional typical section flutter analysis are given. These data are supplemented with data from the Benchmark Active Controls Technology model (BACT) given and in the next chapter of this document. The BACT model was of the same planform and airfoil as the BOO12 model, but with spoilers and a trailing edge control. It was tested in the heavy gas R-12, and was instrumented mostly at the 60 per cent span. The flutter data obtained on PAPA and the static aerodynamic test cases from BACT serve as additional data for the BOO12 model. All three types of flutter are included in the BACT Test Cases. In this report several test cases are selected to illustrate trends for a variety of different conditions with emphasis on transonic flutter. Cases are selected for classical and stall flutter for the BSCW model, for classical and plunge for the B64AOlO model, and for classical flutter for the BOO12 model. Test Cases are also presented for BSCW for static angles of attack. Only the mean pressures and the real and imaginary parts of the first harmonic of the pressures are included in the data for the test cases, but digitized time histories have been archived. The data for the test cases are available as separate electronic files. An overview of the model and tests is given, the standard formulary for these data is listed, and some sample results are presented.

Robert M Bennett↗