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NASA NTRS1987

Bifurcations in unsteady aerodynamics

Nonlinear algebraic functional expansions are used to create a form for the unsteady aerodynamic response that is consistent with solutions of the time dependent Navier-Stokes equations. An enumeration of means of invalidating Frechet differentiability of the aerodynamic response, one of which is aerodynamic bifurcation, is proposed as a way of classifying steady and unsteady aerodynamic phenomena that are important in flight dynamics applications. Accommodating bifurcation phenomena involving time dependent equilibrium states within a mathematical model of the aerodynamic response raises an issue of memory effects that becomes more important with each successive bifurcation.

Tobak, M.↗

NASA NTRS1987

Unsteady transonic flow simulation on a full-span-wing-body configuration

The presence of a body influences both the aerodynamic and aeroelastic performance of wings. Such effects are more pronounced in the transonic regime. To accurately account for the effect of the body, particularly when the wings are experiencing asymmetric modal motions, it is necessary to model the full configuration in the nonlinear transonic regime. In this study, full-span-wing-body configurations are simulated for the first time by a theoretical method that uses the unsteady potential equations based on the small-disturbance theory. The body geometry is modeled exactly as the physical shape, instead of as a rectangular box, which has been done in the past. Steady pressure computations for wing-body configurations compare well with the available experimental data. Unsteady pressure computations when the wings are oscillating in asymmetric modes show significant influence of the body.

Guruswamy, Guru P.↗

NASA NTRS1987

Computational unsteady aerodynamics for aeroelastic analysis

This report summarizes the status of computational unsteady aerodynamics methods for aeroelastic analysis and makes recommendations for future research activities. The flight conditions for which various types of flows exist are described and the aeroelastic phenomena that can occur in those flight regimes are discussed. Some important aeroelastic problems of current interest are described, and the aerodynamic methods needed to analyze them are presented. The capabilities and limitations of existing unsteady aerodynamics methods are discussed. Computer resources required to perform aeroelastic analysis of various flight vehicle configurations are presented. Recommendations for future research are made, and schedules for completion of proposed research tasks are presented.

Whitlow, Woodrow, Jr.↗

NASA NTRS1988

A semianalytical technique for sensitivity analysis of unsteady aerodynamic computations

A semianalytical approach is developed for the sensitivity analysis of linear unsteady aerodynamic loads. The semianalytical approach is easier to implement than the analytical approach. It is also computationally less expensive than the finite difference approach when used with panel methods, which require a large number of panels. The semianalytical approach is applied to an isolated airfoil in a 2-D flow and rotating propfan blades in 3-D flow. Sensitivity coefficients with respect to non-shape-dependent variables are shown for some cases. It is expected that the semianalytical approach will be useful in aeroelastic design procedures particularly when mistuning is present, and that it is potentially useful for shape sensitivity analysis of linear unsteady aerodynamics.

Murthy, Durbha V.↗

NASA NTRS1988

Bifurcations in unsteady aerodynamics-implications for testing

The various forms of bifurcations that can occur between steady and unsteady aerodynamic flows are reviewed. Examples are provided to illustrate the various ways in which bifurcations may intervene to influence the outcome of dynamics tests involving unsteady aerodynamics. The presence of bifurcation phenomena in such tests must be taken into consideration to ensure the proper interpretation of results, and some recommendations are made to that end.

Chapman, Gary T.↗

NASA NTRS1988

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Tiffany, Sherwood H.↗

NASA NTRS1988

An unsteady helicopter rotor: Fuselage interaction analysis

A computational method was developed to treat unsteady aerodynamic interactions between a helicopter rotor, wake, and fuselage and between the main and tail rotors. An existing lifting line prescribed wake rotor analysis and a source panel fuselage analysis were coupled and modified to predict unsteady fuselage surface pressures and airloads. A prescribed displacement technique is used to position the rotor wake about the fuselage. Either a rigid blade or an aeroelastic blade analysis may be used to establish rotor operating conditions. Sensitivity studies were performed to determine the influence of the wake fuselage geometry on the computation. Results are presented that describe the induced velocities, pressures, and airloads on the fuselage and on the rotor. The ability to treat arbitrary geometries is demonstrated using a simulated helicopter fuselage. The computational results are compared with fuselage surface pressure measurements at several locations. No experimental data was available to validate the primary product of the analysis: the vibratory airloads on the entire fuselage. A main rotor-tail rotor interaction analysis is also described, along with some hover and forward flight.

Lorber, Peter F.↗

NASA NTRS1988

Numerical simulation of unsteady incompressible viscous flows in generalized coordinate systems

Several numerical solutions of the three dimensional unsteady incompressible Navier-Stokes equations in generalized coordinate systems are presented. The governing equations are discretized by finite volumes with special care to the accurate approximation of the geometric quantities. The unknowns are the pressure and the volume fluxes over the computational cell faces. This formulation results in a robust fractional step solution method for solving discrete equations. Although this method is formulated for the three dimensional case, only two dimensional unsteady results are given. Results are presented for a lid driven two dimensional cavity flow at Reynolds number of 10,000, and for the flow over a circular cylinder with vortex shedding for several Reynolds numbers in the range 100 less than Re less than 1000.

Rosenfeld, Moshe↗

NASA NTRS1987

An unsteady rotor/fuselage interaction method

An analytical method has been developed to treat unsteady helicopter rotor, wake, and fuselage interaction aerodynamics. An existing lifting line/prescribed wake rotor analysis and a source panel fuselage analysis were modified to predict vibratory fuselage airloads. The analyses were coupled through the induced flow velocities of the rotor and wake on the fuselage and the fuselage on the rotor. A prescribed displacement technique was used to distort the rotor wake about the fuselage. Sensitivity studies were performed to determine the influence of wake and body geometry on the computed airloads. Predicted and measured mean and unsteady pressures on a cylindrical body in the wake of a two-bladed rotor were compared. Initial results show good qualitative agreement.

Egolf, T. Alan↗

NASA NTRS1988

Unsteady transonic algorithm improvements for realistic aircraft applications

Improvements to a time-accurate approximate factorization (AF) algorithm have been implemented for steady and unsteady transonic analysis of realistic aircraft configurations. The algorithm improvements include: an Engquist-Osher (E-O) type-dependent switch to more accurately and efficiently treat regions of supersonic flow, extension of the E-O switch for second-order spatial accuracy in these regions, nonreflecting far field boundary conditions for more accurate unsteady applications, and several modifications which accelerate convergence to steady-state. Calculations are presented for several configurations to evaluate the algorithm modifications. The modifications have significantly improved the stability of the AF algorithm and hence the reliability of the CAP-TSD code in general.

Batina, John T.↗

NASA NTRS1988

Some numerical and physical aspects of unsteady Navier-Stokes computations over airfoils using dynamic meshes

An upwind-biased implicit approximate factorization algorithm is applied to several unsteady flows on dynamic meshes. The thin-layer form of the compressible Navier-Stokes equations is used to solve both laminar and turbulent flows over airfoils pitching about the quarter chord. Numerical aspects of the solutions are investigated, including grid and time step effects. Two methods for determining fluxes - flux-vector splitting and flux-difference splitting - are compared. Flux-difference splitting predicts results more accurately than flux-vector splitting on a coarse mesh, but both methods agree on a fine mesh. Physical aspects of the computations are also examined. An equilibrium turbulent boundary layer model computes generally better unsteady results in comparison with experiment than a nonequilibrium model for the transonic case analyzed. Also, the size and location of the primary shed vortex for an airfoil pitching up at a constant rate is calculated in good agreement with experiment for two pitch rates.

Rumsey, Christopher L.↗

NASA NTRS1988

Prediction of unsteady loads on maneuvering delta wings using time-accurate Euler schemes

Three-dimensional steady and unsteady vortex-dominated flows around sharp-edged delta wings are considered in this paper. The problem is formulated by using the unsteady conservative Euler equations for the flow relative motion with respect to a moving frame of reference. An implicit approximately-factored finite volume scheme is used to solve the resulting equations on a three-dimensional computational grid which is generated by using a modified Joukowski transformation in cross-flow planes at the grid chord stations. The scheme is applied to a delta wing undergoing pitching oscillation around a large angle of attack. The initial conditions correspond to a steady flow around a delta wing of aspect ratio of one, freestream Mach number of 0.3 and mean angle of attack of 20.5. The steady flow results are compared with those of an explicit computational scheme and the experimental data, and they are in good agreement.

Kandil, Osama A.↗

NASA NTRS1988

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↗

NASA NTRS1988

Time-accurate unsteady aerodynamic and aeroelastic calculations for wings using Euler equations

A time-accurate approach to simultaneously solve the Euler flow equations and modal structural equations of motion is presented for computing aeroelastic responses of wings. The Euler flow eauations are solved by a time-accurate finite difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear acceleration method. The aeroelastic configuration adaptive dynamic grids are time accurately generated using the aeroelastically deformed shape of the wing. The unsteady flow calculations are validated wih experiment, both for a semi-infinite wing and a wall-mounted cantilever rectangular wings. Aeroelastic responses are computed for a rectangular wing using the modal data generated by the finite-element method. The robustness of the present approach in computing unsteady flows and aeroelastic responses that are beyond the capability of earlier approaches using the potential equations are demonstrated.

Guruswamy, Guru P.↗

NASA NTRS1987

Computation of unsteady separation using Lagrangian procedures

The interaction between increased knowledge of unsteady separation processes and computational techniques is examined, emphasizing the use of Lagrangian coordinates. Examples include boundary layer solutions of two-dimensional unsteady flows, and separation from rotating and translating spheres. Advances in Lagrangian techniques for the Navier-Stokes equations are illusrated by means of high resolution random-walk computations of the impulsively started circular cylinder.

Van Dommelen, L. L.↗

NASA NTRS1988

The role of unsteady aerodynamics in aeroacoustics

The role of acoustics and unsteady aerodynamics research in understanding the fundamental physics of time-dependent fluid phenomena is reviewed. The key issues are illustrated by considering the sound radiation of turbulent jets and the aeroacoustics of rotating bodies such as helicopter rotors. The importance of computational methods as a link between aerodynamics and acoustics is also discussed. It is noted that where acoustic analogy techniques are sufficiently accurate, unsteady aerodynamics can be used for acoustic prediction. In supersonic problems where acoustics and aerodynamics are coupled, an integrated nonlinear analysis can provide an accurate problem solution.

Pao, S. Paul↗

NASA NTRS1989

CAP-TSD: A program for unsteady transonic analysis of realistic aircraft configurations

The development of a new transonic code to predict unsteady flows about realistic aircraft configurations are described. An approximate factorization algorithm for solution of the unsteady transonic small disturbance equation is first described. Because of the superior stability characteristics of the AF algorithm, a new transonic aeroelasticity code was developed which is described in some detail. The new code was very easy to modify to include the additional aircraft components, so in a very short period of time the code was developed to treat complete aircraft configurations. Finally, applications are presented which demonstrate many of the geometry capabilities of the new code.

Batina, John T.↗

NASA NTRS1989

An efficient method for computing unsteady transonic aerodynamics of swept wings with control surfaces

A transonic equivalent strip (TES) method was further developed for unsteady flow computations of arbitrary wing planforms. The TES method consists of two consecutive correction steps to a given nonlinear code such as LTRAN2; namely, the chordwise mean flow correction and the spanwise phase correction. The computation procedure requires direct pressure input from other computed or measured data. Otherwise, it does not require airfoil shape or grid generation for given planforms. To validate the computed results, four swept wings of various aspect ratios, including those with control surfaces, are selected as computational examples. Overall trends in unsteady pressures are established with those obtained by XTRAN3S codes, Isogai's full potential code and measured data by NLR and RAE. In comparison with these methods, the TES has achieved considerable saving in computer time and reasonable accuracy which suggests immediate industrial applications.

Liu, D. D.↗