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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Comparison of Theodorsen's Unsteady Aerodynamic Forces with Doublet Lattice Generalized Aerodynamic Forces

This paper identifies the unsteady aerodynamic forces and moments for a typical section contained in the NACA Report No. 496, "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen. These quantities are named Theodorsen's aerodynamic forces (TAFs). The TAFs are compared to the generalized aerodynamic forces (GAFs) for a very high aspect ratio wing (AR = 20) at zero Mach number computed by the doublet lattice method. Agreement between TAFs and GAFs is very-good-to-excellent. The paper also reveals that simple proportionality relationships that are known to exist between the real parts of some GAFs and the imaginary parts of others also hold for the real and imaginary parts of the corresponding TAFs.

Perry, Boyd, III↗
NASA NTRS1976

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.↗
NASA NTRS2016

Unsteady Aerodynamic Force Sensing from Measured Strain

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain using the two-step approach. Velocities and accelerations of the structure are computed using the autoregressive moving average model, on-line parameter estimator, low-pass filter, and a least-squares curve fitting method together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm. A cantilevered rectangular wing built and tested at the NASA Langley Research Center (Hampton, Virginia, USA) in 1959 is used to validate the simple approach. Unsteady aerodynamic forces as well as wing deflections, velocities, accelerations, and strains are computed using the CFL3D computational fluid dynamics (CFD) code and an MSC/NASTRAN code (MSC Software Corporation, Newport Beach, California, USA), and these CFL3D-based results are assumed as measured quantities. Based on the measured strains, wing deflections, velocities, accelerations, and aerodynamic forces are computed using the proposed approach. These computed deflections, velocities, accelerations, and unsteady aerodynamic forces are compared with the CFL3D/NASTRAN-based results. In general, computed aerodynamic forces based on the lifting surface theory in subsonic speeds are in good agreement with the target aerodynamic forces generated using CFL3D code with the Euler equation. Excellent aeroelastic responses are obtained even with unsteady strain data under the signal to noise ratio of -9.8dB. The deflections, velocities, and accelerations at each sensor location are independent of structural and aerodynamic models. Therefore, the distributed strain data together with the current proposed approaches can be used as distributed deflection, velocity, and acceleration sensors. This research demonstrates the feasibility of obtaining induced drag and lift forces through the use of distributed sensor technology with measured strain data. An active induced drag control system thus can be designed using the two computed aerodynamic forces, induced drag and lift, to improve the fuel efficiency of an aircraft. Interpolation elements between structural finite element grids and the CFD grids and centroids are successfully incorporated with the unsteady aeroelastic computation scheme. The most critical technology for the success of the proposed approach is the robust on-line parameter estimator, since the least-squares curve fitting method depends heavily on aeroelastic system frequencies and damping factors.

shape sensing↗
NASA NTRS2017

Unsteady Aerodynamic Force Sensing from Strain Data

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain using the two-step approach. Velocities and accelerations of the structure are computed using the autoregressive moving average model, on-line parameter estimator, low-pass filter, and a least-squares curve fitting method together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm.

aerodynamic load sensing↗
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 NTRS1993

Program Determines Minimum-State Approximations To Unsteady Aerodynamic Forces

MIST implements minimum-state method for determining rational approximations of matrix of aerodynamic force coefficients. Accepts complex tabular data representing generalized unsteady aerodynamic forces over set of reduced frequencies. Determines approximations to tabular data in Laplace domain by use of rational functions. Provides capability to select coefficients of denominator in rational approximations, to constrain approximation selectably without increasing size of problem, and determines and emphasizes criticial frequency ranges in determining approximations. Written in ANSI FORTRAN 77.

Karpel, Mordechay↗
NASA NTRS1989

An integrated CFD/experimental analysis of aerodynamic forces and moments

Aerodynamic analysis using computational fluid dynamics (CFD) is most fruitful when it is combined with a thorough program of wind tunnel testing. The understanding of aerodynamic phenomena is enhanced by the synergistic use of both analysis methods. A technique is described for an integrated approach to determining the forces and moments acting on a wind tunnel model by using a combination of experimentally measured pressures and CFD predictions. The CFD code used was FLO57 (an Euler solver) and the wind tunnel model was a heavily instrumented delta wing with 62.5 deg of leading-edge sweep. A thorough comparison of the CFD results and the experimental data is presented for surface pressure distributions and longitudinal forces and moments. The experimental pressures were also integrated over the surface of the model and the resulting forces and moments are compared to the CFD and wind tunnel results. The accurate determination of various drag increments via the combined use of the CFD and experimental pressures is presented in detail.

Melton, John E.↗
NASA NTRS1991

Influence of aerodynamic forces in ice shedding

Stresses in accreted ice on a typical airfoil impact ice caused by aerodynamic forces have been studied using finite element analyses. The objective of this study is to determine the significance of these stresses relative to values needed to cause ice shedding. In the case studied, stresses are not significant (less than 10 percent) when compared to the fracture value for airspeeds below a Mach number of 0.45. Above this velocity, the influence of aerodynamic forces on impact ice stresses should be considered in analyses of ice shedding.

Scavuzzo, R. J.↗
NASA NTRS1989

Vortical sources of aerodynamic force and moment

It is shown that the aerodynamic force and moment can be expressed in terms of vorticity distribution (and entropy variation for compressible flow) on near wake plane, or in terms of boundary vorticity flux on the body surface. Thus the vortical sources of lift and drag are clearly identified, which is the real physical basis of optimal aerodynamic design. Moreover, these sources are highly compact, hence allowing one to concentrate on key local regions of the configuration, which have dominating effect to the lift and drag. A detail knowledge of the vortical low requires measuring or calculating the vorticity and dilatation field, which is however still a challenging task. Nevertheless, this type of formulation has some unique advantages; and how to set up a well-posed problem, in particular how to establish vorticity-dilatation boundary conditions, is addressed.

Wu, J. Z.↗
NASA NTRS1957

Aerodynamic Forces on a Vibrating Unstaggered Cascade

The unsteady aerodynamic forces, [based on two-dimensional incompressible flow considerations], are determined for an unstaggered cascade, the blades of which are vibrating in phase in an approach flow parallel to the blades.

Soehngen, H.↗