# Mathematical modeling of the aerodynamic characteristics in flight dynamics

01 Jan 1984-

TL;DR: The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of non linear functional expansions.

Abstract: Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

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TL;DR: In this article, the authors present a review of reduced-order aerodynamic models for aircraft stability and control analysis, including linear and nonlinear indicial response methods, Volterra theory, radial basis functions, and a surrogate-based recurrence framework.

109 citations

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TL;DR: An approach for the generation of aerodynamic tables using computational fluid dynamics is discussed, and a method to efficiently reduce the number of high-fidelity analyses is reviewed, using a kriging-based surrogate model.

106 citations

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TL;DR: The results show that the ROMs can accurately model the unsteady loads in response to slow and fast pitch and plunge motions by comparison of the model output with time-accurate CFD simulations.

Abstract: The generation of reduced-order models (ROM) for the evaluation of unsteady and nonlinear aerodynamic loads are investigated. The ROM considered is an indicial theory based on the convolution of step functions with the derivative of the input signal. The step functions are directly calculated using the results of RANS simulations and a grid movement tool. Results are reported for a two dimensional airfoil and a UCAV configuration. Wind tunnel data are first used to validate the prediction of static and unsteady coefficients at both low and high angles of attack, with good agreement obtained for all cases. The generation of the aerodynamic models is described. The focus of the paper shifts to assess the validity of studied ROMs with respect to new maneuvres. This is accomplished by comparison of the model output with time-accurate CFD simulations. The results show that the ROMs can accurately model the unsteady loads in response to slow and fast pitch and plunge motions.

81 citations

### Cites methods from "Mathematical modeling of the aerody..."

...[19,20] and a frequency-domain model based on proper orthogonal decomposition by Hall et al....

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TL;DR: In this paper, a 65-deg swept delta wing was tested in both the Institute for Aerospace Research 2 X 3 m low-speed wind tunnel and the 7 X 10 ft Subsonic Aerodynamic Research Laboratory facility at Wright-Patter son Air Force Base.

Abstract: Dynamic wind-tunnel test results of a 65-deg swept delta wing are reviewed. These tests involved bodyaxis rolling motions at moderate (15- to 35-deg) angles of attack in both the Institute for Aerospace Research 2 X 3 m low-speed wind tunnel and the 7 X 10 ft Subsonic Aerodynamic Research Laboratory facility at Wright-Patter son Air Force Base. They included static, forced oscillation, and free-to-roll experiments with flow visualization. Multiple trim points (attractors) for body-axis rolling motions and other unusual dynamic behavior were observed. These data are examined in light of the nonlinear indicial response theory. The analysis confirms the existence of critical states with respect to roll angle. When these singularities are encountered in a dynamic situation, large and persistent transients are induced. Conventional means of representing the nonlinear forces and moments hi the aircraft equations of motion, notably the locally linear model, are shown to be inadequate for these cases. Finally, the impact of these findings on dynamic testing techniques is discussed.

75 citations

01 Mar 1985

TL;DR: In this article, a mathematical model of the aerodynamic contribution to the aircraft's equations of motion is amended to accommodate aerodynamic bifurcations such as, the onset of large-scale vortex shedding.

Abstract: Aerodynamic bifurcation is defined as the replacement of an unstable equilibrium flow by a new stable equilibrium flow at a critical value of a parameter A mathematical model of the aerodynamic contribution to the aircraft's equations of motion is amended to accommodate aerodynamic bifurcations Important bifurcations such as, the onset of large-scale vortex-shedding are defined The amended mathematical model is capable of incorporating various forms of aerodynamic responses, including those associated with dynamic stall of airfoils

74 citations

### Additional excerpts

...with ~ rt n C Ldir - ~ J o an(t - ~,)[a(tl)] dt1 (5)...

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...(5), (6), ••• forms a Volterra series (Refs....

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##### References

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TL;DR: In this paper, an experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described, and an operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models.

Abstract: An experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady fiowfieids about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 are predicted and compared with experiment. Results from comparisons with experimental pressure and skin-friction distributions show improved agreement when including test-section wall boundaries in the computations. Steady-flow results were in good quantitative agreement with experimental data for flow conditions which result in relatively small regions of separated flow. For flows with larger regions of separated flow, improvements in turbulence modeling are required before good agreement with experiment will be obtained. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.

152 citations

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TL;DR: In this paper, the Strouhal number for Reynolds numbers ranging from 48 to 120 was calculated by using the measured width of the wake at the stagnation point in the wake and the result of the stability theory.

Abstract: Two kinds of experiment were made in the wake of a cylinder at Reynolds numbers ranging between 20 and 150. One was a close look at the structure of the vortex street with a stationary cylinder at Reynolds numbers greater than 48. The other experiment was made at lower Reynolds numbers with a cylinder vibrating normal to the flow direction. In this case an artificially induced small-amplitude fluctuation grows exponentially with the rate predicted by the stability theory. Because of the similarity between the two kinds of wake, we postulate that the shedding of the vortex at low Reynolds numbers is initiated by the linear growth, namely, the fluctuation with the frequency of maximum linear growth rate develops into vortex streets. By using the measured width of the wake at the stagnation point in the wake and the result of the stability theory, we could calculate the Strouhal number for Reynolds numbers ranging from 48 to 120. The predicted Strouhal numbers agree well with the values from direct measurements.

118 citations

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TL;DR: Aerodynamics of bodies of revolution in nonplanar motion using nonlinear functional analysis of moments for motion about center of gravity is described in this paper. But the analysis is restricted to a single body of revolution.

Abstract: Aerodynamics of bodies of revolution in nonplanar motion using nonlinear functional analysis of moments for motion about center of gravity

58 citations

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TL;DR: The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation as discussed by the authors, which is in agreement with experimentally determined buffet boundaries, especially at higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

Abstract: The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

15 citations

01 Feb 1981

TL;DR: The results of computer code time dependent solutions of the two dimensional compressible Navier-Stokes equations and the results of independent experiments are compared to verify the Mach number range for instabilities in the transonic flow field about a 14 percent thick biconvex airfoil at an angle of attack of 0 deg and a Reynolds number of 7 million.

Abstract: Results of computer code time dependent solutions of the two dimensional compressible Navier-Stokes equations and the results of independent experiments are compared to verify the Mach number range for instabilities in the transonic flow field about a 14 percent thick biconvex airfoil at an angle of attack of 0 deg and a Reynolds number of 7 million. The experiments were conducted in a transonic, slotted wall wind tunnel. The computer code included an algebraic eddy viscosity turbulence model developed for steady flows, and all computations were made using free flight boundary conditions. All of the features documented experimentally for both steady and unsteady flows were predicted qualitatively; even with the above simplifications, the predictions were, on the whole, in good quantitative agreement with experiment. In particular, predicted time histories of shock wave position, surface pressures, lift, and pitching moment were found to be in very good agreement with experiment for an unsteady flow. Depending upon the free stream Mach number for steady flows, the surface pressure downstream of the shock wave or the shock wave location was not well predicted.

9 citations