Efficient Computation of Unsteady Aerodynamic Loads Using Computational-Fluid-Dynamics Linearized Methods
Abstract
In the present work, generalized aerodynamic forces concerning the time and frequency domains are analyzed. Thereby, the transonic flow regime is of main interest. For this purpose, the low-frequency structural modes of the AGARD 445.6 wing and a wing–fuselage configuration known as the fuselage cropped delta wing are used to compute the corresponding generalized aerodynamic forces with the Euler methods AER-Eu (nonlinear, time domain) and AER-SDEu (linear, frequency domain). Furthermore, a reduced-order model based on the AER-Eu solver is generated as a linear state-space model for fast computations of generalized aerodynamic forces in the discrete time domain. This is realized by recording the responses of the AER-Eu solver to a set of orthogonal step functions. The resulting time series are further processed to extract the impulse responses required for the system identification with the Eigensystem-Realization Algorithm. The transfer of the time domain results into frequency domain is achieved via the Fourier analysis of the time series of the harmonic responses and the extracted impulse responses for modal movement of the body. It is shown that the linear state-space reduced-order model based on appropriate computational-fluid-dynamics conditioning is an efficient way for the computation of generalized aerodynamic forces required in linear aeroelastic analysis.
References
[1] , Introduction to Aircraft Aeroelasticity and Loads, Wiley, West Sussex, England, U.K., 2007, pp. 22–34, 433–434.
[2] , “An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction,” Journal of Guidance, Vol. 8, No. 5, 1984, pp. 620–627. doi:https://doi.org/10.2514/3.20031
[3] , “Development of Reduced-Order Models for Aeroelastic Analysis and Flutter Prediction Using the CFL3Dv6.0 Code,” Journal of Fluids and Structures, Vol. 19, No. 5, 2004, pp. 729–745. doi:https://doi.org/10.1016/j.jfluidstructs.2004.03.004 0889-9746
[4] , “Calculations with ERA Based Reduced Order Aerodynamic Models,” 24th Applied Aerodynamics Conference, AIAA, San Francisco, CA, June 2006; also AIAA Paper 2006-2999.
[5] , “An Optimal Reduced-Order Aeroelastic Modeling Based on a Response-Based Modal Analysis of Unsteady CFD Models,” 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, AIAA, Seattle, WA, April 2001; also AIAA Paper 2001-1525.
[6] , “Efficient Reduced-Order System Identification for Linear Systems with Multiple Inputs,” AIAA Journal, Vol. 43, No. 7, 2005, pp. 1455–1464. doi:https://doi.org/10.2514/1.11225 AIAJAH 0001-1452
[7] , “Aeroelastic Model Reduction for Affordable Computational Fluid Dynamics-Based Flutter Analysis,” AIAA Journal, Vol. 43, No. 12, 2005, pp. 2487–2495. doi:https://doi.org/10.2514/1.11246 AIAJAH 0001-1452
[8] , “Simultaneous Excitation of Multiple-Input/Multiple-Output CFD-Based Unsteady Aerodynamic Systems,” Journal of Aircraft, Vol. 45, No. 4, 2008, pp. 1267–1274. doi:https://doi.org/10.2514/1.34328 JAIRAM 0021-8669
[9] , “Development of Unsteady Aerodynamic and Aeroelastic Reduced-Order Models Using the FUN3D Code,” Proceedings of the International Forum on AeroElasticity and Structural Dynamics, IFASD, Seattle, WA , 2009; also IFASD Paper 2009-030.
[10] , “AGARD Standard Aeroelastic Configuration for Dynamic Response. Candidate Configuration I. Wing 445.6,” NASA TM-100492, 1987.
[11] , “Linear Flutter Prediction for Low Aspect Ratio Wings Using a Small Disturbance Euler Method,” Proceedings of the International Forum on Aeroelasticity and Structural Dynamics, 2009; also IFASD Paper 2009-055.
[12] , Applied System Identification, Prentice–Hall, New York, 1994, pp. 133–228.
[13] , “System/Observer/Controller Identification Toolbox,” NASA TM-107566, 1992.
[14] , “Approximate Riemann Solvers, Parameter Vectors and Difference Schemes,” Journal of Computational Physics, Vol. 43, No. 2, 1981, pp. 357–372. doi:https://doi.org/10.1016/0021-9991(81)90128-5 JCTPAH 0021-9991
[15] , “Implicit Schemes and LU-Decompositions,” Mathematics of Computation, Vol. 37, No. 156, 1981, pp. 385–397. doi:https://doi.org/10.1090/S0025-5718-1981-0628702-9 MCMPAF 0025-5718
[16] , “Small Disturbance Euler Equations: Efficient and Accurate Tool for Unsteady Load Prediction,” Journal of Aircraft, Vol. 37, No. 5, 2000, pp. 770–778. doi:https://doi.org/10.2514/2.2699 JAIRAM 0021-8669
[17] , “Small Disturbance Navier–Stokes Method: Efficient Tool for Predicting Unsteady Air Loads,” Journal of Aircraft, Vol. 43, No. 1, 2006, pp. 17–29. doi:https://doi.org/10.2514/1.14350 JAIRAM 0021-8669
[18] , “Small Disturbance Navier–Stokes Computations for Low-Aspect-Ratio Wing Pitching Oscillations,” Journal of Aircraft, Vol. 47, No. 3, 2010, pp. 737–753. doi:https://doi.org/10.2514/1.45233 JAIRAM 0021-8669
[19] , “Small Disturbance Navier–Stokes Computations Employing the Wilcox k-Omega Turbulence Model,” 27th Congress of International Council of the Aeronautical Sciences, ICAS, Nice, France, 2010; also ICAS Paper 2010-3.10.5.
[20] , “Effective Construction of Linear State-Variables Models from Input/Output Data” Regelungstechnik, Vol. 14, 1966, pp. 545–548. RLSTA5 0370-6001
[21] , “Development of Unsteady Aerodynamic State-Space Models from CFD-Based Pulse Responses,” 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, AIAA, Seattle, WA, April 2001; also AIAA Paper 2001-1213.
[22] , “Identification of Observer/Kalman Filter Markov Parameters: Theory and Experiments” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 2, 1993, pp. 320–329. doi:https://doi.org/10.2514/3.21006 JGCDDT 0162-3192
[23] , “Verfahren Reduzierter Ordnung zur Berechnung Generalisierter Luftkräfte,” Deutsche Gesellschaft für Luft- und Raumfahrtkongress Paper 2010-161220, Sept. 2010.
[24] , “Using Orthogonal Functions for Identification and Sensitivity Analysis of Mechanical System,” Journal of Vibration and Control, Vol. 8, No. 7, 2002, pp. 993–1021. doi:https://doi.org/10.1177/107754602029583 1741-2986
[25] ANSYS ICEM CFD 12.0 User Manual, Ansys, Canonsburg, PA, 2009.
[26] MATLAB 7.9, MathWorks, Natick, MA, 2009.