Development of an indicial function approach for the two-dimensional incompressible/compressible aerodynamic load modelling

Abstract

By using a combined analytical-computational methodology, a unified modelling of aerodynamic indicial functions covering the incompressible, subsonic compressible, transonic, and supersonic flight speed regimes is presented. The procedure is carried out in conjunction with a computational fluid dynamic analysis. For a plunging-pitching airfoil, selected unsteady aerodynamic load expressions have been supplied, and appropriate procedures enabling one to obtain these loads via the indicial function approach have been presented. While a single indicial function is needed to describe the aerodynamic loads in the incompressible flight speed regime, for cases where the compressibility effects play a dominant role, four indicial functions are needed. Having in view the usefulness of indicial functions towards determination of unsteady aerodynamics loads in both time and frequency domains, and implicitly for aeroelastic response and flutter predictions, the advantages of their implementation and use appear evident. Comparisons and validations of the aerodynamic model against numerical, analytical, and experimental results are presented, and pertinent conclusions are drawn.Keywords: linear/non-linear indicial aerodynamic functions, incompressible and compressible flight speed regimes, two-degrees-of-freedom airfoil aerodynamics JAERO88

Nonlinear aeroelastic analysis of high-aspect-ratio wings using indicial aerodynamics

“…where over bar indicates the quantities associated with the leading edge. Many researches have been carried out to determine an approximate form of the indicial function in the subsonic compressible flow [7,8,[14][15][16][18][19][20]. For practical computational purposes including efficiency and simplicity in the aeroelastic analysis, the indicial functions are usually expressed in the exponential form as…”

“…Separating indicial aerodynamic response to non-circulatory and circulatory parts, Leishman [7], approximated the total unsteady indicial lift and pitching moment functions with series of three exponential terms to step changes in angle of attack and pitching rate in subsonic compressible flow. Marzocca et al [18,19] presented the aerodynamic loads of a 2D airfoil subject to translational and pitching motions using a method based on linear/nonlinear indicial functions for various flight speed regimes. Farsadi and Javanshir [20] proposed a new exponential approximation of Mach-dependent indicial functions in the compressible flow regime that are restricted to Mach numbers from 0.5 to 0.8.…”

Effect of thrust on the aeroelastic instability of a composite swept wing with two engines in subsonic compressible flow

“…Extracting the aerodynamic indicial functions for some flight speed regimes, Marzocca et al (2002) studied the aeroelastic stability of a 2D airfoil in compressible flow. Marzocca et al (2006) also proposed a unified approach for the aerodynamic indicial functions to cover the incompressible and compressible flight speed regimes. Based on the indicial functions approach, Mazelsky and Drischler (1952) and Mazelsky (1952) presented an unsteady aerodynamic model in compressible subsonic flow by which the lift and twist moment distributions about the elastic axis of the wing were expressed via the strip theory as…”

Semi-Analytical Reduced-Order Models for the Unsteady Aerodynamic Loads of Subsonic Wings

“…For wings undergoing small variations in the effective angle of attack due to either aircraft motion or vertical gust occurrence [12], the circulatory unsteady airload due to each flow perturbation can conveniently be formulated in terms of Duhamel convolution [13] of the latter with the relative lift-deficiency indicial function [14][15][16]; the contributions of all flow perturbations are then linearly superposed [17][18]. Assuming incompressible potential flow [19], Wagner and Kussner derived the lift-deficiency functions due to a unitary step change in the angle of attack [20] and a unitary sharp-edged vertical gust [21][22] for a thin flat airfoil in the (reduced) time domain, respectively, while Theodorsen [23] and Sears [24][25] solved the same problems in the (reduced) frequency domain.…”