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

Abstract

Abstract. Different semi-analytical reduced-order models for calculating the unsteady aerodynamic loads of subsonic slender wings are proposed. The lift-deficiency functions due to

Semi-Analytical Reduced-Order Models for the Aeroelastic Behavior of Subsonic Flexible Wings via Generalised Plate and Beam Formulations

“…Analogously, the equivalent of Wagner function is suitably approximated with two exponential terms [22,67] Finally, the equivalent of Kussner function is consistently approximated with two exponential terms [22,67] in the reduced time domain too, namely:…”

“…whereas Theodorsen k C and (modified) Sears k C G functions are defined as [26][27][28]: The sectional lift-deficiency coefficient, the related circulation and the wing's downwash gradient may then be approximated as [22,103]: accounts for the initial wake length being set equal to the mean geometric chord and complying with the unsteady realisation of Kutta condition [20,21]. Due to Laplace transformation, the integral convolution process can thus be written as [22]:…”

“…Due to rigorous analytical continuation [41], with s the Laplace variable, a rational approximation [22,67] is suitably adopted for the equivalent of Theodorsen function in the complex reduced frequency p domain, namely:…”

“…Considering all contributions due to bound, trailed and shed vortices of the vortex-ring, the lift-deficiency coefficient from a unit step in the angle of attack is then calculated based on Kutta-Joukowsky theorem and Biot-Savart law as [21][22] …”

“…Modified strip theory (MST) is adopted for the aerodynamic load [15][16], tuned strip theory (TST) being readily resumed for comparison and completeness [17][18]. Peters' in-flow theory is adopted for calculating the two-dimensional unsteady airload around each morphing wing section [19], where approximate lift-deficiency functions [20][21][22] for both a unit step-change in the angle of attack and a unit sharp-edged gust are employed in place of classic Theodorsen/Wagner's and Sears/Kussner's functions [23][24][25][26][27][28], respectively. Both plate-like and beam-like linear models are considered for the structural dynamics, within a unified formulation [29][30].…”