State-Space Realizations and Internal Balancing in Potential-Flow Aerodynamics with Arbitrary Kinematics

Abstract

This paper presents a general state-space realization of the unsteady vortex-lattice method together with a bespoke model-order reduction strategy. The aim is to provide a computationally-efficient aerodynamic description suitable for integration in aeroelasticity with arbitrary kinematics. The state-space realization is obtained from linearization, around arbitrary geometries and static loading conditions, of lifting surfaces and their free wakes. All components of the forces are evaluated in time domain using Joukowski's the

Parametric Reduced-Order Modeling of the Unsteady Vortex-Lattice Method

“…We assume here that structural inputs (perturbation of displacements and velocity of the lifting surfaces) and aerodynamic outputs are both given in generalised coordinates. Non-stationary background flows can be easily added as inputs [17]…”

“…Balanced reduced-order models (ROMs) can have comparable order to the input/output dimensionality of the problem [8,[15][16][17]. They not only retain the modelling flexibility of the full-state model (e.g., to model arbitrary kinematics), but also are highly accurate and, importantly, preserve stability [8,17].…”

“…Efficient low-rank algorithms have been developed to overcome this, but they typically assume a continuous-time formulation [19], which is not available for a general UVLM. In discrete time, low-rank balancing relies either on projection techniques [20] or Smith's iteration [21,22], with the latter been recently used by the authors to construct ROMs for the UVLM [17]. However, while this approach guarantees stability and accuracy and is more efficient than direct balancing algorithms [23][24][25], it still requires relatively large computational resources.…”

“…The starting-point is a discrete-time state-space description of the LUVLM in modal coordinates [17]. The most general implementation is considered: it accounts for arbitrary kinematics of the lifting surfaces and arbitrary inflow conditions, resolves all components of the aerodynamic forces [6], and considers arbitrary wake shapes (that is, "rolled-up" wakes) at the reference condition.…”

“…Frequency-limited balanced truncation (FLBT) not only provides substantial computational savings, but also results in faster convergence rates than internally-balanced truncated ROMs [37], which unnecessary resolve the aerodynamics over the full Nyquist range [17].…”