Dynamic stall and three-dimensional wake effects on isolated rotor trim and stability with experimental correlation and parallel fast-Floquet analysis

Hingeless rotors are susceptible to instabilities of the lead-lag or lag modes, which are at best weakly damped. The lag mode derives its damping primarily from the complex rotor flow field that is driven by interdependent dynamics of airfoil stall and rotor downwash or wake. Accordingly, this dissertation investigates these stall and wake effects on lag damping predictions with a comprehensive experimental correlation. The database refers to a three-bladed rotor operated untrimmed and to a four-bladed rotor operated trimmed. For the untrimmed rotor, the database comprises stability results of lag-damping levels, and for the trimmed rotor, it comprises stability results of lag-damping levels as well as trim results of lateral and longitudinal cyclic pitch controls and steady root flap moments. The dynamic stall representation is based on the ONERA stall models and the unsteady wake is described by a finite-state three-dimensional wake model. The experimental rotor blades are represented by a rigid flap-lag and an elastic flap-lag-torsion models. The predictions are from three aerodynamic theories ranging from a quasisteady stall theory to a fairly comprehensive dynamic stall and wake theory.; This dissertation also addresses the computational aspects of lag-damping predictions by parallel Floquet analyses. In a trimmed flight, the Floquet analysis consists of (i) trim analysis of computing the unknown control inputs that satisfy required flight conditions and the corresponding initial conditions that yield periodic responses, and (ii) the eigenanalysis of the Floquet transition matrix (FTM). The shooting method generates the FTM as a byproduct and is increasingly used for the trim analysis, and the QR method is used almost exclusively for the FTM eigenanalysis. Indeed, the Floquet analysis is widely used for small-order systems (order {dollar}M 100{dollar}); the run time on a conventional sequential computer is simply prohibitive. Nevertheless, the Floquet analysis lends itself well to parallel or concurrent computations. Furthermore, the classical Floquet analysis requires integrations of equations of motion through one period T. However, for rotors with Q identical blades, it is far more economical to use the fast Floquet analysis, which requires integration through a period T/Q. Accordingly, this dissertation develops parallel algorithms for classical- and fast-Floquet analyses comprising parallel shooting and QR methods. These algorithms are applied to study flap-lag stability with dynamic stall and wake under flight trim conditions. The parallel and sequential analyses are compared with respect to computational reliability, saving in run time and growth of run time with increasing order. Other parallel performance metrics such as speedup, efficiency, and sequential and parallel fractions are included as well.