Date of Award
7-14-2020
Degree Name
Doctor of Philosophy (PhD)
Degree Type
Dissertation
Abstract
In this work, the finite-state models of Morillo-Duffy and Fei (including the Adjoint Theorem) are expanded to calculate the coupled inflow and rotor dynamics of a multi-rotor systems. Because the Adjoint Theorem involves coupling of rotor and inflow states with adjoint rotor states (including pure time delays in both types of variables), the resultant coupled dynamics experiences characteristics heretofore not studied in a dynamic system. It is the purpose of this work to study these new and interesting dynamic behaviors that can occur in the physically meaningful context of a coaxial rotor. The work is also interested in how this interesting behavior can be found in real time for applications to flight simulators for coaxial rotors. In order to study this new behavior, this present work first introduces a dynamic inflow model that does more than just compute the flow on a given rotor (as is done with most inflow models). Rather the model must compute for each of two interacting rotors: 1.) the flow above each rotor and 2.) the flow below the upper rotor. This must be done so that the effect of the lower rotor on the upper (and of the upper rotor on the lower) can be found in a flight simulation. The dynamic models of the two rotors are simple blade flapping, no in plane motion or torsion, for both an infinite and a finite number of rotor blades in axial flow. This model will be sufficient for understanding the most significant dynamics of the type of systems in which we are interested. In particular two rotors will be coupled in interesting ways. First, the upper rotor will be affected by the flow due to the lower rotor. This is a standard, state-variable coupling that involves neither adjoint variables nor time delays. However, the upper rotor also affects the dynamics of the lower rotor. In that case, the flow on the lower rotor due to the upper rotor will involve both adjoint states and pure time delays, giving the new and interesting behavior.
Language
English (en)
Chair
David Peters