Simple inflow and structural dynamics of a coaxial rotor with time delays and adjoint variables

The flow field and rotor dynamics of a coaxial rotor system are studied with particular emphasis on the dynamics resulting from the time delays and adjoint variables of coupled induced flow. The adjoint variables must be solved backwards in time.) Solution methods are developed, tested on a single lifting-rotor system, and the processes are confirmed with the closed form solution of the single rotor system. The study of flow between the rotor disks of a coaxial system is based on Fei’s work investigating flow below the rotor disk using the adjoint theorem. In this paper, two cases of input parameters based on load sharing are examined to show the dependence of the velocity states (a1, a2, b1, b2), velocity co-state (d1), and blade flapping state variables on the system inputs in the presence of time delays and adjoint variables.