Model for Vortex Ring State Influence on Rotorcraft Flight Dynamics
The influence of vortex ring state (VRS) on rotorcraft flight dynamics is investigated, specifically the vertical velocity drop of helicopters and the roll-off of tiltrotors encountering VRS. The available wind tunnel and flight test data for rotors in vortex ring state are reviewed. Test data for axial flow, nonaxial flow, two rotors, unsteadiness, and vortex ring state boundaries are described and discussed. Based on the available measured data, a VRS model is developed. The VRS model is a parametric extension of momentum theory for calculation of the mean inflow of a rotor, hence suitable for simple calculations and real-time simulations. This inflow model is primarily defined in terms of the stability boundary of the aircraft motion. Calculations of helicopter response during VRS encounter were performed, and good correlation is shown with the vertical velocity drop measured in flight tests. Calculations of tiltrotor response during VRS encounter were performed, showing the roll-off behavior characteristic of tiltrotors. Hence it is possible, using a model of the mean inflow of an isolated rotor, to explain the basic behavior of both helicopters and tiltrotors in vortex ring state.
Blade twist effects on rotor behaviour in the vortex ring state
Results are shown that give a better understanding of the
factors that influence the initiation and subsequent development
of the vortex ring state (VRS). It is suggested that the onset of VRS is associated with the collapse of the orderly structure of the rotor wake into a highly disturbed, irregular, aperiodic flow state. An analysis of the stability of the wake is presented to show that the location of the boundary of the VRS is influenced by the detailed structure of the rotor wake prior to its breakdown. Time-accurate calculations of the evolution of the rotor wake in the VRS are then presented to obtain more insight into the flows experienced by the rotor in the VRS. These calculations suggest
that the location of the boundary of the VRS, and the
depth of the VRS regime, is sensitive to the blade spanwise
loading distribution, which is influenced by blade twist.
The effects are significant even at low disk loading, but
at high thrust where rotor stall may be encountered, rotors
with and without significant blade twist show marked, and
somewhat counterintuitive, differences in their behaviour
under VRS conditions.
Laminar heat or mass transfer in rectangular channels and in cylindrical tubes for fully developed flow: comparison of solutions obtained for various boundary conditions
Abstract A comparison is made of results obtained with various boundary conditions at the wall of the channels. By comparing blood Sherwood numbers for finite wall resistance with those for constant concentration boundary condition only a small variation is found for various points along the blood channel.