A Low-Order Nonlinear State-Space Model for Delta Wing Leading Edge Vortices

[Abstract] This paper presents a low-order flow model for vortices over a delta wing suitable for feedback flow control design. It combines two fluid dynamics models based on conical flow assumptions for flow field over a delta wing a theoretical wing rock model and an empirical vortex breakdown model, to develop a set of nonlinear state equations describing the dynamics of the flow field as well as the aircraft rolling motion through a series of mathematical transformations and simplifications. The current model assumes virtual control inputs that directly affect the rate (derivative) of the state variables, such as the rate of vortex strength, vortex core velocity and velocity of the vortex break-down point. This generic assumption allows a variety of active flow control effectors and techniques to be applied to the model with suitable (static) modeling of the mapping from the control effectors to the virtual control inputs. By virtue of the conical flow assumption, the model output variables are assumed to be pressure sensors equally spaced span-wise on both upper and lower surface of the wing at a chosen chord-wise (longitudinal) location. The state equation model presented here has been validated with the two existing theoretical and empirical models for the same delta wing configurations that used in the validation of the existing models.