Boundary Control for Suppressing Chaotic Response to Dynamic Hydrogen Blending in a Gas Pipeline

It is known that periodic forcing of nonlinear flows can result in a chaotic response under certain conditions. Such non-periodic and chaotic solutions have been observed in simulations of heterogeneous gas flow in a pipeline with periodic, time-varying boundary conditions. In this paper, we examine a proportional feedback law for boundary control of a parabolic partial differential equation system that represents the flow of two gases through a pipe. We demonstrate that periodic variation of the mass fraction of the lighter gas at the pipe inlet can result in the chaotic propagation of gas pressure waves, and show that appropriate flow control can suppress this response. We examine phase space solutions for the single pipe system subject to boundary control, and use numerical experiments to characterize conditions for the controller gain to suppress chaos.